Image Analytic Tools for Tissue Characterization Using Optical Coherence Tomography

Image analytic tools for tissue characterization using optical coherence tomography

Yu Gan

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

2017

2017

Yu Gan

ABSTRACT

Image analytic tools for tissue characterization using

optical coherence tomography

Yu Gan

Optical coherence tomography (OCT) has been emerging as a promising imaging technique, with a strong capability of non-invasive, in vivo, high resolution, depth-resolved imaging. There is a great potential to use OCT to guide the treatment of arrhythmias, to prevent preterm birth, and to detect breast cancer. To facilitate the clinical applications, this thesis presents three image analytic tools to characterize biological tissue: 1) automated fiber direction analysis; 2) automated volumetric stitching; 3) automated tissue classification. The fiber direction analysis consists of a particle-filter-based 3D tractography scheme and a pixel-wise fiber analysis scheme. The stitching algorithm enlarges the field of view of current OCT system from millimeter to centimeter level by volumetric stitching using scale-invariant feature transform. Based on relevance vector machine, a region-based classification scheme and a grid-based classification scheme are developed to automatically identify tissue composition in human cardiac tissue and human breast tissue. These tools are collaboratively used to study OCT images from cardiac, cervical, and breast tissue.

In cardiac tissue, we apply the fiber orientation analysis to reconstruct 3D cardiac myofibers tractography and perform pixel-wise fiber analysis on the collagen region within human heart. In

addition, we apply the region-based algorithm to segment and classify tissue compositions, such as collagen, adipose tissue, fibrotic myocardium, and normal myocardium, over a single or a stitched OCT volume. Using our algorithm, we observe fiber directionality change over depths and find that the fiber orientation changes more dramatically in atria than in ventricle. We also observe different dispersion patterns within collagen layer.

In cervical tissue, our stitching algorithm enables a paramount 3D view of entire axial slices.

Together with pixel-wise fiber orientation scheme, we analyze the difference of dispersion property within inner/outer regions of four quadrants. We observe two dispersion patterns in pregnant and non-pregnant cervical tissue at the location close to upper cervix. In addition, we discover that an increasing trend of dispersion and an increasing trend of penetration depth from internal orifice (os) to external os.

In breast tissue, we visualize various features in both benign and malignant tissues such as invasive ductal carcinoma (IDC), ductal carcinoma in situ, cyst, and terminal duct lobule unit in stitched

OCT images. Focusing on the automated detection of IDC, we propose a hierarchy framework of classification model and apply our classifier in two OCT systems and achieve both reasonable sensitivity and specificity in identifying cancerous region.

Table of Content

List of Figures ...... ix

List of Tables ...... xxii

Acknowledgement ...... xxiv

Chapter 1 Background and Significance...... 1

1.1 Optical coherence tomography...... 1

1.1.1 Time Domain OCT ...... 3

1.1.2 Fourier Domain OCT...... 4

1.2 OCT techniques in biomedical imaging ...... 5

1.3 Challenges in OCT image analytic tools ...... 7

1.4 Existing OCT image analytic tools ...... 8

1.4.1 Fiber orientation analysis...... 8

1.4.2 Stitching algorithm ...... 9

1.4.3 Automated segmentation and tissue classification ...... 10

1.5 Objective ...... 11

Chapter 2 Automated algorithm for Fiber orientation analysis ...... 13

2.1 Introduction ...... 13

2.2 Three-dimensional orientation and tractography of myofibers ...... 15

2.2.1 Quantification of fiber orientation in three dimensions ...... 15

2.2.2 Tractography of fibers· in three dimensions ...... 19

2.3 Pixel-wise orientation estimations and dispersion analysis ...... 23

2.3.1 Pixel-wise orientation estimation ...... 23

2.3.2 Distribution fitting ...... 25

2.4 Method validation ...... 26

2.4.1 Validation setup ...... 26

2.4.2 Validation of 3D fiber orientation quantification ...... 26

2.4.3 Comparison with manual measurements ...... 27

2.4.4 Rotation test ...... 29

2.4.5 3D tractography ...... 32

2.4.6 Pixel-wise fiber orientation ...... 33

2.4.7 Comparison with intensity gradient technique ...... 34

2.5 Discussion ...... 35

2.6 Conclusion ...... 36 ii

Chapter 3 Automated stitching algorithm to enlarge OCT Field of View ...... 38

3.1 Introduction ...... 38

3.2 Stitching algorithm ...... 39

3.2.1 Algorithm flow ...... 39

3.2.2 Step 1: registration within en face plane ...... 41

3.2.3 Step 2: registration along axial axis ...... 46

3.2.4 Step 3: post-processing ...... 48

3.3 Method validation ...... 50

3.3.1 Validation setup ...... 50

3.3.2 Auto-correction method ...... 51

3.3.3 Stitching accuracy ...... 52

3.3.4 Multiband blending and gain compensation ...... 53

3.4 Discussion ...... 55

3.5 Conclusion ...... 56

Chapter 4 Automated classification of tissue composition ...... 57

4.1 Introduction ...... 57

4.2 Automated classification of myocardium ...... 58 iii

4.2.1 Algorithm flow ...... 58

4.2.2 Layer segmentation ...... 59

4.2.3 Feature extraction ...... 64

4.2.4 RVM classification ...... 66

4.2.5 3D visualization ...... 68

4.3 Automated classification of breast tissue ...... 68

4.3.1 Algorithm flow ...... 68

4.3.2 Adipose classifier ...... 69

4.3.3 IDC classifier ...... 70

4.4 Method Validation...... 70

4.4.1 Validation setup ...... 70

4.4.2 Segmentation results ...... 71

4.4.3 Myocardial classification results ...... 72

4.4.4 Breast classifications results ...... 73

4.5 Discussion ...... 75

4.6 Conclusion ...... 76

Chapter 5 Characterization of cardiac tissue ...... 78 iv

5.1 Background ...... 78

5.1.1 Clinic needs ...... 78

5.1.2 Cardiac imaging ...... 79

5.1.3 Cardiac OCT imaging ...... 81

5.2 Fiber orientation Analysis ...... 81

5.2.1 Experimental setup ...... 81

5.2.2 Depth vs orientation...... 82

5.2.3 Fiber comparison in tractography ...... 83

5.2.4 Directionality map of cardiac imaging ...... 85

5.3 Cardiac tissue over a large field of view ...... 86

5.3.1 Experimental setup ...... 86

5.3.2 Visualization of entire rabbit atrium ...... 87

5.3.3 Visualization of canine atrium ...... 87

5.3.4 Visualization of human atrium ...... 88

5.4 Tissue composition analysis ...... 90

5.4.1 Experimental setup ...... 90

5.4.2 Feature analysis ...... 91 v

5.4.3 Classification results ...... 94

5.4.4 3D classification of collagen thickening region ...... 95

5.5 Discussion ...... 96

5.6 Conclusion ...... 102

Chapter 6 Characterization of cervical collagen fiber network ...... 104

6.1 Background ...... 104

6.1.1 Preterm birth ...... 104

6.1.2 Cervical imaging...... 105

6.1.3 Cervical OCT imaging...... 106

6.2 Enlargement of field of view ...... 106

6.2.1 Image protocol ...... 106

6.2.2 Tissue collection ...... 107

6.2.3 Algorithm validation...... 108

6.2.4 Stitching Cervices ...... 108

6.2.5 Confidence evaluation ...... 109

6.3 Reginal difference in upper cervix ...... 114

6.3.1 Experimental setup ...... 114 vi

6.3.2 Pixel-wise orientation estimation on stitched OCT images ...... 116

6.3.3 Statistical analysis...... 117

6.3.4 Observation ...... 118

6.4 Dispersion analysis over longitudinal direction ...... 119

6.4.1 Experimental setup ...... 119

6.4.2 Visualization over longitudinal direction ...... 120

6.4.3 Feature study on single sample ...... 121

6.5 Discussion ...... 126

6.6 Conclusion ...... 128

Chapter 7 Characterization of breast cancerous region ...... 130

7.1 Background ...... 130

7.1.1 Clinic needs ...... 130

7.1.2 Breast imaging ...... 131

7.1.3 Breast OCT imaging ...... 132

7.2 Stitching experiments and results ...... 133

7.2.1 Experimental setup ...... 133

7.2.2 Stitching human breast tissue ...... 134 vii

7.3 Breast classification...... 135

7.3.1 Experimental setup ...... 135

7.3.2 Adipose classifier ...... 136

7.3.3 IDC classifier ...... 137

7.4 Discussion ...... 139

7.5 Conclusion ...... 140

Chapter 8 Summary and future work ...... 141

8.1 Conclusion ...... 141

8.2 Future work ...... 143

8.2.1 Algorithm optimization ...... 143

8.2.2 Application ...... 144

Bibliography ...... 148

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List of Figures

Figure 1.1 Schemtics of 3D OCT acquisition. a) A-line: axial direction (z) acquisition; b) B-scan: axial(z) and transvers (x) scanning; c) 3D scanning: axial (z) scanning and XY scanning...... 2

Figure 1.2 Schematics of time domain and Fourier domain OCT system. (a) Time Domain OCT;

(b) Spectral Domain OCT; (c) Swept Source OCT ...... 3

Figure 1.3 A-line reconstruction with SDOCT (data was under-sampled by 3 for better visualization). a) Recorded signal and background signal; b) signal after background subtraction; c) signal after λ domain to k domain conversion; d) signal after apodization; e) signal after IFFT.

...... 5

Figure 1.4 Structure of research work in this thesis...... 12

Figure 2.1 Representative OCT en face image of a) cardiac myofiber; b) cervical collagen fiber.

The cardiac fibers show a pattern of streamline and the collagen fibers are crosslinked structure with more dispersion. Scale bar: 500 m...... 15

Figure 2.2 Flowchart of the automated algorithm for quantification of fiber orientation in three dimensions. Components of preprocessing, two-dimensional fiber orientation algorithm and interpolation are used to quantify fiber orientation in en face plane. Edge detection block and plane fitting block are used to back project the fiber orientation from two dimensions to three dimensions.

...... 16

ix line. The intersection of the two planes is the fiber orientation in three dimensions. (b) Angles in three dimensions. The red line represents the fiber. Polar angle ϕ is the angle of fiber with respect to z axis. Azimuth angle θ is the angle of the projection of fiber in en face plane with respect to x axis...... 18

Figure 2.4 Flow diagram of tractography using particle filter method. Sequential clusters of particles are generated, weighted in each iteration. The coordinates of particles in each cluster are weighted summed to estimate the trace of myofibers in OCT image. Neff is a metrics to evaluate whether most of particles are with low weights. Ns is a threshold to determine whether a resampling process is needed...... 20

Figure 2.5 Fiber tracking in en face plane within a right ventricle. a) OCT image in en face plane, with orientation overlaid in coded color. b) Propagation of particles for tracking fiber trace. The fiber trace starts at an anchor denoted as blue dot. The colored lines show the traces how particles propagate from one step to another. The white dots are the estimated trace of fiber. c) Tractography results for multiple fibers. All fibers start at anchors located at the boundary of image. The white lines represent the fiber trace...... 23

Figure 2.6 Pixel-wise fiber orientation analysis. (a) Schematic of determining the orientation in pixel p0. (b) A schematic of generated directionality map; (c) Distribution fitting in the area of interest (yellow box in (b))...... 24

Figure 2.7 Quantification of 3D fiber orientation from three swine hearts: (a) ventricular septum

(Heart I); (b) left atrium (Heart II); (c) left ventricle (Heart III). Light gray shows endocardial surface. Two representative en face OCT images are shown, with 3D fiber orientation overlaid with orientation encoded in color...... 27

Figure 2.8 Comparison of manual fiber orientation measurements of azimuth angle, θ, vs computed

θ based on automated algorithm. The samples are from left atrium (blue circle) and left ventricle

(red triangle) of Heart II over an area of 1mm × 1mm area at an increased depth. The depth was increased from epicardial side to endocardial side in an increment of 25 µm. The results from automated algorithm match the manual measurements...... 29

Figure 2.9 Fiber orientation results in the rotation experiment of azimuth angle. The data was obtained from right ventricle of Heart IV. The reference OCT image and fiber orientations before rotation is shown in (a). During the rotation, we imaged and processed the image when the rotations are (b) 30º (c) 60º (d) 90º. The measured mean value and standard deviation of azimuth angle and polar angle are computed and displayed on the top of each image. The measured change on polar angle, Δϕ’, was within 5º. The change of azimuth angle, Δθ’, matches the rotation in our experiment with respect to reference angle...... 30

Figure 2.10 Fiber orientation results in the rotation experiment of polar angle. The data was obtained from right ventricle of Heart IV. The reference OCT image and fiber orientations before rotation are shown in (a). During the rotation, we imaged and processed the image when the rotations are (b) 30º (c) 60º (d) 90º. The measured mean value and standard deviation of azimuth angle and polar angle are computed and displayed on the top of each image. Light gray shows endocardial surface. The azimuth angle, Δθ’, remains changes little. The change of polar angle,

Δϕ’, matches the rotation in our experiment with respect to reference angle...... 31

Figure 2.11 The tractography of myofibers in three dimensions in ventricular septum. Results are shown in a volume of 2 mm × 2mm × 1mm underneath the surface. The fiber structures are also shown along with fiber trace within en face OCT image (b). The reconstructed fibers match the streamline in original OCT data...... 33

Figure 2.12 Algorithm validation on synthetic data (a), (c) Synthetic data; (b), (d) processed data with pixel-wise fiber orientation information...... 34

Figure 2.13 Directionality map on a en face OCT image from a human cervical sample. (a) Original

OCT image from an en face plane; (b) Pixel-wise directionality map; c(1) – c(3) Histogram of orientation obtained from pixel-wise fiber orientation method in sub-regions from 1 to 3 in (a).

Distribution of fiber orientation in the three regions using pixel-wise fiber orientation method and intensity gradient techniques are compared. Each box is 400 µm × 400 µm...... 35

Figure 3.1 Flowchart of registration algorithm. Scale invariant transform (SIFT) is used for pair matching. Linear regression models are used and least square estimations are calculated in global registration and axial optimization. Axial calibration is based on estimation in first block and edge detection results. An error auto-correction method was used to search and eliminated the unreliable estimation in pair-wise estimation. After all offset are calculated, we use gain compensation and multiband blending method to reduce the artifacts which is caused by the inconsistence of intensity from multiple volumes in the overlapped area...... 40

Figure 3.2 Schematics of registration (a) in three dimensions; (b) within en face plane of camera image; (c) overlapped area in 3D; (d) overlapped B-scans. Within en face plane, the offsets between two volumes are measured through matching its corresponding keypoints in (b). Here, only keypoints that are matched are shown. The centroids of multiple volumes are estimated globally by considering their relative offsets. To register the OCT volumes along axial axis, the B- scans at overlapped area are compared in (d). The displacement of detected edge shows the offset along axial axis among volumes...... 42

Figure 3.3 Schematics of error auto-correction within the en face plane. Each node denotes an OCT volume within en face plane. Each link represents a pair wise offset estimation based on SIFT. The

xii links are color coded based on the error between pair-wised offset estimation and global optimization, which is e (i,j). Dark blue color means the error is within 1 pixel, and red means the error is over 1 pixels. The pruning process is shown from (a) to (c). The initial structure is in (a).

With a deletion of five nodes, only a small number of erroneous links exist in (b). The most reliable tree is established when we delete 17 nodes from (c). The spanning process is shown from (c) to

(e). Nodes are added at each iteration. Only reliable links are added to the tree structure at each iteration. Therefore, the structure of (d) is more reliable than that of (b), though the two figures share the same number of nodes. The constructed tree is shown in (e). With pruning and spanning, we delete the erroneous links and construct an offset tree with highly reliable links...... 46

Figure 3.4 Schematics of post-processing in two dimensions. For all input images, the overlapped region is calculated. Then a gain factor for each volume is computed based on the intensity of overlapped region. The intensity of each volume is tuned by the gain factor. Each B-scan is divided into multiple bands. The banded images are weighted with different matrix based on the idea of blending low frequency band with larger range and blending high frequency band with smaller range. The reconstructed image is the weighted summation of all bands...... 48

Figure 3.5 Measured maximum error between pair-wised offset estimation and global optimization during (a) pruning and (b) spanning process.The x-axis in (a) is in decreased numbers. The curve between 51 to 37 is zoomed in the inserted figure. In pruning, the measured maximum error drops with number of nodes in global estimation. Through link selection, the maximum error remains unaltered with additions of new nodes...... 51

Figure 3.6 Registration results within en face plane (a)with and (b)without error correction. The volumes are not stitched properly without error correction in (a). After error correction, the volumes are well arranged within en face place with a consistent contour of cervix...... 52

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Figure 3.7 Comparison of (a) four stitched volumes and (b) the whole volumes. Four volumes with size of 2.5 mm × 2.5 mm × 2.51 mm were imaged and stitched using our algorithm in (a). Within the same space, another OCT volume with size of 4 mm × 4 mm × 2.51 mm was acquired for comparison. Eight landmarks were specified in each volume, formatting four pairs of distances.

The distances were measured and compared in voxel as a validation the accuracy of stitching algorithm. The maximum mismatch in the two volumes does not exceed 15 voxels...... 53

Figure 3.8 Registration of B-scan results from (a) hard combination of multiple B-scans, (b) gain compensation of multiple B-scans, and (c) gain compensation plus multiband blending of multiple

B-scans. In a zoomed area indicated by dashed yellow rectangular, if hard combined, the two sections approximating the edge has great difference in pixel value in (a1). Gain compensation uniformized the pixel value but a boundary is still visible in (b1). When proceeding with multiband blending, a smooth transition of pixel values is visible over the edge in (c1)...... 54

Figure 4.1 Flowchart of the automated algorithm for tissue classification of OCT images of human atrial tissues. B-scans from the OCT dataset were automatically segmentated into layers. Features were extracted for each layer and input to a classifier. The final output was the tissue composition.

...... 59

Figure 4.2 Flowchart of layer segmentation algorithm ...... 60

Figure 4.3 (a) flowchart for estimation of layer information within B-scan image; (b) schematic of boundary searching algorithm. Layer information, including number of layers and changing point of tissue structure were estimated in (a). Pixels at the boundary of each layer were searched from column to column within a range of Δz pixels over depth in (b)...... 62

Figure 4.4 Example tissue images obtained from OCT, histology, and parametric images. (a)

Original OCT image collected from the left atrium. (b) Trichrome histology of the same sample

xiv used in (a). (c) Attentuation coeffcicient map obtained from (a) (unit: mm-1). (d) Entropy map obtained from (a) (unit: 1). (e) The layer depth map obtained from (a) (unit: pixel). (f) The skewness map obtained from (a) (unit:1). (g) Original OCT image collected from the right atria.

(h) Trichrome histology of the same sample used in (g). (i) Attentuation coeffcicient map obtained from (g) (unit: mm-1). (j) Entropy map obtained from (g) (unit: 1). (k) The layer depth map obtained from (g) (unit: pixel). (l) The skewness map obtained from (g) (unit:1). For different tissue composistion in OCT images, they are showing different signatures in attenuation coefficients, entropy map, layer depth, and skewness. Scale bar: 500 um...... 65

Figure 4.5 Tissue classification algorithm flow. OCT B-scans were first processed to identify adipose region based on regional texture features. B-scans with a small adipose ratio will then be classified into normal stroma and IDC based on frame-based features derived from tissue optical properties...... 69

Figure 4.6 Segmentation results from human atria. (a) & (d) Original OCT images overlaid with automated segmentation result; (b) & (e) corresponding Trichrome histology image; (c) & (e) 3D segmentation results. The automated results in both two dimensions and three dimensions show great agreement with histology images...... 72

Figure 4.7 Two dimensional classification results from human atria. (a) & (d) Original OCT images; (b)&(e) color coded automated classification image; (c)&(e) corresponding Trichrome histology. The classification results show great agreement with histology images...... 73

Figure 4.8 Adipose classification results. (a) Original OCT images; (b) classified results; (c) H&E histology. White grids are non-adipose region and grey grids are adipose region. Scale bar: 1 mm.

...... 74

Figure 4.9 Representative B-scans of correctly identified breast tissue. a) B-scan from normal sample; b) corresponding histology from a); c) B-scan from IDC sample; d) corresponding histology from b). Scale bar: 500 μm...... 75

Figure 5.1 Number of death due to heart disease and cancer in the U.S since 2008, data from [169].

...... 79

Figure 5.2 Fiber orientation as a function of depth. Three volumes of OCT image data were acquired and processed for each chamber from Heart I to Heart III. The relationship is linearly fitted by least square method. The fiber orientations are quantified in each en face plane. The mean of orientation over an area of 1 mm × 1mm is plotted at different depth from epicardial side.

The experiments in different chambers: (a) right atrium, (b) left atrium, (c) right ventricle, (d) ventricular septum and (e) left ventricle. The fiber orientation changes monotonically with depth.

“EP” denotes epicardium. “EN” denotes endocardium...... 83

× 1mm underneath the surface. The fiber structures are also shown along with fiber OCT image in en face plane. The reconstructed fibers match the streamline in original OCT data in (c) left atrium and (d) left ventricle...... 84

Figure 5.4 Directionality map within a human atrial image. (a) en face OCT image of collagen tissue in a human atrium (b) pixel wise fiber orientation analysis on human collagen tissue. (c) fiber distribution of the three regions...... 85

Figure 5.5 Extracted geometric model from a right atrium of a rabbit heart. (a) The rabbit sample;

(b) stitched white light image; (c) segmented rabbit atrium in three dimensions; (d) a typical

xvi stitched B-scan. The geometric model shows detailed 3D features from endocardium to epicardium.

The blue box shows the overall region that we imaged. The red box shows the white light image for a single OCT volume...... 87

(f) 3D segmented tissue. The geometric model shows great agreement in both endocardium and epicardium. The blue box shows the overall region that we imaged. The red box shows the white light image for a single OCT volume...... 88

Figure 5.7 Stitched human atria. (a) 3D volume; (b) stitched camera image (c-e) stitched two dimensional images. Various tissue composition was visualized in stitched OCT images...... 89

Figure 5.8 Statistical analysis of dense collagen, loose collagen, fibrotic myocardium, adipose tissue, and normal myocardium tissue in (a) mean of attenuation coefficient; (b) standard deviation of attenuation coefficient; (c) mean of penetration depth; (d) standard deviation of penetration depth; (e) mean of std filter; (f) std of std filter; (g) mean of range filter; (h) standard deviation of range filter; (i) entropy; (j) Coarseness; (k) homogenity; (l) distance to surface; (m) contrast; (n) energy; (o) skewness; (p) kurtosis. (P<0.05) ...... 93

Figure 5.9 Confusion matrix of classification results ...... 94

Figure 5.10 Three dimensional classification results from human atria. (a) & (d) Original OCT volumes; (b) & (e) histology images; (c) & (e) color-coded classification results. Gold, yellow, red, and blue color represent dense collagen, loose collagen, normal myocardium, and adipose tissue, respectively. The classification results delineated the layer structure and agreed with Trichrome histology ...... 95

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Figure 5.11 Classification of collagen thickening region in human ventricle. a) Stitched white light image; b) stitched OCT B-scans; c) classification results on stitched OCT B-scans; d) classification results on stitched OCT volumes. The classification results successfully delineate the boundary of collagen thickening region...... 96

Figure 5.12 Microstructure of the atria. (a-c) Representative three-dimensional dataset of left atrium: (a) X-Y plane showing myofiber organization; (b) X-Z plane; (c) Y-Z plane. Imaging is possible through the entire atrial wall, where the smallest wall thickness is 0.5mm...... 98

Figure 5.13 Comparison of texture feature within adipose region in OCT B-scans. a) Typical OCT

B-scans with adipose region in focus; b) Typical OCT B-scans when adipose region is out-of- focus. The yellow box with adipose tissue is marked for comparison. Scale bar: 250 mm...... 100

Figure 6.1 Schematic of cervix and uterus position. Modified from Fernandez et al, 2016[203]

...... 105

Figure 6.2 Registered results of (a-d) PG and (e-l)NP samples. In particular, (a, c, e, f, i, k) are stitched camera image in two dimensions while (b, d, f, h, j, l) are stitched OCT volumes. For one

PG sample, 53 volumes are stitched as a new volume of 30 mm × 27 mm × 7 mm. For another PG sample, 54 volumes are stitched as a new volume of 28 mm × 27 mm × 4 mm. We stitched 40 volumes for the one NP sample and formed a whole volume of 20 mm × 24 mm × 5 mm. We stitched 41 volumes for the second NP sample and formed a whole volume of 21 mm × 26 mm ×

5 mm. We stitched 24 volumes for the third NP sample and formed a whole volume of 15 mm ×

19 mm × 5 mm. We stitched 48 volumes for the fouth NP sample and formed a whole volume of

24 mm × 31 mm × 5 mm. Smooth surfaces are observed when multiple volumes are combined.

...... 109

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Figure 6.3 Representative OCT images of (a-d) PG and (e-l) PG cervix. The FOV are 30 mm × 27 mm in (a)-(b), 28 mm × 27 mm in (c)-(d), 20 mm × 24 mm in (e-f), 21 mm × 26 mm in (g)-(h), 19 mm × 15 mm in (i)-(j), 24 mm × 31 mm in (k)-(l) . The image is a 2D plane that is parallel to the surface with a vertical depth of 245 μm. Fiber orientation results were processed for each OCT image. The estimations of orientation were made on each 1000 μm x 1000 μm. The results are color-coded based on confidence value ...... 111

Figure 6.4 Distribution over 12 sub-regions (a) – (l) of non-pregnant (NP) (red) and pregnant (PG)

(blue) samples. For each sub-region with a size of 1000 μm x 1000 μm area, the distribution is averaged over 10 depth with an increment of 49 μm. From (a) to (l), the peak value of distribution in NP is higher than the value in PG, which indicates less dispersion and more regularity...... 113

Figure 6.5 A pixel-wise directionality map on an en face image parallel from and 245 µm beneath the cut surface. (a) directionality map with locations of 400 μm × 400 μm subregions corresponding to 80 pixels × 80 pixels.; (b) OCT image within the white box in (a); (c) directionality map within the white box in (b). Pixels with no fiber information are coded in black.

