The Effects of Meniscal Sizing on the Knee Using

THE EFFECTS OF MENISCAL SIZING ON THE KNEE USING

FINITE ELEMENT METHODS

A dissertation presented to

The faculty of

the Fritz J. and Dolores H. Russ

College of Engineering and Technology

Ohio University

In partial fulfillment

of the requirements for the degree

Doctor of Philosophy

Stephen D. Fening

March 2005

Stephen D. Fening

This dissertation entitled

THE EFFECTS OF MENISCAL SIZING ON THE KNEE USING

FINITE ELEMENT METHODS

STEPHEN D. FENING

has been approved for

the School of Mechanical Engineering

and the Russ College of Engineering and Technology by

Bhavin Mehta Associate Professor of Mechanical Engineering

Dennis Irwin Dean, Fritz J. and Dolores H. Russ College of Engineering and Technology FENING, STEPHEN D. Ph.D. March 2005.

Individual Interdisciplinary Ph.D. – Biomedical Engineering

The Effects of Meniscal Sizing on the Knee Using Finite Element Methods (125pp.)

Director of Dissertation: Bhavin Mehta

The knee, one of the most complex joints in the body, is also one of the most commonly injured joints in humans. Most injuries that occur in the knee either cause meniscal damage or are the function of a previously damaged meniscus, a complex tissue that has been historically underappreciated. Many techniques for the replacement of a damaged meniscus have been surgically explored. The most successful approach thus far has been meniscus allograft, the transplantation of a meniscus from a cadaver to a patient.

This procedure has been performed over the last 25 years with inconsistent results.

Meniscal sizing appears to be a major source of this inconsistency.

The purpose of this dissertation is to study the effects of meniscal sizing on

stresses in the knee joint using finite element methods. All research was conducted on

the porcine based on its similarity to the human knee. MRI and CT scans recreated the

geometry of the knee. CT images were used to construct the shapes of bones and soft

tissues were modeled from MRI. The geometric model included the femur, tibia, and

both menisci. For simplicity, the material model used was a linear isotropic material

even though this model does not adequately model the function of biological tissues. The

geometric model was imported as a STL file and meshed with tetrahedral elements. The

tibia was fully constrained on its distal surface, the menisci were constrained both at the horn attachments and their periphery, and the femur was constrained by a spring element mimicking the behavior of the entire bone of the femur, muscle, tendon, and ligament attachments. A force of 465 Newtons, half of the body weight of the porcine, was applied to the femur. The meniscus was scaled in three dimensions – medial-lateral, anterior-posterior, and proximal-distal – to examine the effects of differently sized menisci. Results demonstrate that all three dimensions are statistically significant, with the medial-lateral dimension being most significant. Even very small changes in meniscal size demonstrated dramatic changes in stress levels.

Approved:

Bhavin Mehta

Associate Professor of Mechanical Engineering

TABLE OF CONTENTS

ABSTRACT...... 4

LIST OF FIGURES ...... 8

LIST OF TABLES ...... 11

CHAPTER 1 INTRODUCTION...... 12 1.1 General knee anatomy...... 12 1.2 Anatomy of the menisci...... 15 1.2.1 Gross Anatomy ...... 15 1.2.2 Architecture...... 19 1.2.3 Vascular Pattern...... 22 1.2.4 Neurophysiology...... 22 1.2.5 Histology...... 23 1.2.6 Function ...... 23 1.2.7 Development & maturation...... 25 1.2.8 Healing...... 26 1.2.9 Anatomical interspecies variation...... 27 1.3 Meniscal injury ...... 28 1.3.1 Tearing ...... 29 1.3.2 Meniscectomy...... 31 1.3.3 Effects of Meniscal Injury ...... 32 1.4 Meniscus allograft & repair ...... 37 1.4.1 Repair...... 37 1.4.2 Meniscus transplant ...... 39 1.4.3 Meniscus allograft...... 41 1.4.4 Pre-operative planning and size matching ...... 42 1.4.5 Surgical technique...... 43 1.4.6 Results of meniscal allograft...... 45 1.5 Software used in research ...... 47 1.5.1 Amira® ...... 47 1.5.2 Algor® ...... 47 1.5.3 LS-DYNA...... 48 1.5.4 Superforge®...... 48 1.5.5 Dytran® ...... 48 1.5.6 MARC®...... 49

CHAPTER 2 LITERATURE REVIEW...... 50

CHAPTER 3 BIOMATERIAL CHARACTERIZATION...... 59 3.1 Determining material properties ...... 59 3.2 Biomaterial properties of cartilage...... 65 3.2.1 Articular cartilage ...... 65 3.2.2 Menisci...... 66 3.3 Biomaterial properties of cortical bone...... 67

CHAPTER 4 DETERMINING GEOMETRY FROM MRI/CT SCANS...... 70 4.1 Approaches to finding geometry...... 70 4.2 Using CT and MR images ...... 71 4.3 Constructing three-dimensional geometries with Amira® ...... 72 4.4 Importing models...... 75

CHAPTER 5 ANALYSIS OF THE KNEE...... 79 5.1 Failed approaches...... 79 5.2 Successful methodology ...... 84 5.2.1 Mesh generation...... 84 5.2.2 Material properties...... 86 5.2.3 Boundary conditions ...... 88 5.3 Design of Experiment (DOE) Setup ...... 92

CHAPTER 6 RESULTS AND CONCLUSIONS...... 97

CHAPTER 7 FUTURE RECOMMENDATIONS...... 115

REFERENCES...... 118

LIST OF FIGURES

Fig. 1.1: Human knee anatomy of a right knee...... 13

Fig. 1.2: Anatomy of the meniscus ...... 16

Fig. 1.3: Attachments of the meniscus to the tibial plateau ...... 17

Fig. 1.4: Movement (in mm) of the menisci during knee flexion with weight bearing ...... 18

Fig. 1.5: Collagen microstructure of articular cartilage ...... 20

Fig. 1.6: Collagen microstructure of the meniscus ...... 20

Fig. 1.7: Synoptic drawing of collagen fibers in the three distinct layers of the meniscus ...... 21

Fig. 1.8: Superior view of a deformed meniscus ...... 24

Fig. 1.9: How collagen in the meniscus behaves over a lifespan...... 26

Fig. 1.10: Interspecies anatomical variation ...... 27

Fig. 1.11: The figure on left shows the menisci of a porcine left knee while the figure on the right shows the menisci of a human right knee...... 27

Fig. 1.12: Radial and circumferential fibers...... 30

Fig. 1.13: Tearing of the meniscus...... 30

Fig. 1.14: Comparison of pressure distribution from an intact knee...... 34

Fig. 1.15: Comparison of contact areas between an intact knee and a knee without menisci...... 35

Fig. 1.16: Comparison of impact absorbing properties of the knee...... 36

Fig. 1.17: Connecting a lesion to vascularized meniscal tissue ...... 38

Fig. 1.18: Lateral meniscus repair...... 39

Fig. 1.19: Bone plug fixation techniques for meniscal allograft...... 44

Fig. 2.1: Two-dimensional representation of a meniscus ...... 51

Fig. 2.2: Stress distribution of a two-dimensional representation of a meniscus...... 52

Fig. 2.3: Comparison of poroelastic material models to a biphasic material model.....54

Fig. 2.4: Meshes produced by various automatic mesh generation techniques ...... 55

Fig. 2.5: ABAQUS mesh and results ...... 56

Fig. 2.6: Dynamic three-dimensional FEA model of the knee ...... 57

Fig. 3.1: Schematic diagram of indentation parameters...... 61

Fig. 3.2: 1 mm, 2mm, and 3 mm indenter drawings ...... 62

Fig. 3.3: 4 mm stainless steel indentation head...... 63

Fig. 3.4: Specimen table apparatus ...... 64

Fig. 3.5: Testing apparatus...... 65

Fig. 3.6: Structural organization of bone ...... 68

Fig. 4.1: MicroScribe© digitizing tool...... 70

Fig. 4.2: Identifying pixels...... 73

Fig. 4.3: Creating voxels ...... 74

Fig. 4.4: Three-dimensional geometry created in Amira® ...... 75

Fig. 4.5: STL file format of the porcine knee ...... 77

Fig. 5.1: FEA mesh in Algor...... 80

Fig. 5.2: FEA mesh in LS-DYNA...... 81

Fig. 5.3: SuperForge® simulation setup ...... 82

Fig. 5.4: Dytran mesh...... 83

Fig. 5.5: STL importation...... 85

Fig. 5.6: Refined mesh of the knee ...... 86

Fig. 5.7: Application of material property ...... 87

Fig. 5.8: Tibial boundary condition...... 88

Fig. 5.9: Lateral meniscus boundary condition...... 89

Fig. 5.10: Medial meniscus boundary condition...... 90

Fig. 5.11: Femoral boundary condition...... 91

Fig. 5.12: Application of Load...... 92

Fig. 5.13: Meniscal origins and scaling dimensions ...... 93

Fig. 6.1: Stress contours on knee over time ...... 100

Fig. 6.2: Stresses on the tibia (in dynes/cm2)...... 102

Fig. 6.3: Stresses on the tibia with automatic contouring ...... 104

Fig. 6.4: Stresses on the menisci (in dynes/cm2)...... 106

Fig. 6.5: Stresses on the menisci with automatic contouring...... 108

Fig. 6.6: Statistical significance of parameters on the tibial plateau...... 109

Fig. 6.7: Statistical significance of parameters on the lateral meniscus...... 112

Fig. 6.8: Statistical significance of parameters on the medial meniscus...... 113

LIST OF TABLES

Table 1.1 Meniscal substitutes and the materials used for each ...... 40

Table 2.1 Material properties from Spilker et al...... 50

Table 3.1 Variation of Young’s modulus with testing techniques ...... 66

Table 3.2 Mechanical properties of articular cartilage ...... 67

Table 3.3 Mechanical properties of cortical bone...... 69

Table 4.1 Three-dimensional export options from Amira® ...... 76

Table 5.1 Number of elements of each entity in mesh ...... 86

Table 5.2 Simplified mechanical properties used in research ...... 87

Table 5.3 DOE control factors...... 93

Table 5.4 Effects of scaling on meniscal sizing...... 94

Table 5.5 Full factorial experimental design ...... 95

Table 5.6 Partial factorial experimental design ...... 96

Table 6.1 Results of partial factorial study...... 98

Table 6.2 Maximum stresses on the tibia ...... 98

Table 6.3 Significance of sources of variation ...... 110

CHAPTER 1 INTRODUCTION

1.1 General knee anatomy

The largest joint in the human body is the knee. During everyday activities, this complex hinge-like joint is subject to constant pounding, bending, and twisting. During movement, the knee rolls, glides, and twists, making its motion very complex. The range of motion in the knee from full flexion to full extension is roughly 140 degrees [1]. The impact of falls and the effects of arthritis further stress the knee to such a great extent that the knee is the most commonly artificially replaced joint in the human body and it is the site most often treated by orthopedic surgeons [2].

