Computational Modeling of Hip Joint Mechanics

COMPUTATIONAL MODELING OF HIP JOINT MECHANICS

Andrew Edward Anderson

A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Department of Bioengineering

The University of Utah

April 2007

ABSTRACT

The hip joint is one of the largest weight bearing structures in the human body.

While its efficient structure may lend to a lifetime of mobility, abnormal, repetitive

loading of the hip is thought to result in osteoarthritis (OA). The etiology of hip OA is

unknown however, due to the high loads this joint supports, mechanics have been

implicated as the primary factor. Quantifying the relevant mechanical parameters in the joint (i.e. cartilage and bone stresses) appears to be central to an enhanced understanding

of this disease. Experimental studies have provided valuable insight into baseline hip

joint biomechanics but they require a protocol that is inherently invasive. Numerical

modeling techniques, such as the finite element method, open the possibility of predicting

hip joint biomechanics noninvasively and could revolutionize the way pathological hips are diagnosed and treated. Unfortunately, hip finite element models to date have used simplified geometry and have not been validated. It can be credibly argued that prior computational models of the hip joint do not have the ability to predict cartilage and bone mechanics with sufficient accuracy for clinical application.

The aim of this dissertation is to develop and validate methods that will facilitate patient-specific modeling of hip joint biomechanics. Toward this objective, subject- specific FE models of the pelvis and entire hip joint were developed. The accuracy of

model geometry, i.e. cortical bone and cartilage thickness, was assessed using phantom

based imaging studies. FE predictions were compared directly with experimental data for purposes of validation. The sensitivity of the models to errors in assumed and measured model inputs was quantified. Finally, recognizing that acetabular dysplasia may be the single most important contributor of hip joint OA, the validated modeling protocols were extended to analyze patient-specific models to demonstrate the general feasibility of the approach and to quantify differences in hip joint biomechanics between a normal and dysplastic hip joint. The developed modeling methodologies have a number of potential longer-term uses and benefits, including improved diagnosis of pathology, patient- specific approaches to treatment, and prediction of the success rate of corrective surgeries based on pre- and post-operative mechanics.

To my father: Richard E. Anderson

“It matters not how long we live but how” Philip James Bailey

TABLE OF CONTENTS

ABSTRACT...... iv

LIST OF TABLES...... ix

LIST OF FIGURES ...... x

ACKNOWLEDGEMENTS...... xiii

CHAPTER

1. INTRODUCTION ...... 1

Motivation...... 1 Research Goals...... 4 Summary of Chapters ...... 5 References...... 8

2. BACKGROUND ...... 10

Forward...... 10 Hip Joint Structure and Function ...... 11 Pelvic and Femoral Bone...... 11 Cartilage...... 13 Labrum, Capsule, Ligaments, Muscles...... 15 Hip Joint Pathology...... 20 Osteoarthritis...... 20 Hip Dysplasia...... 22 Experimental Hip Joint Biomechanics...... 25 Bone Material Properties...... 25 Cartilage Material Properties ...... 27 In-Vitro Studies of Hip Joints...... 29 In-Vivo Studies of Hip Joints ...... 32 Numerical Modeling of Hip Joint Biomechanics ...... 35 Analytical Modeling of the Hip Joint ...... 35 Computational Modeling of the Hip Joint ...... 36 References...... 43

3. A SUBJECT-SPECIFIC FINITE ELEMENT MODEL OF THE PELVIS: DEVELOPMENT, VALIDATION AND SENSITIVITY STUDIES...... 58

Abstract...... 58 Introduction...... 60 Materials and Methods...... 63 Experimental Study...... 63 Geometry Extraction and Mesh Generation ...... 66 Position-Dependent Cortical Thickness...... 69 Assessment of Cortical Bone Thickness...... 71 Material Properties and Boundary Conditions...... 72 Sensitivity Studies...... 73 Data Analysis...... 75 Results ...... 76 Reconstructions of Pelvic Geometry ...... 76 Cortical Bone Thickness...... 77 Trabecular Bone Elastic Modulus...... 80 FE Model Predictions...... 80 Discussion...... 85 References...... 92

4. FACTORS INFLUENCING CARTILAGE THICKNESS MEASUREMENTS WITH MULTI-DETECTOR CT A PHANTOM STUDY...... 97

Abstract...... 97 Introduction...... 99 Materials and Methods...... 102 Phantom Description...... 102 CT Imaging Protocol...... 105 Image Segmentation, Surface Reconstruction, and Measurement of Thickness...... 106 Error Analysis...... 109 Results ...... 110 Contrast Enhanced Scans...... 110 Non-Enhanced Scans...... 115 Discussion...... 117 Study Limitations...... 119 Practical Applications...... 120 References...... 122

5. VALIDATION OF FINITE ELEMENT PREDICTIONS OF CARTILAGE CONTACT PRESSURE IN THE HUMAN HIP JOINT...... 126

Abstract...... 126 Introduction...... 128 Methods...... 130 Experimental Protocol...... 130 Computational Protocol...... 133 Sensitivity Studies...... 136 Data Analysis...... 137 Results ...... 140 FE Mesh Characteristics...... 140 Peak Pressure, Average Pressure, Contact Area...... 141 Contact Patterns...... 142 Misalignment and Magnitude Errors ...... 145 Sensitivity Studies- Cartilage Material Properties and Thickness...... 147 Sensitivity Studies- FE Boundary Conditions ...... 149 Discussion...... 152 References...... 159

6. PATIENT-SPECIFIC FINITE ELEMENT MODELING PROOF OF CONCEPT...... 165

Abstract...... 165 Introduction...... 167 Methods...... 170 Subject-Selection ...... 170 CT Arthrography...... 170 Image Data Analysis and Segmentation ...... 171 FE Mesh Generation, Cartilage Thickness, Material Properties...... 172 FE Boundary and Loading Conditions ...... 174 Sensitivity Studies...... 175 Data Analysis...... 175 Results ...... 177 Discussion...... 182 References...... 189

7. DISCUSSION...... 195

Summary...... 195 Limitations and Future Work...... 200 References...... 205

LIST OF TABLES

Table Page

3.1. Models studied for sensitivity analysis...... 75

3.2. Reconstruction errors for simulated cortical bone...... 78

3.3. Results for all sensitivity models ...... 84

5.1. Misalignment and magnitude errors of FE predicted cartilage contact pressures ...... 146

5.2. Differences of center of pressures between FE and experimental results...... 146

6.1. Differences in FE predicted mechanics between a normal and dysplastic hip joint...... 179

viii

LIST OF FIGURES

Figure Page

2.1. Photograph of plastic hip joint...... 12

2.2. Histological cross-section of cartilage...... 14

2.3. Illustration of hip joint with labrum...... 16

2.4. Illustration of hip joint capsule ...... 17

2.5. Illustration of iliofemoral ligament...... 18

2.6. Volumetric CT scan of patient with acetabular retroversion...... 24

3.1. Schematic of pelvis loading fixture ...... 65

3.2. 3D reconstruction of pelvis from CT image data...... 67

3.3. Finite element mesh of pelvis with close-up of acetabulum...... 68

3.4. Schematic illustrating the special cases considered in in determination of cortical thickness...... 70

3.5. Cortical bone thickness phantom...... 71

3.6. Schematic showing length measurements obtained from cadaveric pelvis and accuracy of geometry reconstruction...... 76

3.7. Contours of position dependent cortical bone thickness of the pelvis...... 79

3.8. Distribution of pelvic Von-Mises stress ...... 82

3.9. Finite element predicted vs. experimentally measured strains for subject-specific and sensitivity models...... 83

4.1. Schematic of phantom used to assess accuracy of cartilage thickness reconstructions ...... 104

4.2. Simulated cartilage RMS and mean residual reconstruction errors for the transverse contrast enhanced CT scans as a function of agent concentration...... 111

4.3. Simulated cartilage RMS and mean residual reconstruction errors for the transverse contrast enhanced CT scans as a function of imaging direction and resolution...... 112

4.4. Simulated cartilage RMS and mean residual reconstruction errors for the transverse contrast enhanced CT scans as a function of joint spacing, agent concentration, imaging direction and resolution ...... 114

4.5. Simulated cartilage RMS and mean residual reconstruction errors for the transverse non-contrast enhanced CT scans as a function of imaging direction and resolution...... 116

5.1. Experimental setup for loading of hip joint ...... 132

5.2. Finite element mesh of the entire hip joint in the walking position with a close-up of the acetabulum...... 135

5.3. Contours of cartilage thickness...... 140

5.4. Finite element vs. experimentally measured average pressure and contact area ...... 141

5.5. Qualitative comparison between finite element and experimentally measured contact pressure ...... 143

5.6. Finite element predicted pressures relative to the femur and acetabulum...... 144

5.7. Percent changes in peak pressure, average pressure and and contact area due to changes in cartilage material properties and geometry...... 148

5.8. Percent changes in peak pressure, average pressure and and contact area due to changes in model boundary conditions...... 150

5.9. Contours of cartilage pressure predicted by the baseline and rigid bone finite element models...... 151

6.1. Fringe plots of acetabular and femoral cartilage thickness for the normal and dysplastic hip joints...... 173

6.2. Comparison of finite element predicted acetabular cartilage pressures between a normal and dysplastic hip joint...... 177

6.3. Finite element predicted acetabular cartilage pressures as a function of anatomical and joint reaction force orientation for the normal and dysplastic hip joint ...... 180

xii

ACKNOWLEDGEMENTS

Financial support from the University of Utah Department of Orthopaedics,

University of Utah Funding Incentive Seed Grant, the Orthopaedic Research and

Education Foundation, and from NIH Grant #F31-EB00555 is gratefully acknowledged.

The University of Utah Department of Radiology (CAMT), Scientific Computing

Imaging Institute (SCI) and Brad Maker of Lawrence Livermore National Lab are also given acknowledgement for their contributions.

CHAPTER 1

INTRODUCTION

MOTIVATION

The hip joint serves a very important biomechanical function. While supporting the majority of the human body (~ 2/3 of total bodyweight) the joint must simultaneously facilitate smooth articulation of the lower limbs to enable bi-pedal gait. During routine daily activities, forces on the order of 5.5 times bodyweight are transferred between the femur and pelvis [1-3]. While its efficient structure may lend to a lifetime of mobility, abnormal, repetitive loading of the hip is thought to result in the breakdown of articular cartilage, resulting in osteoarthritis (OA) [4-7].

Hip joint OA represents a significant burden to society via financial, social and psychological effects. It is estimated that nearly 40 million Americans currently have joint osteoarthritis (~18% of the population) of which nearly 3% of the cases originate at the hip joint [8,9]. To alleviate pain and return the hip to at least the most basic functioning state, nearly 193,000 osteoarthritic hips are replaced annually in the United

States by way of total hip arthroplasty (THA) [10]. While THA has enjoyed a high rate of success in elderly patients (less than 10% require revision THA [10]), the surgery is generally avoided in the younger population due to the limited lifespan of implants and 2

unfavorable results of revision THA. Although a common misconception by the general

public, hip OA is not confined to elderly patients. As detailed later, factors such as

abnormal joint geometry (i.e. hip dysplasia), body weight, occupation, and prior injury

appear to play major roles independently of age [11-13]. Nevertheless, the etiology of hip OA is unknown, in part because it takes so long to develop- a decade or more likely passes before cartilage has fissured to the point where bone contact initiates pain [14].

However, due to the high loads this joint supports, mechanical factors have been implicated as a primary causes [4-7]. Thus, quantifying the relevant mechanical parameters in the joint (i.e. cartilage and bone stresses) appears to be central to an enhanced understanding of this disease [14].

Research on the biomechanics of the hip is not new to orthopedic medicine.

While previous studies have provided valuable insight into baseline hip joint biomechanics, they require a protocol that is inherently invasive. Unlike experimental investigations, computational modeling opens the possibility of predicting hip joint biomechanics noninvasively. In particular, the advent, increased availability and resolution medical imaging modealities provide a means to develop detailed computational models that are based on individual patient geometry. These attractive points, along with a tremendous evolution of computing power, have lead to substantial growth in the field of computational biomechanics.

Although computational models have provided substantial additional insight to hip biomechanics above and beyond that obtained via experimental studies, substantial voids remain. In particular, simplifying model assumptions have often resulted in model 3 predictions that are inconsistent with experimental measurements. Most models have not been validated by direct comparison with experimental data. For an analyst to develop patient-specific models, without having to validate each model independently, it is necessary to demonstrate that: 1) the computational protocol yields results that predict known/measured quantities with sufficient accuracy, and 2) an assessment of model error and uncertainty is accounted for in an effort to gauge how inaccuracies could be propagated due to erroneous model inputs and assumptions.

RESEARCH GOALS

The overall aim of this dissertation is to develop and validate methods that will

facilitate patient-specific modeling of hip joint biomechanics. It is clear that patient-

specific computational models have the potential to revolutionize the way that disorders

of the hip joint are diagnosed and treated. However, first rigorous and validated

protocols that incorporate both computational and experimental techniques must be

established. In this dissertation research, model predictions are compared directly with

experimental data and errors in assumed and measured model inputs, i.e. material

properties, constitutive behavior, geometry, and boundary conditions, are discussed as they pertain to errors in the developed model and in the context of future patient modeling efforts. Second, recognizing that acetabular dysplasia may be the single most important contributor of hip joint OA [17-20], the validated subject-specific finite element modeling protocol is extended to analyze patient-specific models to demonstrate the general feasibility of the approach and to quantify differences in hip joint biomechanics between a normal subject and a patient with acetabular dysplasia. Finally, limitations of the modeling protocol as well as unforeseen challenges in modeling individual patients non-invasively are presented in the context of general hip joint modeling applications but with special emphasis to the study of acetabular dysplasia.

SUMMARY OF CHAPTERS

The structure of this dissertation has been organized to answer the essential

questions that arise when developing a protocol to generate patient-specific models of the

hip joint. The primary objective of Chapter 2 is to provide a working knowledge base

that will serve as reference to the topics covered in the remaining Chapters. Chapter 2

discusses hip joint structure and function and provides further motivation for developing

computational models, in particular, by application of the finite element method. Topics

such as hip osteoarthritis, approaches to quantify hip biomechanics (experimental and

computational), and the importance of computational model verification, validation, and

sensitivity studies are presented.

In the context of hip joint OA, the most fundamental mechanics of interest are

bone and cartilage stresses and strains. In this dissertation computational models are

developed and validated to study the mechanics of bone and cartilage separately in an

effort to maintain simplicity and to control confounding factors (Chapter 3 and Chapter 5,

respectively). Chapter 3 discusses the development and validation of a subject-specific finite element model of the pelvis. Computational predictions of bone strains were validated by direct comparison to experimentally measured strains using tri-axial strain gauges attached to the cortical surface of the pelvis. The influence of measured and assumed model inputs was assessed using sensitivity studies and the geometrical accuracy of the model, in particular, cortical bone thickness, was quantified.

Since computational models often use medical image data as the basis for creating model geometry, it is crucial to demonstrate that the reconstructed geometry is an 6 accurate representation of the true continuum. Although this is important for all computational studies, it becomes absolutely essential when modeling joint contact mechanics between layers of articulating cartilage. Although volumetric computed tomography (CT) data are often used as the basis for constructing joint models, the lower bounds for detecting articular cartilage thickness and the influence of imaging parameters on the ability to image cartilage have yet to be reported. Thus, it was necessary to quantify the accuracy and detection limits of cartilage geometry with CT. To this end, a phantom based imaging study was conducted and is presented in Chapter 4. While the results of this study have application to subject-specific models using cadaveric joints

(Chapter 5), the primary focus of this work was centered around quantifying the accuracy of CT arthrography since this procedure is required to visualize cartilage in live patients, which has direct relevance to patient-specific modeling (Chapter 6). The results of this study are discussed in terms of general clinical applications of CT for imaging articular cartilage in diarthrodial joints.

Chapter 5 presents results for a subject-specific finite element model of the mechanics of cartilage in the hip joint. Finite element predictions of cartilage contact pressures were validated by comparing computational predictions to experimentally measured contact pressures using pressure sensitive film. A physiological experimental and computational loading protocol was employed in an effort to lay the groundwork necessary for creating realistic patient-specific models. Sensitivity studies were included in the analysis to determine the influence of measured and assumed model inputs on the 7 ability to predict cartilage contact pressures. Chapter 5 concludes with a discussion of the model’s limitations.

As discussed in Chapter 2, acetabular dysplasia may be the primary etiology of hip joint OA. Therefore, it was of interest to demonstrate the feasibility of the modeling protocol developed in Chapters 3-5 for application to individual patients with dysplasia.

Chapter 6 presents two patient-specific finite element models: one for a normal volunteer and one for a patient with acetabular dysplasia. Differences in computationally predicted bone and cartilage mechanics are reported and clinical implications of these data are discussed. Chapter 6 concludes with a discussion of the challenges involved with patient- specific modeling and makes recommendations for circumventing these issues in the context of future modeling efforts. Finally, Chapter 7 summarizes the entire dissertation by highlighting the important contributions that were made to the field of hip computational biomechanics along with a discussion of limitations and future research directions. 8

REFERENCES

[1] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

[2] Bergmann, G., Deuretzbacher, G., Heller, M., Graichen, F., Rohlmann, A., Strauss, J., and Duda, G. N., 2001, "Hip Contact Forces and Gait Patterns from Routine Activities," J Biomech, 34, pp. 859-71.

[3] Bergmann, G., 1998, Hip98: Data Collection of Hip Joint Loading on CD-Rom. Free University and Humboldt University, Berlin.

[4] Mankin, H. J., 1974, "The Reaction of Articular Cartilage to Injury and Osteoarthritis (Second of Two Parts)," N Engl J Med, 291, pp. 1335-40.

[5] Mankin, H. J., 1974, "The Reaction of Articular Cartilage to Injury and Osteoarthritis (First of Two Parts)," N Engl J Med, 291, pp. 1285-92.

[6] Mow, V. C., Setton, L. A., Guilak, F., and Ratcliffe, A., 1995, "Mechanical Factors in Articular Cartilage and Their Role in Osteoarthritis," in Osteoarthritic Disorders. American Academy of Orthopaedic Surgeons.

[7] Poole, A. R., 1995, "Imbalances of Anabolism and Catabolism of Cartilage Matrix Components in Osteoarthritis," in Osteoarthritic Disorders. American Academy of Orthopaedic Surgeons.

[8] Felson, D. T., Lawrence, R. C., and Dieppe, P. A., 2000, "Osteoarthritis: New Insights. Part 2. Treatment Approaches," Ann Internal Med, 133, pp. 726-737.

[9] Felson, D. T., Lawrence, R. C., and Dieppe, P. A., 2000, "Osteoarthritis: New Insights. Part I the Disease and Its Risk Factors," Ann Internal Med, 133, pp. 635- 646.

[10] AAOS, 2007,"Questions and Answers about Hip Replacement," National Institute of Arthritis and Musculoskeletal and Skin Disorders.

[11] Anderson, J. J. and Felson, D. T., 1988, "Factors Associated with Osteoarthritis of the Knee in the First National Health and Nutrition Examination Survey (Hanes I). Evidence for an Association with Overweight, Race, and Physical Demands of Work," Am J Epidemiol, 128, pp. 179-89.

[12] Felson, D. T., 1994, "Do Occupation-Related Physical Factors Contribute to Arthritis?," Baillieres Clin Rheumatol, 8, pp. 63-77. [13] Heliovaara, M., Makela, M., Impivaara, O., Knekt, P., Aromaa, A., and Sievers, K., 1993, "Association of Overweight, Trauma and Workload with Coxarthrosis. A Health Survey of 7,217 Persons," Acta Orthop Scand, 64, pp. 513-8.

[14] Macirowski, T., Tepic, S., and Mann, R. W., 1994, "Cartilage Stresses in the Human Hip Joint," J Biomech Eng, 116, pp. 10-8.

[15] Oberkampf, W. L., Trucano, T. G., and Hirsch, C., "Verification, Validation, and Predictive Capability in Computational Engineering and Physics," presented at Foundations for Verification and Validation in the 21st Century Workshop, Johns Hopkins University, Laurel, Maryland, 2002.

[16] Anderson, A., Ellis, B. J., and Weiss, J. A., 2006, "Verification, Validation and Sensitivity Studies in Computational Biomechanics," Computer Methods in Biomechanics and Biomedical Engineering, In Press Dec 2006.

[17] Harris, W. H., 1986, "Etiology of Osteoarthritis of the Hip," Clin Orthop, pp. 20- 33.

[18] Murray, R. O., 1965, "The Aetiology of Primary Osteoarthritis of the Hip," Br J Radiol, 38, pp. 810-24.

[19] Solomon, L., 1976, "Patterns of Osteoarthritis of the Hip," J Bone Joint Surg Br, 58, pp. 176-83.

[20] Stulberg, S. D. and Harris, W. H., "Acetabular Dysplasia and Development of Osteoarthritis of the Hip," presented at Proceedings of the second open scientific meeting of the Hip Society, St Louis, MO, 1974.

CHAPTER 2

BACKGROUND

FORWARD

As discussed below, computational models have the potential to non-invasively estimate hip mechanics for living subjects. However, based on the available in-vivo and in-vitro experimental data, it can be credibly argued that most previous hip joint computational models do not have the ability to predict cartilage and bone mechanics with sufficient accuracy for clinical application. Furthermore, models that have included more realistic geometries have not been validated by direct comparison to experimental data. The purpose of this dissertation is to present novel methods to develop and validate computational models of the hip joint that result in models that indeed have direct clinical applicability to study diseases such as osteoarthritis (OA) and hip dysplasia. This chapter presents the most relevant background information, including: hip joint structure and function, hip pathologies, experimental hip joint biomechanics, and numerical modeling of hip joint biomechanics. 11

HIP JOINT STRUCTURE AND FUNCTION

The hip is a ball and socket joint formed by the articulation of the spherical head of the femur and the concave acetabulum of the pelvis. It forms the primary connection between the lower limbs and skeleton of the upper body. Both the femur and acetabulum are covered with a layer of cartilage to provide smooth articulation and to absorb load.

The entire hip joint is surrounded by a fibrous, flexible capsule to permit large ranges of motion but to prohibit the proximal femur from dislocation. Several ligaments connect the pelvis to femur to further stabilize the joint and capsule. Muscles and tendons provide actuation forces for extension/flexion, adduction/abduction and internal/external rotation.

Pelvic and Femoral Bone

The pelvis forms a girdle which protects the digestive and female reproductive organs. It is formed from three bones: the ilium, ischium and pubis, which fuse together to form the ox coxae, or innominate bone (Figure 2.1). At the point of fusing they form the acetabulum (Figure 2.1). Joints adjacent to the pelvis include the sacroiliac (SI) and pubis joint (Figure 2.1). Many large nerves and blood vessels pass through the pelvis to the lower limbs.

The femur is the longest and strongest bone in the human body. It consists of a head and a neck proximally, a diaphysis (or shaft), and two condyles (medial and lateral) distally. The diaphysis of femur is a simplistic, cylindrical structure, while the proximal femur is irregular in shape, consisting of a spherical head, neck and lateral bony 12

Sacro-Iliac Joint

Ilium

Acetabulum

Pubis Pubis Joint Ischium Femur

Figure 2.1. Photograph of a plastic hip showing the individual bones and joints.

protrusions termed the greater and lesser trochanters. The trochanters serve as the site of

major muscle attachment. The lateral location of these structures offers a mechanical

advantage to assist with abducting the hip [2].

The bony structure of the pelvis is similar to a sandwich composite material,

consisting of a dense, stiff, thin shell of cortical bone (0.7 to 3.2 mm thick, [3]) filled with much less dense trabecular bone. The spherical head of the femur has a thin layer of

subchondral bone where cartilage attaches, which is less stiff than cortical bone. Cortical

bone along the diaphysis of femur is much thicker (up to ~ 7 mm [4]) and supports the large tensile and compressive loads that develop as a result of hip loading. Trabecular 13 bone is found throughout the pelvis and proximal femur but is not as prevalent along the diaphysis of the femur as this area primarily contains marrow.

Cartilage

Cartilage is composed of collagenous fibers and chondrocytes embedded in a firm gel (Figure 2.2). Cartilage has remarkable mechanical properties in that it is strong but flexible and has extremely low coefficients of friction [5]. Cartilage is avascular and anueral [6]. Chondrocytes and their precursor chondroblasts are the only cells in cartilage (Figure 2.2) [5]. Nutrients diffuse through the matrix by way of interstitial fluid, which makes up nearly 60-80% of the total weight of cartilage [7]. In addition, ionic charges in the fluid are thought to facilitate nutrient flow [8]. The solid matrix represents nearly 60% of the dry weight and is composed of proteoglycans, which are large proteins with a protein backbone and glycosaminoglycan (GAG) side chain [7].

The most common GAGs are keratin sulfate and chondroitin sulfate [7]. Matrix fibers make up the remaining dry weight and are composed of collagen type II [7].

