Anthropometric Study of the Femur An Automated Approach
Chi Bang Abe LAU
July 2009
A Thesis Submitted For The Degree Of Doctor Of Philosophy
Surgical & Orthopaedic Research Laboratories
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Abstract
nowledge of anatomy is an elementary step towards the understanding K of the human body. First used by Alphonse Bertillon as an identification system, anthropometry refers to the measurements of human individuals. In orthopaedics, comparative analysis is widely used in the understanding of morphological variance due to races, sex and pathological conditions. The characterization of bone and joint geometry has also been a foundation of modern surgical implant design.
Traditional anthropometric studies rely on physical measurements by means of osteometric table. Recent advancements of 3-D imaging modalities and image processing techniques have empowered more fine-grained anthropometric characterization. The inspiration for the study is:
• the understanding of anatomy originating from the clinical domain have shown to contribute to undesirable inconsistency in the image processing domain.
• the difficulty of existing automated anthropometric methodology in han- dling pathological femur.
• the tedious amount of manual and subjective work involved with the increasing amount of high resolution imaging data.
The aim of the study is to:
• develop a consistent and robust methodology in accurate extraction of anthropometric parameters on the femur.
i • increase the level of automation on the process of anthropometric pa- rameter extraction.
With the bridging of anthropometry and the image processing disciplines, a robust methodology of anthropometric parameter extraction with high level of automation was developed, implemented and tested.
A dataset comprised of femoral CT scans of 19 healthy Australian, 10 healthy Japanese, 15 Japanese diagnosed with primary or secondary hip osteoarthritis and 20 adult sheep was utilized for testing. Intra-class correlation and Cronbach’s α were extensively employed to evaluate the intra-rater, inter- rater and repeated scans consistency of the proposed methodology. High correlation values (mean > 0.95) were noted suggesting a high consistency of the methodology. All healthy and osteoarthritis human datasets were processed successfully. With the structural similarity between the sheep and human femur, the robustness was further demonstrated by accurate processing of the sheep dataset without the need of any modification of the underlying methodology. The methodology proposed is highly automated and requires very few user interactions in the parameter extraction stage.
ii Acknowledgments
his work would not have been possible without the continue support of T my supervisor, Prof. W.R. Walsh, and all fellow members of the Surgical & Orthopaedic Research Laboratories.
I would like to express my sincere gratitude to Dr. Akira Maeyama for his gracious help on acquiring patient data overseas.
I cannot say how grateful I am with my parents, for their values, their character and their unfailing support throughout the years. To my lovely sister Angela, for all her encouragements.
Last, I wish to thank my dear uncle Simon, aunt Mary, and my cousins Joyce, Patrick and little Winnie for all the care and joy you bring during my stay in Australia.
iii iv Contents
1. Introduction 1
2. Anatomy and Bone Histology 5 2.1. Histology of Bone ...... 5 2.1.1. Types of Cells ...... 6 2.1.2. Bone Salt ...... 6 2.1.3. Woven and Lamellar Bone ...... 7 2.1.4. Cortical and Trabecular Bone ...... 8 2.1.5. Modelling and Remodelling ...... 9 2.2. Anatomy of the Human Femur ...... 10 2.2.1. Hip Bone ...... 10 2.2.2. Femur ...... 11 2.2.2.1. Upper End ...... 11 2.2.2.2. Shaft ...... 14 2.2.2.3. Lower End ...... 15 2.2.2.4. Bone Structure ...... 15 2.2.3. Proximal Tibia ...... 16 2.2.4. Patella ...... 16
3. Medical Imaging 19 3.1. Overview ...... 20 3.2. X-ray Imaging ...... 20 3.2.1. Principles ...... 21 3.2.2. Measurement Units ...... 23 3.2.3. Generation of X-rays ...... 23 3.2.4. Applications in Radiology ...... 24
v Contents
3.2.5. Biological Hazards ...... 25 3.2.6. Strengths and Limitations ...... 25 3.3. Computed Tomography ...... 26 3.3.1. Principle ...... 26 3.3.2. Hounsfield Unit Scale ...... 27 3.3.3. Quantitative Computed Tomography ...... 28 3.3.4. Applications in Radiology ...... 28 3.3.5. Biological Hazards ...... 28 3.3.6. Strengths and Limitations ...... 29 3.3.6.1. Beam Hardening ...... 29 3.3.6.2. Partial Volume Averaging ...... 30 3.3.6.3. Photon Starvation ...... 30 3.3.6.4. Metal Objects ...... 31 3.3.6.5. Ring Artifacts ...... 32 3.3.6.6. Helical Artifacts ...... 32 3.4. Dual Energy X-ray Absorptiometry ...... 32 3.4.1. DXA Scores ...... 34 3.4.2. Biological Hazard ...... 35 3.4.3. Strengths and Limitations ...... 35 3.5. Magnetic Resonance Imaging ...... 35 3.5.1. Principles ...... 36 3.5.2. Biological Hazards ...... 36
4. Image Analysis 39 4.1. Overview ...... 40 4.2. Image Acquisition ...... 40 4.2.1. The DICOM Format ...... 40 4.3. Image Segmentation ...... 41 4.3.1. Thresholding ...... 41 4.3.1.1. Fixed Global Threshold ...... 42 4.3.1.2. Adaptive Threshold ...... 43 4.3.2. Region Growing ...... 44 4.3.3. Edge Detection ...... 45 4.3.3.1. Gradient Operators ...... 47 4.3.3.2. Laplacian Operator ...... 51 4.3.3.3. Canny Edge Detector ...... 56 4.3.4. Model Based Techniques ...... 58 4.4. Image Geometric Transformation ...... 59
vi Contents
4.4.1. Affine Transformation ...... 59 4.5. Morphological Processing ...... 62 4.5.1. Preliminaries ...... 62 4.5.2. Dilation and Erosion ...... 64 4.5.2.1. Dilation ...... 64 4.5.2.2. Erosion ...... 65 4.5.3. Opening and Closing ...... 66 4.5.4. The Hit-or-miss Operation ...... 68 4.5.5. Thinning ...... 70 4.5.6. Skeleton ...... 72 4.5.7. Convex Hull ...... 74 4.6. Miscellaneous ...... 77 4.6.1. The Hungarian Algorithm ...... 77
5. Shape Analysis 79 5.1. Overview ...... 79 5.2. Basic Geometrical Shape Parameters ...... 79 5.2.1. Region Based Parameters ...... 80 5.2.1.1. Area ...... 80 5.2.1.2. Centroid ...... 80 5.2.1.3. Eccentricity ...... 80 5.2.1.4. Area Moment of Inertia ...... 81 5.2.1.5. Polar Moment of Inertia ...... 81 5.3. Object Description Techniques ...... 82 5.3.1. Chain Coding ...... 83 5.3.1.1. Principles ...... 83 5.3.1.2. Applications ...... 85 5.3.2. Fourier Descriptors ...... 85 5.3.2.1. Applications ...... 88 5.3.3. Hausdorff Distance ...... 89 5.3.4. Corner Detector ...... 90 5.3.4.1. Moravec Operator ...... 91 5.3.4.2. Plessey Operator ...... 92 5.3.4.3. Curvature Scale Space Detector ...... 94
6. Anthropometric Analysis of the Femur 97 6.1. Overview ...... 97 6.2. Reference Positions and Axes ...... 98 6.3. Anteversion Angle and Reference Axes ...... 98
vii Contents
6.3.1. Physical Measurements ...... 99 6.3.2. 2-D Imaging Techniques ...... 101 6.3.3. 3-D Imaging Techniques ...... 104 6.4. Proximal Measurements ...... 110 6.4.1. Femoral Head ...... 110 6.4.2. Femoral Neck ...... 111 6.4.3. Canal Flare Index ...... 114 6.5. Femoral Shaft ...... 117 6.6. Distal ...... 119
7. Methods 123 7.1. Acquisition ...... 124 7.2. Segmentation ...... 124 7.3. Anthropometric Parameter Extraction ...... 125 7.3.1. Model Alignment ...... 126 7.3.1.1. Lesser Trochanter ...... 127 7.3.1.2. Proximal Femoral Axis ...... 130 7.3.1.3. Transepicondylar Axis ...... 130 7.3.1.4. Affine Transformation ...... 133 7.3.2. Trochanters ...... 136 7.3.3. Femoral Head ...... 136 7.3.4. Distal Posterior Condyles ...... 139 7.3.4.1. Tangential Line Extraction ...... 139 7.3.4.2. Cylinder Fitting ...... 139 7.3.4.3. Posterior Condylar Axis ...... 141 7.3.4.4. Knee Centre ...... 142 7.3.5. Neck Region ...... 142 7.3.5.1. Reslice ...... 142 7.3.5.2. Parameter Extraction ...... 147 7.3.6. Anteversion Angle ...... 149 7.3.7. Trochlear Groove ...... 150 7.3.8. Bow Curvature ...... 151 7.3.9. Misc Parameters ...... 153 7.3.9.1. Greater Trochanter Height ...... 153 7.3.9.2. Femoral Head Offset ...... 153 7.3.9.3. Length ...... 153 7.3.9.4. Canal Flare Index ...... 153 7.3.10. Section Properties ...... 154
viii Contents
7.4. Verification & Testing ...... 155 7.4.1. Inter-rater Variation in Segmentation ...... 155 7.4.2. Intra-rater Variation in Segmentation ...... 155 7.4.3. Variation on CT Voxel Size ...... 155 7.4.4. Reference Axes ...... 156 7.4.4.1. Femoral Axis ...... 156 7.4.4.2. Epicondylar Axis ...... 156 7.4.5. Effect on Posterior Condyles Range Variation ...... 156 7.4.6. Variation on Anteversion ...... 157 7.4.7. Verification using 3-D model ...... 157 7.5. Anthropometric Studies ...... 158 7.5.1. Human Femoral CT ...... 160 7.5.1.1. Australian CT Data ...... 160 7.5.1.2. Japanese OA CT Data ...... 160 7.5.2. Sheep Femoral CT ...... 161
8. Results 163 8.1. Overview ...... 163 8.2. Consistency Test ...... 167 8.2.1. Intra-rater Consistency ...... 167 8.2.2. Inter-rater Consistency ...... 170 8.2.3. Repeated Scans ...... 172 8.3. Parameter Variation ...... 174 8.3.1. Proximal Femoral Axis Variation ...... 174 8.3.2. Variation with Full Femoral Shaft ...... 177 8.3.3. Posterior Condyles Slice Range ...... 179 8.4. Verification with 3-D Model ...... 181 8.5. Comparison ...... 183 8.5.1. Condyles Radius ...... 183 8.5.2. Optimal Flexion Axis ...... 183 8.5.3. Australian & Japanese ...... 186 8.6. Sheep Summary ...... 186
9. Discussion 193 9.1. Overview ...... 194 9.2. Software Selection ...... 195 9.3. Image Acquisition & Segmentation ...... 196 9.3.1. Acquisition Parameters ...... 196 9.3.2. Automated Segmentation ...... 197
ix Contents
9.3.3. Consistency ...... 198 9.4. Performance of the Methodology ...... 200 9.4.1. Automation ...... 200 9.4.2. Accuracy ...... 200 9.4.3. Consistency ...... 201 9.5. Reference Axes Definition ...... 202 9.5.1. Longitudinal Axis ...... 202 9.5.2. Distal Transverse Axis ...... 204 9.6. General Parameter ...... 206 9.6.1. Head Centre ...... 206 9.6.2. Neck ...... 208 9.6.3. Posterior Condyles & Knee Centre ...... 212 9.6.4. Canal Flare Index ...... 216 9.7. Anteversion Angle ...... 217 9.8. Sheep Femur ...... 221
10.Conclusions 223 10.1. Limitations and Future Directions ...... 224
A. Function Summary 225
B. Sample Output File 237
C. CT Acquisition Settings 247
D. Consistence Test Data 251 D.1. Intra-rater Consistency ...... 252 D.2. Inter-rater Consistency ...... 256 D.3. Repeated Scans Consistency ...... 260
E. Results of Parameter Variation 265 E.1. Variation with Full Femoral Shaft ...... 265 E.2. Posterior Condyles Slice Range ...... 265
x List of Figures
2.1. Woven and lamellar bone. OC: osteocytes. HC: Haversian canal. HL: Lamellae. IL: Interstitial lamellae...... 7 2.2. Osteons (Haversian systems) in cortical bone...... 8 2.3. A BMU consisting of osteoblasts and osteoclasts in the resorption and formation of bone...... 9 2.4. Lateral view of the hip bone showing the acetbulum formed by the ilium, ischium and the pubis...... 11 2.5. Femur (anterior and posterior view)...... 12 2.6. Proximal femur in a posterio-medial view showing the trochanters and femoral head region...... 12 2.7. Angle of inclination (Anterior view) is defined as the angle span between the femoral axis and the neck axis, and decrease over active growth period...... 13 2.8. The torsion angle is often defined as the angle spanned by the femoral neck axis and the distal condylar axis...... 14 2.9. Medial view of a right femur, with anterior curvature on the shaft...... 14 2.10. Inferior view of the lower femoral epiphysis...... 15 2.11. Proximal tibia...... 16 2.12. The Patella is a triangular-shared sesamoid bone with the pos- terior surface articates with the patellar surface of the femur. .17
3.1. Electromagnetic Spectrum ...... 21 3.2. Photoelectric Absorption ...... 21 3.3. Compton Scattering ...... 22
xi List of Figures
3.4. Pair Production ...... 22 3.5. The Coolidge X-ray Tube ...... 24 3.6. CT schematic ...... 27 3.7. The Hounsfield Unit Scale ...... 28 3.8. Change of X-ray energy spectrum as it passes through different depth of water ...... 29 3.9. Attenuation profile of X-ray passing through a uniform cylindri- cal phantom ...... 30 3.10. CT image with cupping artifacts on a uniform cylindrical phantom 31 3.11. Streaking artifacts caused by photon starvation on a shoulder phantom ...... 32 3.12. Ring artifacts on a water-filled phantom ...... 33 3.13. Shape distortion in helical scan of a cone-shape phantom .... 33 3.14. Report of a DXA scan ...... 34
4.1. Grey-level histograms with threshold. Left; Single threshold T .
Right: Multi-level threshold (T1 and T2)...... 42 4.2. Left: A non-uniformly illuminated display. Right: Thresholded image...... 44 4.3. Intensity profile across ideal and ramp edge ...... 45 4.4. Effect of noise to ramp edge. Left column (top to bottom): Ramp edge corrupted by random Gaussian noise of σ = 0.1,1.0,10.0 respectively with its profile line plotted. Middle column: First derivatives of the corresponding ramp edges. Right column: Second derivatives of the corresponding ramp edges...... 46 4.5. top: image demonstrating a ramp edge; middle: intensity profile; bottom: first derivative ...... 47
4.6. 3x3 image region with intensity values ix ...... 48 4.7. The Roberts Cross operator kernel (left: vertical, right: horizontal) 48 4.8. Edges extracted from the Roberts (top right), Prewitt (bottom left) and Sobel (bottom right) operators from the circuit (top left) image ...... 49 4.9. Gradient operators under noise Top left: circuit with added noise (Gaussian σ2 = 0.01). Top right: Roberts. Bottom left: Prewitt. Bottom right: Sobel...... 50 4.10. The Prewitt operator (left: vertical, right: horizontal) ...... 50 4.11. The Sobel operator (left: vertical, right: horizontal) ...... 51 4.12. top: ramp edge; bottom: second order derivative of the horizontal intensity profile ...... 51
xii List of Figures
4.13. Laplacian convolution kernels ...... 52 4.14. 3-D plot of a two dimensional Gaussian filter kernel ...... 52 4.15. 5x5 Laplacian of Gaussian kernel ...... 53 4.16. 3-D plot of a two dimensional Laplacian of Gaussian filter kernel 53 4.17. Top left: noisy circuit image (Gaussian σ2 = 1). Top right: zero- crossing threshold = 0, σ = 2. Bottom left: zero-crossing thresh- old = 0.01, σ = 2. Bottom right: zero-crossing = 0, σ = 5...... 55 4.18. 3-D plot of a two dimensional Difference of Gaussian filter kernel 56 4.19. Left: noisy circuit image (Gaussian σ2 = 1). Right: Canny edge
detector (T = 0.1,T2 = 0.2,σ = 1.5]) ...... 57 4.20. Typical adaptation results with the use of deformable model. Note that part of the model is attracted and settled on false boundaries (white arrows)...... 58 4.21. Geometric interpretation of morphological opening ...... 67 4.22. Geometric interpretation of morphological closing ...... 67 4.23. Left: Noisy fingerprint image. Middle: Opening of the image. Right: Opening followed by closing...... 68 4.24. left: Set A (gray). right: foreground template W and background template (W − X ) ...... 69 4.25. left: set Ac (gray). right: A X (gray regions) ...... 69 4.26. Ac (W − X ) in gray ...... 70 4.27. Iterations of a thinning operation. B 1 to B 8: structuring ele- ments for thinning operation. Middle 3 rows: thinning opera- tions using the 8 structuring elements incrementally. Bottom left: Final result after convergence. Bottom right: Conversion to m-connectivity...... 71 4.28. Thickening obtained by thinning operation. Top left: original set A. Top right: Complement of set A. Middle row: iterations of the thinning operation on set (A)c . Bottom: Final result after removal of disconnected islands ...... 72 4.29. Principle of skeleton generation. Maximum-sized disks are positioned with centres on the skeleton...... 73 4.30. Top left: original segmented human chromosome image. Top right: Thresholded image. Bottom left: Skeleton of the image. Bottom right: Skeleton followed by spur removal...... 74
xiii List of Figures
1 4.31. A morphological algorithm to compute the convex hull. X0 :the 1 2 3 4 original set A. X4 , X2 , X8 , X2 : the set at convergence using the structuring elements B 1,B 2,B 3,B 4 respectively. C(A): The final convex hull ...... 76 4.32. Convex hull with extra criteria to limit growth ...... 76
5.1. 8-th directional chain code ...... 83 5.2. Steps in computing the shape number from chain code ...... 84 5.3. Shape reconstruction with different number of Fourier coeffi- cients. P is the number of Fourier coefficients used...... 87 5.4. Typical corner detector workflow ...... 91 5.5. Intensity variation cases, Moravec (1977) ...... 92 5.6. Feature regions in eigenvalue space ...... 94 5.7. Comparison of various corner detectors. Top left: The Moravec operator. Top right: The Plessey operator. Bottom left: The CSS operator. Bottom left: The modified CSS (He and Yung, 2004) .96
6.1. Kingsley’s neck axis definition. Left: posterior point. Middle: anterior point. Right: mid-point...... 100 6.2. Kingsley’s anteversion measurement...... 100 6.3. Anteversion calculation based on the longitudinal functional axis. C: head centre; N: mid-point of the anterior and posterior surfaces of the neck region...... 101 6.4. Anteversion measured on fluoroscopic bed...... 102 6.5. Relationship of true and projected anteversion under different inclination angle...... 103 6.6. Effect of anterior bowing on anteversion angle determination. Left: The long axis defined does not bisect but passes over the ◦ anterior aspect of the greater trochanter, with an extra 12 flexion from the right angle. Right: the adjusted axis bisecting the greater trochanter, and passing through the proximal one fourth of the femur...... 104 6.7. Neck axis determination from a single cross section. A: Head centre; B: mid-point between the anterior and posterior surfaces of the neck...... 105 6.8. Centroid (O) point at the base of the femoral neck...... 106 6.9. Distal transverse axis definitions. Left: The tabletop method. Right: The TEA...... 107
xiv List of Figures
6.10. Distal transverse axis definitions. Left: Area centres of the condyles defined visually. Right: Bisector of angle between the anterior and posterior tangential lines...... 107 6.11. Determination of the trochlear line for rotational reference. Left: The most anterior point of the lateral ridge was marked. Middle: the most anterior point of the medial ridge was marked, and the lateral point projected to the same slice. Right: the final trochlear line (TL); surgical epicondylar axis (SEA); Whiteside’s line (AP); posterior condylar axis (PCA)...... 109 6.12. Number of hospital admission for hip fracture in New South Wales, Australia, 1990–2000...... 112 6.13. The Canal Flare Index is a geometric ratio to describe the shape of the proximal femoral canal...... 114 6.14. Distribution of the Canal Flare Index over the 3 categories, CFI < 3.0: Stovepipe; 3.0
7.1. Amira (Visage Imaging, Inc., Carlsbad, USA) is used for seg- mentation of the CT stacks...... 124 7.2. Mimics (Materialize, Inc., Leuven, Belgium)...... 125 7.3. Profile lines across the lesser trochanter region for base thresh- old value evaluation. In cases where an optimal threshold cannot be chosen, the reference is chosen to avoid over-segmentation when possible...... 126 7.4. The MATLAB development environment running on Gentoo Linux ...... 127
xv List of Figures
7.5. Extraction of PMC for initial lesser trochanter LT1 estimation. . 128
7.6. The initial estimation of the lesser trochanter LT1 (blue) from the candidate list {PMC} (red)...... 129
7.7. Second estimation of the lesser trochanter based on LT1. The furthest coordinates of the image perimeter from the femoral
axis (FALT ) of each cross-section was taken as the PMC2 in the second estimation of the lesser trochanter position...... 129 7.8. Shape outlines on the flattened image. Two sets of line segments
were constructed to estimate the shape outline. {Lτ=3(BWperim)}
(red), {LN=6(BWperim)} (blue), and the final epicondylar point (green)...... 131
7.9. Shape template {LT } for orientation matching...... 132 7.10. Fallback TEA evaluation routine by corner (blue) detection. The figure shows the result of the corner detection with high sensitivity. The sensitivity of the corner sub-routine could be lowered to eliminate false corners and to reduce the number of candidates...... 133 7.11. The reference coordinate system. The proximal femoral axis (FA ) is taken as the longitudinal reference axis and the epicondylar axis (TEA ) is taken as the transverse axis for rotational reference.134 7.12. Axial view of the reference axes ...... 135 7.13. The trochanters (LT and GT) re-evaluated after model alignment.136 7.14. Initial estimation of the femoral head centre. First best-fit sphere (right) estimation of the femoral head based on the proximal head region (blue)...... 137 7.15. Final estimation of the best-fit sphere based on additional datum points...... 138 7.16. Extraction of the posterior condylar line by morphological oper- ations...... 140 7.17. The Lorentzian function...... 140 7.18. The Lorentzian minimization function estimated using a log function...... 141 7.19. Cylinder (PCCYL) fitted to the posterior condyles using the Lorentzian minimization function...... 142 7.20. The knee centre (KC) is defined as the intersection between the cylinder PCCYL and the distal femoral articular surface .....143 7.21. Initial estimation of the neck axis based on femoral head centre HC and NB...... 143
xvi List of Figures
7.22. Flattened PA view of the femur. NBSK was evaluated by mor- phological skeletonization followed by detection of intersections (blue) in the skeleton. The intersection at the neck base (red cross) superior to the lesser trochanter intersection was taken
as NBSK for the initial estimation of the neck axis...... 144
7.23. Thinning operation on the axial slice corresponding to NBSK .
The green dotted line shows the possible candidates of NBSK described in figure 7.22 on page 144. The first intersection between the dotted line and the thinned skeleton was taken as NB...... 145 7.24. First and final neck axis estimation with cylinder fit...... 146 7.25. Point cloud of the final NECK based on NA . Note the appearance the greater trochanter at the top of the reslice neck. This was eliminated in the first estimation of the neck axis...... 147 7.26. Anthropometric measurements based on the neck axis NA and femoral axis FA. NLGT is the neck length from NAstartto the
lateral aspect of the trochanter along the neck axis. NLFAis the
neck length measured from NAstart to the femoral axis. ∠NAFA
is the neck shaft angle. Note that the point NAstartlies on the femoral neck axis but may not coincide with the femoral head centre (HC )...... 148 7.27. Elevation of the neck axis (NAFA) is defined as the anterior displacement of the femoral neck axis with reference to the femoral axis...... 148 7.28. Axes for anteversion angle measurements...... 149 7.29. Trochlear groove extraction...... 151
7.30. A plane PTR was fitted to the trochlear groove...... 152 7.31. Anterior bow curvature...... 152 7.32. The use of nearest site Voronoi diagram in the computation of the greatest inscribed circle...... 154 7.33. Verification of the head neck region on 3-D models created with Mimics ...... 159 7.34. Verification of the femoral length on 3-D model created by Mimics . The measurement in black is FLGT−KC , the distance between the proximal tip of the greater trochanter and knee centre. The measurement line in orange is an estimation of
FLHC −KC + HR, the sum of distance between the femoral head centre and knee centre, plus the femoral head radius...... 160
xvii List of Figures
8.1. The Matlab routine showing the process of sectional properties computation...... 164 8.2. The dependency matrix...... 166 8.3. Difference in anteversion angle with proximal and full femoral shaft as the reference longitudinal axis. The error bars indicate one standard deviation. This shows a substantial difference in the measurements under the use of different reference longitu- dinal axes...... 179 8.4. Box-plot showing difference in anteversion with the proximal and full femoral shaft as the longitudinal reference axis. Upper and lower whisker (black), median (red) and the quartiles (blue) are shown...... 180 8.5. Neck axis elevation (NAFA) relative to the femoral axis with proximal and full femoral shaft as the reference longitudinal axis. The error bars represent one standard deviation...... 180 8.6. Canal flare indices with proximal femoral shaft and full femoral shaft as reference longitudinal axis. Only the oblique index shows a significant difference under the change of reference longitudinal axis...... 181 8.7. Difference between direct measurements on the created 3-D model and that using the proposed methodology. The error bars represent one standard deviation of the measurements. Neck length is the length from the start of the femoral neck to the lateral aspect of the trochanter along the computed neck axis
(NLGT )...... 182 8.8. Difference between the medial and lateral condyle radius. A positive difference indicates the lateral radius is larger than that of the medial and vice versa...... 184 8.9. Displacement of the medial epicondyle relative to the optimal flexion axis...... 185 8.10. Displacement of the medial epicondyle relative to the optimal flexion axis...... 185 8.11. Femoral head and neck measurements of the AU and JP datasets.187 8.12. Anteversion angles of the AU and JP datasets. Significant difference was observed in ∠(NA ,TEA ) and ∠(NA ,CA ) (P<0.05) in which the Japanese dataset has a larger angle than the Australian dataset...... 188
xviii List of Figures
8.13. Femoral length measurements of the AU and JP datasets. The Japanese dataset has a smaller value in all femoral length measurements (P<0.001)...... 189 8.14. Cross-sectional area of the bone section and the medullary canal of the proximal femur. The error bars represent 1 standard deviation of the measurements...... 190 8.15. Moment of inertia across the medio-lateral axis (Ixx) and antero- posterior axis (Iyy) of the proximal femur...... 190 8.16. Summary of measurements of proximal femur and posterior condyles of sheep...... 191 8.17. Summary of femoral length, neck shaft angle and anterior bow of sheep...... 192 8.18. Summary of canal flare index of sheep...... 192
9.1. Effect of anterior bowing on different definitions of the longitu- dinal axis...... 203 9.2. Posterior bow at the femoral metaphysis ...... 218 9.3. The helitorsion angle compared to the anteversion angle. ....220 9.4. The use of full femoral shaft as the longitudinal reference axis in determination of the anteversion angle. Under this reference system, the long axis of the femur and the femoral neck axis are in close proximity in the superior view and neck axis elevation is virtually non-existent...... 220
E.1. Variation between the use of proximal femoral shaft and full femoral shaft as reference longitudinal axis...... 267
xix List of Figures
xx List of Tables
3.1. Causes of X-ray attenuation in water at various photon energies 23 3.2. Man’s exposure to ionizing radiation ...... 25 3.3. Typical Effective Dose in CT (Shrimpton et al., 2003) ...... 29
4.1. The membership relation in set theory ...... 62 4.2. Standard notations in set theory ...... 63 4.3. Logical operations on binary images ...... 64 4.4. Common properties of morphological opening and closing .... 67
5.1. Effect of transformation in Fourier descriptor ...... 88
7.1. Verification measurements on 3-D model...... 158
8.1. Types of ICC...... 168 8.2. Femoral head intra-rater consistency...... 169 8.3. Femoral neck intra-rater consistency...... 169 8.4. Anteversion angles intra-rater consistency...... 170 8.5. Canal flare indices intra-rater consistency...... 170 8.6. Shaft and distal femur intra-rater consistency...... 171 8.7. Femoral length intra-rater consistency...... 171 8.8. Femoral head inter-rater consistency...... 172 8.9. Femoral neck inter-rater consistency...... 172 8.10. Anteversion angles inter-rater consistency...... 173 8.11. Canal flare indices inter-rater consistency...... 173 8.12. Shaft and distal femur inter-rater consistency...... 173 8.13. Femoral length inter-rater consistency...... 174 8.14. Femoral head consistency on repeated scans...... 174
xxi List of Tables
8.15. Femoral neck consistency on repeated scans...... 175 8.16. Anteversion angles consistency on repeated scans...... 175 8.17. Canal flare indices inter-rater consistency on repeated scans. . 175 8.18. Shaft and distal femur consistency on repeated scans...... 176 8.19. Femoral length consistency on repeated scans...... 176 8.20. Variations of the proximal femoral axis due to inconsistent lesser trochanter evaluation. A mean difference of 0.6◦ was observed which is negligible...... 178 8.21. Typical maximum error of the posterior condyles radius due to variation in slice range selection by user...... 182 8.22. Difference on the radius of curvature between medial and lateral condyles in the Australian dataset...... 183 8.23. Difference on the radius of curvature between medial and lateral condyles in the healthy Japanese dataset...... 183 8.24. Statistical comparison between AU and JP femoral head region. 186 8.25. Statistical comparison between AU and JP femoral neck regions.187 8.26. Statistical comparison between AU and JP anteversion angles. 187 8.27. Statistical comparison between AU and JP canal flare index. . . 188 8.28. Statistical comparison between AU and JP distal femur and shaft regions...... 188 8.29. Statistical comparison between AU and JP femoral length. . . . 189
A.1. Function summary of the Matlab subroutines...... 226 A.1. Function summary of the Matlab subroutines...... 227 A.1. Function summary of the Matlab subroutines...... 228 A.1. Function summary of the Matlab subroutines...... 229 A.1. Function summary of the Matlab subroutines...... 230 A.1. Function summary of the Matlab subroutines...... 231 A.1. Function summary of the Matlab subroutines...... 232 A.1. Function summary of the Matlab subroutines...... 233 A.1. Function summary of the Matlab subroutines...... 234 A.2. External Matlab subroutines used in the study. They are obtainable from the Mathworks File Exchange repository. ....235
D.1. Intra-rater consistency data...... 252 D.1. Intra-rater consistency data...... 253 D.1. Intra-rater consistency data...... 254 D.1. Intra-rater consistency data...... 255 D.2. Inter-rater consistency data...... 256
xxii List of Tables
D.2. Inter-rater consistency data...... 257 D.2. Inter-rater consistency data...... 258 D.2. Inter-rater consistency data...... 259 D.3. Repeated scans consistency data...... 260 D.3. Repeated scans consistency data...... 261 D.3. Repeated scans consistency data...... 262 D.3. Repeated scans consistency data...... 263
E.1. Effect of condyles radius on the fitting slice range...... 266
xxiii List of Tables
xxiv Nomenclature
BMC Bone Mineral Content
BMD Bone Mineral Density
CFI Canal Flare Index
CT Computed Tomography
DEXA/DXA Dual Energy X-ray Absorptiometry
DFT Discrete Fourier Transform
DICOM Digital Imaging and Communications in Medicine
DoG Difference of Gaussian
EM Electromagnetic erg force of one dyne exerted for a distance of one centimetre, or 0.1 micro- joule
GT Greater Trochanter
GUI Graphical User Interface
GUI Graphical User Interface
xxv List of Tables
HC Head Centre
HSA Hip Strength Analysis
HU Hounsfield Unit
ICC Intra-Class Correlation
KC Knee Centre
LaTeX This thesis was typeset with LATEX, a document preparation system for the TEX typesetting program.
LoG Laplacian of Gaussian
LT Lesser Trochanter
LyX LyX is the document processor in which this thesis was written on.
MRI Magnetic Resonance Imaging
OA Osteoarithis
PACS Picture Archiving and Communication System
PCL Posterior Cruciate Ligament
QCT Quantitative Computed Tomography rad Radiation Absorbed Dose rem Röntgen Equivalent in Man
SEA Surgical Epicondylar Axis
SI International System of Units
SNR Signal-to-noise Ratio
Sv Sievert
xxvi Nomenclature
TEA Trans-epicondylar Axis
THR Total Hip Replacement
TKR Total Knee Replacement
xxvii Nomenclature
xxviii 1
Introduction
uman anatomy is one of the fundamental aspects in the comprehension H of the human body. Initially used by Alphonse Bertillon in 1882 as a scientific system to identify and match arrested criminals who had previous criminal records, anthropometry refers to the measurements of human in- dividuals. Since then, human anthropometry has been incorporated more extensively in other disciplines such as biomechanics, forensic analysis and orthopaedics.
Particularly, human anthropometry played a key role in the field of or- thopaedics. Most modern surgical prostheses are designed based on anthro- pometric data. Traditionally, anthropometric data are gathered via physical measurements, which often limit its scope to in vitro studies only. The ap- plication of radiographic imaging with its minimal invasive nature allows a wider range of in vivo anthropometry to be studied. Nonetheless, the two dimensional nature of radiographic imaging poses a significant constraint in describing more complex shapes such as those found in the epiphysis of human bones. The simplification of a three dimensional entity into a single radiographic image is likely to shield plenty useful information desir- able for more detailed anthropometric analysis. Measurement error due to dimension-reducing projection is another major concern that affects accuracy and consistency.
The advancements of three-dimensional imaging modalities have brought an- thropometry to another level, eliminating the dimension-reducing deficiency in planar radiographic image, and allow more complex shapes to be measured accurately. Coupled with the increasing adoption of digital image process- ing techniques, more fine-grained anthropometric characterization could be
1 1. Introduction realized.
Nonetheless, the context of human anatomy originating from the clinical domain has shown to contribute to undesirable inconsistency in the context of image processing. Many definitions of anatomical landmarks are based on prominence of anatomical structure. While its accuracy in the clinical domain proved sufficient, its consistency in the image processing domain may not be satisfactory. In pathological cases, precise location of anatomical landmarks could become too subjective. This adds extra difficulty in the image processing domain for more precise analysis. The understanding and manipulation of the anatomical definitions in the different perspectives is critical and is one of the inspirations of the study.
As a starting point, the femur bone was chosen as the study object. Articulating with the hip and knee joints, the femur provides weight support to the skeletal structure at up-right position, and is of particular interest in the field of orthopaedics due to being a common fracture site. With the femur playing an important role in body support and gait cycle, the understanding of its anthropometry is also of importance in bio-mechanics.
Acquisition of higher resolution image is getting more common. A typical clinical computed tomography scanner could acquire images with spatial resolution up to 0.2 mm. The increasing amount of image data makes manual processing a tedious amount of work. The use of automated or semi-automated analysis techniques is thus desirable.
The current study aims to develop a consistent and robust methodology in accurate extraction of anthropometric parameters on the femur from clinical computed tomography images. To avoid the need of manually process an immense amount of work resulting from high resolution image stacks, another objective is to increase the level of automation in the entire process.
Without being very application specific, the scope of the current study is to present a general framework for anthropometric analysis of the femur. The focus is towards the investigation of a more automated means at the parameter extraction procedures in anthropometric analysis to eliminate the massive amount of manual work required.
As a preliminary evaluation of the designed methodology, a dataset comprising of femoral CT scans of 19 healthy Australian, 10 healthy Japanese was used.
2 Intra-class correlation and Cronbach’s α were employed to evaluate the intra- rater, inter-rater and repeated scans consistency of the proposed methodology. All scans were processed successfully, and high correlation values (mean > 0.95) were observed, indicating a satisfactory consistency achieved.
As a further test of robustness of the proposed methodology towards slightly malformed femoral geometry, an additional 15 CT scans of Japanese diagnosed with primary or secondary hip osteoarthritis were tested. All 15 scans were processed successfully. While a more comprehensive and extensive test would be required to demonstrate its performance in various pathological types, the preliminary test showed a potential of the proposed method.
As a sidetrack of the experiment, an additional 20 adult sheep were scanned and processed successfully with the exact methodology. The inspiration of this part of the study originates from the fact that sheep femora is a commonly used animal model in prostheses testing due to its availability and structural similarity to that of human femur. Despite its wide usage of sheep in the area, implants for sheep experiments are mostly designed on a trial and error basis. To the author’s knowledge, no previous study was noted in the literature in an attempt to systematically extract and summarize anthropometric data of sheep femur. As a start, 20 sheep femurs were included in the study to initialize a database of anthropometric data on sheep femur. With more sheep scans data being included in the future, it is anticipated that the database would assist in providing a more systematic and accurate anthropometric data for sheep experiments.
The following page gives an outline of the thesis, with the focus of each chapter.
Thesis Outline
• Chapter 1: An introduction of the overall aims, work undertaken and scope of the study.
• Chapter 2: A review on bone histology and anatomy of the femur.
• Chapter 3: A summary on the basic principles on current imaging modalities for clinical applications, with its strengths and weaknesses discussed.
3 1. Introduction
• Chapter 4: A review on the basic principles on various image analysis techniques employed in the study.
• Chapter 5: A descriptions on the definitions of various geometry mea- surements employed in the study.
• Chapter 6: A review on previous works on anthropometric studies of the femur.
• Chapter 7: A detailed protocol on the methodology proposed for the extraction of anthropometric parameters
• Chapter 8: Test results of the proposed methodology with the focus in consistency measures. Summary and comparison of the human and sheep datasets are also presented.
• Chapter 9: Discussion on the performance and robustness of the proposed methodology with focus on several parameters of interest.
• Chapter 10: Conclusion on the methodology proposed, it strengths and limitations. Further directions are proposed.
4 2
Anatomy and Bone Histology
Contents 2.1. Histology of Bone ...... 5 2.1.1. Types of Cells ...... 6 2.1.2. Bone Salt ...... 6 2.1.3. Woven and Lamellar Bone ...... 7 2.1.4. Cortical and Trabecular Bone ...... 8 2.1.5. Modelling and Remodelling ...... 9 2.2. Anatomy of the Human Femur ...... 10 2.2.1. Hip Bone ...... 10 2.2.2. Femur ...... 11 2.2.3. Proximal Tibia ...... 16 2.2.4. Patella ...... 16
2.1. Histology of Bone
onnective tissue is made up of an organic matrix comprising of three C components, namely the cells, fibres or collagen and ground substance with which the latter two predominate in general.
Bone is a kind of connective tissue that contains an extensive matrix of intercellular materials. Unlike other types of connective tissues, the organic matrix of bone tissue is calcified and is made up of 65% of minerals (Jee, 2001), which contributes to the hardness of the bone and the radiopacity towards many medical imaging modalities based on X-rays. Bone is specialized in
5 2. Anatomy and Bone Histology providing a supportive framework for the body and continuously remodel under the influence of hormonal and other external mechanical environment. Bone remodeling is the ongoing process of the replacement of old or injured bone tissue by new bone tissue.
2.1.1. Types of Cells
There are four types of cells in bone tissue, namely osteogenic cells, osteoblasts, osteocytes and osteoclasts. Located at the endosteum and the inner portion of the periosteum, osteogenic cells are capable of mitotic division and develop into osteoblasts. Osteoblasts are not capable of mitotic division and are the cells that form bone. Osteoblasts secrete collagen and other organic compounds necessary for the formation of bone matrix and are found on the surface of bones and at the margins of growing bone. In the process of bone formation, osteoblasts are encased in the bone matrix they form and remain as osteocytes (Hancox, 1972). Each osteocyte occupies its own cavity or lacunae in the bone matrix and maintains its metabolism in exchanging nutrients and waste with the blood. Osteocytes must be within 100-150μm of a blood vessel to prevent necrosis (Martin and Burr, 1989). Osteoclasts are large multi-nucleated cells that are formed by the fusion of as many as 50 monocytes, which is a type of white blood cell. Osteoclasts resorb bone matrix by means of lysosomal enzymes.
2.1.2. Bone Salt
Calcium hydroxyapatite is the primary bone salt present in bone tissue, with the unit cell formula of 3Ca3(PO4)2-Ca(OH)2. Crystal of calcium hydroxyapatite in bone has a thickness of few unit cells, with a rough dimensions of 5 × 5 × 40 nm.
With its major component being mineral salts, bone is a major reservoir of calcium in which 99% of the total amount of calcium in the body is stored. It serves as a vital component of the homeostatic mechanisms in regulating 2+ + 2− concentrations of Ca ,H , and (HPO4) .
6 2.1. Histology of Bone
(a) Bone is always initially deposited (b) Lamellar bone. as woven bone.
Figure 2.1.: Woven and lamellar bone. OC: osteocytes. HC: Haversian canal. HL: Lamellae. IL: Interstitial lamellae. Reproduced from Hancox (1972).
2.1.3. Woven and Lamellar Bone
From a molecular view, bone is always deposited as woven bone as shown in figure 2.1a. Woven bone serves as a temporary scaffold and is eventually converted to lamellar bone. Woven bone is weaker with collagen fibres ori- ented in all directions and large vascular channels. Osteocytes are scattered throughout the bone matrix.
Lamellar bone is stronger and consists of fine collagen fibres lined in a parallel manner. The fibres are grouped into layers called the lamellae. The central canal of each functional unit is called a Haversian canal, named after Havers (1691) and grouped with its concentric lamellae is named as an osteone or Haversian system. Lamellar bone is replaced in trabeculae and cortical bone at a rate of about 25% and 5% respectively (Martin R.B. and N.A., 1998). The orientation of lamellar bone formation is known to be affected by external machanical stimuli in which the collagen fibres tends to line with the direction of stress (Martin and Burr, 1989).
7 2. Anatomy and Bone Histology
Figure 2.2.: Osteons (Haversian systems) in cortical bone. Reproduced from Taylor et al. (2007). Original images courtesy of Tortora (2002); Colopy et al. (2004).
2.1.4. Cortical and Trabecular Bone
At a macroscopic view, bones can be categorized into cortical (compact) and trabecular (cancellous) bone. Cortical bone is dense and contains only spares vascular channels that form the external layers of all bones. Cortical bone is hard and provides protection to other organs and support for the skeletal system. Cortical bone has a concentric ring structure with which an extensive network of canals are presented across the width of bone, named as the perforating canals or the Volkmann’s canals. The blood vessels, lymphatic vessels and nurves in the perforating canals inter-connect with those in the medullary cavity, periosteum and the Haversian canals (Figure 2.2).
Trabecular bone, also known as cancellous bone or spongy bone are irregular latticework constructed with thin columns of bone called trabeculae of about
8 2.1. Histology of Bone
Figure 2.3.: A BMU consisting of osteoblasts and osteoclasts in the resorption and formation of bone. Reproduced from Taylor et al. (2007).
200 μm in thickness. The space between the trabeculae is filled with marrow or myeloid tissue.
Most short, flat and irregularly shaped bone is made up of trabecular bone. It also exists in epiphyses and around the marrow cavity of the diaphyses of long bones, which are areas that are not subject to enormous mechanical stress. Trabecular bone is usually surrounded by a shell of cortical bone for increased strength and rigidity. The distribution of the types of bone varies depending on the need for strength or flexibility.
2.1.5. Modelling and Remodelling
Wolff (1892) published his seminal in 1892 documenting the observation of bone remodelling, in which the bone undergoes reshaping in response to stresses acting on it. Its classical findings are widely known as the Wolff’s law. While the rationale for the existence of the Wolff’s law has been questioned or challenged (Bertram and Swartz, 1991; Cowin, 1997; Lee and Taylor, 1999), many still ascribe to the idea of Wolff’s law in which bone remodels in response to mechanical stresses to produce an optimal structure adapted to the load.
Frost (1973) has compiled and analysed the bone remodeling phenomenant and the principle summary are quoted as follows:
1. Remodeling is triggered not by principal stress but by “flexure”.
2. Repetitive dynamic loads on bone trigger remodeling.
3. Dynamic flexure causes all affected bone surfaces to drift towards the concavity which arises during the act of dynamic flexure.
Remodelling is accomplished by actions of osteoclasts and osteblasts that form a basic multi-cellular unit (BMU), consisting of around 10 osteoclasts and
9 2. Anatomy and Bone Histology hundreds of osteoblasts. The process could be summarized into activation, resorption and formation stages. The activation stage involves the fusion of monocytes in the formation of osteoclasts. In the resorption stage, the osteoclasts tunnels into cortical bone with the formation of tunnels of about 200 μm is diameter. The excavated tunnel wall is then lined with osteoblasts which the formation of secondary osteon occurs. The central portion or the core of the tunnel are not completely filled, and is left for the Haversian canal.
2.2. Anatomy of the Human Femur
The femur, also commonly known as the thigh bone, is the longest and heaviest bone in the human skeletal system. The femur comprises of a shaft section with two ends, where the proximal end articulates with the hip bone forming the hip joint, and the distal end articulates with the tibia and the patella forming the knee joint.
2.2.1. Hip Bone
The hip bone is a bony structure at the base of the spine, articulating behind the proximal part of the sacrum forming the sacroiliac joint and to the proximal end of the femur forming the hip joint. This results in a connection between the trunk and the lower limbs. The hip bones form the pelvic girdle that meet at the pubic symphysis, and forms the anterior and lateral walls of the pelvis.
Each hip bone is made up of the ilium, ischium and pubis, with which they meet at the acetabulum as shown in figure 2.4 on the next page. The hip bones are initially separated in the acetabulum by the Y-shaped triradiate cartilage and begin to fuse during adolescence.
The acetabulum is a cup-shaped cavity facing laterally downwards, and is formed by roughly one-fifth of the pubis, two-fifths of the ilium and ischium each. The articular surface covered by hyaline cartilage forms a horse-shoe- shaped region.
10 2.2. Anatomy of the Human Femur
Figure 2.4.: Lateral view of the hip bone showing the acetbulum formed by the ilium, ischium and the pubis. Reproduced from Gray (1918).
2.2.2. Femur
The femur is the longest and heaviest bone in the human skeletal system transferring the entire body weight between the trunk and the lower limb, with its length being roughly one-fourth to one-third of the human body length. It consists of two ends and a mid-shaft section. With its proximal end, it articulates with the hip bone forming the hip joint, which is a synovial ball-and-socket joint and with its distal end, it articulates with the tibia and patellar forming the knee joint.
2.2.2.1. Upper End
The head of the femur is a partial two-third sphere that faces upward, forward and medial. The fovea capitis, located slightly below and behind the centre, is a pit in which the ligament of the head of femur is attached. Apart from the fovea capitis, the entire femoral head region is covered with articular surface and in many cases, the articular surface extends upon the anterosuperior region of the neck.
The neck region is a bar of bone connecting the head to the trochanter region. In front, the neck and the trochanter region is separated with a relatively
11 2. Anatomy and Bone Histology
Figure 2.5.: Femur (anterior and posterior view). Reproduced from Moore (2007).
Figure 2.6.: Proximal femur in a posterio-medial view showing the trochanters and femoral head region. Reproduced from Gray (1918).
12 2.2. Anatomy of the Human Femur
Figure 2.7.: Angle of inclination (Anterior view) is defined as the angle span between the femoral axis and the neck axis, and decrease over active growth period. Reproduced from Moore (2007). prominent trochanteric line that runs downwards and medially. The line becomes more indistinguishable near the lesser trochanter and the neck- trochanter ridge, the intertrochanteric crest, is relatively smooth at the back of the femur.
The greater trochanter projects superomedially to where the neck-shaft region joins, and is located above the junction of the shaft laterally, about 10 cm below the iliac crest. The lesser trochanter is a round palpable conical region which extends medially from the posteromedial part of the junction between the neck and the shaft.
The intertrochanteric crest is the ridge that connects the greater trochanter with the lesser trochanter posterially. Compared to the intertrochanteric line which connects the greater trochanter with the lesser trochanter at the anterior side of the femur, the intertrochanteric crest is relatively smoother and more indistinguishable.
The angle of inclination (Figure 2.7) is the angle between the superomedially projected neck and head axis and the shaft-axis and has a typical value of ◦ ◦ ◦ between 110 − 145 , with an average of about 126 . It is usually smaller in female and decreases during the active growth period (Harty, 1957). The angle of inclination of the femur allows the long axis of the neck and head to intersect with the acetabulum cup in a more perpendicular manner, and allows for a large range of motion in the hip joint.
13 2. Anatomy and Bone Histology
Figure 2.8.: The torsion angle is often defined as the angle spanned by the femoral neck axis and the distal condylar axis. Reproduced from Moore (2007).
Figure 2.9.: Medial view of a right femur, with anterior curvature on the shaft. Reproduced from Gardner et al. (1969).
The angle of torsion (Figure 2.8) of the head of the femur, also known as the anteversion angle, is the angle between the long axis of the head and neck region and the transverse axis of the femoral condyles when viewed superiorly along the shaft axis. It is reported the average anteversion angle is ◦ ◦ around 12 −15 (Breathnach, 1965). If the angle is larger than the range, it is called anteverted, and if the angle is less than the normal range, it is called retroverted. The effect of an anteverted and retroverted torsion angle could be noted by external and internal rotation of the femur, causing out-toeing and in-toeing (pigeon toe) respectively (Norkin C., 1992).
2.2.2.2. Shaft
The femoral shaft connects between the proximal and distal femur. A sig- nificant characteristic of the shaft is its anterior curvature (Figure 2.9)ina medial view. The functional role of the anterior curvature is unknown and no correlations have yet been found on the curvature and other functional parameters such as body mass or size.
14 2.2. Anatomy of the Human Femur
Figure 2.10.: Inferior view of the lower femoral epiphysis. Reproduced from Gray (1918).
2.2.2.3. Lower End
The distal end of the femur is characterized by two spirally curved condyles, continuous in front, and separated below and behind the intercondylar fossa (Figure 2.10). The two condyles articulate with the tibial condyles to form the knee joint. The front of the condyles characterizes a vertical groove and divides the patellar surface into two unequal parts.