Although it is traditionally considered one joint, the knee functions more like three separate joints. The first two are located medially and laterally between the femur and the tibia (medial femoral condyle to medial tibial plateau and lateral femoral condyle to lateral tibial plateau). There are four articulating surfaces in this tibiofemoral joint of the knee, one on each of the femoral condyles, and the other two on the corresponding tibial plateaus [1]. These surfaces are covered in articular cartilage. The third joint functions between the patella and the femur [3]. Figure 1.1 shows the anatomy of the knee. Two fibrocartilage menisci are located on the tibial plateau between the femur and the tibia.

Figure 1.1 Human knee anatomy of a right knee [1]

There are four bones in the knee, the femur and the tibia being structurally

predominant. The patella, or kneecap, protects the knee and provides mechanical

advantage to the joint; however, it is not structurally prominent in full extension. The fibula is located lateral to the tibia and also does not play a structural role in the knee.

The femur is located most proximally as shown in Figure 1.1. The distal end of the femur is composed of a medial and a lateral condyle. The tibia has medial and lateral plateaus, which articulate with the condyles of the femur.

Seven major ligaments stabilize the knee. Two of them, the cruciate ligaments, cross one another inside the knee capsule. These ligaments are referred to as the anterior cruciate ligament (ACL) and the posterior cruciate ligament (PCL), based on their sites of attachment on the tibia. These ligaments limit the anterior and posterior movement of the femur and maintain alignment of the medial and lateral condyles [3]. There are also two

14 collateral ligaments: the medial collateral ligament (MCL) and the lateral collateral ligament (LCL). These ligaments stabilize their respective sides of the knee in full extension. Another ligament in the knee is the patellar ligament, so named because it contains the patella. This ligament supports the anterior surface of the knee joint and is the continuation of the quadriceps tendon. Finally, two popliteal ligaments connect the femur and the heads of the tibia and the fibula. These ligaments support the posterior surfaces of the knee [3].

1.2 Anatomy of the menisci

Although once described as the functionless remains of leg muscle, the menisci have been found to play an important role in the biomechanics of the knee in recent years

[1, 4]. As early as 1936, King described the meniscus as being an important piece of the biomechanical make-up of the knee and described degenerative osteoarthritic (OA) changes after meniscectomy [5]. When studying meniscal allograft it is imperative to understand the complicated structure of the menisci.

1.2.1 Gross Anatomy

There are two menisci in the knee located medially and laterally between the

femur and the tibia. These menisci are semilunar shaped fibrocartilage disks that have a

cross-sectional wedge shape [6]. Figure 1.2 shows a diagram depicting the location of

the menisci on the tibial plateau. The distal surface of each meniscus makes contact with

the tibial plateau. The proximal surface contacts the femoral condyles. The distal surface

of each meniscus is convex while the proximal surface is concave [4, 7-9].

Figure 1.2 Anatomy of the meniscus [10]

Both the medial and lateral menisci are firmly attached to the tibia by the anterior and posterior horns of the meniscus. The circumferentially oriented fibers of the meniscus continue as external ligaments, making the connection to the tibia very stable

[6, 7]. Arnoczky in 1992 even described the menisci as being extensions of the tibia that better accommodate the condyles of the femur [4]. While the medial meniscus is considered to be relatively immobile on the tibial plateau, the lateral meniscus is relatively mobile [1].

The medial meniscus is approximately 4.5 cm in length in the anteroposterior direction and is somewhat semicircular in shape [11]. Its thickness ranges from 3 mm to

5 mm and its average volume is 3.45 cm3 [11, 12]. The surface area of the medial tibial plateau is approximately 11.8 ± 1.6 cm2. The medial meniscus covers approximately

46% of this tibial surface as its surface area is 5.5 ± 1.4 cm2 [13]. The anterior horn of the medial meniscus is attached to the tibial plateau in the area of the anterior

17 intercondylar fossa anterior to the anterior cruciate ligament. This attachment is shown in

Figure 1.3 denoted AM. The posterior fibers of the anterior horn attachment also merge with the transverse ligament [4]. The posterior horn of the medial meniscus is attached to the posterior intercondylar fossa, shown in the figure as PM. The peripheral edge of the medial meniscus is attached to the joint capsule via the coronary ligaments [1, 4].

Figure 1.3 Attachments of the meniscus to the tibial plateau [14]

The lateral meniscus in the human is almost circular and covers more surface area

than its counterpart. The lateral meniscus is also approximately 3.5 cm in the

anteroposterior direction with an average volume of 2.9 cm3 [11]. The thickness of the lateral meniscus is also 3 mm to 5 mm [12]. The surface area of the lateral tibial plateau is 10.7 ± 1.1 cm2. The lateral meniscus covers approximately 52% of this surface as its

surface area is 5.6 ± 1.2 cm2 [13]. The anterior horn of the lateral meniscus is attached to

the tibia anterior at the intercondylar eminence and lateral to the attachment of the ACL.

It partially blends with the ACL at this location. This attachment is also shown in Figure

1.3 denoted AL. The posterior horn of the lateral meniscus is attached posterior to the intercondylar eminence anterior to the anterior cruciate ligament, shown in the figure as

PL. A loose peripheral attachment of the lateral meniscus to the tibia further stabilizes the tissue. The posterior horn of the lateral meniscus also attaches to the femur by way of the meniscofemoral ligament [1, 4, 11].

During knee flexion, the menisci move with the femoral condyles and slide back on the tibial surface. The lateral menisci displaces more than its medial counterpart [7].

Figure 1.4 depicts how the menisci move during knee flexion under weight bearing. All dimensions are mean distances and are shown in millimeters.

Figure 1.4 Movement (in mm) of the menisci during knee flexion under weight bearing conditions [15]

1.2.2 Architecture

The mechanical matrix of the menisci is often considered to be composed of two

phases: a solid phase (26% of wet weight) and a liquid or fluid phase (74% of wet

weight) [7, 16]. The solid phase is composed mostly of collagen (60 – 70% of dry weight), proteoglycans, and other proteins [10]. The fluid phase consists of water and interstitial electrolytes. The solid phase behaves more like a fiber-reinforced composite material while the liquid or fluid phase is important in the deformable behavior of the tissue [11, 16]. The combined function of the liquid phase flowing through the solid phase gives the meniscus its viscoelastic properties.

The fibrocartilage material of the meniscus is supported by collagen fibrils which

are able to withstand tensile forces but have comparably low compressive, flexural, and torsional stiffness [17]. In contrast to articular cartilage, which contains almost exclusively Type II collagen, about 98% of the collagen found in menisci is Type I collagen, the same collagen that is predominantly found in tendon [16, 17]. Because of its fiber orientations, fibrocartilage is considered an anisotropic material [11, 18].

Because the most similar behaving material to the fibrocartilage of menisci is articular cartilage, it is useful to compare the fiber arrangements. Figure 1.5 shows the collagen microstructure of articular cartilage. The deep portion of articular cartilage contains predominantly radially oriented fibers while the superficial, or surface portion, contains predominantly circumferentially oriented fibers. The middle layer contains a mixture of the two fiber orientations. Articular cartilage has a fine Type II collagen fibrillar structure [16].

Figure 1.5 Collagen microstructure of articular cartilage [16]

In contrast, the menisci contain course fiber bundles of Type I collagen [16]. The collagen microstructure of the meniscus is shown in Figure 1.6. The interior or deep zone of the meniscus contains primarily circumferentially oriented fibers as depicted by

(C) in the Figure 1.6. The fibers are arranged in large bundles of 20 to 150 µm diameter and continue into the anterior and posterior horn attachments [16]. The superficial zone of the menisci, depicted as (S) in the figure, contains mostly radially oriented fibers approximately 30 to 120 µm thick. This superficial zone seems to act as an envelope for the interior fiber bundles [16].

Figure 1.6 Collagen microstructure of the meniscus [16]

Electron microscopy has revealed that there are three distinct layers to the menisci as shown in Figure 1.7. The first two layers, the superficial network (1) and the lamellar layer (2), make up the superficial zone previously described. The innermost layer (3) makes up the previously described deep zone of the menisci. The architectural makeup of the menisci suggests that the menisci is built for a direct role in biomechanics of the knee [19].

Figure 1.7 Synoptic drawing of collagen fibers in the three distinct layers of the meniscus [20].

Proteoglycans are negatively charged hydrophilic molecules that can retain water

up to 50 times their body weight. Strong networks of collagen fibrils in the inner

portions of the menisci immobilize these proteoglycans. During compressions, they

slowly dissipate the held water and thereby aid in restricting compressive forces [16].

Recently, a microscopic system of canals passing from the surface to deep within

the tissue has been identified. These holes are on the order of 10 µm and are thought to

22 allow for fluid flow through the mechanical pumping mechanism [21]. This pumping would allow nutrients to supply both the menisci and the synovial fluid and aid in the biomechanics of meniscal compression.