The acetabulum is covered with a horseshoe shaped layer of articulating hyaline cartilage ranging from 1.2 to 2.3 mm thick in normal adults [9]. The entire head of the femur is covered with a smooth layer of hyaline cartilage of varying thickness, except for a small depression called the fovea capitis femoris that gives attachment to the ligamentum teres. The thickness of femoral cartilage ranges from 1.0 to 2.5 in the normal adult [9].

Cartilage Matrix Calcified Cartilage Cartilage Calcified Subchondral Bone

Figure 2.2. Through the thickness histological photograph of bovine articular cartilage (stained with Alician Blue). Chondrocytes appear as small dots. Copyright Lutz Slomianka 1998-2006. 15

Labrum, Capsule, Ligaments, Muscles

The hip joint labrum is a ring of fibrocartilagenous tissue that surrounds the rim of the acetabulum (Figure 2.3). It helps to guide normal motion, to prevent dislocation between the femoral head and acetabulum and is thought to act as a seal to prevent loss of interstitial fluid. An in vitro study where the labrum was removed have demonstrated that cartilage is strained to a greater degree than joints with intact labrums for a given load [10], suggesting that greater fluid flow in the latter scenario causes increased cartilage matrix deformation.

The entire hip joint is surrounded by the hip capsule (Figure 2.4). The capsule attaches proximally to entire periphery of the acetabulum, beyond the acetabular labrum.

It also covers the femoral head and neck like a sleeve, eventually attaching to the base of the femoral neck. The capsule consists of two sets of fibers: longitudinal and circular fibers. Circular fibers form a collar around the femoral neck whereas longitudinal retinacular fibers travel along the neck and carry blood vessels.

The capsule is further defined by ligaments. The iliofemoral ligament attaches from the pelvis to the femur and resists excessive extension (Figure 2.5). It is the strongest ligament in the human body and allows one to maintain posture for extended periods without extensive muscular fatigue. The pubofemoral ligament is the most anterior and inferior portion of the fibrous capsule. It attaches to the pubic bone and passes inferolaterally to merge with the iliofemoral portion of the fibrous capsule

(attaching to intertrochanteric line). Overabduction of the hip joint is prevented by this ligament. The ischiofemoral ligament attaches from the ischial part of the acetabulum to 16 the femur and supports the posterior aspect of hip capsule. Finally, the ligament teres connects the head of the femur to the acetabulum (Figure 2.3). Although it supports little or no loads it may serve as an important conduit to supply blood to the head of the femur in some individuals.

Labrum

Figure 2.3. Illustration of hip joint with labrum. Adopted from [1]. 17

Figure 2.4. Illustration of hip joint capsule. Adopted from [1]. 18

Figure 2.5. Illustration of iliofemoral ligament. Adopted from [1]. 19

The hip can flex, extend, abduct, adduct, and rotate using several muscles

attached between the pelvis and femur. Many of the hip muscles are responsible for more

than one type of movement in the hip as different areas of the muscle act on tendons in

different ways. Hip joint flexors include the psoas major, iliacus, rectus femoris,

sartorius, pectineus, adductores longus and brevis, and the anterior fibers of the glutaei

medius and minimus. Hip joint extensors include the glutaeus maximus, assisted by the

hamstring muscles and the ischial head of the adductor magnus. The adductors include

the adductores magnus, longus, and brevis, the pectineus, the gracilis, lower part of the

glutaeus maximus, the glutaei medius and minimus, and the upper part of the glutaeus

maximus. The rotators that cause inward rotation are the glutaeus minimus, anterior

fibers of the glutaeus medius, tensor fasciae latae and the iliacus and psoas major.

Finally, inward rotators include the posterior fibers of the glutaeus medius, the piriformis, obturatores externus and internus, gemelli superior and inferior, quadratus femoris,

glutaeus maximus, the adductores longus, brevis, and magnus, the pectineus, and the

Sartorius.

HIP JOINT PATHOLOGY

The hip is subject to disease due to improper development, acute trauma and prolonged mechanical wear and tear. The most common disorders include arthritis

(rheumatoid arthritis, traumatic arthritis, osteoarthritis), avascular necrosis

(osetochondritis dissecans, Perthes disease), slipped epiphysis, bursitis, developmental dysplasia of the hip and femoro-acetabular impingement. Osteoarthritis and hip dysplasia are the primary thrust of this dissertation, and thus will be the focus of further discussion.

Osteoarthritis

Osteoarthritis is the most common type of arthritis in the hip and is intimately associated with other disorders such as avascular necrosis, slipped epiphysis, impingement and dysplasia. It is also the most common cause of musculoskeletal pain in the United States [11]. Hip OA is a disorder of the entire joint, involving cartilage, bone, synovium, labrum, and capsule [12]. OA is classically associated with more advanced age but is being seen and treated more frequently in younger patients [12].

OA is characterized by a loss of articular cartilage in the predominately load bearing areas of the joint, with eburnation of the underlying subchondral bone and a proliferative response characterized by osteophytosis [13,14]. Gradual loss of the matrix components is thought to be caused by a loss of proteoglycans, although some changes in the integrity of collagen network may be necessary to initiate the disease [15]. It is also thought that OA disrupts the mechanism for fluid support, which may exacerbate solid matrix degeneration [12]. OA is further characterized by an increase in vascularity of 21

surrounding bone. Cysts often form within the surrounding bone and are accompanied by

changes to the joint margin. They may also cause outgrowths of cartilage as well as

osteophyte formation, which may lead to further degeneration. Therefore, the mechanics

of bone in areas adjacent to cartilage may be important to developing a comprehensive

understanding of hip OA.

OA was once thought to be primary or idiopathic in nature. However,

considerable clinical, epidemiological, and experimental evidence supports the concept

that mechanical demand greater than some critical level has a major role in the

development and progression of joint degeneration in all forms of OA. Surveys of

individuals with physically demanding occupations, including farmers, construction

workers, metal workers, miners, and pneumatic drill operators, suggest that repetitive

intense loading is associated with early onset of joint degeneration [16-18]. Excessive

mechanical stress can directly damage articular cartilage and subchondral bone and can

adversely alter chondrocyte function including the balance between synthetic and

degradative activity [19-25].

Although joint loading or overloading can lead to cartilage degeneration, the

precise mechanism remains controversial. Opinions differ concerning the relative

contributions of direct mechanical trauma to articular cartilage versus elevation of articular stresses secondary to stiffening of subchondral bone. No experimental studies to

date have allowed one to directly separate the contributions of hydrostatic and deviatoric

stresses generated by joint loading. Therefore, it is unknown whether degenerative 22

changes are primarily due to excessive loads applied during normal activities or shearing

of cartilage during abnormal motions involving local instability.

In the elderly patient population, hip OA is treated by prosthetic replacement of the hip joint. Nearly 193,000 total hip arthroplasties (THA) are performed each year in the United States [26]. THA is highly successful in relieving pain and restoring movement. However, ongoing problems with wear and particulate debris may eventually necessitate further surgery, including replacement of the prosthesis. Men and patients who weight more than 165 pounds have higher rates of failure [27]. The chance of a hip

replacement lasting 20 years is about 80% [27].

Hip Dysplasia

Developmental dysplasia of the hip (DDH) describes a broad spectrum of

problems, including hips that are unstable, malformed, subluxated (incomplete

dislocation), or completely dislocated [28]. In the broadest sense, DDH is a

developmental deformity characterized by malorientation and a reduction of contact area

between the femur and acetabulum [29]. Subluxation caused by dysplasia of the hip joint

is a primary cause of degenerative joint disease and clinical disability [30]. Subluxation

leads to increased stresses across the hip joint each time the hip is loaded during gait [31].

Consequently, it is thought that the altered biomechanics cause cartilage and bone of the

hip to break down prematurely, leading to early hip osteoarthritis. OA due to hip

dysplasia is commonly treated by THA. Surgical correction of the anatomic

abnormalities associated with hip dysplasia is performed on younger patients via pelvic 23

osteotomy, which preserves the hip joint and associated articular cartilage and delays the

need for prosthetic replacement of the hip. Redirectional acetabular osteotomy

(periacetabular osteotomy) involves cutting the socket free from the pelvis and rotating it

to a new orientation [32-37]. The most common type of dysplasia, referred to herein as

traditional dysplasia, can be diagnosed by evaluation of a 2-D planar radiograph of the hip. Recently, a specific variant of dysplasia, referred to herein as retroversion of the acetabulum, has been identified [38,39]. In the retroverted acetabulum, the acetabular opening and its proximal roof lie at an angle of retroversion with respect to the sagittal plane. Thus, posterior coverage of the femoral head is lost (Figure 2.6).

Retroversion is difficult to diagnose by the untrained clinician since a standard hip

radiograph shows that the hip is normal; nevertheless, the anatomy of the retroverted acetabulum is still pathologic. It is likely that the obscurity of the retroverted acetabulum has often persuaded the clinician into prescribing passive treatments for a potentially aggressive pathology.

Several studies have shown that mild developmental dysplasia, in patients that went unrecognized before, may indeed be the leading cause of osteoarthritis in the hip

[39-43]. Wilson and Poss [44] reported that deformity of the acetabulum is found in 25-

35% of adult cases of OA of the hip. Michaeli et al. [29] estimated that 76% of patients

with OA of the hip have some type of untreated acetabular dysplasia. In contrast to these

reports, other studies have failed to find a statistically significant relationship between

acetabular dysplasia and the risk of hip OA [45-49]. These discrepancies highlight the

need for an improved understanding of hip dysplasia. 24

A) Anterior

Right Left

Left Right Posterior Figure 2.6. Anterior (A) and Posterior (B) view of a volumetric CT scan from a patient with acetabular retroversion of the left hip. The patient’s right hip was considered normal. The lines indicate the edge of the acetabulum. Note excessive forward progression of anterior edge of left acetabulum in image A) and lack of posterior wall coverage of left femur in image B). Courtesy of Christopher L. Peters. 25

EXPERIMENTAL HIP JOINT BIOMECHANICS

The contribution of muscles, ligaments, tendons, and hip capsule serve as vital components when studying general hip joint biomechanics. However, the tissues of primary interest in the context of studying OA and hip dysplasia are bone and cartilage.

In-vitro experimental studies are conducted using whole cadaveric hip joint bones or individual tissue samples that are instrumented with sensing devices such as strain gauges, pressure sensitive film, and force transducers. The objectives of these tests are to

ascertain material properties, to study the effects of interventions and diseases, and to

quantify normal cartilage and bone mechanics. In-vivo studies are difficult to conduct as

access to the hip joint is extremely intrusive. However, several studies have employed

instrumented hip prostheses implanted at the time of THA in patients with OA.

Bone Material Properties

Studies of the material properties of bone date back to the mid 1800s when

Wertheim measured the strength and elasticity of human cortical bone specimens [50]. In

the latter half of the 19th century Julius Wolff published pioneering work regarding bone

remodeling (termed Wolff’s Law, [51]) by stating that if loading on a particular bone

increases, the bone will remodel itself over time to become stronger to resist that

mechanism of loading. The converse was also stated to hold true.

In the mid 20th century Dempster and Liddicoat [52] demonstrated that cortical

bone exhibits different moduli of elasticity when loaded in different directions. The

dependence of the elastic properties on the basic lamellar unit of cortical bone was 26

recognized early by Evans et al. [53,54]. Building on this work, Lang et al. [55,56]

measured cortical bone moduli by assuming transverse isotropy (the plane normal to the

Haversian canals being the plane of isotropy). To investigate the transverse isotropy

assumption further, van Buskirk and Ashman [57] and Katz et al. [58] measured the

anisotropic moduli using ultrasound. They showed that, in general, cortical bone

possesses orthotropic elastic properties, but stiffness in various directions normal to the

Haversian canals did not deviate more than 10%. Direct mechanical tests further

confirmed that cortical bone can be reliably considered as a transversely isotropic

material [59,60]. The reported Young’s moduli for cortical bone have been shown to be

about 20 – 22 GPa along the axis of long bone and about 12 – 14 GPa transverse to it

[61,62].

It is widely accepted that trabecular bone exhibits orthotropic material behavior

(three preferred material directions) [63-65]. It has also been argued that trabecular

alignment corresponds to principal stress directions [51,66,67]. Early work by Chalmers

and Weaver [68] and Galante et al. [68] showed that porosity was far more important

than mineral content in determining material properties. Therefore, apparent rather than calcium-equivalent densities are most often used to identify the remodeling state of bone

[65,69-74]. Dalstra et al. used dual-energy quantitative computer tomography (DEQCT)

to investigate the distribution of bone densities in pelvic bone, and nondestructive mechanical testing was used to obtain Young's moduli and Poisson's ratios in three orthogonal directions for cubic specimens of pelvic trabecular bone [75]. The combined data made it possible to establish empirical relations between apparent density, calcium 27

equivalent density and elastic modulus for pelvic trabecular bone. Dalstra et al. found

that pelvic trabecular bone stiffness ranged from 100 – 250 MPa when using density as a

primary predictor [75].

Bone exhibits rate-dependent material behavior, suggesting that it a viscoelastic

material [76-79]. Linde and Hvid [78,79] demonstrated that the stiffness of trabecular

bone specimens increased significantly as the loading rate was increased incrementally.

Schoenfeld et al. [80] determined the relaxation of trabecular bone and Zilch et al. [81]

demonstrated the viscoelastic behavior of bone through creep and relaxation tests.

Cartilage Material Properties

Cartilage structure and function was described as early as 1743 when William

Hunter presented the paper “Of the Structure and Disease of Articulating Cartilage” [82].

He described the ability of cartilage to deform under pressure and to regain its original

shape when the pressure was removed. He further described how the collagen fibers anchored in the underlying bone ran vertically through the cartilage as: “a mass of short

and nearly parallel fibers rising from the bone, and terminating at the external surface of

the cartilage”. Collagen fiber orientation was investigated further in the late 1800’s when

India ink studies demonstrated that cartilage split lines (i.e. path of collagen fiber

alignment) had a tendency to lay parallel to the articulating surface and to extend radially

[83]. Later work confirmed that collagen fibers are oriented nearly perpendicular to the

calcified interface and change orientation gradually until they are nearly parallel to the

articulating surface [84,85]. 28

Experimental studies demonstrate that cartilage is an inhomogenous tissue.

Cartilage modulus varies extensively depending on the location on the articulating

surface [86,87] and through the depth [88-92]. In addition, cartilage is stiffer when

loaded along the split line direction compared to perpendicular to this direction [93-97].

Cartilage exhibits a tension-compression nonlinearity wherein cartilage has higher

stiffness values in tension than in compressive [88,89,95,98,99]. It is thought that the

higher stiffness in tension versus compression allows cartilage to resist radial expansion

under axial compressive loading and results in increased fluid pressurization and dynamic

stiffness [93,100-103].

Cartilage is viscoelastic due to its high water content and relative mobility of the

fluid phase relative to the solid phase [104-106]. The equilibrium modulus of cartilage is

very low, on the order of 0.3 – 1.5 MPa [104,107,108], yet contact stresses measured in-

vivo routinely exceed 2.0 MPa [109-111]. Several theories have been proposed to

explain how cartilage can routinely support loads higher than what the solid matrix can withstand [112]. McCutchen proposed a self pressurizing, “weeping” mechanism whereby synovial joints are supported mainly by the hydrostatic fluid pressure [113]. In contrast, some have argued that fluid could flow into the cartilage during loading causing a “boosting” effect [114]. Nevertheless, because cartilage in the normal joint is ~70%

liquid, which is essentially incompressible, and because the cartilage layers indeed

consolidate under load ~10% [115] it is more likely that fluid flows out of cartilage layers, corroborating the original “weeping” mechanism [113]. 29

Under cyclic loading at physiological frequencies, interstitial fluid pressures remain elevated [116-118]. The dynamic cartilage modulus under these conditions is orders of magnitude greater than the equilibrium modulus [117,119-121]. Park et al.

[105] demonstrated the rate response of cartilage tissue samples under load controlled unconfined compression using frequencies ranging form 0.1 – 40 Hz. Stress strain curves became markedly steeper, but still nonlinear, at higher loading rates. It was suggested that the nonlinear stress response of cartilage under loading was in part due to the tension-compression nonlinearity. Hysteresis (energy dissipation) was reported as zero at

40 Hz and was not substantial at rates higher than 1 Hz. Minimum and maximum moduli ranged from 14.6 – 65.7 MPa, respectively. These data demonstrate the ability of cartilage to routinely maintain physiological levels of contact stress [105].

In-Vitro Studies of Hip Joints

In vitro experimental studies have served to elucidate hip biomechanics on the macro scale. These studies have helped to elucidate plausible modes of failure (e.g., during automobile side impacts or femur fracture in the elderly), implications of prosthetic replacement (e.g., peri-prosthetic bone shielding), and magnitudes of normal bone and cartilage stresses and strains. Studies with particular relevance to this dissertation are related to the measurement of bone and cartilage stresses and strains in intact hips or hips with simulated dysplasia as they provide baseline experimental data and detail proven methodologies that can be useful when developing and validating computational models of the hip joint. 30

Several studies have used strain gauges to quantify strains in the pelvis [3,122-

127]. Ries et al. [127] dissected four cadaveric pelvi free of soft tissue and instrumented each hemipelvis with ten rosette strain gauges to measure normal pelvic strains in-vitro.

Static loading was applied through the intact hip joint to simulate single leg stance. The medial portion of the pelvis was under tension directed vertically and the lateral ilium was in compression. This strain pattern was consistent with bending applied to the ilium from the action of the abductor and joint reaction forces. Finlay et al. [123] subjected pelvi with 2.5kN of force directed from the femur into the joint. Normal pelvic maximum principal stresses reached ~12 MPa assuming an elastic modulus of 6.2 MPa and Poisson’s ratio of 0.3 for cortical bone.

Oh et al. [128] measured the distribution of strain in the proximal femur under conditions of simulated single-leg stance using strain gauges applied to the cortex.

Strains decreased from proximal to distal in the intact femora under load, and the highest values were in the calcar area. More recently, Kim et al. [129] affixed strain gauges in the proximal femur and subjected it to loads of 900 N. Cortical bone strains ranged from

1700 – 2300 µE. In contrast to Oh et al., they found that strain increased from proximal to distal in the intact femora under load.

Numerous in vitro studies have investigated cartilage hip joint stresses in the intact hip joint [115,130-138]. These studies used pressure sensitive film [130,134-136], piezoelectric sensors [131,132], or instrumented prostheses [115,133,137,138]. Pressure sensitive film is often the measurement technique of choice as it is inexpensive, accommodates various geometries when cut (i.e. spherical femoral heads), and has 31 proven to be reasonably accurate (± 10% error, [139]). Using pressure sensitive film, von

Eisenhart-Rothe measured peak contact stresses of ~9 MPa in intact femoral heads when loaded directly into the acetabulum at 300% bodyweight [134,135]. Adams et al. implanted eleven piezoelectric pressure transducers through the bone of the acetabulum

[132]. Maximum pressure ranged from 4.93 to 9.57 MPa at the interface between acetabular cartilage and subchondral bone, suggesting that high cartilage stresses are likely to occur throughout the thickness of hyaline cartilage in the hip joint.

Brown et al. [133] measured the time variant distributions of intra-articular contact stress from direct measurement of seventeen grossly normal fresh cadaveric hips.

Local stresses were sensed by arrays of 24 compliant miniature transducers inset superficially in the femoral head cartilage. Contact stress magnitude was usually found to rise nearly linearly with applied joint loads in excess of about 1000 N. The sites of maximum local stress were found to underlie the general region of the acetabular dome.

For a resultant joint load of 2700 N, the spatial mean contact stress and peak local contact stress averaged 2.92 MPa and 8.80 MPa, respectively. The full contact stress patterns were irregular and complex, but most commonly the general feature was a central band or

“ridge” of pressure elevation, oriented in an approximately anterior-to-posterior direction.

Rushfeldt et al. [138] measured the in vitro distribution of pressure on the cartilage surface of the human acetabulum using a modified endoprosthesis with fourteen integral pressure transducers. Peak pressures at 2250 N of load were ~11 MPa and decreased with time while the contact area increased. The pressure distribution was neither uniform nor axisymmetric about the load vector. It was concluded that the highly irregular 32 pressure profiles observed are due primarily to cartilage thickness distribution and irregularities at the calcified cartilage interface. Macirowski et al. [115] used a similar prosthesis to measure the total surface on acetabular cartilage when step-loaded by an instrumented hemiprosthesis. Using a combined experimental and computational protocol they found that, even after long-duration application of physiological force, fluid pressure supported nearly 90% of the load within the cartilage network stresses. Their results provided further support for the “weeping” mechanism proposed by McCuthen

[113].

One limitation of experimental studies is that measurements of stress and strain are only obtained at the location of the sensing device. Therefore, a priori knowledge is required to place sensors in meaningful positions. However, for studying specific disorders this information may be unknown. Another limitation is that to analyze individual disorders such as hip OA and dysplasia one would need to obtain cadaveric specimens that exhibited the pathology of interest. Given the challenges of obtaining donor tissue this task would be a very difficult, if not impossible endeavor. Based on these limitations, in vitro experimentation may not be the most appropriate technique for the study of specific hip pathologies.

In-Vivo Studies of Hip Joints

No known methods exist to measure pelvic and femoral bone strains in-vivo.

However, a considerable amount of work has been devoted to measuring hip joint contact pressures and joint reaction forces using instrumented prostheses. Carlson et al. [140] was one of the first to describe the development of a radio telemetrized femoral 33 prosthesis in 1974. In 1985 Hodge et al. [111] implanted a prosthesis into a patient and measured contact stress at 10 discrete locations. Data were acquired during surgery, recovery, rehabilitation, and normal activity, for longer than 1 year after surgery.

Pressure magnitudes were synchronized with body-segment kinematic data and foot-floor force measurements to locate transduced pressure areas on the natural acetabulum and to correlate movement kinematics and dynamics with local cartilage pressures. The data revealed very high local (up to 18 MPa) and non-uniform pressures, with abrupt spatial and temporal gradients.

More recently, Bergmann et al. implanted similar prostheses in 5 patients who underwent THA surgery for treatment of hip OA [109,110]. Gait analysis was performed on each patient and contact pressure data and equivalent joint reaction force were evaluated in parallel with joint kinematics during a variety of daily activities such as walking, stair climbing, descending stairs, and rising from a chair. Joint reaction forces were as high as 5.5 times bodyweight when the subjects rose from a chair, but were generally lower (2.5 times bodyweight) during walking, stair climbing, and descending stairs. Their data also suggested that contact stresses and joint reaction forces correlated well with foot-floor force measurements and demonstrated large inter-subject variation in contact stresses, joint reaction forces and joint kinematics.

Data from instrumented prostheses have yielded contact pressure data that are consistent with experimental studies, suggesting that this technique has the ability to accurately measure hip joint mechanics in vivo. However, the procedure is invasive and limited to a small sample of patients who have already undergone treatment to correct 34

OA. In addition, the technique is limited to the measurement of joint reaction forces associated with implant contact mechanics rather than cartilage stresses [141]. Finally, as with in vitro studies, data from instrumented prostheses only yield mechanical estimates at the contact site rather than an estimate of the mechanics throughout the joint, which may play a vital role in the development and progression of diseases such as OA and hip dysplasia.

NUMERICAL MODELING OF HIP JOINT BIOMECHANICS

Analytical Modeling of the Hip Joint

Analytical approaches to predicting hip joint biomechanics generally use the equations of statics to solve for resultant joint reaction forces. For clarity, “analytical” studies will be described herein as those that can be solved using simplified mathematical equations that do not require discretization of geometry or stipulation of material properties. Several analytical models have been developed to estimate hip joint mechanics [29,142-145]. In previous efforts, the geometry of the acetabulum and femur was assumed spherical by calculating the average radius of the femur and acetabulum by measuring 2-D radiographs [29,142-145]. The equivalent joint reaction force was estimated by summing zero a vertical body force (generally 5/6 bodyweight) and non- vertical abductor muscle force. Contact pressures were found by distributing the force over the estimated area.

Two analytical models have been developed to compare mechanics between normal joints and those affected by acetabular dysplasia [29,142]. Mavcic et al. used a mathematical model of static, single-leg stance based on AP radiographs of normal and dysplastic subjects [142]. Dysplastic hips had significantly larger peak contact stresses than healthy hips (7.1 kPa/N and 3.5 kPa/N, respectively). Michaeli and co-workers also demonstrated notable differences in the location and magnitude of contact stresses between normal cadaveric pelvi and plastic pelvi with simulated dysplasia [29].

Although these studies further support the notion of pathological biomechanics and in particular increased contact stresses in the dysplastic hip, they neglected several 36

important aspects of the biomechanics. For example, idealized geometry was used to

represent all or part of the hip articulation, neglecting the issues of regional and patient-

specific congruency between the femoral and acetabular cartilage layers. Ignoring

cartilage geometry and assuming joints to be concentric likely lead to erroneous estimates

(underestimation) of contact pressure.