The lateral side of the groove is wider, extends further and articulates with the lateral articular facet of the patella. The medial groove is narrower and articulates with the medial articular facet of the patella. Below the intercondylar fossa, the lateral condyle is broad and straight compare with that of the medial condyle which is relatively curved and narrow. The posterior part of the condyles articulates with the tibial condyles only in knee flexion.
The medial surface is convex and rough, and features a prominence named the medial epicondyle. Likewise, the lateral epicondylar is a prominence on the lateral surface of the lateral condyle, but is not as convex as that of the medial epicondyle. A pit immediately above the lateral epicondyle marks the lateral head of the gastrocnemius. Often, a groove that lodges the tendon of the popliteus in knee flexion runs upward and backward of the pit. When the leg extends, a notch in the articular margin lodges the tendon.
2.2.2.4. Bone Structure
Two regional structures of bone masses could be noted from the proximal end of the femur. The calcar femorale is the bar of cortical bone that extends into the neck from the lesser trochanter region on the medial side. The cervical torus is a thickened band of cortical bone on the upper region of the neck
15 2. Anatomy and Bone Histology
Figure 2.11.: Proximal tibia. Reproduced from Moore (2007). between the femoral head and the greater trochanter region on the upper neck.
2.2.3. Proximal Tibia
The tibia (Figure 2.11), also known as the shin bone has a length roughly one-fourth to one-fifth of the body length, and is located on the anterior and medial side of the leg. It transmits body weight from the femur to the ankle and foot. The tibia has an upper and lower end, separated by a shaft, with the upper end rotated more medially than the lower in superior axial view.
The upper end of the tibia is large, expanded and bent slightly backward. The upper surface comprises of the medial and lateral condyles, a large ovoid and smooth surface that articulates with the femoral condyles. Laterally, the tibia articulates with the fibula.
2.2.4. Patella
The patella (Figure 2.12 on the next page), also known as the knee cap, is a triangular-shaped sesamoid bone of roughly 5cm in diameter and is located anterior to the knee joint. It articulates with the patellar surface of the femur.
The anterior surface is convex and contains vertical ridges and many small openings for nutrient vessels. The two lateral and medial borders converge to form the apex. The posterior surface is a smooth and oval area divided into two articular facet; a larger lateral articular facet and a smaller medial articular facet, separated by a vertical ridge. Part of the posterior aspect is not articulated and gives the attachment point of the ligamentum patellae.
16 2.2. Anatomy of the Human Femur
Figure 2.12.: The Patella is a triangular-shared sesamoid bone with the pos- terior surface articates with the patellar surface of the femur. Reproduced from Gardner et al. (1969).
17 2. Anatomy and Bone Histology
18 3
Medical Imaging
Contents 3.1. Overview ...... 20 3.2. X-ray Imaging ...... 20 3.2.1. Principles ...... 21 3.2.2. Measurement Units ...... 23 3.2.3. Generation of X-rays ...... 23 3.2.4. Applications in Radiology ...... 24 3.2.5. Biological Hazards ...... 25 3.2.6. Strengths and Limitations ...... 25 3.3. Computed Tomography ...... 26 3.3.1. Principle ...... 26 3.3.2. Hounsfield Unit Scale ...... 27 3.3.3. Quantitative Computed Tomography ...... 28 3.3.4. Applications in Radiology ...... 28 3.3.5. Biological Hazards ...... 28 3.3.6. Strengths and Limitations ...... 29 3.4. Dual Energy X-ray Absorptiometry ...... 32 3.4.1. DXA Scores ...... 34 3.4.2. Biological Hazard ...... 35 3.4.3. Strengths and Limitations ...... 35 3.5. Magnetic Resonance Imaging ...... 35 3.5.1. Principles ...... 36 3.5.2. Biological Hazards ...... 36
19 3. Medical Imaging
3.1. Overview
edical imaging in general, refers to the techniques of obtaining images of M the human body, mainly for diagnostic purpose in clinical use. It is also considered as a subset of the very widely spanned biological imaging category, which consists of an even larger range of techniques of visualizing different aspects of biological specimens. Medical imaging can be briefly categorized into photography (medical), microscopy, endoscopy imaging, thermography, and radiology. Medical imaging plays a key role in the first step in the image processing process - Image Acquisition. A more detailed description of several commonly used medical imaging techniques in Orthopaedics within the clinical context are discussed below. Focus is placed on X-ray based modalities, which is more commonly used in the field of orthopaedics.
3.2. X-ray Imaging
Discovered in 1895, X-rays are one of the oldest and most widely used source of electromagnetic (EM) radiation in medical imaging. It is also called Röntgen ray, named after the discoverer, Professor Wilhelm Conrad Röntgen, (1845- 1923) from the University of Wurburg.
X-rays are high energy, ionizing EM radiation that lies between ultraviolet light and gamma rays with wavelengths roughly between 10 nanometers − − (10 ∗ 10 9) and 10 picometers (10 ∗ 10 12), equivalent to a frequency of 30 petahertz (30 ∗ 1015) to 30 exahertz (30 ∗ 1018). It can further be divided into hard X-rays and soft X-rays, with soft X-rays having longer wavelengths and thus lower energy. The cutoff wavelength between soft and hard X-rays is around 100 picometers. Note that the soft X-rays spectrum overlaps with extreme ultraviolet, while hard X-rays spectrum overlaps partially with gamma (γ) rays, in their shorter and longer wavelengths ranges respectively. The distinction between gamma (γ) rays and hard X-rays are thus often referred to the source of the radiation instead of a cutoff wavelength, with X-ray generated by the emission of X-ray photons by energetic electron bombardment, and gamma (γ) rays by energy state transition in the nuclei level.
20 3.2. X-ray Imaging
Figure 3.1.: Electromagnetic Spectrum Reproduced from radiology.med.sc.edu
Figure 3.2.: Photoelectric Absorption Reproduced from Dresser Atlas
3.2.1. Principles
Projection X-rays imaging makes use of the fact that different body tissues have different X-ray attenuation. Below are the three main processes that contribute the most towards X-ray attenuation:
• Photoelectric Absorption
Photoelectric absorption occurs when a photon collides with an atom, ejecting one of the orbital electrons from the inner shell of the atom, resulting in atom ionization. In general, photoelectric absorption contributes the most to the total attenuation for low energy X-rays up to 500 keV.
• Compton Scattering
Compton refers to the inelastic photon scattering, which results from a collision with orbital electrons. Some energy is transferred to the electron, which is knocked out of the atom. The frequency of the photon is lowered due to energy losses and direction change. The Compton effect occurs mostly in photons with an energy range of around 2 keV to 2 meV.
• Pair Production
Pair production refers to the effect of the conversion of a photon into an electron and a positron. The process occurs when the incident photon has
21 3. Medical Imaging
Figure 3.3.: Compton Scattering Reproduced from Dresser Atlas
Figure 3.4.: Pair Production Reproduced from Dresser Atlas at least twice the rest mass energy of two electrons (1.022 MeV). It was first observed by Patrick Blackett, the winner of Nobel Prize in Physics in 1948.
Table 3.1 shows the probability of each of the above processes in water at various X-ray photon energies.
The attenuation of a mono-energetic beam passing through a homogeneous material can be expressed by the Beer’s Law.
−μd I = I 0e (3.1)
where I0 is the intensity of the incident radiation, I is the intensity of the transmitted radiation, d is the tissue thickness, and μ is the attenuation coefficient which depends on the electron density and the atomic number of the tissues.
The attenuation is visualized by means of a detector medium such as radio- graphic film. Photostimulable phosphors plates are increasingly adopted in radiography with the advancements of computer technology. It is reusable and the resulting images can be digitized and stored directly into a computer system.
22 3.2. X-ray Imaging
Photoelectric Compton Pair X-ray Photon Energy Absorption Scatter Production 10 keV 95% 5% 0 25 keV (Mammography) 50% 50% 0 60keV (Diagnostic) 7% 93% 0 150 keV 0 100% 0 4MeV 0 94% 6% 10 MeV (Therapy) 0 77% 23% 24 MeV 0 50% 50%
Table 3.1.: Causes of X-ray attenuation in water at various photon energies Reproduced from e-radiography.net
3.2.2. Measurement Units
Röntgen(R) is a unit used to define the radiation field in air. Due to the fact that attenuation of X-rays when passing through different matters vary, a unit called rad(radiation absorbed dose) is defined in the measurement of absorbed dose. 1 rad is equal to the dose of radiation resulting in the absorption of − 100 ergs (10 7 Joules) per gram in any material. rem, abbreviated from röntgen equivalent in man, is the traditional unit for radiation dose measurement, defined as the product of the dose absorbed in R(röntgen) and the biological efficiency. It defines the estimated dose of any radiation that would produce the same biological effect delivered by x or γ radiation.
The SI (International System of Units) unit is sievert (Sv) and is equivalent to 100 rem.
3.2.3. Generation of X-rays
The Coolidge tube, designed by Willian Collidge in 1913, is based on the Crookes tube design. It is one of the most widely used yet simplistic design to produce X-rays. It works as follows: The tungsten cathode filament is heated. Electrons are emitted by the thermionic effect and accelerated due to the high voltage potential set up between the cathode and the anode. The bombardment of high speed electrons to the positively charged, angled anode causes the
23 3. Medical Imaging
Figure 3.5.: The Coolidge X-ray Tube Reproduced from orau.org emission of bremsstrahlung. Bremsstrahlung is the electromagnetic radiation with a continuous spectrum resulting from EM radiation produced by the deceleration of a charged particle when deflected by another charged particle. A window is designed to allow the escape of the generated X-ray photons from the focal spot of the anode.
X-ray generation by the above process is very inefficient and an estimated 99% of energy is wasted as heat. Overheating at the focal spot on the anode thus becomes a severe limitation on the power of X-ray tube. A rotating anode tube is designed to overcome the limitation by sweeping the anode on a rotary disc, thus spreading the heat generated over a larger area.
3.2.4. Applications in Radiology
X-rays visualize the target by measuring the X-rays attenuation after passing though the exposed structure. It is especially effective in the visualization of the pathology of the skeletal system, which has an excellent attenuation coefficient towards X-rays. It is also commonly used in identifying lung diseases. Soft tissues, however, have a lower attenuation coefficient towards X-rays and in general produce less contrast in an X-ray image, which makes discerning fine details more difficult. Phase-sensitive X-ray imaging (Pfeiffer et al., 2006; Schneider et al., 2008) is a new concept in recent years to generate higher contrast from detection of the phase shift of X-rays passing through the sample in addition to X-ray attenuation detection.
24 3.2. X-ray Imaging
Source of Exposure Exposure Seven Hour Aeroplane Flight 0.05 mSv Chest X-ray 0.04 mSv Nuclear Fallout (From atmospheric tests in 0.02 mSv per year 50’s & 60’s) Chernobyl (People living in Control Zones 10 mSv per year near Chernobyl) Cosmic Radiation Exposure of Domestic 2 mSv per year Airline Pilot
Table 3.2.: Man’s exposure to ionizing radiation Reproduced from Australian Radiation Protection and Nuclear Safety Agency
3.2.5. Biological Hazards
Due to the high energy, penetrability and ionizing nature of X-rays, they interact with living tissue resulting in damage to healthy living cells. Under substantial exposure, more serious damage to, for instance the DNA of the cell could occur and may lead to a higher risk of heritable defects and cancer. According to the ARPANSA Radiation Protection Series No. 1 (Republished 2002) published by the Australian Government. The effective dose limit for general public is 1mSv per year, while an occupational dose limit of 20 mSv per year applies. Table 3.2 lists some examples on the radiation dosage received in various events.
3.2.6. Strengths and Limitations
Being one of the oldest modalities in medical imaging, X-ray imaging is a mature technology that provides a very safe, non-invasive and economical diagnostic method in medicine. It is also one of the most commonly and widely used modalities in medical imaging for diagnosis purpose. Nonetheless, studies (Ardran, 1979; Veip, 2005; Pfeiffer et al., 2006; Schneider et al., 2008) have pointed out that conventional X-ray imaging often suffers from lower contrast or dynamic range, especially in cases where different forms of tissue with similar attenuation coefficients are under investigation within the same cross-section. Materials with relatively low X-ray attenuation such as polymers, fiber composites pose another limitation on the application of X-rays because of the low signal-to-noise ratio.
25 3. Medical Imaging
Veip (2005) pointed out that the use of digital X-ray receiver could deliver twice the contrast compared to conventional X-ray film. Still, the upper limit of the dynamic range is bounded by the allowable radiation dosage, while the lower limit of the dynamic range is restrained by the noise floor.
Phase-sensitive X-ray (Pfeiffer et al., 2006) is another new concept that aims to deliver a better contrast by detecting phase changes in addition to X-ray attenuation.
3.3. Computed Tomography
Computed tomography (CT), also known as computed axial tomography (CAT), is one of the most common tomography techniques in medical imaging. An es- timate of 1.06 million CT scans were done in Australia in 1995 (Thompson and Tingey, 1997) and the trend is growing. The concept of tomography was first proposed by an Italian radiologist Alessandro Vallebona in early 1930s based on the concept of projective geometry, to represent a single cross-sectional slice. The first CT system was invented in 1972 by Sir Godfrey Newbold Hounsfield at the EMI Central Research Laboratories (Hayes, the United Kingdom). Allan McLeod Cormack from the Tufts University independently invented a similar process and both were awarded the Nobel Prize in Medicine in 1979.
3.3.1. Principle
CT is another imaging technique utilizing X-rays and is also based upon the fact that different tissues express a different degree of X-ray attenuation. In CT, a thin fan shaped beam of X-rays is emitted from the tube perpendicular to the long axis of the body. An array of detectors are positioned on the opposite side of the X-ray source as shown in Figure 3.6 to convert X-ray intensity into electrical signals. The resulting images are then combined to form the final cross-sectional slice by a method called tomographic reconstruction.
26 3.3. Computed Tomography
Figure 3.6.: CT schematic Reproduced from Medcyclopaedia
3.3.2. Hounsfield Unit Scale
The Hounsfield unit (HU) scale is used in CT, named after Sir Godfrey Newbold Hounsfield, the inventor of the first CT machine. It represents the linear transformation based on the original linear attenuation coefficient μ where adjustments are made such that water and air have values of 0 and -1000 respectively, given in expression 3.2.
μx − μH O 2 X 1000 μ − μ (3.2) H2O air μ μ μ where x , H2O and air are the attenuation coefficients of the scanned tissue, water and air respectively. A change of 1 HU corresponds to around 0.1% of the attenuation coefficient, given the fact that μair 0.
With the large range of values defined in the HU scale, difficulties exist in visualizing the entire spectrum in modern display devices, which can commonly resolve only 256 (8-bit) gray levels. Windowing and contrast compression techniques are often applied to visualize the HU range of interest only. Window centre or window level is the centre value of the visualizing range, while window width is the maximum HU deviation from the window centre in which the shades of gray will be distributed over. For instance, a window center of 1000 and a window width of 100 will effectively display the HU range between (1000±100)HU on screen. Values above 1100 HU or below 900 HU would be displayed as pure white and black respectively.
27 3. Medical Imaging
Figure 3.7.: The Hounsfield Unit Scale Reproduced from Medcyclopaedia
3.3.3. Quantitative Computed Tomography
Quantitative computed tomography (QCT) utilizes a special calibration phan- tom and additional softwares on top of a CT system to achieve more accurate measurements. In orthopaedics, QCT allows a more accurate three dimen- sional volumetric bone mineral measurement. Diagnosis of pathological conditions can be done quantitatively with QCT. As most commercial CT system could be upgraded to perform QCT with minor modifications, QCT may have higher availability and wider acceptance.
3.3.4. Applications in Radiology
CT has become a valuable tool in medical imaging since its introduction, and is used in the diagnosis of a large range of diseases. Examples include diagnostic of complex fractures at extremities and joints; abdominal diseases such as urinary stones and appendicitis; fractures and organ injury due to trauma. Contrast agents such as barium sulfate can be used to further enhance the attenuation difference for more specific diagnosis.
3.3.5. Biological Hazards
While improvements in CT technology have led to a lower overall radiation dose per examination, CT is still considered a high dose diagnostic procedure in radiology. Table 3.3 shows some figures on the average effective radiation dose on several types of CT examinations.
28 3.3. Computed Tomography
Examination Type Typical Effective Dose (mSv) Adult Head CT 1.5 Adult Abdomen CT 5.3 Adult Chest CT 5.8 10-year-old Head CT 1.6 10-year-old Chest CT 3.9
Table 3.3.: Typical Effective Dose in CT (Shrimpton et al., 2003)
Figure 3.8.: Change of X-ray energy spectrum as it passes through different depth of water Reproduced from Barrett and Keat (2004)
3.3.6. Strengths and Limitations
This section below aims to provide an overview on some of the most common artifacts in CT imaging, with focus in the field of orthopaedics.
3.3.6.1. Beam Hardening
When X-ray beams with photons of different energies pass through the exami- nation object, photons with lower energy has a higher attenuation compared to the high energy photons, as shown in figure 3.8. This effect is known as beam hardening.
Beam hardening often shows up in images as cupping artifacts where X- ray beams that pass through the middle portion of a cylindrical object are
29 3. Medical Imaging
Figure 3.9.: Attenuation profile of X-ray passing through a uniform cylindrical phantom Reproduced from Barrett and Keat (2004) hardened more than that those through the edges (Figure 3.9), resulting in lower HU values towards the centre of the cylinder, as shown in Figure 3.10.
Filtration with metallic material to pre-harden the X-ray beam before passing through the examination object is often used to reduce the effect of beam- hardening. Scanners can be calibrated for different pre-defined types of examinations, and specific correction algorithms could be applied during the reconstruction stage to compensate or minimize the effect of beam hardening.
3.3.6.2. Partial Volume Averaging
The partial volume averaging effect occurs on slices across structure edges, due to the effect of averaging the output Hounsfield values across tissues with very different attenuation properties within the same voxel. It is usually observed across the z-axis of the CT volume with anisotropic voxel size, where slice thickness is larger than the spatial resolutions. A smaller slice thickness could minimize the effect of partial volume averaging.
3.3.6.3. Photon Starvation
Photon starvation occurs when insufficient photons reach the detector because of high attenuating region, resulting in a noisy projection and often results in serious streaking artifacts. Figure 3.11 shows a CT cross-section of a
30 3.3. Computed Tomography
Figure 3.10.: CT image with cupping artifacts on a uniform cylindrical phan- tom Reproduced from Barrett and Keat (2004) shoulder phantom where photon starvation occurs when the X-ray beam projects through horizontally.
Photon starvation can be reduced by increasing the tube current, but with a drawback of a higher radiation dose to patient. An alternative solution is to vary the tube current automatically at different angular orientation, a process known as milli-amperage modulation, such that a sufficient tube current is achieved when needed.
3.3.6.4. Metal Objects
Metal objects possess high density and attenuation coefficient that is out of the handling range of normal CT system and can cause serious streaking artifacts. The presence of metal objects in CT examinations are not uncommon in the field of Orthopaedics, where surgical nails and prosthesis are commonly used metal devices.
Metal objects are generally removed from patient’s body before scanning commences. For unremovable metal objects, reduction of streaking artifacts could be achieved with special software correction algorithms by replacing the out-of-range values. Additional measures to reduce artifacts resulting from beam-hardening are always applied, as mentioned in section 3.3.6.1.
31 3. Medical Imaging
Figure 3.11.: Streaking artifacts caused by photon starvation on a shoulder phantom Reproduced from Barrett and Keat (2004)
3.3.6.5. Ring Artifacts
Ring artifacts occurs when one of the detectors among the detector array is out of calibration, as shown in figure 3.12.
3.3.6.6. Helical Artifacts
Helical or spiral CT was introduced in the early 1990s and is commonly used in CT examinations today with the major advantage of speed but with the drawback of shape distortion due to the need of helical interpolation. Figure 3.13 shows a helical scan on a cone-shaped phantom with the shape of the circular cross-section distorted.
3.4. Dual Energy X-ray Absorptiometry
Dual Energy X-ray Absorptiometry (DEXA/DXA) makes use of X-rays to measure bone mineral content (BMC) and also bone mineral density (BMD) indirectly. The principle behind DXA is very similar to traditional X-ray imaging as described in section 3.2.1 on page 21, except that it relies on two distinct energy levels of X-rays with which each has different attenuation coefficient for soft tissues and bone. This allows elimination of the attenuation effect of soft tissue for a more accurate BMD calculation. In orthopaedics,
32 3.4. Dual Energy X-ray Absorptiometry
Figure 3.12.: Ring artifacts on a water-filled phantom Reproduced from Barrett and Keat (2004)
Figure 3.13.: Shape distortion in helical scan of a cone-shape phantom Reproduced from Wilting and Timmer (1999)
33 3. Medical Imaging
Figure 3.14.: Report of a DXA scan Reproduced from www.ammom.com.mx
DXA is currently the “gold standard” for diagnosing osteoporosis. Another use of DXA is body fat content assessment.
DXA for bone densitometry is often performed on lower spine and hips. Mar- shall et al. (1996) have shown that DXA results performed on hip may be a good indicator on relative hip fracture risk.
While most DXA devices use dual-energy X-rays for BMD measurements, newer and more economical portable DXA devices make use of ultrasound on peripheral sites such as heels and forearm. However, its use are currently limited to screening purposes (Kirk et al., 2002) while studies (Barr et al., 2005) show that peripheral DXA could be effective in predicting fracture risk of older women who are at increased risk of future fracture.
3.4.1. DXA Scores
A typical DXA examination results in two primary values reflecting a patient’s bone material density, the T-score and the Z-score. T-score is the bone density compared with what is expected of a young normal patient in the same sex, while Z-score is the bone density compared with a normal individual of the same sex, weight and race as the patient. According to the World Health Organization, a T-score of higher than -1 is considered normal, while a value of between -1 and -2.5 is considered osteopenia, and a value lower than -2.5 is considered osteoporosis.
34 3.5. Magnetic Resonance Imaging
3.4.2. Biological Hazard
DXA employs a very low dose X-ray and it is estimated that the effective dose received by patient per examination on conventional pencil-beam DXA machine is around 0.08 - 4.6 μSv (Njeh et al., 1999). The effective dose received by patient on newer and higher resolution fan-beam DXA examination is reported to be around 6.7 - 31 μSv. It is generally considered that the very low dose of X-ray used in a DXA examination does not pose any biological hazard to the general public.
3.4.3. Strengths and Limitations
DXA is still currently the most widely used method for BMD measurements. It is economical, easily accessible and use very low dose ionizing radiation, which pose negligible biological hazard to the patient.
However, due to the two dimensional nature of DXA scans, Kolta et al. (2005) pointed out that DXA-derived BMD are not true bone mineral density, but, more appropriately, an areal density only. Various studies (Goh et al., 1995; Cheng et al., 1997b; Lekamwasam and Lenora, 2003) have shown that anatom- ical variations and different hip positioning could lead to as much as 50% variations on the resulting BMD values. While the extreme variations re- ported should not happen from a well-trained professional radiologist with proper patient hip positioning, the effect of anatomical variations such as the anteversion angle is still unlikely to be eliminated.
3.5. Magnetic Resonance Imaging
Magnetic resonance imaging (MRI), originally known as nuclear magnetic resonance imaging, could be used in medical imaging to create images of any part of the body in any plane. MRI has a higher contrast on soft tissue com- paring to CT and thus a very suitable candidate for distinguishing pathologic tissue, and imaging in the cardiovascular, and oncological disciplines.
35 3. Medical Imaging
3.5.1. Principles
This section serves only as a brief explanation on the basic principles of MRI. The detail physics involved in MRI is beyond the scope of discussion here. MRI makes use of the nuclear resonance of an elementary subatomic particle with an odd atomic number, such as 1H, 31P or 13C, which acts like a magnetic dipoles. Under strong magnetic field, usually generated by an electromagnet in an MRI machine, the atoms start to align with the axis of the external magnetic field with a resonance frequency known as the Larmor frequency, named after a French physicist. The Larmor equation is
w0 = g B0 (3.3)
where w0 is the Larmor frequency, B0 is the magnetic field and g is the constant gyromagnetic ratio, specific to each type of atomic nucleus mentioned above. However, only a slight majority of atoms are aligned (parallel protons) in the direction of the magnetic field and the remainings are aligned in an opposite fashion (anti-parallel protons). This creates a slight net magnetic moment in the tissues under the strong magnetic field. When a radio wave pulse exactly the same as the Larmor frequency is applied, some of the already aligned protons will be pushed out of their alignment under the original magnetic field. A tiny but detectable change in the magnetic field when the protons relax back to their original states can be detected by a receiver coil.
The realignment of the nuclei relaxation after short pulse in the Larmor frequency is called longitudinal relaxation. The time required for the tissue magnetism to reach back to 63% of the value before the pulse is applied, is termed T1. A common value of T1 is 500ms to 1s. The transverse relaxation time, which is the local de-phasing of the spins after a transverse pulse, is named T2. A common value of T2 is 50ms to 100ms.
By using different time period between the radio pulses, echo time and other parameters, images with very different contrast can be achieved.
3.5.2. Biological Hazards
No ionizing radiation is involved in an MRI examination. MRI thus does not pose the same potential biological hazards as other imaging modalities that
36 3.5. Magnetic Resonance Imaging make use of ionization radiation such as X-rays. The hazards involved in MRI are mainly due to its use of strong magnetic field, which could impose life-threatening danger when any ferromagnetic objects are attracted towards to the magnetic bore.
The strong magnetic strengths may cause potential hazard to electronic circuitry, such as patients with pacemakers installed. Energy transfer via radio frequency may cause heating effect in tissues of the body. The Safety Guidelines for Magnetic Resonance Diagnostic Facilities published by the National Health and Medical Research Council contains details of the safety limit of the average specific absorption rate in different type of scans, such as 4 W/kg over the head region, and 8 W/kg over the trunk. Other countries such as the United States has further recommendations towards maximum acoustic noise level during the use of MRI.
37 3. Medical Imaging
38 4
Image Analysis
Contents 4.1. Overview ...... 40 4.2. Image Acquisition ...... 40
4.2.1. The DICOM Format ...... 40 4.3. Image Segmentation ...... 41
4.3.1. Thresholding ...... 41 4.3.2. Region Growing ...... 44 4.3.3. Edge Detection ...... 45 4.3.4. Model Based Techniques ...... 58 4.4. Image Geometric Transformation ...... 59
4.4.1. Affine Transformation ...... 59 4.5. Morphological Processing ...... 62
4.5.1. Preliminaries ...... 62 4.5.2. Dilation and Erosion ...... 64 4.5.3. Opening and Closing ...... 66 4.5.4. The Hit-or-miss Operation ...... 68 4.5.5. Thinning ...... 70 4.5.6. Skeleton ...... 72 4.5.7. Convex Hull ...... 74 4.6. Miscellaneous ...... 77
4.6.1. The Hungarian Algorithm ...... 77
39 4. Image Analysis
4.1. Overview
s one of the subdivisions of digital signal processing, digital image pro- A cessing focuses on the analysis of images in digital form. Contrary to traditional analog image printouts such as traditional X-rays films, digital images allow the application of much wider analysis and manipulation tech- niques, not limited by the many physical constraints. The more widespread use of digital images in medical imaging such as digital X-rays, CT, MRI imag- ing, and the advancement of micro-computer, makes digital image processing a powerful yet feasible and economical analysis choice. With the comprehensive use of the digital Hospital Information System and picture archiving and communication systems (PACS) throughout Australia (Caffery and Manthey, 2004; Crowe and Sim, 2004), digital images can be transferred easily across hospitals, fascinating collaborations as well as information sharing.
This section aims to provide an overview of image processing techniques, with more focus in the field of biomedical imaging. With the fact that the majority of medical imaging techniques only output grayscale images, the discussion below assumes images are single-channel if not specified.
4.2. Image Acquisition
Image acquisition is the first step of image analysis. Being the initial source of all imaging analysis, the image acquisition step has a profound effect on all the subsequent steps down the analysis pathway. An overview of commonly used clinical medical imaging techniques and their comparison, strengths and artifacts are discussed in section 3onpage19.
Output of the image acquisition step is often stored in a digital form for further processing. In clinical medical imaging; the DICOM (Digital Imaging and Communications in Medicine) format is the most commonly used.
4.2.1. The DICOM Format
Introduced by the American College of Radiology and the National Electrical Manufacturers Association in 1983, The Digital Imaging and Communications
40 4.3. Image Segmentation in Medicine (DICOM, originally known as ACR/NEMA) standard aimed to standardize an image format across different brands of CT and MRI imaging devices. To tailor the use of DICOM in the medical field, the DICOM format is designed to contain multiple data objects, known as attributes, to enable the storage of extra information such as patient information, and modality specific scanning parameters. With the conformance of most major vendors, and the increasing use of PACS within health care network, DICOM is now the de facto digital format for most medical imaging modalities. The DICOM standard is updated four to five times every year according to the standards committee to incorporate new technology and as of this writing, the most current version is the “Base Standard - 2008”.
4.3. Image Segmentation
Image segmentation refers to the process of dividing or separating the image into structural units or to distinguish objects of interest. Specifically in the case of a single object of interest, segmentation is often referred to as a foreground background separation procedure. The section below outlines various commonly used segmentation techniques on gray-scale images. It has to be noted that while image segmentation has always been a major focus in image processing, and large amount of algorithms are available, segmentation are in general, image type-specific, and none are considered close to universally perfect.
4.3.1. Thresholding
Because of its implementation simplicity, thresholding has always been one of the popular segmentation methods. The technique is based on a straight- forward concept on group separation. Given an intensity image I(x, y) with light objects on a dark background, and a level threshold T , the thresholding process is defined as follows:
⎧ ⎨ 1 if I(x, y) > T = I(x, y) ⎩ (4.1) 0 if I(x, y) ≤ T
41 4. Image Analysis
Figure 4.1.: Grey-level histograms with threshold. Left; Single threshold T . Right: Multi-level threshold (T1 and T2). Reproduced from Gonzalez and Woods (2002)
The output of the segmentation is a binary image with regions of interest or objects with a value of 1. An extension to the single thresholding method is to utilize two threshold values T1 and T2 where
⎧ ⎨ 1 ifT ≤ I(x, y) < T = 1 2 I(x, y) ⎩ (4.2) 0 if I(x, y) < T1 or I(x, y) ≥ T2
Figure 4.1 on page 42 shows a histogram representation of the two thresholding techniques. The concept can further be extended to multi-channel images.
With the thresholding segmentation technique, the central question lies upon the method of choosing an optimal threshold T .
4.3.1.1. Fixed Global Threshold
The simplest form of a fixed global threshold is to apply a predefined threshold value T to the entire image. This method depends on a priori knowledge on the intensity range of the region of interest.
Various techniques are designed to obtain an optimal global threshold based on the analysis on the intensity histogram. An iterative method for threshold selection is proposed by Ridler and Calvard in 1978 (Ridler and Calvard, 1978), also known as the intermeans algorithm, and is defined as
ˆ ˆ fgk−1 + bgk−1 Tk = until Tk = Tk−1 (4.3) 2
ˆ where fgk−1 and bgk−1 are the sample mean of the gray values on all foreground and background pixels respectively, with Tk−1 as the threshold value. The
42 4.3. Image Segmentation
initial threshold for foreground background separation, T0 is usually defined as the median value of the image dynamic range. For images with comparable area of foreground and background, the average gray level of the image could be chosen as T0. The average number of iteration needed to reach an unchanged T is reported to be 4. For performance reason, the iteration could be set to stop when the change between Tk−1 and Tk is small.
Another widely used method, the Otsu’s method (Otsu, 1979) aims to search for a threshold to minimize the weighted within-class variance, or equiva- lently to maximize the between-class variance, under the assumption of a bimodal histogram with uniform illumination. In the case of single foreground background separation, the weighted within-class variance is defined as
σ2 = σ2 + σ2 P (T ) P fg(T ) fg(T ) Pbg(T ) bg(T ) (4.4)
where P fg and Pbg are the probabilities of the foreground and background classes under threshold T respectively, and σ2 is the class variance. Practi- cally, an exhaustive search across the grayscale dynamic range is done by maximizing the between-class variance, which is functionally equivalent to minimizing the function in equation 4.4.
While being one of the oldest histogram-based threshold selection algorithms, it is still one of the widely adopted methods (Seo et al., 2004; Yadollahi and Moussavi, 2006). Various extensions and derivatives exist, with Yerly et al. (2007) extending the Otsu method to three dimensional space, and Liao et al. (2001) proposing a multilevel threshold derivative with performance improvement.
4.3.1.2. Adaptive Threshold
Discussion on algorithms in selecting an optimal threshold for global thresh- olding are built on the assumption of constant illumination with acceptable signal-to-noise ratio (SNR). Under uneven illumination, picking a constant global threshold for the entire image will likely under-segment and or over- segment different parts of the image (Figure 4.2 on the following page). One solution to the issue is to divide the image into smaller sub-images and select an optimal threshold value for each child image.
43 4. Image Analysis
Figure 4.2.: Left: A non-uniformly illuminated display. Right: Thresholded image. Reproduced from the NI Developer Zone, National Instruments
4.3.2. Region Growing
One fundamental limitation of histogram-based segmentation techniques is that spatial information is totally discarded in the process. On the contrary, segmentation based on region growing techniques focus on the spatial location of pixels, in the aim of grouping pixels into regions of interest. The grouping criteria are often based on the similarity assumption, in which neighborhood pixels have similar intensity values.
The basic idea is to start with a set of predefined points in the image called “seed” points and regions are grown by iteratively grouping neighborhood pixels which satisfy certain similarity criteria. The procedures of seed points selection is image specific, and often require a prior knowledge of the image type. Without extra prior information, an alternative method of seed point selection is to apply the defined similarity criteria on all pixels across the image, and assign seed points based on the resulting seeded regions.
Additional stopping rules may be imposed on top of the similarity growing criteria. Properties such as total region size, intensity limit, or even limitations on the region shape can be used as stopping criteria for the iterative growing process. Lee et al. (2005) suggested an automated region growing algorithm for tumor segmentation on PET images with low spatial resolution and high variations of intensity by making use of gradient magnitude difference. The authors further suggested that the use of gradient magnitude difference as the growing criteria prevented the problem of over-segmentation commonly observed in traditional region growing techniques with intensity criteria. Alakuijala et al. (1995) proposed a region growing technique that employs seed regions for initialization and expansion limited by natural borders, designed
44 4.3. Image Segmentation
Figure 4.3.: Intensity profile across ideal and ramp edge to give optimal results for interactive and knowledge-based segmentation of volumetric medical images.
Region growing and its derivatives are also commonly used for more automated segmentation in areas where manual segmentation is tedious (Tuduki et al., 2000; Dehmeshki et al., 2008) or in ultrasound imaging (Hao et al., 2000).
4.3.3. Edge Detection
An edge is a set of connected pixels that separates two regions. Note that an edge is in general a more local measure when compared to an ROI boundary. Ideally, the intensity values across an edge is distinct with its intensity profile line perpendicular to the edge being a step function as shown in figure 4.3. Nonetheless, edges are always presented as a more gradual transition of intensity level in practice, due to imperfections introduced in the image acquisition stage. Noise is another major factor in edge detection. This raises the question on the actual location of a blurred or noisy edge and hence various techniques were developed. Figure 4.4 on the following page shows the effects of random Gaussian noise towards a ramp edge and its first and second derivatives. Note that while the ramp edge is still distinguishable when σ = 10.0, the magnification effect of the noise in its first and second derivatives makes the use of derivatives alone in edge detection not very feasible in noisy cases.
From a viewpoint in the frequency domain, edges are considered local regions with high frequency components. Theoretically, edge extraction could be achieved by applying a high-pass filter in, for instance the Fourier domain,
45 4. Image Analysis
Figure 4.4.: Effect of noise to ramp edge. Left column (top to bottom): Ramp edge corrupted by random Gaussian noise of σ = 0.1,1.0,10.0 re- spectively with its profile line plotted. Middle column: First derivatives of the corresponding ramp edges. Right column: Sec- ond derivatives of the corresponding ramp edges. Reproduced from Gonzalez and Woods (2002)
46 4.3. Image Segmentation
Figure 4.5.: top: image demonstrating a ramp edge; middle: intensity profile; bottom: first derivative which is a commonly used frequency representation. However, edge detec- tion performed in the frequency domain is hardly used because of its extra computation complexity.
4.3.3.1. Gradient Operators
As discussed above, edges in real world images are always presented as intensity gradients, and that the first-derivative of an edge gives a good highlight of it. Figure 4.5 shows an exaggerated ramp edge. Its grayscale intensity profile across the horizontal axis and the first derivative, which consist of two distinguish step changes.
The gradient of a certain pixel f (x, y) of an image could be defined as a vector
⎡ ⎤ ∂ −→ f ∇ = Gx = ⎣ ∂x ⎦ f ∂f (4.5) Gy ∂y with direction of the maximum gradient change
Gy α(x, y) = arctan( ) (4.6) Gx
47 4. Image Analysis ⎡ ⎤ i1 i2 i3 ⎣ ⎦ A = i4 i5 i6 i7 i8 i9
Figure 4.6.: 3x3 image region with intensity values ix +10 0 +1 0 −1 −10
Figure 4.7.: The Roberts Cross operator kernel (left: vertical, right: horizontal) and magnitude
−→ ∂f ∂f ∇f =|∇f |= ( )2 + ( )2 (4.7) ∂x ∂y
Note that for performance reason, an approximation on the magnitude ∇f may be used
∇f ≈|Gx |+|Gy | (4.8)
The partial derivatives can be calculated by considering the difference between a pixel and its neighborhood. Figure 4.6 showsa3by3image region A
The Roberts Cross (Roberts, 1965) operator is a simple and computationally quick gradient operator, defined as a 2x2 convolution kernel as shown in figure 4.7.
The first derivative at point i5 in figure 4.6 using the Roberts cross operator is
Gx = i9 − i5 (4.9)
Gy = i8 − i6 (4.10) with the approximate magnitude
∇f ≈|i9 − i5|+|i8 − i6| (4.11)
48 4.3. Image Segmentation
Figure 4.8.: Edges extracted from the Roberts (top right), Prewitt (bottom left) and Sobel (bottom right) operators from the circuit (top left) image Original image courtesy of Steve Decker and Shujaat Nadeem, MIT, 1993.
The approximation reduces the computational complexity to simple arithmetic operations. However, one drawback for this simplification is the loss of isotropic property, but is usually acceptable because the three gradient operators in this section only give isotropic results on vertical and horizontal edges.
The Roberts cross operator has an advantage of simplicity and thus quick to compute. However, because of its small kernel size, the method is very sensitive to noise (Figure 4.9 on the next page, top right), and its performance in blurred edge is poor.
A slight variation of the Robert cross operator is called the Prewitt operator (Prewitt, 1970) (Figure 4.10 on the following page), which is a 3 by 3 kernel with a clear centre compared to the 2 by 2 Robert cross operator.
Another variations based on the Prewitt operator is called the Sobel operator
49 4. Image Analysis
Figure 4.9.: Gradient operators under noise Top left: circuit with added noise (Gaussian σ2 = 0.01). Top right: Roberts. Bottom left: Prewitt. Bottom right: Sobel. Original image courtesy of Steve Decker and Shujaat Nadeem, MIT, 1993.
⎡ ⎤ ⎡ ⎤ +1 +1 +1 −10+1 ⎣ 000⎦ ⎣ −10+1 ⎦ −1 −1 −1 −10+1
Figure 4.10.: The Prewitt operator (left: vertical, right: horizontal)
50 4.3. Image Segmentation ⎡ ⎤ ⎡ ⎤ +1 +2 +1 −10+1 ⎣ 000⎦ ⎣ −20+2 ⎦ −1 −2 −1 −10+1
Figure 4.11.: The Sobel operator (left: vertical, right: horizontal)
Figure 4.12.: top: ramp edge; bottom: second order derivative of the horizontal intensity profile
(Sobel, 1970), with a weighting of 2 instead of unit weighting applied to the centre coefficients, as shown in figure 4.11. Higher emphasis is placed on pixels that are closer to the centre pixel and this leads to a smoothing effect which attribute to a slightly less noise sensitive characteristic compared to the Prewitt and Robert cross operators.
4.3.3.2. Laplacian Operator
Despite using first-order derivatives for edge detection, edge points can be detected by searching for zero crossings of the second-derivative. A second order derivative of an exaggerated ramp edge is shown in figure 4.12.
The Laplacian operator is a second-order differential operator. For a twice differentiable real function f , the Laplacian is defined as
∂2 f ∂2 f ∇2 f =∇•∇f = + (4.12) ∂x2 ∂y2
51 4. Image Analysis ⎡ ⎤ ⎡ ⎤ 0 −10 −1 −1 −1 ⎣ −1 +4 −1 ⎦ ⎣ −1 +8 −1 ⎦ 0 −10 −1 −1 −1
Figure 4.13.: Laplacian convolution kernels
0.02
0.015
0.01
0.005
0 30 30 20 20 10 10 0 0
Figure 4.14.: 3-D plot of a two dimensional Gaussian filter kernel
For digital images, two commonly used discrete convolution kernel for ap- proximation is shown in figure 4.13. Similar to the Sobel edge operator, the left kernel on figure 4.13 is isotropic only on the horizontal and vertical edge, ◦ while the kernel on the right is isotropic on multiples of 45 rotation.
However, the second-order derivative nature of the Laplacian is very sensitive to noise (Figure 4.4 on page 46). To counter this, the image is often smoothed with a Gaussian filter before the Laplacian is applied. The Gaussian filter has the form
2 2 1 − x +y G(x, y) = e 2σ2 (4.13) 2πσ2 where σ is the standard deviation. Figure 4.14 shows a 3-D plot of a two dimensional (30x30) gaussian kernel with σ = 3.
Since convolution operation is associative, the smoothing Gaussian filter and the Laplacian operator could be combined into a single convolution kernel,
52 4.3. Image Segmentation ⎡ ⎤ 00 1 00 ⎢ ⎥ ⎢ 01 2 10⎥ ⎢ ⎥ ⎢ − ⎥ ⎢ 12 16 2 1 ⎥ ⎣ 01 2 10⎦ 00 1 00
Figure 4.15.: 5x5 Laplacian of Gaussian kernel
−3 x 10
1
0
−1
−2
−3
−4 30 30 20 20 10 10 0 0
Figure 4.16.: 3-D plot of a two dimensional Laplacian of Gaussian filter kernel which is more computationally efficient.
2 2 2+ 2 1 x + y − x y LoG(x, y) =− 1 − e 2σ2 (4.14) πσ4 2σ2
The resulting kernel is commonly named the Laplacian of Gaussian (LoG, Marr and Hildreth (1980)), and also known as the Mexican hat function, inspired by the three-dimensional shape as shown in figure 4.16. Figure 4.15 showsa3-Dplotofa5by5Laplacian of Gaussian convolution kernel.
As discussed above, edge points will give rise to zero-crossings in the resulting Laplacian output. Nevertheless, zero-crossings may also occur at any region with changes in the intensity gradient, not necessarily edges. A straightfor- ward approach for zero-crossing detection is to apply a threshold that sets
53 4. Image Analysis all positive pixels to logical 1 and all negative pixels to logical 0, resulting in a binary image. Zero-crossing points can then be retrieved by searching for all foreground pixels that has a background neighbor. One drawback of this technique is the bias of the edge towards either the foreground or background. An alternative is to consider both the foreground and background edge, and choose the one with a lower magnitude of the Laplacian output.
One characteristic of zero-crossing Laplacian output is that all edges are presented in closed curves (Figure 4.17 on the next page) except edges that go off the image boundary. Because of the second-derivative nature of the filter, the LoG is susceptible to noise under insufficient Gaussian smoothing (Figure 4.17 on the facing page), resulting in lots of spurious edges. Apart from increasing the Gaussian smoothing, threshold on the gradients of zeros- crossings could also be applied, having a drawback of amplifying high frequency noise due to the third derivative nature of the operation.
The level of detail of the LoG output is governed by the standard deviation used in the Gaussian smoothing kernel. The higher σ is set, the less level of detail will be retrieved. Also note that while the 3 by 3 convolution kernel ◦ in figure 4.13 on page 52 is only isotropic in 45 rotational increment, LoG kernel used in practice is an isotropic filter, thus it is not possible to extract edge orientation directly from the transformation output.
Computationally, the LoG kernel could easily give rise to extremely positive or negative values which lies out of bound of the original pixel data type. It is important to ensure the output data type is able to handle the larger range of values from the operation.
Several variants of the LoG exist, with the most common one named the Difference of Gaussian (DoG) filter, which is an approximation of the LoG using just the difference of two Gaussians of different size, defined as
−(x2+y2) −(x2+y2) 1 1 2σ2 1 2σ2 DoG(x, y) = e 1 − e 2 (4.15) π σ2 σ2 2 1 2
Figure 4.18 on page 56 shows the plot of a DoG function (σ1 = 3 , σ2 = 2), which is very similar to the LoG filter. Another even coarser approximation is the Difference of Boxes filter, which is the difference of two different-sized mean filter. It has an advantage of being much faster than the LoG operator.
54 4.3. Image Segmentation
Figure 4.17.: Top left: noisy circuit image (Gaussian σ2 = 1). Top right: zero- crossing threshold = 0, σ = 2. Bottom left: zero-crossing threshold = 0.01, σ = 2. Bottom right: zero-crossing = 0, σ = 5. Original image courtesy of Steve Decker and Shujaat Nadeem, MIT, 1993.
55 4. Image Analysis
0.005
0
−0.005
−0.01
−0.015
−0.02
−0.025 30 30 20 20 10 10 0 0
Figure 4.18.: 3-D plot of a two dimensional Difference of Gaussian filter kernel
4.3.3.3. Canny Edge Detector
The Canny edge detector was proposed (Canny, 1986) aiming to construct the optimal edge detection with the criteria of marking as many real edges as possible, marking as close to the real edge as possible, and avoid duplicate marking of edges. Unlike previously discussed gradient operators and the Laplacian operator, the Canny edge detector is a multi-step procedure.
The image is first smoothed using a Gaussian filter for noise reduction using the kernel as described in equation 4.13 on page 52. The gradient is then computed using any gradient operator described in section 4.3.3.1 on page 47 to obtain
= 2 + 2 G(x, y) Gx Gy (4.16) and with gradient orientation
Gy (x, y) θ(x, y) = arctan (4.17) Gx (x, y)
A threshold T is applied to suppress most of the noise while try to keep all edge candidates.
56 4.3. Image Segmentation
Figure 4.19.: Left: noisy circuit image (Gaussian σ2 = 1). Right: Canny edge detector (T = 0.1,T2 = 0.2,σ = 1.5]) Original image courtesy of Steve Decker and Shujaat Nadeem, MIT, 1993.
⎧ ⎨ G(x, y) ifG(x, y) > T = GT (x, y) ⎩ (4.18) 0 otherwise
Edge ridge thinning to GT (x, y) is performed by suppressing all non-maxima pixels. Each non-zero pixel in GT (x, y) is checked and if it is greatest among its two neighbors along the gradient direction, the pixel is kept. If it is not, the pixel is set to zero.
Two binary images GT1 and GT2 are generated using two thresholds T1 and > T2 respectively where T2 T1. Comparatively, the binary image GT1 is more noisy and contains more false positives. The final step involves applying edge linking on image GT2 with the use of pixels in GT1 as bridging purpose only.
The output of the Canny edge detector (Figure 4.19) depends on three ad- justable parameters. The width of the Gaussian smoothing kernel affects the balance point between noise sensitivity and sensitivity towards finer object details. The higher the upper threshold T2, the less edge fragments; and the higher the lower threshold T1,the higher the chance of having edges broken up especially in noisy situation.
One drawback of the Canny edge detector is the defect on Y-junctions, where three edges connect at the same point. Application of the Canny detector will result in having two of the edges linked, with the remaining edge approaching the centre point, but not connecting.
57 4. Image Analysis
Figure 4.20.: Typical adaptation results with the use of deformable model. Note that part of the model is attracted and settled on false boundaries (white arrows).
4.3.4. Model Based Techniques
Recent developments in image segmentation have taken into account more prior information of the object of interest, in order to produce more accurate and robust automatic segmentation outcome. Shapes are one of the commonly used priori information, in which a predefined shape is iterated and refined to a better matched state. Criteria such as strong edges could be used to define the degree of match.
Active shape models (Cootes et al., 1995; Kelemen et al., 1998) a commonly employed refinement approach, which is analogous to that employed by Active Contour Models (commonly known as snakes, Kass et al., 1988). Statistically based techniques are employed for constructing deformable shape templates with the deformation constrained by the statistical parameterization. It is a fast and robust automatic segmentation method, but its segmentation accuracy could be limited due to its restriction to a model with a few parameters (Weese et al., 2001).
Elastically deformable models (McInerney and Terzopoulos, 1996; Staib and Duncan, 1996) is another promising technique in effectively segmenting types of medical images. It has a relatively higher flexibility and is capable of accommodating a higher level of structural variability commonly encountered in anatomical objects. Nonetheless, in non-interactive applications, the ini- tialization template has to be close to the actual object of interest for good performance, making it a major drawback. This is mainly due to the presence of other surrounding features which could incorrectly attract the deformable model towards false boundaries as shown in figure 4.20.
58 4.4. Image Geometric Transformation
Several authors (Kaus et al., 1999; Weese et al., 2001) proposed the use of shape constrained deformable model, in an attempt to combine the benefits of active shape and elastically deformable models. It involves adaptation to the image by means of an external energy from local surface detection, combined with an internal energy constraining the deformable surface to stay close to the predefined shape model. Kaus et al. (1999) reported success in applying the method to MRI images of grade 1-3 brain tumors (meningiomas and astrocytomas) in various locations. Nevertheless, it was pointed out an intrinsic limitation exists; the pre-defined template cannot account for any pathological structures. While successful segmentation was achieved in simple tumors, the authors called for additional investigations in improving the elastic matching technique to explicitly handle pathological structures.
4.4. Image Geometric Transformation
Image output from the acquisition stage may contain irregularities, distortion or other unwanted artifacts. While many modern equipments have sophisti- cated calibration procedures to minimize its effect to the final image quality, image pre-processing is often required to tailor to special analysis need. In medical imaging, extra processing steps for artifact reduction, calibrations as described in section 3onpage19are often done within the image acquisition system, resulting in usually acceptable image quality provided that optimal imaging parameters are employed. However, one uncontrollable factor in real world medical imaging, precise patient or specimen positioning, often exist in practice. While patients are often positioned in a standardized position before any medical imaging procedures commences, the consistence is often not sufficient, or the positioning may not be suitable for analysis purpose. A transformation on the coordinate system may be necessary or desired for ease of analysis.