1.2.3 Vascular Pattern

The vascular supply of the meniscus is delivered from three paired genicular

arteries: the superior, the middle, and the inferior [7, 22]. The parameniscal vessels,

originating in the capsular and synovial tissues of the joint, are oriented predominantly in

a circumferential pattern [23]. These arteries supply the outer 10% to 30% of the medial

meniscus and the outer 10% to 25% of the lateral meniscus with radial branches directed

toward the center of the joint that penetrates the meniscal tissue [4, 23]. The horns of the

menisci are more vascular than the bodies of the menisci [22]. Although the peripheries

of both menisci are vascular, the inner portions are avascular. Therefore, the vast

majority of the nutrition for the menisci is achieved either through diffusion or

mechanical pumping [4].

1.2.4 Neurophysiology

The nerve supply of the meniscus closely follows the vascularization.

Approximately the outer one-third of each meniscus is innervated [7]. The anterior and

posterior horns appear even more innervated [4]. Three distinct mechanoreceptors have

been found in the horns of the medial meniscus, giving rise to the theory that the menisci

play an important role in sensory feedback of the knee [4].

1.2.5 Histology

The menisci are fibrocartilaginous tissues primarily composed of an intracellular

matrix. However, there is a sparse population of cells known as fibrochondrocytes [13].

These cells are responsible for synthesis, maintenance and repair of the intracellular

matrix [13]. There are two types of fibrochondrocytes in the menisci. These types can be

identified at both light and electron-microscopic levels. In the superficial zone, the

fibrochondrocytes tend to be somewhat oval or elongated in shape [21]. In the deeper

zone, the fibrochondrocytes tend to be more rounded. Both types of cells contain

abundant endoplasmic reticulum and a Golgi complex [8].

1.2.6 Function

The principal functions of the menisci are thought to be load transmission and

stabilization [24, 25]. Load transmission is accomplished by the increased contact area

between the femur and the tibia, decreasing contact stress during load transmission [7].

When the menisci is loaded, the circumferentially-oriented collagen fibers create hoop

stresses which counteract the extrusion of the meniscus [7]. Stabilization is

accomplished by targeting areas of contact stress to the optimal locations, otherwise

known as position control [24]. Koski reported that knees without the meniscus had a

greater anterior displacement during movement, demonstrating their use in stabilizing the

knee [6].

Secondary functions of the menisci include, but may not be limited to, shock

absorption, assistance in joint lubrication, maintaining the health of synovial fluid of the

24 knee, and even sensory function [5, 6, 16, 22, 26, 27]. As the knee is compressed, it acts as a shock absorber by elongating the circumferential collagen fibers and by extruding peripherally [6]. The shock absorbing capacity in the intact knee is about 20% higher than knees that no longer have menisci [9, 13]. However, the menisci do not act as a significant shock absorber when viewed in the context of the entire leg [28]. With an intact meniscus, the coefficient of friction in the knee may be as low as 0.001 [29]. The menisci improve joint nutrition by compressing the synovial fluid into the articular cartilage surfaces [6].

Approximately 50-90% of loads on the knee are transmitted through the menisci, depending on the knee flexion angle [7, 17, 26]. During knee extension, approximately

50% of the compressive load is transmitted through the menisci while upwards of 85% of the load is transmitted in 90 degrees of flexion [6]. The lateral meniscus is estimated to carry 70% of the load of the lateral compartment of the knee, while the medial meniscus is estimated to carry about 50% of the load of the medial compartment of the knee [6,

19]. Figure 1.8 shows how a meniscus is deformed and how the components of pressure are distributed when a force is applied.

Figure 1.8 Superior view of a deformed meniscus [1]

1.2.7 Development & maturation

The microanatomy of the meniscus is age-dependant [8]. The menisci appear as a

distinct structure at 8 weeks of fetal development [12]. The menisci in the fetus are

believed to have a more extensive vascular pattern than in the adult [8, 9, 22, 30]. In fact,

in newborns, approximately 50% of the outer region of the menisci is vascularized [26].

Also, prenatal menisci are very cellular in comparison to the adult tissue [30]. No drastic

histological change occurs at birth; the change is more gradual [12, 30]. This may be

caused by the introduction of weight bearing and may explain why the non-weight

bearing anterior and posterior horns retain a more complete blood supply [31].

Degenerative changes in the menisci associated with aging have been

demonstrated [26]. Figure 1.9 shows the changes in collagen percentage (of dry weight)

in different sections of the meniscus. Zone 1 shown in the figure describes the behavior

of the inner portion of the meniscus, zone 2 describes the behavior of the middle zone,

and zone 3 describes the behavior of the outer edge zone.

Figure 1.9 How collagen in the meniscus behaves over a lifespan [26]

1.2.8 Healing

If an injury is within the peripheral vascular zone of the meniscus, the trauma may

be healed; however, if the injury is in the interior avascular zone, the meniscus cannot be

repaired [4, 32]. As for meniscus transplantation, menisci are immunoprivileged tissue that are potentially transplantable [33].

There is still debate over whether it is possible for the human body to regenerate a meniscus if removed. Experiments in rabbits and dogs have shown that after meniscectomy, the removal of menisci, there is regrowth of a structure similar in shape and texture to a meniscus. However, the regenerated tissue was not fibrocartilage [26].

There is evidence of regrowth with human tissues as well, although the everyday use of joints makes this difficult or impossible [4, 26].

1.2.9 Anatomical interspecies variation

Knee joint menisci are found in all mammals [27]. Figure 1.10 shows a

comparison of the mature shape of the left medial menisci in the human, bovine, porcine,

sheep, canine, and monkey. Based on the aggregate modulus of the material, the sheep and porcine menisci were most similar to the human menisci [34]. Figure 1.11 shows a comparison between the porcine menisci and the human menisci.

Figure 1.10 Interspecies anatomical variation [34]

Figure 1.11 The figure on left shows the menisci of a porcine left knee while the figure on the right shows the menisci of a human right knee [27].

1.3 Meniscal Injury

The knee is the most frequently injured joint in the human body for individuals participating in sports. Of all types of knee injuries involved in this population, meniscal injuries are the most common [1, 6, 35-37].

Meniscal injuries are unusual in children, but they become more common in adolescence and beyond [12, 30]. In fact, 60% of individuals over the age of 65 have a degenerative horizontal cleavage tear, although these type of tears stay unnoticed for the most part [12]. The changes in vascularity, histology, and biochemical composition appear to be responsible for this trend [30]. Meniscal injury is seen much more often in the medial meniscus than the lateral meniscus. Medial tears outnumber lateral tears approximately 2.5 to 1 [38].

Treatment of meniscal injuries has greatly changed over the last 30 years.

Initially, the function of the meniscus and its importance to the function of the knee was poorly understood, and total excision was commonly performed as the most viable treatment option [31]. Recent advances in science have shown that the biomechanical consequences of removing the menisci are severe, and a commitment has been made to preserving, or replacing, the menisci [25]. Removing the entire menisci (meniscectomy or total meniscectomy) or a portion of them (partial meniscectomy) is commonly considered to cause degenerative arthritis [39-41]. Partial meniscectomy is less likely to cause osteoarthritis than total meniscectomy [42]. The results of a 13-year follow up study showed that increases in radiographic osteoarthritis were seven-fold after total meniscectomy and four-fold after partial meniscectomy compared to the intact menisci

[27]. In the short term, meniscectomy can have excellent results, but it is clearly not in the best interest of the patient in the long term [31].

1.3.1 Tearing

There are two major classes of tearing in the menisci. The first is traumatic

tearing, often associated with ligament injury in a younger, more active population. The

second is degenerative tearing, which generally occurs in an older population [35, 37].

Traumatic tearing of the menisci generally occurs in patients between the ages of 13 and

40 years of age. These injuries occur more frequently in those participating in sports requiring running, cutting, or physical contact [43]. When an isotropic material fails under tension, the crack propagates in a direction perpendicular to the direction of the applied stress. However, when a meniscus, an anisotropic material, fails under tension, the crack usually propagates parallel to the direction of the applied stress because of the fiber orientation [21]. The majority of collagen fibers are already arranged circumferentially in the direction of applied stress, so the radial fibers tend to fail first.

These fiber orientations are shown in Figure 1.12. Proteoglycans are much weaker than collagen fibers and, when stressed, will fail before the collagen fibers [21]. Excessive compression of the meniscus will not lead to a catastrophic failure, but rather to the creation of circumferential cracks that may propagate into something worse [21]. Figure

1.13 shows a circumferential tear (A) and how a circumferential tear can turn into a bucket handle tear (B).

Figure 1.12 Radial and circumferential fibers [44]

Figure 1.13 Tearing of the meniscus [21]

Vertical transverse tears can also occur, but are much less common than circumferential tears. These tears most commonly occur in the middle third of the lateral meniscus [43].

The symptoms associated with meniscal tears include joint line pain (88%), locking (84%), and joint effusion (69%) [45]. Clinical diagnosis accuracy of meniscal tears can be as low as 60% [45]. However, MRI has shown accuracy rates up to 98% for medial menisci and 90% for lateral menisci in diagnosing meniscal tears [12].

1.3.2 Meniscectomy

For a long time, meniscectomy was the treatment of choice for meniscal tears, as

it was thought to allow for total regeneration of a new meniscus [12]. However, many

clinical studies have documented the degeneration that follows a meniscectomy [46, 47].

Generally, the degree of degenerative change is directly proportional to the amount of

menisci removed [25]. In a study of degenerative changes following meniscectomy of

pediatric patients, after an average time period of 21 years, approximately half of the

patients described progression of symptoms, and 90% had abnormal radiographic results,

hinting that more severe results might be on the way [48].

Many in vitro studies have shown that meniscectomy causes a dramatic increase

in knee joint contact pressure [49, 50]. Beginning as early as 1948, radiographic changes

have been noted after meniscectomy including narrowing of joint space, flattening of the

femoral condyles, and formation of osteocytes [51]. Other joint changes that occur after

meniscectomy include sclerosis of the tibial subchondral bone, softening of the articular

cartilage due to structural and biochemical changes, and formation of a ridge on the

femoral condyle [25, 49, 52].

The effect of meniscectomy on the increase in peak stress on the tibial plateau is directly proportional to the amount of tissue removed during a partial meniscectomy [53].

However, if any or all of the periphery attachments or insertional ligaments are removed, the meniscus can be rendered completely functionless, producing the same results as a total meniscectomy despite the fact that most of the meniscus is intact [53]. When performing a partial meniscectomy, only the loose central portions of the meniscal body need to be removed [53].