Computational Modeling of the Hip Joint

For clarity, “computational” models will be described as a subclass of numerical

models, which requires the geometry of interest to be discretized into smaller

mathematical problems. Constitutive equations and boundary conditions also must be

stipulated during the development of a computational model. The use of computational

modeling is an attractive method for studying hip joint biomechanics. Computer models

have the ability to predict bone and cartilage stresses and strains throughout the

continuum of interest rather than at select measurement locations. With the advent and

availability of medical imaging techniques, individual patient models can be developed

by segmenting image data, which contains detailed geometry and estimates of mechanical

properties. Therefore, gross simplifying assumptions regarding hip joint geometry (i.e.

spherical geometry, concentric articulation of cartilage) are not necessary. Finally, with the exception of radiation exposure during CT, computational models can be developed noninvasively using living subjects, allowing the analysis of individual patients.

Constitutive Models for Bone and Cartilage

Besides providing insight into the contribution of different tissue components to overall tissue material behavior, constitutive models are necessary to represent the properties of tissue in computational models. Constitutive equations with particular relevance to this dissertation will be discussed further.

Although viscoelastic, bone can be considered as an elastic material for many applications [146]. Therefore, under the assumptions associated with linearized elasticity, the material behavior is characterized by a fourth-order elasticity tensor C in the generalized Hooke’s law that relates the Cauchy stress T to the infinitesimal strain tensor ε :

T = C : ε ⇔=TijC ijklε kl . (1.1)

In its most general form, the elasticity tensor involves 21 independent elastic coefficients that must be determined experimentally. In the case of orthotropy, three orthogonal planes of symmetry exist, leaving nine independent coefficients. The number of independent elastic coefficients is reduced further to five for the case of transverse isotropy and to two for the case of isotropy.

Cartilage has been modeled as isotropic-elastic [147], isotropic biphasic [99,148], transversely isotropic biphasic [149], poroviscoelastic [150], and as a fibril reinforced poroelastic material [103]. When cartilage is loaded instantaneously, the response is equivalent to that of an incompressible material [99,102,148,151-154]. In such instances the use of a linearized elastic constitutive model may be appropriate. However, the accuracy of model predictions will degrade as strains increase since the assumption of 38 infinitesimal strain results in spurious strains when the continuum undergoes rigid rotations. Hyperelasticity is based on the existence of a strain energy potential, which generally results in a nonlinear relationship between stress and strain. Poroelastic constitutive models describe the relative contributions of solid and fluid phases to the overall material behavior of cartilage. They were originally developed to describe the mechanics of soils [155,156] and were extended to cartilage using the biphasic theory developed by Mow et al. [99].

Finite Element Modeling of Hip Joint Biomechanics

The finite element (FE) method is a proven technique that has been used extensively to evaluate biomechanical systems. The FE method allows an analyst to obtain a solution for the stress and strain distribution throughout a continuum when the applied loads, boundary conditions and material properties are known. FE model construction can be divided into three distinct steps: 1) pre-processing, 2) stipulation of boundary and loading conditions, and 3) analysis and post-processing. Pre-processing involves discretization of the geometry of interest into small finite elements and has historically been the most challenging aspect when constructing FE models of human joints. However, with the development of commercial segmentation programs this task has become much less daunting as the process is generally automated [157,158]. Next, loading and boundary conditions are applied to the model to govern displacements of individual elements. Constitutive equations and associated material coefficients are specified data. The discretized equations of motion, based on minimization of potential energy, are solved to obtain the displacement field. Strains and then stresses are 39 computed from the displacement field. Finally, model predictions are post-processed to facilitate visualization and data analysis.

A few 3D FE models have been developed to predict bone strains in intact hips

[3,159,160]. Oonishi et al. used measurements from a 3D coordinate measuring machine to generate contours of the horizontal sections of the iliac bone. An FE mesh of the pelvis was constructed using these contours. Simulated muscle forces and bodyweight were applied. Peak cortical bone von-Mises stresses were well below 1 MPa. However, they apparently made a mistake in calculating the magnitude of load from kgf to N whereby instead of multiply by 9.8, they divided by 9.8, making their results almost a factor of 100 too small [3]. Dalstra et al. [3] used CT image data to develop a realistic

3D model of the human pelvis. Cortical bone was assigned a spatially varying thickness, based on measurements from CT image data. Strain gauges were attached to a pelvis to experimentally measure cortical bone strains. FE predictions of cortical bone stress were compared to those measured on the cadaveric pelvis for purposes of validating the model.

FE predictions of von-Mises stress were on the order of ±4 MPa and were in fair agreement with experimental data although no statistical tests were conducted to quantify model accuracy.

Nearly all FE hip joint modeling studies that have analyzed cartilage contact have used two-dimensional, plane strain models [115,161-163] with either rigid [115,161] or deformable bones [162,163]. The earliest FE contact model was reported by Brown and

DiGioia [162]. In this study predicted pressures were irregularly distributed over the surface of the femoral head with values of peak pressure on the order of 4 MPa. 40

Rapperport et al. [163] developed a similar model based on geometry from a radiograph, assuming femoral acetabular surfaces to be spherical and congruent. At 1000 N of applied load peak, pressures were on the order of 5 MPa and a rather uniform contact distribution was observed. Rigid bone models yielded predictions only slightly different than the deformable bone model.

Macirowski et al. [115] utilized a combined experimental/analytical approach to model fluid flow and matrix stresses in a biphasic contact model of a cadaveric acetabulum. This is the only FE study to date to explicitly model the acetabular cartilage thickness. The acetabulum was step loaded to 900 N using an instrumented femoral prosthesis. At the instant load was applied peak contact pressures measured by the prosthesis were on the order of 5 MPa. When the experimentally measured total surface stress was applied to the FE model average predicted pressures (solid stress + fluid pressures) were approximately 1.75 MPa. An important conclusion made in this study was that even small variations in sphericity (up to 0.2 mm) likely influenced the cartilage sealing process since during early step loading high local maxima and irregular, steep pressure gradients were measured. This argument parallels that made by Rushfeldt et al. who concluded that the highly irregular pressure profiles observed during an instrumented prosthesis in-vitro study were likely due to the cartilage thickness distribution and irregularities at the calcified cartilage interface [138].

With the exception of Macirowski’s study, it is evident that the cartilage contact

FE models developed thus far have a tendency to predict lower contact pressures when compared to in-vitro studies that have loaded cadaveric joints with similar forces. The 41 discrepancy between predictions is most likely attributed to the fact that prior computational studies assumed spherical geometry and concentric articulation. Although the computational modeling literature suggests that normal joints may be modeled as spherical structures with concentric articulation [164,165], it has been well documented that the hip joint is neither spherical nor has cartilage with uniform thickness

[9,115,135,166,167].

Very recently patient-specific FE models have been developed to elucidate the biomechanics of dysplastic hip joints [168]. Russell et al. [168] constructed patient- specific, non-linear, contact FE models using CT arthrography image data. A normal model was also generated which was based on geometry from the Visible Human Project

[169]. Peak contact pressures for dysplastic and asymptomatic hips (contra-lateral joints) ranged from 3.56 – 9.88 MPa. There were significant differences between the normal control and the asymptomatic hips and a trend towards significance between asymptomatic and symptomatic joints. They concluded that bone irregularities caused localized pressure elevations and that asymptomatic hips had pathological mechanics.

While these models represent the current state of the art for modeling patient-specific hip joint contact mechanics it remains unknown if the predictions were accurate as the computational modeling protocol was not validated.

Discrete Element Analysis

Discrete element analysis (DEA) (a variant of the FE method) has been used to analyze hip joint contact mechanics [164,170,171]. Cartilage layers were represented using a series of discrete compressive spring elements and tangential shear elements. 42

Yoshida et al. [171] developed a dynamic DEA model to investigate the distribution of hip joint contact pressures using in-vivo data from the literature. The model assumed spherical geometry for the femur and acetabulum and concentric articulation. Peak pressures during simulated walking, descending stairs, and stair climbing were relatively low in comparison to previous experimental measurements. In a similar study Genda et al. [170] generated 3D contact hip DEA models using 2-D radiographs by assuming that the femoral head and the acetabular surface were spherical in shape. They determined that the joint contact area and normalized peak contact pressure were significantly different between men and women. The normalized peak contact pressure was around 1.5

MPa, which again was substantially lower than experimental data form the literature under similar loading conditions. For certain limited instances, DEA may be effective

[172]. However, because direct experimental validation has not been performed for this technique, it is unclear whether or not DEA has the ability to accurately predict hip joint contact mechanics. Furthermore, gross simplifying assumptions are made using this technique (e.g. generation of 3D models from 2D radiographs), which provides an explanation of why DEA estimates of peak pressure substantially underestimate peak pressure when compared to experimental data.

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CHAPTER 3

A SUBJECT-SPECIFIC FINITE ELEMENT MODEL OF THE PELIVS:

DEVELOPMENT, VALIDATION AND SENSITIVITY STUDIES1

ABSTRACT

A better understanding of the three-dimensional mechanics of the pelvis, at the

patient-specific level, may lead to improved treatment modalities. Although finite

element (FE) models of the pelvis have been developed, validation by direct comparison

with subject-specific strains has not been performed, and previous models used

simplifying assumptions regarding geometry and material properties. The objectives of

this study were to develop and validate a realistic FE model of the pelvis using subject-

specific estimates of bone geometry, location-dependent cortical thickness and trabecular

bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions

regarding cortical bone thickness as well as bone and cartilage material properties. A FE

model of a cadaveric pelvis was created using subject-specific CT image data.

Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a

fashion that could be easily duplicated in the computational model. Cortical bone strains

1 Reprinted from Journal of Biomechanical Engineering, Vol. 127, No. 3, Anderson, A.E., Peters, C.L., Tuttle, B.D., Weiss, J.A., “A Subject-Specific Finite Element Model of the Pelvis: Development, Validation, and Sensitivity Studies”, pp: 364-373, 2005, with kind permission from the ASME.

59 were monitored with rosette strain gauges in ten locations on the left hemi-pelvis. FE strain predictions were compared directly with experimental results for validation.

Overall, baseline FE predictions were strongly correlated with experimental results (r2 =

0.824), with a best-fit line that was not statistically different than the line y=x

(Experimental strains=FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis. 60

INTRODUCTION

The acetabulum and adjoining pelvic bones are one of the most important weight bearing structures in the human body. Forces as high as 5.5 times body weight are transferred from the femur to the acetabulum during activities such as running and stair climbing [1-3]. The structure of the pelvis is a sandwich material, with the thin layers of cortical bone carrying most of the load. Despite its efficient structure, the pelvis can become damaged due to altered loading. Side impact forces, such as those generated in car accidents, are notorious for generating pelvic fractures. The fracture itself often causes multiple internal trauma leading to a mortality rate on the order of 12 - 37% [4,5].

In addition to pelvic fractures, it has been hypothesized that subtle alterations in pelvic geometry (i.e., pelvic dysplasia) lead to osteoarthritis [6-11]. In fact, secondary causes of osteoarthritis, such as undiagnosed pelvic dysplasia, appear to be more prevalent among candidates for total hip arthroplasty (THA) than primary arthritis [10-13]. Michaeli et al. reported that nearly 76% of THA recipients exhibited signs of a dysplastic joint - a condition that went unrecognized prior to surgery [3]. Nevertheless, the relationship between pelvic dysplasia and osteoarthritis remains controversial since there is no direct quantitative evidence linking the two together.

Simplified mathematical models, experimental contact analyses, and force telemetry data have been used to estimate joint contact forces at the acetabulum [1-3,14-

21]. These studies provide valuable information concerning overall joint mechanics but do not yield estimates of the surrounding bone stresses and strains. It would be wise to develop methods capable of quantifying the mechanics beyond the acetabular contact 61

interface since there is evidence to suggest that the surrounding bone plays a pivotal role

in the progression of diseases such as osteoarthritis [22-24]. A better understanding of

the mechanics for the entire pelvis could lead to improved implant designs, surgical

approaches, diagnosis, and may present the framework necessary for preoperative

surgical planning. Specifically, an analysis of the stress distribution in and around the pelvic joint may clarify the mechanical relationship between pelvic geometry and predisposition to osteoarthritis.

It is difficult to assess the stress and strain distribution throughout the entire pelvis using simplified mathematical models, implanted prostheses, or via experiments with cadaveric tissue. An alternative approach to analyze pelvic mechanics is the finite

element (FE) method, which can accommodate large inter-subject variations in bone

geometry and material properties. The potential benefit of patient-specific FE analysis

becomes clear when one considers how difficult (if not impossible) it would be to

assemble a population of donor tissue that exhibits a specific pathology such as pelvic

dysplasia.

The objectives of this study were to develop and validate a FE model of the pelvis

using subject-specific estimates of bone geometry, location-dependent cortical thickness

and trabecular bone elastic modulus, and to assess the sensitivity of FE cortical strain

predictions to cortical bone thickness and bone and cartilage material properties. The

following hypotheses were tested: 1) A FE model of the pelvis that incorporated subject-

specific geometry, cortical bone thickness, and position dependent trabecular bone elastic

modulus would accurately predict cortical bone strains. 2) A subject-specific FE model 62 of the pelvis would be more accurate than models that assume average cortical bone thickness and trabecular elastic modulus.

MATERIALS AND METHODS

A combined experimental and computational protocol was used to develop and

validate a subject-specific three-dimensional model of a 68 y/o female cadaveric pelvis

(International Bioresearch Solutions, Tucson, AZ). The pelvic joint was visually screened for large-scale osteoarthritis prior to the study.

Experimental Study

The sacroiliac joint and all soft tissues, with the exception of articular cartilage,

were removed. A registration block and wires were attached to the iliac crest. The block

allowed for spatial registration of experimental and FE coordinate systems, while the

wires served as a guide to reproduce the boundary conditions used in the experimental

model [25]. A CT scan (512x512 acquisition matrix, FOV=225 mm, in-plane

resolution=0.44x0.44 mm, slice thickness=0.6 mm, 354 slices) was obtained in a superior

to inferior fashion using a Marconi-MX8000 scanner (Philips Medical Systems, Bothell,

WA). A bone mineral density (BMD) phantom (BMD-UHA, Kyoto Kagaku Co., Kyoto,

Japan), consisting of 21 rectangular blocks of urethane with varying concentrations of

hydroxyapaptite (0 - 400 mg/cm3, 20 mg/cm3 increments) was also scanned with the

same field of view and energy settings. CT data from the BMD phantom were averaged

over each block to obtain a relationship between CT scanner pixel intensity and calcium

equivalent bone density.

The mounting and loading of the pelvis followed a protocol similar to that

described by Dalstra et al. [26]. The iliac crests were submerged in a mounting pan of 64

catalyzed polymer resin (Bondo, Mar-Hyde, Atlanta, GA) to the depth defined by the

iliac guide wires. Ten three-element rectangular rosette strain gauges (WA-060WR-120,

Vishay Measurements Group, Raleigh, NC), representing 30 channels of data, were

attached to the left hemi-pelvis at locations around the acetabulum, pubis, ischium, and

ilium. Vertically oriented loads of 0.25, 0.50, 0.75, and 1.0 X body weight (559 N) were

applied to the acetabulum by displacing a femoral prosthesis, attached to a linear actuator

(Figure 3.1). The femoral implant was displaced continuously until the appropriate load was reached at which time the displacement was held constant, allowing stress relaxation, until the load relaxed to a value greater than 95% of the original with a load-time slope less than 0.25 N/sec for at least 60 seconds. The average time to reach quasi-static equilibrium for each loading scenario was 6 minutes. An average of the rosette gauge readings (ε1, ε2, ε3) for the last 10 seconds of the equilibrium period was obtained and

then converted to in-plane principal strains (εP, εQ) using the relationship [27]:

ε +ε 1 ε =±13 ()()εε −+−22 εε . (3.1) PQ,12232 2

3D coordinates of the strain gauges and registration block were determined in a

laboratory reference frame using an electromagnetic digitizer (Model BE-3DX,

Immersion Corp., San Jose, CA). Geometric features of the pelvis were digitized to

determine the accuracy of the geometry reconstruction.

LOAD

D E F

G Figure 3.1. Schematic of fixture for loading the pelvis via a femoral implant component. (A) actuator, (B) load cell, (C) ball joint, (D) femoral component, (E) pelvis, (F) mounting pan for embedding pelvis, and (G) lockable X-Y translation table. 66

Geometry Extraction and Mesh Generation

Contours for the outer cortex and the boundary of the cortical and trabecular bone, registration block, and guide wires were extracted from the CT data via manual segmentation (Figure 3.2). Points comprising the contours were triangulated [28] to form a polygonal surface, which was then decimated [29] and smoothed [30] to form the final surface using VTK (Kitware Inc., Clifton Park, NY) [31] (Figure 3.2). A volumetric tetrahedral mesh was created from the final surface to represent the outer cortex (CUBIT,

Sandia National Laboratories, Albuquerque, NM). A 4-node, 24 degree of freedom tetrahedral element was used to represent trabecular bone [32]. This element has three translational and rotational degrees of freedom at each node. Mesh refinement tests were performed with this element using a model of a cantilever beam under a tip load with a thickness that was 10% of the beam length. FE-predicted tip deflections reached an asymptote of 4% error with respect to an analytical solution when at least 3 tetrahedral elements were used through the thickness of the beam.

Cortical bone was represented with quadratic 3-node shell elements [33]. The elements were based on the Hughes-Liu shell [34,35], which has three translational and rotational degrees of freedom per node, with selective-reduced integration to suppress zero-energy modes [36]. The geometry of the shells was based on the nodes of the outside faces of the tetrahedral elements, on the outer surface of the pelvis. The shell reference surface and shell element normal were defined so that the cortical thickness pointed inward toward the interface between cortical and trabecular bone. This approach resulted in an overlap of one cortical bone thickness between the tetrahedral solid 67

element and thin shell element. The elastic modulus for all tetrahedral element nodes in this region of overlap was set to 0 MPa. Mesh refinement tests showed that the 3-node shell was nearly as accurate as using three tetrahedral elements through the thickness of the beam (< 5% error with respect to analytical solution).

A) B) C) P

M L

Figure 3.2. A) - CT image slice at the level of the ilium, showing the registration block (arrow) and the distinct boundary between cortical and trabecular bone. B) - the original polygonal surface representing the cortical bone was reconstructed by Delaunay triangulation of the points composing the segmented contours. C) - polygonal surface after decimation to reduce the number of polygons and smoothing to reduce high- frequency digitizing artifact. A - anterior, P - posterior, M - medial, L - lateral, I - inferior, S - superior. 68

The density of the FE mesh was adjusted until it was at or above the beam mesh density required to achieve an error of 4%. The final surface mesh density was 0.5 shell elements/mm2 with a volumetric density of 2.5 tetrahedral elements/mm3. The final FE model consisted of 190,000 tetrahedral elements for trabecular bone and 31,000 shell elements for cortical bone (Figure 3.3). Acetabular cartilage was represented with 350 triangular shell elements with a constant thickness of 2 mm, determined by averaging the distance between the implant and acetabulum in the neutral kinematic position.

A) B)

Figure 3.3. A) FE mesh of the pelvis, composed of 190,000 tetrahedral elements and 31,000 shell elements. B) close-up view of the mesh at the acetabulum. 69

Position-Dependent Cortical Thickness

An algorithm was developed to determine the thickness of the cortex based on the distances between the polygonal surfaces representing the outer cortex and the boundary between the cortical and trabecular bone. Vectors were constructed between each node on the cortical surface and the 100 nearest nodes on the surface defining the cortical- trabecular boundary. Cortical thickness was determined by minimizing both the distance between the nodes of the surfaces and the angle of the dot product between the surface normal of the cortical surface with that of each corresponding trabecular vector. In areas of high curvature (such as the acetabular rim), special consideration of thickness was necessary (Figure 3.4). When the above-described algorithm reported a thickness value that exceeded 1.5 times the smallest distance between the nodes, the smallest distance between nodes on the two surfaces was used. The minimum value of nodal thickness was assumed to be 0.44 mm or the width of one pixel (FOV= 225, FOV/512 = 0.44 mm/pixel). The algorithm was tested using polygonal surfaces representing parallel planes, concentric spheres, and layered boxes with varying mesh densities.

A) B) C)

n n

Figure 3.4. Schematics illustrating the special cases considered in determination of cortical thickness. Both the distance between the surfaces and the angle of the dot product between the normal vector (n) with that of the vector created by subtracting the trabecular and cortical node coordinates were considered. Nodes on the cortical surface are represented as open circles, while nodes on the trabecular surface are shown as filled circles. Case A) the smallest angle of the dot product between the cortical node and nearest trabecular node neighbor yields the desired thickness measurement. Case B) the smallest distance between nodes provides the desired thickness measurement. Case C) the normal vector (n) from the cortical node does not intersect the trabecular surface. For cases B and C, a weighting scheme was applied such that the smallest distance between the nodes was taken as the cortical thickness when the originally reported thickness value exceeded 1.5 X the smallest distance between nodes on the two surfaces. 71

Assessment of Cortical Bone Thickness

A custom-built phantom was used to assess the accuracy of cortical thickness measurements (Figure 3.5) [37]. Ten aluminum tubes (wall thickness 0.127– 2.921 mm) were fit into a 70 mm dia. Lucite disc. The centers of the aluminum tubes were filled with Lucite rods so that both the inner and outer surfaces of the tubes were surrounded by a soft tissue equivalent material [38,39]. Aluminum has x-ray attenuation coefficient that is similar to cortical bone [37]. The phantom was scanned with the same CT scanner field of view and energy settings used for the cadaveric pelvis and bone mineral density phantom. The z-axis of the scanner was aligned flush with the top edge of the tissue phantom to prevent volume averaging between successive slices. The inner and outer circumferences of the tubes were segmented from the CT image data using the same technique to extract the pelvic geometry. The surfaces were meshed and the thickness algorithm was used to determine wall thickness.

A) B)

Figure 3.5. A) Tissue equivalent phantom containing 10 aluminum tubes used to simulate cortical bone with varying thickness. The phantom was scanned with a CT scanner and manually segmented to determine the accuracy of cortical bone reconstruction. B) cross- sectional CT image of the cortical bone phantom. Changes in thickness can be seen for the thicker tubes but become less apparent as the tube wall thickness decreases. 72

Material Properties and Boundary Conditions

The femoral implant was represented as rigid while cortical and trabecular bone were represented as isotropic hypoelastic. Baseline material properties for cortical bone were E = 17 GPa and Poisson’s ratio (ν) = 0.29 [26]. A linear relationship was established between CT scanner pixel intensity and calcium equivalent density using the

CT image data from the BMD solid phantom:

2 ρca =−=0.0008iINT 0.8037 ( r 0.9938) (3.2)

3 Here ρca is the calcium equivalent density of trabecular bone (g/cm ) and INT is the CT scanner intensity value (0 - 4095). Next, a relationship was used to convert calcium

equivalent density ( ρca ) to apparent bone density ( ρapp ) [40]:

ρ ρ = ca . (3.3) app 0.626

Finally, an empirical relationship was used to convert apparent density of pelvic trabecular bone to elastic modulus for each node [40]:

2.46 E = 2017.3 (ρapp ) , (3.4)

where E is the elastic modulus (MPa) and ρapp is the apparent density of the trabecular bone (g/cm3). Nodal moduli were averaged to assign an element modulus. Acetabular articular cartilage was represented as a hyperelastic Mooney-Rivlin material [41].

Coefficients C1 and C2 were selected as 4.1 MPa and 0.41 MPa, respectively with

Poisson’s ratio=0.4 [42]. 73

A FE coordinate system was created from the polygonal surface of the reconstructed registration block. A corresponding coordinate system was established for the experimental measurements using the digitized coordinates of the registration block

[25]. To establish the neutral kinematic position, a transformation was applied to the FE model to align it with the experimental coordinate system. Nodes superior to the iliac guide wires and nodes along the pubis synthesis joint were constrained to simulate the experiment. Contact was enforced between the femoral implant and cartilage while load was applied to the implant using the same magnitude and direction measured experimentally. Analyses were performed with the implicit time integration capabilities of LS-DYNA (Livermore Software Technology Corporation, Livermore, CA) on a

Compaq Alphaserver DS20E (2 667 MHz processors). Each model required approximately 3 hours of wall clock time and 1.1 GB of memory.

Sensitivity Studies

Sensitivity studies were performed to assess the effects of variations in assumed and estimated material properties and cortical thickness on predicted cortical surface strains. The assumed parameters were cortical bone Poisson’s ratio, trabecular bone

Poisson’s ratio, cartilage elastic modulus, and cortical bone elastic modulus. The estimated parameters were trabecular elastic modulus and cortical bone thickness.