Each 400 µm × 400 µm subregion represents a location for the fiber orientation and dispersion analysis in the A (anterior), P (posterior), L (left), and R (right) quadrants. Along the radial direction, the boxes are divided into inner region (red) and outer region (green)...... 116

Figure 6.6 Representative fiber distributions found in the upper cervix and corresponding 2D von-

Mises fits. The dominant direction 휃 is shown by dotted line. All four subregions are taken from the outer radial zone of the same NP sample (Specimen 5). A subregion with (a) a single family of fibers that have the most alignment (b = 0.820) and (b) highly dispersed fibers that are randomly oriented in the plane. A subregion with (c) two fiber families and (d) three fiber families. (Note: current distribution fitting methodology cannot distinguish the multiple fiber families.) ...... 118

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Figure 6.7 Definition of Region 1 and Region 2. The collagen fiber network in cervical tissue is not homogenous and it has two distinct regions: Region 1, the P/A quadrants in the outer radial zone (horizontal stripe), and Region 2, the rest (vertical stripe) ...... 119

Figure 6.8 Visualization of slices from the same patient a) 3D visualization of multiple cervical slices; b1-d1) en face OCT images from sl1 to sl4; b2-d2) corresponding directionality map of

OCT from sl1 to sl4...... 121

Figure 6.9 Visualization and statistical studies slices from a non-pregnant patient a) 3D visualization of multiple cervical slices; b-e) pixel-wise directionality map of OCT from sl1 to sl6; f) boxplot of concentration parameter; g) boxplot of penetration depth...... 122

Figure 6.10 Visualization and statistical studies slices from a pregnant patient a) 3D visualization of multiple cervical slices; b-e) pixel-wise directionality map of OCT from sl1 to sl6; f) boxplot of concentration parameter; g) boxplot of penetration depth...... 123

Figure 6.11 Measurements of each sample (c1to c9) at different locations to the uterus. a) mean value of concentration parameter b vs locations; b) mean value of penetration depth vs locations.

In general, the concentration parameter shows a decreasing trend and the penetration depth shows an increasing trend over the increased distance to uterus...... 124

Figure 6.12 a) boxplot of concentration parameter b; b) boxplot of penetration depth...... 125

Figure 6.13 Regional comparison of non-pregnant samples. a) concentration parameter in L/R region; b) concentration parameter in A/P region; c) penetration depth in L/R region; d) penetration depth in A/P region...... 126

Figure 7.1 Comparison of stitched OCT images with H&E histology. (a-b) DCIS; (c-d) cysts; (e- f) Terminal duct lobule unit; (g-h) IDC vs adipose tissue. The enlarged OCT images, with a larger

FOV, shows good match with histology image in capturing the morphological details...... 135

Figure 7.2 Classification results of fat region. (a) Comparison of sensitivity and specificity of tissue classification performed on Thorlabs datasets and UHR OCT datasets. (b),(e) and (c),(f) shows color-coded 3D fat maps with corresponding OCT volumes from Thorlabs system in normal and

IDC specimens, respectively. (d),(g) shows color-coded 3D fat map with corresponding OCT volume from UHR OCT system ...... 137

Figure 7.3 Volumetric UHR-OCT images and classification results between IDC and fibrous stroma. b1Two individual B-scans were selected to compare with the corresponding histology. a1)

OCT B-scan from location a in volumetric OCT dataset; a2) corresponding histology of a1; b1)

OCT B-scan from location b; b2) H&E histology of b. The estimated probability shows a good match with H&E histology Scale bar: 250 µm...... 138

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List of Tables

Table 2.1. R Square values of fitting the angle measurements over increased depth range in atrium and ventricle of Heart II...... 28

Table 2.2 Statistic results of rotation experiments. The polar angle and azimuth angle rotation experiments are described in Fig. 2 (c) and Fig.2 (d), respectively. Both polar angle and azimuth angle are measured in each experiment setup. The measurements of change of angle are listed as mean ± standard deviation calculated from Heart I to Heart V...... 32

Table 4.1 List of features used in the classifier ...... 66

Table 4.2 Comparison between automated segmentation and manual measurements from two observers...... 72

Table 5.1 Clinical characteristics of heart donors in dataset ...... 90

Table 6.2 Patient demographics of specimens used for this study. The first column relates patients with figure numbers of their OCT images. Gravidity is equivalent to the total number of pregnancies. Parity data is presented in TPAL recording system. TPAL stands for term, preterm, aborted, and living deliveries, corresponding respectively to each of the 4 digits. VD = vaginal delivery, VTOP = voluntary termination, FT = full term, SAB = spontaneous abortion (micollagen thickeningriage), CS = cesarean section, VBAC = vaginal birth after cesarean, NA = not avaliable.

...... 115

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Table 7.1 Classification results of invasive ductal carcinoma ...... 139

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Acknowledgement

First, I would like to thank my advisor, Dr. Christine P. Hendon, without whom this thesis would not have been possible. The help, guidance, and mentorship Dr. Hendon offered for me through four years in the Structure-Function Image Laboratory provided room for me to grow. Her mentorship has spanned many areas including experimentation, writing, and presenting, all of which are invaluable for my future career development.

I would also like to thank my committee members, Dr. Shih-Fu Chang, Dr. Kristin Myers and Dr.

Andrew Laine, and Dr. John Wright for serving as my committee members and offering advice, support and encouragement.

I am grateful to a group of people whom I closely collaborate with: Dr. Elsa Angelini, Dr. Hanina

Hibshoosh, Dr. David Tsay, Dr. Sheldon Feldman, Dr. Charles Marboe, and William Meiniel, for their constructive ideas and helpful discussions during my graduate pursuit.

I am grateful to my labmates: Xinwen Yao, Yuye Ling, Rajinder Singh-moon, Theresa Lye,

Nathan Lin, Diana Mojahed, and McLean James. Time spent with them in the office and lab is enjoyable and the discussions I have with them provide important feedbacks in a timely fashion to help my work. Great thanks go to Wang Yao, whom I worked with during almost my entire Ph. D. journey for many fruitful discussions and plenty of laughter. Thanks also go to previous labmates who spent a relatively short-time in my lab but together we had great learning experience: Syed

Bin Amir, Yang Zhao, Christopher Aswin Hermawi, etc.

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Special thanks go to parents and my beloved wife for their unconditional love/support and continual encouragement through my long and continuing educational journey.

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This work is dedicated to my parents and

to my wife

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Chapter 1 Background and Significance

This thesis is dedicated to the development of image analytic techniques to characterize biological tissues imaged by optical coherence tomography. We aim to develop analytic tools to facilitate fiber analysis, volumetric image stitching, and tissue classification for the analysis of cardiac tissue, cervical tissue, and breast tissue.

1.1 Optical coherence tomography

Optical coherence tomography is a non-invasive imaging technique based on the principle of low coherence interferometry [1]. In OCT, photons are irradiated using a broadband low coherence source. The reflectivity profile of imaged sample is obtained by interfering backscattered photons from a sample with the photons reflected from a reference beam. A typical OCT system can achieve a high axial resolution at micron level, a penetration depth of up to 2 mm, and video-rate data acquisition. OCT generates volumetric data, as shown in Figure 1.1. The reflectivity profile as a function of depth (axial direction) is known as A-line. By scanning the galvanometers in transvers

(lateral) X direction, we can obtain a 2D image, known as B-scan. With the third direction (Y direction) taken into consideration, it is technically possible to form a three-dimensional dataset.

The image at XY plane is called en face image. In OCT system, the axial resolution and the lateral resolution are decoupled. The axial resolution is equivalent to the coherence length of the illumination source, lc. The coherence length is given by:

2√푙푛2 2푙푛2휆2 푙 = = 0 (1.1) 푐 Δ푘 휋 Δ휆

Where λ0 is the central wavelength of illumination source with a bandwidth of Δλ and Δk is the bandwidth of illumination source in wavenumber. Only when the two paths of light travels with a path difference less than the coherence length, the system can resolve the interference between the two paths. The lateral resolution is determined by the center wavelength and numeric aperture (NA) by:

0.37휆 훿 = 0 (1.2) 푥 푁퐴 In conventional OCT system, there is a tradeoff between the lateral resolution and the imaging depth, which is proportional to the square of spot size. Low numerical aperture (NA) lenses are selected to maintain a long depth of focus in most OCT systems. Depending upon the measured interference pattern, OCT techniques, in general, can be categorized into time domain OCT

(TDOCT) and Fourier domain OCT (FDOCT).

Figure 1.1 Schemtics of 3D OCT acquisition. a) A-line: axial direction (z) acquisition; b) B-scan: axial(z)

and transvers (x) scanning; c) 3D scanning: axial (z) scanning and XY scanning.

1.1.1 Time Domain OCT Time domain OCT (TDOCT) is the first-generation of OCT. It was designed as a modification of Michaelson interferometer by repetitively moving the reference arm. As shown in Figure 1.2 (a), in TDOCT, incident light from a broadband low-coherence length light source is divided into two paths: one path reaches the reference mirror and the other path reaches the sample. The backscattered or reflected light are recombined to interfere. A single channel photoreceiver is utilized to measure the interference fringe. The envelope of detected fringe burst pattern corresponds to the interference between the light from the reference arm and each successive backscattering from sites at every single depth. By monitoring the envelope of detected interference pattern over depth, a depth-resolved reflectivity profile is generated. In general, TDOCT is in shot noise limit. The signal-to-noise ratio (SNR) is determined by the power incident on the sample, power reflectivity of the sample, detection bandwidth, detector quantum efficiency, and center wavelength of light source.

Figure 1.2 Schematics of time domain and Fourier domain OCT system. (a) Time Domain OCT; (b) Spectral

Domain OCT; (c) Swept Source OCT

1.1.2 Fourier Domain OCT Fourier domain OCT (FDOCT) is the second-generation of OCT. In FDOCT, as in Figure 1.2 (b- c), the reference arm is fixed at the position that approximates the position of the sample. Depth- resolved images are generated by measuring the interference pattern in Fourier domain. FDOCT systems can be further subdivided into spectral domain OCT (SDOCT) and swept source OCT

(SSOCT), the latter of which is also alternatively called optical frequency domain imaging, OFDI.

In SDOCT, the light source is broadband and emits continuous wave. The recombined interference signal is measured using a spectrometer and collected simultaneously on an array detector. In

SSOCT, the source is rapidly swept in wavelength. The spectral interference pattern is detected on a single or small number of photoreceivers as a function of time. SDOCT has a more stable phase response due to simultaneous detection pattern of spectral interference and thus achieves a higher speed due to the faster sweeping laser technology. Both SDOCT and SSOCT increase the integration time for A-line reconstruction and significantly improve the system sensitivity by 20 dB over TDOCT without compromising the imaging speed, as demonstrated in [2-4]. Within shot noise limit, the SNR of FDOCT is determined by power incident on the sample, power reflectivity of the sample, and the integration time of camera or sweep time of the swept source. The increased sensitivity enables video-rate B-scan imaging in SDOCT and 4D volumetric imaging in SSOCT

[5-7].

In terms of signal process, the spectral interference pattern in either SDOCT or SSOCT is encoded in its spectral frequency, which represents the entire depth-resolved structure of the sample at the position around the focal spot. The depth-resolved reflectivity profile can thus be reconstructed by inverse Fourier transform. In SDOCT, upon obtaining the spectral interferogram from the spectrometer, an A-line is reconstructed by four steps as shown in Figure 1.3. The first step is to

4 subtract DC component of signal obtained by blocking sample arm from measurements recorded in the spectrometer. Second, the measurements are converted from wavelength (λ) domain to wavenumber (k) domain. This step introduces non-linear conversion and thus requires a linear interpolation in k domain. Third, the spectral interferogram is further windowed (apodized) to reduce the effect on side lobe. Finally, inversed Fourier transform reconstructs the A-line’s reflectivity profile.

Figure 1.3 A-line reconstruction with SDOCT (data was under-sampled by 3 for better visualization). a)

Recorded signal and background signal; b) signal after background subtraction; c) signal after λ domain to k domain conversion; d) signal after apodization; e) signal after IFFT.

1.2 OCT techniques in biomedical imaging

Since invented by Huang et al [8] in 1991, OCT has been rapidly and successfully applied in ophthalmology [9]. Due to its merits of the being non-invasive and depth-resolved, OCT has been

5 applied to image gastrointestinal tract [10] , embryonic heart [11], dermatology [12], pulmonary medicine [13], etc. Notably, there are increasing interests in employing OCT techniques in cardiac imaging, cervical imaging, and breast imaging.

In cardiology, OCT has been commercialized in wide intravascular applications [14-16]. OCT is capable of providing detailed morphological information within the heart wall [17]. In particular,

OCT has been demonstrated to visualize image important cardiac features such as the Purkinjie network [18], atrial ventricular nodes [19, 20], sinoatrial nodes [21], and myofiber organization

[22-25]. Given the fact that the wall thickness in human atria ranges from two to five mm [26],

OCT has the ability to visualize a large percentage of the entire human atrial wall.

In gynecology, OCT has been employed to visualize multiple structures [27]. Normal and neoplastic cervical tissues have been imaged and studied [28]. Endocervical mucus was imaged by endoscopic OCT [29]. Layered structure of the epithelium, the basement membrane, and the stroma have been visualized to identify CIN [30, 31]. OCT also shows great potential in detecting acetic acid for the diagnosis of pre-invasive and invasive neoplasia [32].

In addition, OCT has been used in breast imaging to aid the detection of breast cancer. Facilitated by handheld probes and needle catheters designs, OCT provides a non-destructive high resolution imaging tool to evaluate ex vivo breast tissues [33]. Functional OCT systems, including optical coherence elastography [34-36] and polarized sensitive optical coherent tomography [37-39], have been used to evaluate breast tumor margins.

The growing applications of OCT techniques highlight the needs of developing image analytic tools to extract biological information in OCT images.

1.3 Challenges in OCT image analytic tools

Biomedical image analytics is a highly interdisciplinary field, being at the interface of physics, computer science, medicine, biology, and engineering. As a cross-sectional imaging method, OCT provides volumetric information of tissues. The desirable output of image analytic is in 3D space, which challenges the development of analytic tools. In addition, the image quality of OCT images is limited by its optical system design. How to improve the image quality for analytical purpose becomes a challenge and thus a hot topic in OCT community.

As a coherence imaging modality, OCT suffers the corruption of speckle noise. Speckle noise, with a distinctive granular or mottled appearance, occurs when light from a coherent source scatters at the distance that is close to the coherence length of the light source. Statistically, the speckle noise follows a Rayleigh distribution [40, 41] affected by size and temporal coherence of light source, multiple scattering and phase aberrations of the propagating beam, and aperture of the detector. In OCT, speckle noise degrades the image quality. Various approaches, from both hardware and software aspects, have been proposed to denoise the speckle noise. Without complicating the system and increasing the data acquisition time, algorithmic aspect attracts more attentions in OCT denoising. Starting from averaging [42], median [43] and Wiener filtering kernels [22], there is a shift in applying adaptive filters such as the adaptive median filtering, adaptive Wiener filtering [44], and adaptive wavelet filtering [45]. Recently, the signal sparsity has been explored to denoise the OCT image for retinal imaging [46, 47]. In general, the selection of OCT denoising tools is application specific. Metrics used to evaluate the denoising performance are contrast improvement index, contrast to noise ratio, and peak signal noise ratio. The optimal denoising tool can be selected by evaluating the metrics prior to application.

Image obtained by is the reflectivity profile of sample in responding to the light source. It shows that properties, such as attenuation and scattering of tissue, are affected by central wavelength and bandwidth of light source. For instance, the image quality varies in local contrast and in peak-to- trough ratio using different light sources at different bandwidths [48]. In principle, the OCT intensity image is the reflectivity profile convolved with point spread function, the impulse response of OCT system. This leads to apparent image degradation at depth that is out of focus. In addition to extend the focus through optical design, efforts are taken to deconvolve the original image through image processing to enhance the image quality [49]. Moreover, the point spread function also results in degradation in the evaluation of attenuation coefficients and scattering coefficients. Thus, specific models are proposed to measure the property from OCT images [50-

52].

1.4 Existing OCT image analytic tools

In this thesis, we focus on image analytic tools designed for OCT biological images with aims of aiding the diagnosis and treatment of cardiovascular disease, preterm birth, and breast cancer.

Motivated by these aims, we are interested in developing algorithms to quantify fiber orientations, to stitch volumetric data, and to classify tissue compositions.

1.4.1 Fiber orientation analysis OCT has been demonstrated to be capable of visualizing various fiber types, such as nerve fiber tracts in brain [53, 54], skeletal muscle fibers [55-57], hearts [22, 57], and collagen network [47,

58]. Most fibril structures show a strait pattern in OCT images. Rather than qualitatively describing the fiber morphology, various methods are proposed to quantify the fiber orientations. In [22], an intensity gradient method [59] was modified to estimate the fiber orientation within en face planes in heart image. The estimated angular distribution is based on an exponential weighted

8 contribution of pixel intensity and thus shows good approximation on the estimation of dominant angle within sub-regions. Similarly, local orientation distribution function was constructed based on 2D discrete Fourier transform (DFT) and approximates the dominant fiber trend in [57]. To reconstruct the tractography within heart fiber and nerve fiber, a maximum diffusion scheme, previously used in MRI neural fiber pathway determination [60], was implemented and demonstrated with good agreement with histology in en face plane. Multi-scale decomposition was employed to reconstruct fiber structure in cardiac ultrasound images [61]. As a functional extension of conventional OCT, PSOCT resolved pixel-wise birefringence properties that are directly related to fiber information. It is possible to reconstruct 3D tractography in brain nerve fibers [54] and heart muscles [25] using PSOCT. Due to the subtle fiber information in 3D space,

3D quantifications and tractography of myofibers from OCT intensity are still challenging.

Analytic tools to investigate the fiber orientation in pixel-wise is lacking in OCT community.

1.4.2 Stitching algorithm Characterizing large samples within OCT imaging can be achieved through stitching multiple overlapped 3D volumes. Many current stitching methods for OCT image sets are developed for retinal imaging, where blood vessels with high contrast are a good reference for registration. In addition, retinal tissues have distinctive layered structures, which facilitates the registration of B- scans in 3D space. It is thus feasible to use SIFT to extract features from OCT images for registration [62]. Zawadzki et al [63] registered multiple retinal OCT volumes through manual stitching, then developed a ray cast method to render the volumes and used an annealing algorithm to optimize the alignment among multiple retinal imaging volumes [64]. Multiple OCT volumes are stitched in [65] based on blood vessel matching algorithm. In [66], a B-spline-based deformation method was used to register multiple volumes for a motion-free images of the retinal

9 vessels. Recently, a stitching algorithm is developed to register OCT volumes based on rotation scheme to image small mice heart [67]. In general, the algorithms to stitch OCT volume with weak surface feature is scarce.

1.4.3 Automated segmentation and tissue classification Segmentation algorithm for OCT images have been developed for tissues and organ systems such as retinal [68-70], cartilage[71], blood vessels [72], airway [73] , esophagus [74], and skin [75].

In general, these methods can be categorized into non/semi-automated methods [71, 72, 75] and automated methods [68-70]. The non/semi-automated method requires a large workload and the estimation could be biased. Most automated methods have been developed for segmenting retinal image to assess the macula [68, 69] or the cornea [70]. However, most of existing retinal image segmentation methods were implemented based on prior information of samples. The prior information includes the number of layers and the intensity transition pattern within OCT images.

Representing the reflectivity profile, the OCT intensities are highly correlated to tissue properties.

Numerous algorithms have been developed to automatically classify tissue types in esophagus [76], skin [12, 77], cardiovascular [78], and breast [79, 80] from OCT images. In regard of features extracted for classification, the methods can be categorized into two groups: optical properties and texture information. Optical properties include attenuation coefficient [81], scattering coefficients

[50], spectroscopic information [78], and birefringence [77]. Texture information includes gray level co-occurrence matrix, [82] texture feature coding [76], and fractal analysis [83]. Based on the input and output of the system, the classifier can be pixel-wised [80, 84], A-line based [79], and regional based [10] . The regional based algorithm usually starts from a segmentation algorithm. In terms of classification model, support vector machine [77], decision tree [85], and principle component analysis [78] are employed to automatically estimate the types within the area

10 of interest. Due to the complicated structure in myocardial, to the best of our knowledge,there is no existing algorithm to automate the classification of tissue compositions in cardiac OCT images.

For breast imaging, very few works address issues in automatic identification of breast cancerous region.

1.5 Objective

Overall, there are very limited analytic tools to automatically characterize cardiac tissue compositions, cervical collagen fiber networks, and breast cancer tissues in OCT community. The objective of this thesis is to develop automated image analytic tools to bridge the gaps between

OCT images and clinic interpretations in cardiology and gynecology. We develop three automated analytic tools: 1) direction analysis tool to study the fiber organization; 2) volumetric stitching tool to enlarge the field of view of OCT system; 3) tissue classification tool to automatically identify tissue composition. The tools are designed for three clinical aims: 1) characterization of tissue types within heart to aid the diagnosis and treatment of arrhythmias; 2) analysis of the collagen fiber network within cervix to understand preterm birth; 3) identification of cancerous region within breast to aid the treatment of breast cancer. The framework of each tool is developed in a generic pattern such that multiple imaging applications will benefit from each analytic tool. The relationship between imaging analytic tools and applications is presented in Figure 1.4. We develop algorithms for each aim and validate algorithms from OCT images we obtained from biological samples. The tools are collaboratively applied in the application of cardiac imaging, cervical imaging, and breast imaging. Chapter 2 to 4 present the analytic tools and Chapter 5 to 7 present the application. Chapter 2 will present a fiber analysis tool including 3D fiber tracking scheme and a pixel-wise dispersion analytic scheme. Chapter 3 will provide a generic stitching method to mosaic multiple OCT volumes. Chapter 4 will illustrate the machine learning tool to

11 automatically differentiate tissue composition. Chapter 5 will present the application of fiber analysis tool, stitching tool, and classification tool in myocardial tissue. Chapter 6 will analyze the dispersion of cervical collagen fiber network using the fiber analysis tool and stitching tool.

Chapter 7 will describe the breast tissue analysis using stitching tool and classification tool.

Chapter 8 will summarize the thesis, and propose future work.

Figure 1.4 Structure of research work in this thesis

Chapter 2 Automated algorithm for Fiber orientation analysis

2.1 Introduction

In biology and medicine, fiber refers to a thread-like, filamentary structure [86]. In human organs, fiber appears as either a filament structure constituting the extracellular matrix (ECM) of connective tissue, such as collagen fiber or an elongated, or a threadlike structure, such as muscle fiber or nerve fiber. Fiber is an important structure from mechanical or/and electrical point of view.

The directionality of fiber structure is essential to the normal functionality of many organs. In this chapter, we focused on developing fiber orientation analytic tool to study the organization of cardiac myofibers and cervical collagen fibers.

Cardiac fibers are relatively short, branched fiber with a typical diameter ranges from 10 to 20 µm

[87] in normal human heart. It is an involuntary fiber with single nucleus centrally positioned. The cardiac myofibers exhibit a strait pattern. The myofiber orientation directly influences mechanical contraction where the fibers follow a left-handed helical path near the epicardium and right-handed helical path near the endocardium [88]. Therefore, changes in fiber orientation structure may result in abnormal mechanical contraction of heart, which is observed within patients who suffer from cardiomyopathy [89, 90]. For electrical conduction, action potentials, which propagate along myofibers within cardiac tissue, show a direction-dependence. The structural anisotropy of the myocardium is correlated with the function, where the propagation of electrical wavefront is about three times faster along the longitudinal axis than along the transverse axis of the myofiber [91].

Abnormal myofiber orientation or myofiber disarray would cause conduction abnormalities which can further results in arrhythmia [92] such as atrial fibrillation and ventricular tachycardia. 13

Collagen fibers form a rigid rod-shaped structure and impart tensile strength to the cervix [93]. The collagen in cervix is primarily types I and III in connective tissue stroma and type IV associated with smooth muscles and vascular components. The diameter of a single collagen fibril ranges from

15 to 185 nm, and bundles spread out, with length increasing from 12.4 to 14.7 μm [94]. The cervix is a dense collagenous tissue, where the mechanical integrity of the tissue is attributable to the preferred directionality of its collagen fibers [95]. Mechanical properties of human cervical tissue have been previously measured using standard uni-axial compress/tension tests [96, 97], indentation

[98], permeability tests [99], and aspiration [100-102]. During pregnancy, the cervix becomes softer to accommodate delivery [101]. It is hypothesized that the remodeling of the cervical collagens is the main feature of this softening process. In animal models of pregnancy, it has been shown that this softening is accompanied by a decrease in collagen crosslink [103]; and in human tissue it has been shown that pregnant tissue is more soluble in weak acid solutions compared to non-pregnant tissue [104]. Accompanying this collagen crosslink turnover, it is hypothesized that the overall directionality (i.e. ultrastructure) of the cervical collagen changes, where the collagen fibers lose their preferred directionality and become more disorganized as pregnancy progresses. It would seem, therefore, that investigation is needed to study the change of collagen fiber orientation.

Representative en face OCT images are shown in Figure 2.1. Cardiac myofibers and cervical collagen fibers are in (a) and (b), respectively. The myofibers are arrayed in the pattern of streamline while the collagen fibers appear in a crosslink pattern with more dispersion. We are interested in extracting the subtle fiber structure and analyzing the dispersion pattern.

Figure 2.1 Representative OCT en face image of a) cardiac myofiber; b) cervical collagen fiber. The cardiac fibers show a pattern of streamline and the collagen fibers are crosslinked structure with more dispersion.

Scale bar: 500 m.

2.2 Three-dimensional orientation and tractography of myofibers

2.2.1 Quantification of fiber orientation in three dimensions To quantify the trend of 3D orientation of myofibers, we determined the orientation within en face

(X-Y plane) images and back projected the fiber with respect to the sample surface. The approach is based on assumption that myofibers are approximately parallel to the endocardial and epicardial surface [105-108], with a variation of 4 º to 7 º [109-112]. The flowchart is shown in Figure 2.2, illustrating the framework of our automated method to determine fiber orientation in three dimensions. Specifically, the algorithm includes two components: 1) fiber orientation determination in en face plane and 2) surface plane detection and fitting.