The outcome of partial meniscectomy is better for partial medial meniscectomy than for partial lateral meniscectomy [42]. Results are significantly worse if both the medial and lateral menisci are removed (total meniscectomy) [54]. Degenerative changes occur more rapidly in the lateral compartment of the knee after total meniscectomy [16,

25, 48]. This is due to the greater role of the lateral meniscus in stress protection, while the medial meniscus is more important in joint stabilization [41]. Gender also seems to have some effect on the outcome of meniscectomy, as 45% of men and 10% of women went symptom free after meniscectomy [42].

1.3.3 Effects of Meniscal Injury

The earlier widespread use of meniscectomy has left many patients at risk for

arthritis at an early age [49]. Young patients between the ages of 25 and 40 years of age are now commonly seen presenting disabling arthritis as a result of a meniscectomy [45].

Effects of meniscectomy that contribute to the onset of osteoarthritis include increased contact pressure, decreased contact area, and decreased impact absorption.

Figure 1.14 shows the effects of different meniscal injuries on contact pressure in an intact knee. The first column shows a normal intact knee. The second column shows a knee with a simulated bucket handle tear. This third column shows a partial meniscectomy. Finally, the fourth column shows a total meniscectomy. It is evident by looking at the first row (the neutral knee) that the total meniscectomy has the largest maximum pressure, followed by the partial meniscectomy. The intact knee has the lowest maximum pressure and the bucket handle tear has little or no effect, providing the torn segment maintains its normal anatomic position [38].

Figure 1.14 Comparison of pressure distribution from an intact knee [38]

Figure 1.15 shows a comparison between the contact areas of an intact knee and a knee without the menisci in place. This clearly shows how the contact area is decreased after meniscectomy. After a meniscectomy, experimental results in human cadavaric knees have shown 33 to 50 percent decreases in contact areas and 100 to 300 percent increases in contact pressures [40].

Figure 1.15 Comparison of contact areas between an intact knee and a knee without menisci [1]

Figure 1.16 shows a comparison of the impact absorbing properties of the human knee. The intact knee (A) has a peak impact force of 1360 N. The knee with simulated circumferential tears (B) has a peak impact force of 1520 N. The knee with a complete meniscectomy (C) has a peak impact force of 1640 N. The knee with the cartilage and sub-chondral bone removed (D) has a peak impact force of 1870 N. Finally, the knee with a total knee replacement (E) has a peak impact force of 2390 N [55]. The increase in force as more of the meniscus is removed clearly demonstrates the importance of a fully functional meniscus in the knee.

Figure 1.16 Comparison of impact absorbing properties of the knee [55]

1.4 Meniscus allograft & repair

The treatment of meniscal lesions is the most common surgical procedure performed on the knee [56]. An estimated 1.5 million arthroscopic knee surgeries are performed each year, and more than half are on the meniscus. Treatment of these meniscal tears has changed considerably over the past century. Total meniscectomy, which was favored in earlier years, is now obsolete [56].

The major potential benefit of meniscal transplant is reducing the risk of degenerative osteoarthritis. The potential complications for meniscal transplant are low, but they do exist. These complications include inadequate graft fixation, effusion, immune rejection, thinning or loss of graft, degenerative joint changes, and disease transmission [57].

Despite the use of meniscal allograft transplantations for more than 15 years, it has not become a commonplace procedure. In fact, it is thought by some to be the number one problem in orthopedics today because of the inconsistency of the procedure

[56].

1.4.1 Repair

The first reported meniscal repair was performed in 1883 by Thomas Annandale

[7]. Since then meniscal repair has become the standard procedure for fixing a tear [56].

Clinical studies have proven that meniscal repairs will heal in the vascularized region of

the knee if the knee is stable [42]. Meniscal injuries occurring totally within the vascular

portion of the meniscus are referred to as red-red tears and have the best opportunity for

38 healing. Red-white tears are tears in which part of the tear is in a vascularized region of the meniscus and part is in an avascular region. These tears also will heal, but not with the same success. Finally, white-white tears are tears completely in an avascular portion of a meniscus. These tears theoretically will not heal. However, new procedures are being developed that could allow a surgeon to connect the lesion to a vascularized portion of the meniscus as shown in Figure 1.17 [58]. Modern techniques have allowed less vascularized areas of a meniscus to heal using parameniscal synovial abrasion and fibrin

clots [42, 56].

Figure 1.17 Connecting a lesion to vascularized meniscal tissue [58]

Figure 1.18 shows a lateral meniscus being repaired with sutures. Repairs are

often performed with either an inside-out or outside-in suture technique [59]. Special

staples (also called meniscus arrows) and different types of glue have also been used to

hold the tissue together to allow for healing [59, 60]. Staples and glues used together

have shown improved results over using either one alone [61].

Figure 1.18 Lateral meniscus repair [43]

1.4.2 Meniscus transplant

Despite the current successes of meniscal repair, not all injuries can be repaired

[56]. The first open meniscus transplants were performed in 1984 [56]. Since then,

many different types of transplants have been explored. Table 1.1 shows the many kinds

of meniscal substitutes that have been tried. However, only meniscal allograft, meniscal

autograft, and meniscus scaffold have been applied clinically [56].

Meniscus prosthesis • Teflon • Silastic • Carbon fiber • Dacron Meniscus allograft • Fresh • Viable allografts • Deep-frozen • Lyophilized • Cyropreserved • Glutaraldehyde fixed Meniscus autograft • Patellar tendon • Quadriceps tendon • Achilles tendon • Fat pad • Perichondral tissue Meniscus scaffolds Genetically engineered tissue Meniscus xenograft

Table 1.1 Meniscal substitutes and the materials used for each (adapted from [56])

Meniscal prosthesis is a procedure of implanting a man-made material to act as a meniscus. Meniscus allograft involves taking a meniscus from a human cadaver and implanting it into the patient. Meniscus autograft procedures use human tissues from the patient’s body to mimic the behavior of the meniscal tissue. Meniscal autograft is not recommended for long-lasting meniscal replacement because it does not achieve the material properties of the meniscus [56]. Meniscus scaffolds have been used to successfully repair injured or diseased tissues and organs, however they have not been as successful when repairing tissues that serve a predominantly biomechanical function

[62]. Clinical results for meniscus scaffold are rare, and little or no biomechanical testing has been performed on the tissues [56].

1.4.3 Meniscus allograft

Meniscus allograft uses a meniscus from a human cadaver as the substitute for the absent meniscus in the patient’s knee. Indications for meniscal allograft transplantation include young age (less than 40 years old), pain and swelling unresponsive to conservative treatment, and minimal degenerative changes (including a stable knee and a normal axial alignment) [63, 64]. As of 2003, more than 4000 meniscal allograft transplantations have been performed throughout the world [56]. The goals of meniscus allograft surgery are as follows:

• Reduce pain

• Prevent degeneration of cartilage

• Reduce the risk of osteoarthritis

• Restore optimal mechanical function of the knee [65].

Storage of the meniscus is an important consideration. Fresh transplants are the most immunogenic; however, they present significant logistical problems in storage and

availability [56, 63]. They can be kept in culture for 5-14 days with no apparent loss of

metabolic activity [64]. Deep-frozen meniscal allografts are easier to store, but the deep-

freezing process destroys donor cells [56]. Lyophilized or freeze-dried transplants result

in the decay of the entire ground surface, the destruction of all antigens and enzymes, and

significant shrinkage (up to 2/3) [56, 63]. Cryopreservation is very expensive financially,

42 but may provide similar results to fresh frozen transplants [56, 63]. The glutaraldehyde fixed method may result in shrinkage of the meniscus [56]. It seems that cryopreservation is the best method [57].

Secondary sterilization is necessary to reduce infection from entering the body through the transplant. Sterilization is performed either with ethylene oxide or with gamma-irradiation. Ethylene oxide may induce a secondary synovitis [63]. Gamma- sterilization may weaken collagen structure [56, 63]. The tear strength and tear strain have been found to be similar for both ethylene oxide and gamma-sterilization methods; however, both are lower in tensile strength than the original tissue [66]. Freeze drying is another sterilization technique that has been used to successfully sterilize other tissues; nevertheless, it is not useful with the meniscus because it distorts and dries the tissue [9].

1.4.4 Pre-operative planning and size matching

Exact preoperative planning and size matching are vital to the success of the

meniscal transplantation [14, 56, 67]. Any sizing error of more than a few millimeters

could jeopardize the biomechanical function of the allograft [68].

Radiological examinations such as x-rays, bone scans, computerized tomography

(CT) scans, and magnetic resonance imaging (MRI) are recommended as a part of pre-

operative planning. X-rays assess the degree of arthritis and allow sizing of meniscus

from bony landmarks. Bone scans assess the subchondral bone. CT scans are used for

precise sizing to find the appropriate allograft. Finally, MRI is employed to find information about the existing meniscus, cartilage, ligaments, and tendons and is also

43 used for sizing [56, 64]. Some consider MRI to be the most accurate sizing diagnostic, but it still has a mean difference of 2.25 ± 2.04 mm between the actual dimension and the dimension from the MRI [68].

X-rays are the most common way to size donor menisci and can result in errors up to 32% [25, 56]. X-ray sizing is often performed by matching the overall width of the tibia with the overall width of the donor tibia [42]. However, research has shown that the

thickness of the meniscus is also an important consideration [69]. Thickness cannot be

determined by looking only at an x-ray in the transverse plane.

Using the meniscus from the opposite knee for implant sizing is a controversial

subject. Some studies have shown that the medial and lateral menisci of the opposite

knee can accurately be used for sizing purposes [42]. Other studies have shown the

opposite, indicating that using the contralateral meniscus for sizing may lead to

mismatching [68]. However, all seem to agree that the donor meniscus should come

from the same side and compartment as the recipient knee [9, 42].

Meniscal allografts should be the correct size to prevent degenerative arthritis.

However, there is no clear consensus about the best technique for appropriate size

matching. Studies need to improve the reliability of graft sizing and the effects of

mismatched sizing need to be performed [56, 70].