Variations in assumed parameters were based on standard deviations from the literature

(Table 3.1). The trabecular elastic modulus and cortical thickness were varied to reflect the median and inter-quartile range estimated computationally. The FE models included 74 constant cortical shell thickness (CST), constant trabecular elastic modulus (CTEM), constant shell thickness and elastic modulus (CST/CTEM) and subject-specific models

(position dependent trabecular elastic modulus and cortical thickness), with alterations in cortical bone Poisson’s ratio (SSCV), trabecular bone Poisson’s ratio (SSTV), cortical elastic modulus (SSCM), articular cartilage thickness (ACT) and articular cartilage elastic modulus (ACEM). A sensitivity model (OVERLAP) was analyzed to determine the cortical surface strain effects due to overlap between the cortical shell and tetrahedral elements. For the overlap model the tetrahedral surface nodes were assigned the maximum elastic modulus estimated from the cadaveric CT image data (3829 MPa). The surface nodes were averaged to estimate the elastic modulus for the each tetrahedral element as was done in the subject-specific model. The sensitivity of each model, S, was defined as:

% change in slope S = . (3.5) % change in input parameter

The numerator in (5) is the percent change in slope of the best-fit lines between the sensitivity model and baseline subject-specific model. The denominator is the percent change in the model input parameter between the sensitivity model and the baseline subject-specific model. For those sensitivity models that investigated constant inputs such as cortical thickness and trabecular bone elastic modulus, the change in constant model input parameters was used in the denominator.

Table 3.1. Models studied for FE sensitivity analysis. Deviations in material properties and cortical thickness were taken from experimentally measured/estimated values (EXP) as well as data reported in the literature.

Type Models Analyzed Reference CST Thickness = ± 0, 0.5, 1 SD (0.49 mm) EXP CTEM E = 45, 164, 456 MPa (Quartiles) EXP CST/CTEM Thickness = 1.41 mm, E = 164 MPa EXP SSCV ν=0.2, ν=0.39 [57] SSTV ν=0.29 [55] SSCM E = ± 1 SD (1.62 GPa) [58] ACT Thickness = 0.0, 4.0 mm (Min/Max) EXP ACEM E = 1.36, 7.79 MPa (Min/Max) [59] OVERLAP Surface Tet. Nodes = Max Trabecular Modulus NA

Data Analysis

FE predictions of cortical principal strains were averaged over elements that were located beneath each strain gauge. A rectangular perimeter, representing each strain gauge, was created on the surface of the FE mesh using digitized points from the experiment. Strains for a shell were included in the average if at least 50% of its area was within the perimeter. FE predicted strains were plotted against experimental strains.

Best-fit lines and r2 values were reported for each model at all loads. Statistical tests

(α=0.05) were performed to compare the slope and y-intercept of the subject-specific best-fit line with the line y=x (Experimental Strains=FE Strains) to test the null hypothesis: there was no significant difference between FE predicted strains and experimental strains [43]. Statistical tests were used to test differences between the slope of the best-fit line, and r2 values for each sensitivity model with the baseline subject- specific model [43]. 76

RESULTS

Reconstruction of Pelvic Geometry

The geometry reconstruction techniques yielded a faithful reproduction of the measured geometric features of the pelvis (Figure 3.6). Correlation between measurements on the cadaveric pelvis with the corresponding FE mesh was strong

(r2=0.998). There was no statistical difference between the slope and y-intercept of the regression line and the line y = x.

180 160 y = 0.97x + 2.16, r2= 0.998 140 120 100 80 60 40 20 0 0 20 40 60 80 100 120 140 160 180 Experimental Measurements (mm) FE Measurements (mm)

Figure 3.6. A) schematic showing the length measurements that were obtained from the cadaveric pelvis with an electromagnetic digitizer. Measurements were based on identifiable anatomical features of the iliac wing, ischium, obturator foramen, pubis, and acetabulum. B) excellent agreement was observed between experimental measurements and the FE mesh dimensions, yielding a total error of less than 3%. 77

Cortical Bone Thickness

The thickness algorithm accurately predicted thickness using simple polygonal surfaces with known distances between the surfaces. For parallel planes and concentric spheres, errors were ±0.004%. For the layered boxes, the RMS error was ±2%. For all surfaces, errors decreased with increasing surface resolution. The above errors are based on polygonal surfaces with a resolution similar to the pelvis FE mesh.

The thickness algorithm estimated aluminum tube wall thickness accurately (less than ±10% error) for tubes with thicknesses between 0.762 and 2.9210 mm (Table 3.2).

The reported standard deviation in nodal thickness for these tubes was also less than 10% of the average nodal thickness (Table 3.2). Therefore individual nodal thickness values did not deviate much from the average nodal thickness. However, errors in thickness increased progressively for tubes with wall thickness between 0.127 and 0.635 mm.

Cortical bone thickness ranged from 0.44 - 4.00 mm (mean 1.41 ± 0.49 mm (SD))

(Figure 3.7). Cortical thickness was highest along the iliac crest, the ascending pubis ramus, at the gluteal surface and around the acetabular rim. Cortical bone was thin at the acetabular cup, the ischial tuberosity, the iliac fossa and the area surrounding the pubic tubercle.

Table 3.2. Measurement of aluminum tube wall thickness from CT data. Errors in wall thickness were less than 10% for thicknesses greater than or equal to 0.762 mm. Errors increased progressively as the wall thickness decreased.

True Thickness Estimated Thickness (mm) (mm) (mean ± SD) Error (%) 0.127 0.554 ± 0.094 336 0.254 0.669 ± 0.111 163 0.381 0.638 ± 0.089 67 0.508 0.815 ± 0.079 60 0.635 0.709 ± 0.071 12 0.762 0.825 ± 0.063 8.3 1.016 1.039 ± 0.088 2.2 1.270 1.317 ± 0.077 3.7 2.032 1.982 ± 0.078 -2.5 2.921 2.781 ± 0.108 -4.8

A) B)

2.75 mm

0.44 mm Anterior Oblique Medial Figure 3.7. Contours of position dependent cortical bone thickness with rectangles indicating the locations of the 10 strain gauges used during experimental loading. A) anterior view, B) medial view. Cortical thickness was highest along the iliac crest, the ascending pubis ramus, at the gluteal surface and around the acetabular rim. Areas of thin cortical bone were located at the acetabular cup, the ischial tuberosity, the iliac fossa and the area surrounding the pubic tubercle. Cortical thickness beneath the surface of the strain gauges was similar to the average model thickness of 1.41 mm but deviated less. 80

Trabecular Bone Elastic Modulus

Trabecular elastic modulus ranged from 2.5 - 3829.0 MPa (mean = 338 MPa, median = 164 MPa, inter-quartile range = 45 - 456 MPa). Data were significantly skewed to the right (positively skewed) so the median and bounds of the inter-quartile range were used for sensitivity models rather than the arithmetic mean and standard deviation. Areas of high modulus were predominately near muscle insertion sites and within the subchondral bone surrounding the acetabulum. Areas of low modulus were located near the sacroiliac joint, pubis joint, and along the ischial tuberosity and the interior of the ilium.

FE Model Predictions

FE predicted von Mises stresses for the subject-specific model ranged from 0-44

MPa and were greatest near the pubis-symphasis joint, superior acetabular rim, and on the ilium just superior to the acetabulum for each load applied (Figure 3.8). Baseline FE predictions of principal strains showed strong correlation (r2=0.824) with experimental measurements (Figure 3.9 A) and had a best-fit line that was not statistically different than y=x (Experimental Strains=FE Strains), (Table 3.3).

Coefficients of determination and y-intercept values were not statistically different than the subject-specific model for all sensitivity models analyzed (Table 3.3).

The sensitivity model with constant trabecular elastic modulus, representing the upper bound (456 MPa) of the inter-quartile range, was significantly stiffer (lower strains) than the subject-specific model (Figure 3.9 B) (Table 3.3). Although not statistically significant, models representing the median (164 MPa) and lower bound (45 MPa) of 81 trabecular elastic modulus were also stiffer than the subject-specific model (Figure 3.9

B), (Table 3.3).

Changes in the thickness of the cortical bone had a profound effect on cortical strains (Figure 3.9 C), for both ± 0.5, 1 SD (Table 3.3). Using a ratio of average sensitivities, cortical surface strains were approximately 10 times more sensitive to changes in cortical thickness than to alterations to trabecular bone elastic modulus (Table

3.3). The model with average cortical thickness predicted strains that were statistically similar to subject-specific model results (Table 3.3). FE predictions were significantly stiffer than the subject-specific model predictions when both average thickness and trabecular elastic modulus were used (Table 3.3). Changes to the cortical bone elastic modulus were significantly different than the subject-specific model for E=15.38 MPa but were not for E=18.62 MPa. However, values of the sensitivity parameter for the cortical bone modulus models were actually greater than those for changes to cortical thickness. This suggests that the pelvic FE model was very sensitive to changes in cortical bone modulus despite the fact that statistical significance was not obtained for both models. On average, FE predicted strains were 15 times more sensitive to alterations to the cortical bone elastic modulus than they were to changes in the trabecular bone elastic modulus. The remaining sensitivity models had best-fit lines that were not statistically different than the subject-specific model (Table 3.3). Sensitivity values for the remaining models were also comparable to those of the constant trabecular bone modulus, which suggests that FE predicted strains were not very sensitive to changes in cartilage modulus, cartilage thickness, cortical bone Poisson’s ratio, and trabecular bone 82

Poisson’s ratio (Table 3.3). The best-fit line for the overlap sensitivity model was nearly identical to the subject-specific model, which suggests that FE predicted surface strains were not sensitive to overlap between the cortical shell and trabecular tetrahedral element.

A) B)

5 MPa

0 MPa Anterior Oblique Medial Figure 3.8. Distribution of Von-Mises stress at 1 X body weight. A) anterior view, B) medial view. Areas of greatest stress were near the pubis-symphasis joint, superior acetabular rim, and on the ilium just superior to the acetabulum. 83

Figure 3.9. FE predicted vs. experimental cortical bone principal strains. A) subject- specific, B) constant trabecular modulus, C) constant cortical thickness. For the subject- specific model there was strong correlation between FE predicted strains with those that were measured experimentally with a best-fit line that did not differ significantly from the line y=x (Experimental strains=FE predicted strains). Changes to the trabecular modulus did not have as significant of an effect on the resulting cortical bone strains as did changes to cortical bone thickness. 84

Table 3.3. Results for all FE models including best-fit lines, r2 values and sensitivity parameters. Best-fit lines were generated in reference to experimentally measured values of strain. Lines with slopes significantly different than the subject-subject model are indicated (* p < 0.05, ** p< 0.01). All r2 values were not significantly different than the subject-specific model. Y intercepts for all lines shown were not significantly different from zero. Higher values of sensitivity indicate a greater sensitivity to alterations in the model input/parameter.

Model Type Value Best-Fit Line r2 Sensitivity Subject-Specific NA y = 1.015x + 4.709 0.824 NA Const. Cortical Thick. (mm) 1.41 y = 1.054x – 2.823 0.754 NA 1.66 y = 1.193x + 2.265* 0.732 0.743 1.17 y = 0.890x – 2.820* 0.770 0.914 1.90 y = 1.395x – 2.059** 0.728 0.931 0.92 y = 0.720x – 2.248** 0.789 0.911 Const. Trabecular E (MPa) 164 y = 1.142x + 7.094 0.833 NA 45 y = 1.059x + 5.371 0.841 0.100 456 y = 1.272x + 8.370** 0.810 0.064 Const. Thick. & E (mm, MPa) 1.41, 164 y = 1.204x + 2.559* 0.767 NA Cortical ν ν = 0.2 y = 0.956x + 9.460 0.764 0.187 ν = 0.39 y = 0.898x + 3.294 0.788 0.334 Trabecular ν ν =0.29 y = 1.013x + 4.507 0.824 0.005 Cortical E (GPa) 15.38 y = 0.840x + 6.670** 0.777 1.82 18.62 y = 1.107x + 4.622 0.821 0.951 Cartilage Thick. (mm) 0.0 y = 0.952x + 12.294 0.780 0.062 4.0 y = 1.072x + 5.590 0.841 0.056 Cartilage E (MPa) 1.36 y =1.015x + 4.711 0.824 0.001 7.79 y = 1.019x + 4.715 0.827 0.004 Overlap (MPa) Esuface nodes = 3829 y = 1.024x + 5.119 0.832 NA 85

DISCUSSION

The most accurate FE model predictions were obtained when position-dependent cortical thickness and elastic modulus were used. When constant cortical bone thickness and trabecular bone elastic modulus were used, the model was significantly stiffer than the subject-specific model, so our second hypothesis was accepted. However, FE predictions of cortical strains were not statistically different than predictions from the subject-specific model when an average cortical thickness was used. Cortical shell thicknesses at the locations of the strain gauges were very close to the average thickness for the pelvis, but showed less deviation (1.38 ± 0.27 mm (SD)). Since the sensitivity parameter showed that cortical bone strains were very sensitive to changes in cortical thickness (Table 3.3), this suggests that the similarity in results was most likely attributable to comparable thickness estimates (Figure 3.7).

Cortical bone was represented using 3-node shell elements. This choice was based on compatibility with the tetrahedral elements used for the trabecular bone and considerations of element accuracy. Tetrahedral elements were used for the trabecular bone because they allow automatic mesh generation based on Delaunay tesselation.

Thick shells (wedges) and pentahedral (prismatic) solid elements were considered for the cortex but were later rejected since they produced inaccurate predictions of tip deflection when modeling cantilever beam bending.

Since the geometry of the model was based on the outer cortical surface, with a shell reference surface positioned to align with the top of the cortical surface, there was an overlap between the shell and tetrahedral solid elements. In theory, this overlap could 86 produce inaccurate estimations of cortical surface strain. If this were the case then the sensitivity model that assigned the maximum trabecular elastic modulus to all surface tetrahedral nodes would have been stiffer than the subject-specific model. However, the results showed that this was not the case. To remove the overlap, a layer of thin shells could be placed at the interface between cortical and trabecular bone with thickness defined towards the outer cortex of the pelvis. However, this approach would not represent the surface topology of the pelvis as accurately as meshing the outer surface with tetrahedral elements. FE studies that aim to investigate the mechanics at the interface between cortical bone and trabecular bone should consider modeling the cortex without overlap.

Differences in boundary conditions, material properties and applied loading make it impossible to compare FE predictions of stresses and strains in this study with previous investigations. The peak values of Von-Mises stress in this study appear to be unrealistic since bone would degenerate under such high, repetitive stresses [44]. However, high stresses were confined to a very small area that represented the location of contact between the head of the prosthetic femur and acetabulum and were still well below published values for ultimate stress [44].

It is likely that a more physiological loading condition would generate better femoral head coverage and thus reduce the peak stresses at the contact interface. On average, the Von Mises stresses for cortical bone in the region of contact changed by

29% and 38% when cartilage thickness was reduced to 0 mm or increased to 4 mm, respectively. However, the slopes of the regression lines for these sensitivity models 87 were very similar to the subject-specific model (Table 3.3). Although cortical surface strains were not sensitive to cartilage thickness, the local stresses and strains could be highly dependent on cartilage material properties and thickness. Nevertheless, the average stresses for areas of strain gauge attachment, away from the applied load, were very similar to those reported by Dalstra et al [26]. The value for peak Von-Mises stress was also consistent with Schuller and co-workers who conducted a FE investigation to model single-leg stance in which peak values of Von-Mises stresses were as high as 50

MPa [45].

Early models of the pelvis were either simplified 2-D [46-48] or axisymmetric models [49,50]. Most three-dimensional FE models [26,45,51-56] used simplified pelvic geometry, average material properties and/or did not validate FE predictions of stress and strain. The work of Dalstra et al. was the first and only attempt to develop and validate a three-dimensional FE model of the pelvis using subject-specific geometry and material properties [26]. The FE model was validated using experimental measures of strain in the peri-acetabular region of a cadaveric pelvis, but subject-specific experimental measurements were not performed. Different cadaveric specimens were used for FE mesh generation and experimental tests. In fact, it was reported that the acetabulum of the experimental test sample was 45 mm whereas that of the specimen used for FE geometry and material properties was 62 mm [26]. Subject-specific FE strains were compared to models that assumed constant cortical thickness and elastic modulus. FE model accuracy was more dependent on cortical bone thickness than trabecular elastic modulus, although statistical tests were not performed to support this conclusion. The 88 effect of using average estimates was not investigated. Moreover, the effects of alterations in other bone and cartilage material properties were not investigated.

FE model predictions of cortical strain were relatively insensitive to most model inputs (except cortical thickness and modulus), but it is likely that FE strain predictions would change substantially if an idealized geometry was used rather than a faithful representation of the external geometry. Previously developed FE models of the pelvis have been based on coarse geometric representations. For example, Dalstra et al. hand- digitized 6 mm thick CT slices, which was ten times the thickness used in this study [26].

In this study, the small slice thickness and robust surface reconstruction techniques yielded a very accurate representation of the original geometry (Figure 3.6). The present approach allowed cortical bone thickness to be estimated without laborious hand digitization [26]. While it may be acceptable to model the pelvis with idealized geometry for some applications, it is absolutely crucial to use accurate pelvic morphology if the research objective is to study diseases in which geometry is abnormal such as pelvic dysplasia.

The relative importance of model input parameters will depend heavily on the FE model predictions that are of interest. For this study deviations to the trabecular elastic modulus only had a significant effect on cortical surface strains when the upper inter- quartile range of trabecular bone elastic modulus was assessed. However, one should refrain from concluding that a position-dependent trabecular modulus is not important since it was shown that the model that assumed average cortical thickness and trabecular modulus was not as accurate as the baseline model. In addition, results for position- 89 dependent thickness and constant trabecular modulus were stiffer than the subject- specific model, although the slopes were not significantly different over the entire inter- quartile range. Finally, FE predictions of overall model displacement were altered considerably when a constant trabecular modulus was used (data not shown). This change in model displacement did not result in significant deviations of strain for the cortex beneath the gauges but could have altered the surface strain at other locations.

Therefore, it is recommended that a position-dependent trabecular bone modulus be included to improve overall FE model accuracy.

Although the results of the sensitivity studies suggest that changes in material properties (except for under/over-estimation of cortical bone elastic modulus) were not likely to produce significant changes in cortical bone surface strains, it is likely that strains would be more sensitive to changes in the boundary conditions and applied loading conditions. For this reason, it was not the intent of this proof of concept study to replicate physiological loading conditions. The use of a well-defined experimental loading configuration allowed accurate replication of the loading conditions in the FE model. Future studies will investigate pelvic mechanics under physiological loading conditions using additional experimental data.

A limitation to this study was the fact that the contralateral hemipelvis was not incorporated in the FE model. Nodes along the pubis joint were constrained, but some deflection may have occurred at the pubis joint in the experiment. If this were the case, the strains near the pubis joint and along the ischium should have been much lower than other areas around the acetabular rim. However, strains were found to be greatest at the 90 pubis joint and ischium during the experimental study, which was then confirmed by the

FE results. If compression did occur at the pubis joint, it was probably minimal since deflection to this joint would act as an immediate strain relief to the pubis and ischium.

Palpation of the pubic cartilage demonstrated that the joint appeared to be an extension of the trabecular bone, which suggests that the joint was relatively stiff.

CT is notorious for overestimating the thickness of cortical bone. Measurement accuracy depends largely on the axial and longitudinal resolution of the acquisition matrix and CT scanner collimation. The accuracy also depends on the energy settings, pitch, and reconstruction algorithm. Prevrhal et al. determined that cortical bone thickness could be estimated within 10% for cortices that were equal to or greater than the minimum collimation of the CT scanner, which was approximately 0.7 mm for their scanner. Errors increased progressively for cortices that were less than the minimum collimation [37]. In the present study, a cortical bone phantom was used to assess the measurement limits of the CT scanner and segmentation procedure simultaneously.

Results demonstrated that cortical thickness could be measured down to approximately

0.7 mm thick with less than 10% error.

In conclusion, our approach for subject-specific FE modeling of the pelvis has the ability to predict cortical bone strains accurately during acetabular loading. Cortical bone strains were most sensitive to changes in cortical thickness and cortical bone elastic modulus. Deviations in other assumed and estimated input parameters had little effect on the predicted cortical strains. Our approach has the potential for application to individual patients based on volumetric CT scans. This will provide a means to examine 91 the biomechanics of the pelvis for cases when subject-specific geometry is important, such as in the case of pelvic dysplasia.

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FACTORS INFLUENCING CARTILAGE THICKNESS MEASUREMENTS

WITH MULTI-DETECTOR CT: A PHANTOM STUDY1

ABSTRACT

The purpose of this study was to prospectively assess in a phantom the accuracy and detection limits of cartilage thickness measurements from MDCT arthrography as a function of contrast agent concentration, imaging plane, spatial resolution, joint space and tube current, using known measurements as the reference standard. A phantom with nine chambers was manufactured. Each chamber had a nylon cylinder encased by sleeves of aluminum and polycarbonate to simulate trabecular bone, cortical bone, and cartilage.

Variations in simulated cartilage thickness and joint space were assessed. The phantom was scanned with and without contrast agent on three separate days, with chamber axes both perpendicular and parallel to the scanner axis. Images were reconstructed at intervals of both

1.0 and 0.5 mm. Contrast agent concentration and tube current were varied. Simulated cartilage thickness was determined from image segmentation. Root mean squared and mean

1 Reprint of article In Press: “Factors Influencing Cartilage Thickness Measurements with Multi-Detector CT: A Phantom Study”, Radiology. Anderson, A.E., Ellis, B.J., Peters, C.L., Weiss, J.A. Accepted February 16th 2007.

residual errors were used to characterize the measurements. CT scanner and image

segmentation reproducibility were determined. Simulated cartilage was accurately

reconstructed (<10% error) for thicknesses >1.0 mm when no contrast agent or a low

concentration of contrast agent (25%) was used. Errors grew as concentration of contrast agent increased. Decreasing the simulated joint space to 0.5 mm caused slight increases in error; below 0.5 mm errors grew exponentially. Measurements from anisotropic image data were less accurate than those for isotropic data. Altering tube current did not affect accuracy. This study establishes lower bounds for accuracy and repeatability of cartilage thickness measurement using MDCT arthrography, and provides data pertinent to choosing contrast agent concentration, joint spacing, scanning plane, and spatial

resolution to optimize accuracy. 99

INTRODUCTION

Three-dimensional reconstruction of volumes and surfaces from medical image data has become increasingly common, both for the diagnosis and treatment of patients with joint pathologies and to define patient-specific geometry for computational models and computer-assisted surgery. Of particular interest is the ability to visualize the spatially varying thickness of articular cartilage in diarthrodial joints, which may be useful for preoperative surgical planning (e.g. cartilage transfer procedures), precise quantification of cartilage loss due to osteoarthritis (epidemiological studies), tracking of cartilage degeneration over time, and providing guidelines for interpreting the results of biomechanical models which aim to investigate joint contact mechanics. With a-priori knowledge of the reconstruction error the clinician or researcher can make informed interpretations regarding cartilage thickness.

The advent and availability of multi-detector CT has yielded substantial advances over single detector CT by providing shorter data acquisition times, thinner beam collimation, multi-planar scanning and higher temporal and spatial resolution. Recent evidence suggests that multi-detector CT (MDCT) arthrography may be more sensitive than MRI for detecting cartilaginous lesions [1-5] and quantifying cartilage thickness [6], although fat-suppressed spoiled gradient-echo in the steady state (FS-SPGR) is still considered the best imaging protocol for imaging articular cartilage [7-16]. While a substantial body of research has examined MRI cartilage reconstruction errors (e.g. [17-

22]), less attention has been given to CT arthrography [6, 18, 23]. Nevertheless, estimates of cartilage thickness determined via MRI image data are often validated by 100 direct comparison with CT arthrography results [18, 19], which may erroneously imply that CT arthrography is the “reference standard” for such estimations.

Studies that have compared cartilage thickness measurements estimated from CT arthrography data to those obtained from physical measurements of anatomical sections have generally been qualitative assessments [18, 23]. To our knowledge only one study compared quantitative measurements of cartilage thickness between reconstructed MDCT arthrography images to excised tissue samples [6]. However, the use of harvested cartilage plugs in this study limited the range of cartilage thickness that could be analyzed

[6].