4.4.1. Affine Transformation
Affine transformation is a type of linear geometric transformation converting between two affine spaces, and can be expressed as a linear transformation plus a translation operation. An affine transformation has the following properties:
59 4. Image Analysis
• Preservation of collinearity: all points on a line still lie on a line after transformation
• Preservation of distance ratio: ratio of two collinear line segments remains the same after transformation
Note that although affine transformation preserves collinearity and distance ratio, it may not necessarily conserves angles or actual length.
An affine transformation can be generally expressed as
x = Ax+ B (4.19) where x is a n by 1 vector in n-dimensional space, A is the transformation matrix and B is an n by 1 translation matrix.
Affine transformation is useful in conversions between coordinate systems with a combination of translation, rotation, scaling and shear procedures. Intuitively, only translation, rotation are employed in most coordinate system conversion because of the goal to preserve geometric or actual length consis- tence. Scaling may be used in coordinate system conversion when anisotropic voxels or pixels are being used. For a two dimensional matrix, the affine transformation for translation is defined as
x 10 x t = + x (4.20) y 01 y ty
where tx and ty are the x and y translation respectively. Rotation is defined as
x cosθ −sinθ x = (4.21) y sinθ cosθ y where θ is the angle of rotation counterclockwise about the origin. The transformation for scaling
x s 0 x = x (4.22) y 0 sy y
60 4.4. Image Geometric Transformation
where sx and sy is the scaling factor of x and y respectively. The shearing transformation has two forms
x 1 m x = x (4.23) y 01 y
x 10 x = (4.24) y my 1 y where equation 4.23 is for shearing operation parallel to the x axis and equation 4.24 is for shear parallel to the y axis. mx and my are the shearing factor correspondingly.
Multiple affine transformations could be combined into a single operation using matrix multiplication. Given an affine transform defined by matrix A1 followed by another affine transformation defined by matrix A2, the resultant procedure is equivalent to performing an affine transformation with matrix A
x x = A (4.25) y y
where A = A2 ∗ A1. Note that the matrix multiplication is not commutative, meaning the operation is order dependent.
Homogeneous coordinates are often used as an alternative representation, to combine the transformation matrix A and the translation matrix B. This is done by incorporating the translation matrix using an n+1 by n+1 affine transformation matrix as follows:
⎡ ⎤ ⎡ ⎤ ⎢ x ⎥ ⎢ x ⎥ ⎢ ⎥ AB⎢ ⎥ ⎣ y ⎦ = ⎣ y ⎦ (4.26) 001 1 1 where A and B are the matrices defined in equation 4.19 on the facing page. This representation simplifies the transformation parameter into a single homogeneous matrix and is often used in software packages like Matlab .
61 4. Image Analysis
Representation Explanation
a ∈ Aais an element of A a ∉ Aais not an element of A
Table 4.1.: The membership relation in set theory
4.5. Morphological Processing
The term morphology refers to mathematical morphology which in image processing, denotes the representation and operation of regional shapes or structures. Though originally developed for binary images only, it has been extended to operate on grayscale images and multi-channel images.
Mathematical morphology is built based on the set theory, in which in a binary image, the set of all black pixels could be represented as a set of 2-D vectors in Z2 where each pixel coordinates (x, y) symbolized a 2-D vector. In grayscale images, an extra dimension is added to incorporate the grayscale values, resulting in a set representation in the Z3. The concept can be further extended to multi-channel colour images by set representation in higher dimension. The sections below focuses on morphological operations in binary images with brief mention of operations on single-channel grayscale images.
4.5.1. Preliminaries
The basic relationship between objects in the set theory is the membership relation. Let A beasetinZ2, which is a general representation of a binary image as mentioned above and for any a in Z2, the membership relations are listed in table 4.1.
The content of a set is denoted by two braces, with A = {a} meaning the set A contains an element a,. Furthermore, the expression B = {b|b =−a, fora∈ A} means the set B contains element b in which b is composed by multiplying every element in the set A by −1. Another common notation is the empty set, denoted by Ø. Table 4.2 on the facing page shows a set of commonly used notations in set manipulation.
Logical operations on binary images are often involved in many morphological operations. Unlike the set operations mentioned above, logical operations
62 4.5. Morphological Processing
Relationship Representation Explanation
Subset A ⊆ B every element of set A is an element of set B Proper Subset A B set A is a subset of set B but A = B Union C = A ∪ B set C contains all elements in either set A or B Intersection C = A ∩ B set C contains all elements in A and B Complement A or Ac the set A contains the set of elements not in set A Difference C = A − B or A\B set C contains elements which are member of set A but not set B Cartesian Product C = AxB set C contains all the ordered pairs (a,b) where a ∈ A and b ∈ B Reflection Aˆ defined as Aˆ = {c|c =−a, for a∈ A}, equivalent to flipping an object along the x-axis followed by the y-axis in a 2-D image.
Translation (A)z defined as (A)z = {c|c = a + z, for a∈ A}, equivalent to moving an object in the x-y plane in a 2-D image.
Table 4.2.: Standard notations in set theory
63 4. Image Analysis
Operation Notation Explanation Equivalent Set Operation
AND a • b Logical AND operation Intersection between a and b OR a + b Logical OR operation Union between a and b NOT a¯ Logical NOT operation Complement on a
Table 4.3.: Logical operations on binary images are performed on a pixel by pixel basis, and on images or image windows of exactly the same dimension. Table 4.3 lists the notations of binary logical operations and its equivalent set operations.
4.5.2. Dilation and Erosion
Image dilation and erosion are one of the most fundamental and commonly employed morphological techniques and serve as a basis of a wide range of morphological operations.
4.5.2.1. Dilation
Named after Hermann Minkowski, the dilation operation (Minkowski, 1900) is also known as the Minkowski sum. Dilation of two sets A and B in Z2, denoted by the symbol ⊕, and is defined as
A ⊕ B = {z|(B)z ∩ A = Ø} (4.27) where B is often referred to as the structuring element of the operation. The dilation result of set A and B is the union set of A and set B with all translation z, with which the translated set, (B)z has at least one overlapping element with set A.
On a binary image, dilation could be achieved by superimposing the structuring element on top of each background pixel. If at least one pixel of the structuring element coincides with a foreground pixel, all pixels covered by the structuring
64 4.5. Morphological Processing element are set to the foreground value, or else the pixel values are left unchanged.
Dilation on grayscale images are similar, in which the maximum pixel inten- sity level of the superimposed structuring element window is taken as the output pixel value. This operation in general results in a brightened image, with bright regions surrounded by dark regions enlarged, and dark regions surrounded by bright regions shrank.
Structuring elements are often symmetrical, with square or disk topology. The use of non-symmetrical structuring element will result in a directional operation. Dilation using a 10 pixels vertical structuring element on a binary image could be performed to link only vertical gaps but not horizontal gaps.
4.5.2.2. Erosion
Erosion is another basic morphological operation denoted by the symbol , and is defined as
A B = {z|(B)z ⊆ A} (4.28)
The erosion result of a set A using a structuring element B is the set B with all translation combination z in which (B)z is completely contained in set A.
Erosion of a binary image can be done by superimposing the structuring element over each of the foreground pixels. If for all the pixels in the structur- ing element, the underlying pixels are foreground pixels, the pixels are left unchanged, or else the corresponding pixels in the structuring elements are set to the background value.
Erosion on grayscale images is similar. The minimum pixel intensity level of the superimposed structuring element window is taken as the output pixel value. This operation in general results in a darkened image, with dark regions surrounded by bright regions enlarged, and bright regions surrounded by dark regions shrunk.
Similar to dilation, structuring element are often symmetrical, with square or disc shape. The use of non-symmetrical structuring element will result in a directional erosion operation.
65 4. Image Analysis
4.5.3. Opening and Closing
Morphological dilation and erosion described in previous sections are fre- quently combined to provide more robust operations, namely image opening and closing.
Morphological opening of a set A with a structuring element B is denoted by the symbol ◦ and is defined as
A ◦ B = (A B) ⊕ B (4.29)
Similarly, morphological closing of a set A with a structuring element B is denoted by the symbol • and is defined as
A • B = (A ⊕ B) B (4.30)
From its definition, morphological opening is an erosion followed by a dilation operation, and morphological closing is a dilation followed by an erosion oper- ation. While the usefulness of the two operators may not be straightforward from a set theory interpretation, the geometric interpretation of the two operators give a more direct understanding of the usefulness in morphological image processing. Assuming a ball or disc shaped structuring element B is being used, the resulting boundary of an opening operation could be viewed as the coverage of a rolling ball inside an object along its inner boundary. Fig- ure 4.21 on the facing page shows the morphological opening of a rectangular foreground object using a disc-shaped structuring element. The resulting set is the coverage of the rolling ball inside the object bounded by its boundary.
Similarly, figure 4.22 on the next page shows the geometric interpretation of the morphological closing operation. Instead of tracing the structuring element along the inner boundary, the rolling disc is traced outside the foreground object following the outer object boundary. Note that while we use the term “rolling” in the above description, the structuring element only undergoes translation but not rotation, and this interpretation extends similarly to other non-symmetrical structuring element.
The opening and closing operation are often considered duals of each other. Table 4.4 on the facing page shows some common properties of the opening and closing operations.
66 4.5. Morphological Processing
Figure 4.21.: Geometric interpretation of morphological opening
Figure 4.22.: Geometric interpretation of morphological closing
Property Equation
Duality A ◦ B = Ac • B and A • B = Ac ◦ B
Translation (A)z ◦ B = (A ◦ B)z and (A)z • B = (A • B)z Idempotence (A ◦ B) ◦ B = A ◦ B and (A • B) • B = A • B Extensivity A ⊆ (A • B) Antiextensivity (A ◦ B) ⊆ A
Table 4.4.: Common properties of morphological opening and closing
67 4. Image Analysis
Figure 4.23.: Left: Noisy fingerprint image. Middle: Opening of the image. Right: Opening followed by closing. Reproduced from Gonzalez et al. (2003), original image courtesy of the National Institute of Standards and Technology.
In general, the opening operation separates slightly connected object while closing fill up small holes within the object. Both operations give a smoothed contours, with which the opening and closing operations smooth the contour through the tracing of the inner and outer object boundary respectively, as demonstrated in figure 4.21 on the previous page and figure 4.22 on the preceding page. Figure 4.23 shows the use of opening operation to remove small islands as a result of noise in a fingerprint image using a 3 × 3 square structuring element. Numerous gaps along the ridges of the fingerprint is introduced due to pepper noise on the original ridges, and the closing operator is applied to bridge the gaps.
4.5.4. The Hit-or-miss Operation
Originally defined by Serra (1982), and sometimes known as the hit-and- miss operation, the transformation is one of the basic techniques for shape matching. Denoted by the symbol , the hit-or-miss transformation is defined as
A B = (A X ) ∩ [Ac (W − X )] (4.31) where W is a small window with X enclosed, and X is the shape to be matched. Without loss of generality, a set B = (B1,B2) is always defined in which B1 represents the object template X while B2 represents the background template (W − X ) to aid the geometric illustration. Thus equation 4.31 can be expressed as
68 4.5. Morphological Processing
Figure 4.24.: left: Set A (gray). right: foreground template W and background template (W − X ) Reproduced from Gonzalez and Woods (2002)
Figure 4.25.: left: set Ac (gray). right: A X (gray regions)
A B = (A B1) ∩ [(A B2) (4.32)
The geometric interpretation of the transformation is as follows. A binary image A containing 3 foreground objects, A = X ∪ Y ∪ Z , with background template B2 are shown in figure 4.24.
Figure 4.25 shows the complement or set A and the erosion of set A using X as the structuring element. Geometrically speaking, the result represents a possible match of the template X within set A.
The next step is to compute the erosion of set Ac with the background template (W − X ), as shown in figure 4.26 on the next page.
The final step is to compute the intersection of the two erosion results, giving the final match as shown in figure 4.26 on the following page. While the erosion step shown in figure 4.25 is already a matching operation, the beauty
69 4. Image Analysis
Figure 4.26.: Ac (W − X ) in gray of the hit-or-miss transformation is the additional matching of the background template (W − X ), eliminating objects that contain X .
4.5.5. Thinning
Object representation using line segments are often useful in describing the topology in a simplistic way. Thinning is a commonly used procedure (Elmoutaouakkil et al., 2002; Qiang et al., 2004) to generate topological representation and is based on the hit-or-miss transformation discussed in previous section. Denoted by the symbol ⊗, the thinning transformation is defined as
A ⊗ B = A − (A B) (4.33)
The thinning operation could be treated as a erosion to reduce the thickness of an object while not vanishing it. A more practical interpretation could be made by descriptions using conditional statements using a simple 3 by 3 structuring element with 8-th connectivity. The operation could be interpreted as an erosion operation of zeroing the centre origin pixel if any of the following conditions are not met, or equivalently it is not zeroed only if all the conditions are met:
• it is an isolated pixel
• connectivity will be broken
70 4.5. Morphological Processing
Figure 4.27.: Iterations of a thinning operation. B 1 to B 8: structuring elements for thinning operation. Middle 3 rows: thinning operations using the 8 structuring elements incrementally. Bottom left: Final result after convergence. Bottom right: Conversion to m-connectivity. Reproduced from Gonzalez and Woods (2002)
• line will be shortened
The operation is repeated until no further change is observed in the subsequent step and the final image will be a set of connected paths with unity width giving an approximation of the topology of the object. From the nature of the operation, it could be considered as a conditional recursive erosion operation. In the above case utilizing a 3 by 3 structuring element, having 29 = 512 possible window combination, a look-up table is often pre-calculated to speed up computation. Figure 4.27 shows an example of the thinning operation using a common set of structuring elements (B 1 to B 8). The thinning operation is applied incrementally using each of the structuring elements until convergence and the final output is converted to m-connectivity.
71 4. Image Analysis
Figure 4.28.: Thickening obtained by thinning operation. Top left: original set A. Top right: Complement of set A. Middle row: iterations of the thinning operation on set (A)c . Bottom: Final result after removal of disconnected islands Reproduced from Gonzalez and Woods (2002)
Another useful application of the thinning operation is to reduce the output of the Sobel edge detector described in section 4.3.3.1 on page 47. The operation is useful in reducing the edge to unity width while preserving connectivity and avoiding the path shortening effect.
The dual of morphological thinning is the thickening operation, which is not a commonly used morphological processing technique. Denoted by the symbol , it is defined as
A B = A ∪ (A B) (4.34)
In practice, thickening is usually achieved by thinning the background set Ac followed by a complement operation (Figure 4.28). An extra procedure of removing disconnected islands is always applied to eliminate the side effect of the operation.
4.5.6. Skeleton
Similar to the morphological thinning operation described in previous section, the skeleton of an object is another topological representation. Based on the work of Lantuejoul and Serra (Lantuéjoul, 1978; Serra, 1982), the skeleton of A with structuring element B is defined as
72 4.5. Morphological Processing
Figure 4.29.: Principle of skeleton generation. Maximum-sized disks are positioned with centres on the skeleton. Reproduced from Gonzalez and Woods (2002)
K S(A) = Sk (A) (4.35) k=0 where
Sk (A) = (A kB) − (A kB) ◦ B (4.36) and
K = max{k|(A kB) = ∅} (4.37)
K is chosen such that it is the step before the set A turns into an empty set. The structuring element B is chosen to be an approximation of a disc. Given K and the structuring element B, reconstruction could be done using the equation
K A = (Sk (A) ⊕ kB) (4.38) k=0
Figure 4.29 shows the use of maximum-sized disks in the construction of a skeleton outline. Compared to the morphological thinning operation, the skeleton operation does not guarantee connectivity nor path of unity width.
73 4. Image Analysis
Figure 4.30.: Top left: original segmented human chromosome image. Top right: Thresholded image. Bottom left: Skeleton of the image. Bottom right: Skeleton followed by spur removal. Original image courtesy of Gonzalez et al. (2003)
Figure 4.30 shows the skeleton of a human chromosome, delivering a good rep- resentation on the structural shape of the object. Spur removal is repeatedly applied to remove tiny spurs which is common in a skeleton image.
4.5.7. Convex Hull
Aset{A} is said to be convex if all points lying between the line segment constructed between any two points in {A} lies in {A}. The convex hull C(B) of aset{B} is defined as the smallest convex set containing {B}. The term convex deficiency is often used to denote the set difference {C(B) − B}.
The simplified implementation of computing C(B) can be described as follows:
74 4.5. Morphological Processing
Let B 1,B 2,B 3,B 4 be 4 structuring elements as shown in figure 4.32 on the next page, and define
i = i ∪ = = i = Xk (Xk−1 B ) Afori 1,2,3,4 and k 1,2,3,4... with X0 A (4.39) now define Di to be the convergence of above equation,
i = i i = i D X when Xk Xk−1 (4.40)
The convex hull of A, can be denoted as
4 C(A) = Di (4.41) i=1
The above procedures are equivalent to applying the hit-or-miss transformation (Section 4.5.4 on page 68) iteratively. The hit-or-miss transformation is applied to A using the structuring element B 1 until it converges and the union with A is computed (D1). The same operation is performed with structuring element B 2,B 3,B 4 resulting in D2,D3,D4 respectively. The final convex hull C(A) can be obtained by computing the union of Di . Note that the implementation described above does not necessary produce a smallest convex set containing {A},as illustrated in (Figure 4.32 on the next page). To limit the growth, addition criterion to the above algorithm could be added by imposing limitations to the maximum vertical and horizontal dimensions of C(A) to that of {A} (Figure 4.32 on page 76), or in an even more detailed approach, limitation upon diagonal directions could be applied. The cost of the additional criteria is a higher complexity, thus computational complexity and time.
Various algorithms for computing the convex hull have been proposed. Being one of the simplest while comparatively not very efficient, Jarvis (1973) proposed a 2-D case named the Jarvis march, also known as the gift wrapping algorithm, having a complexity of O(nh) where n is the number of points in {A} and h is the number of points in the final convex hull. A more efficient algorithm was proposed by Graham (1972) reducing the complexity to O(n logn). Other even more efficient methods (Kirkpatrick and Seidel, 1986; Chan, 1996) based on output-sensitive algorithms were proposed, further reducing the complexity down to O(n logh).
75 4. Image Analysis
1 Figure 4.31.: A morphological algorithm to compute the convex hull. X0 :the 1 2 3 4 original set A. X4 , X2 , X8 , X2 : the set at convergence using the structuring elements B 1,B 2,B 3,B 4 respectively. C(A): The final convex hull Reproduced from Gonzalez and Woods (2002)
Figure 4.32.: Convex hull with extra criteria to limit growth Reproduced from Gonzalez and Woods (2002)
76 4.6. Miscellaneous
4.6. Miscellaneous
4.6.1. The Hungarian Algorithm
The Hungarian algorithm, proposed by Kuhn (1955), is a combinatorial opti- mization algorithm for solving assignment problem minimizing or maximizing the total cost associated. A typical example of the method is to find an optimal assignment of worker to job so as to minimize the total cost in which one worker could be assigned to one and only one job.
Starting with an n ×n cost matrix c where cij denotes the cost associated with assigning the i-the worker to the j-th job, the algorithm could be summarized into the following steps:
1. Subtract each row by the row minimum
2. Subtract each column by the column minimum
3. Use the minimum number of lines to cover all zeros in the resulting cost matrix. If k lines are used, and k < n, compute m which is the minimum uncovered number in the cost matrix. Subtract m from all uncovered number, and add m to all number covered with two lines (one horizontal and one vertical) and restart step 3. If k = n,goontostep4.
4. Start from the top row to make assignments. Unique assignment can be made when there is exactly 1 zero in the row. Delete the row and column associated with the assigned element. In the case with which all remaining rows containing more than 1 zero, where unique assignment could not be made, iterate in columns starting from the left-most column. Similar to the row assignment, unique assignment can be made when there is exactly 1 zero in the column. Delete the row and column associated with the assigned element. Switch between row and column assignment until all unique assignments can be made.
5. If there are still unassigned rows in which unique assignment could not be made in step 4, make one arbitrary assignment by selecting an element with a zero, and try step 4 to make further unique row or column assignment.
77 4. Image Analysis
78 5
Shape Analysis
Contents 5.1. Overview ...... 79 5.2. Basic Geometrical Shape Parameters ...... 79 5.2.1. Region Based Parameters ...... 80 5.3. Object Description Techniques ...... 82 5.3.1. Chain Coding ...... 83 5.3.2. Fourier Descriptors ...... 85 5.3.3. Hausdorff Distance ...... 89 5.3.4. Corner Detector ...... 90
5.1. Overview
hape is one of the fundamental factors in anthropometry. While shape S cognition is an instinct nature of human being, its perception in the digital world remains a difficult task. Numerous methods were suggested in characterizing object shape, but their performance and versatility is far from satisfactory. The section below summarized several commonly employed object description techniques.
5.2. Basic Geometrical Shape Parameters
Direct geometrical measurements are one of the most common ways of struc- turally describing an object. This section aims to provide descriptions on some
79 5. Shape Analysis geometric measurement parameters.
5.2.1. Region Based Parameters
5.2.1.1. Area
A 2-D quantity representing the extent of a surface. In digital images where objects are quantized to pixel level, the area is defined as the number of pixels times the individual pixel area.
5.2.1.2. Centroid
The centroid of a geometric shape is defined as
xdA ydA Cx = , Cy = (5.1) A A where A is the area of the shape defined as A = f (x)dx. The centroid on a digital image could be simplified, and denoted as
n n 1 x 1 y Cx = , Cy = (5.2) n n where n is the number of pixels in the shape. In a homogeneous object, the centroid equals to its centre of mass.
5.2.1.3. Eccentricity
The eccentricity (ε) of a two dimensional region is defined as the eccentricity of the ellipse that has the same second-moments as the shape region. The eccentricity of an ellipse with semi-major axis a and distance from the centre ε = c to either focus c is defined as a . Eccentricity is a scale between 0 and 1, in which an ellipse is a circle when ε = 0 and a line segment when ε = 1.
80 5.2. Basic Geometrical Shape Parameters
5.2.1.4. Area Moment of Inertia
The area moment of inertia, also known as the second moment of inertia, or just moment of inertia, measures the resistance of an object towards bending. The area moment of inertia about an x-axis is defined as
2 Ixx = y dA (5.3) where y is the perpendicular distance from the axis to the area element, and A is the element area. Equation 5.3 is valid for sections that are symmetrical about the x-axis. For other cases, equation 5.4 applies.
Ixy = xydA (5.4) where A is the element area, x and y are the perpendicular distance to the element A from the x-axis and y-axis respectively. The parallel axis theorem also states that given the area moment of inertia of an object about the centre of mass, the area moment of inertia of any arbitrary parallel axis Icm is defined as
2 Icm = Icm + Ad (5.5)
where Icm is the area moment of inertia through the centroid, A is the shape area, Icm is the moment of inertia through an axis parallel to that of Icm, d is the perpendicular distance between the axes of Icm and Icm .
5.2.1.5. Polar Moment of Inertia
The polar moment of inertia measures the resistance of an object towards torsion. Analogous to the area moment of inertia, the polar moment of inertia is used in calculation of the twist of an object under torque, and is defined as
2 Jx = r dA (5.6)
4 where Jx is the polar moment of inertia (m ), r is the radial distance from the element to the axis of rotation, A is the infinitely small element area.
81 5. Shape Analysis
5.3. Object Description Techniques
Shape description techniques are widely used in many disciplines in image analysis, from object recognition in computer vision, biological classification, character recognition in optical character recognition (Kuhl and Kuhl, 1963), to visual perception in cognitive science. This section aims to provide a brief outlook in several shape representation techniques and specifically its applications in the field of biomedical engineering which form the bases of various techniques employed in the discussion in following sections.
Shape description usually refers to methods that generate a numerical de- scriptor of a shape and its goal to uniquely characterize a shape based on certain features.
Several properties are considered desirable properties of a good shape descrip- tor:
• Uniqueness: Having a unique representation of shapes is fundamentally critical to allow any shape comparison or retrieval.
• Completeness: This generally refers to obtaining an unambiguous repre- sentation towards a shape.
• Invariance: Shape representation that is invariant under different geo- metrical transformations is generally a desired property especially in real-world applications. This includes translation, rotation and scale invariance.
• Sensitivity: A particularly important aspect in shape representation in shape similarity analysis, where similar shape objects can be distin- guished.
• Efficiency: With the increasingly popular real-time or online shape retrieval applications, shape descriptor with high efficiency or low com- putational complexity is desired.
82 5.3. Object Description Techniques
Figure 5.1.: 8-th directional chain code
5.3.1. Chain Coding
5.3.1.1. Principles
Chain code (Freeman, 1961; Freeman and Saaghri, 1978) was first introduced by Freeman in 1961, by describing a method in encoding any arbitrary curve into a piecewise linear sequence using a pre-defined set of 8 vectors. Figure 5.1 shows the 8 direction of the vectors, and each is represented with an integer from0-7.
The chain code of an arbitrary curve is generated by finding the closest directional approximation when the vector grid is superimposed on points along the curve. The grid is transversed along the entire curve and the resulting sequence generated is the chain code. Other variations exist, using an N-directional vector (N = 2k where N > 8 and k Z ) and is called the general chain code (Freeman and Saaghri, 1978).
Freeman stated that the coding schemes must satisfy the following three objectives:
1. It must faithfully preserve the information of interest.
2. It must permit compact storage and be convenient for display
3. It must facilitate any required processing.
While the above three objectives could be mutually exclusive to a certain level, most of the derivatives were proposed based on different levels of compromising the three ideal goals.
The chain coding scheme of a boundary is dependent on its starting point, which makes it not very suitable in the context of shape matching. One simple normalization method is to treat the chain code as a circular sequence of integers. The starting point is redefined such that the resulting redistributed
83 5. Shape Analysis
Figure 5.2.: Steps in computing the shape number from chain code Reproduced from Gonzalez et al. (2003).
code obtains a minimum magnitude when the code is treated as an integer. To achieve rotational invariance, derivative notation could be used in which an integer is assigned for each change in directions (Figure 5.2). The resulting derivative notation is then normalized by cyclic permutation until a minimum integer value is obtained. The resulting normalized code is called shape number as described by Bribiesca and Guzman (1980). Bribiesca (1999) proposed another derivative chain code based on the shape number, called vertex chain code. The vertex chain code indicates the number of cell vertices that are in touch with the bounding contour of the shape. In 2000, Bribiesca (2000) proposed a chain code representation of three dimensional curves, by computing the relative directional derivatives on a digitalized 3-D curve. Kui Liu and Zalik (2005) applied Huffman coding (Huffman and Huffman, 1952) on top of chain coding, resulting in a shorter code, though considerations towards handling holes within an object is absent. Various other related derivatives (Merrill, 1973; Huo and Chen, 2005) of chain coding were proposed and summarized (Sanchez-Cruz et al., 2007). Chain coding is translation invariant because only the relative directional information on the transversal of the curve is stored, but is not scale invariance.
84 5.3. Object Description Techniques
5.3.1.2. Applications
Chain code and its derivatives are widely used as a base in shape representa- tion because of its information preservation property while having substantial reduction of data size. Martín-Landrove et al. (2007) reported successful use of chain code based analysis in brain tumoral lesions diagnosis on T-2 weighted MRI images. Min and Choi (2006) employs a modified chain code algorithm based on the vertex chain code (Bribiesca, 1999) in connecting intersection points for contour extraction from 3D ultrasound volume of pipe- shaped human organs. Shi and Mao (1995) suggested the use of chain code in the classification of direction and curvature features on movement tracks in frontal chewing patterns.
5.3.2. Fourier Descriptors
Fourier descriptors and its derivatives have been widely used to generate unique shape signatures. Fourier descriptors are based on the discrete Fourier transform (DFT), a specific form of Fourier analysis designed for discrete-time signal in a finite domain. DFT is based on the Fourier transform which transform a function x(t) from the time domain to the frequency domain defined as follows:
∞ − π F (w) = f (t)e 2 witdt (5.7) −∞ where F (w) is the spectrum and w representing the frequency, f (t) is the signal over time t. The original signal f (t) can be reconstructed from F (w) by the inverse Fourier transform:
∞ π f (t) = F (w)e2 wtdw (5.8) −∞
With the inherent discrete-time nature of digital images or signals, DFT is instead more widely employed in the field of digital signal processing. DFT is a transformation of a function from the spatial domain to the frequency domain.
85 5. Shape Analysis
Figure 5.2 on page 84 shows a K-point digital boundary in xy-plane. A full transversal of the boundary yield a list of coordinate pair (x0, y0),(x1, y1),(x2, y2),...,(xK , yK ). The coordinate pairs could be expressed in complex form as:
s(k) = x(k) + iy(k) x(k) = xk , y(k) = yk ,k = 0,1,2,...,K − 1 (5.9)
The Discrete Fourier Transform of equation 5.9 is:
K−1 1 − π X (n) = s(k)e i2 nk/K n = 0,1,2,...,K − 1 (5.10) K K =0
The complex coefficients X (n) are called the Fourier descriptors. The inverse discrete Fourier transform is given by equation 5.11
K−1 π x(k) = X (n)ei2 nk/K k = 0,1,2,...,K − 1 (5.11) K =0
The inverse Fourier transform of equation 5.9 gives back the original s(k) coefficients, as shown in equation 5.12.
K−1 π s(k) = a(n)ei2 nk/K (5.12) n=0
If only the first P coefficients instead of all K coefficients are used in the inverse Fourier transform in equation 5.12, this will yield an approximation of s(k), sˆ(k).
P−1 π sˆ(k) = a(n)ei2 nk/K (5.13) n=0
This approximation still contains the same number of coordinate points as the original boundary, with the high frequency component filtered out. With higher frequency components representing finer details of a shape, the procedure is equivalent to filtering out the level of fine details defined by P. Figure 5.3 on the facing page shows the increase in detail levels of the reconstructed shapes using an increasing number of Fourier coefficients.
One of the desired properties of shape signature is to be as insensitive as possible to various transformations that does not affect the shape boundary.
86 5.3. Object Description Techniques
Figure 5.3.: Shape reconstruction with different number of Fourier coefficients. P is the number of Fourier coefficients used. Reproduced from Gonzalez and Woods (2002).
87 5. Shape Analysis
Transformation Shape boundary Fourier descriptor
Identity s(k) X (n)
Translation s(k) +xy X (n) +xyδ(n) θ θ Rotation s(k)ei X (n)ei Scaling αs(k) X (n)α
Table 5.1.: Effect of transformation in Fourier descriptor
However, the Fourier descriptors are not directly invariant to scale, rotation and translation, but with the properties of Fourier transform, the changes of the descriptor coefficients could be summarized in table 5.1. Rotation scale θ all the Fourier coefficients by a constant term ei while scaling affects the Fourier coefficients by a multiplicative factor of α. Translation of the shape affects only the first coefficient X (0).
5.3.2.1. Applications
Fourier descriptors are a very versatile shape representation technique. Its ability to represent a coarse to fine level of shape detail from the number of Fourier coefficients makes it a very suitable candidate for content-based image retrieval systems, where high efficiency can be achieved by eliminating large amount of dissimilar candidates at coarse level, while finer level of details could be matched with more Fourier coefficients taken into account. Fourier descriptors and its derivatives are widely used in shape representation. In the field of computer vision, Fourier descriptors hold an important role in object recognition (Blumenkrans, 1991), due to its invariance under various transformations. The use of Fourier descriptors combined with other disci- plines, such as multi-resolution or multi-scale representations (Kunttu et al., 2003), is designed, to better anticipate the human vision and recognition ability. Widespread use (Antani et al., 2004; Palmer et al., 2004; Gregory et al., 2004) of Fourier shape representation techniques are also noted in the biomedical field. Younker and Ehrlich (1977) in 1977 has pointed out the potential advantages of utilizing Fourier analysis for efficient measure- ment in morphological variation within biological specimens. Schmittbuhl et al. (2001) reported the use of elliptical Fourier analysis in demonstrating a significant sexual dimorphism on the outline of the human mandible. Schmit- tbuhl et al. further pointed out that the use of elliptical Fourier analysis
88 5.3. Object Description Techniques in shape representation delivers a higher discrimination power compared to traditional metrical approaches. Ostermeier et al. (2001) employed a modified Fourier function for the nuclei shape description of bovine sperm, reporting 0-5 harmonics are sufficient to define and distinguish the nuclei shape for classification purpose. With many complex anatomic outlines not being able to be effectively described by conventional anthropometric measurements, the introduction of Fourier methods is often proven to be more functional and powerful alternatives. Procedures in potential effective representation of the morphological features in distal femur using elliptical Fourier methods has been suggested by Minor and Schmittbuhl (1999) as a more accurate mean for characterization purpose. The number of harmonics necessary for sufficient shape representation varies depending on the outline complexity, with a number of less than 10 generally considered sufficient to incorporate all shape information, as in all above-mentioned studies. Considering in general the number of shape vertices necessary in capturing a simple curved biological shape is likely to be an order of magnitude higher, Fourier descriptors provide shape representation and storage in a more efficient manner.
5.3.3. Hausdorff Distance
Hausdorff distance, named after Felix Hausdorff, is a classical correspondence based technique to measure similarity between shapes by point-to-point match- ing. Given two sets of boundary points A = {a1,a2,...,am} and B = {b1,b2,...,bn}, the Hausdorff distance is defined as
H(A,B) = max(h(A,B),h(B, A)) (5.14) where
h(A,B) = maxmin||a − b|| (5.15) a A b B where h(A,B) is called the Hausdorff distance from A to B, and ||∗|| is the norm, which is usually taken as the Euclidean distance. The Hausdorff distance is thus the distance from a point a A to its nearest neighboring point in B,in which a is the point in A that is furthest away from any point in B. One major drawback for the Hausdorff distance described above is its over-sensitivity to
89 5. Shape Analysis noise, with which a single outlier point within the point sets of two similar shapes will result in a large Hausdorff distance. To circumvent this, Rucklidge (1997) proposed a modified Hausdorff distance
f = th || − || h (A,B) fa A min a b (5.16) b B where instead of the maximum value, the f-th quantile value is chosen.
Comparing to most other shape representation techniques, the Hausdorff distance has a relatively distinct advantage in which partial shape matching could be achieved. However, it is in general not translation, rotation or scale invariant, thus an exhaustive search of all Hausdorff distances with full combination of positions, orientations or scales may be needed in the shape matching procedures. This incurs very high computational requirements. Rucklidge (1997) proposed a modified Hausdorff distance with higher efficiency and is affine invariant, though the computational requirements are still considerably high.
5.3.4. Corner Detector
Corner detection serves as a very important role in feature extraction (Koch and Kashyap, 1985; Sun et al., 2004; Qin et al., 2006) in object description and classification and various corner detectors(Harris, 1987; Kitchen and Rosenfeld, 1982; Smith and Brady, 1997) have been proposed.
In general, most corners detectors (Harris, 1987; Kitchen and Rosenfeld, 1982; Smith and Brady, 1997) works as follows (Figure 5.4 on the next page):
1. Application of a corner operator: With the input image as the source, a corner operator with possibly several other pre-defined parameters is applied to compute a cornerness measure of all pixels in the image. The resulting output is a cornerness map having the same size as the image, representing the likelihood of each pixel being a true corner based on the corner operator defined.
2. Threshold of the cornerness map: Upon the computation of the cor- nerness of every pixel, a threshold is always applied to filter out local
90 5.3. Object Description Techniques
Figure 5.4.: Typical corner detector workflow Reproduced from McGill Centre for Intelligent Machines.
maximas in the cornerness map. The goal is to eliminate all false cor- ners which are shown as local maxima in the cornerness map, while preserving as many true corners as possible. Nonetheless, the dilemma is always present in the selection of an optimal threshold, to balance between the number of false-positive fake corners and the number of true corners detected.
3. Suppression of non-maxima: Upon the threshold on the cornerness map, the final stage involves the marking of the corner points. Non-maximal suppression is applied for all pixels, in which if the cornerness level is not larger than that of its neighborhood, the pixel is discarded. The final set of the resulting suppression is marked as corners.
5.3.4.1. Moravec Operator
Moravec (1977, 1979) proposed the concept of “points of interest”, defined as the occurrence where intensity variations are large in all directions, by computing the local auto-correlation in four directions and taking the lowest of the four.
91 5. Shape Analysis
Figure 5.5.: Intensity variation cases, Moravec (1977) Reproduced from McGill Centre for Intelligent Machines.
A threshold was applied and any local non-maxima were suppressed. However, because the goal of Moravec research was not in accurate identification of corner position, but only to distinct regions in an image that enable registration of consecutive image frames in order to navigate a Standford Cart through a clustered environment. The proposed method is in general considered as a more generalized one. Figure 5.5 shows the general idea of how the algorithm is able to extract regions where the corners reside, where there is only a small minimum intensity variation by shifting the window position (in red) upon 4 directions at positions in cases A or B, while both positions in cases C and D give a large intensity variations for all shifting directions, and thus considered a “point of interest”.
5.3.4.2. Plessey Operator
Harris (1987) pointed out that the proposed algorithm is anisotropic because only four auto-correlation directions were used, or in general only over a discrete set of principle directions, and that the response could be noisy and sensitive to strong edges due to the fact that the minimum of the auto- correlation measurements were taken, but not truly the intensity variations as originally proposed. A new operator was proposed (Harris and Stephens, 1988) as an enhancement to address the limitations and it is commonly referenced as the Harris operator or the Plessey operator.
The general idea of the Plessey operator is that the sum of difference between two neighborhood Moravec windows can be a rough approximation of the gradient and Harris and Stephens proposed the use of a simplified Prewitt
92 5.3. Object Description Techniques operator (Section 4.3.3.1 on page 47) to approximate the intensity variations as shown in equation 5.17.
⎡ ⎤ − + 1 ⎢ 00 1 ⎥ ⎢ ⎥ X :[ −10+1 ]; Y :[ 0 ]; Diagonal : ⎣ 000⎦ (5.17) +1 −10 0
The intensity variations is then defined as
2 δIi δIi V (x, y) = u + v u,v δ δ (5.18) ∀idefinedwith(x,y) centre x y
δIi δIi where δx and δy are calculated with the simplified Prewitt operator in equa- tion 5.17, and different u and v could be selected to denote intensity variations along different directions. To further eliminate noise and to impose empha- sis based on the Euclidean distance from the pixel to the window centre, a Gaussian window w is additionally convoluted with V , and the results could be simplified and expressed as
u Vu,v (x, y) = uv M (5.19) v
AC 2 2 = = δI ⊗ = δI ⊗ = δI δI ⊗ where M , A δ w, B δ w, C δ δ w CB x y x y
The authors further pointed out that the eigenvalues of M, denoted by λ1,λ2 can be categorized as shown in figure 5.6 on the following page.
To extract the final cornerness of each pixels, Harris and Stephens proposed the following cornerness measure:
C(x, y) = det(M) − k(trace(M))2 (5.20)
where det(M) = λ1λ2, trace(M) = λ1 + λ2 and k is a constant.
Threshold and non-maximal suppression are then applied and the resulting non-zero points are marked as final corners.
93 5. Shape Analysis
Figure 5.6.: Feature regions in eigenvalue space Reproduced from McGill Centre for Intelligent Machines
5.3.4.3. Curvature Scale Space Detector
Mokhtarian and Suomela (1998a,b) proposed a corner detection method based on the curvature scale space (CSS) which is more immune to noise and is especially useful in retrieving invariant geometric features at multiple scales.
The CSS technique on a curve Γ parametrized by the arc length parameter u could be expressed as
Γ(u) = (x(u), y(u)) (5.21)
Γσ, the evolved version of Γ is
Γσ = (X (u,σ),Y (u,σ)) (5.22) where X (u,σ) = x(u)⊗g(u,σ) and Y (u,σ) = y(u)⊗g(u,σ), g(u,σ) denotes a Gaus- sian with width σ (the scale parameter). The evolution of Γ gradually smooths the curve with increasing simplification of the shape.
To obtain the zero-crossings of the curvature from different evolved versions of Γ, the curvature could be expressed as:
X σ Y σ − X σ Y σ K σ = u(u, ) uu(u, ) uu(u, ) u(u, ) (u, ) 2 2 1.5 (5.23) (Xu(u,σ) + Yu(u,σ) )
94 5.3. Object Description Techniques where
X σ = δ ⊗ σ = ⊗ σ u(u, ) δu (x(u) g(u, )) x(u) gu(u, ) and
X σ = δ2 ⊗ σ = ⊗ σ uu(u, ) δu2 (x(u) g(u, )) x(u) guu(u, ), and similarly
Yu(u,σ) = y(u) ⊗ gu(u,σ) and
Yuu(u,σ) = y(u) ⊗ guu(u,σ).
The CSS corner detection could be briefly summarized as follows:
1. Apply the Canny edge detector to extract edges from input image.
2. Extract edge contours (gaps filling, T-junctions marking).
3. Compute curvature at σhigh (highest scale) and mark corner candidates (maxima above a predefined threshold).
4. Localize corner candidates via corners tracking in lowest scale.
5. Remove very close corners by comparing with the T-corners marked in step 2.
While the CSS detector is robust with respect to image noise, He and Yung
(2004) pointed out the CSS fails to detect true corners when σhigh is large and prone to false-positives if σhigh is small. An improved algorithm based on the CSS was proposed, introducing an adaptive local threshold in the process of local-maxima identification. This could eliminate points that are detected as local maximum while having a small curvature difference within the region of support, such as rounded corners. Another improvement suggested is the additional criterion on the angle of corner. With the fact that a well-defined corner should have a relatively sharp angle, false corners could be further eliminated by computing the corner angle over its region of support, which is defined as the corner candidate and its two adjacent corner candidates. The process is iterated such that all corners fell under the criterion are eliminated. Figure 5.7 on the next page shows a comparison of various corner detectors on the table test image.
95 5. Shape Analysis
Figure 5.7.: Comparison of various corner detectors. Top left: The Moravec operator. Top right: The Plessey operator. Bottom left: The CSS operator. Bottom left: The modified CSS (He and Yung, 2004) Reproduced from McGill Centre for Intelligent Machines, and He and Yung (2004).
96 6
Anthropometric Analysis of the Femur
Contents 6.1. Overview ...... 97 6.2. Reference Positions and Axes ...... 98 6.3. Anteversion Angle and Reference Axes ...... 98 6.3.1. Physical Measurements ...... 99 6.3.2. 2-D Imaging Techniques ...... 101 6.3.3. 3-D Imaging Techniques ...... 104 6.4. Proximal Measurements ...... 110 6.4.1. Femoral Head ...... 110 6.4.2. Femoral Neck ...... 111 6.4.3. Canal Flare Index ...... 114 6.5. Femoral Shaft ...... 117 6.6. Distal ...... 119
6.1. Overview
nthropometric analysis of the femur involves gathering of geometric A measurements based on a predefined set of reference landmarks. It is an undeniable fact that the complex shape of the femur with variations, give rise to many different interpretations on the reference landmark definitions and analysis techniques.
Traditionally, anthropometric studies only involved physical measurements, and osteometric tables were often employed with the femur being fitted to
97 6. Anthropometric Analysis of the Femur a predefined reference position. Not surprisingly, anthropometric reference landmarks were solely based on anatomical landmarks, which were mostly surface landmarks, and estimations were often employed in cases where virtual axes were involved. The introduction and widespread application of various 3-D imaging techniques (Section 3 on page 19) empower an improved revisit utilizing various imaging techniques in the area, allowing many previously impossible measurements as well as studies in vivo.
The following chapter summarizes various methods in the literature in an- thropometric analysis of the femur, their design inspirations, strengths and limitations.
6.2. Reference Positions and Axes
Axes or reference position definition plays a crucial role being the factor that could significantly affect subsequent measurements. Traditional anthropo- metric studies on femur (Kingsley and Olmsted, 1948; Dunlap et al., 1953; Ryder and Crane, 1953), dating back to early 1900s (Parsons, 1914), used osteometric table and similar devices as a physical platform for anthropometric studies extensively. Their physical devices and specific reference positioning of the femur were often defined to facilitate the measurement of a few specific parameters. Kingsley and Olmsted, 1948 defined the reference position of the bone as that of resting on a smooth horizontal surface, touching the posterior aspect of the two condyles and the posterior aspect of the greater trochanter.
6.3. Anteversion Angle and Reference Axes
The version angle, or anteversion angle is one of the most studied parameters in anthropometric studies of the femur in all time (Croce et al., 1999). From a reference position definition point of view, the parameter provides a very good ground for discussion with the fact that this single parameter involves the definition of the three major axes in the femur, namely the longitudinal or long axis, the neck axis and the distal transverse axis.
98 6.3. Anteversion Angle and Reference Axes
6.3.1. Physical Measurements
Traditional anthropometric studies (Parsons, 1914; Kingsley and Olmsted, 1948) utilizing osteometric table or similar devices often make use of the fact that the posterior aspect of a femur lies on a horizontal surface in a stable equilibrium position with 3 points in contact: the medial and lateral posterior condyles, and the posterior aspect of the greater trochanter. Initially mentioned by Parsons (1914), the femur was laid on a flat surface on its posterior surface with 3 points contact; a hole was drilled and knitting needle was placed in the internal condyle of the femur parallel to the lying surface. The neck axis was defined by drilling with a bradawl from the fovea capitis along the neck axis such that it would come out of the shaft just below the greater trochanter, midway between anterior and posterior aspect of the trochanter.
The concept was better documented and refined by Kingsley and Olmsted (1948), with which the reference position, axes definitions and its derivatives became one of the most widely used bases in anthropometric studies where physical measurements were made (Lausten et al., 1989; Kim et al., 2000a; Jain et al., 2003).
While Kingsley and Olmsted (1948) did not state the exact distal transverse axis definition, its method of anteversion determination implied the use of the posterior condyle axis as the distal transverse axis, which is defined as the posterior tangential line touching the posterior aspect of the two condyles. With the femur lying at its reference position, the long axis being employed is parallel to the horizontal surface, and aligned with the direction of the shaft in an AP view. Kingsley and Olmsted further defined the neck axis based on two points, which is the two mid-points between two sets of points extracted from the anterior and posterior surfaces along the neck axis, under a superior transversal view (Figure 6.1 on the next page). The anteversion angle was measured as the angle between the neck axis and the posterior condyles axis, in the transversal plane along the long axis of the femur (Figure 6.2 on the following page). However, the authors pointed out this method may not be able to accurate measure retroverted femur samples, with which the proximal supporting points with the flat horizontal surface shifted from the greater trochanter region to the head region. To cater the problem, small smooth blocks were placed beneath the supporting points to elevate the entire platform, but it was noted that the natural supporting point could still
99 6. Anthropometric Analysis of the Femur
Figure 6.1.: Kingsley’s neck axis definition. Left: posterior point. Middle: anterior point. Right: mid-point. Reproduced from Kingsley and Olmsted (1948).
Figure 6.2.: Kingsley’s anteversion measurement. Reproduced from Kingsley and Olmsted (1948). occasionally be shifted to the lesser trochanter.
Yoshioka et al. (1987) reported the use of different axes on an osteometric table. Instead of taking the femoral shaft as the long axis, the long axis was constructed by joining the head centre and the attachment point of the posterior cruciate ligament (PCL). The longitudinal axis definition is one of the commonly used mechanical axes (Walmsley, 1933) of the femur in a vertical standing posture. The transverse functional axis was defined as a line through the landmark of the PCL passing through the condyles and parallel to the two epicondylar points. Though different from the commonly employed transverse axis based on the posterior articulated surface, the authors reasoned that the suggested definition would permit a separate analysis on the axial rotation of the distal and proximal aspect of the femur. With the transverse axis defined based on the posterior articulated surface of the distal femur, the two angles
100 6.3. Anteversion Angle and Reference Axes
Figure 6.3.: Anteversion calculation based on the longitudinal functional axis. C: head centre; N: mid-point of the anterior and posterior surfaces of the neck region. Reproduced from Yoshioka et al. (1987). would be aggregated into a single measurement.
With the reference coordinate system based on functional axes, Yoshioka et al. further reported the discrepancy in anteversion definition (Figure 6.3) and the measurements obtained. In another study (Yoshioka and Cooke, 1987), the authors pointed out the transepicondylar axis (TEA) has in general less geometric variations when compared to the posterior condylar axis, and thus would serve as a better alternative definition of the transverse axis.
6.3.2. 2-D Imaging Techniques
Rogers (1931) is one of the first researchers in utilizing fluoroscopy in deter- mining the anteversion angle in vivo. He stated that the angle of version could be measured under a PA fluoroscopic view by externally rotating the femur until the shadow of the femoral head aligns to the shaft axis. The proposed orientation ensures the neck axis is in the direction of the rays, pointing downwards under a superior transversal view and the anteversion is the angle between the tibia and the fluoroscopic bed (Figure 6.4 on the following page).
Ryder and Crane (1953) pointed out the abduction of the femur could sig- nificantly magnify the measured anteversion. Ryder and Crane proposed a method based on two X-ray projections in two orientations. The angle of inclination was calculated based on an AP X-ray while the projected antever- ◦ sion was measured on an X-ray with the hip and knee under 90 flexion and ◦ the femur under 30 abduction. To obtain the true anteversion, Ryder and
101 6. Anthropometric Analysis of the Femur
Figure 6.4.: Anteversion measured on fluoroscopic bed. Reproduced from Rogers (1931).
Crane pre-computed a set of graphs (Figure 6.5 on the next page) mapping the projected anteversion angle to the real anteversion angle under different angles of inclination.
Dunlap et al. (1953) proposed an anteversion discovery technique similar to Ryder and Crane (1953), with which one AP X-ray and one lateral X-ray ◦ were taken after aligning the patient with 90 flexion of the hip and knee. A set of graphs similar to figure 6.5 on the facing page was pre-computed based on trigonometric formula to map the measured torsion angle to the real anteversion angle. One of the significances in Dunlap et al. study is the analysis on the anterior bowing effect towards the anteversion measurement. The authors pointed out that the ignorance of anterior bowing of the femur would lead to under-estimation of the anteversion angle with extra flexion on ◦ the hip joint. A 12 under-estimation in anteversion angle was observed in a case with extreme anterior bowing. The authors further suggested the need of adjustments such that the long axis bisects the greater trochanter and passes through the proximal one fourth of the femur for correct evaluation of the anteversion angle, as illustrated in figure 6.6 on page 104.