Figure 2.2 Flowchart of the automated algorithm for quantification of fiber orientation in three dimensions.

Components of preprocessing, two-dimensional fiber orientation algorithm and interpolation are used to quantify fiber orientation in en face plane. Edge detection block and plane fitting block are used to back project the fiber orientation from two dimensions to three dimensions.

In en face plane, we modified the intensity based gradient algorithm [22, 113] that was previously used to quantify fiber orientation in two dimensions. As the first step of pre-processing, successive en face images at different depths were averaged to achieve higher image quality. The number of averaged images was determined by the depth resolution of OCT system and the diameter of myofibers. In our system design, the empirical setting of number of averaging is four. To sharpen the image, a second order Butterworth high pass filter was convolved with the averaged en face

OCT image. In addition, a median filter was used to reduce speckle noise. For each image pixel (i, j), the intensity gradients in the horizontal (Gx) and vertical (Gy) direction were calculated by convolving two 3 × 3 Sobel filters with en face OCT images. The magnitude of gradient G(i, j) and angle Φ(i, j) was calculated as:

2 2 퐺(푖, 푗) = √퐺푥 (푖, 푗) + 퐺푦 (푖, 푗) (2.1)

퐺푦 Φ(푖, 푗) = 푎 tan ( ) (2.2) 퐺푥

Within a small sub-region W, the angle probability P(ω) (0º ≤ ω ≤ 179º) was:

푃̃(휔)푊 푃(휔)푊 = (2.3) 179 ̃ 푊 ∑휔=0 푃(휔) exp (2 cos[2(휔 − Φ(푖, 푗))]) 푃̃(휔)푊 = ∑ 퐺(푖, 푗) where exp (2) (2.4) (푖,푗)∈푊

This scheme assumed that the gradient in each pixel (i, j) in W follows a Von Mises distribution, analogous to a normal distribution, with mean of Φ(i, j) [113]. In W, the gradient of all pixels was considered and the weighted sum was computed in (2.4). The mean value of ω was regarded as estimation of dominant gradient in W. Note that the fiber orientation is perpendicular to gradient direction in en face plane. The estimated fiber orientation was determined by shifting the gradient direction by 90º. Since the fiber orientation in W is a summation of all local angles Φ(i, j), angle

ω is supposed to follow normal distribution so that the mean of ω is an accurate estimation of fiber orientation. Within some sub-regions, ω calculated from (2.3) were not normal distributed, which resulted in estimations in some sub-regions that were highly erroneous. To overcome this issue, we developed a confidence metric to assess the reliability of the orientation estimation. The metric was defined as the probability where ω equals its mean value divided by standard deviation of ω.

The confidence metric is the inverse of coefficient of variation [114]. If the confidence value was below a threshold, the estimation of a sub-region was considered as unreliable. The fiber orientation in unreliable sub-region would be recalculated by the interpolation of the estimations in its reliable neighboring regions. If all neighboring regions were unreliable, we claimed this region lacks enough fiber information and is likely to be other tissue composition.

To obtain three-dimensional orientation, we projected the measured en face orientation with respect to the sample surface. To determine the angle of the surface plane we detected the edge in each B- scan (X-Z plane) of OCT image by searching the maximum gradient point in a smooth-filtered

17 image. For each voxel in three dimensions, we detected all edge points corresponding to the surface of the voxel. We further employed linear least square method to fit a plane through those edge points. The fitted surface plane was utilized to reconstruct fiber orientation from two dimensions to three dimensions. A schematic of the fiber orientation determination is plotted in Figure 2.3.(a). We draw two planes (represented as planes with dash borders) through the centroid of voxel: one in parallel to the fitted surface plane and the other perpendicular to the en face plane with a projection in en face plane orientated in the direction of its estimated fiber orientation. The two planes intersected to produce a new line, which indicated the 3D fiber orientation. We quantify the estimated fiber orientation with polar angle ϕ and azimuth angle θ in a polar coordinate system, which are plotted in Figure 2.3 (b).

Figure 2.3 Schematic of quantifying fiber orientation in three dimensions (green line) and coordinate system used in our algorithm. (a)Two planes are produced: one is parallel to surface plane and the other is perpendicular to en face plane with a projection in en face plane as the red line. The intersection of the two planes is the fiber orientation in three dimensions. (b) Angles in three dimensions. The red line represents the fiber. Polar angle ϕ is the angle of fiber with respect to z axis. Azimuth angle θ is the angle of the projection of fiber in en face plane with respect to x axis.

2.2.2 Tractography of fibers· in three dimensions

The essence of reconstructing tractography from an OCT image is to estimate the fiber trace. We formulated the fiber tracking problem as state space model and utilized particle filter techniques

[115] to reconstruct tractography [116]. The initial estimation of the fiber tracking step was based on the fiber orientation results in previous section. Thereafter, the myofibers were traked by the particle filtering step incorporating the intensity of OCT image. We generated clusters of particles to track possible fiber trace. The automated algorithm in previous section provided prior probability densities that characterized the properties of particle propagation. The observed OCT image was used to assess the reliability of each particle trace. In particular, the trace of myofiber can be modeled as a sequence of points in image space 푍 = 푧0, 푧1, … , 푧푛. We assume that the propagation trace forms a Markov chain [117]. Let 푧0 the anchor of a fiber. The progressive growing process of a fiber trace can be described as:

푧푛+1 = 푧푛 + 휌푣⃗⃗⃗⃗푛 (2.5) where ρ and ⃗푣⃗⃗⃗푛 are the step size and direction of propagation fiber at step n. The input of the algorithm is the OCT image Y. The output of the algorithm is the coordinates of fiber trace Z.

Here, we use 푣⃗⃗⃗⃗푛 to determine the coordinate of zn. in (2.5) The schematic representing the data flow in the fiber tracking is shown in Figure 2.4.

Figure 2.4 Flow diagram of tractography using particle filter method. Sequential clusters of particles are generated, weighted in each iteration. The coordinates of particles in each cluster are weighte d summed to estimate the trace of myofibers in OCT image. N eff is a metrics to evaluate whether most of particles are with low weights. Ns is a threshold to determine whether a resampling process is needed.

First, we defined the number of particle M and an anchor z0. The principle of particle filtering is to sequentially sample M paths from the anchor z0. All particles propagated in the area of interest

푚 푚 푀 will be used to predicate the coordinates along the fiber trace. Given a set of particles {푧푘 , 푣푘 }푚=1 at step k, the propagation of fiber trace to next step k + 1 was performed through following steps: predication, weighting, resampling (optional) and estimation.

In the predication step, the direction where the particle propagated was determined by the angle probability in the area where the estimation of previous step locates. The propagation model can be expressed as:

푚 푚 푚 푚 푊 푝(푣 푘+1|푧0:푘) = 푝(푣 푘+1|푧푘 ) = 푃(휔) (2.6) where P(ω)W is the probability in (2.4). It has been previously shown that myofibers are nearly parallel to epicardial and endocardial surfaces. Therefore, a variation of 4 º was added to the mean of P(ω)W based on measurements of existing literature [109-112]. Angle ω was the direction that

푚 푚 푚 푣 푘+1 propagated. W denoted the sub-region where particle 푧푘 located. The orientation 푣 푘+1 was

푚 generated based on the probability in (2.6). The coordinate of 푧푘+1 was then computed based on

(2.5).

푚 푚 The weighting step gave a measurement 푤푘+1 of reliability for the propagation from 푧푘 to

푚 푧푘+1. Theoretically, the weights is determined by the weight of previous step and the probability of viewing the observation given the propagated direction [115]. The weight can be represented as:

푚 푚 푚 푚 푤푘+1 ∝ 푤푘 푝(푦푘 |푣푘 ) (2.7)

푚 푚 푤푘+1 푤푘+1 = 푀 푚 (2.8) ∑푚=1 푤푘+1

푚 푚 푚 where 푦푘 is the observation in OCT image when particle propagated from 푧푘 to 푧푘+1. It was

푚 푚 defined as all pixel values (or voxel values in three dimensions) the trace 푧푘 to 푧푘+1 covered in

푚 OCT dataset. If the fiber trace exactly covers푦푘 , the standard deviation of all pixel (voxel) values

푚 in 푦푘 was very low and the predication is considered as being reliable. Therefore, we set the

푚 푚 푚 푚 reciprocal of standard deviation of 푦푘 as an estimation of 푝(푦푘 |푣푘 ) and calculate 푤푘+1 according to (2.7) and (2.8).

The resampling step was called when large numbers of particles had low weights. In this case, most of the particles, indicating the trace with lower possibility, are negligible. To quantify such indication, we measured a metric, Neff, as following:

1 푁푒푓푓 = 푀 푚 2 (2.9) ∑푚=1(푤푘+1)

Neff is an estimation of the degeneracy highly related to the variance of weights [115]. Small value of Neff indicates high degeneracy. If Neff was smaller than a threshold Ns, we eliminated low weighted particles and regenerated them based on the coordinates of particles, which were of higher weights.

The coordinate of the fiber at step k+1 was estimated as the weighted center of M particles. The fiber trace propagated until it was out of the image boundary. The tractography scheme and results are presented in Figure 2.5 at an en face plane within a right ventricle. Figure 2.5 (a) shows the quantification results of fiber orientation computed by the method mentioned in 2.2.1. The estimated fiber orientations in the sub-region were used in prediction step. Figure 2.5 (b) displays the propagation trace of one fiber, which starts at a blue anchor on the right lower corner of OCT

푚 푚 푀 image. The colored segments are the propagation trace {푧푘 , 푣푘 }푚=1for each particle at different steps. The white dots are the weighted center of the particle cluster at each step. The tractography of multiple fibers are shown in Figure 2.5(c). Compared with the OCT image, we successfully reconstruct the fiber in the en face plane. In the 3D volumetric data, our predication and trace scheme is in 3D space, rather than 2D space as shown in Figure 2.5.

2.3 Pixel-wise orientation estimations and dispersion analysis

2.3.1 Pixel-wise orientation estimation In addition to general trace of myofibers. We are also interested in the pixel-wise orientation on biomedical images, especially in collagen region. In cervical images, the collagen fiber shows a crosslink pattern, and the dispersion information of fiber network is a critical factor for computational model. Upon the collection of the three-dimensional data, we generate parallel en face image that is parallel to surface to enhance the visualization of collagen fibers. Fiber orientations were extracted for each pixel by optimizing a pixel-wise fiber orientation method [118,

119] for OCT image datasets. In each en face image, the collagen fiber region was first masked based on the gradient value. Then, the image was enhanced through histogram stretching. The image was sharpened by second order Butterworth high pass filter and subsequently denoised by a median filter.

Figure 2.6 Pixel-wise fiber orientation analysis. (a) Schematic of determining the orientation in pixel p 0. (b)

A schematic of generated directionality map; (c) Distribution fitting in the area of interest (yellow box in (b)).

A weighted summation scheme was utilized to determine the fiber orientation information at each pixel over the entire region. For a pixel of interest, p0, there were multiple candidate directions αj towards its neighboring pixels, p1 and p2. A weight was assigned to each candidate direction as following:

푤j = 푤푖×푤푑 (2.10)

1 푤 = − 푠푡푑(푝 , 푝 , 푝 ) (2.11) 푖 3 1 0 2 1 푤푑 = (2.12) 푑푖푠푡(푝0, 푝2 표푟 푝1)

The weight was determined by two factors, 푤푖 and 푤푑 . The first factor, 푤푖 , was the intensity variations between the pixel of interest (p0) and its neighboring pixels (p1 and p2) along a direction.

The second factor, 푤푑, was the corresponding distance between the pixel of interest (p0) and the neighboring pixel (p1 or p2). The direction, 훼, of target pixel p0 is determined by the weighted circular mean of all direction candidates as following:

푁

훼 = arg (∑ 푤푗× exp (푖훼푗)) (2.13) 푗=1

Where N is the number of direction candidates around pixel p0. Given the direction information of each pixel, we generate the directionality map of the whole OCT image. A schematic of algorithm is shown in Figure 2.6(a).

2.3.2 Distribution fitting Based on the pixel-wise orientation information, we obtained the directionality map as shown in

Figure 2.6(b). The directionality map was further divided into sub-regions. In each sub-region, a

2D von-Mises probability density function,

푒푏 cos(푥−휃) 푃(푥) = (2.14) 2휋퐼0(푏) was fit to the pixel-wise orientation data to determine the fiber direction θ and the concentration parameter b. The two parameters were estimated by a least squares method using MATLAB

(MathWorks, R2014b) function (fit). 퐼0(푏) is a modified Bessel function of the first kind of zero order. Here, 휃 ∈ [0,2휋) is the dominant fiber direction and 푏 > 0 is the concentration parameter

[120]. The concentration parameter b describes the dispersion level of Von Mises distribution.

When 푏 approaches 0, the distribution gets closer to isotropic (circular in 2D case), and as 푏 increases to infinity the distribution gets closer to perfectly aligned fibers. In other words, b is inversely related to fiber dispersion where a low b describes a high fiber dispersion and a high b describes a low fiber dispersion.

2.4 Method validation

2.4.1 Validation setup To validate our methods, five swine hearts were imaged. Three swine hearts (Heart I to Heart III) were acquired through Columbia University’s tissue sharing program. Two hearts （Heart IV to

Heart V）were from local butcher. One human cervical sample was from Columbia University

Medical Center from an Institutional Review Board (IRB) approved protocol. TELESTO, a commercial spectral domain OCT system (Thorlabs GmbH, Germany), was used to image samples.

It was an InGaAs based system centering at 1325 nm, with a bandwidth of 150 nm. The axial and lateral resolutions were 4.9 µm and 5.3 µm in water respectively. The maximum axial line rate was 92 kHz. In our experiment, each volume consists of 600 × 600 × 512 pixels, corresponding to a tissue volume of 4 mm × 4 mm × 1.88 mm. The volumetric scan was performed at 28 kHz.

2.4.2 Validation of 3D fiber orientation quantification We evaluated our 3D fiber orientation algorithm in swine hearts. Representative results are shown in Figure 2.7, where the results in each sub-region are at two depths and shown for the septum

(Heart I), atrium (Heart II) and ventricle (Heart III). The sub-region in (2.3) is a 0.3 mm × 0.3 mm

× 0.03 mm volume in the experiment. The results were compared with the OCT image in en face plane and the surface plane. We found that the estimation of orientation agreed with the streamline in en face image of OCT data and was approximately parallel to surface. The orientation is color coded in unit vector and visualized in the RGB color space (R = |cosθ·cosϕ|, G = |cosθ·sinϕ|, B =

|sinθ|).

Figure 2.7 Quantification of 3D fiber orientation from three swine hearts: (a) ventricular septum (Heart I); (b) left atrium (Heart II); (c) left ventricle (Heart III). Light gray shows endocardial surface. Two representative en face OCT images are shown, with 3D fiber orientation overlaid with orientation encoded in color.

2.4.3 Comparison with manual measurements We sampled a volume over an area of 1 mm × 1mm on the epicardial side (atrial samples) or endocardial (ventricular samples) side and processed our automated algorithm. We set the depth where we firstly screen clear fiber streamline as reference depth (depth = 0 µm). Due to the different structure of samples and image quality in various dataset, the reference depth used in this section can be 0.2166 mm to 0.5508 mm under the surface. The depth was increased in an increment of 25 µm. The measured mean value of azimuth angle, θ, were recorded and linearly fitted at each depth. We found that the relationship between depth and azimuth angle are well linearly fitted with an R2 of 0.7778 within the range of 0 to 500 µm in left ventricle and 0.7748 in left atrium within the range of 0 to 300 µm in a representative heart, Heart II. However, the linear relationship diminishes with increasing depth due to a decrease in image contrast in depth. We compared a range of 300um and 500um within the atrium and ventricle to a range of 1000um in both chambers to assess an appropriate range for evaluating orientation versus depth. We found that the R2 of linear fitting model was dramatically reduced at a range of 1000um in atrium and ventricle. Such limitation exists in all chambers. There are two reasons for this limitation. First,

27 the quality of OCT image degrades when depth increases. The image became darker and shadowing might appear at some depth. Second, it may not be myocardial tissue when depth goes deeper. Besides, we found the validate range is related to thickness of wall. In the following experiments, we present the orientation results from depth of 0 to 300 µm in atrium and 0 to 500

µm in ventricle and ventricular septum.

Table 2.1. R Square values of fitting the angle measurements over increased depth range in atrium and

ventricle of Heart II.

Left Atrium Left Ventricle Depth range (mµ) R square Depth range(mµ) R square 0 to 300 0.7748 0 to 500 0.7778 0 to 1000 0.2160 0 to 1000 0.4154

To validate the method quantitatively, an investigator blinded to the results of algorithm manually measured the fiber orientation on the same area and depth. We compared azimuth angle, θ, from automated algorithm and manual measurement. The comparison is plotted in Figure 2.8. The two linearly fitted models matched very well with slops around 1 and R square values larger than

0.7500.

Figure 2.8 Comparison of manual fiber orientation measurements of azimuth angle, θ, vs computed θ based on automated algorithm. The samples are from left atrium (blue circle) and left ventricle (red triangle) of Heart II over an area of 1mm × 1mm area at an increased depth. The depth was increased from epicardial side to endocardial side in an increment of 25 µm. The results from automated algorithm match the manual measurements.

2.4.4 Rotation test To further validate our three-dimensional fiber orientation algorithm, we designed series of rotation tests. Representative results are shown from a data set acquired from the right ventricle of a swine heart (Heart IV). The experimental protocol was shown in Figure 2.9, where we placed the sample on a base and rotated the base’s azimuth angle in the en face plane with polar angle unchanged. We imaged the sample in increments of 30º of rotation. We computed polar angle, ϕ, and azimuth angle, θ, using the three-dimensional fiber orientation algorithm and presented the results in Figure 2.9. The mean and standard deviation over all sub-regions are shown at the top of each OCT images. Comparing the mean of θ in Figure 2.9(b) (c) (d) with the reference angle in

Figure 2.9(a), the measured Δθ’ were 26.98º, 61.34º and 97.59º respectively. The difference between reference angle and measured angle were within 15% of the reference change of angle.

The experiment demonstrated that our algorithm was able to quantify the changes of angle at en face plane. Importantly, the measured change in polar angle, Δϕ, with respect to the reference were

-2.85 º, -1.56 º, 1.94 º.

During the rotation, we imaged and processed the image when the rotations are (b) 30º (c) 60º (d) 90º. The measured mean value and standard deviation of azimuth angle and polar angle are computed and dis played on the top of each image. The measured change on polar angle, Δϕ’, was within 5º. The change of azimuth angle,

Δθ’, matches the rotation in our experiment with respect to reference angle.

Similarly, we successively rotated the polar angle with an increment of 7.50º on the same sample.

The surface and OCT image are plotted in Figure 2.10 for comparison. The change of polar angle was observed from both quantification results and surface plane. The mean and standard deviation over all sub-regions are also shown at the top of each OCT images. Comparing the mean of ϕ in

(b) (c) (d) with the reference angle in (a), the measured Δϕ’ were 7.13º, 14.57º, 19.36º. The difference between reference angle and measured angle were also within 15% of the reference change, Δθ’, with respect to the reference was 0.04 º, 8.84 º, 0.67 º. This experiment showed that our edge detection and curve fitting methods are feasible among different change of polar angles.

During the rotation, we imaged and processed the image when the rotations are (b) 30º (c) 60º (d) 90º. The measured mean value and standard deviation of azimuth angle and polar angle are computed and displayed on the top of each image. Light gray shows endocardial surface. The azimuth angle, Δθ’, remains changes little.

The change of polar angle, Δϕ’, matches the rotation in our experiment with respect to reference angle.

A summary of the rotational experiments for five samples of each experiment is shown in Table

2.2. The samples are from five swine hearts (Heart I to Heart V). The mean value of the change of angle agrees with reference angle within 1.5 º in both azimuth and polar angle rotation test. We found that the mean and standard deviation of Δϕ’ in azimuth angle rotation is larger than that of

Δθ’ in polar angle rotation test though the reference change of angles are both 0 º. The reason is that amount of light back reflected into the system’s objective is reduced when the surface is tilted, resulting in OCT images with decreased image quality. The image processing results thereby degrades. We found that root-mean-square (RMS) of pixels dropped from 21.45 in Figure 2.10 (a) to 18.39 in Figure 2.10 (d), which indicated a decreased contrast.

Reference (º) Measurements (º) # of samples Δθ’ 90 89.14±7.11 5 Azimuth Angle Rotation Δϕ’ 0 1.76±1.35 5 Δθ’ 0 4.96±4.02 5 Polar Angle Rotation Δϕ’ 15 13.99±3.01 5

2.4.5 3D tractography To validate our tractography algorithm, we processed our approach in three-dimensional space from the dataset obtained in a ventricular septum. A representative result is shown in Figure 2.11.

We predicted the trace of fibers based on the distribution of fiber quantification results. We color- coded the direction along fiber trace in three dimensions, as shown in Figure 2.11, in comparison to the original OCT image volume. Through the comparison with original en face image in (b).

We found that our reconstructed fiber trace matched the straits visible in OCT image among all

32 three datasets. Notably, the fiber tracking algorithm itself is not computational consuming. The overall runtime for the fiber tracking algorithm was less than 7 minutes per volume.

2.4.6 Pixel-wise fiber orientation We validated our pixel-wise fiber recognition algorithm on synthetic data in Figure 2.12. Synthetic data in (a) consists of segments with different width and orientations. Synthetic data in (c) includes a circle with all possible orientations. From the processed results in (b) and (d), our algorithm shows good accuracy in estimating directionality of segments oriented at various orientations (a- b) and circular shape (c-d).

Figure 2.12 Algorithm validation on synthetic data (a), (c) Synthetic data; (b), (d) processed data with pixel- wise fiber orientation information.

2.4.7 Comparison with intensity gradient technique A directionality map using the pixel-wise fiber orientation algorithm of a cervical sample is shown in Figure 2.13(b), in comparison with the OCT en face image in Figure 2.13(a). Figure 2.13(b) shows both fiber trends and detailed dispersion information on pixel-wise. The fiber distribution obtained using the pixel-wise method and the gradient-based method in [22, 24] were compared in Figure 2.13(c). Here, we picked up three sub-regions with different degree of dispersion. In general, the estimated dominant direction using two methods approximate each other within each sub-region. However, the gradient method is unable to capture the actual fiber distribution of the probability of fiber existence at each angle. The new pixel-wise fiber recognition algorithm is superior to the gradient-based method because the pixel-wise method can capture the existence of distinct fiber families at different orientations, especially non-dominant orientations.

Figure 2.13 Directionality map on a en face OCT image from a human cervical sample. (a) Original OCT image from an en face plane; (b) Pixel-wise directionality map; c(1) – c(3) Histogram of orientation obtained from pixel-wise fiber orientation method in sub-regions from 1 to 3 in (a). Distribution of fiber orientation in the three regions using pixel-wise fiber orientation method and intensity gradient techniques are compared.

Each box is 400 µm × 400 µm.

2.5 Discussion

We presented two fiber orientation analytic tools to study the fiber structure in heart and cervix.

For cardiac myofibers, we proposed a gradient-based algorithm to quantify the orientation of myofibers in three dimensions. The rotation test and comparison with manual measurements demonstrate a high accuracy of our method. For collagen networks, we proposed a pixel-wise orientation estimation method to quantify the fiber trend on each pixel and investigate the fiber dispersion on each sub-region. The validation test demonstrated that the pixel-wise fiber recognition algorithm is superior to the gradient-based method in resolving the non-dominant angle in en face OCT images.

To evaluate the accuracy and sensitivity of 3D fiber orientation quantification algorithm, we calculated the variation between computed change of angle and actual change of angle among all results. The measured variation of our algorithm is within 9º in azimuth angle and within 4º in

35 polar angle. It is known that the change of azimuth angle between diastole and systole can be an average of 14 º to 17º [121-123] in parts of ventricle. Therefore, accuracy of our algorithm is sufficient to reliably resolve changes in myofiber orientation during the cardiac cycle. The application of fiber orientation quantification, together with tractography, will be provided in

Chapter 5 for cardiac OCT images.

We validated our algorithm on synthetic data with various angle and width. We were able to estimate the orientation of myofibers on a pixel-wise at various angle in the synthetic data. The method was demonstrated to be superior to existing intensity gradient technique in estimating the non-dominate angle. The major limitation of this method is the digitalization error in OCT images to quantify very small angle change. However, this drawback can be overcome by increasing the number of pixels though it will significantly increase the computational workload. This method resolves detailed fiber structure by considering non-dominate angle and enables further fiber dispersion analysis. We will present the collagen fiber dispersion analysis for the collagen layer in human heart in Chapter 5 and dispersion analysis for cervical samples from pregnant and non- pregnant patient in Chapter 6.

2.6 Conclusion

In this chapter, we propose analytic tools to study fiber structure within cardiac and cervical OCT images. We demonstrate the feasibility of extracting the fiber orientation and reconstructing three- dimensional tractography of myofibers using OCT. We propose and develop a gradient based algorithm to quantify fiber orientation in three dimensions and utilize particle filtering technique to track three dimensional myofibers trace. To study detailed fiber dispersion in collagen fiber

36 networks, we presented a pixel-wise fiber orientation method to quantify the orientation information with sub-regions.

Chapter 3 Automated stitching algorithm to enlarge OCT Field of View

3.1 Introduction

The field of view (FOV) of most OCT systems is limited to the magnitude of millimeters. For some clinical applications, e.g. monitoring the mechanical properties of human cervix tissue [124] or assessing the ventricular septum or identifying cancerous region, such FOV is not sufficient to visualize the whole tissue structure. There is thus an increasing need to extend the FOV. Without complicating the current OCT system design, stitching multiple overlapped OCT volumes into a single three-dimensional dataset serves as a possibility to enlarge the FOV.