CT imaging and subsequent three-dimensional reconstruction of articular cartilage has a variety of clinical and basic science applications. Although CT arthrography is most often performed in an effort to diagnose articular cartilage damage rather than to quantify cartilage thickness, an understanding of the spatial variation in thickness of articular cartilage in joints without visible damage could prove to be a valuable clinical tool. For example, recent evidence suggests that cartilage may actually swell in the early stages of OA [24]. It would be useful, therefore, to quantify cartilage thickness using CT arthrography in patients who complain of pain that may be related to OA but do not have direct evidence of radiographic thinning or localized defects. From the point of view of experimental investigations of cartilage contact mechanics using cadaveric tissues, quantification of differences in reconstruction accuracy between standard CT and CT arthrography would clarify whether cadaveric joints should be completely dissected and imaged with air or if the joint capsule should be left intact to obtain the highest accuracy. 101

The bounds of cartilage thickness detection and hence the ultimate reconstruction error

remains unknown for MDCT arthrography. In addition, the influence of imaging parameters

on the ability to detect and reconstruct articular cartilage from MDCT arthrography image

data has not been assessed. Thus, the purpose of our study was To prospectively assess in a phantom the accuracy and detection limits of cartilage thickness measurements from

MDCT arthrography as a function of contrast agent concentration, imaging plane, spatial resolution, joint space and tube current, using known measurements as the reference standard.

102

MATERIALS AND METHODS

Phantom Description

An imaging phantom was designed and manufactured to quantify the error in reconstructing cartilage thickness (CNA Precision Machine, Ogden, UT) (Figure 4.1).

The phantom body was constructed using nylon (Natural Cast Nylon, Professional

Plastics Inc., Fullerton, CA). Nine chambers were drilled into the phantom body (Figure

4.1). Each chamber was composed of a central nylon cylinder encased by cylindrical sleeves of aluminum and polycarbonate (Standard Polycarbonate, Professional Plastics

Inc., Fullerton, CA). The central nylon cylinder simulated trabecular bone, the cylindrical sleeve of aluminum represented cortical bone, and the outer cylindrical sleeve simulated cartilage (Figure 4.1 B). All aluminum cylinders were machined to a wall thickness of 1.00 mm to represent cortical bone with constant thickness. The polycarbonate cylindrical sleeves were machined to wall thickness values of 0.25, 0.50,

0.75, 1.00, 2.00, and 4.00 mm (Phantom Chambers 1-6, Figure 4.1 A). An outer polycarbonate four-prong spacer was press-fit into each of the chambers between the outer layer of simulated cartilage and adjacent nylon phantom body (Figure 4.1 B). The spacer held the central cylinders securely in place and provided a “joint space” that could be filled with contrast agent. The joint space in phantom chambers 1-6 (Figure 4.1 A) was held constant at 2.0 mm. A varying joint space (0.25, 0.50, and 1.00 mm) with constant simulated cartilage thickness of 2.00 mm was used in the remaining three compartments (Phantom Chambers 7-9, Figure 4.1 A). Finally, nylon threaded caps were used to seal the fluid in the chambers. A micrometer with accuracy of ±0.01 mm was 103 used by the manufacturer to determine the wall thickness tolerance of the aluminum and polycarbonate cylindrical sleeves, representing cortical bone and cartilage, respectively.

The tolerance was reported to be within ± 0.07 mm.

Nylon, polycarbonate and aluminum were chosen because their x-ray attenuation values are similar to trabecular bone, cartilage and cortical bone, respectively [25-28].

The size of the phantom (250 x 250 mm) was representative of a typical field of view

(FOV) for imaging human diarthrodial joints. The outer diameter of each compartment

(outer boundary of simulated cartilage) was kept constant at 52 mm while the diameter of the aluminum sleeve and central nylon cylinder were adjusted between 38–46 mm to accommodate differences in cartilage thickness and joint spacing. This range of cylinder diameters is similar to that reported in the literature for human femoral and humeral heads [29-31]. The range of cartilage thickness (0.25–4.00 mm) was chosen to represent the range reported in the literature for human articular cartilage [32, 33].

104

1 2 3

A) 4 5 6

7 8 9

2 3 B) 4 1

6 5

C) 2 3

6 4 5

Figure 4.1. A) schematic of phantom used to assess accuracy and detection limits of MDCT in the transverse plane. The longitudinal (L) imaging plane is also shown. Simulated cartilage thicknesses of 4.0, 2.0, 1.0, 0.75, 0.5, and 0.25 mm with constant joint space of 2.0 mm were used in chambers 1-6, respectively. A constant thickness of 2.0 mm with joint spaces of 1.0, 0.5, and 0.25 mm were used in chambers 7-9, respectively. B) exploded view of chamber #1 detailing: (1) nylon center cylinder to represent trabecular bone, (2) 1 mm thick aluminum sleeve to represent cortical bone, (3) polycarbonate sleeve to represent cartilage, (4) joint space, (5) polycarbonate four- pronged spacer for creating the joint space, and (6) bulk of the phantom body made using nylon. C) CT scan of the phantom with contrast agent and inset showing image details of chamber #1. Number call-outs correspond to the same details provided above. 105

CT Imaging Protocol

All phantom scans were performed with a Siemens SOMATOM® Sensation 64

CT Scanner (Siemens Medical Solutions USA, Malvern, PA). This scanner makes use of a periodic motion of the focal spot in the longitudinal direction to double the number of simultaneously acquired slices with the goal of attaining improved spatial resolution and elimination of spiral artifacts regardless of spiral pitch. Constant scanning parameters for this study were: 120 kVp, 512 x 512 matrix, 300 mm FOV, and 1 mm slice thickness. A total of 6 fluid scans and 4 non-enhanced scans were performed. The imaging protocol detailed below was performed on three separate days to assess the reproducibility of the

CT scanner and segmentation procedure.

Contrast Enhanced Scans

Contrast agent (Omnipaque 350 mgI/ML, GE Healthcare, Princeton, NJ) was mixed with 1% lidocaine HCL (Hospira Inc., Lake Forest, IL) in separate concentrations

of 25, 50, and 75%. The phantom was scanned using a tube current of 200 mAs for each

of the three concentrations (n = 3 scans) in the “transverse” or frontal plane (Figure 4.1

A). The laser guide was used to align the CT slice axis perpendicular to the phantom

chambers longitudinal axes, thereby minimizing volumetric averaging between slices.

Additional transverse scans were conducted with tube currents of 150 and 250 mAs using

the phantom filled with 50% contrast agent (n = 2 scans). A scan with tube current of

200 mAs was performed on the phantom filled with 50% contrast agent parallel to the

phantom chambers “longitudinal” axes (Figure 4.1 A) to intentionally introduce volumetric averaging. 106

Non-Enhanced Scans

The phantom was scanned without fluid to estimate the error in cartilage thickness

reconstruction for disarticulated, dissected cadaveric joints. Non-enhanced scans were

performed in the transverse plane using tube currents of 150, 200, and 250 mAs (n = 3

scans). A final non-enhanced scan was performed with a tube current of 200 mAs

parallel to the phantom chambers longitudinal axes to intentionally introduce volumetric

averaging between successive slices.

Image Segmentation, Surface Reconstruction, and Measurement of Thickness

Phantom image data were transferred to a Linux workstation for post-processing.

Image data were re-sampled post-CT using 0.5 mm slice intervals for the contrast

enhanced and non-enhanced longitudinal scans to assess changes in accuracy between an anisotropic spatial resolution (0.586 x 1.0 x 0.586 mm) and near isotropic resolution

(0.586 x 0.5 x 0.586 mm). Thinner post-scan reconstructions in the transverse plane would have been ambiguous since the curvature of the phantom chambers did not change as slices were taken through this direction.

Separate splines for the outer surface of the aluminum cylinder, representing cortical bone, and the boundary between the polycarbonate cylinder and air (non- enhanced scan) or contrast agent (enhanced scan), representing the outer layer of simulated cartilage, were extracted from the image data. Both automatic and semi- automatic thresholding techniques were employed using commercial segmentation software (Amira 4.1, Mercury Computer Systems, Chelmsford, MA). 107

Each dataset was automatically thresholded using a masking technique available in Amira 4.1, which allows the user to highlight pixels over a range of defined intensities.

For datasets with contrast agent included, the mask was adjusted incrementally until all of the pixels representing nylon (the bulk of the phantom body) were excluded. Thus, pixels with intensities greater than this value were masked as contrast agent and simulated cortical bone whereas values less were defined as simulated cartilage. The same masking procedure was used for the non-enhanced scan datasets to define the simulated cortical bone boundary; however, the boundary between simulated cartilage and air was defined by reversing the mask such that all pixels representing the nylon body of the phantom were included. As mentioned above, the masking procedure was performed for each CT dataset separately to ensure that the appropriate threshold range was chosen independently of alterations in tube current, contrast agent concentration, spatial resolution or scanner direction. Following masking of all of the datasets it was later determined that inter-scan threshold values varied by less than 5%.

Due to CT volumetric averaging it was necessary to utilize a semi-automatic thresholding technique for datasets where contrast agent was included. However, this procedure was only required for phantom chambers with simulated cartilage thickness of

0.5 and 0.25 mm (chambers 5 and 6, Figure 4.1 A); simulated cartilage thicker than this was effectively segmented by the automatic method, regardless of contrast agent concentration, tube current, spatial resolution or scanner direction. For the 0.5 and 0.25 mm chambers the baseline automatic threshold value was first used to define a general segmentation spline. Next, regions where pixels blended together were separated using a 108 paintbrush tool available in Amira 4.1 such that the resulting spline followed the general boundary between simulated cartilage and contrast agent. Although volumetric averaging was present, the intensity gradient between contrast agent and simulated cartilage was strong enough to allow for easy visual separation. To ensure uniformity, all of the semi-automatic segmentations were performed by the senior author, A.E.A.

Splines were stacked upon one another and triangulated using the Marching

Cubes algorithm [34] to form surfaces that represented the outer surfaces of simulated cortical bone and cartilage. To preserve the native splines of the CT image data, the resulting polygonal surfaces were not altered via decimation or smoothing. A published algorithm was used to assign thickness to each of the nodes defining the simulated cartilage surface [35]. The algorithm has been tested for accuracy using concentric cylinders with known thickness. Reported errors were less than 2% [35].

109

Error Analysis

Thickness values were analyzed to determine the accuracy and detection limit of

MDCT and to investigate the influence of tube current, joint spacing, contrast agent concentration, and imaging plane. The overall thickness accuracy for each phantom chamber was assessed using the root mean squared (RMS) error criteria:

n 12 ⎡ CT Phantom 2 ⎤ RMS = ⎢∑()tti − n⎥ , (4.1) ⎣ i=1 ⎦

where the summation is over the number of surface nodes n and tPhantom is a constant thickness that was assessed by direct manufacturer measurement of the phantom. The mean residual error was calculated to determine the directionality of the error:

n CT Phantom Mean Residual = ∑()tti − n. (4.2) i=1

Statistical Analysis

Descriptive statistics (i.e., quantification of means and standard deviations that cannot ascertain statistical significance) were calculated using statistical software (SPSS

11.5 for Windows 2002, SPSS Inc. Chicago, IL). Specifically, RMS and mean residual errors were averaged for the three days that CT scans were conducted. The resulting means were plotted (SigmaPlot 8.0, Systat Software Inc., San Jose, CA) with standard deviation error bars to indicate the inter-scan variation in reconstruction accuracy.

110

RESULTS

Contrast Enhanced Scans

There were notable differences in the average RMS and mean residual error due to alterations in contrast agent concentration (Figure 4.2). The simulated cartilage of the phantom was accurately reconstructed (less than 10% RMS and mean residual error) for thickness greater than 1.0 mm when the lowest concentration of contrast agent (25%) was used and the direction of the CT scan was transverse to the phantom (Figure 4.2).

Transverse scan RMS errors grew progressively as the concentration was increased from

25% – 75% for values of thickness greater than 0.75 mm (Figure 4.2 A). An increase in contrast agent concentration resulted in a greater tendency for simulated cartilage to be underestimated for values between 1.0 and 4.0 mm thick (Figure 4.2 B). However, a shift in error from under to overestimation occurred as the thickness approached the spatial resolution of the image data (0.586 x 0.586 mm) (Figure 4.2 B).

Substantial differences in average reconstruction errors were also noted when the scanner direction and spatial resolution were altered (Figure 4.3). The anisotropic longitudinal reconstructions at 50% concentration produced RMS and mean residual errors greater than the corresponding transverse and near-isotropic longitudinal dataset at

50% concentration for simulated cartilage thicker than 1.0 mm (Figure 4.3). Finally, altering the tube current resulted in negligible differences over the range of simulated cartilage thickness analyzed (data not shown).

111

140 25% 50% 120 75%

100 60

50 A)

0 Root Mean Squared Error (% of true thickness) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 True Thickness (mm)

120 25% 100 50% 75% 80

50 40 B) 30 20 10 0 -10

Mean Residual Error (% of true thickness) -20

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 True Thickness (mm)

Figure 4.2. Simulated cartilage RMS (A) and mean residual (B) reconstruction errors for the transverse contrast enhanced scan datasets as a function of contrast agent concentration. RMS errors grew progressively as the contrast agent concentration increased (for thickness > 0.75 mm). The directionality of the error was dependent on the contrast agent concentration and simulated cartilage thickness. 112

120 Transverse 50% 110 Longitudinal 50% 100 Longitdinal Isotropic 50% 90 80

(% of true thickness) 70

60 50 40 30 20 10 0 Root Mean Squared Error 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 True Thickness (mm)

100 50% 90 Longitudinal 50% 80 Longitudinal Isotropic 50% 70 60

of true thickness) 50 40 B) 30 20 10 0 -10 -20 Mean Residual Error (% Residual Mean -30 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 True Thickness (mm)

Figure 4.3. Simulated cartilage RMS (A) and mean residual (B) reconstruction errors for the transverse contrast enhanced scan datasets at 50% concentration as a function of imaging plane direction and spatial resolution. Errors were greatest for the anisotropic longitudinal data reconstructions. The longitudinal isotropic reconstructions yielded errors more consistent with the transverse scan results. 113

There were differences in RMS errors over the range of joint spaces studied due to changes in contrast agent concentration and scanner direction (Figure 4.4) but not due to alterations in tube current (data not shown). Errors increased as the concentration of contrast agent was increased (Figure 4.4). RMS errors for each individual transverse scan increased slightly when the joint space was decreased from 2.0 – 0.5 mm; however, below 0.5 mm errors grew exponentially (Figure 4.4). The anisotropic longitudinal dataset (1.0 mm reconstruction) produced greater RMS errors than the corresponding transverse and near-isotropic longitudinal scan datasets (0.5 mm reconstruction) over the full range of joint spaces analyzed (Figure 4.4). Mean residual error analysis indicated that simulated cartilage thickness was underestimated for all datasets and that these errors were the smallest for the transverse 25% scan (data not shown).

Examination of the standard deviation error bars in Figures 4.2 – 4.4 indicated a high level of reproducibility for simulated cartilage between 0.78 – 4.0 mm thick. The standard deviation error bars also did not overlap adjacent results within this range.

Standard deviations were much larger for simulated cartilage 0.25 – 0.5 mm thick and error bars overlapped adjacent data points.

114

35 Transverse 25% Transverse 50% Transverse 75% 30 Longitudinal 50% Longitudinal Isotropic 50% 25 (% of true thickness) (% of 20

0 Root Mean Squared Error 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 True Joint Space(mm) Figure 4.4. Simulated cartilage RMS errors as a function of joint space thickness, contrast agent concentration, imaging plane direction, and spatial resolution. Errors increased as contrast agent concentration increased. Reconstructions from the isotropic longitudinal dataset were more accurate than the anisotropic dataset in the same imaging plane. 115

Non-Enhanced Scans

Reconstructions of the non-enhanced transverse scan at 200 mAs resulted in RMS errors less than 10% for thickness values greater than 1.0 mm (Figure 4.5 A). RMS errors for the non-enhanced scans were within 2% of those reported for the contrast enhanced transverse scans at 25% contrast agent concentration for simulated cartilage

0.78 – 4.0 mm thick. RMS errors grew exponentially for simulated cartilage less than 1.0 mm thick; however, the RMS error leveled out between 0.5 – 0.25 mm (Figure 4.5 A).

The leveling point in the RMS plot aligned well with corresponding points of inflection on the mean residual error plot (Figure 4.5 B). Therefore, the lack of increase in RMS error at 0.25 mm was due to a shift from an underestimation to overestimation of cartilage thickness. RMS errors for the longitudinal and near-isotropic longitudinal scan datasets were similar to the transverse scan for 2.0 and 4.0 mm thick simulated cartilage; however errors grew exponentially below 2.0 mm (Figure 4.5 A). Errors for the longitudinal anisotropic scan were substantially greater than the transverse and near- isotropic longitudinal scans for simulated cartilage less than 2.0 mm thick (Figure 4.5 A).

Altering the tube current from 150 – 250 mAs did not have an appreciable effect on the

RMS or mean residual errors in the transverse plane (data not shown).

As with the contrast enhanced scans, standard deviation error bars of the non- enhanced scans were negligible for thicker simulated cartilage (0.78 – 4.0 mm thick) but increased when thickness was decreased below this range. Standard deviation error bars also did not overlap at adjacent data points within this range but did for thicknesses less than 0.78 mm. 116

160 Transverse 140 Longitudinal Longitudinal Isotropic 120

60 A) 50

0 Root Mean Squared Error (% of true thickness) true (% of Error Squared Mean Root 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 True Thickness (mm)

140 Transverse 120 Longitudinal Longitudinal Isotropic 100

50 40 B) 30 20 10 0 -10

Mean Residual Error (% of true thickness) true (% of Error Residual Mean -20

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 True Thickness (mm)

Figure 4.5. Simulated cartilage RMS (A) and mean residual (B) reconstruction errors for the non-enhanced scan datasets at 200 mAs as a function of imaging plane direction and spatial resolution. RMS errors for the longitudinal isotropic datasets were consistently less than the anisotropic dataset for simulated cartilage less than 2.0 mm thick. 117

DISCUSSION

To our knowledge our study is the first quantify the detection limits and accuracy of MDCT using a phantom. The simulated cartilage of the phantom was accurately reconstructed (less than 10% RMS and mean residual error) for thicknesses greater than

1.0 mm when either no contrast agent or a low concentration of contrast agent (25%) was used. The results of our study also demonstrated that the accuracy of CT cartilage reconstructions were dependent on the concentration of contrast agent, imaging plane direction, spatial resolution and to a lesser extent, joint spacing. Alterations in the scanner tube current did not affect the accuracy of simulated cartilage thickness reconstructions in the range tested for both contrast enhanced and non-enhanced scans.

Care was taken to control confounding factors in our study. The physical thickness of the phantom was measured to a tolerance of ± 0.07 mm, thus variations in the true thickness of the phantom would not have a substantial influence on the perceived values of phantom thickness as assessed by CT. In addition, separate scans were done whenever a new intervention (e.g. scan direction, tube voltage, and contrast agent concentration) was performed in an effort to isolate these effects. The entire protocol was repeated on separate days and only minor inter-scan variation was noted for simulated cartilage between 0.78 – 4.0 mm for both contrast enhanced and non-enhanced scans. Therefore, any differences noted in reconstruction error within this range were due to the intervention studied rather than from confounding factors such as thresholding procedure or CT scanner variability. 118

The results of the contrast enhanced scan reconstructions showed a direct relationship between contrast agent concentration and reconstruction error. An explanation for this finding is as follows: as the concentration was increased larger pixel intensity gradients were established at the boundary between cartilage and contrast agent.

This initiated more intense volumetric averaging at this boundary and resulted in a greater tendency for cartilage thickness to be underestimated. However, a shift in error from under to overestimation occurred as the thickness approached the spatial resolution of the image data (0.586 x 0.586 mm). This was due to the fact that thickness could not drop much below the width of a single pixel without extensive surface decimation and smoothing. Therefore, although CT has been shown to overestimate the thickness of thin structures [25, 26], the results of our study demonstrate that the direction of the error is dependent on the concentration of the joint fluid and spatial resolution of the image data when CT arthrography is used.

El-Khoury et al. [6] compared ankle cartilage measurements obtained from

MDCT double-contrast arthrography and three-dimensional FS-SPGR MRI to physical measurements of excised plugs from cadaveric ankles (ranging from 1 – 2 mm thick) and found that CT was more accurate than MRI. Differences in segmentation methodology, joint geometry, and arthrography technique (double contrast) between this study and our work make exact comparisons impossible. Nevertheless, El-Khoury’s best-fit line of physical plug measurements plotted against MDCT estimates indicated that CT underestimated cartilage thickness by approximately 5% [6], which has the same 119 direction and similar magnitude of error as the 25% concentration agent results of our study over the same range of thickness.

Study Limitations

The results of our study must be interpreted in light of the inherent differences between measurements obtained from a phantom to those taken from experimental studies that use real cartilage specimens. It is well known that articular cartilage exhibits depth and location dependent inhomogeneities in material structure [36-38], and these factors were not part of our study design. In addition, although similar [25-28], small differences will exist between x-ray attenuation values of real tissue to that of the materials used in our phantom. Finally, diarthrodial joints such as the shoulder and hip have spherical geometry but the phantom chambers were cylindrical. Nevertheless, our approach allowed us to eliminate potential confounding factors such as geometry, tissue homogeneity, and measurement technique. In addition, a total of three scans were performed and descriptive statistics utilized to assess reproducibility, which was a statistical methodology consistent with a phantom study related to MRI slice thickness

[39].

For chambers with simulated thicknesses of 0.25 and 0.5 mm it was necessary to use a semi-automatic method to segment simulated cartilage from the contrast enhanced scan datasets. Reconstruction errors from these chambers could have been influenced by user technique. However, the magnitude of the standard deviation error bars for thicknesses within this range were very similar to the non-enhanced scan deviation bars, and a purely automatic segmentation technique was used for the latter datasets. The 120 standard deviations for simulated cartilage less than 0.78 thick were substantial for both contrast enhanced and non-enhanced scans, with bars overlapping adjacent data points; therefore, it appears that there is little difference between contrast enhanced and non- enhanced scans for the thinnest phantom chambers.

The phantom was designed to simulate the interface between cartilage and cortical bone. There was likely some image thinning of polycarbonate due to volumetric averaging between the polycarbonate and adjacent aluminum cylindrical sleeve; however the wall thickness of aluminum was held constant for each phantom cylinder and the thresholding protocol was not biased to changes between phantom chambers or whole datasets. Thus, any errors introduced would be consistent over all datasets, which would eliminate simulated cortical bone as a confounding factor to our study.

Practical Applications

The results of our study provide minimum bounds for the errors in cartilage thickness measurement using MDCT and provide guidelines for practical use. It must be emphasized that the phantom reconstruction errors are likely a best case result since confounding factors were controlled. A lower concentration of contrast agent is likely to reduce the amount of volumetric averaging between cartilage and contrast agent since it was shown that higher concentrations caused the simulated cartilage to appear thinner than its true thickness. In addition, joint spacing should be maximized prior to scanning, which can be done by completely filling the joint capsule with the diluted contrast solution and/or applying traction to the joint. Failure to do so will result in increased errors when the joint space reaches a critical threshold (occurring at 0.5 mm in our 121 phantom study). Finally, CT image reconstructions should be chosen such that isotropic or near-isotropic spatial resolutions are achieved. Fortunately, MDCT (unlike its predecessors) offers the ability to do this without increased radiation dosage to the patient

[40].

From a basic science point of the view the following conclusion can be made: assuming that sufficient joint space is maintained and a low contrast agent concentration is used, one could expect similar cartilage reconstruction accuracies when cadaveric tissues are CT scanned with or without contrast agent since reconstruction errors were similar between non-enhanced and contrast enhanced scan (25% concentration) datasets.

However, given the additional technical challenges of keeping joint fluid within the capsule of a dissected joint, it seems more appropriate to scan the specimen without contrast agent.

In conclusion, the accuracy of MDCT with and without arthrography is dependent on several factors including the contrast agent concentration, joint spacing, imaging plane, and spatial resolution. An improved understanding of the detection limits and accuracy of MDCT cartilage reconstructions will assist in the diagnosis of joint pathologies, interpretation of biomechanical models, and design of epidemiological studies aimed to investigate changes in cartilage thickness.

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[38] Shepherd, D. E., and Seedhom, B. B., 1999, "The 'instantaneous' compressive modulus of human articular cartilage in joints of the lower limb," Rheumatology (Oxford), 38(2), pp. 124-132.

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[40] Hsieh, J., 2003, "Image artifacts: appearances, causes and corrections.," Computed Tomography: principles, design, artifacts, and recent advances, SPIE Press, Bellingham, WA, pp. 167-240.

CHAPTER 5

VALIDATION OF FINITE ELEMENT PREDICTIONS

OF CARTILAGE CONTACT PRESSURE

IN THE HUMAN HIP JOINT

ABSTRACT

Methods to predict contact stresses can provide an improved understanding of load distribution in the normal and pathologic hip. The objectives of this study were to develop and validate a three-dimensional finite element (FE) model for predicting cartilage contact stresses in the human hip using subject-specific geometry from computed tomography image data, and to assess the sensitivity of model predictions to boundary conditions, cartilage geometry, and cartilage material properties. Loads based on in vivo data were applied to a cadaveric hip joint to simulate walking, descending

stairs, and stair-climbing. Contact pressures and areas were measured using pressure

sensitive film. CT image data were segmented and discretized into FE meshes of bone and cartilage. FE boundary and loading conditions mimicked the experimental testing.