1.4.5 Surgical technique

Many different surgical techniques have been proposed for meniscal allograft.

These various techniques can be fit into two major groups: fixation with bone plugs and

44 fixation without bone plugs [57]. The advantage of using soft tissue fixation (without bone plugs) is that size matching is much easier [56]. However, studies have shown that fixation with bone plugs is more effective [25, 63, 71]. Figure 1.19 compares bone plug fixation techniques. For medial meniscus allograft, shown on the figure as (a), the two- bone plug technique is generally recommended [56]. In this technique, the separate bone plugs are inserted into the medial joint space with sutures. The most common bone plug diameter is 9 mm. Because the distance between the horns is small (approximately 1 cm) a keyhole technique is recommended for lateral meniscus allograft, as shown in the figure as (b) [56]. Peripheral sutures are used in both cases to attach the new meniscus to the salvaged peripheral rim of the removed meniscus [56, 72].

Figure 1.19 Bone plug fixation techniques for meniscal allograft [56]

Meniscus allograft can be performed both arthroscopically and with an open surgical technique. There is evidence that meniscal allograft can be performed

45 satisfactorily with an arthroscopic procedure [56]. Therefore, an open surgical technique should only be used for combined procedures, as it brings a greater risk of infection [56].

The knee is braced in full extension post-operatively and the patient maintains limited weight-bearing [63]. Progressive range of motion is initiated at 3 weeks, and full weight-bearing is possible at 7-8 weeks [63]. The patient can return to full activities at 6-

9 months [63].

1.4.6 Results of meniscal allograft

Experimental work in animals has proven that meniscus allograft can heal and

function similar to the original meniscus [33, 42]. Despite the fact that numerous

meniscal allograft transplantations have been performed on humans, long-term clinical

results of the surgery are not clear. This is due to the variation in surgical and fixation techniques, graft processing techniques, numbers of patients, clinical evaluation and

scoring criteria, and the lack of control groups [56]. In addition, long-term results are not

clear because this is a relatively new procedure. However, it is clear that lateral allografts seem to last longer than medial allografts [56].

Short term results suggest that meniscal allografts can provide significant pain

relief [14, 73, 74]. In a study by Cameron and Saha of 67 knees at a mean follow-up of

31 months, 90.5% achieved good to excellent results [75]. Other clinical scoring systems

reveal fair to good results after 2-5 years in 87% of patients [64].

Generally, the meniscus is considered an immunologically privileged tissue,

leading to the belief that rejection should not be a factor in meniscal allograft [9, 76, 77].

However, an immune response is possible due to the presence of class I and II histocompatibility antigens. There is only one report providing clinical evidence of rejection [25]. The risk of HIV transmission from soft tissue allografts is estimated to be

1 in 1 million [42].

A study of contact pressures in the medial tibial plateau after medial meniscal allograft found that the allograft did not consistently restore normal contact mechanics in the knee because of the process of implementation and degree of mismatch sizing [78].

However, the allograft did significantly reduce the contact pressure when compared to meniscectomy [78].

A study of how fixation methods affected contact pressure in the knee presented some interesting results. None of the methods studied restored the original normalized pressure in the knee [78]. Fixation with bone plugs proved to have a lower maximum pressure than with sutures alone [78]. Interestingly, fixation with bone plugs alone versus fixation with bone plugs and peripheral sutures displayed no statistical difference

[78].

1.5 Software used in research

Analyzing the complex geometry of the knee is a complex task. Currently, there are no types of software that directly transfer medical images to an analysis.

Furthermore, various analysis codes were explored to find which softwares worked the best with this particular research. Different softwares used during research are briefly described in this section.

1.5.1 Amira®

Amira® is an advanced three-dimensional visualization and volume-modeling

tool for medical images. This software can be used to create three-dimensional volumes

from two-dimensional medical images such as those obtained from MR or CT images.

Automatic or manual segmenting can be used from multiple planes providing the most

accurate three-dimensional images possible from two-dimensional medical images.

1.5.2 Algor®

Algor® is an emerging finite element analysis program. Its strength is linear

static stress simulations, although it is branching out into other types of analysis. Algor®

has an easy-to-navigate windows-type menu system, but analysis is typically very slow.

It has difficulty handling complex simulations.

1.5.3 LS-DYNA

LS-DYNA is an advanced general-purpose finite element software for analyzing large-scale dynamic structural responses. The main solver involves an explicit formulation, although an implicit formulation is available with limited capabilities [79].

LS-DYNA is commonly used for biomedical applications because of its ability to simulate large-scale deformations and its ability to create an adaptive mesh.

1.5.4 Superforge®

Superforge® is a forging simulation software by MSC software®. It is an easy-

to-use finite volume software tailored to forging applications. Because it uses finite

volume formulations, meshing is simple. However, when using this software for a non-

forging application, required boundary conditions may not be available.

1.5.5 Dytran®

Dytran®, also by MSC software®, uses both finite element and finite volume

solvers together. By combining both Lagrangian and Eulerian formulations, users have a

great deal of flexibility. Dytran® is designed for short-term dynamic events involving

the interaction of fluids and structures.

1.5.6 MARC®

MARC®, also by MSC software®, is an inherently nonlinear finite element

analysis software. The strengths of MARC® include the ability to simulate large-scale

deformations and advanced contact between surfaces. MARC® also provides a robust

remeshing feature with a large number of material models.

CHAPTER 2 LITERATURE REVIEW

Significant advances have been made in creating an accurate finite element model

of the human knee and the menisci. In 1992, Spilker et al. introduced a two-dimensional

finite element analysis representation of a meniscus. At the time, the material model used

was revolutionary and provided more accurate results than the then current standard of a

linear elastic material. This material model was a transversely isotropic biphasic model,

which consisted of a biphasic material composed of both a fluid phase and a solid phase.

In order to utilize this transversely isotropic biphasic material model, Spilker et al.

created their own finite element code. The material properties for the modeled meniscus

are shown in Table 2.1.

Solid and Poisson’s Permeability Young’s modulus Shear modulus fluid contents ratio s -15 Φ = 0.25 κ = 1.26 x 10 E1 = Eθ = 200 MPa υ12 = 2.0 G12 = 0.025 MPa f 4 Φ = 0.75 (m /Ns) E2 = Er = Ez = .055 MPa υ23 = 0.05 G23 = 0.026 MPa

Table 2.1 Material properties from Spilker et al. [80]

Using this material model today with commercial codes is difficult or impossible. The

geometric model of the tissue, while acceptable at the time, is now archaic. To begin

with, the geometry of the meniscus and the knee were approximated by modeling a

toroidal geometry, thereby not taking into account the actual shape of the material. In

addition, the analysis was performed only two-dimensionally, as shown in Figure 2.1,

while the material and the geometry of the meniscus behave three-dimensionally.

Figure 2.1 Two-dimensional representation of a meniscus [80]

Still, the analysis produced some interesting results, as shown in Figure 2.2. The small illustrations in each show the direction of stress being considered. In particular, the analysis demonstrated that the maximum stresses are found in the circumferential direction as shown in (C). In the figure, the whiter areas represent areas of higher stress.

[80]

Figure 2.2 Stress distribution of a two-dimensional representation of a meniscus [80]

Also in 1992, Mow wrote about current modeling techniques and recommended his ideas for future directions. As for material modeling, he stated that the meniscus is

not a linear elastic material and should not be modeled as one. He recommended using

not only a biphasic material but a biphasic material that included a representation of the

anisotropic and nonhomogenous nature of the actual tissue. Mow stated that the area of

most needed improvement was in geometric modeling. At that time, finite element

models were typically modeled either as a two-dimensional object or as an axisymmetric

torus with a wedge-shaped cross section. He stressed that realistic three-dimensional

models of the structure must be used in the future. [13]

A few years later, in 1996, Prendergast et al. sought to use a commercial finite

element code to replicate the earlier results of Spilker. They chose to use three readily

available software applications at that time: DIANA (TNO, Delft, The Netherlands),

MARC (Palo Alto, California, United States), and SWANDYNE (Swansea, United

Kingdom). The goal of the study was to match the previous results of a biphasic material

model with a poroelastic material model, a model traditionally used in soil mechanics

applications. Although a wide variety of testing was not completed, Prendergast et al. did

find that all three commercial codes could be used to accurately model both linear and

nonlinear biphasic materials. Figure 2.3 shows how close all three commercial codes

were in comparison to the earlier results of Spilker for determining the reaction force.

[81]

Figure 2.3 Comparison of poroelastic material models to a biphasic material model [81]

In 1998, Viceconti et al. studied four different methods of automated meshing of the human femur: a mapped mesh, a tetra mesh, a hexa mesh, and a voxel mesh. Samples of these mesh types are shown in Figure 2.4. A mapped mesh, as shown in (a), is a manually controlled mesh that can produce accurate and fast results; however, the manual component of the meshing is extremely time consuming and complex. The next method examined was a tetra mesh, shown in (b) of the figure. This type of mesh is both quick and accurate. The disadvantage of this method, at the time of this study, was that a solid

55 model had to be obtained prior to meshing; however, this problem has been resolved in the current research as described in Chapter 4. Still another method was the hexa mesh, as shown in (c), which also produced accurate results, but took considerably more computational time. Finally, the last method of automatic mesh generation studied was voxel meshing, as shown in (d) of the figure. Voxel meshing has a distinct advantage in that the three-dimensional mesh comes directly from voxels, which are discussed in more detail in Chapter 4. However, the massive number of elements needed to mesh the femur using this method makes the computational time high, and the reported results are poor.

[82]

Figure 2.4 Meshes produced by various automatic mesh generation techniques [82]

Significant advances were made in 2002 by Haut Donahue et al. when they used

CT scans to model the shape of bones and manual digitizing to model cartilage. The cartilage was modeled as a linear elastic material, and bone was modeled as a rigid body.