Though many image registration methods are proposed for image stitching [125, 126], general methods to stitch volumetric OCT data are still scarce. Stitching OCT volumes is challenging because the signal noise ratio (SNR) in OCT image is much weaker than such as computed tomography and magnetic resonance imaging. Conventional features extraction methods such as salient feature region (SFR) [127] and speed up robust feature (SURF) [128] are not sufficient. For the same structure that appears in multiple OCT images, the extracted features can vary due to noise and/or axial position of the sample. Attempts using existing software like XuvTools [129] are likely to fail for the same reason of low contrast compared to other imaging modalities. In addition, for samples that are not stretched, the volumes should be aligned in three dimensions, which increases the difficulty of the global optimization problem. A weak SNR indicates relatively strong noise, which can change the texture of the overlapped area and result in poor correlation

38 and matching between volumes. In addition, in OCT, the volumes should be aligned in three dimensions, which increase the difficulty of global optimization algorithms. Zawadzki et al [63] register multiple retinal OCT volumes through manual stitching, then develop a ray cast method to render the volume and use an annealing algorithm to optimize the alignment among multiple retinal imaging volumes [64]. Multiple OCT volumes are stitched in [65] based on blood vessel matching algorithm. In [66], a B-spline based free form deformation method was used to register multiple volumes for a motion-free composite image of the retinal vessels. Most of current OCT stitching methods are developed for retinal imaging, where blood vessels are a good reference for registration. Furthermore, the retinal tissues have a clear layered structure, which enables the layer information to help register B-scans in 2D. It is still challenging to stitch multiple OCT volumes with poor features on surface for organs like cervix, breast, or hearts.

3.2 Stitching algorithm

3.2.1 Algorithm flow To stitch multiple volumes, our algorithm consists of three steps, as shown in Figure 3.1: 1) registrations within the en face plane, 2) registration along axial axis, and 3) post processing process. In Step 1, the registration is based on camera images. In Step 2 and Step 3, we use OCT images for the registration and post processing. For the first step of registration, a) we pair individual volumes based on their scale invariant features [125] in camera images. We measure the offset between each pair of volumes. b) Then we formulate a linear regression model between the measured offsets and the centroid of each volume in a global coordinate system. The least square estimation of the regression model is the global optimization registration results within en face plane. c) An auto-correction method is used to eliminate the erroneous estimates in pairwise offsets. For the second step of registration, based on the estimation of offsets within the x-axis

39 and y-axis, a) we calculate the overlapped area between any pair of volumes and measure displacements along axial axis by comparing the measured edge in each volume. b) Another linear regression model is used to obtain the global offsets in the axial direction. With the global offsets in x-, y-, and z- axes, all volumes are stitched and visualized in 3D. c) Error auto-correction is conducted to eliminate erroneous estimation along axial axis. Lastly, for the third step of post- processing, a) a post processing procedure including gain compensation and b) multiband blending is used to smooth the transition band in adjacent volumes.

Figure 3.1 Flowchart of registration algorithm. Scale invariant transform (SIFT) is used for pair matching.

Linear regression models are used and least square estimations are calculated in global registration and axial optimization. Axial calibration is based on estimation in first block and edge detection results. An error auto - correction method was used to search and eliminated the unreliable estimation in pair-wise estimation. After all offset are calculated, we use gain compensation and multiband blending method to reduce the artifacts which is caused by the inconsistence of intensity from multiple volumes in the overlapped area.

3.2.2 Step 1: registration within en face plane We consider the camera image of each volume as the reference for the registration within the en face plane. The SIFT algorithm described in [125] is applied to each image. Over one hundred keypoints are extracted in each image automatically [130]. A Best-Bin-First (BBF) algorithm [126] is used to search for matched keypoints within other images. A normalized descriptor, DES, with a dimension of 128, is assigned to each keypoint. The local descriptor is based on the gradient in a small area and thereby was robust to illumination and brightness changes in the RGB camera image caused by movement of transition stage. Within (3.1), DESi and DESj are the descriptors of keypoint sets in volume i and j respectively. For a given descriptor of a keypoint des ∈ DESi, the set of distance (Disdes) is defined as,

퐷푖푠−푑푒푠 = {acos (푑푒푠 ∙ 푑푒푠푘)|푘 ∈ 퐷퐸푆푗} (3.1) where ● is the dot product of two vectors. The calculated distance is the angle between two normalized vectors. A match is considered valid only if the distance to the nearest neighbor is less than a ratio times of the distance to the second-nearest neighbor. An optimal ratio we empirically used for our dataset is 0.45. If at least one of the match relationships can be established between keypoints in volume i and volume j, we consider the two volumes paired. Suppose there are K keypoints matched between two volumes. The offsets, Dxij and Dyij , can be estimated as following,

퐾 퐷푥 = 푚푒푑푖푎푛({푥 − 푥 } ) (3.2) 푖푗 푖푘 푗푘 푘=1

퐾 퐷푦 = 푚푒푑푖푎푛({푦 − 푦 } ) (3.3) 푖푗 푖푘 푗푘 푘=1 where (xik, yik) and (xjk, yjk) are the coordinates of the kth matched keypoint. Figure 3.2(a) shows a typical match between volume i and volume j.

Figure 3.2 Schematics of registration (a) in three dimensions; (b) within en face plane of camera image; (c) overlapped area in 3D; (d) overlapped B-scans. Within en face plane, the offsets between two volumes are measured through matching its corresponding keypoints in (b). Here, only keypoints that are matched are shown. The centroids of multiple volumes are estimated globally by considering their relative offsets. To register the OCT volumes along axial axis, the B-scans at overlapped area are compared in (d). The displacement of detected edge shows the offset along axial axis among volumes.

Next, we stitch all volumes in a global space. Denoting the centroid of the volume i (i = 1, 2, …,

T N) as (xi, yi), we denote the centroids in all volumes as a vector c = [x1 x2 … xN y1 y2 … yN] .

Within the en face plane, the sample is moved linearly along x-axis and/or y-axis. Therefore, the offsets between two adjacent volumes are maintain in a global space. The geometric relationship between offsets and centroid of OCT volumes are shown in Figure 3.2(a). Suppose there are M

T pairs of volumes. The measured offset, d = [dx1 dx2 … dxM dy1 dy2 … dyM] , had a linear relationship with centroid vector c as

푊푐 = 푑 (3.4)

W is a matrix with dimension of 2M×2N. Let the mth pair be the offsets between volume i and volume j. The mth row and (m+M)th row of W is given by the following rows:

푚푡ℎ 푟표푤 ∶ [… 0 1 0 … 0 − 1 0 … 0 0 0 … 0 0 0 … ]

(푚 + 푀)푡ℎ 푟표푤 ∶ [… 0 0 0 … 0 0 0 … 0 1 0 … 0 − 1 0 … ]

The ith column in mth row and (i+N)th column in (m+M)th row equal to 1 while The jth column in mth row and (j+N)th column in (m+M)th row equal to -1. The least square estimation of (3.4)is

푐̂ = (푊푇푊)−1푊푇푑 (3.5)

In our experiment, the matrix WTW may not be full rank. A generalized inverse can be used to solve (3.5). Here, we use Moor-Penrose pseudo inverse of the matrix during implementation.

Though the images are paired based on SIFT features, there is a possibility that the estimated offset may be erroneous due to the mismatched SIFT features in poor featured images. Since we are globalizing the offset among all volumes, the error may increase when more volumes are involved.

To avoid the increased error, we propose an error auto-correlation method to detect and eliminate the erroneous pairwise estimates. Suppose the center of each volume is a node in 2D space and the estimated offsets are the links connecting all nodes. Considering a link connecting node i and j, we are using a metric e(i, j) to measure the mismatch between pair-wise estimation ep(i, j) and globalized estimation eg(i, j). The metric is defined as

푒(푖, 푗) = |푒푝(푖, 푗) − 푒푔(푖, 푗)| (3.6)

Theoretically, if the estimation of ep(i, j) is erroneous, the globalized estimation eg(i, j) should be quite different due to error accumulation. Also, if estimation ep(i, j) is accurate and the global optimization is computed based on reliable nodes, difference between ep(i, j) and eg(i, j) will vanish.

Inspired from the Dijstra algorithm [131] in graph theory, we devise the error correction scheme by employing two steps: a pruning process and a spanning process. The pruning process constructs a reliable set of nodes to ensure an accurate global estimation for each link by reducing unreliable nodes. Spanning process enlarges the number of nodes in the tree while keeping high accuracy by only adding the reliable nodes.

Algorithm 1 outlines our method to prune the original trees. In each iteration, we examine the error e(i, j) and delete the node that causes the largest error. The iteration ends when the maximum of error is smaller than a threshold. This results in a reliable subset of nodes.

Algorithm 1. Pruning process. Starting from all nodes, the algorithm progressively eliminates the node that causes largest error. The nodes in the list of good nodes construct most reliable tree structure with all pair-wised links at high accuracy.

Input: Set of nodes S, matrix of links L, threshold th. Output: List of good nodes Sg, list of bad nodes Sb. Sg = S; Sb = []; E = error_estimate (S, L); while max(E) > th do node_id = find_max_error(S, L, E); delete_node_link(S, L); Sg = delete_node (Sg, node_id); Sb = add_node (Sb, node_id); E = error_estimate (S, L); end

Algorithm 2 outlines our method to add nodes to the reliable subset. In each iteration, we add a new node, where the new node is from original dataset. All newly created links will be examined and the link that causes large error will be deleted. The algorithm ends upon addition of all nodes and maintenance of all reliable links.

Algorithm 2. Spanning process. Starting from list of good nodes, the algorithm iteratively add nodes and links from list of bad nodes. When one node is added, every newly constructed link will be examined. The links that will cause large error are eliminated.

Input: List of good nodes Sg, list of bad nodes Sb , set of nodes S, matrix of links L, threshold th. Output: Set of all nodes S’ , matrix of links L’ . S’ = Sg; L’ = L; foreach s ∈ Sb do S’ = add_node (S’, s); Sb = delete_node (Sb, s); E = error_estimate (S, L); L’ = add_links (L’, s); foreach link l ∈ s to S’ do E = error_estimate (S, L); if max(E) > th then link_id = find_max_error_link(S, L, E); delete_link(l, link_id); else break end end end

An illustration of error auto-correction is shown Figure 3.3. There are 53 nodes in the original tree at the beginning as shown in (a). The magnitude of the link shows the displacement. The colors of links refer to e(i, j) of the link. Blue represents an error smaller than 1 pixel while red represents an error larger than 1 pixel. For each step, the node causing maximum e(i, j) is deleted. The pruning process will not terminate until the maximum e(i, j) of the remaining links drops below a set threshold. Figure 3.3(a) to (c) shows the pruning process, where nodes in (c) form a set of nodes including all reliable nodes and pairwise links.

Based on the reliable set of nodes, a spanning process is executed by adding new nodes and links, as shown in Figure 3.3 (d) to Figure 3.3 (e). At each step, one node is added to the whole set of nodes. The links between newly added nodes and existing nodes are examined based on the measurement of e(i, j). If the link causes large e(i, j), the link will be deleted from the entire tree structure.

Figure 3.3 Schematics of error auto-correction within the en face plane. Each node denotes an OCT volume within en face plane. Each link represents a pair wise offset estimation based on SIFT. The links are color coded based on the error between pair-wised offset estimation and global optimization, which is e (i,j). Dark blue color means the error is within 1 pixel, and red means the error is over 1 pixels. The pruning process is shown from (a) to (c). The initial structure is in (a). With a deletion of five nodes, only a small number of erroneous links exist in (b). The most reliable tree is established when we delete 17 nodes from (c). The spanning process is shown from (c) to (e). Nodes are added at each iteration. Only reliable links are added to the tree structure at each iteration. Therefore, the structure of (d) is more reliable than that of (b), though the two figures share the same number of nodes. The constructed tree is shown in (e). With pruning and spanning, we delete the erroneous links and construct an offset tree with highly reliable links.

3.2.3 Step 2: registration along axial axis Based on the estimation of cˆ , we can arrange the volumes as overlapped tiles in a single space.

However, the volumes are not perfectly stitched because there are variations along axial axis due to adjustment of the sample axial position during imaging. To register multiple volumes along the axial direction, we use the surface edge within B-scans as the reference. We calculate the overlapped region between volume pairs. A typical example is shown in Figure 3.2 (c). To calibrate

46 the displacement along the axial direction, we obtain B-scans from two volumes at the same position within the overlapped region at two orthogonal directions (Figure 3.2 (c)). The tissue surface edge within each B-scan is determined by searching for the maximum gradient after smoothing the image with a median filter. The displacements of two edges are measured along x axis or y axis. A typical scenario of overlaid edges is drawn in Figure 3.2 (d). The measured offset

∆zxij between volume i and volume j is computed as the median value of all displacements between edges in volume i and j along x axis. Similarly, we have ∆zyij between volume i and volume j along the y axis. If two estimated displacements agree with each other, e.g., within 5 pixels, we take the average of the two estimations as the final offset between volume i and j. Similar to the registration within the en face plane, a linear relationship can be formulated between the z coordinates of

T T centroid in all volumes, z = [z1 z2 … zN] , and the measured offset, d2 = [dz1 dz2 … dzM ] as following

푉푧 = 푑2 (3.7) where mth row of V can be written as

[ 0 1 0  0 -1 0  0].The entry of ith column equals to 1 while the entry of jth column is -1. The least square estimation of (3.7)is

푇 −1 푇 푧̂ = (푉 푉) 푉 푑2 (3.8)

Finally, we aligned all volumetric dataset based on estimation of cˆ and zˆ . Similarly, we process the error correction along the axial axis. The mismatch between pairwise estimation and global

47 estimation are calculated. Pruning and spanning process are employed to minimize the mismatch.

Unlike the case within en face plane, the mismatch is computed in one dimension.

3.2.4 Step 3: post-processing With all offsets between volumes globally estimated, we next combine the volume into a stitched volume. For the overlapped region among multiple volumes, the contrasts vary a lot, especially for the samples that have distinctive topology. In that case, there will be a visible edge in the combined volume. To solve this issue, we use two processes to normalize and smooth the combined volume: gain compensation and multi-band blending. Gain compensation is to normalize the brightness of each volume and multi-band blending is to smooth the edge between multiple overlapped volumes. A schematic of the post processing process is depicted in Figure 3.4.

Figure 3.4 Schematics of post-processing in two dimensions. For all input images, the overlapped region is calculated.

Then a gain factor for each volume is computed based on the intensity of overlapped region. The intensity of each volume is tuned by the gain factor. Each B-scan is divided into multiple bands. The banded images are weighted with different matrix based on the idea of blending low frequency band with larger range and blending high frequency band with smaller range. The reconstructed image is the weighted summation of all bands.

3.2.4.1 Gain compensation

Within equations (3.9) and (3.10), gi, gj are the gain factors for the overlapped volume i and j. To accurately estimate the gain factor for each volume, we define an error function of gain g based on overlapped number of voxels and intensity values as following [125]:

푛 푛 2 2 1 (푔푖퐼푖푗 − 푔푖퐼푗푖) (1 − 푔푖) 퐸 = ∑ ∑ 푁푖푗( 2 + 2 ) (3.9) 2 휎 휎푔 푖=1 푗=1 푁

2 2 Where Nij is the number of voxels in volume i overlapped with volume j. 휎푁 and 휎푔 are normalized intensity error and gain respectively. Iij is the mean of intensity of all voxels in i overlapped with volume j. The gain can be calculated by setting ∂E/∂gi = 0. To solve (3.9), for each i, we have

푛 푛 푛 푛 2 2 1 2푁푖푗퐼푖푗퐼푗푖 1 ( 2 ∑ 퐼푖푗푁푖푗 − 2 ∑ 푁푖푗) 푔푖 − ∑ 2 푔푗 = 2 ∑ 푁푖푗 (3.10) 휎 휎푔 휎 휎푔 푁 푗=1 푖=1 푗=1 푁 푖=1

Generally, we have n equations for n gains. The gain can be uniquely solved in those linear equations.

3.2.4.2 Multiband blending

After gain compensation, the volumes are normalized to a level that shows a uniform brightness level. However, the edge of the combined volumes can still be distinct due to the difference in

SNR levels within overlapped volumes, where the surface within the region of overlap had different axial heights. Here, we use a multiband blending technique [125, 132] to smooth the edges. The main idea of multiband blending is to divide the original image into multiple bands and assign different weight to each band. If we have N overlapped images, we assign a weight function

49 to each image W(x,y) = w(x)w(y) where w(x) varies linearly from value of 1 at the center to value of 0 at the edge. The image n has a weight matrix as 푊푛(푖, 푗) defined as following:

푛 1, 푖푓 푊 (푖, 푗) = arg 푚푎푥 { n } 푊푛 (푖, 푗) = { 푚푎푥 푗 W (i, j) (3.11) 푚푎푥 0, 표푡ℎ푒푟푤푖푠푒

Both the original image and weight matrix are divided into multiple bands through convolution with a Gaussian filter by computing the following in equations:

푛 푛 퐼(푘+1)휎 = 퐼푘휎 ∗ 푔휎′ (3.12)

푛 푛 푛 퐵(푘+1)휎 = 퐼푘휎 − 퐼(푘+1)휎 (3.13)

푛 푛 푊(푘+1)휎 = 푊푘휎 ∗ 푔휎′ (3.14)

푛 푛 푛 Where 퐼0 is the original image and푊0 is 푊푚푎푥(푖, 푗). 푔휎′ is a Gaussian of standard deviation

n n n 푛  ' (2k 1) .The K bands of original image consists of B , B2 ,..., B(K1) and 퐼푘휎. The overlapped

푛 images are linearly combined using corresponding weight 푊푘휎 and their corresponding weights.

3.3 Method validation

3.3.1 Validation setup Three-dimensional volumetric data was imaged from a human cervix sample. The cervix specimen was acquired from a nonpregnant hysterectomy patients using an Institutional Review Board (IRB) approved protocol at the Columbia University Medical Center [98]. The data were acquired using a commercial spectral domain OCT system, Telesto (Thorlabs GmbH, Germany). It is an InGaAs based system centering at 1325 nm, with a bandwidth of 150 nm. The axial and lateral resolutions are 6.5 μm and 15 μm in air, respectively. The maximum axial line rate is 92 kHz. In our

50 experiment, each volume consists of 800 × 800 × 512 pixels, corresponding to a tissue volume of

4 mm × 4 mm × 1.8 mm.

3.3.2 Auto-correction method Using the same data set from Figure 3.3, we demonstrate our auto-correction method by plotting the maximum error e(i, j) versus number of nodes in the pruning process and the spanning process in Figure 3.5. Of note, Figure 3.5 (a) is plotted using decreasing number of nodes. We observed a drastic decrease in the maximum error with a decrease in the number of nodes. Within this example, when the number decreases from 53 to 52 a drastic change is observed because the node that was removed had a large number of the links that were inaccurate. If we consider that node, most of the estimations are incorrect. If that node is deleted, the error is largely reduced. The error decreased to <1 pixel when a reliable set of nodes, which in this example dataset was 37. For the spanning process, error stayed at a low value because we added reliable links for each new node within each iteration.

The impact of the use of error correction is shown in Figure 3.6 (a) and (b). The stitched en face image without error correction is shown in (a) and the stitched en face image after error correction is shown in (b). Without error correction, obvious errors in pairwise offsets are observed, where we can see discontinuity in the sample boundary in some areas. We have observed this in other datasets when the number of volumes to be stitched is large. Large errors exist and the contour of the sample is inaccurate. After the error correction step is applied, the offsets between volumes are well estimated and contour of cervix is very smooth in Figure 3.6(b).

3.3.3 Stitching accuracy We set up an evaluation test to test the accuracy of our method. We obtained an OCT volume of 4 mm × 4 mm × 2.51 mm (800 × 800 × 512 voxels) of a plastic cap as ground truth. Then, we imaged the same space with four overlapped volumes of 2.5 mm × 2.5 mm × 2.51 mm (500 × 500 × 512 voxels). The volumes were stitched and compared with the ground truth. We set four pairs of landmarks at ground truth and then specified the same landmarks within the stitched volume. The

3D distances between pair of landmarks were measured using the software in Amira, as shown in

Figure 3.7. Difference in measured distance between stitched volume and ground truth is

11.64±2.32 voxels, showing good correspondence between stitched volume and ground truth.

OCT volume with size of 4 mm × 4 mm × 2.51 mm was acquired for comparison. Eight landmarks were specified in each volume, formatting four pairs of distances. The distances were measured and compared in voxel as a validation the accuracy of stitching algorithm. The maximum mismatch in the two volumes does not exceed 15 voxels.

3.3.4 Multiband blending and gain compensation The impact of the steps of our registration algorithm are shown in Figure 3.8, using results from a

PG human cervical sample as an example. First, A representative stitched B-scan is shown in (a)-

(c) to show the impact of the post processing step. Figure 3.8 (a) shows the stitched B-scan with hard combination, where images are combined by averaging the overlapped regions. Figure 3.8 (b) shows the stitched B-scan after gain compensation and (c) shows the results after gain compensation and multiband blending. For the same area, marked as (a1), (b1), and (c1), the transition band from one B-scan to the other is very distinctive in the results using hard

53 combination. Generally, the pixel value on the right half of (a1) is lower than the value on the left half. After gain compensation, as shown in (b1), the pixel values were generally decreased in the left half to match the pixel value in the right half. However, the boundary is still very clear. With both gain compensation and multiband blending, as shown in (c1), the transition between left half and right half is smooth and the boundary is nearly invisible.

Figure 3.8 Registration of B-scan results from (a) hard combination of multiple B-scans, (b) gain compensation of multiple B-scans, and (c) gain compensation plus multiband blending of multiple B-scans.

In a zoomed area indicated by dashed yellow rectangular, if hard combined, the two sections approximating the edge has great difference in pixel value in (a1). Gain compensation uniformized the pixel value but a boundary is still visible in (b1). When proceeding with multiband blending, a smooth transition of pixel values is visible over the edge in (c1).

3.4 Discussion

We present a method to stitch multiple OCT volumes with the aim of increasing the field of view of image scanning. The algorithm is validated on OCT data collected from human a cervical sample and a plastic cap. It was demonstrated that the auto-correction is necessary to stitch large set of OCT volumes. The stitching algorithm achieved a good accuracy in comparison with landmark from non-stitched volume. The multiband band blending and gain compensation algorithm enhanced the visualization of stitched data.

Compared with existing registration method for retinal images [62-66], our work does not rely on any contrast structures. Our work can be readily adapted to other samples with low-contrast features. For stitching tissue lacking high contrast structures, efforts are made to stitch volumes in stretched bladder [133]. In our study, we stitch large numbers of volumes within samples that were not stretched. Furthermore, our error correction method and multiband blending step aided in ensuring and accurate and smooth combination in 3D space. The error correction is necessary when number of volumes are large. Although such improvement maybe relatively small when number of volumes is small, it may have an impact on seeing the fiber orientation. The limitation lies in the large data acquisition time of imaging large amount of volumes. For current setup, dehydration is inevitable and the dehydration will cause the shrinkage of sample, leading to mis- registration in translational movement. In addition, the pixel size of white light image is larger than the voxel size in OCT volumes. That is, even though the volumes are well matched in white light images, small variation still exist in voxels. This results in boundary effects in visualization, especially when the surface is with much topology.

In general, this generic method can enable an enlarged FOV for image analysis. The detailed application will be provided in Chapter 4, Chapter 5, and Chapter 6 for cardiac images, cervical images, and breast images.

3.5 Conclusion

We present an automatic registration method to stitch multiple OCT volumes based on SIFT and least square estimation in three dimensions. An auto-correction method was proposed to increase the robustness of our algorithm in stitching large number of volumes. Multiband-blending and gain compensation method were employed to enhance the 3D visualization. By showing a large view of cervical sample for validation, we demonstrate our algorithms’ ability in automatic stitching.

Chapter 4 Automated classification of tissue composition

4.1 Introduction

In this chapter, we mainly focus on developing automated algorithm to identify various tissue types within cardiac tissue and breast tissue with the aims of aiding the treatment of cardiovascular disease and breast cancer.

Cardiovascular disease (CVD) is the leading cause of mortality and morbidity in the United States

[134]. An important factor in the pathophysiology of CVD is the composition and remodeling of the myocardium. Myocardial tissue includes muscle, adipose tissue, collagen fibers, and fibrotic myocardium, and the relative percentage of each varies by chamber and with the progression of disease. The presence of adipose, thickened collagen layer, and diffusion of myocardial fibrosis are associated within arrhythmogenic cardiomyopathy [135], severe myocardial scar [136], and cardiomyopathy [137], respectively. Therefore, characterization of myocardial tissue can facilitate the evaluation of tissue remodeling, identification of arrhythmogenic substrates, and diagnosis of

CVD. OCT has been demonstrated to have the ability to image cardiac tissue at a fast rate with a high resolution. Previous research efforts demonstrated that OCT can image important features within the heart [138] such as the purkinjie network [18], atrial ventricular nodes [19, 20], sinoatrial nodes [21], and myofiber organization [22-25]. There is a great potential to classify tissue compositions within human atria via OCT imaging. However, manual interpretation of OCT images is time consuming and not applicable for analysis on large 3D volumetric datasets.

Therefore, automated identification of tissue composition in human atria from OCT images is greatly needed.

With an earlier median age at diagnosis, the breast cancer incidence for young female is especially high. There is an unmet need to detect breast cancer especially at the early stage. Thus, many imaging techniques have been utilized to image breast tissue for cancer detection. The most established technique for breast cancer detection is the mammogram [139], a screening method that provides tomographic images of the breast by using low-dose X-rays. Despite its efficacy, a major disadvantage of mammograms is that the use of radiation often yields false positives.

Automated whole breast ultrasound (AWBU) [140] has been suggested in combination with mammograms for breast cancer detection in dense-breasted women, as AWBU offers sensitivity comparable to MRI at only a fraction of the MRI cost. However, AWBU also produces a larger number of false positives compared to mammograms. Diffuse optical tomography (DOT) [141] has the ability to detect suspicious lesion in breast but it is limited to detecting large areas of cancer infiltration due to the relatively low spatial resolution. OCT has been extensively used in visualizing human breast structure to aid cancer detection [33-39, 142]. However, a robust algorithm for automated cancerous region detection is still in need in OCT community.

4.2 Automated classification of myocardium

4.2.1 Algorithm flow To identify tissue compositions within OCT images, we proposed a region-based classification method. A schematic of the workflow for the analysis of two-dimensional images is shown in

Figure 4.1. The algorithm consists of three steps: layer segmentation, feature extraction, and tissue classification. In each B-scan, OCT images were first segmented into multiple regions. Within the segmented region, features such as optical properties, texture analysis, and high order statistical

58 moments were extracted. The features were inputs to a tissue classifier, whose output was the tissue type for the region.