Fair to good qualitative correspondence was obtained between FE predictions and experimental measurements for simulated walking and descending stairs, while excellent agreement was obtained for stair-climbing. Experimental peak pressures, average pressures, and contact areas were 10.0 MPa (limit of film detection), 4.4-5.0 MPa and 127

321.9-425.1 mm2, respectively, while FE predicted peak pressures, average pressures and contact areas were 10.8-12.7 MPa, 5.1-6.2 MPa and 304.2-366.1 mm2, respectively.

Misalignment errors, determined as the difference in root mean squared error before and after alignment of FE results, were less than 10%. Magnitude errors, determined as the residual error following alignment, were approximately 30% but decreased to 10-15% when the regions of highest pressure were compared. Alterations to the cartilage shear modulus, bulk modulus, or thickness resulted in ±25% change in peak pressures, while changes in average pressures and contact areas were minor (±10%). When the pelvis and proximal femur were represented as rigid, there were large changes, but the effect depended on the particular loading scenario. Overall, the subject-specific FE predictions compared favorably with pressure film measurements and were in good agreement with published experimental data. The validated modeling framework provides a foundation for development of patient-specific FE models to investigate the mechanics of normal and pathological hips. 128

INTRODUCTION

It is estimated that 3 percent of all adults over the age of 30 in the United States have osteoarthritis (OA) of the hip [1], causing pain, loss of mobility and often leading to the need for total hip arthroplasty. Considerable clinical, epidemiological, and experimental evidence supports the concept that mechanical factors play a major role in the development and progression of OA [2-5]. For example, it has been demonstrated that a combination of duration and magnitude of contact pressures and shear stresses on the acetabular and femoral cartilage of hips with acetabular dysplasia can predict the onset of OA [6,7].

The ability to evaluate hip joint contact mechanics on a patient-specific basis could lead to improvements in the diagnosis and treatment of hip OA. To this end, both experimental and computational approaches have been developed to measure and predict hip contact mechanics (e.g. [6,8-14]). Experimental studies have been based on either in vitro loading of cadaveric specimens [8,10,13,14] or in vivo loading using instrumented femoral prostheses implanted into live patients [11,15-17]. While in vitro experimental studies have provided baseline values of hip joint contact pressure, testing protocols are inherently invasive, mechanical data are limited to the measurement area, and specific joint pathologies cannot be readily studied. The use of instrumented prostheses represents the current state of the art for experimental study of in vivo hip mechanics

[11,15-17]. However, the method is highly invasive and existing data are from older patients who have already been treated for advanced OA. There are no experimental methods available to assess hip contact mechanics noninvasively on a patient-specific basis. 129

Computational modeling is an attractive alternative to experimental testing since

it is currently the only method that has the potential to predict joint contact mechanics

noninvasively. Prior computational approaches have included the discrete element

analysis (DEA) technique [18-20] and the finite element (FE) method [9,12,21]. These

models have proven useful in the context of parametric or phenomenological

investigations. However, their ability to accurately predict patient-specific contact

mechanics is questionable due to over-simplification of joint geometry and an absence of

model validation.

Before computational models can be applied to the study of patient-specific hip

joint contact mechanics, it is necessary to demonstrate that the chosen modeling strategy

can produce accurate predictions and to quantify the sensitivity of model predictions to

variations in known and unknown model inputs [22]. The objectives of this study were:

1) to develop and validate a finite element (FE) model of hip joint contact mechanics

using experimental measurements of cartilage contact pressure under physiological loading, and 2) to assess model sensitivity to several measured and assumed model

inputs.

130

METHODS

A combined experimental and computational protocol was used to develop and

validate a subject-specific FE model of a 25 y/o male cadaveric hip joint (body weight =

82 kg). The joint was screened for osteoarthritis and the cartilage was determined to be

in excellent condition (Tonnis Grade 0) [23].

Experimental Protocol

All soft tissue with the exception of articular cartilage was removed. The

acetabular labrum was dissected free from cartilage. Kinematic blocks were attached to

the femur and pelvis for spatial registration between FE and experimental coordinate

systems [24]. The blocks were used to define anatomical axes for referencing joint

loading angles using Bergmann’s coordinate system definition [15,16]. A volumetric CT

scan of the hip was obtained (512 x 512 acquisition matrix, 320 mm field of view, in

plane resolution = 0.625 X 0.625 mm, 0.6 mm slice thickness) using a Marconi MX8000

CT scanner (Phillips Medical Systems, Bothell, WA). The femur was dislocated from the acetabulum to ensure separation between the acetabular and femoral cartilage in the image data. A solid bone mineral density phantom (BMD-UHA, Kyoto Kagaku Co.,

Kyoto, Japan) was included to correlate CT voxel intensities with calcium equivalent bone density [25,26]. The aforementioned scanner settings produce thickness errors of less than 10% for simulated cartilage [27,28] and bone [25] when geometry is at least 1.0 and 0.75 mm thick, respectively.

Experimental loading was based on published data for in vivo hip loads [15,16].

Bergmann et al. reported hip joint anatomical orientations (flexion, abduction, rotation) and equivalent hip joint forces (magnitude and direction) during routine daily activities 131

for 4 patients with instrumented femoral prostheses [15,16]. Data for the average patient were used in the present study to simulate walking, stair-climbing and descending stairs.

A custom loading apparatus was developed to apply the kinematics that corresponded to these loading conditions (Figure 5.1).

The iliac crests of the pelvis were cemented into a mounting pan in neutral anatomical orientation (anterior iliac spine in plane with plane of pubis symphysis,

[15,16]) and attached to a lockable rotation frame (Figure 5.1 A). The frame was flexed and abducted relative to the vertical axis of the actuator to simulate the orientation of the equivalent hip joint force vector for each loading scenario. The femur was potted and attached to a lockable ball joint (Figure 5.1 B). Three-dimensional orientation of the joint was achieved by flexing, abducting and rotating the femur relative to the pelvis.

Equivalent joint reaction force angle and anatomical orientation were confirmed by digitizing the loading fixture surfaces (joint force) and planes of the kinematic blocks

(anatomical orientation) using a Microscribe-3DX digitizer (Immersion Corp., San Jose,

CA) with a measured positional accuracy of ±0.085 mm [29]. The digitized points were fit to planes, and angles between the planes were calculated. The orientation of the pelvis and femur fixtures were adjusted until the direction of the joint reaction force vector and anatomical orientation angles were within ± 1° of those reported by Bergmann’s average subject.

Pressure sensitive film (Sensor Products Inc., Madison, NJ) was used to measure joint contact pressures. Pilot testing demonstrated that low sensitivity range film (1.7-10

MPa) was best suited for measuring pressures produced during applied loading. Prior to dissection, different film sizes were cut into a rosette pattern using a knife plotter. The 132 rosette that maximized contact area and minimized overlap was chosen (Figure 5.1 C).

Small notches were cut in the anterior, posterior, and medial aspects of the rosette to reference the location of contact pressures relative to the hip joint.

A) B) C)

Load Cell Pelvis Ball Joint Mounting Femur Pan Pot

Locks

Figure 5.1. Experimental setup for loading of hip joint. A) schematic of lockable rotation frame and cement pan used to constrain and orient the pelvis relative to the actuator plane. B) femur pot attached to a lockable ball and socket joint. C) pressure sensitive film, cut into a rosette pattern, on the surface of the femoral cartilage. Polyethylene sheets were used to keep the pressure film dry. 133

Peak loads for each activity were simulated by displacing the femur into the acetabulum at a constant rate. For each activity, the rate of actuator displacement was adjusted until peak loads were achieved within 0.33 sec, representative of the time required by the average subject reported by Bergmann et al [15,16]. Three to four cycles of preconditioning were necessary to obtain the correct displacement rate. The pressure film was then attached to the head of femur between sheets of polyethylene. Planes of the kinematic blocks were digitized to establish an experimental coordinate system in neutral orientation. The femur was then displaced into the acetabulum until the target load was achieved. The actuator was returned to its starting position at the same displacement. The three notches on the film were digitized. The specimen was allowed to recover between trials for over 100 times the interval that was needed to reach peak load. The entire protocol was repeated 3 times for each loading scenario. The films were stored in a dark location for 48 hours following testing [30] and then scanned and converted to digital grayscale images. An independent calibration curve was established to relate pixel intensity to pressure [31].

Computational Protocol

Commercial software was used to segment surfaces of the cortical bone, trabecular bone, cartilage and kinematic blocks in the CT image data (Amira 4.1,

Mercury Computer Systems, Boston, MA). Splines representing the outer surface of cortical bone were obtained from automatically thresholded images [25]. Cartilage was segmented from air using a threshold value that was found to achieve the greatest accuracy for reconstructing simulated cartilage in a phantom based imaging study

[27,28]. The boundary between trabecular and cortical bone was segmented both 134 automatically and semi-automatically. When cortical and trabecular bone blended together in the image data they were manually separated.

Triangular surfaces were generated for each structure using the Marching Cubes algorithm [32]. The outer cortical surface facets were decimated to a density consistent with our previous study [25]. Cartilage surfaces were decimated and smoothed slightly to remove visible triangular irregularities and segmentation artifact. The triangular surface mesh for cortical bone was converted to a quadratic 3-node shell element mesh [25,33-

35]. Position dependent shell thickness was assigned to each node, based on the distance between adjacent trabecular bone boundary nodes [25]. The resulting pelvis and femur cortical meshes consisted of 13,562, and 4,196 elements, respectively (Figure 5.2), representative of the mesh density that has been shown to produce accurate predictions of cortical bone strains in prior pelvic FE modeling [25]. The interiors of the cortical shell meshes were filled with tetrahedral elements to represent trabecular bone of the femur and pelvis [25]. The final pelvis and femur trabecular bone tetrahedral meshes consisted of 227,108 and 82,176 elements, respectively, which were densities consistent with prior pelvic FE modeling [25].

Acetabular and femoral cartilage surfaces were imported into FE preprocessing software (TrueGrid, XYZ Scientific, Livermore, CA) and hexahedral element meshes were created. Convergence studies were performed by increasing the number of elements through the thickness incrementally while the overall aspect ratios were held constant by adjusting the in-plane mesh resolution. The meshes for acetabular and femoral cartilage were considered converged if there was less than a 5% change in contact area, peak pressure and average pressure between subsequent meshes. 135

A) B)

Figure 5.2. A) finite element mesh of the entire hip joint in the walking kinematic position. B) close-up at the acetabulum. Triangular shell elements indicate cortical bone. Cartilage was represented with a hexahedral element mesh, with three elements through the thickness.

Cartilage was represented as an incompressible, neo-Hookean hyperelastic

material [36] with shear modulus G=6.8 MPa [37]. Incompressibility was enforced using the augmented Lagrangian method [38]. Cortical bone was represented as hypoelastic, homogenous, and isotropic with elastic modulus E=17 GPa and Poisson’s ratio ν=0.29

[39]. Trabecular bone was represented as isotropic hypoelastic with ν=0.20 [26]. An

average elastic modulus was calculated for each tetrahedral element using empirical

relationships from the literature [25,26] and the BoneMat software [40]. Overlap

between the shell and tetrahedral solid elements [25] was accounted for by assigning an

elastic modulus of 0 MPa to all tetrahedral elements that shared nodes with shell

elements.

To establish the neutral kinematic position of each loading scenario, the FE model

was transformed from the CT coordinate system to the appropriate experimental 136

reference system [24]. Nodes superior to the pelvis cement line, those residing within the

sacroiliac (SI) and pubis joint, and those inferior to the cement line of the potted femur

were defined rigid according to anatomical boundaries determined experimentally. The

rigid femur nodes were constrained to move only in the direction of applied load, while the nodes at the pubis, SI and cement line were fully constrained. The Mortar method was used to tie acetabular and femoral cartilage to the acetabulum and femoral head, respectively [41,42]. Contact between the femoral and acetabular cartilage was enforced using the penalty method [43]. All analyses were performed using NIKE3D [43].

Sensitivity Studies

Sensitivity studies were performed to investigate how changes in assumed cartilage material properties, thickness and FE model boundary conditions affected predictions of cartilage contact mechanics. The baseline cartilage shear modulus was altered by ± 1 SD (G=10.45 and 2.68 MPa) using standard deviations for human cartilage

[44]. To ascertain the effects of the assumption of cartilage incompressibility, bulk to shear modulus ratios of 100:1 (ν=0.495) and 10:1 (ν=0.452) were analyzed. To account

for differences in segmentation threshold intensity between real and simulated cartilage

[27,28], the baseline threshold value used to segment cartilage was adjusted by ± 50%.

Updated cartilage FE hexahedral meshes were generated based on these surfaces. To quantify the affects of model boundary conditions, three separate cases were analyzed: 1) bones were assumed rigid, 2) the rigid constraint at the pubis joint was removed, and 3) trabecular bone was removed so that deformation of only the cortical bone was considered. Separate models were generated for each loading activity, yielding a total of

27 models. 137

Data Analysis

A program was developed to compare FE predicted cartilage contact pressures with results from pressure sensitive film. The program allowed for the investigation of two types of error: 1) misalignment between FE and experimental results, and 2)

differences in the magnitude of contact. First, the program converted the grayscale

images of pressure to fringed color using the calibration curve. Next, FE pressure

predictions were transformed into a synthetic film image with the same dimensions,

including rosette cuts, as the pressure films. Surface nodes of the femur cartilage FE

mesh were fit to a sphere and then flattened by a spherical-to-rectilinear coordinate

transformation. The synthetic image was aligned with the pressure film image using the experimentally digitized notches on the pressure film. The rosette cuts on the experimental film were duplicated in the synthetic FE pressure film image by moving the

FE pressure results circumferentially, according to the wedge angle of the rosette.

Separate synthetic FE images were created and aligned for each experimental image since the pressure films were not placed in the exact same anatomical position between loading trials. Finally, a difference image between each synthetic and experimental image was created.

A root mean squared (RMS) error criterion was used to assess the degree of similarity by comparing pixel intensity values between FE and experimental images.

Only those pixel intensities within a user specified range were compared. This range was taken as the full sensing range of the film (1.7-10 MPa) but was also determined for

smaller 2 MPa bins of pressure to assess the ability of the FE models to predict pressures

within specific ranges. Further constraints were made in the calculation of RMS error 138

because, in this study, the experimental film data were considered the “truth”.

Specifically, if a pixel in the synthetic FE image indicated a pressure within the specified range but the corresponding experimental film pixel did not, then the pixel was not included in the calculation. However, if an experimental pixel was within the range but its corresponding FE pixel was not, then the pixel was included.

Misalignment error was also distinguished from magnitude error. Misalignment error could occur due to fitting the FE mesh to a sphere, from inaccurate digitization of the notches used to align the results, or from FE model inaccuracies. Misalignment error was quantified independently by calculating the RMS error real time while the synthetic

FE image was rigidly rotated about a spherical coordinate system. The rotations required to minimize RMS error, along with the re-calculated anterior, posterior, and lateral positions of the notches were recorded. Misalignment error was then expressed as the difference in pre and post alignment RMS error whereas magnitude error was taken as the post alignment error.

Peak pressure, average pressure, contact area, and center of pressure were calculated for each experimental film and synthetic FE image after the synthetic FE films were aligned with experimental images to minimize RMS error. FE peak pressure was determined by recording the maximum FE pressure value within the region of experimentally measured contact. Experimental peak pressures were calculated as the maximum experimental film pixel intensity. Pixel intensities that indicated pressures within the film range (1.7-10 MPa) were used to determine FE and experimental average pressures. Contact area was calculated by multiplying the number of pixels within the detectable pressure range of the film by the area of each pixel (0.0154 mm2). The center 139

of pressure (COP) was found by determining the center of the image, which was

weighted according to pixel intensity. The difference in the centers of pressure between images (FE synthetic film COP - experimental film COP) was expressed as the anatomical difference in anterior/posterior and medial/lateral positions over the detectable range of the film.

Similar analyses were performed for the sensitivity studies. First, a baseline image was created for each baseline FE model from which subsequent sensitivity study predictions were compared. RMS errors were calculated per above. Changes in peak and average pressure, and contact areas were calculated per the methodology discussed above, but a larger pressure range was used (0.5 - 10 MPa) since the pressure range was no longer limited by the film. For the cartilage sensitivity studies, percent changes in peak pressure, average pressure and contact area were reported as combined results from the three loading scenarios analyzed. For the boundary condition sensitivity studies, results were reported as percent changes with respect to each loading scenario.

140

RESULTS

FE Mesh Characteristics

Cortical bone thickness in the pelvis and femur averaged 1.8±0.8 and 2.9±2.3

mm, respectively. The resulting trabecular bone modulus in the pelvis and femur

averaged 270±188 and 295±198 MPa, respectively. Three elements through the cartilage

thickness were necessary to yield converged FE predictions. The final mesh for acetabular and femoral cartilage consisted of 15,000 and 23,415 elements, respectively

(Figure 5.2). Cartilage thickness in the acetabular and femoral cartilage meshes was

1.6±0.4 and 1.5±0.5 mm, respectively as estimated using the cortical bone thickness

algorithm [25] (Figure 5.3). The final FE model was composed of ~400k elements

(Figure 5.2), and each analysis took on the order of 2 hours of wall clock time.

2.0 mm

0.8 mm

Figure 5.3. Contours of cartilage thickness. Femoral and acetabular cartilage was thickest in the anterormedial and superior regions, respectively.

141

Peak Pressure, Average Pressure, Contact Area

Experimental pressures ranged from 1.7-10.0 MPa (range of film detection). All pressure films recorded pressures at the upper limit of film detection (10 MPa).

However, less than 5% of the total pixels fell into this category. FE predictions of peak

pressure were 10.78, 12.73 and 11.61 MPa for walking, descending stairs and stair-

climbing, respectively. Experimental average pressure and contact area ranged from 4.4-

5.0 MPa and 321.9-425.1 mm2, respectively, while FE predicted average pressure and

contact area ranged from 5.1-6.2 MPa and 304.2-366.1 mm2, respectively (Figure 5.4).

8 500 Average FE Pressure Average Exp. Pressure 450 7 Average FE Contact Area Average Exp. Contact Area

400 Area (mm Contact Average 6 350 5 300

4 250

200 3 150 Average Pressure (MPa) 2

2 ) 100 1 50

0 0 Walking Descending Stairs Stair-Climbing

Figure 5.4. FE predicted and experimentally measured average pressure (left y-axis) and contact area (right y-axis). FE models tended to overestimate average pressure and to underestimate contact area during simulated walking and descending stairs. There was excellent agreement between FE predictions and experimental measurements for stair- climbing. Error bars indicate standard deviation. 142

Contact Patterns

The experimental pressure recordings revealed bi-centric patterns of contact

during simulated walking and descending stairs and a more or less mono-centric pattern

during simulated stair-climbing (Figure 5.5 top row). Experimental pressure distributions

were similar during simulated walking and descending stairs, with a horseshoe shaped bi-

centric contact pattern directed anterorlaterally to posterormedially. As the femur was

rotated internally during simulated stair-climbing the contact pattern was oriented in a

lateral to medial direction (Figure 5.5 top row). Overall, the magnitude and location of

FE predicted contact pressures corresponded well with experimental measures. However, experimental bi-centric contact patterns during simulated walking and descending stairs were not predicted by the FE models (Figure 5.5 middle row).

Patterns of FE-predicted contact varied with the loading activity (Figure 5.6 B).

The majority of contact occurred along the lateral aspect of the acetabulum for all three loading activities (Figure 5.6 bottom row). The contact area moved from anterior to

posterior as the resultant load vector changed from shallow extension during descending

stairs to more moderate flexion angles during walking and stair-climbing (Figure 5.6

bottom row).

143

Walking Descending Stairs Stair-Climbing Posterior

10 MPa Experimental Medial FE Lateral

0 MPa Difference Difference

Figure 5.5. Top row - experimental film contact pressures (representative results are shown). Bi-centric patterns of contact were observed during simulated walking and descending stairs, while a mono-centric pattern was observed during stair-climbing. Middle row - FE synthetic films. Models predicted mono-centric, irregularly shaped patterns of contact. Bottom row - difference images, indicating locations where contact was not predicted by the models. The best qualitative correspondence was during stair- climbing. Note: FE synthetic films and difference images are shown prior to manual alignment with experimental results. 144

Walking Descending Stairs Stair-Climbing 8 MPa

Superior-Anterior View

0 MPa Oblique Lateral View

Figure 5.6. FE predicted contact pressures on the femur (top) and acetabulum (bottom). Acetabular cartilage contact pressures moved from anterior to posterior as the equivalent joint reaction force vector changed from shallow extension during descending stairs to deep flexion during stair-climbing. The highest contact pressures primarily occurred near the lateral region of the acetabulum. 145

Misalignment and Magnitude Errors

Difference images, calculated prior to manual alignment between FE synthetic

and experimental films, further clarified the degree of qualitative agreement between FE synthetic and experimental films (Figure 5.5 bottom row). Differences in contact pressure were greatest for descending stairs and were least during stair-climbing (Figure

5.5 bottom row). Overall, misalignment errors were less than 7% (Table 5.1). The rotations and resulting translations of the experimental film fiducials required to minimize RMS errors were less than 3° and 5 mm for walking and stair-climbing but were substantially higher for the descending stairs case (22° and 9 mm) (Table 5.1).

Following manual alignment, residual RMS errors were on the order of 30%. As suggested by the difference images, errors were greatest for descending stairs and least for stair-climbing (Figure 5.5 bottom row). When RMS error was plotted in 2 MPa pressure bins, RMS errors decreased to around 10-15% at the maximum bound of pressure analyzed (8-10 MPa). This finding indicates that FE models were best suited for predicting the higher stressed regions of cartilage, corroborating the good qualitative correspondence between FE synthetic and experimental films in these locations (Figure

5.5).

Differences in center of pressure locations, as calculated over the entire film detection range, were less than 10 mm (Table 5.2). The smallest difference in the COP occurred for stair-climbing, while the largest difference occurred during descending stairs. In general, COPs for the FE models were directed more lateral (-) and anterior (+) to experimentally measured COPs.

146

Table 5.1. FE misalignment and magnitude errors. Misalignment error was calculated as the reduction in total RMS error after the synthetic films were manually rotated to minimize RMS error between FE and experimental films. Magnitude error was the residual error following alignment. The rotations required to align results and associated changes in the positions of the film fiducials are shown.

Misalignment RMS Magnitude RMS Rot X (°) Rot Z (°) ∆ Position Error (%) (±SD) Error (%) (±SD) (±SD) (±SD) mm (±SD) Walking 0.24 (0.11) 32.03 (0.26) 2.37 (1.00) -0.77 (0.38) 2.26 (2.22) Descending Stairs 6.59 (2.58) 33.75 (2.90) 1.60 (1.13) -22.55 (1.06) 9.31 (0.34) Stair-Climbing 2.49 (2.51) 26.74 (0.14) 3.05 (6.86) 2.65 (7.70) 4.73 (0.00)

Table 5.2. Differences in centers of pressure between synthetic FE and experimental films (negative = lateral/posterior, positive = medial/anterior).

Center of Pressure Difference (mm) Medial/Lateral (±SD) Anterior/Posterior (±SD) Walking -6.88 (1.34) 7.22 (1.39) Descending Stairs -7.92 (0.32) 8.09 (0.86) Stair-Climbing 0.14 (0.196) 3.08 (0.93) 147

Sensitivity Studies - Cartilage Material Properties and Thickness

Changes of ±50% to the shear modulus resulted in approximately a ±30% change in FE predictions of peak pressures, while changes in average pressure and contact area were around ±10% (Figure 5.7 A). Lowering the cartilage Poisson’s ratio from ν=0.5 to

ν=0.495 did not have an appreciable effect (Figure 5.7 B). However, a further decrease in the Poisson’s ratio to 0.452 resulted in a 25% decrease in peak pressures, while changes in average pressure and contact area were less than 10% (Figure 5.7 B). Altering the thickness of femoral and acetabular cartilage (~ 10% change average cartilage thickness) resulted in less than a ±10% change in FE predictions (Figure 5.7 C). RMS differences between baseline and all cartilage sensitivity study results were approximately 6.5%, indicating that the spatial distributions and magnitudes of contact pressure did not change substantially.

148

A) B) 40 0

30 -5 20 +1S -1SD -10 10 -15 0 100:1 -20 -10 Percent Change Percent Percent Change Percent -25 -20 10:1 Peak Pressure -30 Peak Pressure -30 Average Pressure Average Pressure Contact Area Shear Modulus Contact Area Bulk:Shear -40 -35

C) 10 8 +50 -50% 6 % 4 2 0 -2

Percent Change -4 -6 Peak Pressure -8 Average Pressure Cartilage Thickness -10 Contact Area

Figure 5.7. Percent changes in peak pressure, average pressure and contact area due to alterations in cartilage material properties and geometry. A) effects of changes to the shear modulus by ±1 SD. B) effects of changes to cartilage compressibility (100:1, 10:1 bulk to shear ratios). C) effects of altering the cartilage thickness. Error bars indicate standard deviations over the three loading activities analyzed. 149

Sensitivity Studies - FE Boundary Conditions

Rigid bone models decreased computation times from ~2 hours to <10 minutes.