The model includes the tibia, femur, both menisci, articular cartilage, the ACL, the MCL, and the transverse ligament. It ignores the fibula, patella, and all other tendons and ligaments as they are thought to be trivial in the structural integrity of the joint in full extension. A hexa mesh was used to mesh the geometry, as shown in (a) of Figure 2.5. It was then analyzed in ABAQUS (HKS Inc., Pawtucket, RI). The force used for analysis was 800N, or one body weight. The contact pressure results are shown in (b) of the figure. [83]

A B

Figure 2.5 ABAQUS mesh and results [83]

Later, in 2003, Haut Donahue et al. extended their research to further investigate

finite element analysis of menisci. Using the model they created in Haut Donahue et al.

(2002), they reached three conclusions about meniscus replacement. First, the material of

the menisci should be modeled as a linear elastic and transversely isotropic material.

Using this material gave errors of only around 5% compared to experimental results while a linear elastic and merely isotropic material gave errors of more than 30%.

Second, when tissues are chosen for replacement of the meniscus, the circumferential modulus, axial/radial modulus, and horn stiffness are the most important material characteristics and must be considered when choosing a material, whether it is from an allograft, autograft, or even a man-made material. Finally, the stiffness of bone plug attachment is crucial to the success of the replacement. When bone plugs are used, weight bearing must be avoided until the bone plugs have fused. [84]

Pfeiler studied the dynamic response of the human knee using finite element analysis in 2004. The models were created from CT scan data and were constructed with brick elements, as shown in Figure 2.6. Material properties were defined as linear elastic and isotropic. This is one of the first studies to examine the dynamic effect of a force on the knee. The force applied was a 100N preload and a 65 kg mass, or a resulting force or roughly 740N.

Figure 2.6 Dynamic three-dimensional FEA model of the knee [85]

Finite element analysis techniques have been used to model the function of the knee. Early models were created in two-dimensions to simplify the complex geometry of bones and other tissues. Recently, three-dimensional models have become more common in attempts to accurately replicate the actual geometries of the tissues. Many different material models have been examined with mixed results. Although there is evidence that modeling biological tissues as a simple linear elastic and isotropic material is not as accurate as some other methods, there is no gold standard for these material properties.

The goal of this dissertation is to create three-dimensional models of the knee to examine the effects of meniscal sizing on knee stress. Because of the nature of this work, more emphasis will be placed on replicating accurate geometric models of the knee rather than using an ideal material model.

Improving meniscal sizing has many benefits as previously discussed. Finite element analysis is a particularly appealing method of studying meniscal sizing because of the difficulty in replicating the true in vivo behavior of the knee joint. Research examining meniscal sizing using this approach has not been performed up until now; although, the results could greatly benefit the future treatment of knee injuries.

CHAPTER 3 BIOMATERIAL CHARACTERIZATION

When it comes to biomedical materials in general, the most important material properties are stiffness and ultimate strength [86]. Stiffness represents the deformation for a given load while ultimate strength represents the load that causes failure. Stiffness is dependent on the relationship between stress and strain [86]. Stress, the force per unit

area, measures the load on a material sample. Strain is a measure of the displacement of

a sample in response to stress.

3.1 Determining material properties

The material properties of cartilage have been tested using many techniques.

They include confined compression creep testing, unconfined compression testing, shear

testing, indentation testing, and tensile testing [87]. Cartilage has been shown to be a

structure of materials and cannot be modeled as a single material. Because it is a

structure, it is impossible to use small samples for testing without disrupting the structural

integrity of the tissue [87]. All of the testing methods listed above except for indentation testing require the tissue to be cut into small sample sizes, destroying the structural integrity of the tissue. For this reason, indentation testing is a particularly appealing method for characterizing the material properties of the menisci.

As with most biological materials, the meniscus is a multi-phasic anisotropic material that exhibits a time-dependent behavior. However, because material cannot be exactly replicated, assumptions must be made to allow for a more simple model of the material [88]. Indentation testing allows us to model the complicated structure of the

60 meniscus with a simple linear elastic model, requiring only Young’s Modulus E and

Poisson’s ratio ν.

Indentation testing is a nondestructive form of testing that is commonly used for determining the material properties of articular cartilage [88-90]. The indentation testing procedure used was developed by Jin and Lewis [90]. The advantage of this indentation procedure is that it does not require a separate testing technique to determine the

Poisson’s ratio of the material; rather, it utilizes the nondestructive nature of indentation testing to solve for Poisson’s ratio. This method is based on the mathematical model of a

cylindrical indentation test created by Hayes et al. in 1972 [91]. In this procedure, a

cylindrical punch with radius a indents to either a known load p or a known depth w. The

material to be indented is bonded to a flat plate and has a known thickness h. The

equation for this model is shown in Equation 1 where G is the aggregate modulus of the

material, ν is the Poisson’s ratio for the material, and κ is the correction factor that

accounts for the finite layer effect. Figure 3.1 shows a schematic diagram of these

parameters.

p 4Ga = κ (a / h,υ) (1) w 1−υ

Figure 3.1 Schematic diagram of indentation parameters [88]

Because indentation testing is nondestructive, the test can be performed a second time on the same area of the same specimen, this time with a different radius a. Dividing

Equation 1 with one radius by Equation 1 with a second radius produces Equation 2.

⎛ p ⎞ ⎜ ⎟ ⎝ w ⎠ a κ()a / h,υ 1 = 1 1 (2) ⎛ p ⎞ a κ(a / h,υ) ⎜ ⎟ 2 2 ⎝ w ⎠2

Here, the only unknown is the ratio of the correction factors, which are dependent on a, h, and ν. Because a and h are known, we can use an interpolating program developed by Jin and Lewis to determine Poisson’s ratio [90]. Now, there is only one remaining unknown left in Equation 1, so we can solve for the aggregate modulus G. Then, using Equation 3, we can solve for Young’s modulus.

E = 2G(1+ν ) (3)

This procedure was validated by Jin and Lewis using an ELF 3200 testing apparatus and a sample of polyethylene rubber 2 mm thick with known material properties [90].

Our experimental setup also used an ELF 3200 testing apparatus by EnduraTec

(Minneapolis, MN). Three different size indentation heads were manufactured in-house out of stainless steel. These indenters were manufactured with cylindrical radii of 1 mm,

2 mm, and 4 mm. Drawings of these indenters are shown in Figure 3.2. The end of each tip is an exact cylinder for at least 0.02 inches, more than the required indentation depth.

Figure 3.3 shows a magnified view of the actual 4 mm indentation head.

Figure 3.2 1 mm, 2 mm, and 3 mm indenter drawings

Figure 3.3 4 mm stainless steel indentation head

To hold the specimen, a specimen table was manufactured in-house out of 2024 aluminum. A diagram of this table is shown in Figure 3.4. The specimen was attached to the top part of the specimen table via sutures, and the bottom part attached the table to the testing apparatus. By adjusting set screws in the middle piece, the specimen could be maneuvered in two dimensions providing the ability to test any part of the specimen without resuturing it to the table.

Figure 3.4 Specimen table apparatus

Before testing the tissue, two rubber samples with known material properties similar to the material properties of a meniscus were tested on the apparatus as shown in

Figure 3.5. The results of the testing were inconsistent and did not match the known material properties of the rubber sample. One reason for this could be the way the correction factor κ was determined. The iterative interpolating program used to solve the nonlinear equation did not converge consistently. Another reason could be that this procedure was developed for use on articular cartilage, and we were using it on the fibrocartilage material of the meniscus.

Figure 3.5 Testing apparatus

3.2 Biomaterial properties of cartilage

Cartilage behaves as a fiber-reinforced, porous, and permeable composite material

[16]. Load bearing is believed to play an important role in the health of cartilage [87].

The visual appearance of cartilage alone is not enough to determine its ability to function as a load bearing material. Further testing, such as mechanical testing or biochemical analysis, must be used [92]. The greatest indicator of the mechanical properties of cartilage is the water content [92]. The modulus of the material decreases with increased water content in a linear relationship [92].

3.2.1 Articular cartilage

Articular cartilage exhibits both a viscoelastic and a biphasic response under tension, compression, and shear [93]. A biphasic model is a common method for

66 modeling articular cartilage. In this model, the solid phase of articular cartilage is modeled as a hyperelastic isotropic material [94].

Table 3.1 shows the variation of Young’s modulus with various compressive testing techniques, on the articular cartilage of the patella. Poisson’s ratio has been indirectly calculated between 0.37 and 0.47 using confined compression testing [95].

Tensile testing verified Poisson’s ratio to be between 0.37 and 0.50 using direct calculations [95]. This shows how sensitive the testing methods can be – even testing the same area of the same type of tissue can result in dramatically different mechanical properties.

Testing method Young’s modulus (MPa) Indentation 2.25 Confined compression 0.7 Unconfined compression 8.4 – 15.3

Table 3.1 Variation of Young’s modulus with testing techniques (adapted from [95])

Cartilage exhibits its viscoelastic behavior because of the fluid flow of the liquid phase through the solid phase of the tissue [96]. This flow is related to tissue permeability through the hydraulic permeability coefficient k, which can have values ranging between 4.0 x 10-16 and 21.7 x 10-16 m4/Ns [95].

3.2.2 Menisci

The menisci are composed of fibrocartilage, an anisotropic nonlinear viscoelastic material [11, 97]. They are nonhomogeneous, which signifies that the material properties

67 of the tissues change depending on which position of a meniscus is being tested [53].

The mechanical properties also are dependent on age and level of degenerations [87, 92].

The material properties for menisci are not as widely available as the properties of articular cartilage. Table 3.2 shows a comparison between the material properties of articular cartilage and the material properties of a meniscus. The stiffness of a meniscus is only half of the stiffness of articular cartilage and dissipates more energy under dynamic loading [16]. The permeability, which relates to shock absorption, is only about one-sixth that of the permeability of articular cartilage [16].

Site Compression (MPa) Permeability (m4/Ns) Articular Cartilage 0.79 4.70 x 10-15 Meniscus 0.42 0.81 x 10-16

Table 3.2 Mechanical properties of articular cartilage (adapted from [16])

3.3 Biomaterial properties of cortical bone

A depiction of the structural organization of bone is shown in Figure 3.6. At the macrostructure level, bone is composed of two types of bone material: cancellous (or trabecular) bone and cortical (or compact) bone. Cancellous bone occupies the inner regions of bones. Structurally, it is composed of small trabecular struts and marrow- filled cavities [98]. The outside of bone has a denser material known as cortical bone.