4.2.2 Layer segmentation For the first step, we divided OCT images into multiple layers through segmentation for future feature extraction and classification. Compared with existing segmentation methods, segmenting

OCT images of atrial tissue is challenging. Within prior work, layer boundaries were automatically determined by minimizing a cost function [68] or building a minimum weight graph [69]. The weighting scheme and searching order are determined by prior knowledge of the layer structure, such as empirical thickness measurement and knowledge of bright–to-dark transition patterns between two layers. Unfortunately, neither empirical thickness measurement or transition patterns is consistent for atrial tissue. In the atrium, layer thicknesses and tissue composition vary within a normal heart depending on the region that is imaged. Furthermore, the layer thicknesses and tissue composition change with the progression of disease. Therefore, the first step of our algorithm is layer segmentation, which includes pre-processing, layer information estimation, and boundary searching to identify the number of layers. A detailed flowchart of the layer segmentation steps is depicted in Figure 4.2. The pre-processing step improves the image quality through denoising, and

59 flattens the image to reduce the boundary searching range. The layer information estimation step determines the number of tissue compositions and identifies starting points for boundary searching.

The image is segmented after boundary searching.

Figure 4.2 Flowchart of layer segmentation algorithm

4.2.2.1 Pre-processing

The pre-processing procedure includes image denoising and flattening. Given that OCT images are generally corrupted by speckle noise [143], we used a block matching 3D (BM3D) [144-146] method to denoise OCT images and enhance the boundaries. Briefly, for the BM3D algorithm we divide the original OCT image into multiple blocks and denoise similar blocks. The BM3D method exploits the sparsity of structural information and is thus considered to be a good tool to denoise speckle noise and enhance boundary information. To reduce the searching range and maintain a smooth searching shape, we flattened and shifted the filtered image based on the tissue surface. To flatten/shift image in a fast manner, we under-sampled the original image. In cardiac tissue, the most hyper reflective surface is in the endocardium. Within a down-sampled A- line, we thus estimated the location of the maximum pixel value as the axial location of the surface. Then

60 the image was shifted based on an interpolation of the axial location of the maximum value-pixels within the down-sampled image.

4.2.2.2 Layer information estimation

After image denoising and flattening, we estimated layer information within each OCT image. The layer information consisted of the number of layers and the initial point for boundary searching between layers. To count the number of layers, we analyzed averaged A-lines in the OCT image.

Since the A-line around the center of B-scan has a better signal noise ratio (SNR), we analyze the

A-lines around the center. To ensure an accurate estimation, we selected five segments around the center. For each A-line, 20 A-lines were averaged. In each averaged A-line, the intensity curve was linearly fitted using a sliding window. The algorithm flow of linear fitting is shown in Figure

4.3 (a). We first set the location of the maximum pixel value as the first anchor. Within a window, the intensity was linearly fitted. We calculated the root mean square deviation (RMSD) error as following:

N ˆ 2 RMSD  (yi  yi ) N (4.1) i1 where yˆ i is the linearly fitted estimation and yi is the original intensity value. If the RMSD is below a threshold, it is assumed that the window is still within the same layer and thus the original window is extended to cover more range. Otherwise, if the RMSD is higher than the threshold this iteration of layer searching is completed and we record the end of the window as the changing point. In the next layer, we set a new anchor that is one initial window size away from the recorded changing point to start a new linear fit. Since the A-line data is with noisy fluctuation in intensity, a fixed distance between the changing points and the new anchor is needed to ensure that we are analyzing a new layer rather than repeatedly searching in the previous layer. In this study, we

61 empirically set the initial window size as 10 pixels and the window size is extended 3 pixels for each iteration. The estimation was a piecewise linear function. The number of layers in the OCT image was defined by the number of linear pieces within the A-line. In our implementation, we deleted any two neighboring changing points that were too close (<30 pixels) and set a new changing point that locates in the middle of two deleted changing points. If the changing points were due to high standard deviation of the intensities within the pixels around the peak of the A- line, the changing point would be deleted as well. Each changing point of the piecewise linear function was considered as one of the candidates used as initial boundary points for boundary searching. Upon determining the number of layers and changing points in each segment, we used a voting system to globally estimate the number of layers and corresponding initial boundary points.

4.2.2.3 Boundary searching

The boundaries were searched from the center of the image and progressed outward to the left and right. The boundary search algorithm minimizes the following function:

E( f )  Edata ( f )  Esmooth( f ) (4.2) where f is the label of the estimated surface, Edata(.) is the energy of each pixel, and Esmooth(.) is the energy quantifying smoothness of estimated surface. To minimize E(f), we set a cost function c(x, z) as following:

푐(푥, 푧) = 푐 푔(푥, 푧) + 푐 푖(푥, 푧) + 1 2 (4.3) 푐3푝(푥, 푧) where g(x, z) is the gradient in the axial direction; i(x, z) is the intensity; p(x, z) is a weight defining layer structure. The term Edata(f) in (4.2)is represented by g(x, z) and i(x, z) and the term Esmooth(f) in (4.2) is represented by p(x, z). In general, the largest value of c(x, z) in (4.3) corresponds to lowest energy in (4.2). The smoothness, p(x, z), is determined by the changing points obtained from layer information estimation step. Generally, for each column, p(x, z) is large when (x, z) is close to changing points and is small when the pixel is in the middle of two estimated changing points. Three factors are weighted by c1, c2, and c3 with a relationship of c1 + c2 + c3 = 1. Multiple boundaries were searched with the assumption that each boundary intersected with one a column once. For each layer, starting from the changing point (from anchor for the first boundary), we searched the boundary from one column to another. The searching range was [-Δz, Δz] of the determined boundary point in the previous column. Figure 4.3(b) presents a schematic of boundary searching algorithm, starting from Col(i-1). The cost of 2Δz pixels were examined and the pixel with the highest weight was considered to be the boundary of the layer within Col(i). We then estimated the boundary for the next column. The searching algorithm was run in parallel for multi- layers within an image.

4.2.3 Feature extraction Within each segmented region, we extracted features from the OCT images to study different patterns of tissue compositions. The extracted features can be divided into three categories: measured optical properties, statistical moments, and texture analysis.

Measured optical properties: Optical property parameters that we studied were attenuation coefficients (mm-1) and penetration depth (mm). Attenuation coefficient is measured based on the method mentioned in [147]. Penetration depth is defined as the depth at which the intensity drops to 1/e of its original intensity [148] when light first reaches the layer. Additionally, we calculated the distance between centers of layers to the tissue surface.

Statistical moments: We performed histogram equalization and median filtering on raw OCT data.

Then, we calculated the statistics of high moments (skewness and kurtosis), on the intensities of the denoised image within the whole layer to analyze the distribution of intensity for various tissue types.

Texture analysis: We encoded OCT images with texture on equalized and filtered OCT images.

Texture feature number (TCN) [149] is assigned to each pixel. In TCN, the local feature of each pixel is represented by the intensity change of its eight surrounding pixels. We analyzed the statistics of the TCN number within each layer. In particular, we calculated the coarseness and homogeneity from the histogram of the TCN. We also quantified the mean and standard deviation from the default texture analysis tool in Matlab, such as range filter and std filter, within each region. We also quantify entropy within the region. In addition, we constructed grey level co- occurrence matrix (GLCM) [150] to extract more texture. Specifically, contrast, energy, and correlation were computed by setting the number of levels to 16.

Representative parametric images obtained from left and right atrial samples are shown in Figure

4.4, where we presented typical pixel-based features, A-line-based feature, and layer-based feature.

From pixel-based parametric images, such as attenuation coefficients and entropy in Figure 4.4(c)-

(d) and Figure 4.4(i)-(j), large variation can be observed within a single layer. In A-line-based features, such as penetration depth and distance to the surface, there are smaller variations in each layer and the difference between tissue compositions can be well observed. For layer-based features, we performed texture analysis on pixels within the whole layer. It is more representative as shown in Figure 4.4 (f) and (l). To simplify our model, we averaged the pixel-based and A-line- based features of the layer. This results in a vector of features for each layer. The number of entries in the vector is the number of features. In this study, we calculate 16 features in feature extraction, as listed in Table 2.

Figure 4.4 Example tissue images obtained from OCT, histology, and parametric images. (a) Original OCT image collected from the left atrium. (b) Trichrome histology of the same sample used in (a). (c) Attentuation coeffcicient map obtained from (a) (unit: mm-1). (d) Entropy map obtained from (a) (unit: 1). (e) The layer depth map obtained from (a) (unit: pixel). (f) The skewness map obtained from (a) (unit:1). (g) Original OCT image collected from the right atria. (h) Trichrome histology of the same sample used in (g). (i) Attentuation coeffcicient map obtained from (g) (unit: mm-1). (j) Entropy map obtained from (g) (unit: 1). (k) The layer depth map obtained from (g) (unit: pixel). (l) The skewness map obtained from (g) (unit:1). For different tissue composistion in OCT images, they are showing different signatures in attenuation coefficients, entropy map, layer depth, and skewness. Scale bar: 500 um.

Table 4.1 List of features used in the classifier

Feature Description

1 Attenuation coefficients (mean) Mean value of attenuation coefficient 2 Attenuation coefficients (std) Standard deviation of attenuation coefficient 3 Penetration depth (mean) Mean value of penetration depth 4 Penetration depth (std) Standard deviation of penetration depth 5 Std filter value (mean) Mean value of standard deviation filtering results 6 Std filter value (std) Standard deviation value of standard deviation filtering Results 7 Range filter (mean) Mean value of range filtering results 8 Range filter (std) Standard deviation value of range filtering results 9 Entropy Entropy of the pixel values 10 Coarseness (TCN) Coarseness analysis of texture code number 11 Homogeneity (TCN) Homogeneity feature of texture code number 12 Contrast (GLCM) Contrast feature from GLCM 13 Energy (GLCM) Energy feature from GLCM 14 Distance to surface The distance between the center of the layer and the surface 15 Skewness Skewness within the whole layer 16 Kurtosis Kurtosis within the whole layer

4.2.4 RVM classification The relevance vector machine (RVM) [151] is used to classify tissue compositions. For each feature vector x, the probability of the vector belonging to a specific tissue composition c is determined by the following equation:

B p(c 1| w, x)   (ii (x)) (4.4) i1 where w is the weight, (x) is a kernel function,  () is a sigmoid function, and B is the number of vectors. A zero mean Gaussian prior is typically chosen for computational convenience for the weights.

1 αi -1 αi 2 - p(w |α ) = N(w |0, α ) = ( ) e 2 ( 4 . 5 ) i i i i 2π

The distribution is determined by the values of the hyper-parameters αi. Given a dataset of input

n n vectors with known tissue composition, D {(x , c ),n 1,2,...,N} .The hyperparameter αi can be set by maximizing the marginal likelihood

N   p(D | )   p(D | w) p(w | )dw   p(c n | x n , w)( ) B / 2 exp( wT w)dw (4.6) n1 2 2

Here, we use Gull-MacKay method to update αi.

New values for the weight vector w are estimated by calculating the derivative of the expectation of the weights ∇E[w] and the Hessian matrix of the weights H. Using a Newton update method, the new weights are estimated as:

W new  w  H 1 (E) (4.7)

The classifier alternates in updating hyperparameters and weights. After obtaining a converged w, the training of classifier terminates. Following the training, we estimate the probability of each unknown layer belonging to specified tissue composition.

RVM is a Bayesian framework of the support vector machine (SVM), which is widely used in classification [82, 152] and segmentation [153]. Compared with the SVM model, RVM obtains sparser solutions for weight vector w. This is done by adopting a non-Gaussian prior for multiple hyperparameters αi, which only requires a limited number of weights w to be “active”. Once the values for the hyperparameter are optimized, most of the hyperparameters tend to move towards

67 infinity. This results in most weights getting closer to zero, and becoming “irrelevant” in establishing a decision boundary. Only relevant weights are retained, which produce a significantly lower number of relevance vectors compared to SVM.

4.2.5 3D visualization Given boundary information from the B-scans, we reconstructed the volumetric classification for myocardial tissue. Upon estimating the boundary from each B-scan, each layer can be roughly estimated. The detected boundary was arranged along the direction perpendicular to the B-scan.

We further smoothed the estimated surface using a median filter and reconstruct the 3D surface based on the smoothed plane. The estimated layer boundaries at each B-scan were modified accordingly. We then performed the tissue classification algorithm on each fine-tuned region in each B-scan. After performing the classification algorithm on each B-scan, the three-dimensional classification results were realigned. We overlaid the tissue composition with OCT volumetric data in an HSV scheme. In this study, tissue composition is encoded as hue; saturation and value are encoded as intensity. All 3D results are visualized using the software package Amira 5.4.3

2012 (Zuse Institute Berlin, Germany).

4.3 Automated classification of breast tissue

4.3.1 Algorithm flow Due to the similarity in features, it remains a challenge in OCT image processing of breast tissue to directly differentiate normal stromal tissue from cancerous tissue. We notice that adipose tissue exhibits a distinctive characteristic honeycomb texture. Therefore, our approach is to decouple the automated classification procedure by first identifying large adipose regions, with intact honeycombing features which normally corresponds to non-neoplastic areas, using an adipose

68 classifier [154]. Thereafter, regions not classified as adipose will be classified as normal stroma of fibroelastic origin or cancer. Detailed algorithm flowchart is presented in Figure 4.5.

4.3.2 Adipose classifier we extracted region-based local features, including standard deviation, entropy, and homogeneity of the OCT intensity signal. Every frame was first smoothed by a 21-by-21 mean filter to suppress the noise and the grid size was chosen to be around 20 pixels to achieve the optimal results. The features were then input into a trained machine learning model, relevance vector machine [151,

155, 156], and the model will assign a tissue type to that region. Frames that contained 25% or less adipose tissue in the effective regions (intensity signal above SNR threshold) will be classified as solid tissue and sent to the IDC classifier for examination.

4.3.3 IDC classifier We identified four parameters based on the signal penetration and backscattering strength in the

OCT image as input to the IDC classifier. For feature extraction, a single scattering model [78,

157, 158] for homogenous media was incorporated to model the detected OCT signal from the sample arm, where 휇̅̅푏̅ was the effective backscattering coefficient, 퐼푠 the incident light intensity in the sample arm, 푙푐 the coherence length of the light source, and 푆̂(푧) the 6-dB sensitivity fall- off induced by the spectrometer. The coupling efficiency was assumed to be constant along the A- line and over the B-scan to avoid the complexity. 푆̂(푧) can be decoupled from the A-line profile by measuring the center of the scan as well as the 6-dB sensitivity fall-off range of the system

(푧푐, 푧푤) [157]. The first two parameters were the mean and variance of the penetration depth across a single B-scan. The penetration depth was defined as the axial distance where the intensity drops to e-1 of its peak value from the tissue-air interface and was correlated with the attenuation coefficient 휇푡 of the tissue. The other two parameters were the mean and variance of “decay range” across a single B-scan. The decay range was defined as the axial distance from the tissue-air interface to the location where the magnitude of A-line intensity is 10 dB above the noise floor. It was correlated with both the effective backscattering coefficient 휇푏 and attenuation coefficient 휇푡 of the sample.

4.4 Method Validation

4.4.1 Validation setup We imaged human hearts under a protocol approved from the National Disease Research

Interchange (NDRI). Fresh tissue samples were shipped submerged in ice-cold phosphate-buffered saline and received within 48 hours of donor death. Breast tissue specimens were excess tissue not

70 required for diagnosis as defined by the department of pathology collected from patients undergoing surgical procedures at Columbia University Medical Center (CUMC).

All samples were imaged ex vivo, using a spectral domain OCT system, Telesto (Thorlabs

GmbH, Germany). The system is centered at 1325 nm and with a bandwidth of 150 nm, with a axial of 6.5 μm and a lateral resolutions of 15 μm, both in air. All datasets were acquired at 28 kHz.

In our experiments, each volume consists of 800 × 800 × 512 voxels, corresponding to a tissue volume of 4 mm × 4 mm × 2.51 mm (in air).

4.4.2 Segmentation results Figure 4.6 shows two typical segmentation results of human atrial OCT volumes. In Figure 4.6(a)-

(c), three layers are dense collagen (dark blue in histology), loose collagen (light blue in histology), and normal myocardium (red in histology) while in Figure 4.6(d)-(f), three layers are dense collagen (dark blue in histology), adipose tissue (white in histology), and normal myocardium (red in histology). In general, segmented boundaries match the visible boundaries in Trichrome histology. Moreover, we conducted a quantitative comparison between automated segmentations and manual segmentations from two observers for images from all 15 human hearts with corresponding histology. The results are listed in Table 3. The difference between automated segmentation and manual segmentation was 51.78 ± 50.96 µm, which is of the same order of magnitude of results provided by the two investigators, 42.22 ± 33.87 µm. To visualize boundaries in 3D, multiple consecutive B-scans were segmented based on the filtered surface using the method in Section 3D visualization. The 3D segmentation results are presented in, Figure 4.6(c) and Figure

4.6(f).

The automated results in both two dimensions and three dimensions show great agreement with hi stology images

Table 4.2 Comparison between automated segmentation and manual measurements from two observers.

Automated vs Observer 1 Automated vs Observer 2 Observer 1 vs Observer 2 Mean [μm] Std[μm] Mean [μm] Std[μm] Mean [μm] Std[μm]

RA 42.26 57.48 51.72 61.12 42.89 55.57 LA 64.14 45.13 44.27 46.36 42.22 33.87

4.4.3 Myocardial classification results We performed classification experiments on 60 B-scans from 15 human hearts. Typical classification results are shown in Figure 4.7. Like segmentation results, we performed comparison between automated classifications and Trichrome histology and present the comparison in Figure

4.7 (a) to (f), of which (a) and (d) are raw OCT images; (b) and (e) are colorcoded classifications;

(c) and (f) are histological images. The tissue compositions were color coded in HSV where hue encoded the tissue composition, saturation and value encoded intensity. Two layers are dense collagen (dark blue in histology) and adipose tissue (white in histology) in Figure 4.7(a) to (c) while dense collagen (dark blue in histology) and fibrotic myocardium (purple in histology) in

Figure 4.7 (d) to (f). Both classification results agree with the Trichrome histopathology.

4.4.4 Breast classifications results We performed adipose classification on human breast tissue. A representative 2D B-scan classification results is presented in Figure 4.8. The grey grid in (b) indicates adipose region and the white region corresponds to non-adipose region. The corresponding OCT images (a) and H&E histology were provided for comparison. The grids with SNR lower than a threshold will not be classified. From (b), it is clear that the adipose classifier successfully pinpointed the isolated adipose structure embedded in stroma region.

Figure 4.8 Adipose classification results. (a) Original OCT images; (b) classified results; (c) H&E hist ology.

White grids are non-adipose region and grey grids are adipose region. Scale bar: 1 mm.

We also validated our IDC classifier for breast tissue. The training data on 96 B-scans from 12 human samples. The correctly identified B-scans are provided in Figure 4.9. One B-scan from normal sample and one B-scan from IDC sample are presented in comparison. From the two representative OCT images, we found that normal tissue shows deep decay range with large variation while the IDC tissue shows low decay range with small variation. The probability estimated for each tissue type is related to the heterogeneity of the region of interest. For future study on the accuracy of the classifier, we consider the tissue type with the highest probability as the binary output of tissue classifier. We achieved an overall accuracy of 71.15%.

500 μm.

4.5 Discussion

Our algorithm builds probabilistic models to differentiate tissue compositions in OCT, and achieved a good accuracy to identify tissue composition within human cardiac and breast samples ex vivo. The methods, region-based or grid-based, can be potentially applied to the classification of tissues including oral tissue [159], skin tissue [160, 161], and intravascular OCT images [78,

162].

In the pre-processing step of cardiac classification, we detected the surface to shift image. The image shifting, widely used in existing segmentation method [68, 69], is necessary to determine the layer boundaries. We found that the difference between estimated layer boundaries and manual segmentation results were 203.61µm in LA and 259.35 µm in RA if we process our algorithm 75 without then flattening step. In the feature extraction step, our texture analysis is based on segmented atrial layers. We thus analyze the coarseness and homogeneity features in TCN. The index-wise TCN feature could be considered if we extend our algorithm to non-segmented image.

More detailed application of the region-based classifier in cardiac image analysis will be discussed in Chapter 5.

For breast classification, the accuracy of hierarchy framework is determined by both adipose classifier and IDC classifier. The adipose classifier serves as pre-selection of the suspicious region.

The speediness is more important than accuracy in adipose classifier. The threshold at which to input the tissue into IDC classifier needs to be tuned to maximize the efficiency of the whole algorithm. The IDC returns a frame based results regarding to the probability of cancer occurrence.

To increase the efficiency of the classifier, texture features was used to classify tissue at the first level and optical properties are used to identify IDC at the second level. Note that all classification results are based on one OCT system. More applications, detailed sensitivity and specificity evaluation, and the classification results from other OCT system will be discussed in Chapter 7.

4.6 Conclusion

We have developed image processing tools to classify tissue compositions in human cardiac and human breast OCT images. We proposed an automated algorithm to segment layer structures within endomyocardium. Features including optical properties, high moment statistics, and texture analysis were extracted and compared. Based on extracted features, a RVM based probabilistic model was used to identify tissue composition of segmentation. For breast tissue classification, we proposed a hierarchical framework to identify cancerous region. We first detect isolated region on a grid based scheme using texture feature. We then extract optical properties and use a frame-

76 based method to estimate the ratio of suspicious cancerous region. The validation experiments show good accuracy of our method, in terms of both segmentation and classification.

Chapter 5 Characterization of cardiac tissue

5.1 Background

5.1.1 Clinic needs Cardiovascular disease (CVD), a broad term for a range of diseases affecting the heart and blood vessels, has dominated as the leading contributor of mortality and morbidity in the United States for decades [163] as shown in Figure 5.1. In general, CVD can be categorized into coronary disease, heart failure, arrhythmias, and valve disease. Among various types of CVD, arrhythmia is an abnormal rhythm of the heart featured by irregular beating and may prevent the heart pumping enough blood to meet the body’s need. Arrhythmia, due to its high risk of clinical emergencies like cardiac attack, attracts enormous attentions from researchers and clinicians. In terms of therapy for arrhythmia, radiofrequency ablation (RFA) has replaced antiarrhythmic-drug therapy for treatment of many types of arrhythmia [164]. During RFA, long flexible catheter is inserted through a vein into patient’s groin and threaded to patient’s heart to correct structural abnormalities that cause arrhythmia. With heat delivered to correct rhythm, RFA works by collagen thickening or destroying small areas of myocardial tissue or conduction system that are critical to the initiation or maintenance of cardiac arrhythmias [165]. Lesion is created on the endocardial surface afterwards. However, inaccurate heat delivery is risky. The creation of over-ablated lesion in the myocardium is related to a theoretic increased risk of thromboembolism, the blockage of a blood vessel by a blood clot that has broken away from its site of origin [166]. In addition, two treatments are required for many patients to successfully terminate the arrhythmias. There is an underlying substrate of arrhythmias caused by myocardial remodeling. The heart geometry and fiber structure is remodeling during a range of disease process [167] and the collagen thickenings from infarction

78 or replacement fibrosis provide a substrate for arrhythmias [168]. Therefore, a better understanding of the relationship between ultrastructure and electrical conduction will greatly benefit the treatment of arrhythmias. The characterization of myocardial ultrastructure, such as myofibers, collagen thickening, and fibrosis, are the prerequisite to understand the pathophysiologic link between ultrastructure and arrhythmias.

Figure 5.1 Number of death due to heart disease and cancer in the U.S since 2008, data from [169].

5.1.2 Cardiac imaging Both invasive and non-invasive technologies are employed to image human heart. Fluoroscopy, real time X-ray with low dosage, is the mostly used image modality to guide RFA. The usage of dose enhances the trace of catheter both within heart chambers and in contact with heart wall [170].

Nonetheless, it also raises the risk of radiation dose, especially in the case that complex interventional procedures are needed. Ultrasound, intracardiac echocardiography (ICE) [171], can be used to guide the procedure of RFA via identifying the anatomic location of the catheter and to

79 ensure the contact of catheter to heart wall. However, ICE still suffers from low image contrast and is unable to image the ablation region within complicated region, such as atrial vestibule [172].

In addition to the guidance of RFA, computational models of cardiac biomechanics and electrophysiology have been used to study cardiovascular disease. Computed tomography (CT) and magnetic resonance imaging (MRI) are utilized to build a patient-specific model of cardiac biomechanics [173]. Diffusion tensor MRI are also used to build a geometrical atrial model [174] to understand the properties and build an electrical physiological model. Recently, a submillimeter

DTMRI imaging of entire atria has shown heterogeneous angle distribution throughout different regions of the atria data [175].

Myocardium is the largest layers within heart wall. Cardiac muscle fiber dominates the myocardium layer. Characterization of the myofiber structure, especially the fiber orientations, can help to identify arrhythmia substrates and associating electrograms with functional measurements. Traditional studies included sectioning the myocardium and staining with histology [121], which requires a huge labor of sectioning. The chemical processing of histology is generally believed to impact the evaluation of histology. DTMRI has been developed to measure the fiber architecture in hearts [167, 176, 177]. The fiber direction is based on the measurement of diffusion of water within heart and the principle direction of diffusion tensor is regarded as the myofiber direction. Another modality being explored for fiber orientation is ultrasound. Lee et al.

[178] developed an echocardiography-based shear wave imaging to map myocardial fiber structure.

Optical systems have also been utilized to capture fiber orientation in recent publications. To study embryonic growth in left ventricle, confocal microscopy was used to reconstruct myofiber images and computed local transmural myofiber angle distribution in [179]. Tsai et al. performed second harmonic generation microscopy of the collagen fibers in myocardium [180]. Polarized light

80 imaging, which was formerly utilized to reconstruct three-dimensional fiber tract in brain [181], has been recently used to model fiber structure in heart [182] based on optical birefringence properties.