While the method compensates for the anteversion magnification due to femoral abduction, Ryder and Crane (1953) pointed out the method is still subject to two main sources of error: an inaccurate patient positioning when the X-rays are performed; and inaccurate location of the axes on the X-rays
102 6.3. Anteversion Angle and Reference Axes
Figure 6.5.: Relationship of true and projected anteversion under different inclination angle. Reproduced from Ryder and Crane (1953).
films. The authors made an estimation of a maximum of ±10o of error from the true anteversion angle, but stated that the occurrence of this worse case scenario should be rare.
Evaluation of rotational alignment from the epicondylar axis during knee arthroplasty was also studied (Berger et al., 1993). Berger et al. suggested the use of epicondylar axis as an alternative anatomic axis for rotational measurement of the femoral component when the posterior condylar axis ◦ cannot be used, and reported high consistence of ±1.2 when compared to that with the posterior condyle axis. It was reported that the mean angle between ◦ the posterior condyle axis and the suggested epicondylar axis is 3.5 for male ◦ and 0.3 for female. There is one discrepancy between the epicondylar axis definition and that defined by Yoshioka et al. (1987). Berger et al. defined the surgical epicondylar axis (SEA) as the vector connecting the lateral epicondylar prominence and the medial sulcus below the medial epicondyle while Yoshioka et al. employed the definition with which the medial and lateral prominence of the epicondyles were selected.
Nevertheless, Kinzel et al. (2005) reported the surgical identification of the SEA to be error prone. Stout pins were inserted to the entry points of the ◦ SEA on 74 knees and only 70% were found to be within 3 of the true SEA determined by post-operative CT scans. It was suggested that the error could be attributed to the visual mis-perception by the overall directional alignment
103 6. Anthropometric Analysis of the Femur
Figure 6.6.: Effect of anterior bowing on anteversion angle determination. Left: The long axis defined does not bisect but passes over the ◦ anterior aspect of the greater trochanter, with an extra 12 flexion from the right angle. Right: the adjusted axis bisecting the greater trochanter, and passing through the proximal one fourth of the femur. Reproduced from Dunlap et al. (1953). of the intra-operative epicondylar pins, while only the entry point should be considered theoretically.
6.3.3. 3-D Imaging Techniques
The above-mentioned studies are either based on physical measurements on cadavers or 2-D imaging techniques. With the availability of 3-D imaging techniques, anthropometric studies are more often performed in 3-D digital images, which not only provide a better flexibility, but permit more sophisti- cated and possibly accurate analysis to be performed. Kim and Kim (1997) pointed out the accuracy of using 2-D imaging techniques such as X-rays in anteversion determination had always been adversely affected by the mal- positioning of patients with inexact abduction. Inaccurate hip flexion and rotation would lead to additional error in inclination angle determination. The difficulties in selecting reproducible anatomical landmarks on 2-D images introduce further error in the process. Høiseth et al. (1988) reported the radially asymmetric property of the femoral neck, and further concluded the impossibility to precisely evaluate the neck centre by any combination of bi-plane projections of the neck.
104 6.3. Anteversion Angle and Reference Axes
Figure 6.7.: Neck axis determination from a single cross section. A: Head centre; B: mid-point between the anterior and posterior surfaces of the neck. Reproduced from Murphy et al. (1987).
Weiner et al. (1978) documented the application of CT in anthropometric study and reported the use of CT allowed a visual portrayal of the neck axis to be superimposed on the distal transverse axis for direct measurement of the anteversion angle. Comparison to previous 2-D imaging techniques with special and complicated positioning devices also reviewed the simplicity of the method.
Hernandez et al. (1981) reported similar findings on the advantages of utilizing CT for anteversion determination. Distal fixation on the ankle was achieved by a foot-board with the patient in a supine position. The longitudinal axis is effectively the functional axis though the authors did not define it specifically. The commonly employed posterior condyle axis was defined as the transverse axis. With the fact that the axial CT scans intersected the neck region in an oblique way, the neck axis was evaluated on a single CT section (Figure 6.7). Similarly, Weiner et al. (1978) employed a similar method in neck axis definition.
Murphy et al. (1987) compared various methods in axes definition and pointed out the deficiency of the neck axis definition on a single cross-section (Weiner et al., 1978; Hernandez et al., 1981). A two dimensional cross-section should not be used in determination of the neck axis, which is a three dimensional attribute. It is reported that the above method underestimated the anteversion ◦ angle by about 10 when compared to their physical measurement method (Billing, 1954). The author suggested an improvement of incorporating an extra CT cross-section. The head centre was determined on one cross-section, and the other endpoint was selected as the centroid of the femoral diaphysis
105 6. Anthropometric Analysis of the Femur
Figure 6.8.: Centroid (O) point at the base of the femoral neck. Reproduced from Murphy et al. (1987). on a cross-section at the base of the neck (Figure 6.8).
Murphy et al. (1987) further compared 4 commonly employed definitions on the transverse axis; the traditional tabletop method, the TEA (Figure 6.9 on the facing page), area centres determined by estimation of the centres of the medial and lateral condyles visually, and a angle bisector line constructed based on the anterior and posterior tangential lines (Figure 6.10 on the next page). It was reported that all four methods described introduce small errors into the determination of the anteversion angle when compared to the physical measurements, with which the centroid method (method C in figure 6.10 on the facing page) produced highest consistence, seconded by the tabletop method. With clinical relevance added into considerations, it was suggested the tabletop method delivered the best combinations of simplicity and reproducibility.
Construction of 3-D models based on the acquired CT scan for anthropometric analysis was also noted (Abel et al., 1994; Miura et al., 1998). Abel et al. (1994) reported the use of reconstructed model based on CT images in quantitative assessment on the femoral and acetabular anteversion. The authors pointed out the construction of a 3-D model allowed visual rotation in all three reference planes, and thus could minimize positional error.
Kim and Kim (1997) documented a more well-defined and systematic approach in extracting anthropometric data from CT data. The longitudinal axis was defined as a 3-D least-square best-fit line on centroids computed from the axial CT images over the entire shaft portion of the femur. The centre of the neck was determined by selection of an arbitrary point N0 on the neck surface and creation of a variable 3-D plane passing through N0. Iterations were performed to minimize the cross-sectional area of the 3-D plane under free rotation under the constraint of passing through N0. The femoral neck centre was defined as the centroid point of the resulting 3-D plane and the the neck axis was constructed as a vector passing though the head and neck centre
106 6.3. Anteversion Angle and Reference Axes
Figure 6.9.: Distal transverse axis definitions. Left: The tabletop method. Right: The TEA. Reproduced from Murphy et al. (1987).
Figure 6.10.: Distal transverse axis definitions. Left: Area centres of the condyles defined visually. Right: Bisector of angle between the anterior and posterior tangential lines. Reproduced from Murphy et al. (1987).
107 6. Anthropometric Analysis of the Femur coordinates. The posterior condyle axis was selected as the transverse axis. An iterative procedure was designed to adjust the position of the medial and lateral condylar contact points until a tangential line contacting the condyles were achieved.
Similar studies to the above mentioned were performed (Kim et al., 2000a,b). Extra comparisons were done between the proposed method and the 2-D CT method used by previous studies (Hernandez et al., 1981; Murphy et al., 1987; Weiner et al., 1978) in axes and anteversion angle determination. While the simplified method based on some cross-sectional CT images was proven to have acceptable accuracy, the proposed 3-D processing would give even closer figures compared to the physical measurements.
Mahaisavariya et al. (2002) further enhanced the use of CT images and utilized various reverse engineering software to reconstruct a point cloud model of the femur for anthropometric analysis. Best-fit functions were applied in determination of the femoral head centre, and the neck axis was defined based on an iterative approach in minimizing cross-sectional area of the neck isthmus. Various additional parameters were measured, including the femoral head height, mid-shaft isthmus location. One significance of this study is the measurement of the level of anterior bowing of the femoral shaft in terms of a bow angle across the shaft isthmus. Various researches (Egol et al., 2004; Harma et al., 2005) reported the mismatch between the anterior bow curvature and that of the intramedullary nails, which could lead to iatrogenic fractures (Gausepohl et al., 2002), or anterior distal femoral cortex penetration (Ostrum and Levy, 2005).
Apart from the abovementioned transverse axis definitions in the determina- tion of distal femoral rotation and anteversion angle, other studies (Whiteside and Arima, 1995; Won et al., 2007) have suggested the use of additional distal axes as a secondary rotational reference.
With an increasing focus on the precision in TKR with computer-assisted surgery, reference distal femoral axes are constantly being employed for accurate rotational alignment of the femoral prosthesis. This is important for correct patella tracking and ensures a correct varus-valgus positioning in knee flexion. While the SEA were often used, its inaccuracy in knee with valgus deformity was observed (Anouchi et al., 1993). Whiteside and Arima (1995) evaluated the use of the anteroposterior axis (Figure 6.11 on the next page) of the distal femur as the reference axis for rotational alignment
108 6.3. Anteversion Angle and Reference Axes
Figure 6.11.: Determination of the trochlear line for rotational reference. Left: The most anterior point of the lateral ridge was marked. Middle: the most anterior point of the medial ridge was marked, and the lateral point projected to the same slice. Right: the final trochlear line (TL); surgical epicondylar axis (SEA); Whiteside’s line (AP); posterior condylar axis (PCA). Reproduced from Wonetal.(2007). of the femoral component in valgus knees and reported less occurrence of patella tracking problem when compared to that using the traditional posterior condyle axis clinically. Arima et al. (1995) reported a similar findings in which the Whiteside line served as a more accurate axis for rotational evaluation in valgus knee. However, various studies (Middleton and Palmer, 2007; Wonetal., 2007) have pointed out that while the Whiteside line performed better in a valgus knee, its variations would be too large to be employed as the principle rotational reference. Middleton and Palmer (2007) observed a ◦ variation of Whiteside line measurements having a standard deviation of 4.7 when compared to SEA, and suggested the Whiteside line alone should not be used alone as the axis for rotational alignment.
Won et al. (2007) examined the possibility of utilizing the trochlear line as an alternative reference axis for femoral rotation in total knee replacement (TKR). While the use of the SEA in anthropometric studies was well-studied and proved to be robust, the authors pointed out the need to establish other axes because of the reported difficulty in precisely locating the sulcus of the medial epicondylar during surgery (Griffin et al., 2000). The use of the trochlear line (Figure 6.11) to reference the SEA was shown to have similar variability when compared to that of the Whiteside’s line (Whiteside and Arima, 1995)orthe posterior condylar axis (Figure 6.11). It was suggested that the trochlear line may be considered as an additional reference axis for evaluation of femoral rotational alignment in TKR apart from the posterior condylar line.
109 6. Anthropometric Analysis of the Femur
While X-rays and CT images are still one of the most common imaging techniques in 3-D anthropometric analysis, other imaging modalities such as ultrasound were also being used. Moulton and Upadhyay (1982) reported the use of ultrasound for anteversion determination and the authors concluded that ultrasound was not able to deliver a very clear picture for accurate anteversion computation. However, it was further suggested that the ionizing radiation involved in CT scans may be too invasive for general anthropometric analysis. Lausten et al. (1989) reported similar findings, further adding that ultrasound did not correspond well with the physical measurements of anteversion angle, but CT showed a good correlation with measurements on cadavers.
6.4. Proximal Measurements
This section aims to give a brief summary on the methodology and findings of previous anthropometric studies. Note, however, that because of a wide variation of the definitions of some anthropometric parameters, caution should be taken in direct comparison on the measured results across different studies.
6.4.1. Femoral Head
The femoral head is generally considered a sphere-like structure and its radius is used comprehensively for parametrization. Its measurement method could be categorized into two groups, physical measurements using calipers; and digital measurement on X-rays or 3-D imaging modalities such as CT.
With the use of caliper, Dwight (1905) reported a mean head diameter of 43.84 mm female, 49.68 mm over 200 American Caucasian sample each, spotting a gender difference of 5.84 mm. Parsons (1914) reported similar figures on the English femurs, with a mean of 49 mm for male and 43.4 mm for female, with the slightly lower values possibly due to absence of cartilage in the measurements. The authors further reported the right side has an average radius of 2 mm higher than that of the left in female. Noble et al. (1988) reported an average head diameter of 46.1 mm on 200 American cadavers, in which the figure agrees with the averages mentioned above.
110 6.4. Proximal Measurements
Mahaisavariya et al. (2002) performed 108 head diameter measurements on the Thai population head by means of a 3 dimensional sphere fitting function on segmented CT point cloud, reporting an average diameter of 43.98 mm, 2.08 mm lower then Caucasian figures reported by Noble et al. (1988).
Noble et al. (1988) also reported an average femoral offset to the femoral axis to be 43 mm ranging between 23.6 mm to 61.0 mm with a standard deviation of 6.8 mm, indicating possibly a wide variation of proximal femoral geometry even within the Caucasian population.
6.4.2. Femoral Neck
The femoral neck has always been a popular area of interest in anthropometric studies, mainly associated with a large number of femoral neck fracture. Boufous et al. (2004) reported a total of more than 5000 neck fracture incident in New South Wales (Australia) in 2000, based on the Inpatient Statistics Collection covering all inpatient separations from acute-care hospitals aged 50 and above. Comparison of the data with previous years further revealed 41.2% and 31.2% incident increase in male and female population (Figure 6.12 on the following page), though the age-adjusted data remained practically unchanged.
The femoral neck shaft angle of a healthy individual has a range from around ◦ ◦ ◦ 100 to 150 . Noble et al. (1988) reported an average angle of 124.7 and most other studies (Yoshioka et al., 1987; Rubin et al., 1992; Leung et al., 1996; Mahaisavariya et al., 2002; Gnudi et al., 2002; Zebaze et al., 2005)have ◦ ◦ reported a similar average ranged between 122 − 130 .
El-Kaissi et al. (2005) analyzed DXA output of 62 post-menopause Canadian Caucasian women with hip fracture, with 608 age-matched controls, and concluded that the fracture group has a wider neck width and a reduced cortical thickness, further pointing out the fracture risk is influenced by BMC, neck width, medial cortical thickness of the femoral shaft. Similar studies (Gómez Alonso et al., 2000; Gnudi et al., 2002; Bergot et al., 2002) based on DXA, or its derivative hip structural analysis, also confirmed BMD, and in general, proximal femoral geometry are closely associated with neck fracture risk.
111 6. Anthropometric Analysis of the Femur
Figure 6.12.: Number of hospital admission for hip fracture in New South Wales, Australia, 1990–2000. Reproduced from Boufous et al. (2004).
While DXA is still the gold-standard in evaluation of BMD, together with hip strength analysis (HSA, Martin and Burr, 1984) procedures delivering addi- tional geometric parameters, the evaluation of 3-D geometric measurements from a 2-D DXA are prone to unavoidable rotational, magnification errors Beck (2003); Gregory et al. (2004). BMD measurements are also reported (Goh et al., 1995) to vary significantly in rotational misalignment.
In a study (Noble et al., 2003) to quantify the anthropometric difference be- tween dysplastic and healthy individuals among Japanese population using CT, it was pointed out rotational orientation could severely affect anteversion, and canal width under standard AP X-rays examination. In dysplastic femur, the anteversion and minimum canal width over the isthmus would be overes- timated, in which the authors reasoned this as the cause why surgeons tend to favor the use of undersized cemented prosthesis, which allows a greater flexibility intraoperatively.
Kolta et al. (2005) evaluated the feasibility of potentially employing stereo- radiographic 3-D reconstruction algorithm (Bras et al., 2004) from two planner DXA images with a generic proximal femur model. The authors reported a very high degree of precision (mean error = 0.8 mm, 95% of errors < 2.1 mm)
112 6.4. Proximal Measurements to the CT-based reconstructed model in vitro. While the proposed technique has great potential given its low radiographic dosage and cost comparing to other 3-D modalities, parameters extracted from the DXA-derived model, and its robustness in vivo are yet to be examined.
Similar analysis has also been studied using other imaging modalities. Manske et al. (2006) evaluated the use of MRI in correlating cortical bone in the femoral neck region with failure load on simulated sideways fall, reporting association between failure load and cortical cross-sectional area as well as second area moment of inertia.
QCT is also an emerging technology due to its ability to deliver true volumetric BMD instead of areal BMD as in DXA. The correlation between DXA and QCT has been found to be highly significant (Masala et al., 2003; Link et al., 2004). Significant correlation has also been reported (Link et al., 2004) between QCT and conventional spiral CT, allowing the possibility of BMD evaluation with routine spiral CT with the application of a conversion factor. The additional 3-D information from QCT has also allowed finite element analysis to be performed Faulkner et al. (1991a). However, it has to be noted that the effective radiation dosage of a QCT examination is significant higher when compared to that of DXA Faulkner et al. (1991b).
Cheng et al. (1997a) reported QCT and DXA had a similar ability to predict femoral strength in vitro, though several small-scaled studies (Cheng et al., 1997a; Bousson et al., 2006) showed that the combination of the QCT and DXA model did not deliver significantly improved prediction accuracy towards hip fracture risk and densitometric parameters remained the most significant individual parameter. Large-scale comparison on the effectiveness of QCT in fracture prediction is still to be examined.
Notwithstanding, conclusion in the application of ultrasound in the prediction of proximal femoral strength and fracture risk varies. It is known that relationship exists between density and ultrasound propagation through bone (Kang and Speller, 1998; McCloskey et al., 1990; Agren et al., 1991; Tavakoli and Evans, 1991). It has been hypothesized that ultrasound measurements may deliver additional information towards the trabecular orientation and micro-structure (Glüer et al., 1993; Nicholson et al., 1994). Most studies (Glüer et al., 1993; Schott et al., 1995; Turner et al., 1995; Lochmüller et al., 1998) have reported ultrasound has comparable as well as independent predictive ability towards hip fracture risk. Nevertheless, numerous studies (Baran
113 6. Anthropometric Analysis of the Femur
Figure 6.13.: The Canal Flare Index is a geometric ratio to describe the shape of the proximal femoral canal. Reproduced from Noble et al. (1988). et al., 1991; Faulkner et al., 1994; Nicholson et al., 1997) also suggested only low to moderate correlation exists between ultrasound measurements and BMD.
Various studies (Tian et al., 2003; Gregory et al., 2004; Chen et al., 2005)have attempted to automate part of the parameter extraction process. Tian et al. (2003) developed an automated method in neck shaft angle computation from planar X-rays images for osteoporotic fracture screening. The authors reported a 94% accuracy of fracture classification based on the neck shaft angle among their testing dataset. (Gregory et al., 2004; Chen et al., 2005) also reported success in automatic proximal femoral contour extraction based on active shape contour (the snake algorithm, Kass et al., 1988), while limitations of the algorithms on pathological and odd cases exist.
6.4.3. Canal Flare Index
The Canal Flare Index (CFI), defined by Noble et al. (1988) as a single geometric index in categorizing the proximal femoral canal shape. The CFI is defined as the ratio of the intra-cortical width of the femur, at the section 20 mm proximal to the lesser trochanter and at the section of the canal isthmus as shown in figure 6.13. Three categories were defined, with CFI less than 3.0 defined as stovepipe canals, CFI between 3.0 and 4.7 as normal canals,
114 6.4. Proximal Measurements
Figure 6.14.: Distribution of the Canal Flare Index over the 3 categories, CFI < 3.0: Stovepipe; 3.0
Several derivatives of the CFI exist. Laine et al. (2000) suggested the meta- physeal canal flare index, defined as the ratio between the medio-lateral width of the femoral canal at the level 20 mm proximal and 20 mm distal to the lesser trochanter. It was proposed that the metaphyseal CFI would deliver a more specific description on the metaphyseal dimension, and thus enable a closer fit to especially newer generations of cementless femoral stem for better osseo-integration and stress transfer at the metaphyseal region. Similar indices were proposed by Husmann et al. (1997) to measure the flare at the metaphyseal region and a similar distribution was observed between the two studies.
Another derivative of the CFI suggested by Laine et al. (2000) is the neck- oriented CFI, which is defined as the ratio between the longest oblique dimen- sion at the level 20 mm proximal to the lesser trochanter and the isthmus width.
The cortical index was proposed by Dorr et al. (1990) based on the femoral score in an osteoporosis study (Barnett and Nordin, 1960). It is defined as the ratio between the sum of medial and lateral cortical thickness and the femoral endosteal diameter, at 100 mm below the lesser trochanter. A high
115 6. Anthropometric Analysis of the Femur
Figure 6.15.: Algorithm proposed by Fessy et al. on the choice of femoral implant based on CFI (C.M.I.) and cortical index (F.F.I.). Reproduced from Fessy et al. (1997). cortical index implies thick cortices. Gruen (1997) measured the cortical index on pre-operative radiographs of 110 THR patients and reported a moderate correlation between the index and body mass index, age, weight, in which significant higher indices were observed in the degenerative group than the fracture group, leading to a conclusion that the cortical index provides an indication of bone quality.
Fessy et al. (1997) reported the anatomical basis for the choice of femoral implant in THR and reported both the CFI and cortical index serves an impor- tant role in the determination if a custom implant is preferable (Figure 6.15). The authors further pointed out the benefits of the utilizing ratio instead of absolute measurements as a effective solution to the inherent deficiency of undesirable magnification in radiographic films.
116 6.5. Femoral Shaft
Figure 6.16.: Datum points along the anterior and posterior wall of the medullary canal for anterior bow curvature evaluation. Reproduced from Harper and Carson (1987).
6.5. Femoral Shaft
One of the most distinguish features on the femoral shaft is its anterior bowing. With the use of intramedullary nails being the current gold standard (Harper and Carson, 1987; Harma et al., 2005) in diaphyseal femoral fracture, many studies have been surrounding the goodness of fit between nails design and actual femoral shaft morphology.
Harper and Carson (1987) evaluated the anterior curvature of 14 adult cadaver femora on lateral radiograph by fitting a curve to 20 datum points defined along the anterior and posterior wall of the medullary canal. The authors reported an average radius of curvature of 111.4 cm with a range from 68.9 cm to 188.5 cm. Comparison were made with 4 brands of intramedullary rods and it was noted that the radius of curvature of 3 out of 4 rods (2 with Kuntscher design and one with Grosse-Kempf design) fell above the observed curvature in the femora. Similar findings were reported by other researchers (Egol et al., 2004; Harma et al., 2005; Ostrum and Levy, 2005).
The authors pointed out the curvature mismatch between intramedullary rods and the medullary canal could possibly lead to iatrogenic comminution (Christie and Court-Brown, 1988; Simonian et al., 1994; Apivatthakakul and Arpornchayanon, 2001) during insertion. Rod deformation during insertion would result in inaccuracy in alignment devices for distal interlocking screws
117 6. Anthropometric Analysis of the Femur
Figure 6.17.: Evaluation of anterior bowing with plain digital photography. Reproduced from Egol et al. (2004). placement. Impingement of the nail into medial and anterior cortices has also been reported in the Chinese population Leung et al. (1996).
It was also suggested that the most appropriate site for proximal access of the intramedullary rod is the junction of the femoral neck and the greater trochanter slightly anterior to or in the pyriformis recess, which is easily identifiable clinically. This could prevent additional stress on superior femoral neck. Similar entry point suggestion was also made by Gausepohl et al. (2002).
Numerous studies (Egol et al., 2004; Ostrum and Levy, 2005) confirmed the curvature mismatch between medullary canal and current intramedullary rods. Complications such as anterior distal femoral cortex penetration (Ostrum and Levy, 2005) were also reported.
Mahaisavariya et al. (2002) quantified the bowing by fitting circle over the femoral canal cross-sections, with the shaft isthmus defined as the section with the smallest circle diameter. Two straight lines were fitted to the derived circle centres proximal and distal to the shaft isthmus respectively and the the acute angle between the two constructed lines was defined as the bow angle. The average bow angle reported by the method over 108 Thai cadaveric ◦ femora is 5.75 .
Egol et al. (2004) studied 892 femurs from two museums in New York and
118 6.6. Distal
Figure 6.18.: Instant centre of rotation of the knee on the sagittal plane. Two points A1 and B1are displaced to A1 and B1 respectively. The intersection of the perpendicular bisectors of the two lines connecting A1 A1 and B1B1 is defined as the centre of rotation. Reproduced from Frankel et al. (1971).
Ohio (USA) by means of plain digital photography. Three lines were drawn, with the first immediately below the lesser trochanter, the second immediately above the flare of the of the distal condyles and the third one defined as the mid-point between the former two (Figure 6.17 on the facing page). Circle fitting was performed based on the 3 extracted coordinates to evaluate the anterior curvature. An average radius of curvature of 120 cm was reported, with a range from 56 cm to 326 cm. While no relationship between anterior curvature and age was found, it was found that blacks had a larger radius of curvature than whites, which confirms with other literature (Ballard and Trudell, 1999). Contrary to Egol et al. findings, Harma et al. (2005) reported high correlation (r =−0.234, p < 0.017) between age and anterior medullary curvature in female Anatolia population only, which was not reported by other similar studies.
6.6. Distal
The major structure of the distal femur is the medial and lateral condyles that articulate with the tibia, and analysis of the distal femur is often linked to kinematics study of the knee joint.
Traditional analysis of knee kinematics on the sagittal plane uses the method of instantaneous centres of rotation (Frankel et al., 1971; Walker et al., 1972; Blankevoort et al., 1990), in which the centres are reported to move within the knee flexion cycle. This implies that there is no single axis of rotation of
119 6. Anthropometric Analysis of the Femur
Figure 6.19.: The optimal knee flexion axis. Reproduced from Churchill et al. (1998). the knee. However, the above model does not take into account any out of plane motion during the knee flexion cycle and is reported to introduce error in out of plane movements Panjabi et al. (1982).
More recent studies (Jonsson and Kärrholm, 1994; Sheehan, 2007) employed the helical axis method, an extension to the instantaneous centre of rotation to three dimensions. It was reported that the knee undergoes translations during flexion cycle, and was concluded that the knee does not rotate about any fixed axis. However, Elias et al. (1990) pointed out the fact that the posterior aspect of the femoral condyles are circular in shape in the sagittal view. It was also reported that from 10◦ to 150◦ knee flexion, the tibia rotates around the circular posterior condyles with a radius of curvature of 21mm. The centre line of rotation was observed to pass through the attachment region of the medial and lateral collateral ligaments, suggesting the existence of a fixed centre of rotation.
Hollister et al. (1993) further suggested the kinematics of the knee can be modeled as rotations across two fixed axes, where the flexion-extension axis passes through the medial and lateral collateral ligaments and superior to the crossing points between the anterior and posterior cruciate ligaments. The longitudinal axis is roughly parallel to the long axis of the tibia. It was concluded that motion due to each of the two axes contributes to varus-valgus, internal and external rotation as neither they are mutually orthogonal, nor they align to the coronal or sagittal plane.
Further investigation was performed by Churchill et al. (1998) in an attempt to confirm the model proposed by Hollister et al. (1993) and to search for
120 6.6. Distal
Figure 6.20.: The knee joint centre (filled circle) defined by projecting the mid- point (circle) of the transepicondylar axis (dots) to the optimal flexion axis (A). Reproduced from Hagemeister et al. (2005). the optimal flexion axis of the knee. 15 cadaveric knees were studied in a simulated load-bearing environment and the optimal flexion and longitudinal rotational axes were identified successfully in all specimens. Additional analysis revealed the optimal flexion axes of all specimens coincide with the centre of best-fit circles (Figure 6.19 on the preceding page) of the posterior condyles when viewed along the evaluated optimal flexion axis. The mean distance on the medial and lateral side is 2.8 mm (±1.2 mm) and 3.1 mm (±1.8 mm). It was also reported the location and orientation of the anatomical transepicondylar axis closely matches the optimal flexion axis. In the medial plane, the epicondylar point was in average 0.2 mm (std dev = 2.4 mm) and 0.14 mm (std dev = 2.7 mm) posterior and distal to the optimal flexion axis respectively. The lateral epicondyle point to flexion axis is similar but slightly more distal. An average of 2.9◦ of angular difference between the TEA and the optimal flexion axis was observed.
Churchill et al. (1998) study further confirmed a close relationship between morphology of the distal femur and knee kinematics, in which functional geometric measurements provide an accurate mean of evaluating bone mor- phology.
Various definitions of the knee joint centre has also been proposed (Holden and Stanhope, 1998; Hagemeister et al., 2005). The mid-point of the femoral epicondyles were one of the simplest and common way of knee joint centre definition (Li et al., 2004; Holmberg and Lanshammar, 2006; Stefanyshyn et al., 2006).
Hagemeister et al. (2005) defined the knee joint centre based on the optimal flexion axis method (Churchill et al., 1998). The mid point of the transepi-
121 6. Anthropometric Analysis of the Femur condylar axis was evaluated and projected on the computed optimal flexion axis as shown in figure 6.20 on the preceding page. The authors further pointed out that the definition of the knee joint centre on the optimal flex- ion axis is more repeatable when compared to taking the mid-point of the transepicondylar axis.
The use of functional methods (Croce et al., 1999; Stagni et al., 2000; Besier et al., 2003; Hagemeister et al., 2005) instead of pure anatomical landmarks in determination of joint centres have been praised. Initially employed by Cappozzo (1984) in the use of femoral head centre as a functional landmark, various researchers (Croce et al., 1999; Besier et al., 2003) have suggested the use of functional methods as an effective way to reduce variability and dependency on the accurate location of anatomical landmarks. Croce et al. (1999) further addressed the difficulties associated with accurate location of anatomical landmarks with the fact most anatomical landmarks are not discrete points but relatively large and curved areas and thus their determi- nation by means of palpation or other means is more susceptible to intra and inter-rater variability.
122 7
Methods
Contents 7.1. Acquisition ...... 124 7.2. Segmentation ...... 124 7.3. Anthropometric Parameter Extraction ...... 125 7.3.1. Model Alignment ...... 126 7.3.2. Trochanters ...... 136 7.3.3. Femoral Head ...... 136 7.3.4. Distal Posterior Condyles ...... 139 7.3.5. Neck Region ...... 142 7.3.6. Anteversion Angle ...... 149 7.3.7. Trochlear Groove ...... 150 7.3.8. Bow Curvature ...... 151 7.3.9. Misc Parameters ...... 153 7.3.10. Section Properties ...... 154 7.4. Verification & Testing ...... 155 7.4.1. Inter-rater Variation in Segmentation ...... 155 7.4.2. Intra-rater Variation in Segmentation ...... 155 7.4.3. Variation on CT Voxel Size ...... 155 7.4.4. Reference Axes ...... 156 7.4.5. Effect on Posterior Condyles Range Variation ...... 156 7.4.6. Variation on Anteversion ...... 157 7.4.7. Verification using 3-D model ...... 157 7.5. Anthropometric Studies ...... 158 7.5.1. Human Femoral CT ...... 160 7.5.2. Sheep Femoral CT ...... 161
123 7. Methods
Figure 7.1.: Amira (Visage Imaging, Inc., Carlsbad, USA) is used for seg- mentation of the CT stacks.
7.1. Acquisition
T images were acquired following the default acquisition settings sug- C gested by the radiologist. Details on the settings are included in ap- pendix C on page 247.
7.2. Segmentation
Amira (Visage Imaging, Inc., Carlsbad, USA, figure 7.1) was used as the primary software for the image segmentation process. CT images in DICOM format were imported into Amira. Two label fields were created for the segmentation of all bone, and cancellous bone region respectively. Primary and secondary thresholds were chosen depending on several criteria: histogram analysis of several cross-sections around the lesser trochanter region and bone type. Several samples of each bone type with similar scanning parameters were imported to Mimics (Materialize, Inc., Leuven, Belgium, figure 7.2 on the next page) and profile lines (Figure 7.3 on page 126) were drawn across the cross-sectional slices around the lesser trochanter and femoral neck regions for evaluation of a suitable base threshold that includes the cortical region but not under-segmenting its neighborhood. The determined base thresholds were
124 7.3. Anthropometric Parameter Extraction
Figure 7.2.: Mimics (Materialize, Inc., Leuven, Belgium). used as a reference for the particular bone and scan type. Minor adjustments to the base threshold values were applied to several samples due to a lower average of HU values.
While the base threshold values usually suffice in segmenting a large portion of the femur, the femoral head, neck and the regions distal to the epicondylar axis are prone to over-segmentation due to the relatively lower HU values compared to the rest of the femur. Extra region growing procedure was applied locally in Amira to ensure the inclusion of the entire femur. The fovia capitis, which is the attachment point of the ligament teres, is mostly cartilaginous and thus has a relatively lower contrast with surrounding tissues under CT. Thus, the fovia capitis was included as part of the bone region with as estimated convex hull applied on the local region. Volume smoothing with a 3 × 3 × 3 cubic window was applied to the label fields. The two segmented label fields were then exported, resulting in two stacks of binary image mask stored in DICOM format. Note that both the in-plane spatial resolution and the slice thickness were preserved.
7.3. Anthropometric Parameter Extraction
This section aims to provide the detailed procedure of the methodology of the parameter extraction stage. One of the main design goals of the methodology is to eliminate as much subjective user interactions as possible, delivering consistent and accurate anthropometric parameters. For verification, testing
125 7. Methods
Figure 7.3.: Profile lines across the lesser trochanter region for base threshold value evaluation. In cases where an optimal threshold cannot be chosen, the reference is chosen to avoid over-segmentation when possible. and application, the proposed methodology was implemented in MATLAB (Mathworks Inc., MA, USA), a numerical processing environment for algorithm development.
Minimal user interactions exist mostly in confirmations during the initial estimation phase to ensure a sensible automatic initial estimation is fed into the programme for further fine-tuning. Minor user interactions were introduced in some steps designed as a fall-back procedure when the auto- mated subroutines fail. For user interactions which involve higher level of subjectivity, extra measures were taken to minimize the effect of intra-rater and inter-rater subjectivity on the final outcome.
For simplicity reason, the procedure discussed in subsequent subsections is fully-automated routines, unless otherwise specified.
7.3.1. Model Alignment
The two exported DICOM binary image stacks from the preceding step were loaded into the program. Bone orientation was detected and confirmed by users and the image stacks were cropped to the minimum bounding box containing the entire femur, and were flipped to a proximal starting position along the z-axis and anterior-posterior along the y-axis.
126 7.3. Anthropometric Parameter Extraction
Figure 7.4.: The MATLAB development environment running on Gentoo Linux .
7.3.1.1. Lesser Trochanter
The lesser trochanter, defined as the pyramidal prominence at the proximal and posterioral-medial aspect of the femur was identified in two stages. The first stage computes an estimation of the rough lesser trochanter position while the second computes a more accurate estimation based on the former result.
The distal posterior condylar axis was first estimated to provide a rough rotational reference of the femur with the method as described in figure 7.16 on page 140. The angular orientation of the posterio-medial direction was defined based on the estimated condylar axis by externally rotating the axis ◦ by 45 . A mask M having a gradient towards the posterio-medial direction was generated (Figure 7.5a on the following page) and applied to each cross- section. The posterioral-medial coordinates (PMC) of each cross-section BW were extracted starting from the mid-shaft slice transversing proximally. The red cross on figure 7.5b on the next page shows the the position of PMC on a single cross-section. The procedure on a single slice could be denoted by
PMC = {(x, y)|M(x, y) = max(M ⊗ BW )} (7.1)
127 7. Methods
PMC
(a) An example of the image mask(b) The most posterio-medial coordi- M for the extraction of the most nates of a slice (PMC) with its value posterio-medial coordinates of each taken as the pixel value of the cross-section. masked cross-section.
Figure 7.5.: Extraction of PMC for initial lesser trochanter LT1 estimation.
LT1 = {(x, y)|M(x, y) = max(M(PMC))} (7.2) local where PMC is the coordinates values, M is the generated mask, and BW is the original cross-sectional binary image. For simplicity reason, only the first coordinates were chosen for each slice if more than one point satisfied the above criterion. The pixel values of the PMC coordinates were then analyzed starting from the mid-shaft as a series, with the first local maximum chosen to be the first lesser trochanter estimation (LT1).
Note from figure 7.6 on the facing page that the initial estimation LT1 may not be sufficiently accurate due to the position variations during the image acquisition stage. With variations in patient positioning and anthropometric variations, the true lesser trochanter position is likely to be deviated from the local maximum of the posterioral-medial coordinates. Refinement of LT1 was achieved by calculating the distance from the femoral axis to the perimeter of the slices. A temporary femoral axis (FALT ) was constructed by computing a least-square best fit line to the centroids extracted from 10mm distal of LT1 to
30mm distal of LT1. Slice range ±5mm of the LT1 was selected and perimeter points ({PMC2}) furthest away from the FALT for each slice was computed as shown in figure 7.7 on the next page. An extra criterion is set up such that PMC2 is limited to the posterioral-medial quadrant of each slice to further
128 7.3. Anthropometric Parameter Extraction
Figure 7.6.: The initial estimation of the lesser trochanter LT1 (blue) from the candidate list {PMC} (red).
FALT
PMC2
Figure 7.7.: Second estimation of the lesser trochanter based on LT1. The furthest coordinates of the image perimeter from the femoral axis (FALT ) of each cross-section was taken as the PMC2 in the second estimation of the lesser trochanter position.
129 7. Methods
ensure the selected candidates would be in a close proximity to LT1. The operation on a single cross-section could be expressed as
PMC2 = {(x, y)| BW (x, y) = max(|perim(BW ) − femoral axis|)} (7.3) where perim(M) is the perimeter of the image. The datum point with the maximum distance; LT0 = max({PMC2}) to the femoral axis was picked as the final lesser trochanter point.
7.3.1.2. Proximal Femoral Axis
Centroid coordinates of cross-sections slices from 20mm proximal to 80mm distal to LT0 were computed. The proximal femoral axis (FA0) is defined as the least-square best-fit line of the centroid coordinates computed in the preceding step. Singular value decomposition was employed in determining the best-fit line. The decomposition of an m × 3 matrix A containing the list of centroid coordinates of the proximal cross-sections could be decomposed to the form below:
A = USVT (7.4) where the columns of U contains the eigenvectors of AAT . U is an m × m matrix, S is an m ×3 matrix containing the singular values of A, and the rows of V T contains the eigenvectors of AT A. The matrix U and V are called the left and right singular vectors of A. The best fit vector is the right singular vector of A with the smallest singular value.
7.3.1.3. Transepicondylar Axis
The anatomical transepicondylar axis (TEA , also commonly known as the epicondylar axis) is defined as the two most prominent points medially and laterally in the epicondylar region. The axis definition requires perfect posi- tioning of the patient, which is practically unachievable. To determine the epicondylar axis without a perfect positioning, slices around the epicondylar region were flattened to produce a binary image BWEA as shown in figure 7.8 on
130 7.3. Anthropometric Parameter Extraction
{Lτ =3(BWEA)}
{LN =6(BWEA)} EL
Figure 7.8.: Shape outlines on the flattened image. Two sets of line segments were constructed to estimate the shape outline. {Lτ=3(BWperim)} (red), {LN=6(BWperim)} (blue), and the final epicondylar point (green).
the facing page. Coordinates of the image perimeter BWperim were extracted, connected straight line segments were fitted to provide an estimation of the shape outline with the procedure as follows:
• Starting from an arbitrary perimeter coordinates, the endpoint of a straight line segment are transversed along the perimeter points cov- ering as many coordinates points as possible, limited by the maximum deviation off the covered perimeter segment, defined by the tolerance τ.
• A new line segment is created from the endpoint of the preceding line segment and the process repeats until the entire list of perimeter coordi- nates are transversed.
Two sets of line segments were created (Figure 7.8 on page 131), {Lτ=3(BWperim)} with tolerance of 3 pixels, and {LN=6(BWperim)} with number of line segments equal to 6. LN=6(BWperim) was generated with tolerance parameter τ increased until the shape could be estimated by 6 segments.
Figure 7.9 on page 132 shows the predefined template {LT } comprising 6 points. {LT } was scaled and translated to approximately match the size of the
131 7. Methods
{LT }
Figure 7.9.: Shape template {LT } for orientation matching.
foreground object in BWEA. The Hungarian method (Section 4.6.1 on page 77) was then applied to map coordinates points between {LT } and {LN=6(BWperim)} (blue line segments in figure 7.8 on the preceding page) minimizing the allocation resources, defined as the Euclidean distance between the allocation pairs. The template prevents mis-identification of the epicondylar points in cases of severe rotation of the femur during image acquisition.
Automated identification of the epicondylar points {EM ,EL} in {LN=6(BWperim)} was achieved by retrieving the mapped coordinates corresponding to the template coordinates. The epicondylar points {EM ,EL} were then further refined by determining the closest datum points within {Lτ=3(BWperim)} (Figure 7.8 on the previous page). The relevant z-coordinates of {EM ,EL} were also retrieved.
While the abovementioned method is robust in identifying the correct epi- condylar points, minor errors were encountered in some cases where the local epicondylar region is edgy. A dialog was used to confirm the selection accuracy and a fallback selection method was employed if insufficient accuracy was indicated by the user. List of corners datum points of BWperim were identified (Figure 7.10 on the facing page) based on the method proposed by He and Yung (2004) explained as follows:
1. A binary edge map is obtained using the Canny edge detector and the edge contours are extracted with gaps filled. In our case where the
binary image BWEA comprises of a single region with no holes (Euler number equals to one) is used, this is equivalent to taking the perimeter of the image.
2. The curvature of the contour is computed at a low scale such that all true corners are retained.
132 7.3. Anthropometric Parameter Extraction
Figure 7.10.: Fallback TEA evaluation routine by corner (blue) detection. The figure shows the result of the corner detection with high sensitiv- ity. The sensitivity of the corner sub-routine could be lowered to eliminate false corners and to reduce the number of candidates.
3. All local maxima of the curvature are taken as initial corner candidates, and rounded corners and false corners resulting from boundary noise are excluded from the candidate list.
7.3.1.4. Affine Transformation
The standardized coordinates system is defined as follows:
• The proximal femoral axis FA0 defined in section 7.3.1.2 on page 130 is aligned such that it is parallel to the new z-axis, which is the long axis of the new model
• The model is rotated axially such that the epicondylar axis TEA0 defined in section 7.3.1.3 on page 130 is parallel to the x-axis
Figure 7.11 on the next page shows an illustration of the 3 reference axes in the standardized coordinates system. The direction of the 3 reference axes Vx ,Vy ,Vz of the coordinates system could be denoted by
133 7. Methods
Figure 7.11.: The reference coordinate system. The proximal femoral axis (FA ) is taken as the longitudinal reference axis and the epicondylar axis (TEA ) is taken as the transverse axis for rotational reference.
⎧ ⎪ ⎪ − ∗ ⎨⎪Vx : TEA0 n FA0 − × ⎪Vy : (Vx Vz ) (7.5) ⎪ ⎩⎪ Vz : FA0
where n is the scaling factor such that Vx is orthogonal to FA0 and passes through TEA0, denoted by
TEA0 FA0 n = (7.6) 2 |FA0|
Vy is defined as the vector cross product of Vx and Vz and negatively signed to conform to the right-handed Cartesian coordinates system, as illustrated in figure 7.12 on the facing page.
The transformation matrix of the scaling operation on CT with anisotropic voxels is given by
⎡ ⎤ ⎢ pixel width 000⎥ ⎢ ⎥ ⎢ 0 pixel height 00⎥ = ⎢ ⎥ Ts ⎢ ⎥ (7.7) ⎣ 00slice thickness 0 ⎦ 00 01
134 7.3. Anthropometric Parameter Extraction
Figure 7.12.: Axial view of the reference axes
The rotational transformation matrix could be expressed as
⎡ ⎤ ⎢ [ Vx ]0⎥ ⎢ ⎥ ⎢ [ V ]0⎥ = ∗ ⎢ y ⎥ ∗ T inv(Ts) ⎢ ⎥ Ts (7.8) ⎣ [ Vz ]0⎦ 0001
where inv(Ts) is the matrix inverse of Ts. In practice the transformation matrix T is transposed in MATLAB because column vectors instead of row vectors were used. Additional translation and cropping were applied to the rotated model such that the entire femur is contained in the smallest bounding box.
Upon aligning the model to the standardized coordinates system, the same transformation was applied to the lesser trochanter, proximal femoral axis, and the epicondylar axis.
LT = T ∗ LT0 (7.9)
FA= T ∗ FA0 (7.10)
TEA = T ∗ TEA0 (7.11) where LT , FA , TEA are the transformed lesser trochanter, femoral axis and trans-epicondylar axis respectively.
135 7. Methods
Figure 7.13.: The trochanters (LT and GT) re-evaluated after model alignment.
+ For simplicity reasons, the notation BW (n)|n ∈ Z is used to denote the n- th cross-sectional slice of the transformed binary image stack beginning proximally and BW is used to denote the entire image stack onwards in the discussion below.
7.3.2. Trochanters
The lesser trochanter point LT was re-evaluated after transformation to the new coordinates system to further eliminate errors introduced due to the arbitrary positioning of the femur in the original CT scans. Same algorithms were applied as described in section 7.3.1.1 on page 127.
Coordinates of the most proximal point of the greater trochanter region were automatically extracted by analyzing the proximal regions of the femur. The greater trochanter region was identified by region growing techniques from BW (0) to BW (k) where k is chosen as the most distal slice in BW just before the greater trochanter and the head region merge. The head region was identified as the medial region and the proximal tip of the greater trochanter region was extracted and denoted by GT as shown in figure 7.13.
7.3.3. Femoral Head
To automate the process, the femoral head centre (HC ) was evaluated in two stages. The first stage involves a coarse estimation of the head centre based
136 7.3. Anthropometric Parameter Extraction
(a) Datum points used for initial estimation (b) Initial estimation of the fitted sphere. (blue).
Figure 7.14.: Initial estimation of the femoral head centre. First best-fit sphere (right) estimation of the femoral head based on the proximal head region (blue).
on the partial contours of the proximal femoral head region. With the greater trochanter region eliminated based on 3-D region growing from the datum point GT, edge points of the proximal head region were extracted as shown in figure 7.14 where h is the height of the head measured from the trough point between the head and greater trochanter region. The base level of the trough point was measured by searching for the first slice where the greater trochanter and the head region merged. A sphere was fitted to the partial contours in a least-square sense resulting in the first estimation of the femoral head centre HC0 and head radius HR0.
Based on the HC0 and HR0, additional surface points were extracted as shown in figure 7.15 on the following page, with extra medial part of the head included. The least-square best-fit sphere to the refined point set was computed and its radius HR and centre coordinates HC were taken as the final estimation of the femoral head radius and centre respectively. Two offsets measurements of the head centre were made; the femoral axis offset measures the distance between the head centre to the femoral axis on the transverse plane; and the vertical offset to the lesser trochanter.
137 7. Methods
(a) Inclusion of additional datum points for(b) The second estimation of the fitted sphere. the second estimation of the femoral head centre.
Figure 7.15.: Final estimation of the best-fit sphere based on additional datum points.
138 7.3. Anthropometric Parameter Extraction
7.3.4. Distal Posterior Condyles
Manual selections were made by the user specifying the starting and ending slices. The slice range was selected such that the femoral condyles below or posterior to the intercondylar fossa were included.
7.3.4.1. Tangential Line Extraction
For each slice k, the posterior tangential line touching the medial and lateral condyles were computed and the two touching coordinates were extracted as the datum points which represents the most prominent points of the two condyles.
To extract the two datum points (COmed(k) & COlat(k)) for slice k, a convex hull Convex(BW (k)) and the difference BW (k) −Convex(BW (k)) was computed as shown in figure 7.16 on the next page. Centroid of the posterior notch region
Cnotch(k) (Figure 7.16b on the following page) around the intercondylar fossa was calculated and used as a reference datum point. COmed(k) and COlat(k) were defined as the closest convex hull polygon coordinates to Cnotch(k) medially and laterally respectively (Figure 7.16c on the next page).
7.3.4.2. Cylinder Fitting
A cylinder was then fitted to the set of datum points {CO}.
{CO} = {COmed,COlat}
The Lorentzian minimization function was employed as the error function. The original Lorentzian function (Figure 7.17 on the following page) is given by:
1 1 Γ L(x) = 2 (7.12) π − 2 + 1 Γ 2 (x x0) ( 2 ) where x0 is the centre and Γ specifies the width at its half maximum. The Lorentzian minimization function can be simplified as:
error = ln(1 + x2) (7.13)
139 7. Methods
BW(k) BW(k) ∩ Convex(BW(k))
Cnotch(k)
(a) Convex hull Convex(BW (k)) of BW (k). (b) BW (k) − Convex(BW (k)). Cnotch(k) is taken as the centroid point of the pos- terior notch region.
COlat(k) COmed(k)
(c) Final posterior condylar line of BW (k) (green). This is equivalent to the tan- gential line touching the medial and lateral condyles.
Figure 7.16.: Extraction of the posterior condylar line by morphological opera- tions.
1 1 y = 1 Γ π 2 Γ 2 0.8 (x−x0) +( 2 )
0.6 y 0.4 Γ=2,x =0 0.2 0
0 −5 0 5 x
Figure 7.17.: The Lorentzian function.
140 7.3. Anthropometric Parameter Extraction
y=log(1+x2) 4
3
y 2
1
0 −6 −4 −2 0 2 4 6 x
Figure 7.18.: The Lorentzian minimization function estimated using a log function. which is symmetric and is zero when x = 0, as shown in figure 7.18. The Lorentzian function is robust in rejecting outliers with minimal effect on the final fit, and is thus very effective in minimizing error due to datum points at the posterior extreme of the condyle edges. . Figure 7.19 on the following page shows the final cylinder fit with axis PCCYL vec and radius PCCYLr .
7.3.4.3. Posterior Condylar Axis
The posterior condylar axis (CA ) is defined as the the two datum points on the posterior lateral and medial condyles touching the tangential plane parallel to FA . With the use of CA being only a determination of the axial rotation, simplification is made to ignore the evaluation of the z-coordinates of the axis.