This harder, more brittle type of bone is responsible for most of the load transmission through bone [99].

Figure 3.6 Structural organization of bone [98]

At the microstructure and sub-microstructure level, collagen fibers align themselves into a planar layer of collagen fibers known as a lamella. Three to eight lamella are wrapped concentrically around a canal to form an osteon [98]. Osteons are arranged parallel to the long axis of the bone. The resulting canals in the center of these osteons, referred to as Haversian canals, supply the bone with a blood supply [3].

At the nanostructure and sub-nanostructure level, the collagen fibers used on the lamella are composed of multiple parallel strands of collagen fibrils [98]. Collagen fibrils are made of collagen molecules and bone mineral crystals. Like the osteons, these collagen molecules are also aligned parallel to the long axis of the bone.

Cortical bone is composed of the mineral hydroxyapatite, the fibrous protein collagen, and water [100]. Type I collagen is the main organic component, although

there are small amounts of Type III and Type VI collagen as well [100]. The density of

wet cortical bone is 1990 kg m-3 [100].

There is evidence that the mechanical properties of cortical bone vary at different

structural levels [98]. The Young’s modulus of a macrostructural wet specimen typically

ranges from 14 to 20 GPa while the Young’s modulus of a microstructural wet specimen

is closer to 5.4 GPa, a significant difference. Currently, there is no mechanical testing

data for the nanostructural level [98].

Bone is commonly modeled as a transverse isotropic material [100]. The

mechanical properties used for modeling cortical bone as an isotropic material are shown

in Table 3.3. The yield strength of bone has been found to be 114 MPa [100].

Femur Tension Femur Tension Femur Compression (Ultrasonic (Mechanical Testing) (Mechanical Testing) Testing) Elastic Moduli (GPa): E1 12.0 12.8 11.7 E2 13.4 12.8 11.7 E3 20.0 17.7 18.2 Shear Moduli (GPa): G12 4.5 - - G13 5.6 3.3 - G23 6.2 3.3 - Poisson’s ratios: ν12 0.38 0.53 0.63 ν13 0.22 - - ν23 0.24 - - ν21 0.42 0.53 0.63 ν31 0.37 0.41 0.38 ν32 0.35 0.41 0.38

Table 3.3 Mechanical properties of cortical bone (adapted from [100])

CHAPTER 4 DETERMINING GEOMETRY FROM MRI/CT SCANS

4.1 Approaches to finding geometry

Two ways to virtually mimic the three-dimensional geometry of an object are through digitizing and through three-dimensional imaging. Digitizing involves using a digitizing device, such as the MicroScribe© shown in Figure 4.1, to find three- dimensional point coordinates on the surface of an object. These points are usually taken in splines, so they can later be more easily transformed into a three-dimensional solid.

Digitizing can replicate an object quickly and relatively inexpensively; however, the accuracy is limited. Also, it cannot replicate interior voids. Digitizing biological tissues can be especially difficult because it requires being able to physically trace the outside borders of the tissues. This makes it impossible to digitize an intact knee without completely dissecting it. Therefore, digitizing soft tissues in their native positioning may be impossible.

Figure 4.1 MicroScribe© digitizing tool

Another way to determine the shape of an object is through three-dimensional imaging. Three-dimensional imaging involves reconstructing the three-dimensional geometry by using a finite number of two-dimensional images. Usually, in medical objects, these images are from CT scans or MR images. While segmenting is more cost expensive due to the cost of actually generating MR and CT images, it is generally more accurate. Furthermore, three-dimensional imaging can identify interior voids, which is not possible when using digitizing methods. Creating three-dimensional geometries from two-dimensional images is a non-destructive method, providing the ability to obtain the geometries in their native positions.

4.2 Using CT and MR images

CT scanners use an x-ray source that rotates around a specimen to measure its density. The specimen table can be translated to image different slices along the same plane with a set spacing between each plane. Images from CT scans are gray scale, where darker tones represent objects or tissues with a lower density and lighter tones represent objects or tissues with a higher density [101]. CT, or computed tomography, imaging was developed in the 1970s and quickly took over traditional methods such as x- rays for determining three-dimensional geometry of structures.

Magnetic resonance imaging (MRI), also developed in the 1970s, uses a very strong magnetic field to align the nuclei of hydrogen protons [101]. Similar to CT, grayscale images are produced in parallel planes with a set spacing between each plane.

T1 and T2, two common types of contrast weighting, can be used to examine tissues of

72 different densities of hydrogen. Tissues with very little hydrogen, such as bone, appear as a darker tone in both contrasts. Tissues with more hydrogen have a lighter tone [101].

Because MRI does not use x-rays, it is not as harmful to the human body as CT.

CT scanned images are most accurate when determining the geometry of dense tissues such as bones. MR images are most useful when used to determine the shape of softer tissues. Using CT scans alone would result in poor imaging of soft tissues, and using MRI alone would result in poor imaging of bone. Therefore, it is useful to use both imaging techniques together to form a reconstructed three-dimensional geometry where the bone is retrieved from CT scan images and the soft tissue is retrieved from MR images.

However, using MR and CT images together presents a challenge. The structure that is imaged has to be in an identical anatomical position for both imaging techniques.

The first step in doing this is to lock the tissue in a set position. This was accomplished by embedding the structure into a foam casting. Because the foam casting was nonmetallic, it was capable of being imaged with both a MRI and with a CT scan in exactly the same anatomic position.

4.3 Constructing three-dimensional geometries with Amira®

The first step in creating three-dimensional geometries is segmenting each image.

This is done by thresholding a certain range of tissue. For example, Figure 4.2a shows an original CT scan, while the white region in Figure 4.2b shows the bone thresholded. In this case, each pixel, or unit of area, within the thresholded area is then considered to be

73 bone. Error is introduced when only a portion of a pixel is one type of tissue. In a case where half of the pixel is bone (white) and the other half is soft tissue (black) the pixel color would be blended to average the materials together. Thresholding this pixel would be difficult; either the entire pixel would be included as bone, or the entire pixel would be excluded, regardless of where the actual tissue boundary is found. This demonstrates why an increased number of pixels lead to an increased accuracy.

A B

Figure 4.2 Identifying pixels

The next step involved in reconstructing the three-dimensional geometry is to take the two-dimensional pixels and turn them into three-dimensional voxels. Voxels are volumetric representations of pixels that have the same surface area, but they also have a third dimension, the distance between slices, included. This is demonstrated in Figure

4.3. Voxels are most accurate when the distance between slices is the same as the pixel dimensions, making the pixels perfect cubes [101]. In our case, the CT scans used a 0.59

74 mm pixel size with 1 mm spacing between each slice. The MR images were created using a 0.75 mm pixel size and a 0.75 mm slice thickness.

Figure 4.3 Creating voxels [101]

The final step is to stack the layers of voxels on top of one another to create the solid geometry. Then, programs like Amira® can use numerical algorithms to smooth the surfaces and create triangular surface meshes that represent the surface geometries.

Next, virtual lights are added to illuminate the surfaces and improve the sense of three- dimensionality. Figure 4.4 shows the bones of a left porcine hind limb created in

Amira®.

Figure 4.4 Three-dimensional geometry created in Amira®

4.4 Importing models

After we have three-dimensional geometries of the tissues, the next step is to convert them into a file format that we can use in finite element analysis (FEA). Table

4.1 shows different three-dimensional file formats that can be exported using Amira®.

The advanced visualization formats can be used to create advanced images to view the geometry; however, they are not useful for FEA. FEM (finite element method) file formats, such as Fluent, Hypermesh©, and I-DEAS, are designed to be used in either finite element analysis or finite volume analysis programs. The Fluent file format is created specifically for Fluent, which is a fluid flow analysis program that is not particularly useful for modeling bones and soft tissues. The Altair HyperWorks© file format can be used with HyperMesh©, an extensive meshing program, to create three- dimensional surface meshes. The I-DEAS format is another file format that represents

76 the surface geometry for a specific software application, in this case I-DEAS. One modeling format, the AutoCad® file format, represents the surface geometry by using two-dimensional triangles. Two specialized formats, the Stanford triangle format and the

Amira® internal format, are available for specific software applications. These specialty formats are not useful for transferring the geometry and cannot be imported using common engineering softwares. The final format available for transferring the geometry is in an STL file. An STL, or stereolithography, file uses two-dimensional triangles to represent the surface of the geometry. The resulting surface is accurate, but the resulting triangles can have poor aspect ratios, making them difficult to turn into a three- dimensional mesh.

Advanced visualization formats AVS file format (*.inp) Open Inventer file format (*.iv) WaveFront standard format (*.obj) FEM formats Fluent file format (*.cas) Altair HyperWorks© software file format (*.hmascii) I-DEAS universal file format (*.unv) Modeling format AutoCad® file format (*.dxf) Specialized formats Stanford triangle format for points and surfaces (*.ply) Amira® internal format (*.surf) Surface triangulation Stereolithography file format (*.stl)

Table 4.1 Three-dimensional export options from Amira®

Although the files differ in format, the FEM, modeling, and surface triangulation formats create the same basic surface geometry. This surface geometry is formed by multiple two-dimensional triangles. The different formats allow them to be read by

77 various commercial softwares. Figure 4.5 shows an STL representation of the left porcine knee demonstrating how two-dimensional triangles are used to represent the three-dimensional surface of the geometries.

Figure 4.5 STL file format of the porcine left knee (anterior view)

One method for transferring the geometry to a finite elements analysis program for meshing is to first convert the STL file into a solid model. This can be performed using a program such as 3DStudio Max®. The first step is to import the STL geometry.

Next, right click on the object and select convert to editable patch. Next, run an optimizer to reduce the number of vertices. Finally, right click on the object and convert it to “NURBS.” The resulting file can then be exported as an IGS file and can be imported by a solid modeling program. However, with this procedure, each original surface triangle is converted to a surface. Thus, the IGS file will contain a multitude of

78 surfaces. This presents a computational problem for solid modeling programs and becomes difficult to derive a mesh from when using to a meshing program.