5.1.3 Cardiac OCT imaging OCT is able to provide detailed morphological information within heart wall [17] through either catheter-based OCT system [183, 184] or benchtop OCT system [20]. OCT has been demonstrated to visualize image important features within the heart [138] such as the purkinjie network [18], atrial ventricular nodes [19, 20], sinoatrial nodes [21], and myofiber organization [22-25]. For fiber orientation, two dimensional fiber orientation was determined in excised heart preparation after fixation and through the use of optical clearing to increase contrast [22, 23] or polarization sensitive optical coherence tomography (PSOCT) for optical axis orientation [185]. Furthermore, fiber orientation information from OCT images was corresponded to conduction velocity measured with optical mapping [20] and used to characterize the specialized conduction system such as the sinoatrial nodes [21]. Overall, there are very few image analytic tools to study the fiber arrangement and tissue composition within cardiac OCT images.

5.2 Fiber orientation Analysis

We employ the method proposed in Chapter 2 to study the fiber orientation trend, tractography, and directionality map within animal hearts.

5.2.1 Experimental setup Three-dimensional image sets were generated from healthy swine (n = 5) hearts ex vivo. Three swine hearts (Heart I to Heart III) were acquired through Columbia University’s tissue sharing program. Animals were fresh and each heart was removed at room temperature. Two other swine

81 hearts (Heart IV and Heart V) were obtained from a local butcher. Samples were dissected from right atrium, left atrium, right ventricle, left ventricle, and ventricular septum respectively. After dissection of heart, OCT images were immediately collected on both the endocardial and epicardial sides.

TELESTO, a commercial spectral domain OCT system (Thorlabs GmbH, Germany), was used to image samples. It was an InGaAs based system centering at 1325 nm, with a bandwidth of 150 nm. The axial and lateral resolutions were 4.9 µm and 5.3 µm in water respectively. The maximum axial line rate was 92 kHz. In our experiment, each volume consists of 600 × 600 × 512 pixels, corresponding to a tissue volume of 4 mm × 4 mm × 1.88 mm. The volumetric scan was performed at 28 kHz. Four successively acquired OCT images were averaged.

5.2.2 Depth vs orientation We studied the relationship between depth and orientation in all heart chambers and septum. Three volumes were imaged in each chamber and ventricular septum from three swine (Heart I to Heart

III). To compare the rate at which the azimuth angle, θ, changes with depth, we set the azimuth angle, θ, at reference depth as 0 º and plot the relative angle at the increased depth in Figure 5.2.

The measurements were linearly fitted with an R2 ranging from 0.5105 to 0.8876, demonstrating a nearly linear relationship between depth and orientation within all samples. Among all dataset, the curves were well fitted, with an R2 ranging from 0.5105 to 0.8876, which proved a nearly linear relationship between depth and orientation in all samples. The slopes of the orientation versus depth varied in different part of heart. We perform ANOVA test on the slopes in all chambers and ventricular septum, finding that the atrium has a statistically higher slope than the ventricle with a p-value of 0.0026. Even in the same chamber, the slopes may vary. For example, in Figure 5.2(e),

82 the slopes in Vol 1 and Vol 3 are quite different and both were much smaller than the slopes in atrium.

The fiber orientations are quantified in each en face plane. The mean of orientation over an area of 1 mm ×

1mm is plotted at different depth from epicardial side. The experiments in different chambers: (a) right atrium,

(b) left atrium, (c) right ventricle, (d) ventricular septum and (e) left ventricle. The fiber orientation changes monotonically with depth. “EP” denotes epicardium. “EN” denotes endocardium.

5.2.3 Fiber comparison in tractography

To study the fiber trend, we processed our approach in three-dimensional space from the dataset obtained in ventricle, and atrium. The seeds were randomly generated on the boundary of the area of interest. And the fiber trace is predicted based on the distribution of fiber quantification results.

In each volume, the orientation of the myofiber was color encoded in three dimensions. Three representative results are presented in Figure 5.3(a) to (b) in comparison to the original OCT image volume. We found most of the fibers aligned at the same orientation. Meanwhile, the orientation slightly changed along each single fiber trace. In the left atrium, which is shown in Figure 5.3(a), apparent orientation change was observed with increased depth. We compared the tractography results with en face image in Figure 5.3(c) to (d). The reconstructed fibers are crossing the en face plane, which indicates that the fibers intersected with en face plane in a manner shown in Figure

5.3(a). In addition, we found that our reconstructed fiber trace matched the straits visible in OCT image among all three datasets.

Figure 5.3 The tractography of myofibers in atrium and ventricle. Our quantification and tractography algorithms enable the reconstruction of fiber structure in myocardium tissues. Results are compared with OCT image in (a) left atrium and (b) left ventricle in a volume of 2 mm × 2mm × 1mm underneath the surface. The fiber structures are also shown along with fiber OCT image in en face plane. The reconstructed fibers match the streamline in original OCT data in (c) left atrium and (d) left ventricle.

To evaluate the results of the fiber tracts in three dimensional spaces, we calculated the angle between the surface plane and fiber tract within the three datasets shown in Figure 5.3. The measurements in left atrium and left ventricle are 2.25 ± 0.89 º, 2.94 ± 2.06 º (mean ± standard deviation), respectively. The results show that the fiber tracts computed by the algorithm are nearly parallel to surface.

5.2.4 Directionality map of cardiac imaging Collagen fiber also shows up in heart tissue, especially in human heart. In human atria, there is a thicken collagen in the endocardial side. The collagen fibers are not well orientated as myofibers, resulting more scattering and less penetration depth in the atrial imaging. Due to the large variation in fiber orientation, it is necessary to quantify the fiber orientation on a pixel basis. An example of fiber orientation analysis is shown in Figure 5.4. In an en face image that is parallel to the surface, the fiber orientation is determined in each pixel. Three representative regions are selected. In each region, a histogram of the fiber orientation is plotted and fitted with normal distribution to initially compare the dispersions. The distribution shows to which extent the fibers orient at the same direction. In Figure 5.4, it is shown that region 2 has different fiber orientation from region 1 and region 3. Though orientated similar orientation, region 3 indicates larger dispersion than region 1.

It is thus possible to use dispersion of distribution as a metric to quantify the dispersion of collagen fibers within atria.

5.3 Cardiac tissue over a large field of view

We then stitched multiple OCT volumes based on the improved method [186] from Chapter 3 to enlarge the field of view.

5.3.1 Experimental setup Rabbit heart (n = 1) was acquired through Columbia University’s tissue sharing program. The heart was dissected and underwent two-hour phosphate-buffered saline (PBS) submergence before imaging. The right atrium was opened, flattened, and imaged from the endocardial side. Canine hearts (n = 3) were obtained from Washington University in St. Louis. During heart dissection, the atria were isolated and flattened by opening the vena cava and the RSPV. Then we fixed the hearts in 4% PFA for 36 hours before dehydrating them in 70% ethanol and shipping. During imaging, the atria was flattened and pinned to a cork sheet. To minimize dehydration during image, all samples are seated on gauze with ethanol. Each atrial sample was imaged from both the epicardial and the endocardial side. Human heart samples (n = 1) were collected from National Disease

Research Interchange (NDRI). All experiments were conducted at room temperature.

All volumetric OCT images were collected from a spectral domain OCT system, Telesto (Thorlabs

GmbH, Germany). The light source of OCT system centers at 1325 nm with a bandwidth of 150 nm. The axial and lateral resolutions are 6.5 μm and 15 μm in air, respectively. The OCT system works at a scan rate of 28 kHz. Each volume consists of 800 × 800 × 512 voxels, corresponding to a tissue volume of 4 mm × 4 mm × 2.51 mm in air. Multiple volumes were obtained at the region of interest. There was an overlap proportion of 10% to 20% between two adjacent volumes. Each volume has a corresponding white light image, delineating the same FOV on the tissue. The white light images and OCT images were taken simultaneously. The two images were calibrated using the factory settings of the Telesto system.

5.3.2 Visualization of entire rabbit atrium We first validated our algorithm in a rabbit atrium. We acquired 13 volumes from endocardial side of the atrium. The results are shown in Figure 5.5. The stitched white light image Figure 5.5(b) shows an agreement with Figure 5.5 (a), which is the camera image of the atrium. The boundaries between hollow space and endocardium or epicardium are visible in typical B-scans in Figure

5.5(b). A three-dimensional model is reconstructed in Figure 5.5 (c), showing detailed 3D features.

A stitched OCT B-scan is shown in Figure 5.5 (d).

Figure 5.5 Extracted geometric model from a right atrium of a rabbit heart. (a) The rabbit sample; (b) stitched white light image; (c) segmented rabbit atrium in three dimensions; (d) a typical stitched B-scan. The geometric model shows detailed 3D features from endocardium to epicardium. The blue box shows the overall region that we imaged. The red box shows the white light image for a single OCT volume.

5.3.3 Visualization of canine atrium We then validated our algorithm in a fixed canine atrium. We collected 54 volumes from endocardial side and collected 59 volumes from the epicardial side. The results are shown in Figure

5.6. The stitched white light image from epicardium/endocardium are shown in Figure 5.6(c)/(d) in comparison with the original camera image in Figure 5.6(a)/(b). Figure 5.6(e) shows the stitched

B-scans from both sides and Figure 5.6(f) presents the 3D visualization of the geometric model.

The two-side information are overlaid based on prior information about the imaging area within the atrial tissue. The results provide a solution to build a geometric atrial model for a large animal heart in which OCT system is not able to image through the atrial wall.

Figure 5.6 Extracted geometric model from an atrium of a fixed canine heart. (a) the epicardium of atrial sample; (b) the endocardium of atrial sample; (c) stitched white light image of atrial sample; (d) stitched white light images of atrial sample; (e) a typical stitched B-scan from stitched; (f) 3D segmented tissue. The geometric model shows great agreement in both endocardium and epicardium. The blue box shows the overall region that we imaged. The red box shows the white light image for a single OCT volume.

5.3.4 Visualization of human atrium Lastly, we validate our algorithm on human heart. We acquired 33 OCT volume over a space of

15 mm × 31 mm × 4mm. Each volume is with a size of 4mm × 4mm × 1.88 mm. The 3D visualization of the stitched volume is shown in Figure 5.7 (a). The stitched camera image within the same area is depicts in Figure 5.7 (b). The stitched images at X-Z plane (B-scan), Y-Z plane, and X-Y plane (en face) are shown in Figure 5.7(c), Figure 5.7(d), and Figure 5.7(e), respectively.

Blue, red, and green dash lines represent X-Y plane, Y-Z plane, and X-Z plane. In general, the

88 volumes are smoothly combined in both 2D and 3D. With a larger FOV, we observe multiple tissue types, such as adipose tissue, fibrotic tissue, and normal myocardium, in over a large space.

To further optimize our method, we will develop an algorithm to remove the artifacts in original

OCT volumes and develop classifications method to automatically detect different tissue type in the stitched OCT over the whole atrium.

Figure 5.7 Stitched human atria. (a) 3D volume; (b) stitched camera image (c-e) stitched two dimensional images. Various tissue composition was visualized in stitched OCT images.

5.4 Tissue composition analysis

5.4.1 Experimental setup Human hearts (n=15) were obtained under two approved protocols from the National Disease

Research Interchange [187]. The inclusion criteria for the first NDRI protocol are based on the following diagnosis: end stage heart failure, cardiomyopathy, coronary heart disease, or myocardial infarction. The second protocol requests normal hearts. Fresh tissue samples were shipped submerged in ice-cold phosphate-buffered saline and received within 48 hours of donor death. Detailed characteristics of the donor hearts within this study are listed in Table 5.1.

Table 5.1 Clinical characteristics of heart donors in dataset

Characteristic Value N 15 Demographic Profile Age in yrs, median (interquartile range) 66.0 (62.25 – 69.75) Male, n (%) 5 (33.3) BMI, median (interquartile range) 29.25 (24.3 – 34.2) Medical History, n (%) Diabetes 6 (40.0) Hypertension 2 (13.3) Heart Failure 2 (13.3) Cardiomyopathy 1 (13.3) Cause of death, n(%) Cardiac arrest 3(20.0) Cardiopulmonary arrest 3(20.0) Respiratory arrest 1(6.7) Respiratory failure 2(13.3) Chronic obstructive pulmonary disease 4(26.7) Congestive heart failure 2(13.3) Complete characteristics were not available for all donors

All samples were imaged ex vivo, using a spectral domain OCT system, Telesto I (Thorlabs

GmbH, Germany). The system is an InGaAs based system with its source centered at 1325 nm and a bandwidth of 150 nm. The axial and lateral resolutions are 6.5 μm and 15 μm in air, respectively.

All datasets were acquired at 28 kHz. In our experiments, each volume consists of 800 × 800 ×

512 voxels, corresponding to a tissue volume of 4 mm × 4 mm × 2.51 mm (in air). To extract the raw OCT data, the post-processing algorithm, including λ to k space interpolation, windowing, and Fourier transform was implemented using Matlab 2014b (Mathworks, Inc., Massachusetts).

Sections of tissue from the imaging field of view were processed for histopathology. Samples were sectioned parallel to the direction of the B-scans. Sample pieces were cut corresponding to the size of the OCT volume, fixed in formalin for ~24 hours and then placed in ethanol (20%) for ~24 hours. After fixation, samples were stained with Masson Trichrome. For 33.3% of the samples, histology was taken every 2 mm to ensure multiple matches between histology and the OCT image set. For validation, two investigators, blind to the automated results, segmented and classified the images based on the histology. One way analysis of variance (ANOVA) with Tukey multiple comparison test tissue were performed to detect differences between the tissue compositions for each of the extracted features. A p-value of 0.05 was considered statistically significant. All statistical analysis was conducted with the software package Prism 6.03 2013 (GraphPad Software,

Inc, CA).

5.4.2 Feature analysis We performed statistical comparison of features for five tissue compositions: normal myocardium, loose collagen, adipose tissue, fibrotic myocardium, and dense collagen. Representative measurements from optical properties, statistics, and texture analysis were shown in Figure 5.8

Statistical analysis of dense collagen, loose collagen, fibrotic myocardium, adipose tissue, and normal myocardium tissue in (a) mean of attenuation coefficient; (b) standard deviation of attenuation coefficient; (c) mean of penetration depth; (d) standard deviation of penetration depth;

(e) mean of std filter; (f) std of std filter; (g) mean of range filter; (h) standard deviation of range filter; (i) entropy; (j) Coarseness; (k) homogenity; (l) distance to surface; (m) contrast; (n) energy;

(o) skewness; (p) kurtosis. (P<0.05). In general, we found that features from OCT images of endomyocardium had a strong correlation with tissue composition. We found that normal myocardial tissue was not significantly different from the other four tissue compositions but significant in homogeneity. Loose collagen was not significant different from fibrotic in homogeneity and energy but showed statistical difference in statistical moments (kurtosis) and optical properties (attenuation coefficients). Within texture analysis, dense collagen was not significant with adipose tissue in homogeneity but significant in energy. Similar observations were found in the rest of features. We thus used the whole set of features to achieve the best classification performance.

(f) std of std filter; (g) mean of range filter; (h) standard deviation of range filter; (i) entropy; (j) Coarseness;

(k) homogenity; (l) distance to surface; (m) contrast; (n) energy; (o) skewness; (p) kurtosis. (P<0.05)

5.4.3 Classification results A leave-one-out experiment was conducted on the whole dataset. We use OCT images from 14 hearts as training data and use the images from the rest one heart as testing data. The experiment was repeated in a way such that images from any heart will be the testing data once. We obtained the confusion matrix to assess overall accuracy, Figure 5.9. The accuracy is evaluated on a layer- wise basis. The final tissue classification for the region was the class with the highest probability.

Using this identification rule, we achieved an average accuracy of 80.41%for classifying the five tissue compositions.

Figure 5.9 Confusion matrix of classification results

Representative three-dimensional classification results are shown in Figure 5.10. The classified tissue compositions are overlaid the original 3D dataset using the HSV colorcode scheme. Gold, yellow, red, and blue hue represents dense collagen, loose collagen, normal myocardium, and adipose tissue, respectively. In Figure 5.10(a) to (c), three tissue compositions of dense collagen,

94 loose collagen, and normal myocardium are well classified and tissue compositions of dense collagen and adipose tissue are well specified in Figure 5.10(d) to (f).

Figure 5.10 Three dimensional classification results from human atria. (a) & (d) Original OCT volumes; (b)

& (e) histology images; (c) & (e) color-coded classification results. Gold, yellow, red, and blue color represent dense collagen, loose collagen, normal myocardium, and adipose tissue, respectively. The classification results delineated the layer structure and agreed with Trichrome histology

5.4.4 3D classification of collagen thickening region In addition to the analysis on atria, we also processed our algorithm on ventricle. Specifically, we implemented our algorithm to identify the collagen thickening region. During the development of myocardial infarction, healthy myocardium is progressively replaced by fat or fibrous tissue, showing an enlarged dense collagen layer at endocardium. As shown in Figure 5.11, our algorithm accurate delineate the boundary of collagen thickening region in both 2D and 3D case. It is possible to evaluate the thickness of dense collagen to assess the development of myocardial infarction for clinical study.

OCT volumes. The classification results successfully delineate the boundary of collagen thickening region.

5.5 Discussion

We implemented our analysis tool in the study of fiber structure within cardiac tissues. We confirmed the fiber directionality change along with depth. The tractography was reconstructed in both atrium and ventricle. We confirmed that the fiber structure is nearly parallel to surface. Fiber dispersion patterns were studied based on directionality map and we conclude that dispersion analysis shows great potential to evaluate fiber disarray.

Our method and experimental design demonstrates great potential for in vivo tractography of myofibers. First, our method can reconstruct the fiber tractography on fresh tissue. In existing work, an optical clearing that usually takes up to 24 hours to prepare tissue must be performed [22, 23] to enhance the image contrast. Second, our method has the sensitivity to capture change of angle.

Given the fact that the heart is dynamically beating during in vivo experiment, our method sheds light on achieving dynamic and real-time monitor of heart beating.

Considering the swine hearts are from different source, we investigated the image data from fresh and purchased heart. The attenuation coefficients in purchased heart are higher than fresh heart.

Generally, the images collected from fresh heart have higher intensity and stronger contrast.

However, we did not observe significant differences in the slope, change in fiber orientation with depth, between the two subgroups.

One limitation in our method is that the performance may degrade when depth increases to more than 1mm. However, such limitation does not affect the role that our method plays in most of applications. For small animals, like mice, the thickness of ventricle is much less than 1 mm [188].

Furthermore, for clinical translation of performing an optical biopsy, standard endomyocardial biopsies of the ventricle sample 1mm cubed volumes [189], similar to the FOV of an OCT volume.

In addition, we can screen the majority of myocardium in swine atria. Figure 5.12 presents a typical

OCT image that was acquired from a volume of atrium. The minimum thickness of atrial wall can be around 0.5 mm, which is within the scan depth of our OCT system. Another limitation is that the heart is not in motion and we capture static image of the myocardium in our experiment. When imaging a beating heart in vivo or in situ [16], there will be a need to develop motion compensation algorithms. In the future, we would like to optimize the algorithm to run in near real time.

Among various imaging modalities currently used to extract fiber orientation, OCT-based method is promising from many aspects. The data acquisition time is shorter in OCT than that in DTMRI.

Moreover, the OCT system is able to provide a more morphologically detailed than DTMRI system and ultrasound-based system due to its high resolution. In addition, our method can be adapted with existing PSOCT systems [185]. Currently, we identify the myofibers based on the gradient information. We foresee that the birefringence and optical axis orientation measured in PSOCT can be additional weighting factors to be used in our particle filtering algorithm to track fibers.

In the future, we would extend our algorithm to analyze in vivo imaging of the myocardium using catheter-based OCT system [190]. It has been previously demonstrated that in vivo imaging of the myocardium is possible with a catheter once it is in contact with the tissue wall, displacing the blood [191]. Moreover, gating algorithms [192] will be utilized to reconstruct dynamic images of myofibers throughout the cardiac cycle. It is recently reported that 3D images can be reconstructed through forward image OCT catheter using MEMS [193]. We envision that our method can be

98 applied to catheter-based OCT three-dimensional images of myocardium tissues. The three- dimensional fiber information can help to diagnose the disarray of myofibers and identify myocardial infarction. Moreover, it is also possible to utilize our method to applications such as monitoring collagen fibers for wound healing [1], tracking white matter for brain disease [116], and assessing the muscular dystrophy [194]. Identifying fiber tractography in three dimensions will promote the development of these applications.

In addition to reconstructing tractography, we implemented a pixel-wise fiber orientation method to study the fiber information on each pixel. The current limitation of this method is the performance can be affected by the windows size due to the digitization of image. And also the current runtime for the shifting and weighting scheme is over couple of minutes for a single en face image. Meanwhile, the major upside of this method is that it has been demonstrated to be superior to the intensity based algorithm in terms of capturing non-dominant angle.

We implemented the stitching algorithm into various atrial OCT volumes including rabbit, canine, and human heart. To the best of our knowledge, it is the first time that an entire rabbit atrium is reconstructed. Our method shows geometric details at the surface of endothelium and epithelium.

In addition to geometric details, various tissue composition was visible in the stitched human heart, enabling the automated classification algorithm over a large field of view. We observed that in human atria, the tissue composition varies a lot among different locations.

In the future, our framework of registration can be extended to other feature poor organs, such as skin, esophagus. This geometric model can be potentially incorporated into an EP model [195] to simulate the functionality of heart beating and aid the diagnosis and treatment of cardiovascular

99 disease. In terms of algorithm, the algorithm can be further improved in better determination of the overlay of two stitched volumes from endocardial and epicardial sides.

We presented an automated algorithm to characterize tissue compositions in human atrial tissue.

Our classification algorithm had an 18% false positive rate of normal myocardium being misclassified as fibrotic myocardium. The tissue regions with small diffusion of fibrosis in myocardium contributed towards this high false positive rate. Moreover, the detection rate in adipose tissue was comparatively low because when adipose tissue is located at different depths, the texture pattern varies. The adipose tissue is in a honeycomb structure when it is imaged in focus. When out of focus, the adipose tissue appears as an area of isolated dots presenting different texture features. A comparison of B-scans with in-focus and out-of-focus adipose regions is presented in Figure 5.13.

Figure 5.13 Comparison of texture feature within adipose region in OCT B-scans. a) Typical OCT B-scans with adipose region in focus; b) Typical OCT B-scans when adipose region is out-of-focus. The yellow box with adipose tissue is marked for comparison. Scale bar: 250 mm.

One limitation of our study is that the time between donor’s death and heart imaging varies among samples. We found that the viability of imaging is degraded when we compared OCT images from early shipped heart with the late shipped heart. We will consider the deliver time as a factor to normalize the OCT image in the future; moreover, the process of fixation during histology may

100 result in shrinkage of the cardiac sample. It can impair the accuracy of correlation between histology and OCT image. In this study, we manually matched a small number of histology and the OCT images. Serial sections of histology can ensure that the variety of tissue features are observed. However, care will need to be taken to account for the fact that multiple samples are used in a training set from a single patient/chamber. Furthermore, imaging depth has an influence on image quality of OCT B-scans. Thus, to minimize the variations of imaging depth, we i) maintain the distance between the tissue surface and the objective the same range in all our experimental scenarios and ii) adjust image contrast based on the same thresholding and histogram equalization. With the translation towards in vivo use with a forward viewing catheter probe [196], contact imaging will be necessary and the sample location within the image will be constant to normalize the feature extraction.

In the future, we will need to implement a robust algorithm that take into account arbitrary shapes in which regions of tissue may present itself. Although most of endomyocardial tissue show layered structure [197], we notice there is a possibility that certain tissue compositions such as adipose tissue or mixture of myocardium and blood vessel appear in circular shape. It is possible that such a contour would not be not identified in the column to column search scheme. To overcome this drawback and make our algorithm more generalized, we will have a circular identification process and a refilling process. In particular, we can try using the Hough transform to find circles in the B-scan and employ the snake algorithm to delineate the circular contour.

Intensity value inside the circle will be refilled with the mean value of its neighboring pixels outside the circle. Then, we expect our layer segmentation and tissue classification method will be applicable in tissue classification of more tissue types.

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An important application of this work is for the development of improved cardiac models. We will incorporate atrial tissue characterization results into sample specific electrical physiology models of the human atria. A 3D finite element model [174] will be built based on geometry of human atria. Tissue composition is important for understanding conduction properties and arrhythmia substrates. A second application is towards the goal of performing an ‘optical biopsy’. Biopsy is currently the gold standard for the diagnosis of heart failure. Most of biopsy samples are around

1 to 2 mm3 [198], similar to the size of volumetric data we usually acquired in OCT system. We will extend our tissue classification algorithm to model of ventricular myocardial characterization and data acquired with high resolution OCT system. Our classification algorithm has the potential to guide the procedure of endomyocardial biopsy by avoiding areas with increased collagen thickening or and performing optical biopsies where conventional biopsy is unsafe. Lastly, our classification method can be used to aid the treatment of atrial fibrillation, radiofrequency ablation

[26]. Currently, the adipose region between catheter and tissue interference is a major factor that impair the success of RFA, the identification of tissue composition can provide good guidance for ablation operation to avoid the adipose region and facilitate the evaluation of ablation performance in both atria and ventricles.

5.6 Conclusion

We applied our image analytic tools in cardiac OCT dataset from canine, swine, rabbit, and human heart. We observed fiber direction change over depth and quantify the fiber tracts through the reconstruction of tractography. Fiber disarray was studied using pixel-wise method. We enlarged current field of view to centimeter level to visualize the entire rabbit atrium, both endocardial and epicardial sides of canine heart, and human heart with various tissue composition. Our

102 classification results show great accuracy in identifying the tissue composition in atria and specifying the collagen thickening region in ventricle.

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Chapter 6 Characterization of cervical collagen fiber network

6.1 Background

6.1.1 Preterm birth Preterm birth, defined as delivery before at least 37 weeks of gestation, occurs in 12% to 13% of all pregnancies in United States [199]. Preterm delivery is responsible for 70% to 80% of all neonatal deaths and significant neonatal morbidity [200]. In addition to high risk of neonatal death, the financial cost for managing preterm birth is much higher than that for normal deliver. It is important to minimize the incidence of preterm birth from both health and financial aspect.