The method employed is similar to that shown in figure 7.16 on the preceding page. Slices in the distal femur region were flattened producing an inferior view and a convex hull was fitted. The posterior condylar axis is the closest posterior medial and lateral convex hull coordinates to the inter-condylar notch (Figure 7.16 on the facing page). This is equivalent to the anatomical posterior condylar axis. Note that the term posterior is not necessarily equivalent to the most posterior coordinates of the two condyles under the current coordinates system where TEA is taken as the transverse axis. The TEA is usually not parallel to the CA and thus the most posterior points of the medial and lateral condyles may not necessarily coincide with the condylar axis. Instead, the posterior condylar axis should more clearly be expressed as the tangential line touching the two condyles posteriorly in an inferior view of the femur.
141 7. Methods
Figure 7.19.: Cylinder (PCCYL) fitted to the posterior condyles using the Lorentzian minimization function.
7.3.4.4. Knee Centre
A plane orthogonal to PCCYL vecwas created with equal mean distance to the lateral (COlat) and medial (COmed) datum points on the condyles. The knee centre KC is defined as the point of the distal intersection between the plane and the distal articular surface as shown in figure 7.20 on the next page.
7.3.5. Neck Region
Analysis in the neck region was done in two stages, reslice of the image stack and extraction of parameters.
7.3.5.1. Reslice
The neck region was resliced such that the cross-sections intersect the long axis of the neck orthogonally, or equivalently aligning the true neck axis with the z-axis. Neck axis evaluation can be divided into two steps, an initial estimation of the neck axis based on existing landmarks, and optimization of the first estimation based on the neck surface point cloud extracted from the first step.
142 7.3. Anthropometric Parameter Extraction
Figure 7.20.: The knee centre (KC) is defined as the intersection between the cylinder PCCYL and the distal femoral articular surface
Figure 7.21.: Initial estimation of the neck axis based on femoral head centre HC and NB.
143 7. Methods
NBSK
Figure 7.22.: Flattened PA view of the femur. NBSK was evaluated by mor- phological skeletonization followed by detection of intersections (blue) in the skeleton. The intersection at the neck base (red cross) superior to the lesser trochanter intersection was taken as NBSK for the initial estimation of the neck axis.
Two coordinates were chosen as the initial neck axis vector (Figure 7.21 on the preceding page), the femoral head centre (HC ) and virtual datum point
NB (NBx ,NBy ,NBz ) at the base of the femoral neck, as defined below.
A posterior-anterior view (x-z plane) was generated as shown in figure 7.22. The reason for adopting a posterior-anterior (PA) view instead of a more commonly used anterior-posterior (AP) view is to avoid extra flipping of the existing coordinates system and has no effect on the final outcome. A morphological skeletonization described in section 4.30 on page 74 was applied to create a skeleton image as shown in figure 7.22 in white. All proximal intersections (blue dots in figure 7.22), defined as pixels connected to more than 2 skeletal paths, were identified. The intersection coordinates NBSK at the neck base was extracted, denoted by the second intersection tracing the
144 7.3. Anthropometric Parameter Extraction
(NBx,NBy)
Figure 7.23.: Thinning operation on the axial slice corresponding to NBSK . The green dotted line shows the possible candidates of NBSK described in figure 7.22 on the preceding page. The first intersection between the dotted line and the thinned skeleton was taken as NB. skeletal path proximally from the mid-shaft section, or equivalently the first intersection tracing the skeletal path proximally after the lesser trochanter region. The extracted point NBSK is shown in red in figure 7.22 on the preceding page and (NBx ,NBz ) was taken as the x-y coordinates of NBSK .
To obtain the y-coordinate NBy of NB, morphological thinning, as explained in section 4.5.5 on page 70 , was applied to the axial slice corresponding to NBSK , as illustrated in figure 7.23. The coordinates of the first intersection between the thinned path and the NBSK locus and was computed and the datum point is taken as NB.
The vector NB − HC was selected as the initial estimation of the neck axis (NA0). NECK0 (Figure 7.24 on the following page) was resliced and cropped from BW as follows:
NECK0 = TN1 ∗ BW (7.14)
where TN1 is the affine transformation matrix based on the initial neck axis
145 7. Methods
(a) The neck region NECK0 after first esti- (b) The final neck axis NA is defined as the mation. Evaluation of the final neck long axis of the fitted cylinder. axis (NA) with cylindrical fitting. NA0 is the initial neck axis estimation.
Figure 7.24.: First and final neck axis estimation with cylinder fit.
estimation NA0.
Two methods were designed in the second estimation of the neck axis. The first method involved a cylinder fitting routine to represent the resliced neck region with a cylinder under optimal orientation and dimensions. Figure 7.24 shows the rotated and cropped neck region with a cylinder fitted to the neck region in a least-square sense, and the axis of the fitted cylinder is shown in blue. An alternative second method involved computing the geometric centre points (centroid) of all cross-sections in NECK0 and fitting a 3-D line to all the centroids in a least square sense by the use of singular value decomposition as described in section 7.3.1.2 on page 130. The axis evaluated was defined as the final neck axis (NA). An affine transformation matrix TN2 was constructed for the conversion from NA0 to NA.
Upon defining the final neck axis, BW was rotated and cropped by applying the transformation matrix TN2 ∗ TN1,
NECK = TN2 ∗ TN1 ∗ BW (7.15) resulting in the final resliced neck region as shown in figure 7.25. With the
146 7.3. Anthropometric Parameter Extraction
40
30
20
10
0 140 100 120 80 60 100
Figure 7.25.: Point cloud of the final NECK based on NA . Note the appearance the greater trochanter at the top of the reslice neck. This was eliminated in the first estimation of the neck axis. fact that the final neck axis may not necessary coincide with the head centre (HC ), an extra datum point NAstart was constructed as the point on the NA which is closest to HC .
7.3.5.2. Parameter Extraction
Measurements in the neck region were based on the defined neck axis NA , and are summarized as follows (Figure 7.26 on the following page):
• Neck length to femoral axis (NLFA)
• Neck length to greater trochanter (NLGT )
• Neck angle (∠NAFA)
• Distance from NA to HC (NAHC)
• Elevation of the NA on FA (NAFA, figure 7.27 on the next page)
The resliced stack (NECK ) now provides a true cross-sectional geometry of the neck region. A list of parameters were extracted for each of the cross-sectional slice, namely
• Cross-sectional Area
ε = c • Eccentricity a
147 7. Methods
Figure 7.26.: Anthropometric measurements based on the neck axis NA and femoral axis FA. NLGT is the neck length from NAstartto the lateral aspect of the trochanter along the neck axis. NLFAis the neck length measured from NAstart to the femoral axis. ∠NAFA is the neck shaft angle. Note that the point NAstartlies on the femoral neck axis but may not coincide with the femoral head centre (HC ).
Figure 7.27.: Elevation of the neck axis (NAFA) is defined as the anterior displacement of the femoral neck axis with reference to the femoral axis.
148 7.3. Anthropometric Parameter Extraction
(a) Anteversion angles based on the femoral neck axis NA .
(b) Anteversion angles based on the axis HCF A defined by the femoral head cen- tre (HC ) and the femoral axis (FA ).
Figure 7.28.: Axes for anteversion angle measurements.
• Area moment of inertia Ixy = xydA 2 • Polar moment of inertia Jx = r dA
Details of the definition and representation of the above properties are dis- cussed in section 5.2 on page 79.
7.3.6. Anteversion Angle
With the model already aligned with the epicondylar axis and the proximal femoral axis, the anteversion angle, defined as the internal axial rotation of the femoral neck relative to distal transverse axis was computed. Under various definitions of anteversion across different axes combinations, the angles measured could be summarized as follows:
149 7. Methods
• ∠(NA ,TEA )
• ∠(NA ,CA )
An additional axis HCF A joining the femoral head centre (HC ) to the proximal femoral axis FA was constructed, and the torsion angles between HCF A and the distal transverse axes (epicondylar axis TEA , condylar axis CA ) were calculated.
• ∠(HCF A,TEA )
• ∠(HCF A,CA )
2 extra angles between the distal transverse axes (∠(TEA ,CA )) and proximal axes (∠(HCF A,NA )) were also measured for later comparison.
7.3.7. Trochlear Groove
Located at the distal femur, the trochlear groove is a depression on the patellar surface and articulates with the two posteriorly articulated facets of the patellar. The following analysis is to extract the position of the groove, which is the saddle and the coordinates of the medial and lateral ridges on the edge of patella surface.
Manual selections were made by the user on the slice range in which the trochlear groove region located.
Each image within the selected region was analyzed and the groove and ridges coordinates extracted. A convex hull C(BW ) was fitted and the coordinates of the convex hull were identified as shown in figure 7.29a on the next page in blue. The original image was then subtracted from the convex image, denoted by BW −C(BW ), as shown in figure . Upon removal of small islands, the centroid coordinates Cnotch(k) of the top-most region were identified. A vertical offset was added to shift Cnotch(k) to Cnotch(k) for more reliable ridge points evaluation. The two coordinates of the ridges (RImed & RIlat) were defined as the closest convex hull points on the medial and lateral side of Cnotch(k) (Figure 7.29a on the facing page). This is equivalent to the contact points of the tangential line over the trochlear groove.
Upon identification of the ridges on the trochlear groove, a tangential line was computed passing through the datum points RImed and RIlat. The trough
150 7.3. Anthropometric Parameter Extraction
Cnotch(k) RI lat(k) RI lat(k)
RI med(k) RI med(k)
Cnotch(k) TR(k)
Convex(BW(k))
(a) Extraction of the tangential line touch-(b) Groove point on the cross-section ing the medial (RIlat(k)) and lateral BW (k). (RImed(k)) trochlear ridges from the convex hull (Convex(BW (k))).
Figure 7.29.: Trochlear groove extraction. point TR(k) was defined as the coordinates on the trough perimeter furthest from the tangential line (Figure 7.29b).
Three datum points were extracted from each image within the user-selected range, resulting in three sets of datum points, {RImed}, {RIlat}, {TR}.
A plane PTR was then constructed fitting on the set {TR} as shown in figure 7.30 on the following page. The angle between the plane and the femoral axis (FA ) on the coronal plane was measured as the trochlear groove angle (∠TR).
7.3.8. Bow Curvature
The anterior bow is defined as the anterior curvature of the medullary canal along the femoral shaft (Section 6.5 on page 117). Centroid coordinates of the each femoral canal cross-sections were computed from the lesser trochanter to 100mm proximal to the distal femur. The centroid points could roughly be estimated as an arc in the sagittal view. A circle was fitted to the centroid coordinates (Figure 7.31 on the following page) in a least-square manner and the centre coordinates and the radius of curvature were used as an estimation on the anterior bow curvature in later analysis.
151 7. Methods
Figure 7.30.: A plane PTR was fitted to the trochlear groove.
Figure 7.31.: Anterior bow curvature.
152 7.3. Anthropometric Parameter Extraction
7.3.9. Misc Parameters
A list of extra geometric properties or anthropometric parameters was ex- tracted based on the landmarks coordinates obtained in previous sections.
7.3.9.1. Greater Trochanter Height
The greater trochanter height (GTH) is defined as the vertical distance between the most proximal point (GT) of the greater trochanter and the trough between the greater trochanter and the neck base region as shown in figure 7.14a on page 137 denoted by the label h.
7.3.9.2. Femoral Head Offset
The femoral head offset is defined as the antero-medial shift of the femoral head centre (HC ) from the proximal femoral axis on the transverse plane.
7.3.9.3. Length
A number of length measurements were recorded. The FLGT−KC is the distance in millimeter between the proximal tip of the greater trochanter (GT)tothe knee centre (KC). FLHC −KC is the distance in millimeter between the femoral head centre (HC ) to the knee centre (KC).
An additional 2 measurements were made based on the mechanical axis.
DistHC−TEA and DistLT −TEA measure the perpendicular distance from the epi- condylar axis TEA to head centre (HC ) and lesser trochanter (LT ) respectively.
7.3.9.4. Canal Flare Index
The classic canal flare index (CFIml) is defined as the ratio between the medio- lateral width of the femoral canal at the level 20mm proximal to the lesser trochanter to that of the femoral isthmus. Likewise, the anterio-posterior canal flare index (CFIap) is defined as the anterio-posterior width of the femoral canal at the above femoral sites.
153 7. Methods
Figure 7.32.: The use of nearest site Voronoi diagram in the computation of the greatest inscribed circle.
Two derivatives of the original canal flare index were computed (Laine et al.,
2000). The metaphyseal canal flare index (CFImetaphyseal) which is defined as the ratio between the medio-lateral width of the femoral canal at the level 20 mm proximal and 20 mm distal to the lesser trochanter. The neck-oriented canal flare index (CFIoblique) is defined as the ratio between the longest oblique dimension at the level 20 mm proximal to the lesser trochanter and the width at the isthmus level.
7.3.10. Section Properties
A list of properties was extracted for each cross-section for both the entire bone section and the cancellous bone region. A more detailed description of individual parameters are stated in section 5.2 on page 79.
• Area.
• Moment of inertia: Ixx, Iyy, Jx (polar moment of inertia), Ixy , principle angle.
• Radius of the greatest inscribed circle in the cancellous bone region only with the use of Voronoi diagram.
• Cortical thickness (medial, lateral, anterior, posterior).
154 7.4. Verification & Testing
7.4. Verification & Testing
7.4.1. Inter-rater Variation in Segmentation
With the majority of manual user-interactive work involved in the image segmentation stage, a test is conducted to evaluate the inter-rater error towards the final anthropometric parameters. 5 human femoral CT stacks were selected at random and were segmented using Amira by two different users according to the reference protocol described in previous sections. The segmented CTs were then processed by a single user for parameter extraction and the output pairs were compared to measure the inter-rater variations.
7.4.2. Intra-rater Variation in Segmentation
Intra-rater variations in image segmentation were determined by segmenting the same set of CT multiple times followed by parameters extraction. Re- segmentation of the same CT dataset was done on different day to minimize possible memory effect. The list of extracted parameters was then compared and the correlation coefficient and Cronbach’s alpha were computed to examine the level of variation.
7.4.3. Variation on CT Voxel Size
The proposed methodology was designed to handle any voxel dimension, including isotropic voxel, bounded by the resource limitation of the processing workstation. To test against the feasibility of direct comparison between CT stacks of different voxel size, the variation due to different CT voxel size was studied. 4 sets of CT stacks comprising of 2 repeated scans of 2 human femurs having different in-plane resolution as well as slice thickness were retrieved from the laboratories CT database. The CTs were segmented and processed and output parameters compared to evaluate the variation due to different voxel size.
155 7. Methods
7.4.4. Reference Axes
7.4.4.1. Femoral Axis
Accuracy of FA evaluation (Figure 7.3.1.2 on page 130) depends upon the detection accuracy of the lesser trochanter datum point (LT ).5stacksof human femoral CT were selected randomly and comparison was done on the effects on FA resulting from shifting the automatically detected LT datum point by ±3mm along the z-axis.
7.4.4.2. Epicondylar Axis
The primary purpose of the epicondylar axis (TEA ) is to provide a rotational reference in the model alignment stage. While the epicondylar points may not be perfectly and accurately located at times, it is desirable for any TEA deviation to have a minimal effect on other anthropometric parameters. 3 sets of human femoral CTs were segmented and processed according to the ◦ proposed protocol. Each TEA of the sets were manually altered by ∼+5 ◦ and ∼−5 via the fallback manual corners selection interface as described in section 7.3.1.3 on page 130 and a list of general anthropometric parameters were extracted and variations compared.
7.4.5. Effect on Posterior Condyles Range Variation
While one of the main targets of the design is to automate the anthropometric parameter extraction stage, manual user interaction was still required to select the starting and ending slice of the posterior condyles. Comparison on the extracted parameters (PCCYL vec, PCCYLr , KC) were done on 5 human femur CT stacks to study the consistency of the method and the variations due to user subjectivity.
Each CT stack was processed following the procedure described in above sections. The reference posterior condyles starting slice BW (refstart) was selected as the most proximal slice possible in which both the lateral and medial condyles were visible. The reference ending slice BW (refend) is defined as the most distal slice before the medial and lateral condyles divide into two separate regions on the axial slice. The reference slice range ([refstart,refend])
156 7.4. Verification & Testing represents the largest range in which the user could select according to the protocol. The slice range was processed and the extracted parameters were taken as the reference values.
Slice range of [refstart+3,refend−3] was taken as the normal range of subjective error due to intra-rater variation and analysis was applied and compared with the reference values.
Additional morphological analysis and comparison with the reference values were done on slice ranges of [refstart − 5,refend], [refstart,refend − 5], [refstart +
5,refend − 5], to further evaluate the performance of the methodology with extreme user input.
7.4.6. Variation on Anteversion
Dunlap et al. (1953) pointed out ignoring the anterior bowing effect would ◦ lead to an under-estimation of the anteversion by as much as 12 due to the extra flexion of the hip joint, while most other previous studies (Ryder and Crane, 1953; Kim and Kim, 1997) take the approach of utilizing the entire femoral shaft when defining the femoral long axis. Our proposed methodology by default utilizes the proximal femoral shaft for evaluation of the FA , and allows user to alter the slice range if desired.
10 sets of human femoral CT data (5 random healthy Australian and 5 healthy Japanese) were segmented and processed with the proposed methodology and their anteversion angles (∠(NA ,TEA ),∠(NA ,CA ),∠(HCF A,TEA ),∠(HCF A,CA )), sec- tion 7.3.6 on page 149 recorded and taken as the reference. Each dataset was then re-processed with the femoral axis (FA ) incorporating the full femoral shaft from the lesser trochanter to the start of the distal metaphyseal flare. The resulting anteversion angles were compared against the additional femoral flexion with respect to the reference FA to study its effect due to anterior bowing.
7.4.7. Verification using 3-D model
To verify the parameters extracted in our proposed procedure using 3-D models, 5 sets of segmented human femoral CT were processed with Mimics .
157 7. Methods
Parameter Equivalent Estimation from 3-D model created in Mimics HR The femoral head radius was measured by taking average of 4 diameter measurements (Figure 7.33a on the facing page). NLGT The neck length measured from the femoral head centre to the lateral aspect of the trochanter along an estimated neck axis (Figure 7.33b on the next page). ∠NAFA An estimated neck shaft angle was measured on the anterior and posterior aspect of the femoral surface and the average was taken (Figure 7.33c on the facing page). FLHC −KC The femoral length measured from the femoral head centre (HC ) to the knee centre (KC). The actual measurement will overestimate the value by roughly 1× head radius (Figure 7.34 on page 160). FLGT−KC The femoral length measured from the proximal tip of the greater trochanter (GT) to the estimated knee centre (KC) (Figure 7.34 on page 160).
Table 7.1.: Verification measurements on 3-D model.
Segmented CT was used throughout the verification step to eliminate the effect of possible variation in segmentation. The aim of the test is not to compare the relatively accuracy, but to provide an external assurance using a third party application.
3-D models were generated and a list of parameters were measured as shown in table 7.1. Note that majority of the anthropometric parameters involve the use of virtual axes and datum points defined throughout the proposed procedure and thus direct verification by means of 3-D model generated from the same stack of segmented CT would only be able to give a minor subset of the entire parameter set with unavoidable subjective estimation. The procedure aims to provide an external assurance independent on the automated subroutines, to ensure the implemented procedure coincide with the proposed methodology.
7.5. Anthropometric Studies
The proposed methodology was concurrently being applied and refined during its development stage in several studies. While the studies are still ongoing at the time of this writing, its inclusion mainly aims at demonstrating the
158 7.5. Anthropometric Studies
(a) Femoral head radius (HR) was evaluated by(b) An estimation of the parameter NLGT ,the taking the average of four diameter measure- femoral neck length defined from the head ments to minimize the effect of centre to the lateral aspect of the trochanter along the direction of the neck axis. The actual measurement shown in orange is NLGT + HR.
(c) Neck shaft angle (∠NAFA).
Figure 7.33.: Verification of the head neck region on 3-D models created with Mimics .
159 7. Methods
Figure 7.34.: Verification of the femoral length on 3-D model created by Mimics . The measurement in black is FLGT−KC , the distance between the proximal tip of the greater trochanter and knee centre. The measurement line in orange is an estimation of FLHC −KC + HR, the sum of distance between the femoral head centre and knee centre, plus the femoral head radius. versatility of the future application of the proposed methodology, and to provide a source of broad-ranged femoral CT data for on-the-go testing purpose.
7.5.1. Human Femoral CT
7.5.1.1. Australian CT Data
15 sets of healthy femoral CT data were retrieved from the laboratories CT database and were extensively used as the primary testing samples during the development of the methodology.
7.5.1.2. Japanese OA CT Data
CT data was collected and processed from an ongoing study with the Fukuoka University Hospital (Japan) aiming to study the anthropometric properties of patients with hip joint osteoarthritis (OA) that require total hip arthroplasty. Two categories of data were being acquired, CT data from healthy Japanese patients, and patients with OA. The CT acquired from OA patients are pre- operative CT for surgical planning purpose; while the CT dataset of healthy Japanese patient was acquired from the hospital radiology database. All scans were done with 1mm spatial resolution and slice thickness and stored in DICOM format.
160 7.5. Anthropometric Studies
Additional comparison was planned between the acquired healthy Japanese CT dataset, with the Australian CT dataset described in previous subsection. A total of 15 sets of OA data and 10 sets of healthy CT data were collected and processed at the time of this writing.
7.5.2. Sheep Femoral CT
The sheep femur has, in general, a similar structure when compared to that of human and the proposed methodology could be applied directly to sheep femoral CT data without any need of modification, further allowing a more direct comparison between the morphology of human and sheep femur.
20 sets of sheep femoral CT data were collected at the time of this writing and processed with the proposed methodology aiming to construct a database of sheep femoral anthropometric data. The data aims to provide valuable and precise anthropometric information for prosthesis design and testing done on sheep, which is a commonly used animal model.
161 7. Methods
162 8
Results
Contents 8.1. Overview ...... 163 8.2. Consistency Test ...... 167 8.2.1. Intra-rater Consistency ...... 167 8.2.2. Inter-rater Consistency ...... 170 8.2.3. Repeated Scans ...... 172 8.3. Parameter Variation ...... 174 8.3.1. Proximal Femoral Axis Variation ...... 174 8.3.2. Variation with Full Femoral Shaft ...... 177 8.3.3. Posterior Condyles Slice Range ...... 179 8.4. Verification with 3-D Model ...... 181 8.5. Comparison ...... 183 8.5.1. Condyles Radius ...... 183 8.5.2. Optimal Flexion Axis ...... 183 8.5.3. Australian & Japanese ...... 186 8.6. Sheep Summary ...... 186
8.1. Overview
he proposed methodology was implemented and tested in Matlab (Mathworks T Inc., MA, USA) with a graphical user interface (GUI) for illustration and user interaction (Figure 8.1 on the following page). As described in the previous section, most part of the routine are fully automated. The final routine comprises of around 10000 lines of code (including comments) and
163 8. Results
Figure 8.1.: The Matlab routine showing the process of sectional properties computation. with 2000 lines of code incorporated from external sources as listed in the appendix A, table A.2 on page 235. A brief summary of the dependencies of the core functions is listed in figure 8.2 on page 166. A more detailed descriptions of individual sub-routines are listed in appendix A on page 225.
A total of 44 human femoral CT and 20 sheep femoral CT stacks were processed. All anthropometric parameters were successfully extracted using our proposed methodology. Of all 44 human femoral CT, 23 scans were acquired from 19 healthy adult Australian (sex and age unknown) cadavers retrieved from the laboratories CT database (Appendix C on page 247). Within the 23 scans, 3 were repeated scans on the same femur, and 2 were paired femur from the same donor. 19 scans of unique individuals were used as the Australian dataset after removal of the duplicates and paires which were utilized for later verification steps. 25 stacks of CTs were acquired from Fukuoka University Hospital (Fukuoka, Japan) radiology database, in which 10 were healthy individual and 15 were diagnosed with either primary or secondary hip osteoarthritis. 10 pairs of sheep femora (adult crossbred wethers, 15–24 months) were studied. The sheep femurs were previously used in another animal study where a small 6 mm drill hole was created at the distal end of the femoral shaft. The drill hole did not fall within our region of interest in any of our anthropometric parameters and thus has no effect on the processed outcome. All CT datasets were processed and results exported to a tab-delimited text format. A sample
164 8.1. Overview output file was included in appendix B on page 237.
165 8. Results
Figure 8.2.: The dependency matrix. t femur_anthro_gui align_model_axis bone_orientation_detection crop_bone_mask est_lesser_trochanter export_to_file find_anterior_bow find_anteversion_angle find_canal_flare_index find_condylar_cyl_fit find_epicondylar_axis find_femoral_axis find_femur_length find_greater_trochanter find_greater_trochanter_height find_head_centre find_head_epicondylar_dist find_head_offset find_lesser_tro_epicondylar_dis find_lesser_trochanter find_neck_props find_post_condylar_axis find_section_props find_shaft_section_props find_skel_intersection fix_bone_orientation get_files gui_disp lineseg load_bone_mask recrop_bone_mask reslice_neck sim_xray_dexa trochlear_groove_analysis uigetfiles waitbar
femur_anthro_gui + 0 align_model_axis + 1 bone_orientation_detection + 1 corner > 1 crop_bone_mask + 1 cvoronoi E > 1 cylinder_fit > 1 deleteoutliers > 1 drawedgelist > 1 est_lesser_trochanter + 1 euclidean_distance > 1 export_to_file + 1 export_to_mat E > 1 export_workspace E > 1 extrema > 2 find_anterior_bow + 1 find_anteversion_angle + 1 find_best_fit_circle > 2 find_best_fit_plane > 1 find_best_fit_sphere > 1 find_canal_flare_index + 1 find_condylar_cyl_fit + 1 find_condylar_tangential_line > 2 find_epicondylar_axis + 1 find_femoral_axis + 2 find_femur_length + 1 find_greater_trochanter + 1 find_greater_trochanter_height + 2 find_head_centre + 1 find_head_epicondylar_dist + 1 find_head_offset + 1 find_lesser_tro_epicondylar_dist + 1 find_lesser_trochanter + 1 find_neck_props + 1 find_post_condylar_axis + 1 find_section_props + 1 61 module(s) find_shaft_section_props + 1 find_skel_intersection + 1 findn > 1 fix_bone_orientation + 2 gen_circle > 1 get_files + 1 gui_disp E + 27 gui_msg > 2 hungarian > 1 import_workspace E > 1 lineseg + 1 load_bone_mask + 1 maxlinedev > 1 recrop_bone_mask + 1 reslice_neck + 1 sim_xray_dexa + 1 sortclasses > 1 split > 1 tomm > 16 topixel > 11 trochlear_groove_analysis E + 1 uiGetFiles > 0 uigetfiles + 0 waitbar + 9 [+: a caller >: not S: script (red) E: calls f/eval..] write > 1 333 21 5 2 51 2 8 6 41 3 3 51 1 1 24 3 5 32 1 0 1 11 2 7 13 0 1 36 caller(s) [+: link ο: recursive ♦: caller=module]
166 8.2. Consistency Test
8.2. Consistency Test
With one of the main goals of this study is to present a consistent and reliable methodology as a platform for future larger-scaled anthropometric studies, it is necessary to ensure the proposed techniques do not suffer from unacceptable variations under normal usage.
The intra-class correlation coefficient (ICC) is a variation decomposition method to evaluate the overall variance due to between-subject variability. Ranged from 0 to 1, the ICC will approach 1.0 when there is no variance between targets. The theoretical ICC formula could be expressed as follows:
σ2 ICC = B (8.1) σ2 + σ2 B W
σ2 σ2 where B is the between-subject variance, W is the variance between cases. A summary of the types of ICC and a brief description is provided in table 8.1 on the following page.
The Cronbach’s α is another commonly used index to evaluate internal consis- tency reliability, defined by the formula below.
N N c¯ α = (8.2) N − 1 v¯ + (N − 1) c¯ where N is the total number of items, c¯ is the mean of all inter-item covariance, and v¯ is the average variance.
With a range from negative infinity to 1, Cronbach’s α increase when the av- erage inter-item correlation increases. A general rule of thumb of a minimum alpha of 0.7 is required to reach good consistency.
All ICC and Cronbach’s α test in this section was undertaken using SPSS (SPSS Inc., Chicago, Illinois, USA) version 15.
8.2.1. Intra-rater Consistency
The aim for the intra-rater consistency test is to evaluate the effect of variations in repeated segmentation by the same user towards the anthropometric
167 8. Results
ICC type SPSS equivalent Description model ICC(1,1) One-way random Each judge is considered a random effects, single selection among all possible judges measure. and rate all subject of interest. ICC(1,k) One-way random Same as ICC(1,1) but the unit of effects, average measures is an average of k judges measure. instead of results from an individ- ual judge. ICC(2,1) Two-way random Both judges and subject of interest effects, single are considered a random selection measure. among all possible judges and sub- jects. ICC(2,k) Two-way random Same as ICC(2,1), but he unit of effects, average measures is an average of k judges measure. instead of results from an individ- ual judge. ICC(3,1) Two-way mixed All judges of interest rate all sub- model, single ject of interest. Here judges are measure. considered a fixed effect and the subject of interest is a random se- lection from all possible subjects. ICC(3,k) Two-way mixed Same as ICC(3,1), but the unit of model, average measures is an average of k judges measure. instead of results from an individ- ual judge.
Table 8.1.: Types of ICC.
168 8.2. Consistency Test
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
Radius (HR) 0.999 0.991 1.000 0.999 Femoral axis offset 0.999 0.983 1.000 1.000 Vertical offset to lesser 0.980 0.809 0.998 0.993 trochanter
Table 8.2.: Femoral head intra-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Neck length to femoral 0.999 0.994 1.000 1.000 axis (NLFA) Neck length to lateral 0.995 0.956 1.000 0.997 greater trochanter (NLGT ) Neck shaft angle (∠NAFA) 0.926 0.429 0.992 0.953 Neck axis elevation (NAFA) 0.972 0.000 0.999 0.998 Neck axis to head centre 0.975 0.760 0.997 0.983 distance (NAHC)
Table 8.3.: Femoral neck intra-rater consistency. parameters extracted. The segmentation was performed according to the same protocol and each tested subject was segmented and re-segmented on a different day to minimize possible memory effect.
Two consistency tests were conducted, namely the ICC and the Cronbach’s α. ICC was evaluated using the ICC(2,1) model, a two-way random effects model of single measure with a 95% confidence interval (C.I.). The Cronbach’s α was computed in additional to the ICC. While each of the listed parameters below were tested as independent variables, it was grouped and presented in 6 tables for clarity purpose.
With the femoral head radius evaluated based on a two staged sphere-fit estimation and the proximal femoral axis being a function axis not depending solely on an individual anatomical landmark, the effect of variations in seg- mentation was found to be minimal having an excellent ICC and Cronbach’s α (Table 8.2).
Parameters in the neck region (Table 8.3) showed a varying ICC. ICC of
169 8. Results
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
∠(TEA ,CA ) 0.566 -0.229 0.940 0.759 ∠(HCF A,TEA ) 0.984 0.888 0.998 0.992 ∠(HCF A,CA ) 0.983 0.809 0.998 0.994 ∠(NA ,TEA ) 0.978 0.842 0.998 0.990 ∠(NA ,CA ) 1.000 0.997 1.000 1.000
Table 8.4.: Anteversion angles intra-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Distance from LT to 0.965 0.668 0.996 0.988 isthmus
CFIml 0.990 0.908 0.999 0.994
CFIap 0.965 0.751 0.996 0.980
CFIoblique 0.950 0.494 0.995 0.985
CFImetaphyseal 0.994 0.959 0.999 0.997
Table 8.5.: Canal flare indices intra-rater consistency. the neck shaft angle, while still satisfactory, is relatively lower. This could possibly be attributed to the low inter-subject variance within our sample set, in which the errors were magnified. A low ICC on the distance between neck axis to head centre was under expectation due to the low average magnitude (~ 1 mm), which is around the sensitivity limit of the scan resolution.
Similarly, the angle between the transepicondylar axis and the posterior condyles axis (Table 8.4) has an expected lower ICC and confidence interval due to the sensitivity limit being reached. Quantization error in CT and very minor segmentation variations would induce a significant within-subject variance, leading to a lower correlation value.
8.2.2. Inter-rater Consistency
To further evaluate the possible variations due to subjectivity in the segmenta- tion stage to the final outcomes, 5 CT stacks were segmented by two different users with the same protocol. The ICC and Cronbach’s α were computed.
170 8.2. Consistency Test
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Posterior condyles radius 0.998 0.899 0.999 0.993 (PCCYLr ) Trochlear groove angle 0.965 0.766 0.996 0.983 (∠TR) Anterior bow radius 0.998 0.980 1.000 0.999 (BOWr )
Table 8.6.: Shaft and distal femur intra-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
FLGT−KC 1.000 0.999 1.000 1.000
FLHC −KC 1.000 1.000 1.000 1.000 Head centre to epicondylar 0.999 0.995 1.000 0.999 (DistHC−TEA) Lesser trochanter to 0.999 0.989 1.000 0.999 epicondylar (DistLT −TEA) Greater trochanter height 0.925 0.469 0.992 0.954 (GTH)
Table 8.7.: Femoral length intra-rater consistency.
171 8. Results
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
Radius (HR) 0.998 0.985 1.000 0.999 Femoral axis offset 0.998 0.984 1.000 0.999 Vertical offset to lesser 0.985 0.690 0.999 0.997 trochanter
Table 8.8.: Femoral head inter-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Neck length to femoral 0.995 0.957 1.000 0.997 axis (NLFA) Neck length to lateral 0.999 0.995 1.000 1.000 greater trochanter (NLGT ) Neck shaft angle (∠NAFA) 0.944 0.649 0.994 0.971 Neck axis elevation (NAFA) 0.994 0.959 0.999 0.997 Neck axis to head centre 0.865 0.279 0.985 0.944 distance (NAHC)
Table 8.9.: Femoral neck inter-rater consistency.
Similarly, a two-way random effects model of single measure was employed in the calculation of the ICC.
The inter-rater ICC values and Cronbach’s α has a very similar range when compared to the intra-rater consistency with the inter-rater consistency marginally lower in some cases. This could possibly be a result from a greater variation in user subjectivity in the segmentation stage.
8.2.3. Repeated Scans
To allow direct comparison between a larger range of CT, a consistency test over repeated scans of the same subject was conducted. All repeated scans were conducted on different day, and it was observed that all pairs experienced slight orientation variations. 4 out of 5 pairs of the CT were scanned with different spatial resolution and slice thickness.
A one-way random effect model of the ICC was employed in this case because
172 8.2. Consistency Test
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
∠(TEA ,CA ) 0.873 0.255 0.986 0.923 ∠(HCF A,TEA ) 0.992 0.937 0.999 0.995 ∠(HCF A,CA ) 0.997 0.864 1.000 0.999 ∠(NA ,TEA ) 0.983 0.863 0.998 0.993 ∠(NA ,CA ) 0.993 0.941 0.999 0.997
Table 8.10.: Anteversion angles inter-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Distance from LT to 0.964 0.705 0.996 0.978 isthmus
CFIml 0.986 0.899 0.998 0.993
CFIap 0.976 0.806 0.997 0.985
CFIoblique 0.995 0.963 0.999 0.997
CFImetaphyseal 0.979 0.846 0.998 0.991
Table 8.11.: Canal flare indices inter-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Posterior condyles radius 0.918 0.377 0.991 0.947 (PCCYLr ) Trochlear groove angle 0.961 0.747 0.996 0.981 (∠TR) Anterior bow radius 0.981 0.842 0.998 0.993 (BOWr )
Table 8.12.: Shaft and distal femur inter-rater consistency.
173 8. Results
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
FLGT−KC 1.000 0.997 1.000 1.000
FLHC −KC 1.000 1.000 1.000 1.000 Head centre to epicondylar 1.000 0.999 1.000 1.000 (DistHC−TEA) Lesser trochanter to 0.999 0.987 1.000 1.000 epicondylar (DistLT −TEA) Greater trochanter height 0.979 0.857 0.998 0.990 (GTH)
Table 8.13.: Femoral length inter-rater consistency.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
Radius (HR) 0.972 0.799 0.997 0.984 Femoral axis offset 0.993 0.917 0.999 0.998 Vertical offset to lesser 0.935 0.565 0.993 0.962 trochanter
Table 8.14.: Femoral head consistency on repeated scans. of the fact that the 5 pairs of CT were acquired from different scanners.
Consistency of the extracted parameters in repeated scans were in general slightly lower compared to that of the intra and inter-rater test. This is within expectation with the fact that variations in repeated scans could be considered as a combined effect of intra-rater variations, patient orientation variations and scanning parameter variations.
8.3. Parameter Variation
8.3.1. Proximal Femoral Axis Variation
The proximal femoral axis was used as the reference longitudinal axis through- out the study. While the axis was defined in a functional manner which minimized the direct reliance on a precise location of a single anatomical landmark, the slice range employed in the evaluation of the femoral axis is
174 8.3. Parameter Variation
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Neck length to femoral 0.969 0.780 0.997 0.986 axis (NLFA) Neck length to lateral 0.993 0.939 0.999 0.996 greater trochanter (NLGT ) Neck shaft angle (∠NAFA) 0.979 0.811 0.998 0.987 Neck axis elevation (NAFA) 0.840 0.235 0.982 0.922 Neck axis to head centre 0.781 -0.023 0.975 0.867 distance (NAHC)
Table 8.15.: Femoral neck consistency on repeated scans.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
∠(TEA ,CA ) 0.158 -0.309 0.811 0.383 ∠(HCF A,TEA ) 0.955 0.648 0.995 0.983 ∠(HCF A,CA ) 0.997 0.974 1.000 0.999 ∠(NA ,TEA ) 0.973 0.785 0.997 0.989 ∠(NA ,CA ) 0.991 0.919 0.999 0.996
Table 8.16.: Anteversion angles consistency on repeated scans.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Distance from LT to 0.912 0.484 0.990 0.952 isthmus
CFIml 0.968 0.711 0.997 0.989
CFIap 0.969 0.783 0.997 0.983
CFIoblique 0.971 0.677 0.997 0.991
CFImetaphyseal 0.778 -0.243 0.975 0.848
Table 8.17.: Canal flare indices inter-rater consistency on repeated scans.
175 8. Results
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower Posterior condyles radius 0.936 0.604 0.993 0.966 (PCCYLr ) Trochlear groove angle 0.957 0.665 0.995 0.984 (∠TR) Anterior bow radius 0.936 0.604 0.993 0.966 (BOWr )
Table 8.18.: Shaft and distal femur consistency on repeated scans.
ICC 95% C.I. Parameter ICC Cronbach’s α Upper Lower
FLGT−KC 0.999 0.991 1.000 0.999
FLHC −KC 0.999 0.994 1.000 1.000 Head centre to epicondylar 0.993 0.913 0.999 0.998 (DistHC−TEA) Lesser trochanter to 0.993 0.931 0.999 0.997 epicondylar (DistLT −TEA) Greater trochanter height 0.926 0.540 0.992 0.959 (GTH)
Table 8.19.: Femoral length consistency on repeated scans.
176 8.3. Parameter Variation governed by the accurate location of the lesser trochanter. It was estimated that a possible variation of 1–3 mm may exist in the evaluation of the lesser trochanter, mainly due to possible quantization error in the CT scans.
Our use of only the proximal femoral axis as the longitudinal axis is relatively prone to this error when comparing to most other similar studies that adopted the full femoral shaft axis. A simple test was performed to compare the angular variations of the proximal femoral axis by a shifting of the lesser trochanter position superoinferiorly by ±3 mm. 5 subjects were chosen at random and the reference proximal femoral axis (FA ) was computed based on the default automatic procedures. The position of the lesser trochanter was then shifted superoinferiorly by ±3 mm and the proximal femoral axis re-calculated (FA ). Table 8.20 on the following page shows the angular difference between the reference proximal femoral axis and that with altered ◦ lesser trochanter positions. A mean difference of 0.60 was observed which is negligible.
8.3.2. Variation with Full Femoral Shaft
To study the effect of using the proximal femoral shaft as longitudinal axis to the anteversion angles, 10 (5 healthy Australian and 5 healthy Japanese) CT datasets were randomly selected and processed using the proximal femoral axis and full femoral shaft axis as the longitudinal. It was noted that there is a very significant difference in all anteversion angles, and neck axis elevation relative to the longitudinal femoral axis.
As shown in figure 8.3 on page 179, a huge reduction of the anteversion angles is shown when the full femoral shaft is used as the reference longitudinal axis. Note that the large standard deviation as presented in the error bars are the result of the population variance, not the variance of the difference. To further illustrate the huge changes in anteversion angles, a box-and-whisker plot was constructed as shown in figure 8.4 on page 180. The red line indicates the median difference, blue box denotes the interquartile range. The range bounded by black is the upper and lower whisker, which is equal to the range in this case, because no outlier was present.
The anterior elevation of the neck axis relative to the longitudinal femoral axis has shown a significant change of 11 mm with the switch of the longitudinal
177 8. Results
ID FA [ x y z] Lesser FA [ x y z] Angular trochanter difference z-shift (mm) (degree) [-0.052 -0.194 10R [-0.042 -0.201 +3 0.980] 0.67 0.979] [-0.033 -0.207 −3 0.978] 0.63 [0.089 -0.177 29L [0.083 -0.178 +3 0.980] 0.33 0.980] [0.079 -0.179 −3 0.981] 0.26 [-0.063 -0.176 71L [-0.079 -0.180 +3 0.982] 0.90 0.981] [-0.085 -0.181 −3 0.980] 0.40 [0.008 -0.156 67L [-0.009 -0.167 +3 0.988] 1.17 0.986] [0.000 -0.162 −3 0.987] 0.58 [-0.059 -0.153 03R [-0.051 -0.158 +3 0.987] 0.53 0.986] [-0.043 -0.162 −3 0.986] 0.50 Mean 0.60
Table 8.20.: Variations of the proximal femoral axis due to inconsistent lesser trochanter evaluation. A mean difference of 0.6◦ was observed which is negligible.
178 8.3. Parameter Variation
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Figure 8.3.: Difference in anteversion angle with proximal and full femoral shaft as the reference longitudinal axis. The error bars indicate one standard deviation. This shows a substantial difference in the measurements under the use of different reference longitudinal axes. reference axis as shown in figure 8.5 on the next page. The canal flare index based on the longest oblique dimension, CFIoblique, has shown to have a larger variation between the two reference longitudinal axis while the other 3 CFI are very consistent. Other parameters involving measurements with respect to the femoral reference axis have shown to be highly consistent between the two settings (Appendix E.1 on page 265).
8.3.3. Posterior Condyles Slice Range
The reference slice range was defined as the maximum possible slice range. The proximal limit is chosen with which the condyles start visible to the image cross-section and the distal limit is chosen in which the condyles are no longer inter-connected via the anterior aspect of the femur.
The typical maximum erroneous selection range is defined as 3 slices inferior to the proximal limit to 3 slices superior to the distal limit. This is equivalent to a 6mm of total range reduction for the first 3 samples with slice thickness of 1mm and 12 mm of total range reduction for the last 2 samples with slice thickness of 2 mm. It was observed that the variation in radius is very minimal with a mean of 0.72 mm (Table 8.21 on page 182). A number
179 8. Results
30
25
20
15
10
Difference (degree) 5
(HCFA , TEA ) (HCFA , CA ) (NA, TEA ) (NA, CA )
Figure 8.4.: Box-plot showing difference in anteversion with the proximal and full femoral shaft as the longitudinal reference axis. Upper and lower whisker (black), median (red) and the quartiles (blue) are shown.
Figure 8.5.: Neck axis elevation (NAFA) relative to the femoral axis with proximal and full femoral shaft as the reference longitudinal axis. The error bars represent one standard deviation.
180 8.4. Verification with 3-D Model
Figure 8.6.: Canal flare indices with proximal femoral shaft and full femoral shaft as reference longitudinal axis. Only the oblique index shows a significant difference under the change of reference longitudinal axis. of additional erroneous range with more extreme limits were tested and is included in appendix E.2 on page 265 for reference.
8.4. Verification with 3-D Model
Verification was done in Mimics on 5 sets of CT. 3-D model was created and measurements were made on the surface mesh. The aim of the test is to provide an assurance on the measurements using our proposed methodology with the application of a more direct method using a third party tool. All measurements on the 3-D surface meshes were done manually and visually. Figure 8.7 on the next page shows the mean difference of the 5 parameters measured with reference to the parameters measured using our proposed methodology. The mean difference was small, while a larger deviation on the percentage difference on femoral neck length, femoral head radius and the neck shaft angle was observed.
181 8. Results
ID Slice Reference Radius with typical Difference (mm) thickness radius max selection error (mm) (mm) (mm) 67L 1 22.5 22.0 -0.5 03R 1 21.0 22.0 1.0 14L 1 17.8 17.9 0.1 71L 2 22.2 24.9 2.7 OBL 2 18.5 18.8 0.3 Mean 0.72
Table 8.21.: Typical maximum error of the posterior condyles radius due to variation in slice range selection by user.
(a) Mean difference. (b) Percentage difference.
Figure 8.7.: Difference between direct measurements on the created 3-D model and that using the proposed methodology. The error bars repre- sent one standard deviation of the measurements. Neck length is the length from the start of the femoral neck to the lateral aspect of the trochanter along the computed neck axis (NLGT ).
182 8.5. Comparison
Min Max Mean Medial condyle (mm) 17.3 26.0 21.5 Lateral condyle (mm) 18.8 29.5 22.6 Difference (mm) -2.9 4.5 1.2
Table 8.22.: Difference on the radius of curvature between medial and lateral condyles in the Australian dataset.
Min Max Mean Medial condyle (mm) 16.4 20.3 18.3 Lateral condyle (mm) 15.1 23.2 18.3 Difference (mm) -3.0 2.9 0.0
Table 8.23.: Difference on the radius of curvature between medial and lateral condyles in the healthy Japanese dataset.
8.5. Comparison
8.5.1. Condyles Radius
The posterior condyles has a circular shape profile in the sagittal view. To study the difference of the radius of curvature between the two condyles, circle-fitting was applied to the extracted medial and lateral posterior condyles datum points to evaluate the radius of curvature of the Australian dataset.
Contrary to previous findings, we observed a 1.2 mm larger average radius of curvature of the lateral condyle in our Australian dataset (Table 8.22). The healthy Japanese dataset showed roughly the same radius of curvature between the condyles (Table 8.23).
8.5.2. Optimal Flexion Axis
Recent studies (Hollister et al., 1993; Churchill et al., 1998)havesuggested knee kinematics could reliably be represented using 2 non-orthogonal axes; a flexion axis and a longitudinal rotational axis on the tibia. The optimal knee flexion axis, or sometimes known as the geometric centre axis, is usually determined by fitting two separate circles to the medial and lateral condyles
183 8. Results
Figure 8.8.: Difference between the medial and lateral condyle radius. A positive difference indicates the lateral radius is larger than that of the medial and vice versa. in the sagittal plane and connect the centres of the circles. It was discovered the fitting of 2-D circles to the condyles may be error prone due to undesirable rotational variations. Thus a cylinder fitting procedures were employed in the evaluate of the optimal flexion axis.
To verify whether the optimal femoral axis coincide with the transepicondylar axis, comparison was conducted on our Australian dataset to quantify the difference between the optimal flexion axis and the transepicondylar axis.
The optimal knee flexion axis was evaluated using the fit cylinder method and the anteroposterior and superoinferior distance between the axis and the two epicondylar points were computed. The angle between the transepicondylar axis and the optimal flexion axis was also calculated.
As shown in figure 8.9 on the facing page, the medial epicondyle is in general anterior and superior to the optimal flexion axis. The mean anterior and superior displacement is 13.1 mm and 8.2 mm respectively. The lateral epicondyle is of a closer proximity to the optimal flexion axis relatively, with an average of 4.4 mm anterior and 2.7 mm superior displacement (Figure 8.10 on the next page). The mean angle between the transepicondylar axis and the optimal flexion axis is 7.3◦ with a standard deviation of 1.9◦. It is concluded that the epicondyles are in general not in close proximity to the optimal flexion axis.
184 8.5. Comparison
Figure 8.9.: Displacement of the medial epicondyle relative to the optimal flexion axis.
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Figure 8.10.: Displacement of the medial epicondyle relative to the optimal flexion axis.
185 8. Results
Parameter P-value Mean difference ∗ Radius (HR) 0.001 2.5 Femoral axis offset 0.028∗ 5.9 Vertical offset to lesser trochanter 0.001∗ 9.8
Table 8.24.: Statistical comparison between AU and JP femoral head region.
8.5.3. Australian & Japanese
To evaluate if there is any observable difference using our methodology between the healthy Australian and Japanese datasets, a comparison was made to the processed parameter set.
Independent two-tailed Student t-test was computed using SPSS . The Levene’s test was performed for each variables to determine if equal variance of the two datasets could be assumed. With the significance level of the Levene’s test taken to be 0.05, only two variables showed that equal variance could not be assumed. For the two variables, non-parametric Mann-Whitney test was performed in which equal variance is not assumed with a slight penalty of the degree of freedom. Entries with which non-parametric tests were performed are marked by a superscript hash sign (#) in table 8.26 on the facing page and table 8.27 on page 188.
A significance level of 0.05 was selected in the test to reject the null hypothesis, and the mean difference is the mean value of the Japanese dataset subtracted from that of the Australian dataset. Variables that are statistically significant is marked by an asterisk (∗).
The Japanese tends to have a smaller femur in general. A smaller femoral head, shorter femoral length, shorter neck, and smaller posterior condyles were observed. It was however noted that the Japanese dataset has a larger anterior bowing of the femoral shaft and a larger anteversion.
8.6. Sheep Summary
The inclusion of ovine data is to systematically gather anthropometric data for sheep femur,which is a commonly used animal model in prosthesis testing in
186 8.6. Sheep Summary
Parameter P-value Mean difference ∗ Neck length to femoral axis (NLFA) 0.026 6.0 Neck length to lateral greater <0.001∗ 11.8 trochanter (NLGT ) Neck shaft angle (∠NAFA) 0.686 -0.8 ∗ Neck axis elevation (NAFA) 0.004 2.2 Neck axis to head centre distance 0.589 -0.1 (NAHC) Greater trochanter height (GTH) 0.223 1.5
Table 8.25.: Statistical comparison between AU and JP femoral neck regions.