Representing the bones as rigid structures affected both the magnitude (Figure 5.8 A) and spatial distribution (Figure 5.9) of cartilage contact pressure, but the degree of effect depended on the loading activity. RMS differences in synthetic films between baseline and rigid bone models averaged 29.2±5.5%. FE predictions of peak pressure, average pressure and contact area were altered but also varied according to the loading scenario analyzed (Figure 5.8 A). When the rigid constraint on the pubis joint was removed, FE predictions changed on the order of -15 to +5% (Figure 5.8 B). Finally, when the trabecular bone was removed, i.e. only the cortical shells supported the cartilage, changes in FE predictions ranged from -25 to +5% (Figure 5.8 C). Average RMS differences between baseline results and the latter boundary condition sensitivity studies were only

3.1%.

150

A) B) 120 5 Peak Pressure 100 Average Pressure WDSSC Contact Area 80 0 60

40 -5 20

0 Change Percent Percent Change W DS SC -10 -20 Peak Pressure -40 Average Pressure Rigid Bones Contact Area Pubis Joint Free -60 -15

C) 10 WDSSC 5

-5

-10

-15 Percent Change -20 Peak Pressure -25 Average Pressure Contact Area Trabecular Bone Removed -30

Figure 5.8. Percent changes in peak pressure, average pressure and contact area due to alterations in boundary conditions. A) effects of a rigid bone material assumption. B) effects of removing the pubis joint constraint. C) effects of removing the trabecular bone from the FE analysis. W, DS, SC indicate walking, descending stairs, and stair-climbing, respectively. 151

Walking Descending Stairs Stair-Climbing

Posterior 10 MPa Medial Baseline FE Lateral id g Ri 0 MPa Anterior

Figure 5.9. Contours of cartilage contact pressure predicted by the baseline (top row) and rigid bone FE models (bottom row) for the three loading activities. The largest effect of the rigid bone assumption occurred for simulated walking and descending stairs. 152

DISCUSSION

To our knowledge this is the first study to validate FE predictions of cartilage contact pressure with experimental measurements in the human hip joint. The FE model provided very reasonable predictions of both the spatial distribution and magnitude of cartilage contact pressure under the simulated loading conditions. Excellent predictions were obtained for simulated stair-climbing. The posterior aspect of the bi-centric experimental contact pattern was not predicted by the FE model for walking and descending stairs. Nevertheless, the magnitude of pressure in these locations was low in comparison to the anterior region where the FE models provided more reasonable correspondence.

Small manual rotations of the pressure film were necessary to minimize RMS errors for simulated walking and stair-climbing. In contrast, the descending stairs case required a substantial amount of manual rotation (Table 1). It is likely that the majority of misalignment error was due to the method of digitizing the film fiducials during the experiment. It was necessary to move the linear actuator up by ~20 mm to access the film markers. It was assumed that this displacement resulted in a perfect vertical translation for purposes of defining the marker coordinates, but when the coordinates were plotted relative to the translated model they did not reside on the surface of the cartilage. This offset was minor during walking and stair-climbing but was greater during descending stairs. The femur was in extension for this loading activity and when the translation was applied, the femoral neck would have contacted the edge of the acetabulum, resulting in an offset of the film marker coordinates. Contact in this location 153

would not have occurred with the hip in moderate and deep flexion during walking and

stair-climbing.

The finding that RMS magnitude errors decreased when the bounds of pressure

were increased suggest that the models were best suited for predicting localized “hot

spots”. Therefore, the modeling strategies developed herein may be well suited for

predicting the primary region of contact, which may be sufficient for many patient-

specific modeling applications.

FE predictions of average pressure and contact area were not overly sensitive to

changes in the cartilage shear modulus, bulk modulus or thickness (±10%). However,

greater changes in peak pressure were noted (up to ~25%). This finding demonstrates

that peak pressure prediction requires more accurate model inputs for cartilage geometry

and material properties than for average pressure prediction.

Computational models of the hip have often represented bones as rigid structures

[12,45], which is an attractive simplification because solution times are greatly reduced.

The present study demonstrated that the assumption of rigid bones can alter predictions

of cartilage contact stresses in the hip. The effect is modulated by the specific boundary

and loading conditions in the model. Because the consequence of the rigid bone

assumption cannot be assessed without a direct comparison to the case of deformable bones, investigators should use caution when representing the bones as rigid for modeling cartilage contact mechanics in the human hip.

Although the contralateral pelvis was left intact in the experimental study, the FE models assumed that the pubis joint was rigid. The results of the sensitivity study that removed the pubis constraint demonstrated only minor differences in FE predicted 154 cartilage contact mechanics, thereby giving credence to this model assumption. While this simplification was warranted for the current study, it may not be appropriate for models where load is directed more medially (e.g. simulations of side-impact loading

[46]).

Since the reported elastic modulus of trabecular bone is orders of magnitude less than cortical bone, we investigated whether or not trabecular bone needed to be represented in the models. The results of the sensitivity study suggest that it plays little mechanical role with regard to cartilage contact stresses. Therefore, for patient-specific modeling applications it may be appropriate to exclude trabecular bone assuming that similar boundary and loading conditions are assigned.

Experimental studies have used pressure sensitive film to measure hip joint contact pressures under similar loading conditions [8,13,14]. Peak pressures measured by von Eisenhart-Rothe et al. [13] ranged from 7 MPa at 50% body weight to 9 MPa at

300% body weight, in fair agreement with the results of the current study. Bi-centric, horseshoe shaped patterns extended from the anterior to posterior aspect of the femur were noted [13]. Afoke et al. [8] measured peak pressures on the order of 10 MPa at

350% body weight and the anterorsuperior surface of the cartilage was identified as an area of high pressure [8]. It is worth mentioning that all of the aforementioned studies predicted irregular, non-symmetric pressure distributions [8,13,14].

Large differences in material properties, geometry and boundary conditions make it impossible to directly compare the FE predictions from this study with prior modeling studies, but some general trends can be identified. Nearly all FE hip joint modeling studies to date have used two-dimensional, plane strain models [9,12,21,45] with either 155 rigid [12,45] or deformable bones [9,21]. To our knowledge, the earliest FE contact model was reported by Brown and DiGioia [9]. In this study, FE predicted pressures were irregularly distributed over the surface of the femoral head. Values of peak pressure were on the order of 4 MPa at loads representative of those applied in the current study.

Rapperport et al. [21] developed a similar model that predicted peak pressures on the order of 5 MPa at 1000 N of load. Using rigid bone models resulted in predictions only slightly different than the deformable bone model.

Macirowski et al. [12] used a combined experimental/analytical approach to model fluid flow and matrix stresses in a biphasic contact model of a cadaveric acetabulum. This is the only previous FE study to explicitly model the acetabular cartilage thickness. The acetabulum was step loaded to 900 N using an instrumented femoral prosthesis, yielding peak contact pressures on the order of 5 MPa. When the experimentally measured total surface stress was applied to the FE model, average predicted pressures (solid stress + fluid pressures) were approximately 1.75 MPa. The lower range of pressure used to determine average pressures was not specified, making it impossible to directly compare average results. However, scaling the applied load of our model to 900 N and assuming a lower bound of 0.3 MPa to calculate average pressure

(lowest pressure isobar indicated by Macirowski et al.) yields average pressures of

2.47±0.29 MPa over the three loading scenarios analyzed, which is in good agreement with Macirowski et al’s predictions.

Yoshida et al. [20] developed a dynamic DEA model to investigate the distribution of hip joint contact pressures using the Bergmann gait data. The model assumed spherical geometry and concentric articulation. Qualitatively our predictions of 156

primary contact during simulated walking, descending stairs, and stair-climbing are in

good agreement with the results of this study, but the spatial distributions of contact were

markedly different. Peak pressures during walking, descending stairs, and stair-climbing

were substantially less than those predicted in the current study (3.26, 3.77, 5.71 MPa,

respectively).

With the exception of the study by Macirowski et al., the FE models developed

herein predicted higher contact pressures than previous FE and DEA studies. This

discrepancy is most likely due to the assumptions of spherical geometry and concentric

articulation in the prior computational studies. Although the literature suggests that

normal hips may be modeled as spherical structures with concentric articulation [19,47],

the hip joint is not spherical and cartilage thickness is nonuniform [12,48,49]. The aforementioned computational models assumed a cartilage modulus ranging from 10-15

MPa [9,21] yet cartilage was given a baseline modulus of ~40 MPa (G=6.8 MPa) in the current study. While one might expect that a higher modulus would result in higher contact pressures, the results of our sensitivity studies demonstrate that this is not the case, as changes in the cartilage shear modulus of ±50% resulted in only a ±25% and

±10% change in peak and average contact pressures, respectively. Even with a 25% reduction, peak pressures predicted in this study were still nearly double those reported previously [9,18-20].

Several limitations of the current study must be mentioned. First, experimental loads were based on average in vivo data from older patients who had already undergone treatment for advanced hip OA. Given the large inter-patient variation in joint kinematics observed by Bergmann et al. [15,16] the use of average data loading data likely did not 157

accurately represent the actual kinematics for the specimen in this study. Our approach is

justified since the objective of the experimental protocol was to apply realistic loading

and boundary conditions that could be reproduced in the FE simulations for model

validation. A limitation of film pressure measurement is that the technique records a

“high watermark” rather than measurements of time-loading history [50,51]. However,

film measurements have been shown to be equivalent to the contact stresses resulting

from an incompressible elastic analysis [52], making the use of pressure film appropriate

in the current study. Results from the pressure measurements indicate that contact occurred beyond the perimeter of the film during simulated walking and descending stairs. While it would be desirable to capture the entire region of contact, it was not feasible to do so using larger rosettes as they caused excessive overlap and crinkle artifact during pilot testing.

The acetabular labrum was removed in this study, yet it has been suggested that the labrum helps to maintain fluid pressurization in the hip [45,53]. The labrum was removed because its material properties are unknown, making its inclusion a potential confounding factor. It is possible that leaving the labrum intact would have altered the experimentally measured and computationally predicted contact pressures [45,53].

Although actions of individual muscles were not considered, the equivalent joint reaction force was based on in vivo data [15,16]. The primary focus of the present research was to quantify cartilage contact pressures in the peri-acetabular region rather than bone stresses in areas where muscles were attached. Therefore, we could justifiably model the action of all muscles as a single equivalent force vector acting through the hip joint. 158

Although cartilage exhibits biphasic material behavior [54], it was represented as incompressible hyperelastic in this study. In vitro studies suggest that fluid flow is minimal during fast loading [12,53], making our assumption of incompressibility warranted given the loading rates used in the experiments. We recently demonstrated the equivalence between biphasic and incompressible hyperelastic FE predictions during instantaneous loading [55]. Cartilage also exhibits depth dependent material properties

[56], variation in stiffness over its surface [44,57] and tension-compression nonlinearity

[58]. Incorporating these aspects might have resulted in different, perhaps better, predictions of contact stress magnitude and distribution. Future modeling efforts should investigate the importance of these effects via sensitivity studies.

In conclusion, our approach for subject-specific FE modeling of the hip joint produced very reasonable predictions of cartilage contact pressures and areas when compared directly to pressure film measurements. Predictions were in good agreement with other experimental studies that used pressure film, piezoelectric sensors and instrumented prostheses [8,12-14,59,60]. The sensitivity studies established the modeling inputs and assumptions that are important for predicting contact pressures. The validated FE modeling procedures developed in this study provide the basis for the future analysis of patient-specific FE models of hip cartilage mechanics.

159

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CHAPTER 6

PATIENT-SPECIFIC FINITE ELEMENT MODELING:

PROOF OF CONCEPT

ABSTRACT

Acetabular dysplasia may be the leading cause of premature osteoarthritis (OA) of

the hip [1-6]. However, the relationship between geometric alterations to the acetabular

geometry [7,8] and cartilage [9,10] associated with dysplasia and the resulting cartilage

biomechanics are poorly understood. The objectives of this study were to demonstrate

the feasibility of patient-specific finite element (FE) modeling by investigating

differences in cartilage biomechanics between a normal and dysplastic hip joint and to

assess the sensitivity of model predictions to changes in joint loading. Institutional

review board approval was obtained to perform CT arthrography under fluoroscopic control. Computed tomography (CT) image data were segmented and meshed using a previously validated protocol [11-13]. Model loading was based on in-vivo data from the literature and simulated conditions of walking, stair-climbing, and descending stairs

[14,15]. Cartilage stresses were substantially elevated in the dysplastic joint. Mean cartilage peak pressures, average pressures, and shear stresses in the dysplastic joint were

28.4, 6.7, and 6.6 MPa, respectively whereas the normal model predicted values of 18.6, 166

3.6, and 3.8 MPa, respectively. Surprisingly, contact areas in the dysplastic hip joint (976.1 - 1143.3mm2) were greater than those predicted in the normal joint (512.3 -

579.6 mm2). The results from this proof of concept study suggest that patients with dysplasia may have altered cartilage biomechanics, providing the motivation for efforts to analyze a population of subjects.

167

INTRODUCTION

Several studies have shown that mild developmental dysplasia may indeed be the leading cause of osteoarthritis in the hip [2-6,16]. Wilson and Poss [6] found deformity of the acetabulum in 25-35% of adult cases of hip OA. Harris et al. [2] estimated that

40% of patients with hip OA have some type of untreated hip dysplasia. Aronson [1] and

Bombelli et al. [17,18] estimate that as many as 76% of patients with hip OA have some type of untreated acetabular dysplasia. In contrast to these reports, other studies have failed to find a statistically significant relationship between acetabular dysplasia and the risk of hip OA [19-24]. The discrepancies in the literature motivate the need for an improved understanding of the biomechanics of the dysplastic hip.

It is believed that the biomechanics of the hip plays an important role in the development of osteoarthritis in the dysplastic joint [2,16,25-27]. Subluxation

(incomplete dislocation) caused by dysplasia of the hip joint is a primary cause of degenerative joint disease and clinical disability [25]. It is believed that subluxation leads to increased stresses across the articulating surface each time the hip is loaded during gait

[17,18]. Consequently, it is thought that altered biomechanics causes cartilage and bone of the hip to degenerate prematurely, leading to early hip osteoarthritis. Differences in joint biomechanics between normal and dysplastic hips may have important implications for predicting the development and progression of hip OA and for developing treatment strategies, but few attempts have been made to quantify these differences.

Mathematical and computational models are an attractive methodology for studying hip dysplasia since they may have the ability to non-invasively predict joint 168

mechanics on a patient-specific basis. A handful of analytical and computational studies

have inferred cartilage contact pressures in dysplastic hips as a means to differentiate

their mechanical environment [27-29]. Analytical studies use simplified mathematical

statics calculations based on 2-D geometry, bodyweight, and estimated muscles forces to

solve for equivalent joint reaction forces, contact pressures, and contact area [27-29].

Although analytical studies further support the notion of pathological biomechanics and

in particular increased contact stresses in the dysplastic hip, they neglect several

important aspects. These studies used idealized geometry to represent all or part of the hip articulation, neglecting the issues of regional and patient-specific congruency between the femoral and acetabular cartilage layers.

Unlike analytical approaches, computational models have the ability to predict joint mechanics using calculations that are based on three-dimensional geometry. This is a significant advantage since hip dysplasia is a three-dimensional pathology [30,31].

Rigid body spring models (RBSM) and the finite element (FE) method have been applied to illustrate mechanical differences between normal and dysplastic joints [32,33]. Most models have made simplifying assumptions regarding model geometry and have utilized modeling protocols that have not been validated. However, prior to patient-specific modeling it is necessary to demonstrate that the chosen computational protocol produces accurate models [34].

The objectives of this study were to demonstrate the feasibility of patient-specific finite element (FE) modeling by investigating differences in cartilage biomechanics between a normal and dysplastic hip joint and to assess the sensitivity of model 169

predictions to changes in joint loading. Patient-specific FE models were constructed and analyzed using a protocol that has been subjected to extensive validation [11-13].

170

METHODS

Subject Selection

Approval to recruit and image subjects for CT arthrography was obtained from the University of Utah Institutional Review Board. Informed consent was obtained from a patient with dysplasia and a normal control subject. The pathological hip was from a

35 y/o female patient (body weight = 149 lbs.) who had been diagnosed with an excessively anteverted hip. The normal control was a 27 y/o male (BW = 147 lbs) with no history of dysplasia or hip pain. The traditionally dysplastic patient had a center edge angle [25] of 0°, acetabular angle of Sharp [25] of 47°, and pre-operative Harris Hip

Score [2,25] of 57. A Tonnis grade of 1 was assigned to this patient (increased sclerosis of the head and acetabulum and slight lipping at the joint margins [35]). There was no evidence of visible joint narrowing in the pre-operative radiograph.

CT Arthrography

CT arthrography was performed to enable detection of cartilage layers in the image data. The pathologic joint (left hip) was injected for the subject with dysplasia whereas a random assignment was made for the normal control subject (left hip). An 18- gauge needle was inserted into the hip joint capsule under fluoroscopic control. A solution consisting of equal parts of contrast agent (Omnipaque, Nycomed Amersham,

Princeton, NJ) and 1% Lidocaine (Hospira Inc., Lake Forest, IL) was injected into each hip joint capsule. A small amount of epinephrine (0.1 ml) was included to keep the fluid within the capsule. Approximately 20 ml of solution was injected into each subject’s hip 171 capsule. Following injection the subject was transferred to the CT scanner via a wheelchair to limit joint loading and associated fluid loss.

Immediately prior to scanning the joint was passively flexed, abducted, and rotated to ensure that the articulating surfaces of cartilage were coated with contrast agent

[36]. A Siemans Somatom 64 CT (Siemens Medical Solutions USA, Malvern, PA) scanner was used to acquire volumetric CT data of each subject’s pelvis and proximal femur in a supine position (120 kVp, 250 mAs, 512 x 512 matrix, FOV = 300 mm, 1 mm slices, 0.586 x 0.586 x 1.0 mm voxel resolution, ~400 slices). The scan started at the superior iliac crest on the pelvis and ended at the superior third of the femur.

Image Data Analysis and Segmentation

DICOM images were transferred to a Linux workstation for post-processing. The data were re-sampled at 0.5 mm slice thicknesses to achieve a near isotropic voxel resolution (0.586 x 0.585 x 0.5 mm), which has been shown to produce more accurate reconstructions of cartilage thickness than anisotropic resolutions [12]. Separate splines representing the outer layer of cartilage, outer cortex, and boundary between cortical and trabecular bone were automatically and semi-automatically segmented using commercial software (Amira 4.1, Mercury Computer Systems, Chelmsford, MA.) Pixel threshold values assigned to bone were based on our previous modeling efforts [34]. Cartilage boundaries were delineated using a threshold value from a phantom-based imaging study of cartilage [12]. In most regions bone and cartilage could be segmented automatically.

However, some regions demonstrated volumetric averaging, requiring semi-automatic segmentation. Manual segmentation tools available in Amira were used to further define 172

boundaries in these regions. Although volumetric averaging was present, the boundaries

between tissue structures could be easily discerned by visual inspection.

Triangular surfaces were generated for each structure using the Marching Cubes

algorithm [37]. The outer cortical bone surface facets were decimated to a density

consistent with our previous study [11,34]. Cartilage surfaces were decimated and smoothed slightly to remove visible triangular irregularities and segmentation artifact

[11].

FE Mesh Generation, Cartilage Thickness, Material Properties

The triangular surface mesh for cortical bone was converted to a quadratic 3-node shell element mesh [11,34,38,39]. Position dependent shell thickness was assigned to each node, based on the distance between adjacent trabecular bone boundary nodes [34].

Acetabular and femoral cartilage surfaces were imported into FE preprocessing software

(TrueGrid, XYZ Scientific, Livermore, CA) and hexahedral element meshes were created

[11]. Cartilage thickness for the acetabular and femoral cartilage mesh geometries was also assessed using the cortical bone thickness algorithm [34]. The final normal and dysplastic hip joint FE meshes (Figure 6.1) had densities consistent with our prior hip joint FE modeling studies [11,34].

Trabecular bone was neglected in this study as we previously demonstrated that it has little effect on the prediction of cartilage contact pressures and cortical bone strains

[11,34]. Cartilage was represented as an incompressible, neo-Hookean hyperelastic

material [40] with shear modulus G=6.8 MPa [41]. Incompressibility was enforced using the augmented Lagrangian method [42]. Cortical bone was represented as hypoelastic, 173 homogenous, and isotropic with elastic modulus E=17 GPa and Poisson’s ratio ν=0.29

[43].

Figure 6.1. Patient-specific FE meshes of normal (top) and dysplastic (bottom) hip joints. Insets show details of FE discretization. Note lack of anterior femoral head coverage and incongruence in the dysplastic hip. 174

FE Boundary and Loading Conditions

Stair-climbing, walking, and descending stairs were simulated using average in-

vivo instrumented prostheses gait data [14,15]. These data describe both the anatomical

orientation of the hip as well as the magnitude and direction of the equivalent joint

reaction force vector throughout the gait cycle. Data at peak loading for each scenario

(~2.5 times bodyweight) were used to drive the FE simulations.

The CT coordinate axes of each subject’s FE mesh were transformed into an

embedded joint coordinate system that used the convention described by Bergmann

[14,15]. Specifically, the Xp axis originates at the center of a vector passing through the

center of the left and right femoral heads and is aligned along that vector, while the Zp axis is aligned upwards, passing through the center of the L5-S1 vertebral body. The Yp axis is perpendicular to Xp and Zp and points in the ventral direction.

The femur was flexed, abducted, and rotated relative to the pelvis so that 3D kinematic alignment was identical to that for Bergmann’s average subject. Next, the entire hip joint was flexed and abducted so that a vertically directed force in the Z-axis would result in the correct equivalent joint reaction force vector for Bergmann’s average subject [11,14,15]. Reaction force data were scaled based on patient body weight.

Nodes residing within the sacroiliac (SI) and pubis joint and those at the base of the proximal femur diaphysis were defined as rigid [11,34]. The rigid nodes at the base of the proximal femur were constrained to move only in the direction of applied load, while the nodes at the pubis and SI joints were fully constrained [11,34]. The Mortar method was used to tie acetabular and femoral cartilage to the acetabulum and femoral 175 head, respectively [44,45]. Contact between the femoral and acetabular cartilage was enforced using the penalty method [46]. All analyses were performed using the nonlinear, implicit FE code NIKE3D [46].

Sensitivity Studies

Sensitivity studies were performed for each model to assess the effects of altering joint kinematic angles and direction of equivalent joint reaction force using the standard deviations reported by Bergmann [14,15]. 15 cases were analyzed per subject, yielding a total of 30 FE analyses. For each loading scenario there were 5 models: 1 baseline, 2 to assess the effects of variations in joint reaction force (± 1 SD) and 2 to assess variations in joint kinematics (± 1 SD of flexion, abduction, rotation). One standard deviation in the kinematic and reaction force data represented nearly 50% of the baseline values.

Data Analysis

If damage due to habitual mechanical overload is the instigating factor in the onset of OA, this implies that mechanical measures of stress are the critical factors defining the overload conditions. Therefore, peak contact pressure, average pressure and maximum shear stress for cartilage were determined from each FE model. Contact area was also calculated using a method described in our prior work [11] since this measure may provide indirect insight into material stresses and studies have suggested that contact area is reduced in the dysplastic joint [28,29,33]. Qualitative anatomical differences in the location of cartilage contact were also interpreted. All quantitative results were 176 reported as means and standard deviations based on combined data for the baseline model and all sensitivity models for each loading scenario.

177

RESULTS

Computational measurements of cartilage thickness demonstrated that cartilage in

the dysplastic hip was slightly thicker than that of the normal hip. Acetabular and

femoral cartilage thickness was 1.22±0.47 and 1.36±0.31 mm for the dysplastic hip, and

1.14±0.36 and 1.01±0.35 mm for the normal hip (Figure 6.2). Both the dysplastic and

normal subject had thicker cartilage in the medial aspect of the femur (Figure 6.2 left

column). A small region of thick cartilage was also noted along the lateral aspect of both

femurs (Figure 6.2 left column). The normal subject had thicker cartilage in the

superorlateral region of the aceteabulum whereas cartilage was thicker in the posterior aspect in the dysplastic acetabulum (Figure 6.2 right column).