Unfortunately, most of preterm birth is spontaneous, thus the cause of such birth remains unknown in the community of obstetrics. To date, no measure has been proved to successfully prevent the occurrence spontaneous birth. However, research has at least revealed that spontaneous birth eventually involves premature remodeling and dilation of cervix [201]. Mechanically, cervix is a barrier that holds the baby before the delivery, as shown in Figure 6.1. To understand the mechanism of spontaneous preterm birth and further prevent it happening, it is important to build a computational model to simulate the premature remodeling and dilation. Specifically, the premature change in mechanical properties of cervix is induced by alterations of cervical tissue extracellular matrix (ECM) content. In cervix, collagen content contributes the major dry weight of ECM [202] and exists as fibers in a hierarchical network embedded in viscous ground substances, such as proteins. Therefore, the ultrastructure of collagen fiber network is a critical factor of computational model of cervix.

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Figure 6.1 Schematic of cervix and uterus position. Modified from Fernandez et al, 2016[203]

6.1.2 Cervical imaging Many imaging modalities [204-210] have been utilized to study the collagen structure of cervix.

Ultrasound imaging [204] has the ability to detect the change of collagen and microstructure and demonstrated the anisotropic nature of collagen fiber structure, although the collagen fiber network is not resolved in ultrasound imaging. X-ray diffraction studies [205] found three radial zones of preferentially aligned collagen fibers, where collagen fibers along the outer edge and next to the inner canal predominately run parallel to the canal and collagen fibers in the mid-stromal area run circumferentially around the canal. Additionally, DTMRI [206] confirmed the inner and middle zones but the outer zone was not resolved. Second harmonic generation (SHG) data also describes a region of circumferential collagen fibers in non-pregnant cervix [207, 208]. To identify the smooth cell that co-exists with collagen fiber, immunohistochemistry (IHC) methods has been used to evaluate smooth muscle cell content and distribution throughout human cervix and correlate if the content of smooth muscle influences regional cervical tissue contractility [209]. Recently,

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Mueller matrix polarimetry is attached to a standard colposcopy system to enable the characterization of collagen birefringence [210, 211] and validated with SHG measurements. To date, the size of the region of these circumferential collagens and the level of fiber dispersion are still elusive, and the collagen organization of the pregnant human cervix is not studied.

6.1.3 Cervical OCT imaging Cervical OCT imaging has been shown encouraging results in visualizing detailed morphological structure [27]. The first OCT cervical imaging was initiated in 1997 in [212]. Since then, in vitro normal and neoplastic cervical tissue were imaged and studied in [28]. The signal decay rate over the depth of epithelia in OCT cervical biopsy specimen was statistically analyzed in [213].

Afterwards, most of OCT cervical imaging works focus on the aid of cancer detection [214]. A linear discriminant analysis (LDA) [30] method was developed to identify cervical intraepithelial neoplasia (CIN) grade 2 or higher by analyzing the layered structure of the epithelium, the basement membrane, and the stroma. In addition to cancerous structure. Measuring birefringence,

PS-OCT was employed to identify CIN [31]. In addition, OCT has been used as an adjunct to unaided visual inspection with acetic acid for the diagnosis of pre-invasive and invasive neoplasia of the uterine cervix in [32]. The epithelium cervical layer has been imaged by OCM in [215]. In general, most of the cervical studies in OCT community focus on measuring the optical property of cancerous region to aid the detection of cervical cancer. The collagen imaging and analysis study within cervix is scarce.

6.2 Enlargement of field of view

6.2.1 Image protocol Three-dimensional volumetric image-sets were obtained from human cervical samples imaged ex vivo. OCT image-sets were acquired using a commercial spectral domain OCT system, Telesto 106

(Thorlabs GmbH, Germany). It is an InGaAs based system centering at 1325 nm, with a bandwidth of 150 nm. The axial and lateral resolutions are 7.5 μm and 15 μm in air, respectively. The maximum axial line rate is 92 kHz. In our experiment, each volume consists of 800 × 800 × 512 pixels, corresponding to a tissue volume of 4 mm × 4 mm × 2.51 mm. Samples were placed on a linear translation stage underneath the objective. For each sample, we obtained multiple volumes.

The sample was moved along x-axis or y-axis on the translation stage. Since the surfaces of the sample were not flat, the axial position of the sample was adjusted to make sure that sample is well focused. Therefore, there were offsets at x, y, and axial directions. There was an overlap of 10% to 20% between two adjacent volumes. Each volume has a corresponding color-camera image, delineating the FOV on the tissue. The camera images and OCT images were calibrated by using factory settings in Thorlab.

6.2.2 Tissue collection All samples were collected from an Institutional Review Board (IRB) approved protocol at

Columbia University Medical Center, where three PG and ten NP patients were consented. Three to four mm thick whole axial slices of cervical tissue, cut perpendicular to the inner canal, were obtained after the patients underwent a hysterectomy. The 2nd slice from the internal os of the cervix was used in this study, where other tissue slices will be analyzed in future studies. The average ages of PG patients and NP patients were 29 and 42.7 respectively. Hysterectomies were performed on NP patients for benign indications and on PG patients for suspected abnormal placentation (accreta/ increta/percreta). These cesarean hysterectomies were performed prior to the onset of labor. Samples were analyzed after clearance by Pathology.

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6.2.3 Algorithm validation 6.2.4 Stitching Cervices The algorithm was applied to all 13 samples. Six representative three-dimensional reconstructions of the stitched volumes of cervical axial slices are shown in Figure 6.2, along with the stitched camera image. Figure 6.2(a)-(d) are of two cervical axial slices from two PG patients. In Figure

6.2(a)-(b), 53 volumes are stitched as a new volume of 30 mm × 27 mm × 7 mm. In Figure 6.2 (c)-

(d), 54 volumes are stitched as a new volume of 28 mm × 27 mm × 4 mm.

Figure 6.2 (e)-(l) are of four cervical axial slices from four NP patients. In Figure 6.2 (e)-(f), We stitched 40 volumes and formed a whole measuring 20 mm × 24 mm × 5 mm. In Figure 6.2 (g)-

(h), we stitched 41 volumes and formed a volume measuring 21 mm × 26 mm × 5 mm. In Figs.

Figure 6.2 (i)-(j), we stitched 24 volumes and formed a volume measuring 15 mm × 19 mm × 5 mm. In Figure 6.2 (k)-(l), we stitched 48 volumes and formed a volume of 24 mm × 31 mm × 5 mm. All stitching results demonstrate that our method can provide a full view of the cervical axial slice.

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Figure 6.2 Registered results of (a-d) PG and (e-l)NP samples. In particular, (a, c, e, f, i, k) are stitched camera image in two dimensions while (b, d, f, h, j, l) are stitched OCT volumes. For one PG sample, 53 volumes are stitched as a new volume of 30 mm × 27 mm × 7 mm. For another PG sample, 54 volumes are stitched as a new volume of 28 mm × 27 mm × 4 mm. We stitched 40 volumes for the one NP sample and formed a whole volume of 20 mm × 24 mm × 5 mm. We stitched 41 volumes for the second NP sample and formed a whole volume of 21 mm × 26 mm × 5 mm. We stitched 24 volumes for the third NP sample and formed a whole volume of 15 mm × 19 mm × 5 mm. We stitched 48 volumes for the fouth NP sample and formed a whole volume of 24 mm × 31 mm × 5 mm. Smooth surfaces are observed when multiple volumes are combined.

6.2.5 Confidence evaluation We first evaluated the fiber dispersion based on intensity based technique. With a large field of view to visualize the ultrastructure of human cervical axial slices using optimized stitching algorithm for large samples with low contrast features and surface topology, we can now investigate the collagen fiber orientation and dispersion within cervical axial slices from NP and

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PG patients. The intensity based gradient algorithm that was previously used to quantify fiber orientation in the myocardium was used to quantify collagen fiber orientation [22, 24]. After the stitched volume is obtained, we determine the three-dimensional surface of the whole volume.

Then, we obtain a plane parallel to the surface of the volume. Ten images are averaged along axial direction to reduce noise and improve the measurement of collagen fiber orientation. The fiber orientation algorithm is then applied to the plane. Briefly, the fiber orientation algorithm is as follows. To sharpen the image, a second order Butterworth high pass filter is convolved with the averaged image. In addition, a median filter is used to reduce speckle noise. For each image pixel

(i, j), the intensity gradients in the horizontal (Gx) and vertical (Gy) direction are calculated by convolving two 3 × 3 Sobel. The magnitude of gradient G(i, j) and angle Φ(i, j) was calculated based on (2.1) to (2.4).

This scheme assumes that the gradient in each pixel (i, j) in W follows a Von Mises distribution, analogous to a normal distribution, with mean of Φ(i, j) [59]. In W, the gradient of all pixels was considered and the weighted sum was computed. The mean value of angle ω is regarded as estimation of dominant gradient in sub-region W. For the cervical samples analyzed, we observed cases where the orientation departed from a Von Mises distribution, indicating that multiple orientations maybe present. To quantify the dispersion, we define a confidence value c as:

P() c  (6.1)  where  is the mean value of angle ω and  is the standard deviation of angle angle ω. The directionality maps are shown in Figure 6.3 in both PG cervical samples (a-d) and NP cervical samples (e-l). For each sample, we determine the fiber orientation in each 1000 μm × 1000 μm sub-region. Within Figure 6.3, representative OCT images are taken at 245 μm below the surface

110 in all volumes. Results are shown at 10 depths below 245 μm with an increment of 49 μm for a typical NP and PG sample. The color of the vector on fiber orientation maps were encoded with a confidence value defined (6.1). We observe that the fiber orientation in the NP cervix is more regular with high confidence level. The estimation in PG cervix is less regular and with lower confidence, especially at the region close to inner canal. Moreover, we observed that the orientation does not vary within the depth between 245 μm and 735 μm regardless if the sample was PG or NP.

Figure 6.3 Representative OCT images of (a-d) PG and (e-l) PG cervix. The FOV are 30 mm × 27 mm in (a)-

(b), 28 mm × 27 mm in (c)-(d), 20 mm × 24 mm in (e-f), 21 mm × 26 mm in (g)-(h), 19 mm × 15 mm in (i)-

(j), 24 mm × 31 mm in (k)-(l) . The image is a 2D plane that is parallel to the surface with a vertical depth of

245 μm. Fiber orientation results were processed for each OCT image. The estimations of orientation were made on each 1000 μm x 1000 μm. The results are color-coded based on confidence value 111

Figure 6.4 shows a dispersion analysis of collagen fibers within 1000μm × 1000μm × 490μm sub volumes (marked as boxes), corresponding the approximate dimensions of individual elements used within Finite Element analysis for cervical ultra-structure [95]. The probability distribution of orientations calculated from (2.4) in twelve sub-regions over each axial slice is plotted. In particular, the regions locate at anterior, posterior, left, and right side of inner canal are evaluated.

Within each side, 3 locations are selected to represent inner, middle, and outer region. As shown in Figure

6.4, the inner region is defined as the first full window closest to inner canal. The outer region is defined as the last full window distant to the inner canal. The middle region is the window in the middle of inner region and outer region. Figure 6.4(a)-(l) compared the distribution between a representative NP sample

(red colored curve) and representative PG sample (blue colored curve) at the twelve regions described above.

The probability is ploted as a function of angle. In general, the distribution of NP sample has a higher peak value than the distribution of PG sample, which implies that the orientation of collagen fiber bundles show less dispersion and more regularity for NP sample. Generally, the sub-regions close to inner canal (k, e, f, and l) shows larger dispersion than the polar plot on the distant sub-regions (a, b, g, and h).

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Figure 6.4 Distribution over 12 sub-regions (a) – (l) of non-pregnant (NP) (red) and pregnant (PG) (blue) samples. For each sub- region with a size of 1000 μm x 1000 μm area, the distribution is averaged over 10 depth with an increment of 49 μm. From (a) to (l), the peak value of distribution in NP is higher than the value in PG, which indicates less dispersion and more regularity.

To further analyze the dispersion of fiber organization, the confidence value, which gives an indication of fiber dispersion, was evaluated at all 12 locations for 13 cervical samples. Higher confidence values indicate increased directionality and lower dispersion. The mean and standard deviation are summarized in Table 6.1. We observe that the confidence from NP samples is higher than the confidence measured within the PG samples, indicating an increase in fiber dispersion within the PG cervical samples. In addition, a general trend is observed within both PG and NP samples, where the region adjacent to the inner canal has lower confidence (higher dispersion) than the middle and outer regions.

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Table 6.1 Statistic of the confidence value at inner region (e, f, d, l), middle region (c, d, i, j), and outer region (a, b, g, h) from pregnant and non-pregnant samples. The confidence value is measured as mean ± standard deviation NP [x10-4] (n=10) PG [x10-4] (n=3) p-value Inner region 1.25±0.15 1.15±0.16 0.07 Middle region 1.31±0.16 1.23±0.16 0.13 Outer region 1.30±0.23 1.26±0.22 0.63 All locations 1.28±0.18 1.21±0.17 0.05

6.3 Reginal difference in upper cervix

To better our dispersion analysis, we employed pixel-wise method to analyze the fiber directionality and use Von Mises distribution in the following experiment.

6.3.1 Experimental setup Thirteen human cervices were collected from consented hysterectomy patients by an IRB approved protocol at Columbia University Medical Center (Table 6.2). Among the cervices, 11 were from non-pregnant (NP) patients undergoing hysterectomy for benign indications and 2 were from pregnant (PG) patients undergoing cesarean hysterectomy due to abnormal placentation. Patient age ranges from 36 to 49 and parity number from 0 to 5. The cervices were sliced perpendicular to the inner canal immediately after hysterectomy using a custom-built slicer. The thickness of each slice was 3-5 mm. Axial slices within the upper half of cervix were excised. In this study, we analyzed the slice that is closes to uterus for each cervix. All samples were kept on dry ice and then stored at -80oC for later imaging. This study was approved by the Columbia University IRB, with an IRB protocol Number: IRB-AAAL4005. Study participants gave their consent by signing a written consent form that was approved by the Columbia University IRB. A more detailed protocol used for sample collection and preparation is described in our earlier work.

Before OCT imaging, cervical slices were thawed in phosphate buffered saline (PBS) overnight at

4C, and the surface closer to the internal os was microtomed. During the imaging procedure, the cervical slice was laid on top of a gauze soaked in PBS to keep the tissue hydrated. Samples were

114 imaged using a commercial OCT system, Telesto I (Thorlab GmbH, Germany). The system is an

InGaAs based system with its source centered at 1325 nm and a bandwidth of 150 nm. The axial and lateral resolutions are 6.5 μm and 15 μm in air, respectively. In our experiments, each volume consisted of 900 × 900 × 512 voxels, corresponding to a tissue volume of 4.5 mm × 4.5 mm × 2.51 mm (in air). Samples were placed in a linear translation stage underneath the objective. For each sample, we obtained multiple volumes. There was an overlap proportion of at least 10% between two adjacent volumes. A white light camera obtained an image of the sample corresponding to the

OCT FOV. The camera images and OCT images were calibrated by the default factory setting.

= full term, SAB = spontaneous abortion (micollagen thickeningriage), CS = cesarean section, VBAC = vaginal birth after cesarean, NA = not avaliable.

Specimen ID Age Pregnancy Status Gravidity / Parity Obstetric History 1 42 NP 5/1041 1 VD, 3 VTOP 2 41 NP 6/4024 4 FT VD, 1 VTOP, 1 SAB 3 46 NP 0/0000 NA 4 40 NP 2/0020 VTOP, SAB 5 43 NP 1/1001 VD 6 49 NP 1/1001 VD 7 46 NP 4/1031 VD, 3 VTOP 8 40 NP 3/3003 3 VD 9 48 NP 9/5045 5 FT VD, 4 VTOP 10 36 NP 4/4004 4 CS 11 46 NP 3/3003 VD, CS, VBAC 12 30 PG 5/1031 CS, 3 SAB 13 42 PG 5/2022 NA

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6.3.2 Pixel-wise orientation estimation on stitched OCT images A typical example of the pixel-wise method on a stitched OCT cervix image comprised of 24 OCT volumes is shown in Figure 6.5. The original OCT image is an en face image 245 µm parallel to the cut surface. From the pixel-wise directionality map, such as Figure 6.5 (a), we observe a circumferential trend of fiber in the outer zone. From a zoom-in box in Figure 6.5 (b) and Figure

6.5 (c) corresponding to a 4 × 4mm region, it shows fiber directions can vary dramatically within a small region. Similar circumferential trends and direction variation patterns are observed in all other cervical samples.

80 pixels.; (b) OCT image within the white box in (a); (c) directionality map within the white box in (b).

Pixels with no fiber information are coded in black. Each 400 µm × 400 µm subregion represents a location for the fiber orientation and dispersion analysis in the A (anterior), P (posterior), L (left), and R (right) quadrants. Along the radial direction, the boxes are divided into inner region (red) and outer region (green).

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6.3.3 Statistical analysis A group of analysis of variance (ANOVA) tests were performed in MATLAB using one-way

ANOVA function (anova1) and multiple comparison function (multcompare) to compare the von-

Mises fiber ultrastructure parameters (b and θ) between NP and PG specimens and among NP specimens with different parity. The data normality was verified by Kolmogorov–Smirnov test in

MATLAB (kstest function) before performing the ANOVA analysis. The homogeneity of these fiber ultrastructural parameters within individual sample slices were assessed by comparing results between circumferential quadrants, inner and outer radial zones.

In the circumferential direction, the cervical slice was divided into four anatomical quadrants. In the radial direction, the cervical slice was divided into inner and outer zones. The border between the inner and outer radial zones was manually determined by differentiating the distinct patterns of fiber orientation of the two zones. The radial direction was also subdivided into 400 μm × 400

μm subregions as described by the pixel-wise fiber tracking method above.

When b and θ were compared between different samples, averages were taken of the results from all 400 μm × 400 μm subregions within the quadrant and radial zone. When comparing b and θ, the variance of b and θ along radial direction within each quadrant and zone were also measured by calculating the standard deviation. All ANOVA tests were performed in MATLAB using the anova1 function where a p-value of 0.05 was considered statistically significant.

2D von-Mises distribution provides a close fit to the raw fiber dispersion data. Concentration parameter b can be as high as 0.820 and as low as 0.010 as shown in Figure 6.6(a)(b). For certain subregions, more than one family of fibers can be observed where the current 2D von-Mises

117 analysis cannot capture these distinct fiber families (Figure 6.6 (c)(d)). The fitting for multiple families of fibers will be discussed in discussion.

Figure 6.6 Representative fiber distributions found in the upper cervix and corresponding 2D von -Mises fits.

The dominant direction 휃 is shown by dotted line. All four subregions are taken from the outer radial zone of the same NP sample (Specimen 5). A subregion with (a) a single family of fibers that have the most alignment

(b = 0.820) and (b) highly dispersed fibers that are randomly oriented in the plane. A subregion with (c) two fiber families and (d) three fiber families. (Note: current distribution fitting methodology cannot distinguish the multiple fiber families.)

6.3.4 Observation In general, we found the following two regions of dispersion pattern [216]. The NP cervical tissue samples measured in this study have two regions with distinct fiber directionality and dispersion

118 properties. The posterior and anterior of the outer zone is labeled Region 1 and the remaining parts of the cervix (left and right of outer zone and all inner zones) are labeled Region 2 (Figure 6.7).

For a NP cervix, Region 1 and Region 2 have different fiber dispersions between Regions and similar dispersions within each Region. However, when a NP cervix becomes a PG cervix, Region

1 will have a shift in the fiber dispersions so that the properties are similar to Region 2 while

Region 2’s properties do not shift. In other words, Region 1 is more sensitive to pregnancy status and remodels more dramatically than that happened in Region 2 during pregnancy. The arguments above are verified by ANOVA test in Result section by comparing Region 1 in NP with Region 2 in NP and all Regions in PG

6.4 Dispersion analysis over longitudinal direction

6.4.1 Experimental setup We imaged nine human cervices from consented hysterectomy patients by an IRB approved protocol at Columbia University Medical Center. Eight cervices were from non-pregnant (NP)

119 patients undergoing hysterectomy for benign indications and one were from pregnant (PG) patients undergoing cesarean hysterectomy due to abnormal placentation. The samples were collected by sectioning immediately after hysterectomy using a custom-built slicer. The cervices were sliced perpendicular to the inner canal. The thickness of each slice was 3-5 mm. Patient age ranges from

36 to 49 with parity numbers range from 0 to 5. Multiple axial slices (3-5) from upper half of cervix to external os were excised. All samples were kept on dry ice and then stored at -80oC for later imaging. This study was approved by the Columbia University IRB.

6.4.2 Visualization over longitudinal direction To visualize the slices from the same patient, we aligned them in 3D space as shown in Figure 6.8.

For each slice, we obtained an en face image that is 245 µm parallel to the cut surface We compared the difference of fiber patterns over longitudinal direction. In (a), we found that the dimension of axial slice increases from internal os to external os. Also, the diameter of inner canal enlarged at sl4. Notably, in sl1, the slice closest to uterus, the muscle shows distinctive circumference trend in

OCT images, indicating larger smooth muscle ratio in sl1 than sl2 and sl4. This validates the measurements in [209]. We processed the directionality map for sl1 to sl4. The results are shown at the third column. Similar to the trend we observe from OCT images, in the directionality map, we observe more distinctive circumference trend in sl1 than sl2 and sl4. We hypothesize that there is a change in fiber structure and tissue composition at different depth within cervix.

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Figure 6.8 Visualization of slices from the same patient a) 3D visualization of multiple cervical slices; b1-d1) en face OCT images from sl1 to sl4; b2-d2) corresponding directionality map of OCT from sl1 to sl4.

6.4.3 Feature study on single sample To validate the hypothesis, we quantitatively compare fiber dispersion from internal os to external os. As the division in Figure 6.5, we analyzed the concentration parameter, b, in (2.14) a sub- region of 4 mm * 4mm. To study the tissue property, we measured the penetration depth of OCT image in each corresponding volume. Penetration depth is defined as the depth at which the intensity drops to 1/e of its original intensity [148] when light first reaches the interface. A representative study on non-pregnant sample is shown in Figure 6.9. The results show a decreasing trend in concentration parameter and an increasing trend in penetration depth.

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Similar trend was observed when we analyze on a pregnant sample as shown in Figure 6.10. The increasing trend in penetration and decreasing trend in concentration parameters were both confirmed in pregnant sample. Importantly, sl2, the slice which is closest to uterus, shows significant difference (p<0.05) in ANOVA test in comparison with other slices.

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6.4.3.1 Study on overall trend

We measured the dispersion parameters and penetration parameters for all nine samples. The mean values of each slice/sample are plot in Figure 6.11.

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Figure 6.11 Measurements of each sample (c1to c9) at different locations to the uterus. a) mean value of concentration parameter b vs locations; b) mean value of penetration depth vs locations. In general, the concentration parameter shows a decreasing trend and the penetration depth shows an increasing trend over the increased distance to uterus.

We found 7 out of 9 samples showed decreasing trend of concentration value and 6 out of 9 samples showed increasing trend of penetration depth when the location was away from uterus.

Since we only have one pregnant sample, our study focus on the non-pregnant sample (n = 8).

Grouping all non-pregnant sample, we boxplot the statistics of penetration depth and concentration parameter in Figure 6.12. According to the ANOVA test, sl2 showed a significantly higher value of concentration parameter b than sl6, indicating lower dispersion in the location close to uterus.

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Figure 6.12 a) boxplot of concentration parameter b; b) boxplot of penetration depth.

6.4.3.2 Reginal study

In addition to the study on the overall slice, we are also interested in the difference among quadrants. We thus grouped the axial slice into left/right (LR) regions and posterior/anterior regions. We compared the trend in each group and plot the boxplot in Figure 6.13. The increasing trend of penetration depth and decreasing trend of concentration parameter was also observed in quadrants. Importantly, we found the L/R regions showed a larger value of concentration parameters than A/P regions. Also, the L/R regions showed a smaller value of penetration depth than A/P regions. That is, the difference does not only exist in longitudinal direction regarding the uterus but also exist in quadrants. The difference pattern is in align with our observation in [216] at the upper cervix region.

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Figure 6.13 Regional comparison of non-pregnant samples. a) concentration parameter in L/R region; b)

concentration parameter in A/P region; c) penetration depth in L/R region; d) penetration depth in A/P

region.

6.5 Discussion

We applied a fiber orientation algorithm to analyze the collagen fiber dispersion patterns within different areas of the cervix and between a pregnant (PG) and non-pregnant (NP) sample. We visualized the circumferential orientation of collagen fibers within axial cervical slices.

Specifically, we show initial evidence that the collagen network remodels in pregnancy, where pregnant cervical collagen fibers maintain an overall circumferential direction but they are more dispersed when compared to the nonpregnant state.

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We believe the regional differences in collagen fiber properties within a single sample and between samples are influenced by the anatomical and loading environment of the cervix in the pelvic region. The cervix is the lower portion of uterus. Cardinal ligaments attach this portion laterally

(i.e. left and right), and the bladder lies anterior to the cervix separated by loose connective tissue.

The positioning, symmetry, and shape of the uterus and cervix drive the patterns of cervical stress and stretch and can be vastly different for each person [217]. Often in pregnancy the cervical axis is angled posteriorly from the uterine axis. This positioning leads to increased tissue loads and stretching in the anterior and posterior sections of the cervix [203]. The angle of the cervix with the uterus can be a potential cause of the increased anisotropy in Region 1 of the cervix, and the fact anatomical factors vary widely between patients can explain the variability between samples.

Related research [218] of finite element analysis of human uterus and cervix also supports the heterogeneity of fiber dispersion we find between quadrants. The FEA analysis demonstrates that the collagen directionality and dispersion play a role in resisting physiological relevant deformation during pregnancy. Further studies with larger patient populations must be conducted to understand the mechanical loads on the cervix and cervical tissue remodeling behaviors during pregnancy.

This research presented in this chapter has the following limitations. First, as discussed earlier, the collagen fiber network is three-dimensional but fiber orientation and dispersion were only studied in two dimensions. Longitudinal fibers cannot be verified in this research because OCT images were stitched in the plane that is perpendicular to the inner canal. Second, only the available slice that is closest to the internal os had been studied. We selected the first slice to start our analysis because the internal os is the location of premature funneling [218] and maximum stress [203] during pregnancy. The premature funneling is often followed by opening from the rest of the

127 cervical inner canal and preterm birth. As we found in different quadrants, it is highly possible that the cervix is heterogeneous in the longitudinal direction since the percentage and type of biological and chemical components have been found to be different along longitudinal direction [202] and the inner zone was found to disappear as we approach to the external os [219]. Third, due to the limited number consented patients, we have a smaller database comparing to research that uses animal tissue.