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(a) Femoral head. (b) Femoral neck.
Figure 8.11.: Femoral head and neck measurements of the AU and JP datasets.
Parameter P-value Mean difference
∠(TEA ,CA ) 0.735# -0.3 ∠(HCF A,TEA ) 0.584 -1.6 ∠(HCF A,CA ) 0.525 -1.9 ∗ ∠(NA ,TEA ) 0.044 -5.8 ∗ ∠(NA ,CA ) 0.044 -6.1
Table 8.26.: Statistical comparison between AU and JP anteversion angles.
187 8. Results
Figure 8.12.: Anteversion angles of the AU and JP datasets. Significant difference was observed in ∠(NA ,TEA ) and ∠(NA ,CA ) (P<0.05) in which the Japanese dataset has a larger angle than the Australian dataset.
Parameter P-value Mean difference Distance from LT to isthmus 0.213 11.1
CFIml 0.946 0.0
CFIap 0.793 0.0
CFIoblique 0.299 0.1 #∗ CFImetaphyseal 0.016 -0.1
Table 8.27.: Statistical comparison between AU and JP canal flare index.
Parameter P-value Mean difference ∗ Posterior condyles radius (PCCYLr ) <0.001 3.8 Trochlear groove angle (∠TR) 0.604 2.1 ∗ Anterior bow radius (BOWr ) 0.011 235.3
Table 8.28.: Statistical comparison between AU and JP distal femur and shaft regions.
188 8.6. Sheep Summary
Parameter P-value Mean difference ∗ FLGT−KC <0.001 64.7 ∗ FLHC −KC <0.001 63.4 Head centre to epicondylar <0.001∗ 58.5 (DistHC−TEA) Lesser trochanter to epicondylar <0.001∗ 49.4 (DistLT −TEA)
Table 8.29.: Statistical comparison between AU and JP femoral length.
Figure 8.13.: Femoral length measurements of the AU and JP datasets. The Japanese dataset has a smaller value in all femoral length measurements (P<0.001).
189 8. Results
Figure 8.14.: Cross-sectional area of the bone section and the medullary canal of the proximal femur. The error bars represent 1 standard deviation of the measurements.
Figure 8.15.: Moment of inertia across the medio-lateral axis (Ixx) and antero- posterior axis (Iyy) of the proximal femur.
190 8.6. Sheep Summary
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Figure 8.16.: Summary of measurements of proximal femur and posterior condyles of sheep. the field of Orthopaedics. It also demonstrates the robustness of the proposed methodology in handling datasets with similar structure. 19 sheep femur were successfully processed without the need of core methodology modification. The data is sorted according to the average magnitude and plotted below.
191 8. Results
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Figure 8.17.: Summary of femoral length, neck shaft angle and anterior bow of sheep.
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Figure 8.18.: Summary of canal flare index of sheep.
192 9
Discussion
Contents 9.1. Overview ...... 194 9.2. Software Selection ...... 195 9.3. Image Acquisition & Segmentation ...... 196
9.3.1. Acquisition Parameters ...... 196 9.3.2. Automated Segmentation ...... 197 9.3.3. Consistency ...... 198 9.4. Performance of the Methodology ...... 200
9.4.1. Automation ...... 200 9.4.2. Accuracy ...... 200 9.4.3. Consistency ...... 201 9.5. Reference Axes Definition ...... 202
9.5.1. Longitudinal Axis ...... 202 9.5.2. Distal Transverse Axis ...... 204 9.6. General Parameter ...... 206
9.6.1. Head Centre ...... 206 9.6.2. Neck ...... 208 9.6.3. Posterior Condyles & Knee Centre ...... 212 9.6.4. Canal Flare Index ...... 216 9.7. Anteversion Angle ...... 217 9.8. Sheep Femur ...... 221
193 9. Discussion
9.1. Overview
he main goal of the project is to develop a methodology for the extraction T of anthropometric parameters of the femur, to serve as a platform for further analysis. Numerous anthropometric studies (Section 6onpage97) have been conducted in literature, from physical measurements on osteometric table (Parsons, 1914; Kingsley and Olmsted, 1948; Yoshioka and Cooke, 1987), to the utilization of modern medical imaging techniques including X-rays (Rogers, 1931; Dunlap et al., 1953; Ryder and Crane, 1953), MRI (Iwaki et al., 2000; Manske et al., 2006; Sheehan, 2007) and CT (Weiner et al., 1978; Høiseth et al., 1988; Kim and Kim, 1997; Kim et al., 2000a). The studies span a wide range of applications, such as analysis of racial difference, categorizing data for prosthesis design, comparison of anthropometric difference or changes in pathological cases, evaluation of fracture risk. The accurate understanding of the geometric properties of the bone is vital and fundamental for many of the analysis abovementioned.
During the initial stage of the study, it was noticed that while most of the anthropometric parameters are well-defined in the anatomical aspect, many definitions remain ambiguous in the image processing domain. It is understandable that as most of the anthropometric measurements evolved from the clinical domain, human anatomy plays a major role towards their definitions. Nonetheless, with the increasing application of image processing techniques in the medical field, the problem of ambiguity in anatomical definitions surfaced.
Several studies (Croce et al., 1999; Besier et al., 2003; Hagemeister et al., 2005) have pointed out the difficulty in precise and consistent location of anatomical landmarks. Croce et al. (1999) have pointed out the intrinsic reason for the positional inconsistency in the use of anatomical landmarks due to the fact that anatomical landmarks are generally defined as relatively large and curved region instead of discrete points. This could possibly incur undesirable inter and intra-rater inconsistency in the process of locating anatomical landmarks for anthropometric study. An effective way to overcome the inherent limitation is to incorporate function methods in the evaluation of anthropometric parameters (Croce et al., 1999; Stagni et al., 2000; Besier et al., 2003; Hagemeister et al., 2005).
The deficiency of the anatomical definitions in the image processing aspect inspired the investigation of the proposed methodology, in which the definition
194 9.2. Software Selection is more consistent and reproducible, reducing as much subjective judgment of landmarks identification as possible.
One derived advantage of a consistent and well-defined anatomical definitions is the possibility of higher level of automation with the methodology not dependent on subjective user input which could significantly increase inter and intra-rater consistency.
The robustness of the methodology was another major concern. It was noted that while many methodologies documented in literature (Section 6onpage97) are robust in terms of processing healthy femur, the outcomes on pathological samples are far from satisfactory. This could possibly due to the use of geometric assumptions no longer being valid when the structure is deformed. It was thus one of the criteria to try to develop a methodology that allows pathological samples to be processed.
The sections below discusses various aspects of the proposed methodology, the performance and robustness, the consistency observed, the reason for various measurements, a brief summary and comparison on the datasets acquired, the limitations and future directions.
9.2. Software Selection
Several software packages were used in this study. Amira (Visage Imaging, Inc., Carlsbad, USA) was used due to its extensive image segmentation capabilities. Morphological functions and other semi-automatic functions such as edge tracing and local region growing provided a good tool-set for an efficient and consistent segmentation process.
Matlab (Mathworks Inc., MA, USA) was used extensively in the imple- mentation of the proposed methodology. While the proposed methodology is language independent, the Matlab package provided a very comprehensive set of functions for image and signal processing and thus served as a very good platform for prototyping.
Nevertheless, it was noted that the use of Matlab in the prototype had resulted in significant performance penalty in several occasions. The applica- tion of affine transformation (Section 7.3.1.4 on page 133) to large CT dataset in the model alignment stage has suffered from low performance and could
195 9. Discussion take up to several minutes to complete on an Intel Pentium 4 personal computer. Similar operation using the Amira software package, for instance is in general a few times faster. Even so, with the fact that the processing in our Matlab routine is mostly automated, the impact of the performance drawback is considered minimal.
Mimics (Materialize, Inc., Leuven, Belgium) was used as the reverse engi- neering software package in the creation of 3-D model for verification purpose. While it was noticed that Mimics may not be as fine-grained and robust as other functional-specific software packages in model creation, the functionality is sufficient for our verification purpose. The intuitive interface allows direct measurements on the generated model, eliminating the need of additional software packages for this purpose.
9.3. Image Acquisition & Segmentation
Computing tomography was employed as the primary acquisition technique due to its high availability and good reflection on bone structure. While the ideal CT number, the Hounsfield unit, theoretically represents only the average X-rays attenuation of the corresponding voxel, artifacts such as beam hardening or photon starvation have been shown to have a profound effect on the final Hounsfield value. Various findings (Levi et al., 1982; Groell et al., 2000) have suggested extra caution should be taken in the adoption of direct Hounsfield values for clinical diagnostics due to the variations observed on intra-scanner and inter-scanner output. Specifically, unacceptable variations in soft tissues and similar low attenuation masses have been confirmed (Boland et al., 1998; Maki et al., 1999) in various studies.
9.3.1. Acquisition Parameters
Nonetheless, it was noted within our datasets from various scanners that the Hounsfield value of bone are relatively consistent, possibly due to a higher attenuation coefficient leading to a higher signal to noise ratio, and thus less prone to the varying effect of background attenuation. Our observation confirms with Groell et al. (2000) study in quantifying CT number variations under different image acquisition parameters and across two different scanners.
196 9.3. Image Acquisition & Segmentation
Still, extra caution has been taken in the process of base threshold value selection in the study. Manual examinations were performed on several image stacks from each of the scanners/parameter group, with analysis on the histogram and profile line. It was discovered that a value of 200 HU served as a good base reference for thresholding the periosteal boundary from the surrounding soft tissue; and 500 HU being a good base reference for thresholding cancellous bone from cortical bone in our datasets as a result of the analysis on the profile lines as shown in figure 7.3 on page 126. The use of 200 HU for reference in segmentation of the periosteal boundary in femur for CT-based computer navigation system in THR was reported (Sugano et al., 2001). In the analysis, Sugano et al. further reported that the accuracy of surface registration of the periosteal boundary of the femur does not vary significant within the range of 110–320 HU. Other studies have documented the optimal Hounsfield value for segmentation of trabecular bone to be within the range of 300–600 HU (Aamodt et al., 1999; Hua J, 1993). In our study, the reference base threshold values were chosen in favor to the avoidance of under-segmentation, and slight amount of manual work were required especially in the proximal and distal extremes.
9.3.2. Automated Segmentation
With image segmentation being one of the key steps in image processing, attempts have been made in automating the segmentation process without much success. One of the major difficulties encountered was achieving a precise and consistent segmentation between the acetabulum and the femoral head, especially in the osteoarthritis patient where the joint space are not well defined.
Active contour models (Kass et al., 1988), also commonly known as snakes, defined as an energy minimizing spline or deformable template matching, are often employed in tackling the above-described problem. Gregory et al. (2004) developed a technique based on active shape modeling in measuring the morphometry of proximal femur in AP radiography and reported an accuracy of 2.2 mm of median point-to-point error could be achieved. Chen et al. (2005) employed a similar algorithm with additional shape constraints to automatically extract femoral contours from X-rays images whilst pointing out the deficiency in handling odd or pathological cases.
197 9. Discussion
More complex techniques have been proposed by Zoroofi et al. (2003)in automatic segmentation of the femur from CT, delivering a 54% success rate within a dataset of 60 patients. Challenges remains in the complexity and variations of the CT, particularly in pathological cases with bone deformation, when coupled with the possible artifacts from the image acquisition stage.
The inconsistency and low robustness of automatic segmentation (Zoroofi et al., 2003; Chen et al., 2005) has led to the decision of adopting a more conservative approach in current study. Amira was chosen as the primary segmentation tool with its versatile set of image segmentation tool including region growing and edge tracing, which extensively accelerated the segmentation process upon applying a base threshold.
Extra investigations were performed in designing the segmentation protocol as discussed in previous section (Section 9.3.1 on page 196). The amount of extra manual work involved depends upon the bone quality of individual patient, and more work is usually involved in pathological dataset.
9.3.3. Consistency
With the manual segmentation involving significant amount of user interaction, individual subjectivity is expected to be one of the main sources of error in the entire study. Additional testing was performed to quantify the effect of user subjectivity towards the final outcome. Intra-rater and inter-rater variability were conducted to evaluate the consistency among users (Section 8.2 on page 167).
The Intra-class Correlation Coefficient (ICC) has been extensively employed (Ginja et al., 2007; Tannast et al., 2007; Delgado-Martínez et al., 2000)as a consistency test in evaluating inter and intra-rater variability. An ICC value of 0.7 or higher (Baumgartner and Chung, 2001) is generally consid- ered good consistency. Intra-rater variability evaluated using ICC on most general parameters resulted in a correlation coefficient of 0.95 (mean 0.96) or above (Section 8.2.1 on page 167). ICC of ∠(TEA ,CA ), the angle between the transepicondylar and posterior axis, was lower than the generally required 0.7 threshold to be considered consistent (Table 8.4 on page 170). Further investigations revealed the low correlation is attributed to other causes. The angle was found to have a very low value (mean 6.3◦) in which any variation
198 9.3. Image Acquisition & Segmentation involved would affect the measurement relatively significantly. Removing the parameter ∠(TEA ,CA ) resulted in a mean ICC of 0.98 and Cronbach’s alpha of 0.99, a strong evidence of high intra-rater consistency.
Inter-rater variability evaluated using ICC resulted in similar ranges, with mean ICC of 0.974 and Cronbach’s alpha of 0.987, concluding the effect of segmentation variations is minimal with our proposed methodology.
All previous anthropometric studies in the literature reviewed were based on a single preset image acquisition protocol. To be able to utilize a wider range of input source, the ability to process and compare datasets obtained from different scanner sources is desirable. With different scanning protocols adopted in our sources, the validity of direct comparison between scans of different resolutions aroused. The question further extended to the consis- tency between repeated scans where patient positioning would vary. Another significant factor is the influence of partial volume averaging (Section 3.3.6.2 on page 30) especially in lower resolution scans with anisotropic voxels.
A promising mean correlation coefficient of 0.921 was obtained in our repeated scan test, with a mean Cronbach’s alpha of 0.953. It should safely be concluded that direct comparison between scans of different resolution is feasible and a slice thickness of 2 mm could still deliver accurate results.
While the inter and intra-rater ICC segmentation tests were designed to evaluate the reliability of a single variable (segmentation) per test, the results represented an aggregated consistency measures, including possible variations due to the methodology design. With consistency being one of the fundamental properties in anthropometric study, it was noted that the ICC could serve as an additional selection criterion to distinguish the robustness between different extracted parameters.
It was observed, in general, that measurements that are derived from a func- tional method such as various fitting procedures acquire a higher consistency in both inter and intra-rater tests when compared to those that measures directly upon anatomical landmarks. This confirms with various studies (Croce et al., 1999; Besier et al., 2003; Hagemeister et al., 2005) and could be explained by the fact that anatomical landmarks are usually small distinctive regions instead of discrete points. More detailed discussion on the use of functional methods in the study are discussed in the following sections.
199 9. Discussion
9.4. Performance of the Methodology
9.4.1. Automation
The implication of the methodology is two-folded. It provides a consistent method in extracting anthropometric parameters with minimal subjective user judgments involved. The consistent and well-defined methodology allows comprehensive automation, delivering a good platform for further comparison and analysis.
The procedure implemented in Matlab is mostly automated, with several minor user interactions, mostly for confirmation and initialization purposes. Upon loading the segmented CT stacks and confirming a few orientation parameters, steps that require user interaction could be summarized as follows:
• Confirmation of the automatically evaluated transepicondylar axis with the option of a semi-automatic fall-back method.
• Selection of the starting and ending slice range of the posterior condyles for cylinder fitting.
• Selection of the starting slice range of the distal trochlear groove.
Extra care and tests were taken in the automatic procedure to minimize the effect of subjective user input in the above steps. A corner detection procedure was added in the semi-automatic fall-back method (Figure 7.10 on page 133) in the case when automatic discovery of the transepicondylar axis failed. The effect of shifting the slice range in posterior condyles fitting was recorded (Section 8.3.3 on page 179). The resulting procedure in Matlab could easily be performed by users without specific knowledge in anthropometric studies.
9.4.2. Accuracy
Accuracy of measurements based on CT is well-established. Numerous studies (Laine et al., 1997; Kim et al., 2000b; Prevrhal et al., 2003) have confirmed a high accuracy on measurements taken from CT images, having additional benefits of obtaining three dimensional measurements which is not possible
200 9.4. Performance of the Methodology with traditional radiography. Prevrhal et al. (2003) investigated the accuracy of CT in thickness measurements over thin structure under various scan resolutions and reported that the sensitivity highly correlates with the slice thickness, which is usually the largest singleton dimension, and the intersec- tion angle of the measurements with the scanner axis. With the majority of our measurements significantly above the sensitivity of current CT systems, it is safe to assume sufficient accuracy is delivered in our CT datasets.
3-D models were generated using Mimics to provide an assurance on the correctness of the Matlab implementation based on a third-party tool. 5 parameters including length measurements, neck shaft angle, head diameter and neck length were measured and compared with values extracted using our methodology (Section 8.4 on page 181). Differences of up to 3 mm and 3 degrees were observed. Taking into account the fact that all measurements were taken in Mimics by visual inspection, which would undoubtedly incorporate a small amount of error, the difference was considered acceptable, and that the correctness of our implementation could be assumed.
9.4.3. Consistency
Traditional Pearson’s correlation coefficient (r) suffers from the limitation of only providing a measurement on the correlation between variables, but does not provide an indication on the level of absolute agreement (Müller and Büttner, 1994). For instance, a measurement which is always a double of the reference one will give a perfect Pearson’s correlation coefficient of 1, while their absolute agreement is poor. ICC provides a more robust evaluation of concordance, which is more suitable in the evaluation of intra and inter- rater consistency and was thus used extensively in testing of consistence and concordance in the study.
Several variations of ICC were described by Shrout and Fleiss (1979). Based on a detailed explanation by McGraw and Wong (1996) on the specific ICC class to use, ICC(2,1) (Table 8.1 on page 168) was selected in our intra and inter-rater consistency test with which both the judge and subject of interest are assumed to be a random selection, while ICC(1,1) was employed in our repeated scans test with which each scanner (judge) did not scan all the tested samples (subject of interest). Another commonly used reliability test using Cronbach’s α (Cronbach, 1951) was performed in additional to the ICC. In
201 9. Discussion both cases, excellent intra and inter-rater consistency were observed and it is concluded that the proposed methodology achieve the goal of being internally consistent.
9.5. Reference Axes Definition
There are several reference axes schemes generally being adopted in anthro- pometric studies (Dunlap et al., 1953; Yoshioka and Cooke, 1987; Noble et al., 1988; Whiteside and Arima, 1995) of the femur as discussed in section 6.2 on page 98. Several aspects were considered in the definition of reference axes. With variation in patient positioning during the image acquisition stage, anatomical landmarks employed in the computation of reference axes should be independent on patient position or orientation, well-defined and reproducible for high consistency and accuracy. The ease of initial estima- tion without an accurate reference frame is highly preferred, especially in automation of the entire process. The robustness of the reference axes, as its applicability towards different type of femur including pathological type, was also considered.
9.5.1. Longitudinal Axis
Traditional anthropometric studies utilizing osteometric table often employ the natural stable sitting position as its reference frame. Most studies (Parsons, 1914; Kingsley and Olmsted, 1948; Lausten et al., 1989; Jain et al., 2003) rely on the fact that most femurs sit on the flat osteometric table on its posterior surface with 3 supporting points (the distal posterior condyles, and the posterior aspect of the greater trochanter), and defined the reference frame based on the stable sitting position. One inherent drawback (Kingsley and Olmsted, 1948) of the definition is the inability to handle retroverted femur, where the proximal supporting point would shift to the posterior surface of the femoral head.
Anthropometric studies based on CT and other 3-D imaging modalities have higher flexibility to allow definition of virtual axes not based on anatomical landmarks. Most studies (Lee et al., 1992; Kim and Kim, 1997; Mahaisavariya et al., 2002) adopted a more functional approach with the longitudinal axis
202 9.5. Reference Axes Definition
(a) The use of full femoral shaft axis as (b) The use of proximal femoral axis as the longitudi- the longitudinal axis. Note that the nal axis. The axis bisects the greater trochanter axis no longer bisect the proximal independent on the amount of anterior bowing. femur, but passes through the proxi- mal aspect of the greater trochanter.
Figure 9.1.: Effect of anterior bowing on different definitions of the longitudinal axis. Reproduced from Dunlap et al. (1953). defined as an estimation of the femoral shaft in a best-fit sense which is highly consistent.
Anteversion angle is a measurement that is significantly affected (Dunlap et al., 1953; Ryder and Crane, 1953) by the definition of the longitudinal axis. Dunlap et al. further pointed out the ignorance of anterior bowing of the femoral shaft would under-estimate the anteversion angle by as much as 12◦. In cases of moderate anterior bowing, the full femoral axis no longer bisect the proximal femur but passes over the anterior aspect of the greater trochanter. Taking into account the anterior bowing, the proximal femoral axis was chosen as the default longitudinal axis in this study and singular value decomposition was employed to obtain the 3-D best-fit estimation of the long axis based on cross-sectional centroid coordinates. It was observed that the use of proximal femoral axis as the reference longitudinal axis has an additional benefit of closely aligning with the long axis of femoral prosthesis in THR, thus may provide a more clinically-related measurement in the proximal regions such as neck shaft angle and neck length. To provide extra flexibility, extra options were incorporated into the user interface to allow the use of entire femoral shaft as the longitudinal axis.
203 9. Discussion
One possible drawback of our modified long axis definition is the higher vari- ability due to less cross-sections used. The lesser trochanter was selected as the anatomical landmark to locate the proximal and distal limits in longitu- dinal axis evaluation. It was noted that the conical eminence of the lesser trochanter is easily identifiable, but CT artifacts, due to partial volume aver- aging could adversely affect the accuracy, especially in the case of anisotropic voxels with large slice thickness. Nevertheless, our consistency tests showed that the deviation is minimal (mean 0.60◦, σ=0.27◦) in misjudgment of the lesser trochanter by ±3 mm superoinferiorly from the automatic evaluated location.
The use of mechanical axis as the reference longitudinal axis was also studied. Yoshioka and Cooke (1987) reasoned that the axes of motion maybe a more appropriate approach to evaluate angular geometry of the hip and knee, and thus employed the mechanical axis as the principal reference longitudinal axis. The mechanical axis (Walmsley, 1933) was defined as the femoral head centre to the attachment point of the posterior cruciate ligaments (PCL). While the author agreed with the arguments suggested, various practical difficulties were observed. The attachment point of the PCL is well-defined anatomically but could be hardly distinguishable in CT. Second, the PCL- femoral interface is a region rather than a discrete point, the representation of the PCL attachment region with a discrete point would be inconsistent. The adoption of mechanical axis as reference would potentially be feasible in other imaging modalities such as MRI, but not in the case of CT.
9.5.2. Distal Transverse Axis
The transverse axis provides a rotational reference in additional to the longi- tudinal axis. Most anthropometric studies based on osteometric table have employed the posterior medial and lateral condyles as the rotational reference evaluated with the tabletop method as described by Murphy et al. (1987). The posterior condyles supporting points depend upon other factors such as the amount of anterior bowing of the femoral shaft, and thus are not very well-defined anatomical landmarks. Murphy et al. (1987) further pointed out that the condylar axis suffers from rotational variations if excessively proximal or distal cross-sections are used in axis evaluation. Nonetheless, its locations are trivial in cadaveric studies, and are clinically correlated to the horizontal plane when knee flexion is 90◦.
204 9.5. Reference Axes Definition
We adopted the use of transepicondylar axis (TEA) as a rotational reference, as first proposed by Weiner et al. (1978). The TEA is simple and, in general, well-defined in CT. From a technical point of view, the epicondylar promi- nences are not affected by the orientation of the femur. The TEA may serve as a rotational reference for comparative study in total knee arthroplasty. Additionally, the epicondyles could be the only reliable anatomical landmarks left in some revision TKR (Griffin et al., 2000). Numerous studies (Berger et al., 1993; Stiehl and Abbott, 1995; Poilvache et al., 1996; Olcott and Scott, 1999) have reported the importance of the TEA in the role as a rotational reference of the femoral component in TKR. However, thick soft tissue and the inconspicuous morphology of the medial epicondyle (Griffin et al., 2000) have shown to introduce extra error (Jenny and Boeri, 2004; Siston et al., 2005; Yau et al., 2005) in the accurate location of the TEA in clinical settings. Under appropriate segmentation, the adverse effect of soft tissue could be eliminated while the obscure structure of the medial epicondyle was found to adversely affect the accurate location of the TEA in our CT datasets.
The proposed automatic TEA evaluation subroutine failed to identify several cases, where the semi-automatic fall-back procedures were applied. The reason was a lack of distinguishable prominence on the medial epicondyle (Griffin et al., 2000).
Unlike the longitudinal axis which is a functionally derived axis from a large set of datum points, the TEA could be significantly affected by inaccurate evaluation of any one of the epicondylar points. The intra and inter-rater consistency test (Section 8.2.1 on page 167) showed the TEA has a slightly lower correlation coefficient, implying the posterior condylar axis may have an edge for consistent rotational reference purpose. Note however that the posterior condylar axis was evaluated after the reference system was set up, in which possible variations due to the use of superior or inferior extremes of the condyles described by Murphy et al. (1987) were minimized or eliminated.
While it has to be admitted the transverse axis has a larger variation than anticipated, the extra rotational variance were tested to have minimal and negligible effect on other parameters being extracted. More discussion on the variations of the TEA observed in our study is discussed on section 9.7 on page 217.
The use of surgical epicondylar axis (SEA) suggested by Berger et al. (1993) has also been studied. It is defined as the the line connecting the lateral
205 9. Discussion epicondylar prominence to the sulcus inferior to the medial epicondylar, the attachment point of the medial collateral ligament. However, similar to the location of PCL attachment point, the SEA is deemed not suitable in CT images because of the location difficulty of the medial epicondylar sulcus. This has also been reflected in studies (Kinzel et al., 2005; Lustig et al., 2008) involving the use of SEA with CT, in which radio-oblique objects needed to be inserted as landmarks prior to scanning.
Whiteside and Arima (1995) suggested the use of the anteroposterior axis (also known as the Whiteside line) as a rotational reference instead of the TEA or the posterior condylar axis. It was reported that the use of the anteroposterior axis as a rotational reference of the femoral component reduced significantly the number of patellar tracking problem that required realignment in valgus knee. Nevertheless, other studies (Middleton and Palmer, 2007; Wonetal., 2007) have reported the anteroposterior axis alone has too large variation to be employed as the rotational reference. It was noticed from our datasets that the anteroposterior axis were hard to be well-defined because of the variation observed down the patellar groove superoinferiorly which would affect the anterior reference point of the axis. In cases of osteoarthritis in the knee, it was not uncommon to observe large osteophytes in the intercondylar notch or around the trochlear groove region, leading to extra difficulty in the determination of the Whiteside line (Yauetal., 2008).
9.6. General Parameter
9.6.1. Head Centre
The femoral head offset, defined as the distance between the head centre and the proximal femoral shaft, is one of the important factors being studied in THR (Abraham and Dimon, 1992; Davey et al., 1993).
Optimal femoral head offset in THR could minimize the chance of hip dislo- cation (Bourne and Mehin, 2004) and maximize range of motion (McGrory et al., 1995). Austin et al. (2003) have pointed out that femoral offset is a powerful tool for increasing THR stability without affecting the leg length. This could reduce the chance of leg length inequality, which could contribute to ipsilateral knee pain, low back pain, sciatic nerve palsy and even aseptic
206 9.6. General Parameter loosening (Friberg, 1983; Edeen et al., 1995; Bose, 2000; Gurney et al., 2001). A lateral offset is reported to have an effect of increase stability, decrease wear and reduction of joint reactive force if used appropriately (Davey et al., 1993) while the decrease of femoral offset could lead to an increase of polyethylene wear in THR (Sakalkale et al., 2001).
Femoral head offset also serves a significant role in hip resurfacing (Beaulé et al., 2007). Silva et al. (2004); Loughead et al. (2005) both reported the decrease in femoral offset after hip resurfacing when compared to stemmed implant. While the effect of femoral offset has been studied more extensively in traditional THR, the actual effect of an decrease in femoral offset in hip resurfacing is not well-defined (Girard et al., 2006).
Accurate femoral head centre evaluation serves as an important basis to understand the morphology of proximal femur and correct measurement of the head offset. The modeling of the femoral head by sphere fitting has been a well-established and accurate technique in the determination of the head centre and diameter (Kim et al., 2000a,b; Mahaisavariya et al., 2002; MacLatchy and Bossert, 1996). Kim et al. (2000a) proposed an automatic routine in obtaining a sphere estimate of the femoral head from CT. This involved extracting contours of the head region proximal to the femoral neck and fitting circle to every contour line. Pairs of circles were then used to generate several fitted sphere, in which they were averaged resulting in the final sphere estimate.
A two phase evaluation was adopted in our sphere fitting procedures. The initial phase provided estimation from a set of datum points obtained at the proximal aspect of the femoral head. However, under-estimation of the femoral head diameter was observed in numerous cases. In the several cases of pathologically deformed femur, the measured diameter is erroneous because the femoral head was far from perfectly spherical. Cases with small femoral neck-shaft-angle would lead to insufficient datum point and result in erroneous outcome.
To circumvent this, a second phase was designed to capture further surface datum points for a more robust fitting. The medial aspect of the head was included into the fitting algorithm and the outcome is satisfactory and highly consistent. The close fitting was confirmed by the close match of the outcome with manual measurements (Figure 8.7 on page 182). The infero-medial aspect of the femoral head was not included in the estimation because the capital
207 9. Discussion drop osteophytes observed in numerous cases would introduce unnecessary error in our fitting procedures.
The use of other fitting methods by means of reverse engineering from 3-D model was also investigated. Numerous studies have (Mahaisavariya et al., 2002; Song et al., 2007) presented accurate and reproducible femoral head fitting routines based on 3-D surface model created from CT. While accurate and consistent, the 3-D modeling approach suffers from the need of immense amount of manual work. Even so, improvements have been seen in newer software packages such as Mimics in the lengthy model creation procedures with more encapsulation of technical details.
9.6.2. Neck
Apart from the previously discussed (Section 9.6.1 on page 206) femoral head offset, which is primarily caused by the orientation of the femoral neck, the neck region is another main focus in anthropometric studies.
With 5000 neck fracture recorded in New South Wales (Australia) alone in 2000, and a still increasing trend as reported by Boufous et al. (2004), fracture risk prediction has always been an area of focus.
While it is widely accepted that BMD serves as a good prediction factor of hip fracture (Cummings et al., 1993; Nicholson et al., 1997; Lochmüller et al., 1998; Barr et al., 2005), an increasing amount of studies have reported neck geometry being an additional prediction factor (Gómez Alonso et al., 2000; Pulkkinen et al., 2004; El-Kaissi et al., 2005). El-Kaissi et al. (2005) reported the observation of a wider neck width and reduction of cortical thickness in fracture patients and Pulkkinen et al. (2004) confirms the combination of BMD with geometric measures improved the assessment of fracture risk.
Relationship with BMD and neck geometry during aging has been suggested by Kaptoge et al. (2003). Based on the fact that the cross-sectional modulus, a measurement of bending resistance, does not decrease at the same rate as BMD during aging, it was suggested that part of the effect of aging in BMD could be a result from the expansion of the bone envelope. While no quantitative relationship between the two has been documented, this gives an insight on the possible role neck geometry could bear.
208 9.6. General Parameter
Racial difference has also been investigated. Nakamura et al. (1994) reported that Japanese women have a substantially lower incidence of hip fracture than North American whites due to different geometric characteristics of the femoral neck. Despite lower femoral neck bone mass, it was shown that the lower risk of structural failure in the femoral neck of Japanese women is attributed primarily to a shorter femoral neck and a smaller neck shaft angle. Other studies (Bergot et al., 2002; Pulkkinen et al., 2004) have also confirmed the use of femoral neck length and upper femoral geometry in improving the assessment of hip fracture.
While various studies abovementioned have suggested relations between fracture risk and femoral neck geometry exist, there is not yet a widely accepted conclusion. Bouxsein and Karasik (2006) suggested the limited knowledge could, in part, be attributed to the predominant use of 2-D imaging techniques to estimate bone geometry. The adoption of 3-D imaging would be needed to better characterize the relationship between bone geometry and skeletal fragility. While the use of hip strength analysis (Martin and Burr, 1984; Lou Bonnick, 2007) based on DXA may deliver an estimation of 3-D geometry, various studies (Beck, 2003; Gregory et al., 2004) have pointed out its use suffers from unavoidable rotational and magnification errors. This further strengthens the significance of our proposed methodology to deliver a consistent and accurate 3-D geometric understanding of the proximal femur.
Based on existing 2-D DXA, the application of stereo-radiographic 3-D recon- struction from standard biplanar DXA images has also been reported (Kolta et al., 2005), though its robustness is yet to be confirmed. Still, this indicates the increasing focus of three dimensional structure which could deliver a more accurate representation of anatomy.
Accurate evaluation of the neck axis is essential for the calculation of the anteversion angle, which is one of the most important geometric parameters determining the relative rotational orientation between the proximal and distal femur. Details of the anteversion angle will be discussed in later section (Section 9.7 on page 217).
Accurate and robust evaluation of the neck axis has always been a challenging task in anthropometric studies. Commonly described as a tapered cylinder in shape, analysis of the femoral neck poses great challenges because of its variability and the lack of distinguishable anatomical landmarks. Kingsley
209 9. Discussion and Olmsted (1948) commented on the determination of the true longitudinal neck axis as the most difficult part of his anthropometric study.
Numerous methods of neck axis identification on cadaveric studies were documented (Section 6.4.2 on page 111). The method of evaluating two mid- points between the anterior and posterior neck surfaces in superior view (Kingsley and Olmsted, 1948) was most commonly employed. The inherent restriction of the method and its derivatives is the inability to take into consideration the cross-sectional shape in the evaluation of the neck axis.
The use of 3-D imaging methods in general allows a more fine-grained evalua- tion of the neck axis Hernandez et al. (1981). However, most scanning protocols produce an oblique view of the neck region by default. This introduces extra difficulty in the identification of the neck axis without further post-processing. The use of a single oblique cross-section in the evaluation of the true neck axis (Weiner et al., 1978; Hoaglund and Low, 1980; Hernandez et al., 1981) has been criticized Murphy et al. (1987). More robust techniques involving the use of optimization techniques to obtain a orthogonal cross-section with minimized area has also been suggested (Kim et al., 2000b; Mahaisavariya et al., 2002).
In a study of the morphometry of the hip in developmental dysplasia patient, Sugano et al. (1998) utilized the centroids of a wider range of neck region (21 mm) in the evaluation of the neck axis from a reconstructed 3-D model. However, no details were provided on the actual methodology and the reason of why 21 mm of neck region was chosen was not documented.
One inherit limitation of the methods reviewed above is the use of only a fixed partial or localized region in the evaluation of the neck axis. Høiseth et al. (1988) reported the radially asymmetric property of the femoral neck, and further pointed out the impossibility to precisely evaluate the neck centre by any combination of bi-planar projections. We have observed that the reliance on such a localized region could be error prone especially in pathological cases where the neck shape is deformed. To overcome this shortcoming, our proposed technique tried to take into account a larger region of the neck in the estimation of the true neck axis.
Morphological skeletonization (Section 4.5.6 on page 72) on flattened AP image was found to provide a automatic yet reliable initial estimation of the neck base within all our CT datasets, allowing the entire neck axis evaluation to
210 9.6. General Parameter be fully automatic. Skeleton intersections (Figure 7.22 on page 144) were incorrectly identified in several cases when an extra skeleton branch was generated proximal to the lesser trochanter, leading to a less accurate initial estimate. Even so, subsequent steps in the optimization procedures were able to rectify the minor deviation. The proposed method with the use of morphological skeletonization (Section 7.3.5.1 on page 142) delivered a robust approach for bootstrapping the initial neck axis by automatically adapting to the morphology of individual femur, and is independent on the neck shaft angle and neck length.
The second phase of neck axis evaluation was based on the initial estimation obtained above. Two different algorithms were proposed and tested in our final design. The cylinder fitting optimization procedures (Figure 7.24 on page 146) were initially conceptualized with the thought of modeling the neck as a cylindrical shape. This has an advantage of taking into account the shape of the entire neck region rather than limiting the definition to a selective localized neck region. With the optimization procedures proposed, the need for using the head centre as one of the reference points is avoided. The cylinder fitting procedures identified the neck axis in all our human CT dataset except one case where severe deformation of the head neck region was observed with a shortened neck. The insufficient cross-sections of the neck region resulted in a bad cylinder fitting. Despite this extreme pathological case, the cylinder fitting algorithm was found to be very robust in the evaluation of human femoral neck axis.
The main drawback of modeling the neck region as a cylindrical shape is the inaccuracy encountered when applying the algorithm to our sheep dataset. It was noted that the morphology of sheep femoral neck has considerable difference when compared to the human. The sheep neck is more cylindrical at the femoral head end and gets more fanned out and more flattened in the coronal plane at the neck base than that of the human. Further investigations suggested that the use of areal centroids on the cross-sections delivered a more reliable outcome and is able to handle all our human and sheep datasets.
One additional difficulty was encountered at the definition of the neck base. The femoral neck extends from the femoral head till the intertrochanteric line. However, it was noticed that the inclusion of the neck region approaching the intertrochanteric line would over-estimate the neck shaft angle due to the asymmetric fanning inferiorly to the lesser trochanter region. A more conservative approach was adopted in which the extreme end of the neck base
211 9. Discussion was excluded in our calculation but whether the approach is optimal is yet to be concluded.
The proposed algorithm does not rely on the femoral head centre as a reference point of the neck axis. Kingsley and Olmsted (1948) cited the term “capit- o-collar” axis documented by Pearson and Bell (1919) who implied the head may not be centred on the femoral neck. Thus the femoral head centre should not be considered in the evaluation of the neck axis. Measurements on our human dataset showed that a mean distance of 1.21mm (range: 0.22–2.88mm) exists between the computed femoral head centre and neck axis. While this maybe considered a confirmation with observation by Kingsley and Olmsted, the difference could be originated from errors involved in the process.
A lower intra, inter-rater consistency of the distance from neck axis to head centre was observed. A possible reason is the low value (mean 1.21mm) of the attribute, in which the sensitivity limit of our CT datasets is reached. With the slice thickness of our human CT dataset ranging from 1mm to 2mm, a lower consistency on the measurement due to quantization error is not surprising.
Consistency test of intra and inter rater resulted in high correlation for neck shaft angle (ICC > 0.9) and neck length (ICC > 0.99). The largest neck shaft angle variation of 2.5◦ was observed under repeated CT scan of the same femur under different resolution. To our knowledge, no previous studies have documented their neck axis evaluation consistency on intra, inter-rater and on repeated scans.
It was observed that the neck axis, when extended laterally, lies anterior to the proximal femoral axis by an average of 10.7mm in our Australian dataset. The neck axis elevation was noted to have a slightly lower consistency in our intra, inter-rater and repeated scan test. It was suspected the lower consistency is attributed to the pivoting effect of the neck axis where the error of measurement is being magnified.
9.6.3. Posterior Condyles & Knee Centre
Traditional studies have demonstrated the use of instantaneous centre of rotation (Frankel et al., 1971; Walker et al., 1972; Blankevoort et al., 1990) and helical axis (Jonsson and Kärrholm, 1994; Sheehan, 2007) to represent
212 9.6. General Parameter knee kinematics. This implies the rotation of knee does not have a fixed axis of rotation. Recent studies (Hollister et al., 1993; Churchill et al., 1998) however have confirmed that knee kinematics could be modeled with two fixed non-orthogonal axes. Churchill et al. (1998) concluded that the optimal knee flexion axis agreed with the rotational centre of the posterior femoral condyles, which has a circular shape profile. This has shown that knee kinematics could be closely associated and modeled with the functional morphology of bone. While the accurate determination of the rotational centre of the femoral condyles may not be straight forward in clinical environment, the use of imaging techniques based on 3-D data would allow the optimal flexion axis to be evaluated consistently and accurately.
Motion of knee is constrained by the articular geometry of the articular surfaces and the muscle forces acting on it and various studies have reported the representation of the knee or distal femoral geometry by various means, including the use of digitizer Zoghi et al. (1992) ,3-D imaging techniques (Siu et al., 1996) and mathematical model (Imran and O’Connor, 1997). Li et al. (2006) have pointed out the importance of the understanding of the condyles geometry in analyzing reaction force in the cruciate ligaments. Added the fact that the posterior condylar axis have been reported to be in use as an rotational alignment in TKR (Matsuda et al., 1998, 2004), the study of the geometry of the posterior condyles would provide additional information in the understanding of knee kinematics.
Churchill et al. (1998) utilized electro-magnetic position sensors in the deter- mination of the optimal knee flexion axis and obtain the best-fit circles of the medial and lateral condyles on the 2-D plane orthogonal to the evaluated opti- mal flexion axis. Without prior knowledge to the experimental optimal flexion axis, the entire fitting procedures were not constrained to two dimensional. It was observed that without the extra planar constrain, the fittings of individual circle to each posterior condyles could be error prone. To circumvent this, cylinder fitting procedures were employed to model the medial and lateral condyles as a single entity to provide additional rotational constrain.
The proposed cylinder fitting subroutines to model the posterior condyles resulted in negligible fitting error in all our datasets. Over an average of 40 condyles datum points used for fitting on each femur, the average sum of error is 3.8 across our Australian dataset. Note that the Lorentzian minimization (Figure 7.18 on page 141) was applied to minimize impact of possible outliers due to the inclusion of datum points at the superior extreme. Thus the sum
213 9. Discussion of error calculated does not correspond directly to the sum of fitting error in millimeter.
Additional tests were done to evaluate the effect of subjective user slice range selection towards the cylinder radius (Section 8.3.3 on page 179 and appendix E.2 on page 265). It was concluded that the effect of subjective user range selection was minimal under normal conditions. Larger errors were observed in samples with a larger slice thickness and it was found that a minimum of around 15 slices are necessary to give an accurate and consistent cylinder fitting. This pose a limitation on the maximum slice thickness that could be used in the image acquisition stage.
Based on the optimized cylinder fit, the knee joint centre could easily be obtained by taking the mid-point on the cylinder axis. While the mid point of the epicondyles were often used (Stagni et al., 2000; Li et al., 2004; Coventry et al., 2006; Stefanyshyn et al., 2006; Holmberg and Lanshammar, 2006), Hagemeister et al. (2005) reported a higher repeatability in the the definition of knee joint centre by the circle fitting procedure rather than adopting the transepicondylar axis. This conforms to our findings in which the location of the epicondyles exhibit a larger variation in our consistency tests compared to the cylinder fitting procedure.
However, our definition of knee joint centre was slightly different to that proposed by Churchill et al. (1998). The main reason for the modification is the need for an undergoing study to identify a consistent and repeatable reference datum point on the knee surface for a patella tracking experiment Bertollo (2007) and the fact that the knee joint centre proposed by Churchill et al. is not positioned on bone surface. Based on the joint centre defined by Churchill et al., the joint centre was deliberately projected back to the most inferior point on the knee joint surface as shown in figure 6.20 on page 121. It was noted that the defined joint centre is of close proximity to the posterior cruciate ligaments attachment point in the intercondylar notch, in which it was sometimes being used as a anatomical landmark to define the mechanical axis of the femur (Yoshioka et al., 1987; Croce et al., 1999).
Excellent consistency of the cylinder evaluation was obtained in all intra, inter-rater and repeated scan test. A maximum radius discrepancy of merely 0.91 mm was observed in a pair of repeated scan test, where the slice thickness of one of the scans was 2 mm. The high repeatability could be attributed to the fact that the cylinder is evaluated based on a functional method and not
214 9.6. General Parameter relying on the accurate location of a particular anatomic landmark. Numerous studies (Croce et al., 1999; Besier et al., 2003; Hagemeister et al., 2005)have confirmed the use of functional methods in defining joint centre and axis as an effective way to reduce variability when compared to pure anatomical landmarks definition.
One drawback of our cylinder fitting method is the inability to quantify the radii of curvature of the medial and lateral condyles individually. Most studies (Churchill et al., 1998; Iwaki et al., 2000; Besier et al., 2003) reported a slightly larger (~2 mm) radius of curvature on the medial condyle relative to the lateral condyle, while fewer studies (Lustig et al., 2008) reported no difference in the radii of curvature of the condyles. Additional test were done to evaluate the radius of curvature of the individual condyle. Contrary to previous studies, we observed that the lateral condyles of our Australian dataset have a slight 1.2 mm larger radius of curvature than the medial condyle. The healthy Japanese dataset, however, showed no significant difference between the two condyles. Further investigation was performed by constructing 3-D models using Mimics and confirmed the findings.
One possible explanation for the discrepancy observed when compared to previous findings is the absence of an experimental optimal knee flexion axis in the study. Without the prior definition of the experimental optimal flexion axis, our circle fitting procedures are not constrained to the plane that is orthogonal to a particular axis. While the fitted circles to the condyles are theoretically more optimal with the extra 2 degrees of freedom in the optimization process, the medial and lateral circles are likely to be not parallel. It was observed from the 3-D models generated in Mimics that the judgment of the radius of curvature depends highly upon the orientation of the bone and thus a priori definition of the experimental flexion axis may explain the difference observed.
Churchill et al. (1998) pointed out that the medial and lateral epicondyles coincide with the optimal flexion axis of the knee. Nonetheless, various studies (Elias et al., 1990; Hollister et al., 1993; Lustig et al., 2008) reported the condyles centre does not coincide with the mid-point of the epicondyles. Comparison within the Australian (Section 8.5.2 on page 183) dataset showed a significant difference between the best-fit cylindrical condyle axis and the epicondylar points. The medial epicondylar point has an average of 13.1 mm anterior to and 8.2 mm superior to the cylinder axis. The lateral epicondylar point is however of a closer proximity to the cylinder axis, with an average
215 9. Discussion anterior and superior displacement of 4.4 mm and 2.7 mm respectively. Even so, the average angular discrepancy of 7.3◦ between the two axes would be too large to conclude the two axes coincide.
9.6.4. Canal Flare Index
The canal flare index (CFI), initially defined by (Noble et al., 1988), is an effective index to describe the flare shape of the proximal medullary canal. The classical CFI is defined as the ratio of the intra-cortical width of the femur, at the section 200 proximal to the lesser trochanter and that of the canal isthmus. Three categories were defined, namely stovepipe, normal and champagne-fluted canals. Other derivatives of the CFI exists, aiming to provide additional information on the medullary flare (Section 6.4.3 on page 114).
Relationship between CFI and pathological conditions in various population groups have been reported (Yang et al., 2005, 2006; Liu et al., 2007; Kawate et al., 2008). Other studies have pointed out the CFI variation in different races (Khang et al., 2003) and age groups (Noble et al., 1995).
Fessy et al. (1997) reported that CFI is one of the important factors in the implant choice in THR
3 derivatives of the classical flare index proposed by previous studies (Sec- tion 6.4.3 on page 114) have also been measured.
Attempts have been made in the usage of Fourier descriptors in the represen- tation of the proximal medullary shape (Section 5.3.2 on page 85). Based on the methods suggested by Kuhl and Giardina (1982), a preliminary study was done in which multiple measurements of the canal width were made and an elliptical Fourier descriptors were applied to construct a shape representation of the canal flare. Instead of using only a ratio of two measurements to quantify the flare, the use of Fourier descriptor takes into consideration of the entire flare shape. It was noted that the Fourier harmonics were able to distinguish a more fine-grained difference such as the concavity of the canal and would be a plausible tool to describe the full canal shape when extended to three dimensional. Nonetheless, even the difference of shapes pair could be quantified by computing the sum of difference between the two harmonics sets, we were unable to conglomerate the harmonics outcome to sort into a specific shape category.
216 9.7. Anteversion Angle
9.7. Anteversion Angle
The anteversion angle is one of the most studied anthropometric parameter and is closely related to total hip replacement. Excessive or insufficient antev- ersion in hip arthroplasty may lead to component impingement, dislocation, subluxation, limited range or motion or aseptic loosening (Masaoka et al., 2006; Kessler et al., 2008; Kleemann et al., 2003).
The anteversion angle involves the definition of two axes, namely the distal transverse axis and the femoral neck axis. With both of the axes not being very well-defined, numerous definitions and methodology exists in the deter- mination of the anteversion angle. The distal posterior condylar axis (Parsons, 1914; Kingsley and Olmsted, 1948) obtained by the tabletop method is by far the most commonly used distal transverse axis. The use of a height gauge (Figure 6.1 on page 100) in the determination of the neck axis Kingsley and Olmsted (1948) has also been extensively applied (Lausten et al., 1989; Kim et al., 2000a; Jain et al., 2003) in anthropometric studies based on osteometric table.
Yoshioka and Cooke (1987) recommended the use of the transepicondylar line as the transverse axis because of less geometric variation involved when compared to the posterior condyles. However, consistency test of our proposed methodology slightly favor the use of the posterior condylar axis especially in the case of repeated scan test with different scanning resolution (Table 8.10 on page 173).
While both the use of the posterior condylar axis and transepicondylar axis in anteversion calculation were statistically consistent in our intra, inter-rater and repeated scan test (ICC > 0.9), it was noted that anteversion angles based on the transepicondylar axis resulted in a slightly larger discrepancy.
The anteversion angle is not a direct angle between any two axes, but a projected angle on the transverse plane, and thus highly dependent on the viewing perspective. Dunlap et al. (1953) pointed out the influence of the anteversion angle due to the anterior bowing of the femoral shaft. It was suggested that the proximal one fourth of the femur should be used as the longitudinal axis such that the axis bisects the greater trochanter. This forms the basis as to why the proximal femoral shaft was chosen as the longitudinal axis as discussed in section 9.5.1 on page 202.
217 9. Discussion
Figure 9.2.: Posterior bow at the femoral metaphysis Reproduced from Noble et al. (1988).