Femur Acetabulum Posterior Superior

1.75 mm NORMAL P os t erior Medial

0.0 mm DYSPLASI

Anterior Inferior

Figure 6.2. Fringe plots of femoral (left column) and acetabular (right column) cartilage thickness in the normal (top row) and dysplastic (bottom row) hip joints. 178

Peak cartilage contact pressure, average pressure and maximum shear stress for the dysplastic patient were consistently higher than those for the normal subject during all three activities (Table 6.1). Surprisingly, contact areas were larger for the dysplastic hip joint (Table 6.1). 179

Table 6.1. Average FE model results (± SD) for the dysplastic and normal hip. A total of 15 models were analyzed for each subject- 3 baseline (walking, stair-climbing, descending stairs) and 12 sensitivity models (4 for each loading scenario).

Max. Press. Average Press. Max Shear Contact Area (MPa) (±SD) (MPa) (±SD) (MPa) (±SD) (mm2) (±SD) DYSPLASIA Walking 30.3 (2.9) 6.8 (0.5) 8.6 (1.5) 1143.3 (99.42) Stair Climbing 29.3 (6.1) 7.1 (0.9) 5.5 (1.8) 976.1 (141.5) Descending Stairs 25.6 (2.2) 6.1 (0.6) 5.8 (1.3) 1084.0 (249.9) NORMAL Walking 16.1 (0.9) 3.3 (0.4) 3.8 (0.6) 569.3 (89.0) Stair Climbing 20.0 (1.3) 3.7 (0.5) 4.0 (0.6) 512.3 (62.4) Descending Stairs 19.7 (1.7) 3.9 (0.3) 3.6 (1.1) 579.6 (86.0)

Fringe plots of cartilage contact pressures elucidated the origins of altered loading

in the dysplastic hip (Figure 6.3 top). Anterior wall cartilage pressures were nearly non-

existent in the normal model where most of the load was distributed along the superior

aspect of the acetabulum (Figure 6.3 bottom). The pattern of contact demonstrated was more or less mono-centric over the three loading scenarios analyzed (Figure 6.3 bottom).

In contrast, for the dysplastic hip, the distal anterior horn of the acetabular cartilage was consistently in contact during all three loading scenarios (Figure 6.3 top). 180

Walking Stair-Climbing Descending-Stairs

20 MPa

DYSPLASIA

0 MPa NORMAL

Figure 6.3. Lateral inferior oblique view of FE predicted contact pressures for the three loading scenarios simulated. Top row) dysplastic hip. Bottom row) normal hip. Note that the results shown are for the best case (lowest peak and average pressures) for each of the subjects. Dysplastic contact pressures were higher and the location of contact was altered when compared to the normal hip joint model. 181

When compared to the baseline model, the location of contact did not change

substantially when the joint kinematics and kinetics were altered in all of the sensitivity

models for each subject. As shown in the fringe plots of cartilage contact pressure for the

normal and dysplastic joints for 10 of the 30 cases (Figure 6.4), the general location and

magnitude of contact did not change substantially intra-subject following alteration of both the joint angles and angles of the equivalent force vector. Fringe plots of the

additional 20 analyses are not shown due, but those analyses also demonstrated little

variation as indicated by the small standard deviations in Table 6.1.

Avg. Kinematics +1 SD Flexion, -1 SD Flexion, +1 SD Angles of -1 SD Angles of Avg. Kinetics Abduction, Rotation, Abduction, Rotation, Joint Reaction Force Joint Reaction Force 20 MPa Avg. Kinetics Avg. Kinetics Avg. Kinematics Avg. Kinematics

NORMAL

DYSPLASIA 0 MPa

Figure 6.4. Lateral inferior oblique view of FE predicted contact pressures for 10 of the 30 sensitivity studies analyzed (walking loading scenario only). Top row) normal subject. Bottom row) dysplastic patient. The location of contact did not change substantially following alteration of the joint angles and angles of the equivalent force vector (separated by columns). 182

DISCUSSION

This study developed realistic three-dimensional FE models of the hip joint to compare joint biomechanics between a normal and dysplastic hip. This is the first patient-specific modeling study to our knowledge to utilize a computational protocol that had been previously validated by comparing subject-specific FE model predictions directly with experimental measurements [11-13]. Model predictions suggested that cartilage stresses were elevated in the dysplastic hip joint, which may provide a mechanical explanation as to why persons with hip dysplasia frequently develop hip joint

OA.

The predicted patterns of contact pressure and bone stress can be interpreted

directly in terms of the type of acetabular dysplasia. Anteversion of the acetabulum

creates poor anterior support of the femur, which causes the anterior wall to be loaded

more than normal. The fringe plots of cartilage stress indicated that this was the case for

the anteverted joint where a localized “hot spot” of cartilage stress was noted. The

posterior aspect of the acetabulum was also contacted resulting in a distinct bi-centric contact pattern which was likely due to incongruent mating between the femur and

acetabulum (Figure 6.1). The normal acetabulum was not excessively tilted anteriorly

and was more spherical in shape when qualitatively compared to the dyplastic joint.

Therefore, most of the cartilage contact occurred on the superior wall of the joint, resulting in a mono-centric pattern of contact.

The dysplastic FE model predicted contact areas that were larger than the normal

control, which was contradictory to several studies reported in the literature [28,29,33]. 183

A possible explanation for this was that the location of contact in the dysplastic joint was predominately confined to areas that were nearly parallel to the principal direction of loading, whereas the normal joint had substantial support perpendicular to the load.

Therefore, greater compressive and shear strains were required to carry the applied load in the dysplastic joint, resulting in larger contact areas. Although limited by the small sample size, the results of this study suggest that the location of contact may be more important than the absolute value of contact area when assessing joint mechanics in the dysplastic hip. This conclusion augments recent data reported by Armand et al. [47].

They developed pre and post-operative computational models to analyze changes in peak pressures and contact areas following peri-acetabular osteotomy and found that while 9 of

12 cases showed decreased peak pressure after surgery, the mean changes in contact area were not statistically significant.

Several attempts have been made to quantify the biomechanics associated with dysplasia. Mavcic et al. [27] used a mathematical model of static, single-leg stance based on AP radiographs of normal and dysplastic subjects. Dysplastic hips had significantly larger peak contact stresses than healthy hips (7.1 kPa/N and 3.5 kPa/N, respectively).

Michaeli and co-workers combined experiments and computer modeling to predict the contact stress in the human hip joint and to investigate differences in location and magnitude of contact stresses between normal cadaveric pelvi and plastic pelvi with simulated dysplasia [29]. Their computational model was based on 3-D reconstructions from CT image data that was fit to spheres to represent femoral and acetabular geometry.

The surface of each sphere was discretized into 0.5 mm2 patches. At each surface patch 184

the dot product between the applied load and a vector normal to the patch was calculated

and the total load was divided among the patches. Computational predictions of contact pressure, as calculated by dividing the force magnitude by the surface area of each patch, were nearly 7 times less than those measured by the pressure film in the cadaveric and plastic pelvi. They concluded that the technique was not proven to yield accurate predictions of contact stress in dysplastic joints [29]. Nevertheless, Hipp et al. [28]

applied this computational model to analyze joint contact pressures for 70 dysplastic and

12 normal hips. Contact areas were 26% smaller and contact pressures were 23% higher

in dysplastic hips. Peak pressures for dysplastic hips were on the order of 7 MPa.

Genda et al. [32] used a three-dimensional rigid body spring model (RBSM) to

compare hip joint mechanics between 112 normal and 66 dysplastic hip joints.

Geometric models were made from conventional anteroposterior radiographs with the

assumption that the acetabular surface was spherical. At 4.5 times bodyweight the mean

peak pressures for normal hips was around 3 MPa. Mean contact pressures for the

dysplastic hips were not reported, however the model with the largest peak pressure

predicted a value of 16 MPa.

Peak pressures reported in the aforementioned studies consistently underestimated

those measured in vitro [7,8,48-52] and in vivo [15,53] and were substantially less than

those predicted in the current study. This discrepancy is likely attributed to the

assumption of spherical joints and uniform cartilage thickness. Anthropometric studies

have demonstrated that the hip joint is neither concentric nor has uniform cartilage

thickness [54-56] and that even normal joints demonstrate irregular patterns of cartilage 185

contact with steep pressure gradients [7,8,49-52]. Therefore, an accurate representation of the three-dimensional geometry of the hip joint may be a necessary precursor to predicting accurate biomechanics.

Recently, Russell et al. [33] generated realistic three-dimensional FE models of six dysplastic, five asymptomatic and one normal subject using CT arthrogram data.

They reported significant differences between the normal control and the asymptomatic hips and trend towards significance between the asymptomatic hips and the symptomatic hips of patients afflicted with DDH, suggesting that the contralateral hip in DDH is also affected. Peak contact pressures for the symptomatic and asymptomatic hips ranged from

3.56 – 9.88 MPa whereas normal hip peak pressures ranged from 1.75 – 1.89 MPa. The peak pressures in the current study were substantially elevated in comparison to these results despite very similar boundary and loading conditions. One of the reasons for this discrepancy could be that Russell et al. applied a substantial amount of smoothing to the articulating surface of femoral and acetabular cartilage. In addition, they assumed a cartilage elastic modulus of 10 MPa, which is roughly 4 times less than the modulus used in the current study.

Several limitations of the current study must be mentioned. First, only one patient-specific FE model was analyzed for each subject group, eliminating the ability to perform statistical tests. However, the primary objective of this paper was to demonstrate the feasibility of the FE method for modeling hip dysplasia. Future modeling efforts could use this patient-specific modeling protocol to investigate a more reasonable sample size. In addition, both patient-specific FE models were loaded using identical kinetics 186 and kinematics based on average in-vivo data. While inaccurate kinematics could be a source of modeling error, our sensitivity studies demonstrate that the spatial distribution of contact pressures are clearly more dependent on joint geometry than variations in kinematics or loading vector direction. Nevertheless, it is possible that some intermediate kinematic position would place the joint in an optimal position that could result in reduced peak bone and cartilage stresses. This in fact may be the reason why our patient- specific models predicted peak cartilage pressures that were higher than those predicted by previous models [27-29,33,51,57] and measured in-vitro [7,8,48-52]. This will be investigated in future studies.

Our prior work [12] has demonstrated that cartilage thickness reconstruction errors based on CT arthrogram image data increase exponentially when cartilage thickness reaches a critical value (around 1 mm). This could present a challenge while studying OA since the disease is predominately associated with a loss of cartilage

[58,59]. Nevertheless, studies have shown that cartilage in patients with dysplasia is actually thicker than normal joints during the early onset of symptoms [9,10,60].

Average cartilage thicknesses for the models analyzed in our study demonstrated that cartilage was thicker in the dysplastic joint and was above the critical threshold for obtaining accurate reconstructions for both models analyzed. Model accuracy would likely degrade if patients with thinner cartilage were studied, and thus it is presently recommended that our modeling technique should not be applied to patients who have cartilage thicknesses that are predominantly less than 1 mm. 187

Trabecular bone was not modeled in this study since we demonstrated that it has

little effect on the prediction of cartilage stresses in the hip [11]. However, it is well

known that trabecular bone architecture and density are sensitive to localized stresses (i.e.

Wolff’s Law [61]). Therefore, a better understanding of trabecular bone orientation,

density and mechanics may provide valuable insight into the biomechanics of hip

dysplasia. Because we did not explicitly validate trabecular bone stresses and strains

[13], we are hesitant to predict trabecular bone mechanics on a patient-specific basis. In addition, the acetabular labrum was removed in this study, yet it has been suggested that the labrum helps to maintain fluid pressurization in the hip [62,63]. It is possible that leaving the labrum intact would have altered the predicted contact patterns and magnitudes. Although actions of individual muscles were not considered, the equivalent

joint reaction force was based on in vivo data [14,15], which justifies our method of

modeling the action of all muscles as a single equivalent force vector. Finally, cartilage

exhibits depth dependent material properties [64], variation in stiffness over its surface

[65,66] and tension-compression nonlinearity [67] yet was modeled as an isotropic,

homogenous material. Future patient-specific modeling efforts should investigate the

importance of these effects via sensitivity studies.

It is unlikely that mathematical or computational models that use simplified or

idealized representations of the articular surface geometry (e.g., [27-29]) provide accurate

insight into differences between normal and dysplastic hips. Our protocol allows for

realistic three-dimensional models to be developed and analyzed non-invasively using

patient-specific CT arthrogram image data. The modeling protocol could be improved by 188 including patient-specific kinematics, more sophisticated cartilage constitutive equations and by incorporating the acetabular labrum. In conclusion, the results from this proof of concept study suggest that patients with dysplasia may have altered joint biomechanics and motivates future modeling efforts to analyze a greater number of subjects.

189

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[53] Hodge, W. A., Fijan, R. S., Carlson, K. L., Burgess, R. G., Harris, W. H., and Mann, R. W., 1986, "Contact Pressures in the Human Hip Joint Measured in Vivo," Proc Natl Acad Sci U S A, 83, pp. 2879-83.

[54] Bullough, P., Goodfellow, J., Greenwald, A. S., and O'Connor, J., 1968, "Incongruent Surfaces in the Human Hip Joint," Nature, 217, pp. 1290.

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[60] Nishii, T., Sugano, N., Tanaka, H., Nakanishi, K., Ohzono, K., and Yoshikawa, H., 2001, "Articular Cartilage Abnormalities in Dysplastic Hips without Joint Space Narrowing," Clin Orthop Relat Res, pp. 183-90.

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CHAPTER 7

DISCUSSION

SUMMARY

The research described in this dissertation investigated the mechanics of the human hip joint and developed novel experimental and computational tools that will facilitate future studies of the hip. Further, the results of this dissertation may be applied to the study of other joints such as the knee and shoulder.

Experimental hip joint tests were conducted to measure pelvic cortical bone strains and cartilage contact stresses in separate studies. Detailed computational protocols were developed and validated by comparing finite element (FE) predictions directly with bone strains and cartilage contact stresses measured experimentally. Model sensitivity studies were performed to analyze the effects of altering assumed and measured inputs including material properties, geometry, and boundary conditions. The ability of computed tomography (CT) to accurately reconstruct cortical bone and cartilage thickness was also determined using phantoms. Finally, the feasibility of patient-specific FE modeling was demonstrated by developing and analyzing FE models of a normal and dyplastic hip joint. The results of this proof of concept study indicated altered biomechanics in the dysplastic hip, motivating further study of this patient population. 196

The results of the bone modeling study demonstrated the accuracy of the

FE method for quantifying bone strains and has direct relevance to the study of hip dysplasia and OA as it is believed that bone mechanics play an important role in the progression of these pathologies [1,2]. Although previous models of the pelvis have been described [3,4], direct validation between computational predictions and experimental measurements was not performed. The accuracy of

CT reconstructions of cortical bone was also quantified in this study and it was determined that cortical bone should be at least 0.7 mm thick to obtain accurate geometrical reconstructions. The pelvis analyzed in this study rarely had thickness below this critical threshold. Thus, our approach for modeling the cortex as a layer of thin shells has direct applicability to the analysis of patient- specific models, assuming that subjects have cortical bone with sufficient thickness. The results of the parameter studies demonstrated that predictions of cortical bone strains were most sensitive to changes in cortical bone thickness.

Therefore, the cortical bone thickness algorithm developed herein will be useful for constructing accurate FE models in the future. Finally, the model detailed in this study may have the ability to serve as a template for studying general biomechanics of the pelvis or to investigate changes in bone stresses and strains due to surgical procedures such as peri-acetabular osteotomy (PAO) or total hip arthroplasty (THA).

Prior to developing subject and patient-specific joint contact stress models it was important to demonstrate that cartilage thickness could be accurately reconstructed from CT image data. The results from the phantom imaging study 197

suggested that cartilage should be at least 1.0 mm thick to ensure accurate (<10% error) reconstructions. Additionally, it was shown that cadaveric hips could be imaged without contrast agent as errors in the “dry” scans were nearly identical to those when using a low concentration of contrast agent. It is generally assumed that CT underestimates the thickness of thin tissues due to volumetric averaging

[5,6], but the results of this study demonstrate that the direction of the error during

CT arthrography is dependent on several parameters such as contrast agent concentration, scanner direction, and spatial resolution. From our recent experience working alongside radiologists, we have found that the choice of contrast agent concentration generally depends on the particular radiologist who is performing the injection. It is hoped that the results of this study will circulate to a larger audience of clinicians and scientists who may be unaware of the consequences of using higher concentrations.

The FE modeling study of cartilage contact was the first to validate predictions directly with experimental pressures measurements. Overall, the FE model demonstrated good qualitative and quantitative correspondence between computational predictions and experimental data. Prior hip joint contact models assumed spherical geometry and concentric articulation between opposing layers of cartilage [7-11]. Therefore, most models have predicted pressures that are substantially less than those measured experimentally. In addition, many studies have made the assumption of rigid bones [12,13] yet the results of this study demonstrated that this model simplification may lead to erroneous estimates of contact stress and area. Modeling errors decreased when larger bounds of 198 pressure were compared, and thus the protocol discussed herein may be more suitable for generating models that can predict highly stressed regions of cartilage as opposed to the entire pattern of contact.

Hip dysplasia may be the primary etiology of OA in the hip joint

[2,14,15]. Because the geometric pathologies associated with hip dysplasia are three-dimensional [16-19], it was important to develop techniques to analyze joint mechanics without simplifying assumptions regarding bone and cartilage geometry. Although mathematical and computational models have been developed to study hip dysplasia [8,9,14,20-22], the patient-specific models presented in Chapter 6 represent one of the first three-dimensional modeling efforts. Recent three-dimensional models [22] represent significant improvements over 2-D techniques however this particular protocol was not validated. The patient-specific models described in this dissertation demonstrated differences in joint biomechanics between normal and dysplastic hips. Changing the direction of loading and the anatomical orientation using standard deviations reported in the literature did not alter the pattern of cartilage contact substantially.

Therefore, it is likely that the topology of the joint surfaces primarily drives the patterns of hip joint contact rather than the underlying boundary and loading conditions. Nevertheless it is possible that some intermediate kinematic position would provide a “path of least resistance” that would likely reduce pressures from the values that were predicted in this study. It will be important to analyze several additional patient-specific FE models to learn more about the pathological mechanics of hip dysplasia. 199

The primary purpose of this dissertation was to develop and validate protocols to generate patient-specific models of the hip joint. After review of the joint modeling literature, it is clear that substantial effort has been directed towared model “development” yet the notion of model “validation” has been largely neglected. Model credibility must be established before clinicians and scientists can be expected to extrapolate information and decisions based on model predictions [23]. Although it has been argued that absolute model validation is impossible [24,25] it is hoped that the protocol developed herein has

been subject to enough scrutiny that it will be accepted as an appropriate

methodology for generating patient-specific hip joint models. If a similar

combined experimental and computational approach is adopted by analysts who

wish to study other joints such as the knee and shoulder, peer acceptance will ultimately be improved.

200

LIMITATIONS AND FUTURE WORK

One of the primary critiques of using the FE method for studying joint biomechanics is that it is very time consuming to segment surface geometry from medical image data [9], potentially limiting the amount of subjects that could be analyzed in a given study. The surface used to create the pelvic mesh in Chapter

3 took nearly one month to manually segment from the CT image data. However, recent commercial segmentation programs have made the process of data segmentation nearly automated. By using a commercial program (Amira 4.1, where) we were able to reduce the time to segment the pelvic surface from one month to less than three hours.

Is it believed that the architecture of trabecular bone is primarily dictated by the stress history [26]. Therefore, it would be beneficial to predict trabecular bone stresses and strains in both normal and pathological hips since this could provide insight into why diseases such as OA develop. It was not possible to experimentally measure trabecular bone strains in the pelvic FE modeling study

(Chapter 3). Therefore, caution should be exercised when interpreting patient- specific trabecular bone mechanics using models formulated from the protocol discussed in Chapter 3. Nevertheless, predictions of cortical bone stresses corresponded well with experimental measures despite changes in the trabecular bone modulus and Poisson’s ratio. Therefore, this modeling approach for the analysis of patient-specific cortical bone mechanics does not require one to stipulate a preferred material direction for trabecular bone. 201

The labrum was removed in the cartilage contact stress study (Chapter 5) and was not segmented and meshed in the patient specific FE study (Chapter 6).

The locations of contact stresses in the subject-specific model were primarily on the lateral aspect of the acetabulum during each loading scenario studied.

Therefore it is possible that the labrum may also serve some (albeit limited) load

bearing function in the intact joint. To model the labrum it would first be

necessary to perform material testing to ascertain its material properties as these

have not been reported in the literature. Given its preferred circumferential alignment of collagen is it quite possible that the transversely isotropic model described by Quapp and Weiss [27] would work well and this will be investigated in future experimental and computational studies.

During loading of both normal and pathological joints it is likely that the hip joint follows a path of least resistance in an effort to minimize energy [28].

To obtain FE model convergence it is often necessary to limit the degrees of

freedom of the model, thus eliminating rigid body modes. This assumption is

appropriate when the same boundary conditions have been applied

experimentally. However, this could result in substantial elevations in patient-

specific models since the exact boundary conditions are not known a-priori.

Although the parameteric studies detailed in Chapter 6 indicated that cartilage contact pressures were not sensitive to changes in the kinetics and kinematics, only extreme positions were analyzed. Therefore, it is likely that these models overestimated cartilage contact pressures in both the normal and dysplastic joint. 202

Several possible approaches could be adopted to resolve the possible need for patient-specific kinematics. First, using the basis of minimization of energy, an algorithm could be developed to incrementally rotate and translate the femur relative to the acetabulum, prior to model loading, until the distance between opposing layers of cartilage was minimized. Then the model could be constrained to move only in the direction of applied load. This technique would require an analyst to assume it is the differences in joint congruence rather than deformation that dictates the preferred kinematics of the hip joint. A second approach, which could also be used in conjunction with the former, is related to patient-specific gait analysis. The kinematic position at any point in the gait cycle could be quantified using surface markers and standard motion capture technology. The peak reaction force at the hip measured in-vivo corresponds very well with peaks of force plate readings [29,30]. Therefore, an estimate of the joint reaction force could be based on a linear scaling of the force plate data.

Based largely on the work described in this dissertation, our laboratory has recently obtained federal funding to continue the study of hip dysplasia. This ongoing work will more thoroughly characterize the biomechanics of hip dysplasia by developing additional patient-specific FE models. Several subject- specific FE hips will also be tested experimentally and subsequent FE models will be validated using methodologies very similar to those described in this dissertation. Dynamic measurements of cartilage contact pressures will be recording using a novel tactile pressure sensor. More realistic constitutive equations will be used to model the tension-compression behavior of cartilage. 203

Finally, patient-specific models will be developed for two different manifestations of dysplasia (i.e. “traditional” dysplasia and acetabular retroversion). It is hoped that this study will elucidate the mechanics of dysplasia and result in better diagnosis and treatment of young adults who are afflicted with this disease.

The long-term goals of this research are to improve the diagnosis and treatment of acetabular dysplasia and to extend the applicability of hip joint FE modeling. Treatment decisions for patients with acetabular dysplasia currently follow a simplified procedure with surgical decision making primarily based on empiric recommendations and past outcomes. Patients are roughly divided into those who manifest instability due to acetabular undercoverage (usually classic dysplasia) and those with acetabular overcoverage (retroversion [16-18]) or impingement [19,31]. In reality there is likely a spectrum of abnormal hip morphology in terms of severity and location of stress transmission [16-19].

Using patient-specific modeling techniques could delineate the true spectrum of this disease process by quantifying the degree of stress transfer from the acetabulum to the femoral head and primary location of contact, which could fundamentally change the way that acetabular dysplasia is diagnosed and treated.

Many orthopaedic surgeons are unaware of multiple facets of the dysplasia diagnosis and their potential implications for joint degeneration. Improved diagnostic ability translates into more appropriate surgical treatment [31].

Recognizing the mechanical consequences of different forms of dysplasia allows earlier identification of “at risk” hips so that earlier treatment can be initiated, hopefully delaying the need for THA. 204

Patient-specific FE models of the hip joint have a number of potential longer-term uses and benefits, including improved diagnosis of pathology, patient-specific approaches to treatment, and prediction of the long-term success rate of corrective surgeries based on pre- and post-operative mechanics. Patient models could potentially be applied to quantify changes in mechanical loading due to surgical intervention, allowing one to assess the efficacy of different approaches to osteotomy. In addition, these techniques could be utilized in longer-term prospective studies in an effort to correlate surgical correction with

changes in mechanical loading and outcome. Currently, success is measured by

avoidance of a total hip arthroplasty and is not correlated with any preoperative

variable other than the relatively crude radiographic measurements [31].

Hip joint FE modeling may also assist the development of other treatment

methods, such as osteochondral autografting of defective cartilage in patients with

dysplasia. Allograft techniques require mapping of the articular cartilage

anatomy, including cartilage thickness and underlying bone geometry, to

understand how geometric and mechanical abnormalities affect cartilage

mechanics. As tissue engineering techniques continue to improve, autologous

cartilage cell tissue engineering could offer the same type of treatment potential.

205

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