The OCT imaging and fiber analytic tools presented here is suited for our application because it offers tissue fiber ultrastructure characteristics at a length scale appropriate for implementation into a previously developed fiber-based continuum material model for human cervical tissue [218].

Additionally, the whole sample fiber maps inform the implementation of tissue architecture into large-scale finite element models of pregnancy. Lastly, OCT is a nondestructive technique, which allows for ultrastructural, biochemical, and mechanical analysis to be conducted on a single sample.

In future work, mechanical tests will be conducted to determine corresponding material behavior, and the structural importance of the regional ultrastructural properties of the cervix will be explored in finite element models of human pregnancy.

6.6 Conclusion

We measured the heterogeneity of local fiber orientation and dispersion in human tissue slices from the upper cervix using an OCT pixel-wise fiber orientation algorithm. We found that human cervical tissue has a distinct collagen fiber ultrastructure where collagen fiber orientation and dispersion vary according to anatomical quadrants. We found that in non-pregnant cervical sample, the anterior and posterior quadrants have highly aligned circumferential collagen fibers that are less dispersed than the left and right quadrant. Overall, we found that the non-pregnant samples

128 examined here had more aligned and less dispersed collagen fibers than pregnant tissue. We also observe that the ultrastructure, particularly penetration depth and fiber dispersion, increases over longitudinal direction from internal os to external os in cervix.

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Chapter 7 Characterization of breast cancerous region

7.1 Background

7.1.1 Clinic needs Breast cancer is the leading cause of cancer death in women aged between 20 and 59 [220]. Breast cancer can be generally divided into two categories: carcinomas and sarcomas. Carcinomas arises from the epithelial component of breast, such as lining cells in lobules and ducts while sarcomas are from the stroma (connective tissue). Overall, the majority of the breast cancers are carcinomas from epithelial cells [221]. Moreover, more than 90% of carcinomas show ductal epithelium differentiation. At the early stage of carcinoma, cancer cells locate in the duct, known as ductal carcinoma in situ (DCIS). When cancer cell develops and infiltrates outside duct region, it becomes invasive ductal carcinoma (IDC) and exists in a wide region of breast tissues. Typical treatment of breast cancer includes lumpectomy and mastectomy. Lumpectomy is the conservative operation removing the tumor and some tissues surrounding the tumor. In contrast, mastectomy refers to the removal of the entire breast to ensure the isolation of all possible cancerous regions. For early breast cancer treatment, lumpectomy plus radiation therapy is considered as effective as mastectomy. Therefore, it is highly desired to detect the cancerous region at the early stage to minimize the harm to patient. Upon breast removal in lumpectomy, a general question is that whether the whole cancerous region has been completely removed or whether a re-excise is required. Intraoperative histological assessment that usually takes at least 25-30 minutes, is time consuming and does not directly reduce the re-excise rate [222]. The surgical margin status is considered as a strong indicator for local recurrence following lumpectomy. In addition, there is a

130 significant number of over-diagnosed cases amongst rapidly increasing numbers of DCIS each year [223]. The early detection of cancerous region, particularly DCIS, can reduce the over- diagnosis and avoid unnecessary mastectomy. Therefore, it is of great clinical significance to identify the breast cancer to aid lumpectomy or to prevent over-diagnosis.

7.1.2 Breast imaging Though the imaging screen techniques has been significantly improved to identify large mass of malignant cancer region by mammography [224], electrical impedance tomography [225], and diffuse optical tomography [141], delineating tumor margin region to aid conservative surgery is still challenging due to their spatial resolution. In clinic practice, intraoperative gross examination and histologic examination have been used to assess the surgical margins [226]. A positive region that is close to margin will lead to a re-excise operation. However, the analysis is time consuming and the sampling area is very limited in histology, especially in the case that only one side of paraffin embedded tissue is available for histology. Therefore, various imaging modalities [227-

234] have been investigated to assess tumor margin in breast tissue based on optical properties of normal and cancerous tissue. Nonlinear microscopy [227] provides histology-grade visualization of breast tissue sections in freshly excised tissue. Fluorescence techniques, including confocal fluorescence microscopy [229], florescence lifetime imaging [228], two photon fluorescence lifetime imaging [234], showed encouraging results in providing detailed morphological structure.

However, the application of microscopy-based techniques is usually limited by a small field of view

(FOV) and lack of depth information. To assess the surgical region at a deeper range, efforts has been done by using optical spectroscopy [230, 231], impedance measurement[233], and RF spectroscopy [232]. However, the lateral resolutions of techniques are not sufficient to delineate a continuous boundary of surgical margin. A dual modality scheme, consisting of auto fluorescence

131 lifetime imaging and light reflectance spectroscopy, was proposed in [231] with an automated multinomial logistic regression classification model for intraoperative margin detection. This study was still based on very limited data and the individual fluorophores for the two lifetime components are not well studied. In addition to the detection of IDC, the detection of DCIS can be achieved by ductoscopy [235], which provides intraductal cellular or tissue information. Similar to other endoscopic techniques, ductoscopy only images the tissue at surface. In general, a real-time, nondestructive, an imaging technique that has a larger FOV, sub-cellular resolution, and depth- resolved imaging modality is desired for intraoperative assessment of breast cancer.

7.1.3 Breast OCT imaging In breast imaging, OCT was first introduced in the community of breast cancer management as a non-destructive high resolution imaging tool to evaluate tumor morphology in ex vivo breast tissue

[33]. Due to the high-speed and wide-field imaging capability, OCT has been implemented in intraoperative settings [236] as well as handheld probes and needle catheters [237-240] to enable ex vivo and in vivo assessment of tumor margin. Especially, efforts have been made to drive towards computer-aided detection (CAD) of breast cancer in OCT needle biopsy by exacting useful information from OCT signal [80, 84, 237, 241, 242]. Moreover, functional OCT systems were also introduced to breast tumor margin assessment with enhanced imaging contrast. Physical properties of the tissue, such as elasticity [34-36] and optical birefringence [37-39] can be mesured from additional mechanical and optical detection channels, respectively. Besides, in order to match the resolution provided by traditional histology, OCT systems with enhanced lateral resolution, such as optical coherence microscopy (OCM) [243] and full-field (FF) OCT [244], were developed to generate micro-meter resolution en face images of freshly excised breast tissue. These en face preferential OCT systems clearly provide images showing good correlations with histology.

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However, they inherited some limitations from those microscopy techniques, such as compromising depth of focus. The limited depth of focus may be mediated by wavefront correction, yet it may cause more complications in the system. Ultrahigh resolution (UHR) OCT generally categorizes OCT systems with axial resolution less than 5 µm enabled by a broadband light source.

Just as the conventional OCT system, the depth of focus can be extended if the lateral resolution is compromised to a certain degree. The overall image quality is still improved due to a superior axial resolution. The improvement in signal penetration may be critical to some applications. For example, a larger margin width is usually more appreciated for ductal carcinoma in-situ (DCIS)

[245, 246]. A recent study [142] demonstrated that UHR OCT may enable high resolution 3D visualization of a variety of tissue types in freshly excised breast tissue to aid in differentiation of malignancy with an appreciable imaging depth.

Though large efforts have been made to image breast tissue with OCT, most of the works focus on showing the capability of visualization of typical breast features for intraoperative assessment.

The investigation of automated classifier is limited to small number of samples and tissue composition. The study of automatically identifying cancerous region is particularly scarce in OCT community.

7.2 Stitching experiments and results

7.2.1 Experimental setup Three-dimensional OCT volumetric images were taken on samples from 19 patients at Columbia

University Medical Center, including both healthy breast tissue and the ones with structural anomalies. Samples were acquired from the Department of Pathology and Cell Biology’s tissue bank within 12 hours after resection and stored in PBS until imaging. After imaging, samples were fixed in 10% formalin for ~24 hours and processed for H&E histology.

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All samples were imaged ex vivo at room temperature, using a commercial OCT system, Telesto I

(Thorlabs GmbH, Germany). The system has a center wavelength at 1325 nm and a bandwidth of

150 nm. The axial and lateral resolutions of the system are 6.5 μm and 15 μm in air respectively.

All data were acquired at a 28 kHz line rate. In our experiments, we have a subset of the samples imaged with two scales. For large-scale images, each B-scan was 2.52 mm × 10 mm laterally corresponding to 512 pixels × 600 pixels, and for small-scale, that was 2.52 mm × 4 mm laterally corresponding to 512 pixels × 600 pixels. The dataset acquired with the large-scale imaging setting undersampled the spot size of the OCT objective.

7.2.2 Stitching human breast tissue We applied our algorithm to stitch human breast tissue. Typical results are shown in the following figures. With the increased FOV, we observe that the morphological details are similar pattern with the H&E histology, which is the good standard for pathology. In (a), duct structure with necrosis is shown in both histology and OCT images. Multiple cyst structures were captured in (c).

Terminal duct lobule unit (TDLU), including a cluster of lobule structure, shows an isolated pattern in (e). For invasive ductal carcinoma (IDC), the boundary between IDC and adipose tissue is well delineated in (h). Overall, the stitching algorithm enhanced the global visualization of detailed breast structure within OCT image.

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Figure 7.1 Comparison of stitched OCT images with H&E histology. (a-b) DCIS; (c-d) cysts; (e-f) Terminal duct lobule unit; (g-h) IDC vs adipose tissue. The enlarged OCT images, with a larger FOV, shows good match with histology image in capturing the morphological details.

7.3 Breast classification

7.3.1 Experimental setup Two SDOCT systems were used to acquire volumetric images from the excised breast tissue specimens: a commercial system (Thorlabs Telesto I) at 1300nm and a previous reported home- built ultrahigh resolution (UHR) OCT system at the optical window of 800nm. The commercial

135 system has an axial resolution of 6.5 µm and lateral resolution of 15 µm in air, with an imaging range of 2.52 mm [247]. The UHR OCT system has an axial resolution of 2.7 µm and lateral resolution of 5.5 µm in air, with an extended imaging range of 1.8 mm and a 6-dB sensitivity fall- off range of 0.89mm enabled by a supercontinuum source (NKT Extreme EXR-9) and a customized spectrometer. The customized spectrometer features a modified Cooke triplet lenses optimized for the focusing performance on a 2048-pixel line-scan camera within the wavelength range from 740 nm to 940 nm.

Multiple three-dimensional OCT volumetric images were acquired on both the top and bottom sides of the specimens, covering the entire surface area of the specimens. Within one specimen, different volumes represented different locations. For the UHR-OCT system, OCT volumes were taken at 32kHz linerate (sensitivity > 93 dB). Each volume had 800-by-800-by-1024 pixels, covering 3mm-by-3mm-by-1.78mm in space, with an acquisition time of 20 s per volume. For the

1300nm system, the linerate was 28kHz (volume acquisition time 23.6 s, sensitivity > 96 dB), and the volume size is 800-by-800-by-511 pixels covering 4mm-by-4mm-by-2.52 mm in space.

Specimens were all imaged fresh in free space. During the imaging process, PBS spray was applied to prevent the sample from drying. For the image comparison study, the specimens were manually transferred from one system to the other, located and orientated the same way with respect to the scanning beam using best effort. All OCT images were presented without scaling by tissue refractive index

7.3.2 Adipose classifier We compared the sensitivity and specificity of adipose classification results based on OCT images from 1300 nm OCT system and UHR OCT system in Figure 7.2(a). In general, classification in

UHR OCT images achieved higher sensitivity (94%) and specificity (93%) than the sensitivity

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(91%) and specificity (76%) in 1300 nm OCT images. We applied our algorithm on volumetric

OCT images in Figure 7.2 (b)-(d) and obtained corresponding the color-coded OCT volumes in

Figure 7.2 (e)-(g). In particular, Figure 7.2 (b) and (c) are from normal and cancerous specimen from 1300 nm OCT system, respectively. We calculated adipose ratio within normal and IDC specimens and found that the adipose ratio (52.3 ± 29.4%, n = 6) in normal tissue was higher than that in cancerous tissue (12.4 ± 10.1%, n = 4). This observation was further confirmed from corresponding histology. We also classified the adipose tissue within an UHR OCT volume.

Original intensity data along with color-coded result were presented in Figure 7.2 (d) and Figure

7.2 (g), respectively. We found that in UHR OCT images we were able to capture more isolated adipose structures.

3D fat maps with corresponding OCT volumes from Thorlabs system in normal and IDC specimens, respectively. (d),(g) shows color-coded 3D fat map with corresponding OCT volume from UHR OCT system

7.3.3 IDC classifier Selected OCT images of normal fibrous stroma and IDC from UHR OCT and Thorlabs system were presented in Figure 7.3 (a)-(d) as a qualitative comparison. It appeared that optical signal can

137 penetrate deeper in normal fibrous stroma than in IDC. In addition, OCT intensity signal from normal stroma appeared to be more heterogeneous across the lateral field of view of 3 mm ~ 4 mm, compared with that from IDC specimens. The lateral heterogeneity resulted in a larger variation, especially in the decay range. 152 B-scans from UHR OCT system and 104 B-scans from Thorlabs system were separately employed for IDC classification, and the validation results were listed in

Table 7.1. In particular, for a limited number of dataset, we achieved an overall accuracy of 84%, sensitivity of 89% and specificity of 71% for classification based on UHR OCT images, which were better than the results (overall accuracy of 71%, sensitivity of 83%, and specificity of 53%) based on Thorlabs images. In addition, we further applied our algorithm in 3D dataset. We extracted the features in each B-scan and the RVM returned a probability of how likely this B- scan belonged to IDC tissue type. The color-coded probability bar was shown in Figure 7.3 with yellow indicating normal and blue indicating IDC.

Figure 7.3 Volumetric UHR-OCT images and classification results between IDC and fibrous stroma. b1Two individual B-scans were selected to compare with the corresponding histology. a1) OCT B-scan from location a in volumetric OCT dataset; a2) corresponding histology of a1; b1) OCT B-scan from location b; b2) H&E histology of b. The estimated probability shows a good match with H&E histology Scale bar: 250 µm.

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Table 7.1 Classification results of invasive ductal carcinoma

UHR OCT system Telesto system

Histology Histology Total Histology Histology Total (positive) (negative) (positive) (negative) OCT (positive) 93 14 107 53 19 72 OCT (negative) 11 34 45 11 21 32

Total 104 48 64 40

Sensitivity Specificity Overall accuracy Sensitivity Specificity Overall accuracy = 89.42% = 70.83% =83.55% = 82.81% = 52.50% =71.15%

7.4 Discussion

We applied our stitching and classification tools in the analysis of human breast tissue. Both benign and malignant pattern were observed in stitched OCT images. Cancerous regions with IDC was automatically identified using the hierarchical framework in OCT systems working at two wavelengths.

There are still some limitations in our study. First, the number of IDC specimens is limited because the mastectomy-produced tissues yield too many variations in cancer types, such as phyllodes tumor (n=2), fibrotic focus carcinoma (n=1), and mucinous (n=2). Moreover, the duration of the sample submerging in RPMI was unknown. Second, although UHR images may produce better delineations on different tissue types, the UHR system exhibits higher noise floor because of the supercontinuum light source. As a result, the effective imaging range that allows imaging with high SNR is also limited, and it may give rise to the inaccuracy for signals dwelling beyond the 6- dB fall-off range. For the commercial 1300nm system, on the other hand, the SLD source provides shot noise limited imaging performance and longer wavelengths allow the photon to travel deeper into the tissue. Therefore, for features below 0.5mm from the tissue surface, they were usually better delineated in the OCT images produced by the 1300nm system. More systematic comparison needs to be performed to identify the uniqueness of each OCT system in terms of identifying unique tissue features. 139

In future, we will improve the protocol and try to perform the OCT imaging session in the intraoperative setting to get more accurate results. For the needs of real time processing, additional efforts, such as improvement in the hardware, the application of distributed computing, and corresponding graphical user interface, will be implemented to speed up the current runtime and better the operation of image acquisition.

7.5 Conclusion

We stitched multiple OCT breast image to view at a wider field of view. We have showed qualitatively and quantitatively that UHR OCT images may enable better visualization of detailed features in different types of breast tissue. UHR OCT images of new breast cancer types such as phyllodes tumor, necrotic tumor, and fibrotic focus carcinoma are provided for future references.

RVM based stochastic tissue classification methods presented here show great potential for automated classification of different tissue types in human breast tissue.

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Chapter 8 Summary and future work

8.1 Conclusion

Optical coherence tomography has emerged as a promising imaging modality that provides high penetration, high sensitivity, and high axial resolution of morphological information. In this thesis, we present image analytic tools to bridge the gap between OCT morphological information and the applications of cardiac imaging, cervical imaging, and breast imaging. We develop automated algorithms to study fiber structure, to enlarge the field of view, and to identify tissue compositions.

We perform experiments to validate image processing tools through a number of biological images that are obtained from animal (swine/rabbit/canine) and human samples. We demonstrate that the algorithms are accurate and robust to characterize various tissues including cardiac myofibers/collagen/adipose, cervical collagen fiber network, and breast adipose/stroma/cancerous tissue.

In Chapter 2, we investigate and develop two analytic tools to study fiber structure in OCT images.

We quantify cardiac fiber orientation in 3D space by projecting to the plane parallel to surface and employing particle filtering technique to reconstruct the tractography. We generate pixel-wise directionality map based on a weighted-sum scheme of intensity variations.

In Chapter 3, we present a generic stitching method to enlarge the field of view of current OCT system. To address this issue, we develop a 3D registration method based on the scale invariant feature transform at en face plane and surface curvature over the axial direction. We utilize a linear

141 model to build the relationship between pair-wise displacement and global coordinate. We utilize a least square estimation to estimate the global coordinates.

In Chapter 4, we present two tools for automated classifications for OCT images. First, we propose a region-based automated method to classify layer structures using OCT. We segment regions without use of prior knowledge on tissue architecture and subsequently extract features within each segmented region. We apply a relevance vector machine model to perform automated classification. Second, we integrate a relevance vector machine tool into a hierarchical framework to identify isolated adipose region on a grid-based scheme. For the region with high infiltration, we propose frame-based method to estimate the ratio of target region.

In Chapter 5, we summarize applications of the three image analytic tools. We employ the 3D tractography method to reconstruct fiber arrangement within cardiac samples. The stitching algorithm shows promising results in a large region of atria in both rabbits and human heart samples. Region-based classification method automatically delineates and identifies the tissue composition within the layers in endomyocardium.

In Chapter 6, we provide a detail analysis on fiber dispersion. Within an enlarged field of view, we visualize the directionality on each pixel. The image analytic tools enable statistical dispersion analysis of cervical fiber structure over the upper cervix. We observe two dispersion patterns within upper cervix and study the difference of dispersion between non-pregnant and pregnant cervical samples. We investigate the difference from internal os to extern os in fiber dispersion and penetration depth.

In Chapter 7, we stitch multiple breast volumetric data to visualize features in malignant and benign samples and validate the stitch results with histology. The grid-based classification method

142 shows good accuracy in two OCT systems and our frame-based classification method has successfully estimated the ratio of cancerous region in each OCT B-scan.

8.2 Future work

This thesis develops image analytic tools for tissue characterization in OCT images of cardiac, cervical, and breast tissues. With the availability of these analytic tools, there still remains several open challenges and many unmet needs in analyzing OCT images. In the following, we discuss several topics for future direction.

8.2.1 Algorithm optimization 8.2.1.1 Training strategy for large scale machine learning

The machine learning tools we develop in this thesis is based on a comparatively small dataset of training and testing. For clinic applications, a larger dataset is necessary to address needs from diverse patient subjects, which require large-scale analytic tools. The large-scale machine learning, such as deep learning, is demanding and particularly challenging in areas of biomedical image acquisitions due to difficulties in obtaining consents from various patient groups. The high expenditure of receiving expert annotation and scarcity of disease dictionary also adds to the challenge. Since it is practically impossible to obtain full set of data at the beginning stage of training, it is important to develop a selective training strategy to include truly informative data and to eliminate the misclassified negative samples and the over-represented samples in parallel.

Questions remains on how to dynamically quantify the quality of a training data.

8.2.1.2 Cross-platform biomedical images analysis

Extensive OCT images have been and will continue to be generated with tremendous variations and diversities. Since the image quality of OCT images are affected by the central wave length of

143 light source. Different OCT system may result in different reflectivity profile. There is a need to develop an analytic tool that is robust among various platforms to facilitate image segmentation and tissue classification. Theoretically, OCT images collected from various platforms are a projection of inherent feature into different domain. The cross-platform problem can be considered as a sparse representation problem, which searches the most compact representation of an image.

The problem could be potentially solved by enforcement of the similarity of sparse representation among images.

8.2.1.3 Auto-correction of out-of-focus images

In optical imaging system, the image quality is in principle limited by the numerical aperture of objective. There is always a need to image wider and deeper. In addition to developing stitching tools [186, 248] to enlarge the FOV of optical system, it will be important to deepen the range of imaging. During imaging acquisition, most biological samples are impossible to be perfectly flat under a given imaging modality/condition. Thus, some areas in volumetric imaging will be out- of-focus and present blur, leading to false negative in classification algorithm. Without increasing the hardware expenditure, exploration into the possibility of using machine learning tools to correct out-of-focus images will be an interesting research topic.

8.2.2 Application 8.2.2.1 Analytic tools for catheter-based OCT system

The three image analytic tools are proposed and validated in bench-top system. To aid the diagnosis and treatment in clinic, it is desired that the image analysis can be performed on human body without excising tissue samples. In OCT community, catheters or needles have been developed to image myocardium [190], cervix [29], and breast [34]. In the future, we would extend our algorithm to analyze in vivo images from catheter-based OCT system. Improvement

144 will be made to address the effects of motion on registration and fiber tracking and new features will be extracted from catheter-based OCT images for tissue classification.

8.2.2.2 Incorporating tissue characteristics into computational models

With an ultimate goal of quantifying the mechanical environment of pregnancy and determining how cervix functions as a resistive barrier to prevent preterm birth, our study of fiber directionality and dispersion provides parameters of a continuous fiber distribution material model for human cervix [218]. With the fiber material model built, we can input the fiber model into a finite element model [203], together with other parameters ( e.g. membrane-uterus interaction, membrane mechanical properties) to facilitate the mechanical simulation of pregnancy.

8.2.2.3 Automated imaging platform

In Chapter 3, we present an automated algorithm to enlarge the OCT field and successfully image the entire rabbit atria. However, it is still challenging to image even larger sample such as a whole set of human atria, larger than rabbit heart that we tested. Due to large size, collecting OCT images for whole human atria is more time consuming than for a rabbit atrium, leading to more dehydration during image acquisition. Dehydration causes shrinkage of sample size and results in mis-registration in translational movement. To overcome this issue, future work will focus on both improving the imaging protocol to minimize dehydration and developing algorithms that consider shrinkage and rotation of samples during data acquisition.

8.2.2.4 Classification of more tissue types

Due to limited data accessibility, our study does not cover the automated classification of endomyocardial biopsy (EMB) and ductal carcinoma in situ (DCIS). EMB is the standard diagnosis of inflammatory and assessment of the heart transplant rejection. The inflammatory

145 region or amyloid region in biopsy exhibits a scattered pattern rather than layered structure in myocardium. Current EMB technique suffers from the limitation of low diagnostic yield due to heterogeneity of infiltrative disease and missed biopsy. We will need to improve our region-based cardiac classification algorithm to pixel-based algorithm to automate the classification tool to aid biopsy.

The early detection of DCIS could potentially reduce the over-diagnosis and avoid unnecessary mastectomy. According to the limited samples we have collected, large variation exists in different grades of DCIS and the duct structures vary dramatically at different cross-section planes. An improved feature extraction and selection method will be desired to apply our current classification method in identifying DCIS and the segmentation various duct structure will be an interesting topic to improve the detection rate of DCIS.

8.2.2.5 Real time processing

The analytic tools we developed in this thesis were processed off-line. To meet the clinical needs, it is desired to implement the tools in real time processing. This raises the needs for better data management and acceleration of processing speed. It will be beneficial to implement a parallel computing scheme for the proposed image analytic tools to facilitate computer-aided diagnosis.

Graphics processing unit (GPU) allows massive parallel computing and can significantly outperform its CPU counterparts. We can possibly boost the processing time by programming our algorithm in GPU.

8.2.2.6 Clinical translation of breast surgical margin detection

The breast cancer detection method has great potential to be translated to the breast surgical margin detection in clinics. In breast conserving surgery (also known as lumpectomy), it is required that

146 tumor removal, usually with size of 1~2 centimeter at each dimension, should be performed with a clean margin, with only healthy tissue surrounded. Failure to achieve clean margins in the initial surgery results in a re-excision procedure. Latest study has reported that the re-excision rate is among 11–46% for invasive carcinoma and ductal carcinoma in situ (DCIS) [249]. With similar sample size as lumpectomy, our experiments demonstrate accuracy in detecting cancerous region within a depth up to 2 mm. It is promising to translate our breast cancer study to surgical margin detection.

8.2.2.7 3D fiber tracking scheme for other imaging modalities

Though it was originally developed for OCT images, the analytic tools we developed in this thesis have great potential to be applied in other imaging modalities, especially for 3D imaging. The particle-filter-based fiber tracking method is a generic framework targeting on extracting subtle

3D fiber trend from intensities. The idea of quantifying sub-volume distribution and reconstructing trace through particle filtering is also applicable to other 3D imaging modalities. Particularly, we envision that this technique could be beneficial for the applications of reconstructing collagen fiber structure in second harmonic images [250, 251] and skeletal fiber in ultrasound images [252, 253].

Overall, future work will span from algorithm optimization to application extension. In algorithm optimization, focus will be deep machine learning tools, cross-platform analysis, and image enhancement. Future application of our work will include image analysis on catheter-based OCT system, computational modeling, more complicated tissue type classification, real time processing, clinical translational study, and extension of developed image analytic tools to other imaging modality.

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