Notwithstanding, most anthropometric studies (Kingsley and Olmsted, 1948; Lausten et al., 1989; Kim et al., 2000a; Jain et al., 2003) have chosen to adopt the full femoral shaft as the longitudinal axis implicitly or explicitly. We anticipate that it could be due to the simple and well-defined tabletop method proposed by Kingsley and Olmsted (1948), in which the longitudinal axis is implicitly close to the full femoral shaft axis. The difficulty in defining the proximal femoral axis on an osteometric table would possibly limit the use of the proximal femoral axis for practicability reason.
One interesting and less documented parameter measured is the proximal metaphysis posterior bowing. Noble et al. (1988) documented the observation of a compensating posterior bow at the proximal femoral metaphysis that leads to an average anteroposterior displacement of 8 mm between the medullary axis and the cross-sectional centroid at the site of conventional neck osteotomy. An angle α was defined as the angle between the anterior and posterior bow intersection (Figure 9.2). Nishihara et al. (2003) followed the method suggested and reported a larger α angle in dysplastic femora while both authors did not present a precise definition of how the posterior bow is being measured. Most other studies (Barsoum et al., 2007) briefly documented the existence of a proximal posterior bowing in femoral stem design without much quantitative information given.
In an attempt to evaluate the angle α, it was discovered that a clear and consistent definition could not be made. There was no anatomical landmark with which a reference datum point could be defined, and the angle is highly
218 9.7. Anteversion Angle dependent on the viewing perspective or the rotational alignment of the femur. Instead, the anteroposterior elevation of the neck axis based on the proximal femoral axis delivers a more consistent and well-defined measurement.
A mean neck axis elevation of 10.7 mm (Range: 7.6–15.0 mm) was observed in our Australian dataset while a mean of 8.6 mm (Range: 6.0–9.9 mm) was recorded in our Japanese dataset and is statistically different (P=0.002).
From a geometric point of view, the elevation of the femoral neck may sig- nificantly affect the anteroposterior offset of the femoral head. With an average anteversion angle of 10◦ with reference to the transepicondylar axis (∠(NA ,TEA )) and an average neck length of 50 mm observed, the anterior ◦ femoral head offset due to femoral neck anteversion alone is 8.7 mm (50×sin10 ). Compare with an average neck axis elevation of 10.7 mm, it is deduced that the anterior femoral head offset with reference to the proximal femoral axis is a resultant effect of both the femoral neck anteversion and the neck anterior offset.
With the assumption of our longitudinal axis being closely aligned to the long axis of the femoral component in THR, it may imply the need to apply additional anteversion on the femoral component that has none or insufficient anterior neck offset, to achieve the necessary anterior offset of the femoral head to mimic the original hip morphology. A comparison between the commonly used neck anteversion angle and the anteversion computed using the femoral ◦ ◦ axis (∠(HCF A,TEA ), ∠(HCF A,CA )) revealed a mean difference of 15 and 10 in our Australian and Japanese datasets respectively. This implies if the same anterior femoral head offset is to be obtained, an additional 10◦–15◦ of anteversion would need to be applied to the femoral component in THR. It was noted that some hip arthroplasty systems (e.g. the Zimmer APR Hip System) incorporate a 10◦of anteversion into their femoral stem design. Several clinical studies (Gill et al., 2002; Barsoum et al., 2007) have pointed out that an increase in the anteversion by 10◦–20◦ on the femoral component increases stability and possibly reduce the chance of impingement or dislocation. From a morphological point of view, It is felt that one of the reasons of the act may be back-traced to the basic principle in the attempt to restore a closer original morphological structure of the femur.
A few studies (Husmann et al., 1997; Argenson et al., 2002) documented measurements of the helitorsion angle which is the torsion angle between the posterior condyle axis and the cross-sectional plane 20 mm proximal to the
219 9. Discussion
Figure 9.3.: The helitorsion angle compared to the anteversion angle. Reproduced from Husmann et al. (1997).
Figure 9.4.: The use of full femoral shaft as the longitudinal reference axis in determination of the anteversion angle. Under this reference system, the long axis of the femur and the femoral neck axis are in close proximity in the superior view and neck axis elevation is virtually non-existent. Reproduced from Moore (2007). lesser trochanter. Husmann et al. (1997) pointed out 25% of his dataset has an anteversion helitorsion difference of larger than 10◦. While the definition of helitorsion is different from our definition of the neck axis elevation, it was observed that the angular difference could possibly be affected by the elevation of the neck axis over the proximal femoral axis.
With reference to the comparison done using a different longitudinal reference axis (Section 8.3.2 on page 177), it was noted that the anterior displacement of the neck axis changed significantly from an average of 9 mm (proximal femoral shaft as reference) to -2.6 mm (full femoral shaft as reference), which lead to a reasonable general assumption that the neck axis crosses the femoral axis as shown in figure 9.4. The negligible neck axis displacement when adopting the full femoral shaft as the reference longitudinal axis may explain why the parameter is seldom studied in literature.
220 9.8. Sheep Femur
9.8. Sheep Femur
19 adult crossbred wethers femur were processed successfully without the need of modification of the core methodology proposed. Several parameters were scaled down due to a smaller-sized femur in sheep in the process of evaluating the reference axes, and were all adjustable in the GUI. The main aim of the inclusion of sheep femur is to demonstrate the robustness of the methodology and also to initialize a database to systematically record anthropometric parameters in sheep femur, which is a common animal model being used in the field of Orthopaedics.
It was noted that while the sheep femur may have distinct difference when compared to that of healthy human, structural similarity exist. The same applies to human femur with pathological conditions. This explains the robust- ness of relying on a structural method in the measurement of anthropometric parameters. For instance, the use of morphological skeletonization in the initial estimation of the neck axis offers a more adaptive approach to accom- modate variations observed in sheep, and human with pathological conditions without the need of manual tuning.
While the sheep and human femur share a similar coarse structure, several distinguishable differences were observed. The femoral neck of sheep tends to fan out asymmetrically to a larger extent and is relatively more flattened in the coronal plane. This implies the reliance on a single cross-section in the determination of the neck axis could be error prone. The use of a cylindrical representation of the region were also discovered not optimal for the case, as discussed previously (Section 9.6.2 on page 208).
The use of transepicondylar axis (TEA) as a rotational reference may not be optimal in the case of sheep because of the relatively large indistinguishable prominence of the epicondyles. Manual selection based on the fallback TEA estimation was always necessary, and even so, it was observed that the inconspicuous epicondyles caused extra difficulty in the selection. The use of the posterior condylar axis in the evaluation of the anteversion angle would be more accurate.
The spherical surface of the femoral head in sheep is less than that of human. This may explain the more restricted range of motion in hip joint of sheep when comparing to that of human. The use of optimization procedures in the sphere fitting procedure in the representation of sheep femoral head would
221 9. Discussion be an advantage here due to the fact that direct measurements on the partial sphere surface may not be feasible.
Another major difference apart from the general size is the canal flare index.
The mean value of CFIml is between 3 to 4 in our human dataset, and coincides with the literature (Noble et al., 1988; Laine et al., 2000) while the value observed in our sheep dataset is of a much lower value of 1.84, which is categorized as stovepipe. This may have an influence on the selection or design in the use of sheep model for study involving femoral stem.
Apart from a demonstration on the robustness of the proposed methodology, the future application of the methodology on sheep femur would enable a more detailed and quantitative summary on its morphology, which would possibly deliver valuable information in future experimental design in the use of sheep as an animal model in orthopaedic studies.
222 10
Conclusions
methodology has been developed and implemented in the extraction of A anthropometric parameters of the femur. This provides a robust platform for future anthropometric analysis (Section 7.5 on page 158).
The method was tested to have a very high intra, inter and repeated scan consistency. This could be attributed to several causes. The extensive use of functional methods instead of direct reliance on anatomical landmarks significantly reduce the effect of possible variations in anatomical landmarks location. Parameters evaluated based on a functional method such as the cylindrical fitting of the posterior condyles has shown to have, in general, a higher ICC and Cronbach’s α when compared to other parameters such as the CFI.
The use of functional methods together with the structural approach further allowed the proposed methodology to process the osteoarthritis datasets, in which deformation of the proximal femoral geometry is common. It was observed that in processing femurs with pathological conditions, assumptions on the absolute locations of anatomical features may no longer hold true, and more adaptive techniques were necessary. For instance, the application of morphological skeletonization in the first estimation of the neck axis have proven to deliver an adaptive technique catering a diverse range of femoral geometry.
The robustness of the proposed method was further demonstrated by the application to the sheep femoral datasets. With sheep being used as a common animal model in orthopaedics in, for instance, femoral implant testing, a comprehensive understanding of the femoral geometry of sheep would be advantageous.
223 10. Conclusions
Automation in the anthropometric parameter extraction stage has also be achieved. While the proposed methodology is not fully automated, very few user interactions were necessary.
10.1. Limitations and Future Directions
While the consistency tests conducted resulted in very high consistency within our intra-rater, inter-rater test settings in segmentation, the image segmenta- tion stage was expected to be still the main source of inconsistency. Attempts have been made to automate the image segmentation step without much suc- cess. Further investigation on the improvements towards a more automated segmentation algorithm would be desirable.
It was noted that the use of CT in the study may not be optimal. CT is inherently poor in imaging articular cartilages, posing a limitation in which the cartilage structure would be ignored in anthropometric studies. MRI has been another emerging image modality with which articular cartilages could be imaged. Quantitative CT has also proven to provide accurate BMD information in additional to bone geometry. The combination of bone morphology and accurate 3-D BMD figures may be a new ground in areas such as fracture risk prediction. Further investigation on the incorporation of other imaging modalities in the study would be desirable.
As a proof of concept, the primary use of the CT datasets in this study is to demonstrate the robustness of the proposed methodology. It has to be admitted that the small sample size, and the lack of detailed biological information on part of the datasets are limitations of the work. Due to this limitation, direct anthropometric comparison between literature and our datasets was not performed. Even though many of our measurement results fall within the coarse range of that reported in the literature, further conclusions shall not be made at this stage because of a lack of statistical power.
Likewise, the number of sheep samples may not be sufficient to quantify the morphological properties and its variations in the present study. A larger dataset would be necessary to further unleash the full potential of the proposed methodology in anthropometric analysis.
224 A
Function Summary
225 A. Function Summary Sub- functions file Calls in from Calls to subroutines. 93 1 194 15 0 1 1 16 1 211 3173 1 2 19 1 1 19 1 103 0 1 17 2 1326 33 0 154 66 1263 0 1 155 10 Lines Calls Identify corners of an image 407 0 1 51 6 Description The main function initiatingGUI and the callback functions Apply affine transformation based on the longitudinal and transverse reference axes Detect whether theproximal CT or distal stack starting is Resize the CT volume toest the bounding small- box Compute the Voronoi diagram, and the largest inscribed circle Cylinder fittingLorentzian based minimization function onRemove the outliers of a serieson based their deviation from the mean Table A.1.: Function summary of the Matlab corner cvoronoi cylinder_fit deleteoutliers Name (m-file) crop_bone_mask align_model_axis femur_anthro_gui bone_orientation_detection
226 Table A.1.: Function summary of the Matlab subroutines. Name (m-file) Description Lines Calls Calls Calls in Sub- to from file functions
drawedgelist Draw lines connecting consecutive 89 0 1 14 1 2-D coordinates est_lesser_trochanter Second estimation of the lesser 119 5 1 20 1 trochanter by locating the most prominent point away from the proximal femoral axis
euclidean_distance Compute the euclidean distance be- 35 0 1 4 1 tween points
export_to_file Export results to delimited text file 244 2 1 7 1
export_to_mat Export results to mat file format 46 0 1 5 1 export_workspace Export entire Matlab workspace 50 0 1 6 1 to file
extrema Compute the global maxima points 146 0 2 14 1 from a time series
find_anterior_bow Compute the radius of curvature of 100 5 1 10 1 the anterior bow 227 find_anteversion_angle Calculate the anteversion angles 54 1 1 4 1 A. Function Summary Sub- functions file Calls in from Calls to subroutines. 70 2 159 14 0 2 1 13 1 89 0 1 8 1 115 0135 2 0 7 1 1 9227 8 1 1317 33 6 1 1 44 1 Lines Calls Description Estimate the best-fitbased on 2-D a circle listdinates of input 3-D coor- Estimate the best-fit 3-D planea on set of 3-D coordinates Compute the canal flare indicesthe of proximal femoral shaft Cylinder fitting tocondyles the posterior Compute the posterior tangential line touching the medialeral and condyles lat- Construct thebased epicondylar on the medial axis and lateralcondyles epi- on a list of input 3-D coordinates Table A.1.: Function summary of the Matlab Name (m-file) find_best_fit_circle find_best_fit_plane find_best_fit_sphere Estimate the best-fit sphere based find_condylar_cyl_fit find_epicondylar_axis find_canal_flare_index find_condylar_tangential_line
228 Table A.1.: Function summary of the Matlab subroutines. Name (m-file) Description Lines Calls Calls Calls in Sub- to from file functions
find_femoral_axis Evaluate the femoral axis by fitting 119 4 2 21 1 a best-fit line using singular value decomposition find_femur_length Compute various measures of the 28 1 1 3 1 femoral length find_greater_trochanter Locate the superior tip of the 61 3 1 13 1 greater trochanter find_greater_trochanter_height Compute the height of the supe- 79 3 2 25 1 rior tip of the greater trochanter to the trough between the femoral head and the proximal aspect of the trochanter
find_head_centre Evaluate the femoral head centre 200 5 1 26 1 find_head_epicondylar_dist Measure the perpendicular dis- 29 1 1 3 1 tance from the femoral head to the epicondylar axis 229 A. Function Summary Sub- functions file Calls in from Calls to subroutines. 20 131 1 1 3 1 1 3 1 47 3 1 9 1 191 2 1241 4 15 1 1 399 34 5 1 1 33 1 Lines Calls Description Compute the offsetfermoal between the headtrochanter and and femoral axis theMeasure the lesser distance between the lesser trochanter and the epicondy- lar axis First estimationtrochanter of by locating theposterio-medial the coordinates lesser along most the femoral shaft Compute cross-sectional properties of the resliced femoral neckimages binary Evaluate the posterioraxis condylar Compute cross-sectional properties of the femoral shaft Table A.1.: Function summary of the Matlab Name (m-file) find_neck_props find_head_offset find_section_props find_lesser_trochanter find_post_condylar_axis find_lesser_tro_epicondylar_dist
230 Table A.1.: Function summary of the Matlab subroutines. Name (m-file) Description Lines Calls Calls Calls in Sub- to from file functions
find_shaft_section_props Compute cross-sectional properties 173 3 1 16 1 of the proximal femoral shaft find_skel_intersection Determine the locations of the in- 97 2 1 19 1 tersection points on a morphologi- cal skeleton
findn A helper function to find the index 33 0 1 6 1 in an 3-D matrix satisfying certain criteria
fix_bone_orientation Flip the imported CT to a proximal- 37 1 2 5 1 starting and anterior-top position gen_circle Generate coordinates of a circle 20 0 1 6 1 with a given centre coordinates and radius get_files Dialog box for selection of input 47 0 1 7 1 files gui_disp Print message to the output pane 45 1 27 15 1 231 on the GUI A. Function Summary Sub- functions file Calls in from Calls to subroutines. 26 0 278 7 1 1 184 3 092 1 1 2 9 1 1 13 1 25 0 1 7 1 104 1 1 10 1 280 0 1 34 8 Lines Calls workspace Description Print message to the message pane on the GUI Compute the optimal assignment by means ofline connecting segments straight Load the binary bone maskCOM in format DI- Helper function to findof the maximum deviation point from ajoining line the endpoints of an edge Crop the bone matrix toest the bounding small- box Compute an estimation of an edge with the Hungarian method. Table A.1.: Function summary of the Matlab lineseg gui_msg hungarian maxlinedev Name (m-file) load_bone_mask import_workspace Import Matlab recrop_bone_mask
232 Table A.1.: Function summary of the Matlab subroutines. Name (m-file) Description Lines Calls Calls Calls in Sub- to from file functions
reslice_neck Reslice the neck region such that 587 7 1 51 1 the cross-sections are perpendicu- lar to the long axis of the neck
sim_xray_dexa Illustration a flattened image of dif- 175 1 1 27 6 ferent orientation sortclasses Group list of coordinates based on 137 0 1 6 1 its connectivity split Split a string into smaller strings 18 0 1 2 1 based on the locations of delimiter
tomm Convert coordinates unit from pixel 29 0 16 5 1 to millimeter
topixel Convert coordinates unit from mil- 25 0 11 5 1 limeter to pixel trochlear_groove_analysis Compute the best-fit plane on the 209 3 1 36 1 trochlear groove region 233 A. Function Summary Sub- functions file Calls in from Calls to subroutines. 48 0 0 4 1 48 0 0 4 1 81 0 1 24 3 449 0 8 70 6 Lines Calls interface Description Alternative dialog boxple for mulit- input files selection with a Dialog box for multiple inputselection files Display a progress bar forprocess lengthy Helper function to write text to file Java Table A.1.: Function summary of the Matlab write waitbar uigetfiles uiGetFiles Name (m-file)
234 Subroutine name Author Company/Affiliation Date arrowPlot.m Emmanuel P. Dinna 2005 corner.m He Xiaochen HKU EEE Dept. ITSR 2005 cvoronoi.m Novaski & Barczak 1997 deleteoutliers.m Brett Shoelson 2003 drawedgelist.m, Peter Kovesi School of Computer 2006 lineseg.m, Science & Software maxlinedev.m Engineering. The University of Western Australia extrema.m Carlos Adrián Vargas Universidad De 2004 Aguilera Guadalajara, Mexico fEfourier.m, David Thomas 2006 rEfourier.m hungarian.m Alex Melin 2006 lmin.m, lmax.m Serge Koptenko Guigne International 1997 Ltd. MagnetGInput.m Michael Robbins 2003 save2pdf.m Gabe Hoffmann 2007 split.m Gerald Dalley 2004 uiGetFiles.m Shanrong Zhang Department of 2004 Radiology, University of Texas Southwestern Medical Center uipickfiles.m Douglas M. Schwarz 2006 waitbar.m Peder Axensten 2006 euclidean_distance.m Alister Fong 2003 sortclasses.m Siew Teng Lee 2003
Table A.2.: External Matlab subroutines used in the study. They are obtain- able from the Mathworks File Exchange repository.
235 A. Function Summary
236 B
Sample Output File
Listed below is a sample output file generated by the subroutines. The file contains results of the anthropometric parameters extracted, exact coordinates of various landmarks and error of fitting functions. It is saved in a tab- delimited plain text format and could be imported to various spreadsheet or statistical analysis software packages for further processing. For clarity purpose, the file output is splitted into various tables.
File /file_path/anonymous
Pixel Spacing (mm)
xy 0.27
z2
Orientation
ap anterior
lr right
start proximal
Femoral axis ref point 60.49,41.38,124.12
Lesser trochanter 35.11,54.26,70.00
Greater trochanter
coords 70.21,36.60,14.00
height 12
237 B. Sample Output File
base_coords 63.00,21.21,26.00
Head
centre 21.82,22.72,21.34
radius 20.52
error 0.73
fa_offset 42.94
lt_offset 48.66
Posterior Condyles
cylinder
vector 0.99,-0.12,-0.02
pt 49.37,101.88,411.86
radius 19.45
err 1.2
knee_centre 46.02,89.64,426.00
axis
mpt 28.73,123.96
lpt 70.22,118.90
Neck axis start coords 21.70,22.27,21.66
Neck length to FA 48.99
Neck length to lateral GT 71.71
Neck shaft angle 125.12
Neck axis elevation 8.79
Neck axis to head centre distance 0.57
Anteversion angles
TEA_CA 6.94
238 HC_FA_TEA 25.77
HC_FA_CA 32.71
NA_TEA 14.93
NA_CA 21.87
Trochlear groove plane 1.00,-0.19,-0.08,0.00
Trochlear groove angle -3.39
Anterior bow centre 53.60,1188.41,95.31
Anterior bow radius 1149.61
Femoral length
GTKC 416.1
HCKC 410.87
Head centre epicondylar distance 391.75
Lesser trochanter epicondylar distance 338.83
Canal flare indices
isthmus_LT_dist 104
ml 3.55
ap 2.26
oblique 1.21
metaphyseal_ml 0.41
239 B. Sample Output File 12345678910 12345678910 30.4 30.4 30.4 30.59 30.68 30.83 31.03 31.29 31.43 31.43 -623 -565 -1694 -1543 -930 527 2542 3436 2992 3618 1435 1427 1425 1409 1385 1340 1296 1226 1171 1101 39.21 39.19 39.17 39.26 39.37 39.32 39.34 39.25 39.32 39.17 171931 169673 167242 163760 158087 150143 142842 132067 121406 109777 157127 155262 156870171904 153480 169651 148485 166965 136900 163529 126670 157997 110205 150122 142442 99633 131527 86212 120995 109222 Ixx Iyy Ixy Ip1 moi Area slice_no Centroid polar_moi 329032 324913 323835 317009 306482 287022 269112 241731 220628 195434 princ_angle -0.04 -0.04 -0.16 -0.15 -0.1 0.04 0.16 0.16 0.14 0.15 Orientation 87.59 87.75 80.72 81.47 84.47 -87.72 -81.07 -81.07 -82.18 -81.27 Eccentricity 0.29 0.29 0.25 0.25 0.25 0.3 0.34 0.41 0.43 0.47 mm_from_head MajorAxisLength 43.8 43.63 43.35 43.14 42.75 42.36 42.01 41.53 40.75 39.96 MinorAxisLength 41.87 41.74 41.95 41.73 41.42 40.44 39.5 37.85 36.84 35.3 Neck section properties
240 Ip2 157101 155240 156593 153248 148395 136879 126270 109665 99222 85657 241 B. Sample Output File 25 27 29 31 33 35 37 39 41 50 54 58 62 66 70 74 78 82 927 833 762 708 685 644 539 438 333 -0.2 -0.2 -0.11 0.16 0.35 0.45 0.48 0.45 0.11 61.3 60.1 59.1 57.7 56.6 56.3 56.6 57.8 59.3 62.3 61.2 60.3 59.1 57.5 56.6 57.2 58.6 60.5 36.0 37.036.6 38.2 37.8 39.6 39.0 40.8 40.4 41.6 41.9 42.0 43.0 41.6 42.8 40.7 42.4 41.0 1348 1202 1120 1098 1090 1058 985 881 769 97403 81887 7564230747 76340 19284 79439 7210 78988 70761 -8574 -20899 57660 -26554 42630 -24671 -13048 -1485 91146 78058 74813 74975 71704 66147 57836 51319 42460 242228 175159 137537 128804 128174 121060 104923 78164 55507 248486 178988 138366 130170 135909 133901 117849 84505 55676 339631 257046 213179 205145 207613 200048 175685 135824 98137 Ixx Iyy Ixy Ip1 Ip2 moi area slice_no centroid can_area polar_moi princ_angle can_centroid mm_proximal Proximal shaft section properties
242 can_moi
Ixx 243651 176747 139278 130947 129023 121112 105329 78686 56722
Iyy 97938 82754 76493 77031 80826 80835 71417 58323 42682
polar_moi 341590 259501 215771 207978 209849 201948 176747 137009 99404
Ixy 31620 20457 8427 -7358 -19814 -26244 -24155 -12459 -1234
princ_angle -0.2 -0.21 -0.13 0.13 0.34 0.46 0.48 0.44 0.09
Ip1 250217 181006 140389 131933 136123 134054 117885 84595 56830
Ip2 91373 78495 75382 76045 73726 67893 58861 52414 42574
gic
x 64.3 62.7 60.4 54.3 55.5 56.9 57.4 58.3 59.0
y 38.8 39.1 39.7 40.1 40.4 40.6 40.6 40.2 39.8
r 16.1 15.6 15.2 15.0 14.6 14.3 13.9 13.6 13.2
gic_can_centroid
r 14.2 14.5 14.6 14.2 12.7 12.0 11.7 11.3 12.0
shaft_curve
medial 35.9 38.6 41.8 43.6 47.1 48.4 49.2 51.6 51.9
lateral 77.1 76.6 75.3 74.2 73.4 72.1 71.8 71.6 71.0 243 B. Sample Output File 25 30 35 40 45 50 55 60 65 70 7.71 6.65 5.32 5.32 6.38 8.51 7.45 8.51 7.98 8.51 61.3 58.4 56.3 58.7 60.2 60.7 60.9 60.9 60.7 60.4 4.52 3.19 3.99 4.52 5.05 6.12 7.18 7.71 8.25 7.45 36.0 38.9 41.6 41.1 40.1 39.9 39.9 40.1 40.3 40.5 2.93 2.66 3.19 3.99 4.79 5.59 5.59 5.85 5.85 6.12 91146 75338 66147 47703 29798 23229 21067 20540 21067 20900 97403 75344 7898830747 49833 -589 30121 24502 -26554 22915 22742 -6067 23825 1697 24168 3048 3512 3720 3855 3838 248486 131278 133901 67112 39033 31795 29588 29026 29214 28675 242228 131272 121060 64982 38709 30522 27740 26824 26456 25408 Ixx Iyy Ixy Ip1 Ip2 moi lateral medial slice_no anterior centroid polar_moi 339631 206616 200048 114815 68830 55024 50655 49566 50280 49576 princ_angle -0.2 0.01 0.45 0.34 -0.19 -0.4 -0.48 -0.53 -0.62 -0.71 mm_proximal 50 60 70 80 90 100 110 120 130 140 cortical_thickness Shaft section properties
244 posterior 1.33 2.13 2.13 3.19 3.46 5.05 5.32 6.12 6.92 6.65
area 1348 1106 1058 823 652 583 559 553 557 553
can_area 927 733 644 386 227 171 149 135 120 118
can_eccentricity 0.74 0.63 0.85 0.75 0.37 0.39 0.57 0.61 0.58 0.58
can_orientation -12.6 9.5 31.6 36.2 23.9 -67.5 -56.4 -59.7 -63.3 -65.5 245 B. Sample Output File
246 C
CT Acquisition Settings
247 C. CT Acquisition Settings (mA) Current X-ray Tube modulation 120 auto 120 150 120 180 120120 150 120 150 180 120120 150 180 120120 150 180 120 180 120 150 KV) KVP (Peak 1 2 2 2 1 1 2 2 2 1 2 1 Slice (mm) Thickness Pixel (mm) Spacing Time (ms) Scanner Exposure Toshiba Asteion 750Toshiba Asteion 750 0.36 Toshiba Asteion 750 0.27 0.38 Toshiba Asteion 750Toshiba Asteion 750 0.26 0.4 Toshiba Asteion 750Toshiba Asteion 750 0.36 Toshiba Asteion 0.31 750Toshiba Asteion 0.38 750 0.25 ID 71L 99L 67L 68L 07L 71R 48R 67R 78R 67L-2 Toshiba Asteion 750 0.26 67R-2 Toshiba Asteion 750 0.29 Australian dataset All Japanese dataset Toshiba Aquilion 500 0.63
248 21R Toshiba Asteion 750 0.28 2 120 150
OBL Toshiba Asteion 750 0.25 2 120 150
03R Toshiba Asteion 750 0.47 1 120 80
04R Toshiba Asteion 750 0.28 2 120 150
06R Toshiba Asteion 750 0.26 2 120 150
14L Toshiba Asteion 750 0.26 2 120 150
22L Toshiba Asteion 750 0.34 2 120 150
22L-2 Toshiba Asteion 750 0.25 1 120 80
EDR Toshiba Asteion 750 0.27 2 120 150
TTR Toshiba Asteion 750 0.25 2 120 150
W5L Toshiba Asteion 750 0.44 1 120 180
W4R Toshiba Asteion 750 0.34 1 120 180
All sheep dataset Toshiba Asteion 750 0.24 0.5 120 80 249 C. CT Acquisition Settings
250 D
Consistence Test Data
251 D. Consistence Test Data Table D.1.: Intra-rater consistency data. 9 9 9 9 13 12 12 12 14 16 17.8 17.8 17.9 18.0 22.6 22.1 22.0 23.0 19.9 20.6 40.3 40.3 42.562.7 42.2 62.8 58.6 67.8 58.6 68.2 52.2 88.9 53.9 88.5 48.4 86.0 46.3 86.6 73.7 71.5 ID 53R 53R-2 28R 28R-2 67L 67L-2 67R 67R-2 TTR TTR-2 FA Head radius radius 19.8 19.8 20.4 20.3 26.3 26.3 26.4 26.0 22.3 22.6 height Greater lt_offset 39.6 39.6 56.5 54.7 55.0 55.0 52.2 53.2 50.0 49.7 fa_offset 38.8 38.8 36.2 36.2 50.4 50.2 49.8 51.2 40.1 39.9 Condyles lateral GT trochanter Neck length to Neck length to D.1. Intra-rater Consistency
252 D.1. Intra-rater Consistency Table D.1.: Intra-rater consistency data. 7.7 7.6 7.8 7.6 9.5 9.7 10.8 10.5 9.2 9.1 0.5 0.5 0.6 0.9 1.9 1.7 1.5 2.2 0.9 1.6 -1.2 -7.1 1.1 1.0 12.2 12.9 -13.8 -12.7 -10.0 -9.6 120.9 120.9 127.8 127.2 124.7 123.2 121.9 122.6 127.5 123.2 ID 53R 53R-2 28R 28R-2 67L 67L-2 67R 67R-2 TTR TTR-2 angle angles NA_CA 41.6 41.6 27.0 27.7 13.1 13.5 30.1 32.3 6.8 9.4 distance TEA_CA 10.2 10.2 9.9 9.9 4.9 9.9 5.8 5.7 4.5 4.1 NA_TEA 31.4 31.5 17.1 17.8 8.2 3.6 24.2 26.6 2.3 5.3 elevation Trochlear Neck axis Neck shaft HC_FA_CA 50.6 50.6 38.1 37.9 21.7 22.6 39.8 40.7 22.1 20.5 head centre Anteversion Neck axis to groove angle HC_FA_TEA 40.5 40.5 28.3 28.0 16.9 12.7 33.9 34.9 17.6 16.4
253 D. Consistence Test Data Table D.1.: Intra-rater consistency data. 774 775 738 747 967 953 854 1235 968 978 111 111 109 108 130 129 125 132 110 108 311.0 311.0 301.1 303.6 365.6 365.3 365.1 360.5 328.1 328.1 355.5 355.5 362.2 363.3 423.6 421.5 423.3 419.0 383.2 382.5 ID 53R 53R-2 28R 28R-2 67L 67L-2 67R 67R-2 TTR TTR-2 ml 5.10 5.10 3.00 3.27 2.97 2.89 3.19 3.18 3.02 2.96 GTKC 376.7 376.7 382.2 382.1 455.9 456.8 454.8 453.2 412.4 412.5 radius HCKC 371.9 371.9 381.2 381.3Lesser 448.0 448.1 445.5 445.1 402.5 401.9 indices distance distance trochanter Canal flare epicondylar epicondylar Head centre Anterior bow Femoral length isthmus_LT_dist
254 D.1. Intra-rater Consistency Table D.1.: Intra-rater consistency data. 0.57 0.57 0.36 0.38 0.40 0.40 0.41 0.41 0.37 0.37 ap 2.23 2.23 2.35 2.35 2.39 2.60 1.78 1.78 2.84 2.77 ID 53R 53R-2 28R 28R-2 67L 67L-2 67R 67R-2 TTR TTR-2 oblique 1.11 1.11 1.18 1.20 1.23 1.29 1.11 1.09 1.31 1.32 metaphyseal_ml
255 D. Consistence Test Data Table D.2.: Inter-rater consistency data. 9 9 10 11 14 14 14 14 12 12 17.94 17.99 17.18 18.07 19.91 20.58 22.84 21.24 21.98 22.01 67.78 67.66 63.05 63.22 73.66 73.88 88.55 89 85.98 85.35 42.47 41.85 39.94 40.85 48.38 48.55 57.9 58.7 52.24 51.44 ID 28R 28R-2 53R 53R-2 TTL TTL-2 67L 67L-2 67R 67R-2 FA Head radius 20.4 20.4 19.5 19.8 22.3 22.5 26.4 26.2 26.4 26.3 height Greater lt_offset 56.5 55.2 40.8 40.3 50.0 49.7 56.1 55.8 52.2 50.2 fa_offset 36.2 36.3 38.9 39.2 40.1 39.8 49.9 50.7 49.8 49.8 Posterior Condyles lateral GT trochanter Neck length to Neck length to Cylinder radius D.2. Inter-rater Consistency
256 D.2. Inter-rater Consistency Table D.2.: Inter-rater consistency data. 1.1 0.3 -2.8 -3.5 -10.0 -9.0 12.6 13.6 -13.8 -8.0 0.6 0.8 0.6 0.5 0.9 1.5 1.9 2.2 1.5 1.6 7.82 7.55 7.86 7.37 9.15 8.68 11.01 9.35 10.79 10.88 127.81 126.56 120.77 120.65 127.46 128.82 124.99 123.97 121.85 120.39 ID 28R 28R-2 53R 53R-2 TTL TTL-2 67L 67L-2 67R 67R-2 angle angles NA_CA 27.0 27.6 41.7 41.5 6.8 10.0 13.4 14.7 30.1 29.8 distance TEA_CA 9.9 9.9 8.8 10.4 4.5 4.1 8.4 7.6 5.8 3.3 NA_TEA 17.1 17.8 32.9 31.1 2.3 5.9 5.0 7.1 24.2 26.4 elevation Trochlear Neck axis Neck shaft HC_FA_CA 38.1 38.0 50.7 50.2 22.1 20.5 24.3 22.8 39.8 39.2 head centre Anteversion Neck axis to groove angle HC_FA_TEA 28.3 28.1 42.0 39.8 17.6 16.4 15.9 15.2 33.9 35.9
257 D. Consistence Test Data Table D.2.: Inter-rater consistency data. 738 747 775 764 968 977 1843 1823 854 884 109 110 111 106 110 108 128 130 125 127 301.1 302.9 310.9 311.0 328.1 328.1 362.6 363.2 365.1 367.1 362.2 362.9 356.8 356.4 383.2 382.5 421.7 421.9 423.3 423.4 ID 28R 28R-2 53R 53R-2 TTL TTL-2 67L 67L-2 67R 67R-2 ml 3.00 3.06 5.27 5.67 3.02 2.92 2.84 2.84 3.19 3.23 GTKC 382.2 382.2 377.5 378.4 412.4 410.5 455.0 455.1 454.8 454.6 radius HCKC 381.2 380.8 372.1Lesser 372.6 402.5 402.0 446.4 446.1 445.5 445.4 indices distance distance trochanter Canal flare epicondylar epicondylar Head centre Anterior bow Femoral length isthmus_LT_dist
258 D.2. Inter-rater Consistency Table D.2.: Inter-rater consistency data. 0.36 0.37 0.52 0.55 0.37 0.37 0.40 0.40 0.41 0.41 ap 2.35 2.35 2.46 2.64 2.84 2.77 2.57 2.59 1.78 1.75 ID 28R 28R-2 53R 53R-2 TTL TTL-2 67L 67L-2 67R 67R-2 oblique 1.18 1.18 1.12 1.13 1.31 1.32 1.25 1.26 1.11 1.10 metaphyseal_ml
259 D. Consistence Test Data Table D.3.: Repeated scans consistency data. 48.58 48.42 44.34 44.94 60.76 61.25 58.62 58.7 52.24 56.01 z 1112211212 xy 0.63 0.63 0.36 0.26 0.34 0.25 0.38 0.26 0.38 0.29 ID 10R 10R-2 14L 14L-2 22L 22L-2 67L 67L-2 67R 67R-2 FA Head (mm) radius 22.89 22.85 22.03radius 21.94 24.72 18.95 25.11 19.09 26.34 18.15 26.21 17.78 26.38 23.59 25.46 22.68 22.6 21.24 21.98 22.71 height 8 8 10 12 16 15 13 14 12 12 lt_offset 50.67 50.01 52.13 53.17 53.18 53.23 54.95 55.77 52.15 51.93 fa_offset 38.19 38.37 35.75 36.19 52.88 53.28 50.44 50.71 49.78 51.73 Pixel Spacing Neck length to D.3. Repeated Scans Consistency
260 D.3. Repeated Scans Consistency Table D.3.: Repeated scans consistency data. 9.16 9.59 11.02 10.8 9.24 8.67 9.53 9.35 10.79 10.04 1.67 1.3 0.89 0.8 1.38 1.72 1.9 2.24 1.53 1.85 71.68 71.56 73.13 71.9 91.55 91.53 88.87 89 85.98 88.17 131.23 130.75 133.14 132.31 123.1 122.95 124.71 123.97 121.85 123.67 ID 10R 10R-2 14L 14L-2 22L 22L-2 67L 67L-2 67R 67R-2 angle angles NA_CA 8.39 7.98 13.51 14.03 10.65 10.61 13.11 14.68 30.07 32.25 distance TEA_CA 6.95 5.91 7.23 12.12 6.06 6.97 4.89 7.61 5.83 8.66 NA_TEA 1.44 2.08 6.28 1.92 4.59 3.64 8.22 7.07 24.24 23.59 elevation Neck axis lateral GT Neck shaft HC_FA_CA 20.24 20.68 34.35 34.6 20.7 20.13 21.74 22.81 39.77 40.7 head centre Anteversion Neck axis to HC_FA_TEA 13.29 14.77 27.12 22.49 14.64 13.16 16.85 15.2 33.94 32.04 Neck length to
261 D. Consistence Test Data Table D.3.: Repeated scans consistency data. -7.7 -9.12 7.37 12.66 12.87 13.43 12.2 13.55 -13.75 -8.17 369.55 367.82 424.68 418.01 450.87 451.89 423.62 421.85 423.33 420.02 316.23 315.33 369.22 363.07 392.37 394.12 365.64 363.15 365.12 362.1 579.79 589.01 1036.56 916.38 1361.75 950.69 966.91 1822.87 853.68 1176.23 ID 10R 10R-2 14L 14L-2 22L 22L-2 67L 67L-2 67R 67R-2 GTKC 392.76 392.33 443.84 446.18 483.95 485.18 455.85 455.11 454.77 453 radius HCKC 388.88 389 442.94Lesser 442.04 475.17 476.56 447.95 446.06 445.52 445.62 indices distance distance Trochlear trochanter Canal flare epicondylar epicondylar Head centre groove angle Anterior bow Femoral length
262 D.3. Repeated Scans Consistency Table D.3.: Repeated scans consistency data. 117 118 121 116 130 128 130 130 125 126 0.39 0.39 0.41 0.42 0.4 0.4 0.4 0.4 0.41 0.4 ap 2.4 2.3 1.51 1.57 2.36 2.36 2.39 2.59 1.78 1.8 ID 10R 10R-2 14L 14L-2 22L 22L-2 67L 67L-2 67R 67R-2 ml 4.2 4.27 3.22 2.98 3.23 3.17 2.97 2.84 3.19 3.1 oblique 1.2 1.2 1.09 1.11 1.24 1.24 1.23 1.26 1.11 1.12 isthmus_LT_dist metaphyseal_ml
263 D. Consistence Test Data
264 E
Results of Parameter Variation
E.1. Variation with Full Femoral Shaft
E.2. Posterior Condyles Slice Range
The first and second slice range of each sample is the reference slice range and the typical maximum erroneous range respectively. The last row of each sample are more extreme slice ranges. Entries marked with an asterisks (*) are ranges that are insufficient to produce an accurate fitting, and are not included in the table.
265 E. Results of Parameter Variation
Slice Condyles ID thickness Slice range Knee centre radius (mm) 2667L 1 430–469 22.5 (46.5, 93, 468) 1 433–466 22.1 (46.9, 93.8, 468) 1 435–469 22.1 (46.5, 96.75, 467) C003R 1 422–453 21.0 (56.2, 96.4, 453) 1 425–450 22.0 (56.6, 94.1, 454) 1 427–453 22.7 (56.6, 94.1, 454) C014L 1 433–461 17.8 (42.5, 98.2, 459) 1 436–458 17.9 (42.5, 97.8, 460) 1 438–461 17.9 (42.8, 97.8, 460) 71cm 2 218–236 22.2 (49.1, 114.6, 470) 2 221–233 24.9 (50.2, 104.0, 472) 2 223–231 na* na* BOB 2 225–240 18.5 (47.0, 41.6, 476) 2 228–237 18.8 (47.2, 41.6, 476) 2 220–235 na* na*
Table E.1.: Effect of condyles radius on the fitting slice range.
266 E.2. Posterior Condyles Slice Range
! !
(a) Proximal femur and posterior condyles ra- (b) Femoral length and anterior bow radius. dius.
Figure E.1.: Variation between the use of proximal femoral shaft and full femoral shaft as reference longitudinal axis.
267 E. Results of Parameter Variation
268 Bibliography
Aamodt, A., Kvistad, K. A., Andersen, E., Lund-Larsen, J., Eine, J., Benum, P., and Husby, O. S. (1999). Determination of hounsfield value for ct-based design of custom femoral stems. J Bone Joint Surg Br, 81(1):143–147. 197
Abel, M. F., Sutherland, D. H., Wenger, D. R., and Mubarak, S. J. (1994). Evaluation of ct-assisted scans and 3-d reformatted images for quantitative assessment of the hip. J Pediatr Orthop, 14(1):48–53. 106
Abraham, W. D. and Dimon, J. H. (1992). Leg length discrepancy in total hip arthroplasty. Orthop Clin North Am, 23(2):201–209. 206
Agren, M., Karellas, A., Leahey, D., Marks, S., and Baran, D. (1991). Ultra- sound attenuation of the calcaneus: a sensitive and specific discriminator of osteopenia in postmenopausal women. Calcif Tissue Int, 48(4):240–244. 113
Alakuijala, J., Laitinen, J., Sallinen, S., and Helminen, H. (1995). New efficient image segmentation algorithm: competitive region growing of initial regions. In Proc. IEEE 17th Annual Conference Engineering in Medicine and Biology Society, volume 1, pages 409–410 vol.1. 44
Anouchi, Y. S., Whiteside, L. A., Kaiser, A. D., and Milliano, M. T. (1993). The effects of axial rotational alignment of the femoral component on knee stability and patellar tracking in total knee arthroplasty demonstrated on autopsy specimens. Clin Orthop Relat Res, (287):170–177. 108
269 Bibliography
Antani, S., Lee, D., Long, L. R., and Thoma, G. R. (2004). Evaluation of shape similarity measurement methods for spine x-ray images. Journal of Visual Communication and Image Representation, 15(3):285–302. 88
Apivatthakakul, T. and Arpornchayanon, O. (2001). Iatrogenic femoral neck fracture caused by mal-insertion of a curved intramedullary nail. Injury, 32(9):727–729. 117
Ardran, G. M. (1979). The application and limitation of the use of x-rays in medical diagnosis. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 292(1390):147–156. 25
Argenson, J., Flecher, X., Ryembault, E., and Aubaniac, J. (2002). Femur morphology in patients with sequelae of congenital hip dislocation: a ra- diographic and computed tomography analysis of 312 cases. J Bone Joint Surg Br, 84-B(SUPP_I):65–c. 219
Arima, J., Whiteside, L. A., McCarthy, D. S., and White, S. E. (1995). Femoral rotational alignment, based on the anteroposterior axis, in total knee arthro- plasty in a valgus knee. a technical note. J Bone Joint Surg Am, 77(9):1331– 1334. 109
Austin, M. S., Hozack, W. J., Sharkey, P. F., and Rothman, R. H. (2003). Stability and leg length equality in total hip arthroplasty. J Arthroplasty, 18(3 Suppl 1):88–90. 206
Ballard, M. E. and Trudell, M. B. (1999). Anterior femoral curvature revisited: race assessment from the femur. J Forensic Sci, 44(4):700–707. 119
Baran, D. T., McCarthy, C. K., Leahey, D., and Lew, R. (1991). Broadband ultrasound attenuation of the calcaneus predicts lumbar and femoral neck density in caucasian women: a preliminary study. Osteoporos Int, 1(2):110– 113. 113
Barnett, E. and Nordin, B. E. (1960). The radiological diagnosis of osteoporosis: a new approach. Clin Radiol, 11:166–174. 115
Barr, R. J., Adebajo, A., Fraser, W. D., Halsey, J. P., Kelsey, C., Stewart, A., and Reid, D. M. (2005). Can peripheral dxa measurements be used to predict fractures in elderly women living in the community? Osteoporos Int, 16(10):1177–1183. 34, 208
270 Bibliography
Barrett, J. F. and Keat, N. (2004). Artifacts in ct: recognition and avoidance. Radiographics, 24(6):1679–1691. 29, 30, 31, 32, 33
Barsoum, W. K., Patterson, R. W., Higuera, C., Klika, A. K., Krebs, V. E., and Molloy, R. (2007). A computer model of the position of the combined component in the prevention of impingement in total hip replacement. J Bone Joint Surg Br, 89(6):839–845. 218, 219
Baumgartner, T. A. and Chung, H. (2001). Confidence limits for intraclass reliability coefficients. Measurement in Physical Education and Exercise Science, 5(3):179–188. 198
Beaulé, P. E., Harvey, N., Zaragoza, E., Duff, M. J. L., and Dorey, F. J. (2007). The femoral head/neck offset and hip resurfacing. J Bone Joint Surg Br, 89(1):9–15. 207
Beck, T. (2003). Measuring the structural strength of bones with dual-energy x- ray absorptiometry: principles, technical limitations, and future possibilities. Osteoporos Int, 14 Suppl 5:S81–S88. 112, 209
Berger, R. A., Rubash, H. E., Seel, M. J., Thompson, W. H., and Crossett, L. S. (1993). Determining the rotational alignment of the femoral component in total knee arthroplasty using the epicondylar axis. Clin Orthop Relat Res, (286):40–47. 103, 205
Bergot, C., Bousson, V., Meunier, A., Laval-Jeantet, M., and Laredo, J. D. (2002). Hip fracture risk and proximal femur geometry from dxa scans. Osteoporosis International, 13(7):542–550. 111, 209
Bertollo, N. (2007). Investigation of the effects which the removal of the central one-third of the patella tendon in an ovine model has on patellar position and knee kinematics. PhD thesis, School of Medicine, University of New South Wales, Australia. 214
Bertram, J. E. and Swartz, S. M. (1991). The ’law of bone transformation’: a case of crying wolff? Biol Rev Camb Philos Soc, 66(3):245–273. 9
Besier, T. F., Sturnieks, D. L., Alderson, J. A., and Lloyd, D. G. (2003). Repeatability of gait data using a functional hip joint centre and a mean helical knee axis. J Biomech, 36(8):1159–1168. 122, 194, 199, 215
271 Bibliography
Billing, L. (1954). Roentgen examination of the proximal femur end in children and adolescents; a standardized technique also suitable for determination of the collum-, anteversion-, and epiphyseal angles; a study of slipped epiphysis and coxa plana. Acta Radiol Suppl, 110:1–80. 105
Blankevoort, L., Huiskes, R., and de Lange, A. (1990). Helical axes of passive knee joint motions. J Biomech, 23(12):1219–1229. 119, 212
Blumenkrans, A. (1991). Two-dimensional object recognition using a two- dimensional polar transform. Pattern Recognition, 24(9):879–890. 88
Boland, G. W., Lee, M. J., Gazelle, G. S., Halpern, E. F., McNicholas, M. M., and Mueller, P. R. (1998). Characterization of adrenal masses using unen- hanced ct: an analysis of the ct literature. AJR Am J Roentgenol, 171(1):201– 204. 196
Bose, W. J. (2000). Accurate limb-length equalization during total hip arthro- plasty. Orthopedics, 23(5):433–436. 207
Boufous, S., Finch, C. F., and Lord, S. R. (2004). Incidence of hip fracture in new south wales: are our efforts having an effect? Med J Aust, 180(12):623– 626. 111, 112, 208
Bourne, R. B. and Mehin, R. (2004). The dislocating hip: what to do, what to do. The Journal of Arthroplasty, 19(4, Supplement 1):111–114. 206
Bousson, V., Le Le Bras, A., Roqueplan, F., Kang, Y., Mitton, D., Kolta, S., Bergot, C., Skalli, W., Vicaut, E., Kalender, W., Engelke, K., and Laredo, J.-D. (2006). Volumetric quantitative computed tomography of the proximal femur: relationships linking geometric and densitometric variables to bone strength. role for compact bone. Osteoporosis International, 17(6):855–864. 113
Bouxsein, M. and Karasik, D. (2006). Bone geometry and skeletal fragility. Current Osteoporosis Reports, 4(2):49–56. 209
Bras, A. L., Laporte, S., Bousson, V., Mitton, D., Guise, J. A. D., Laredo, J. D., and Skalli, W. (2004). 3d reconstruction of the proximal femur with low-dose digital stereoradiography. Comput Aided Surg, 9(3):51–57. 112
Breathnach, A. S. (1965). Frazer’s Anatomy of the Human Skeleton.J.&A. Churchill., London, 6th edition. 14
272 Bibliography
Bribiesca, E. (1999). A new chain code. Pattern Recognition, 32(2):235–251. 84, 85
Bribiesca, E. (2000). A chain code for representing 3d curves. Pattern Recog- nition, 33(5):755–765. 84
Bribiesca, E. and Guzman, A. (1980). How to describe pure form and how to measure differences in shapes using shape numbers. Pattern Recognition, 12(2):101–112. 84
Caffery, L. and Manthey, K. (2004). Implementation of a web-based tel- eradiology management system. J Telemed Telecare, 10 Suppl 1:22–25. 40
Canny, J. (1986). A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell., 8(6):679–698. 56
Cappozzo, A. (1984). Gait analysis methodology. Human Movement Science, 3(1-2):27–50. 122
Chan, T. (1996). Optimal output-sensitive convex hull algorithms in two and three dimensions. Discrete and Computational Geometry, 16(4):361–368. 75
Chen, Y., Ee, X., Leow, W., and Howe, T. (2005). Automatic extraction of femur contours from hip x-ray images. Computer Vision for Biomedical Image Applications, pages 200–209. 114, 197, 198
Cheng, X. G., Lowet, G., Boonen, S., Nicholson, P. H., Brys, P., Nijs, J., and Dequeker, J. (1997a). Assessment of the strength of proximal femur in vitro: relationship to femoral bone mineral density and femoral geometry. Bone, 20(3):213–218. 113
Cheng, X. G., Nicholson, P. H., Boonen, S., Brys, P., Lowet, G., Nijs, J., and Dequeker, J. (1997b). Effects of anteversion on femoral bone mineral density and geometry measured by dual energy x-ray absorptiometry: a cadaver study. Bone, 21(1):113–117. 35
Christie, J. and Court-Brown, C. (1988). Femoral neck fracture during closed medullary nailing: brief report. J Bone Joint Surg Br, 70(4):670. 117
Churchill, D. L., Incavo, S. J., Johnson, C. C., and Beynnon, B. D. (1998). The transepicondylar axis approximates the optimal flexion axis of the knee. Clin Orthop Relat Res, (356):111–118. 120, 121, 183, 213, 214, 215
273 Bibliography
Colopy, S. A., Benz-Dean, J., Barrett, J. G., Sample, S. J., Lu, Y., Danova, N. A., Kalscheur, V. L., Vanderby, R., Markel, M. D., and Muir, P. (2004). Response of the osteocyte syncytium adjacent to and distant from linear microcracks during adaptation to cyclic fatigue loading. Bone, 35(4):881–891. 8
Cootes, T. F., Taylor, C. J., Cooper, D. H., and Graham, J. (1995). Active shape models—their training and application. Comput. Vis. Image Underst., 61(1):38–59. 58
Coventry, E., O’Connor, K. M., Hart, B. A., Earl, J. E., and Ebersole, K. T. (2006). The effect of lower extremity fatigue on shock attenuation during single-leg landing. Clin Biomech (Bristol, Avon), 21(10):1090–1097. 214
Cowin, S. (1997). The false premise of wolff’s law. Forma, 12:247–262. 9
Croce, U. D., Cappozzo, A., and Kerrigan, D. C. (1999). Pelvis and lower limb anatomical landmark calibration precision and its propagation to bone geometry and joint angles. Med Biol Eng Comput, 37(2):155–161. 98, 122, 194, 199, 214, 215
Cronbach, L. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3):297–334. 201
Crowe, B. and Sim, L. (2004). Implementation of a radiology information system/picture archiving and communication system and an image transfer system at a large public teaching hospital–assessment of success of adoption by clinicians. J Telemed Telecare, 10 Suppl 1:25–27. 40
Cummings, S. R., Black, D. M., Nevitt, M. C., Browner, W., Cauley, J., Ensrud, K., Genant, H. K., Palermo, L., Scott, J., and Vogt, T. M. (1993). Bone density at various sites for prediction of hip fractures. the study of osteoporotic fractures research group. Lancet, 341(8837):72–75. 208
Davey, J. R., O’Connor, D. O., Burke, D. W., and Harris, W. H. (1993). Femoral component offset. its effect on strain in bone-cement. J Arthroplasty, 8(1):23– 26. 206, 207
Dehmeshki, J., Amin, H., Valdivieso, M., and Ye, X. (2008). Segmentation of pulmonary nodules in thoracic ct scans: A region growing approach. IEEE Transactions on Medical Imaging, 27(4):467–480. 45
274 Bibliography
Delgado-Martínez, A. D., Rodríguez-Merchán, E. C., Ballesteros, R., and Luna, J. D. (2000). Reproducibility of patellofemoral ct scan measurements. Int Orthop, 24(1):5–8. 198
Dorr, L. D., Absatz, M., Gruen, T. A., Saberi, M. T., and Doerzbacher, J. F. (1990). Anatomic porous replacement hip arthroplasty: first 100 consecutive cases. Semin Arthroplasty, 1(1):77–86. 115
Dunlap, K., Shands, A. R., Hollister, L. C., Gaul, J. S., and Streit, H. A. (1953). A new method for determination of torsion of the femur. J Bone Joint Surg Am, 35-A(2):289–311. 98, 102, 104, 157, 194, 202, 203, 217
Dwight, T. (1905). The size of the articular surfaces of the long bones as characteristic of sex; an anthropological study. American Journal of Anatomy, 4(1):19–31. 110
Edeen, J., Sharkey, P. F., and Alexander, A. H. (1995). Clinical significance of leg-length inequality after total hip arthroplasty. Am J Orthop, 24(4):347– 351. 207
Egol, K. A., Chang, E. Y., Cvitkovic, J., Kummer, F. J., and Koval, K. J. (2004). Mismatch of current intramedullary nails with the anterior bow of the femur. J Orthop Trauma, 18(7):410–415. 108, 117, 118, 119
El-Kaissi, S., Pasco, J., Henry, M., Panahi, S., Nicholson, J., Nicholson, G., and Kotowicz, M. (2005). Femoral neck geometry and hip fracture risk: the geelong osteoporosis study. Osteoporosis International, 16(10):1299–1303. 111, 208
Elias, S. G., Freeman, M. A., and Gokcay, E. I. (1990). A correlative study of the geometry and anatomy of the distal femur. Clin Orthop Relat Res, (260):98–103. 120, 215
Elmoutaouakkil, A., Peyrin, F., Elkafi, J., and Laval-Jeantet, A.-M. (2002). Segmentation of cancellous bone from high-resolution computed tomography images: influence on trabecular bone measurements. IEEE Transactions on Medical Imaging, 21(4):354–362. 70
Faulkner, K. G., Cann, C. E., and Hasegawa, B. H. (1991a). Effect of bone dis- tribution on vertebral strength: assessment with patient-specific nonlinear finite element analysis. Radiology, 179(3):669–674. 113
275 Bibliography
Faulkner, K. G., Glüer, C. C., Majumdar, S., Lang, P., Engelke, K., and Genant, H. K. (1991b). Noninvasive measurements of bone mass, structure, and strength: current methods and experimental techniques. AJR Am J Roentgenol, 157(6):1229–1237. 113
Faulkner, K. G., McClung, M. R., Coleman, L. J., and Kingston-Sandahl, E. (1994). Quantitative ultrasound of the heel: correlation with densitometric measurements at different skeletal sites. Osteoporos Int, 4(1):42–47. 114
Fessy, M. H., Seutin, B., and Béjui, J. (1997). Anatomical basis for the choice of the femoral implant in the total hip arthroplasty. Surg Radiol Anat, 19(5):283–286. xv, 116, 216
Frankel, V. H., Burstein, A. H., and Brooks, D. B. (1971). Biomechanics of internal derangement of the knee. pathomechanics as determined by analysis of the instant centers of motion. J Bone Joint Surg Am, 53(5):945– 962. 119, 212
Freeman, H. (1961). On the encoding of arbitrary geometric configurations. IEEE Eletr. Comp., EC-10:260–268. 83
Freeman, H. and Saaghri, A. (1978). Generalized chain codes for planar curves. Proceedings of the 4th International Joint Conference on Pattern Recognition, Kyoto, Japan, pages 701–703. 83
Friberg, O. (1983). Clinical symptoms and biomechanics of lumbar spine and hip joint in leg length inequality. Spine, 8(6):643–651. 207
Frost, H. M. (1973). Bone remodelling and its relation to metabolic bone diseases. Springfield, IL. 9
Gardner, E., Gray, D., and O’Rahilly, R. (1969). Anatomy. A Regional Study of Human Structure. W. B. Saunders Company, Philadelphia, 3rd edition. 14, 17
Gausepohl, T., Pennig, D., Koebke, J., and Harnoss, S. (2002). Antegrade femoral nailing: an anatomical determination of the correct entry point. Injury, 33(8):701–705. 108, 118
Gill, H. S., Alfaro-Adrián, J., Alfaro-Adrián, C., McLardy-Smith, P., and Murray, D. W. (2002). The effect of anteversion on femoral component stability assessed by radiostereometric analysis. J Arthroplasty, 17(8):997– 1005. 219
276 Bibliography
Ginja, M. M. D., Gonzalo-Orden, J. M., Jesus, S. S., Silvestre, A. M., Llorens- Pena, M. P., and Ferreira, A. J. A. (2007). Measurement of the femoral neck anteversion angle in the dog using computed tomography. Vet J, 174(2):378–383. 198
Girard, J., Lavigne, M., Vendittoli, P.-A., and Roy, A. G. (2006). Biomechanical reconstruction of the hip: a randomised study comparing total hip resur- facing and total hip arthroplasty. J Bone Joint Surg Br, 88(6):721–726. 207
Glüer, C. C., Wu, C. Y., and Genant, H. K. (1993). Broadband ultrasound attenuation signals depend on trabecular orientation: An in vitro study. Osteoporosis International, 3(4):185–191. 113
Gnudi, S., Ripamonti, C., Lisi, L., Fini, M., Giardino, R., and Giavaresi, G. (2002). Proximal femur geometry to detect and distinguish femoral neck frac- tures from trochanteric fractures in postmenopausal women. Osteoporosis International, 13(1):69–73. 111
Goh, J. C., Low, S. L., and Bose, K. (1995). Effect of femoral rotation on bone mineral density measurements with dual energy x-ray absorptiometry. Calcif Tissue Int, 57(5):340–343. 35, 112
Gonzalez, R. C. and Woods, R. E. (2002). Digital Image Processing (2nd Edition). Prentice Hall. 42, 46, 69, 71, 72, 73, 76, 87
Gonzalez, R. C., Woods, R. E., and Eddins, S. L. (2003). Digital Image Processing Using MATLAB. Prentice-Hall, Inc., Upper Saddle River, NJ, USA. 68, 74, 84
Graham, R. L. (1972). An efficient algorith for determining the convex hull of a finite planar set. Information Processing Letters, 1(4):132–133. 75
Gray, Henry, .-. (1918). Anatomy of the human body, by Henry Gray. 20th ed., thoroughly rev. and re-edited by Warren H. Lewis. Philadelphia: Lea & Febiger, 20th edition. 11, 12, 15
Gregory, J., Testi, D., Stewart, A., Undrill, P., Reid, D., and Aspden, R. (2004). A method for assessment of the shape of the proximal femur and its relationship to osteoporotic hip fracture. Osteoporosis International, 15(1):5–11. 88, 112, 114, 197, 209
277 Bibliography
Griffin, F. M., Math, K., Scuderi, G. R., Insall, J. N., and Poilvache, P. L. (2000). Anatomy of the epicondyles of the distal femur: Mri analysis of normal knees. J Arthroplasty, 15(3):354–359. 109, 205
Groell, R., Rienmueller, R., Schaffler, G. J., Portugaller, H. R., Graif, E., and Willfurth, P. (2000). Ct number variations due to different image acquisition and reconstruction parameters: a thorax phantom study. Comput Med Imaging Graph, 24(2):53–58. 196
Gruen, T. (1997). A simple assessment of bone quality prior to hip arthroplasty: cortical index revisited. Acta Orthop Belg, 63 Suppl 1:20–27. 116
Gurney, B., Mermier, C., Robergs, R., Gibson, A., and Rivero, D. (2001). Effects of limb-length discrepancy on gait economy and lower-extremity muscle activity in older adults. J Bone Joint Surg Am, 83-A(6):907–915. 207
Gómez Alonso, C., Díaz Curiel, M., Hawkins Carranza, F., Pérez Cano, R., and Díez Pérez, A. (2000). Femoral bone mineral density, neck-shaft angle and mean femoral neck width as predictors of hip fracture in men and women. Osteoporosis International, 11(8):714–720. 111, 208
Hagemeister, N., Parent, G., de Putte, M. V., St-Onge, N., Duval, N., and de Guise, J. (2005). A reproducible method for studying three-dimensional knee kinematics. J Biomech, 38(9):1926–1931. 121, 122, 194, 199, 214, 215
Hancox, N. (1972). Biology of Bone. University Press, Cambridge. 6, 7
Hao, X., Bruce, C., Pislaru, C., and Greenleaf, J. (2000). A novel region growing method for segmenting ultrasound images. In Proc. IEEE Ultrasonics Symposium, volume 2, pages 1717–1720 vol.2. 45
Harma, A., Germen, B., Karakas, H., Elmali, N., and Inan, M. (2005). The comparison of femoral curves and curves of contemporary intramedullary nails. Surgical and Radiologic Anatomy, 27(6):502–506. 108, 117, 119
Harper, M. C. and Carson, W. L. (1987). Curvature of the femur and the proximal entry point for an intramedullary rod. Clin Orthop Relat Res, (220):155–161. 117
Harris, C. and Stephens, M. (1988). A combined corner and edge detection. In Proceedings of The Fourth Alvey Vision Conference, pages 147–151. 92, 93
278 Bibliography
Harris, C. G. (1987). Determination of ego-motion from matched points. Third Alvey Vision Conference, pages 189–192. 90, 92
Harty, M. (1957). The calcar femorale and the femoral neck. J Bone Joint Surg Am, 39-A(3):625–630. 13
Havers, C. (1691). Osteologia Nova, or some new observations of the bones. Cartilage, S. Smith, London. 7
He, X. and Yung, N. (2004). Curvature scale space corner detector with adap- tive threshold and dynamic region of support. In Proc. 17th International Conference on Pattern Recognition ICPR 2004, volume 2, pages 791–794 Vol.2. xiv, 95, 96, 132
Hernandez, R. J., Tachdjian, M. O., Poznanski, A. K., and Dias, L. S. (1981). Ct determination of femoral torsion. AJR Am J Roentgenol, 137(1):97–101. 105, 108, 210
Hoaglund, F. T. and Low, W. D. (1980). Anatomy of the femoral neck and head, with comparative data from caucasians and hong kong chinese. Clin Orthop Relat Res, (152):10–16. 210
Holden and Stanhope (1998). The effect of variation in knee center location estimates on net knee joint moments. Gait Posture, 7(1):1–6. 121
Hollister, A. M., Jatana, S., Singh, A. K., Sullivan, W. W., and Lupichuk, A. G. (1993). The axes of rotation of the knee. Clin Orthop Relat Res, (290):259–268. 120, 183, 213, 215
Holmberg, B. and Lanshammar, H. (2006). Possibilities of texture based motion analysis. Comput Methods Programs Biomed, 84(1):1–10. 121, 214
Hua J, Mai S, W. P. (1993). Determination of the hounsfield unit in ct-scan for designing custom femoral stems. Proc ISSCP Amelia Island, Fl, 11:2. 197
Huffman, D. and Huffman, D. (1952). A method for the construction of minimum-redundancy codes. Proceedings of the IRE, 40(9):1098–1101. 84
Huo, X. and Chen, J. (2005). Jbeam: multiscale curve coding via beamlets. IEEE Trans. Image Processing, 14(11):1665–1677. 84
Husmann, O., Rubin, P. J., Leyvraz, P. F., de Roguin, B., and Argenson, J. N. (1997). Three-dimensional morphology of the proximal femur. J Arthroplasty, 12(4):444–450. 115, 219, 220
279 Bibliography
Høiseth, A., Reikerås, O., and Fønstelien, E. (1988). Aspects of femoral neck anteversion. theoretical considerations and experimental results. Acta Radiol, 29(6):689–694. 104, 194, 210
Imran, A. and O’Connor, J. J. (1997). Theoretical estimates of cruciate ligament forces: effects of tibial surface geometry and ligament orientations. Proc Inst Mech Eng [H], 211(6):425–439. 213
Iwaki, H., Pinskerova, V., and Freeman, M. A. (2000). Tibiofemoral movement 1: the shapes and relative movements of the femur and tibia in the unloaded cadaver knee. J Bone Joint Surg Br, 82(8):1189–1195. 194, 215
Jain, A., Maheshwari, A. V., Nath, S., Singh, M., and Nagar, M. (2003). Anteversion of the femoral neck in indian dry femora. Journal of Orthopaedic Science, 8(3):334–340. 99, 202, 217, 218
Jarvis, R. (1973). On the identification of the convex hull of a finite set of points in the plane. Image Processing Letters, 2:18–21. 75
Jee, W. S. S. (2001). Integrated Bone Tissue Physiology: Anatomy and Physiol- ogy. In: Cowin S.C. ed. Bone Mechanics Handbook. CRC Press, Boca Raton. 5
Jenny, J.-Y. and Boeri, C. (2004). Low reproducibility of the intra-operative measurement of the transepicondylar axis during total knee replacement. Acta Orthop Scand, 75(1):74–77. 205
Jonsson, H. and Kärrholm, J. (1994). Three-dimensional knee joint movements during a step-up: Evaluation after anterior cruciate ligament rupture. Journal of Orthopaedic Research, 12(6):769–779. 120, 212
Kang, C. and Speller, R. (1998). Comparison of ultrasound and dual en- ergy x-ray absorptiometry measurements in the calcaneus. Br J Radiol, 71(848):861–867. 113
Kaptoge, S., Dalzell, N., Loveridge, N., Beck, T. J., Khaw, K.-T., and Reeve, J. (2003). Effects of gender, anthropometric variables, and aging on the evolution of hip strength in men and women aged over 65. 208
Kass, M., Witkin, A., and Terzopoulos, D. (1988). Snakes: Active contour models. International Journal of Computer Vision, 1(4):321–331. 58, 114, 197
280 Bibliography
Kaus, M., Warfield, S., Jolesz, F., and Kikinis, R. (1999). Adaptive template moderated brain tumor segmentation in mri. 59
Kawate, K., Ohneda, Y., Ohmura, T., Yajima, H., Sugimoto, K., and Takakura, Y. (2008). Computed tomography-based custom-made stem for dysplastic hips in japanese patients. J Arthroplasty. 216
Kelemen, A., Szekely, G., and Gerig, G. (1998). Three-dimensional model- based segmentation of brain mri. In Proc. Workshop on Biomedical Image Analysis, pages 4–13. 58
Kessler, O., Patil, S., Stefan, W., Mayr, E., Colwell, C. W., and D’Lima, D. D. (2008). Bony impingement affects range of motion after total hip arthroplasty: A subject-specific approach. J Orthop Res, 26(4):443–452. 217
Khang, G., Choi, K., Kim, C.-S., Yang, J. S., and Bae, T.-S. (2003). A study of korean femoral geometry. Clin Orthop Relat Res, (406):116–122. 216
Kim, J. S. and Kim, S. I. (1997). A new measurement method of femoral anteversion based on the 3d modeling. In Proc. 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, vol- ume 1, pages 418–421 vol.1. 104, 106, 157, 194, 202
Kim, J. S., Park, T. S., Park, S. B., Kim, J. S., Kim, I. Y., and Kim, S. I. (2000a). Measurement of femoral neck anteversion in 3d. part 1: 3d imaging method. Med Biol Eng Comput, 38(6):603–609. 99, 108, 194, 207, 217, 218
Kim, J. S., Park, T. S., Park, S. B., Kim, J. S., Kim, I. Y., and Kim, S. I. (2000b). Measurement of femoral neck anteversion in 3d. part 2: 3d modelling method. Med Biol Eng Comput, 38(6):610–616. 108, 200, 207, 210
Kingsley, P. C. and Olmsted, K. L. (1948). A study to determine the angle of anteversion of the neck of the femur. J Bone Joint Surg Am, 30(3):745–751. 98, 99, 100, 194, 202, 209, 210, 212, 217, 218
Kinzel, V., Ledger, M., and Shakespeare, D. (2005). Can the epicondylar axis be defined accurately in total knee arthroplasty? Knee, 12(4):293–296. 103, 206
Kirk, J. K., Nichols, M., and Spangler, J. G. (2002). Use of a peripheral dexa measurement for osteoporosis screening. Fam Med, 34(3):201–205. 34
281 Bibliography
Kirkpatrick, D. G. and Seidel, R. (1986). The ultimate planar convex hull algorithm? SIAM Journal on Computing, 15(1):287–299. 75
Kitchen, L. and Rosenfeld, A. (1982). Gray level corner detection. Pattern Recognition Letters, 1(2):95–102. 90
Kleemann, R. U., Heller, M. O., Stoeckle, U., Taylor, W. R., and Duda, G. N. (2003). Tha loading arising from increased femoral anteversion and offset may lead to critical cement stresses. J Orthop Res, 21(5):767–774. 217
Koch, M. and Kashyap, R. (1985). A vision system to identify occluded industrial parts. In Proc. IEEE International Conference on Robotics and Automation, volume 2, pages 55–60. 90
Kolta, S., Bras, A. L., Mitton, D., Bousson, V., de Guise, J. A., Fechtenbaum, J., Laredo, J. D., Roux, C., and Skalli, W. (2005). Three-dimensional x-ray absorptiometry (3d-xa): a method for reconstruction of human bones using a dual x-ray absorptiometry device. Osteoporos Int, 16(8):969–976. 35, 112, 209
Kuhl, F. and Kuhl, F. (1963). Classification and recognition of hand-printed characters. Proceedings of the IEEE, 51(3):522–522. 82
Kuhl, F. P. and Giardina, C. R. (1982). Elliptic fourier features of a closed contour. Computer Graphics and Image Processing, 18(3):236–258. 216
Kuhn, H. W. (1955). The hungarian method for the assignment problem. Naval Research Logistics Quarterly, 2:83–97. 77
Kui Liu, Y. and Zalik, B. (2005). An efficient chain code with huffman coding. Pattern Recognition, 38(4):553–557. 84
Kunttu, I., Kunttu, I., Lepisto, L., Rauhamaa, J., and Visa, A. (2003). Multi- scale fourier descriptor for shape classification. In Lepisto, L., editor, Proc. 12th International Conference on Image Analysis and Processing, pages 536–541. 88
Laine, H. J., Kontola, K., Lehto, M. U., Pitkänen, M., Jarske, P., and Lindholm, T. S. (1997). Image processing for femoral endosteal anatomy detection: description and testing of a computed tomography based program. Phys Med Biol, 42(4):673–689. 200
282 Bibliography
Laine, H. J., Lehto, M. U., and Moilanen, T. (2000). Diversity of proximal femoral medullary canal. J Arthroplasty, 15(1):86–92. 115, 154, 222
Lantuéjoul, C. (1978). La squelettisation et son application aux mesures topologiques des mosaïques polycristallines. PhD thesis, School of Mines. 72
Lausten, G. S., Jørgensen, F., and Boesen, J. (1989). Measurement of an- teversion of the femoral neck. ultrasound and computerised tomography compared. J Bone Joint Surg Br, 71(2):237–239. 99, 110, 202, 217, 218
Lee, D. Y., Lee, C. K., and Cho, T. J. (1992). A new method for measurement of femoral anteversion. a comparative study with other radiographic methods. Int Orthop, 16(3):277–281. 202
Lee, T. C. and Taylor, D. (1999). Bone remodelling: should we cry wolff? Ir J Med Sci, 168(2):102–105. 9
Lee, Y.-B., Song, S.-M., Lee, J.-S., and Kim, M.-H. (2005). Tumor segmentation from small animal pet using region growing based on gradient magnitude. In Proc. 7th International Workshop on Enterprise networking and Computing in Healthcare Industry HEALTHCOM 2005, pages 243–247. 44
Lekamwasam, S. and Lenora, R. S. J. (2003). Effect of leg rotation on hip bone mineral density measurements. J Clin Densitom, 6(4):331–336. 35
Leung, K. S., Procter, P., Robioneck, B., and Behrens, K. (1996). Geometric mismatch of the gamma nail to the chinese femur. Clin Orthop Relat Res, (323):42–48. 111, 118
Levi, C., Gray, J. E., McCullough, E. C., and Hattery, R. R. (1982). The unreliability of ct numbers as absolute values. AJR Am J Roentgenol, 139(3):443–447. 196
Li, G., Most, E., Sultan, P. G., Schule, S., Zayontz, S., Park, S. E., and Rubash, H. E. (2004). Knee kinematics with a high-flexion posterior stabilized total knee prosthesis: An in vitro robotic experimental investigation. J Bone Joint Surg Am, 86(8):1721–1729. 121, 214
Li, G., Suggs, J., Hanson, G., Durbhakula, S., Johnson, T., and Freiberg, A. (2006). Three-dimensional tibiofemoral articular contact kinematics of a cruciate-retaining total knee arthroplasty. J Bone Joint Surg Am, 88(2):395–402. 213
283 Bibliography
Liao, P. S., Chen, T. S., and Chung, P. C. (2001). A fast algorithm for multilevel thresholding. J. Comput. Inf. Sci. Eng., 17:713–727. 43
Link, T. M., Koppers, B. B., Licht, T., Bauer, J., Lu, Y., and Rummeny, E. J. (2004). In vitro and in vivo spiral ct to determine bone mineral density: Initial experience in patients at risk for osteoporosis. Radiology, 231(3):805– 811. 113
Liu, R., Wang, C., and Wang, K. (2007). Morphological changes of proximal femur in patients with crowe ii/iii developmental dysplasia of hip and their implication to total hip arthroplasty. Zhongguo Xiu Fu Chong Jian Wai Ke Za Zhi, 21(10):1050–1053. 216
Lochmüller, E. M., Zeller, J. B., Kaiser, D., Eckstein, F., Landgraf, J., Putz, R., and Steldinger, R. (1998). Correlation of femoral and lumbar dxa and calcaneal ultrasound, measured in situ with intact soft tissues, with the in vitro failure loads of the proximal femur. Osteoporos Int, 8(6):591–598. 113, 208
Lou Bonnick, S. (2007). Hsa: Beyond bmd with dxa. Bone, 41(1, Supplement 1):S9–S12. 209
Loughead, J. M., Chesney, D., Holland, J. P., and McCaskie, A. W. (2005). Comparison of offset in birmingham hip resurfacing and hybrid total hip arthroplasty. J Bone Joint Surg Br, 87(2):163–166. 207
Lustig, S., Lavoie, F., Selmi, T. A. S., Servien, E., and Neyret, P. (2008). Relationship between the surgical epicondylar axis and the articular surface of the distal femur: an anatomic study. Knee Surg Sports Traumatol Arthrosc, 16(7):674–682. 206, 215
MacLatchy, L. M. and Bossert, W. H. (1996). An analysis of the articular surface distribution of the femoral head and acetabulum in anthropoids, with implications for hip function in miocene hominoids. Journal of Human Evolution, 31(5):425–453. 207
Mahaisavariya, B., Sitthiseripratip, K., Tongdee, T., Bohez, E. L. J., Sloten, J. V., and Oris, P. (2002). Morphological study of the proximal femur: a new method of geometrical assessment using 3-dimensional reverse engineering. Med Eng Phys, 24(9):617–622. 108, 110, 111, 118, 202, 207, 208, 210
284 Bibliography
Maki, D. D., Birnbaum, B. A., Chakraborty, D. P., Jacobs, J. E., Carvalho, B. M., and Herman, G. T. (1999). Renal cyst pseudoenhancement: beam- hardening effects on ct numbers. Radiology, 213(2):468–472. 196
Manske, S., Liu-Ambrose, T., de Bakker, P., Liu, D., Kontulainen, S., Guy, P., Oxland, T., and McKay, H. (2006). Femoral neck cortical geometry measured with magnetic resonance imaging is associated with proximal femur strength. Osteoporosis International, 17(10):1539–1545. 113, 194
Marr, D. and Hildreth, E. (1980). Theory of edge detection. Royal Society of London Proceedings Series B, 207:187–217. 53
Marshall, D., Johnell, O., and Wedel, H. (1996). Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures. BMJ, 312(7041):1254–1259. 34
Martin, R. B. and Burr, D. B. (1984). Non-invasive measurement of long bone cross-sectional moment of inertia by photon absorptiometry. J Biomech, 17(3):195–201. 112, 209
Martin, R. B. and Burr, D. B. (1989). Structure, function, and adaptation of compact bone. Raven Press, New York. 6, 7
Martin R.B., B. D. and N.A., S. (1998). Skeletal tissue mechanics. Springer, New York. 7
Martín-Landrove, M., Pereira, D., Caldeira, M. E., Itriago, S., and Juliac, M. (2007). Fractal analysis of tumoral lesions in brain. Conf Proc IEEE Eng Med Biol Soc, 2007:1306–1309. 85
Masala, S., Tarantino, U., Marinetti, A., Aiello, N., Fiori, R., Sorge, R. P., and Simonetti, G. (2003). Dxa vs qct: in vitro and in vivo studies. Acta Diabetol, 40 Suppl 1:S86–S88. 113
Masaoka, T., Yamamoto, K., Shishido, T., Katori, Y., Mizoue, T., Shirasu, H., and Nunoda, D. (2006). Study of hip joint dislocation after total hip arthroplasty. Int Orthop, 30(1):26–30. 217
Matsuda, S., Matsuda, H., Miyagi, T., Sasaki, K., Iwamoto, Y., and Miura, H. (1998). Femoral condyle geometry in the normal and varus knee. Clin Orthop Relat Res, (349):183–188. 213
285 Bibliography
Matsuda, S., Miura, H., Nagamine, R., Mawatari, T., Tokunaga, M., Nabeyama, R., and Iwamoto, Y. (2004). Anatomical analysis of the femoral condyle in normal and osteoarthritic knees. J Orthop Res, 22(1):104–109. 213
McCloskey, E. V., Murray, S. A., Charlesworth, D., Miller, C., Fordham, J., Clifford, K., Atkins, R., and Kanis, J. A. (1990). Assessment of broadband ultrasound attenuation in the os calcis in vitro. Clin Sci (Lond), 78(2):221– 225. 113
McGraw, K. O. and Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1(1):30–46. 201
McGrory, B. J., Morrey, B. F., Cahalan, T. D., An, K. N., and Cabanela, M. E. (1995). Effect of femoral offset on range of motion and abductor muscle strength after total hip arthroplasty. J Bone Joint Surg Br, 77(6):865–869. 206
McInerney, T. and Terzopoulos, D. (1996). Deformable models in medical image analysis: a survey. Medical Image Analysis, 1(2):91 – 108. 58
Merrill, R. D. (1973). Representation of contours and regions for efficient computer search. Commun. ACM, 16(2):69–82. 84
Middleton, F. R. and Palmer, S. H. (2007). How accurate is whiteside’s line as a reference axis in total knee arthroplasty? The Knee, 14(3):204–207. 109, 206
Min, K. and Choi, Y.-J. (2006). Adaptive reconstruction of pipe-shaped human organs from 3d ultrasonic volume. Comput Med Imaging Graph, 30(2):109– 121. 85
Minkowski, H. (1900). Über die begriffe länge, oberfläche und volumen. Jahresber. Deutsch. Math.-Verein, (9):115–121. 64
Minor, J. M. L. and Schmittbuhl, M. (1999). Importance of elliptic fourier methods for morphometry of complex outlines: application to the distal human femur. Surg Radiol Anat, 21(6):387–391. 89
Miura, T., Matsumoto, T., Nishino, M., Kaneuji, A., Sugimori, T., and Tomita, K. (1998). A new technique for morphologic measurement of the femur. its application for japanese patients with osteoarthrosis of the hip. Bull Hosp Jt Dis, 57(4):202–207. 106
286 Bibliography
Mokhtarian, F. and Suomela, R. (1998a). Curvature scale space for robust image corner detection. In Proc. Fourteenth International Conference on Pattern Recognition, volume 2, pages 1819–1821 vol.2. 94
Mokhtarian, F. and Suomela, R. (1998b). Robust image corner detection through curvature scale space. IEEE Trans on Pattern Analysis and Machine Intelligence, 20(12):1376–1381. 94
Moore, K. L. (2007). Essential clinical anatomy. Baltimore, MD : Lippincott Williams & Wilkins, c2007. 12, 13, 14, 16, 220
Moravec, H. (1977). Towards automatic visual obstacle avoidance. In Proceed- ings of the 5th International Joint Conference on Artificial Intelligence, page 584. xiv, 91, 92
Moravec, H. (1979). Visual mapping by a robot rover. In Proceedings of the 6th International Joint Conference on Artificial Intelligence, pages 599–601. 91
Moulton, A. and Upadhyay, S. S. (1982). A direct method of measuring femoral anteversion using ultrasound. J Bone Joint Surg Br, 64(4):469–472. 110
Murphy, S. B., Simon, S. R., Kijewski, P. K., Wilkinson, R. H., and Griscom, N. T. (1987). Femoral anteversion. J Bone Joint Surg Am, 69(8):1169–1176. 105, 106, 107, 108, 204, 205, 210
Müller, R. and Büttner, P. (1994). A critical discussion of intraclass correlation coefficients. Statistics in Medicine, 13(23-24):2465–2476. 201
Nakamura, T., Turner, C. H., Yoshikawa, T., Slemenda, C. W., Peacock, M., Burr, D. B., Mizuno, Y., Orimo, H., Ouchi, Y., and Johnston, C. C. (1994). Do variations in hip geometry explain differences in hip fracture risk between japanese and white americans? J Bone Miner Res, 9(7):1071–1076. 209
Nicholson, P. H., Haddaway, M. J., and Davie, M. W. (1994). The dependence of ultrasonic properties on orientation in human vertebral bone. Phys Med Biol, 39(6):1013–1024. 113
Nicholson, P. H., Lowet, G., Cheng, X. G., Boonen, S., van der Perre, G., and Dequeker, J. (1997). Assessment of the strength of the proximal femur in vitro: relationship with ultrasonic measurements of the calcaneus. Bone, 20(3):219–224. 114, 208
287 Bibliography
Nishihara, S., Sugano, N., Nishii, T., Tanaka, H., Yoshikawa, H., and Ochi, a. (2003). Comparison of the fit and fill between the anatomic hip femoral com- ponent and the versys taper femoral component using virtual implantation on the orthodoc workstation. Journal of Orthopaedic Science, 8(3):352–360. 218
Njeh, C. F., Fuerst, T., Hans, D., Blake, G. M., and Genant, H. K. (1999). Radiation exposure in bone mineral density assessment. Appl Radiat Isot, 50(1):215–236. 35
Noble, P. C., Alexander, J. W., Lindahl, L. J., Yew, D. T., Granberry, W. M., and Tullos, H. S. (1988). The anatomic basis of femoral component design. Clin Orthop Relat Res, (235):148–165. 110, 111, 114, 115, 202, 216, 218, 222
Noble, P. C., Box, G. G., Kamaric, E., Fink, M. J., Alexander, J. W., and Tullos, H. S. (1995). The effect of aging on the shape of the proximal femur. Clin Orthop Relat Res, (316):31–44. 216
Noble, P. C., Kamaric, E., Sugano, N., Matsubara, M., Harada, Y., Ohzono, K., and Paravic, V. (2003). Three-dimensional shape of the dysplastic femur: implications for thr. Clin Orthop Relat Res, (417):27–40. 112
Norkin C., L. P. (1992). Joint Structure and Function. F.A. Davis, Philadelphia., 2nd edition. 14
Olcott, C. W. and Scott, R. D. (1999). The ranawat award. femoral component rotation during total knee arthroplasty. Clin Orthop Relat Res, (367):39–42. 205
Ostermeier, G. C., Sargeant, G. A., Yandell, T., and Parrish, J. J. (2001). Mea- surement of bovine sperm nuclear shape using fourier harmonic amplitudes. J Androl, 22(4):584–594. 89
Ostrum, R. F. and Levy, M. S. (2005). Penetration of the distal femoral anterior cortex during intramedullary nailing for subtrochanteric fractures: a report of three cases. J Orthop Trauma, 19(9):656–660. 108, 117, 118
Otsu, N. (1979). A threshold selection method from gray level histograms. IEEE Trans. Systems, Man and Cybernetics, 9:62–66. minimize inter class variance. 43
288 Bibliography
Palmer, M., Pons, G. X., and Linde, M. (2004). Discriminating between geographical groups of a mediterranean commercial clam (chamelea gallina (l.): Veneridae) by shape analysis. Fisheries Research, 67(1):93–98. 88
Panjabi, M. M., Goel, V. K., and Walter, S. D. (1982). Errors in kinematic parameters of a planar joint: guidelines for optimal experimental design. J Biomech, 15(7):537–544. 120
Parsons, F. G. (1914). The characters of the english thigh-bone. J Anat Physiol, 48(Pt 3):238–267. 98, 99, 110, 194, 202, 217
Pearson, K. and Bell, J. (1919). A study of the long bones of the english skeleton. Draper’s Co. Research Memoire, University of London. 212
Pfeiffer, F., Weitkamp, T., Bunk, O., and David, C. (2006). Phase retrieval and differential phase-contrast imaging with low-brilliance x-ray sources. Nat Phys, 2(4):258–261. 24, 25, 26
Poilvache, P. L., Insall, J. N., Scuderi, G. R., and Font-Rodriguez, D. E. (1996). Rotational landmarks and sizing of the distal femur in total knee arthroplasty. Clin Orthop Relat Res, (331):35–46. 205
Prevrhal, S., Fox, J. C., Shepherd, J. A., and Genant, H. K. (2003). Accuracy of ct-based thickness measurement of thin structures: Modeling of limited spatial resolution in all three dimensions. Medical Physics, 30(1):1–8. 200, 201
Prewitt, J. (1970). Object Enhancement and Extraction Picture Processing and Psychophysics. New York: Academic Press. 49
Pulkkinen, P., Partanen, J., Jalovaara, P., and Jämsä, T. (2004). Combination of bone mineral density and upper femur geometry improves the prediction of hip fracture. Osteoporosis International, 15(4):274–280. 208, 209
Qiang, C., Yu-jun, S., and De-shen, X. (2004). A novel segmentation method of handwritten chinese number character strings. In Proc. ICARCV 2004 8th Control, Automation, Robotics and Vision Conference, volume 2, pages 1123–1128 Vol. 2. 70
Qin, Z., Shi, S., Xu, J., and Fu, H. (2006). Method of license plate location based on corner feature. In Proc. Sixth World Congress on Intelligent Control and Automation WCICA 2006, volume 2, pages 8645–8649. 90
289 Bibliography
Ridler, T. W. and Calvard, S. (1978). Picture thresholding using an iterative slection method. IEEE Transactions on Systems, Man and Cybernetics, SMC-8(8):630–632. Cited By (since 1996): 230. 42
Roberts, L. G. (1965). Machine perception of three-dimensional solids. J.T. Tippet, editor, Optical and Electro-optical Information Processing, MIT Press, pages 159–197. 48
Rogers, S. P. (1931). A method for determining the angle of torsion of the neck of the femur. J Bone Joint Surg Am, 13(4):821–824. 101, 102, 194
Rubin, P. J., Leyvraz, P. F., Aubaniac, J. M., Argenson, J. N., Estève, P., and de Roguin, B. (1992). The morphology of the proximal femur. a three- dimensional radiographic analysis. J Bone Joint Surg Br, 74(1):28–32. 111
Rucklidge, W. J. (1997). Efficiently locating objects using the hausdorff distance. International Journal of Computer Vision, 24(3):251–270. 90
Ryder, C. T. and Crane, L. (1953). Measuring femoral anteversion; the problem and a method. J Bone Joint Surg Am, 35-A(2):321–328. 98, 101, 102, 103, 157, 194, 203
Sakalkale, D. P., Sharkey, P. F., Eng, K., Hozack, W. J., and Rothman, R. H. (2001). Effect of femoral component offset on polyethylene wear in total hip arthroplasty. Clin Orthop Relat Res, (388):125–134. 207
Sanchez-Cruz, H., Bribiesca, E., and Rodriguez-Dagnino, R. M. (2007). Ef- ficiency of chain codes to represent binary objects. Pattern Recognition, 40(6):1660–1674. 84
Schmittbuhl, M., Minor, J. M. L., Taroni, F., and Mangin, P. (2001). Sexual dimorphism of the human mandible: demonstration by elliptical fourier analysis. Int J Legal Med, 115(2):100–101. 88
Schneider, T., Coan, P., Habs, D., and Reiser, M. (2008). Application of brilliant x-rays in mammography : Development and perspectives of phase contrast techniques. Radiologe. 24, 25
Schott, A. M., Weill-Engerer, S., Hans, D., Duboeuf, F., Delmas, P. D., and Meunier, P. J. (1995). Ultrasound discriminates patients with hip fracture equally well as dual energy x-ray absorptiometry and independently of bone mineral density. J Bone Miner Res, 10(2):243–249. 113
290 Bibliography
Seo, J., Seo, J., Kim, K., Kim, J., Park, K., and Chung, H. (2004). Measurement of ocular torsion using digital fundus image. In Kim, K., editor, Proc. 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEMBS ’04, volume 1, pages 1711–1713 Vol.3. 43
Serra, J. (1982). Image Analysis and Mathematical Morphology. Academic Press, London. 68, 72
Sheehan, F. T. (2007). The finite helical axis of the knee joint (a non-invasive in vivo study using fast-pc mri). J Biomech, 40(5):1038–1047. 120, 194, 212
Shi, C. S. and Mao, Y. (1995). Extracting direction and curvature features of jaw movement traces with chain code. J Oral Rehabil, 22(3):237–239. 85
Shrimpton, P., Miller, H., Lewis, M., and Dunn, M. (2003). Doses from computed tomography (ct) examinations in the uk - 2003 review. National Radiological Protection Board. xxi, 29
Shrout, P. E. and Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2):420–428. 201
Silva, M., Lee, K. H., Heisel, C., Rosa, M. A. D., and Schmalzried, T. P. (2004). The biomechanical results of total hip resurfacing arthroplasty. J Bone Joint Surg Am, 86-A(1):40–46. 207
Simonian, P. T., Chapman, J. R., Selznick, H. S., Benirschke, S. K., Claudi, B. F., and Swiontkowski, M. F. (1994). Iatrogenic fractures of the femoral neck during closed nailing of the femoral shaft. J Bone Joint Surg Br, 76(2):293–296. 117
Siston, R. A., Patel, J. J., Goodman, S. B., Delp, S. L., and Giori, N. J. (2005). The variability of femoral rotational alignment in total knee arthroplasty. J Bone Joint Surg Am, 87A(10):2276–2280. 205
Siu, D., Rudan, J., Wevers, H. W., and Griffiths, P. (1996). Femoral articular shape and geometry. a three-dimensional computerized analysis of the knee. J Arthroplasty, 11(2):166–173. 213
Smith, S. M. and Brady, J. M. (1997). Susan?a new approach to low level image processing. International Journal of Computer Vision, 23(1):45–78. 90
Sobel, I. (1970). Camera models and machine perception. In Ph.D. thesis. 51
291 Bibliography
Song, W., Ou, Z., Zhao, D., and Wang, W. (2007). Computer-aided modeling and morphological analysis of hip joint. In Proc. 1st International Conference on Bioinformatics and Biomedical Engineering ICBBE 2007, pages 1218–1221. 208
Stagni, R., Leardini, A., Cappozzo, A., Benedetti, M. G., and Cappello, A. (2000). Effects of hip joint centre mislocation on gait analysis results. J Biomech, 33(11):1479–1487. 122, 194, 214
Staib, L. H. and Duncan, J. S. (1996). Model-based deformable surface finding for medical images. IEEE Transactions on Medical Imaging, 15(5):720–731. 58
Stefanyshyn, D. J., Stergiou, P., Lun, V. M. Y., Meeuwisse, W. H., and Worobets, J. T. (2006). Knee angular impulse as a predictor of patellofemoral pain in runners. Am J Sports Med, 34(11):1844–1851. 121, 214
Stiehl, J. B. and Abbott, B. D. (1995). Morphology of the transepicondylar axis and its application in primary and revision total knee arthroplasty. J Arthroplasty, 10(6):785–789. 205
Sugano, N., Noble, P. C., Kamaric, E., Salama, J. K., Ochi, T., and Tullos, H. S. (1998). The morphology of the femur in developmental dysplasia of the hip. J Bone Joint Surg Br, 80(4):711–719. 210
Sugano, N., Sasama, T., Nakajima, Y., Sato, Y., Nishii, T., Iida, T., Nakagawa, K., Ono, K., Nishihara, S., Tamura, S., Yonenobu, K., and Ochi, T. (2001). Effects of ct threshold value to make a surface bone model on accuracy of shape-based registration in a ct-based navigation system for hip surgery. International Congress Series, 1230:319–324. 197
Sun, L., Tang, Y., and You, X. (2004). Corner detection for object recognition by using wavelet transform. In Proc. International Conference on Machine Learning and Cybernetics, volume 7, pages 4347–4351 vol.7. 90
Tannast, M., Kubiak-Langer, M., Langlotz, F., Puls, M., Murphy, S. B., and Siebenrock, K. A. (2007). Noninvasive three-dimensional assessment of femoroacetabular impingement. J Orthop Res, 25(1):122–131. 198
Tavakoli, M. B. and Evans, J. A. (1991). Dependence of the velocity and attenuation of ultrasound in bone on the mineral content. Physics in medicine and biology, 36(11):1529–1537. 113
292 Bibliography
Taylor, D., Hazenberg, J. G., and Lee, T. C. (2007). Living with cracks: Damage and repair in human bone. Nat Mater, 6(4):263–268. 8, 9
Thompson, J. E. M. and Tingey, D. R. C. (1997). Radiation doses from computed tomography in australia. Technical report, Australian Radiation Laboatory. 26
Tian, T. P., Chen, Y., Leow, W. K., Hsu, W., Howe, T. S., and Png, M. A. (2003). Computing neck-shaft angle of femur for x-ray fracture detection. Computer Analysis of Images and Patterns, pages 82–89. 114
Tortora, G. J. (2002). Principles of Human Anatomy. Wiley, New York. 8
Tuduki, Y., Murase, K., Izumida, M., Miki, H., Kikuchi, K., Murakami, K., and Ikezoe, J. (2000). Automated seeded region growing algorithm for extraction of cerebral blood vessels from magnetic resonance angiographic data. In Proc. 22nd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, volume 3, pages 1756–1759 vol.3. 45
Turner, C. H., Peacock, M., Timmerman, L., Neal, J. M., and Johnson, C. C. (1995). Calcaneal ultrasonic measurements discriminate hip fracture inde- pendently of bone mass. Osteoporos Int, 5(2):130–135. 113
Veip, Y. A. (2005). Determination of the dynamic range of digital x-ray receivers. Med Tekh, (5):8–10. 25
Walker, P. S., Shoji, H., and Erkman, M. J. (1972). The rotational axis of the knee and its significance to prosthesis design. Clin Orthop Relat Res, 89:160–170. 119, 212
Walmsley, T. (1933). The vertical axes of the femur and their relations. a contribution to the study of the erect position. J Anat, 67(Pt 2):284–300. 100, 204
Weese, J., Kaus, M., Lorenz, C., Lobregt, S., Truyen, R., and Pekar, V. (2001). Shape constrained deformable models for 3d medical image segmentation. 58, 59
Weiner, D. S., Cook, A. J., Hoyt, W. A., and Oravec, C. E. (1978). Com- puted tomography in the measurement of femoral anteversion. Orthopedics, 1(4):299–306. 104, 105, 108, 194, 205, 210
293 Bibliography
Whiteside, L. A. and Arima, J. (1995). The anteroposterior axis for femoral rotational alignment in valgus total knee arthroplasty. Clin Orthop Relat Res, (321):168–172. 108, 109, 202, 206
Wilting, J. E. and Timmer, J. (1999). Artefacts in spiral-ct images and their relation to pitch and subject morphology. Eur Radiol, 9(2):316–322. 33
Wolff, J. (1892). Das gesetz der transformation der knochen, hirschwald, berlin. 9
Won, Y.-Y., Cui, W.-Q., Baek, M.-H., Yun, T.-B., and Han, S.-H. (2007). An additional reference axis for determining rotational alignment of the femoral component in total knee arthroplasty. J Arthroplasty, 22(7):1049–1053. 108, 109, 206
Yadollahi, A. and Moussavi, Z. (2006). Apnea detection by acoustical means. Conf Proc IEEE Eng Med Biol Soc, 1:4623–4626. 43
Yang, P., sheng Wang, C., zheng Wang, K., Shi, Z.-B., and liang Gong, F. (2005). Selection of femoral prosthesis in total hip replacement for ankylosing spondylitis. Di Yi Jun Yi Da Xue Xue Bao, 25(12):1468–1473. 216
Yang, P., Wang, C., and Wang, K. (2006). Effect of morphological changes in proximal femur on prothesis selection of total hip arthroplasty in patients with ankylosing spondylitis. Zhongguo Xiu Fu Chong Jian Wai Ke Za Zhi, 20(4):448–450. 216
Yau, W. P., Leung, A., Chiu, K. Y., Tang, W. M., and Ng, T. P. (2005). In- traobserver errors in obtaining visually selected anatomic landmarks dur- ing registration process in nonimage-based navigation-assisted total knee arthroplasty: a cadaveric experiment. J Arthroplasty, 20(5):591–601. 205
Yau, W. P., Leung, A., Liu, K. G., Yan, C. H., Wong, L. S., and Chiu, K. Y. (2008). Errors in the identification of the transepicondylar and anteroposterior axes of the distal femur in total knee replacement using minimally-invasive and conventional approaches: a cadaver study. J Bone Joint Surg Br, 90(4):520–526. 206
Yerly, J., Hu, Y., Jones, S. M., and Martinuzzi, R. J. (2007). A two-step procedure for automatic and accurate segmentation of volumetric clsm biofilm images. J Microbiol Methods, 70(3):424–433. 43
294 Bibliography
Yoshioka, Y. and Cooke, T. D. (1987). Femoral anteversion: assessment based on function axes. J Orthop Res, 5(1):86–91. 101, 194, 202, 204, 217
Yoshioka, Y., Siu, D., and Cooke, T. D. (1987). The anatomy and functional axes of the femur. J Bone Joint Surg Am, 69(6):873–880. 100, 101, 103, 111, 214
Younker, J. L. and Ehrlich, R. (1977). Fourier biometrics: Harmonic amplitudes as multivariate shape descriptors. Systematic Zoology, 26(3):336–342. 88
Zebaze, R. M. D., Jones, A., Welsh, F., Knackstedt, M., and Seeman, E. (2005). Femoral neck shape and the spatial distribution of its mineral mass varies with its size: Clinical and biomechanical implications. Bone, 37(2):243–252. 111
Zoghi, M., Hefzy, M. S., Fu, K. C., and Jackson, W. T. (1992). A three- dimensional morphometrical study of the distal human femur. Proc Inst Mech Eng [H], 206(3):147–157. 213
Zoroofi, R., Sato, Y., Sasama, T., Nishii, T., Sugano, N., Yonenobu, K., Yoshikawa, H., Ochi, T., and Tamura, S. (2003). Automated segmenta- tion of acetabulum and femoral head from 3-d ct images. IEEE Trans. Inform. Technol. Biomed., 7(4):329–343. 198
295 Bibliography
296