Another method is to transfer the geometry directly to a meshing program. This method makes it possible to regenerate the surface mesh and create a solid mesh based on the new surface mesh. The advantage of this method is cutting out the middle software, saving both time and accuracy. The disadvantage is that it can be difficult to make changes to the original three-dimensional geometry created from Amira®.

CHAPTER 5 ANALYSIS OF THE KNEE

To analyze the behavior of the knee using finite element methods, it is important to replicate the true behavior of the knee as closely as possible when choosing the geometry, the material properties, and the boundary conditions. The general approach to solving the behavior of the knee by finite element method is to first import the geometry into an analysis software or a preprocessing program. The second step is to mesh the geometry. For the studies in this dissertation, all of the meshing had to be created in three dimensions because of the complex nature of the shapes involved. After meshing, the third step is to assign material properties to each element in the mesh. Many different material models exist for modeling the behavior of various types of material. Fourth, boundary conditions must be applied to the mesh to simulate constraints and forces that are placed on the knee in vivo. All of these steps comprise pre-processing steps, and none is insignificant in its level of difficulty or their effect on the accuracy of an analysis. The next step is the processing step, where the analysis is actually run. This step involves a lot of computational work, but minimal human interaction. Finally, the results are read and interpreted during a post-processing step.

5.1 Failed approaches

Because of its general ease of use, the first finite element analysis software attempted was Algor®. Although the strength of this software is in dealing with linear static analysis and the solution to this problem more realistically required a nonlinear solution, it was attempted first because of its ease of use. The surface remeshing

80 algorithm in this software produced a combination of three and four noded elements. The solid meshing algorithm had difficulty creating a solid mesh from the surface mesh and only completed the meshing procedure in a fraction of the attempts. Figure 5.1 displays a solid mesh produced by Algor®, showing the three and four noded surface elements.

The software completed the mesh of the femur and tibia but could not handle the complex shape of the menisci. Because of the complex shapes of the femur and the tibia,

Algor® could not handle contact between the bones and therefore could not be used to run the analysis.

Figure 5.1 FEA mesh in Algor

In the next attempt, LS-DYNA, a respected nonlinear finite element analysis program that is commonly used to simulate biomechanical structures, was used. Figure

5.2 shows the model in ETA FEMB, one of two preprocessors for LS-DYNA, the other being MSC Patran®. ETA FEMB allowed meshing to be either done directly from an

STL mesh or imported from another meshing program. LS-DYNA is more complex than

Algor® but allows for much more flexibility. When it was used for this application, the estimated solution time was around 3000 hours. Furthermore, the computers used could not handle the size of the simulation and would time out before returning results.

Therefore, use of this software was also not a viable approach.

Figure 5.2 FEA mesh in LS-DYNA

After having difficulty with LS-DYNA, a nonlinear finite element analysis package, and Algor®, a linear finite element analysis package, a different approach was attempted. In this attempt, a finite volume analysis program, SuperForge®, was used.

Figure 5.3 shows the STL file imported into SuperForge®. Because it was suspected that

LS-DYNA did not converge due to gross deformation of the meniscus, the change from finite elements to finite volumes was made. SuperForge® is a specialty finite volume

82 software that focuses on forging applications. The desired analysis resembles a forging procedure, where the femur is the top dye, the tibia is the bottom dye, and the menisci are the billets. This method converged rapidly and clearly showed deformation of the menisci. However, SuperForge® was unable to simulate multiple billets (or in this case multiple menisci), thereby allowing only one side of the knee to be simulated at a time.

Furthermore, desired boundary conditions could not be applied to the meniscus, resulting in an inaccurate portrayal of the behavior of the menisci. Therefore, this software was also not useful.

Figure 5.3 SuperForge® simulation setup

After having some success with a finite volume approach, and some with a finite element approach, the next approach focused on combining the two methods. Dytran® has the ability to combine finite elements, which in this case were used for modeling the

83 behavior of bones, with finite volumes, which were used for modeling the behavior of soft tissues such as the menisci. Figure 5.4 shows a mesh in Patran®, the preprocessor for Dytran®. This figure depicts the proximal end of the tibia and both menisci. Because the tissues are so near to one another and are complex shapes, it was difficult to create an accurate finite volume mesh for the menisci. Additionally, modeling the meniscus purely as a fluid is not accurate because the material has such significant structural properties.

Therefore, Dytran® was not a useful software for this research; however, in the future, it could be used to create a model of a meniscus that has both a solid phase with finite elements and a liquid phase with finite volume, thereby more accurately depicting the true biphasic nature of the tissue.

Figure 5.4 Dytran mesh

5.2 Successful methodology

The successful approach utilized Marc®, a nonlinear finite element analysis package. Marc® was useful because of its advanced meshing capabilities and its ability to simulate large-scale deformations. This section walks through the steps needed to create a successful finite element model to be used in Marc®.

5.2.1 Mesh generation

When creating a solid mesh from surfaces, it is first necessary to create a surface mesh and then generate the solid mesh from the surface mesh. The mesh density of the solid mesh is controlled by the mesh density of the surface mesh. The first step in generating a solid mesh was to import the geometry of the object into the meshing software. In this case, the geometry was defined by an STL surface mesh. A STL mesh, as shown in Figure 5.5, is a surface mesh that represents the surface geometry of an object. As shown, the STL surface mesh was non-uniform and some of the surface mesh elements have poor aspect ratios. Therefore, before a solid mesh can be created, the surface mesh must be refined. Before refining the surface mesh, the STL mesh was first cleaned up by a sweeping operation, which resulted in the deletion of 7732 duplicate nodes.

Figure 5.5 STL importation

The surface mesh was then refined using the Patran® surface mesher in Marc

Mentat®, a preprocessor for Marc®. The element sizes for the surface mesh of the femur and tibia were 0.35 cm, and the element size for the surface meshing of the menisci was

0.125 cm. These meshing sizes were chosen using a trial and error method based on which mesh sizes produced a good quality solid mesh. The solid mesh was then constructed using the tetrahedral auto mesher in Marc Mentat®, as shown in Figure 5.6.

Table 5.1 shows the number of elements constructed for the solid mesh of each entity.

Figure 5.6 Refined mesh of the knee

Entity Number of Elements Femur 3448 Tibia 4632 Lateral Meniscus 3801 Medial Meniscus 3868

Table 5.1 Number of elements of each entity in mesh

5.2.2 Material properties

Modeling the material properties in a finite element application is not an insignificant task. Furthermore, there is little or no verification that any of the current models are accurate for the tissues being studied. Therefore, a gross simplification in the material model allowed research to be more focused on the finite element geometric modeling rather than the material modeling. Table 5.2 shows the mechanical properties used for the isotropic material of this simplification. Although these properties will not

87 exactly replicate the behavior of the biomaterials, they are a good starting point in the creation of a true finite element replication of the human knee. Figure 5.7 shows the application of the material properties to the model.

Material Young’s Modulus Poisson’s Ratio Mass Density (dyne/cm2) (g/cm3) Cortical Bone 1.7 x 1011 0.3 1.85 Menisci 8.0 x 107 0.45 0.80

Table 5.2 Simplified mechanical properties used in research (adapted from [85])

Figure 5.7 Application of material property

5.2.3 Boundary conditions

After applying material properties to the model, the next step was to apply boundary conditions. Contact was established between all parts and a coefficient of friction of 0.002 was assigned between each, a common approximation for friction in the knee joint. The first boundary condition was a fixed displacement boundary condition applied to the distal surface of the tibia to simulate the tibia being completely stationary on its bottom surface, as shown in Figure 5.8.

Figure 5.8 Tibial boundary condition

The next boundary condition was applied to the lateral meniscus, as shown in

Figure 5.9. The horns of the lateral meniscus were fully constrained in the lateral-medial and anterior-posterior directions. This simulated the rigid horn attachments of the

89 menisci and allowed for the proximal-distal translation necessary for future changes to the size of the menisci. The periphery of each meniscus was constrained with the same constraints used for the horns, simulating the peripheral attachment of the lateral meniscus to the tibial plateau.

Figure 5.9 Lateral meniscus boundary condition

The boundary conditions for the medial meniscus are similar to those of the lateral meniscus. As shown in Figure 5.10, the horns and the periphery are displacement constrained in the lateral-medial and anterior-posterior directions but unconstrained in the proximal-distal dimension.

Figure 5.10 Medial meniscus boundary condition

The femoral boundary condition was the next boundary condition applied, as shown in Figure 5.11. The femur was glued to a rigid body, as shown in blue in Figure

5.11. The rigid body was then constrained to the origin using two spring linkages. The first link constrained anterior-posterior movement, and the second link constrained medial-lateral movement. Both of these springs were assigned a spring stiffness of

1,000,000 dynes per centimeter to simulate the behavior of the long part of the bone of the femur and muscle, ligament, and tendon attachments that hold the femur in place.

This value was chosen because it restricted the femur from dislocating the knee but still allowed it to move on the tibial plateau.

Figure 5.11 Femoral boundary condition

The final boundary condition was applied to the rigid body, as shown in Figure

5.11. Because the rigid body was glued to the top surface of the femur, the force acted as though it was being distributed over the entire proximal surface of the femur. This force was applied in the proximal-distal direction from proximal to distal. The magnitude of the force was 4.65 x 107 dynes, or the equivalent of 465 Newtons. This magnitude of the force represents half of the total weight of the pig (209 lb). This force was chosen to mimic a typical force that might be applied to the joint. There was no information found from literature detailing a more accurate force on the porcine knee. This force was applied in a linear fashion over the entire length of the simulation (0.25 seconds), as shown in Figure 5.12.

Figure 5.12 Application of Load

5.3 Design of Experiment (DOE) Setup

The goal of this dissertation was to determine how sizing of the menisci effects stresses in the joint. For this dissertation, the size of each meniscus will be changed by scaling it around an axis specific to each meniscus, as shown in Figure 5.13. This figure also shows the medial-lateral scaling dimension and the anterior-posterior scaling dimension. The proximal-distal scaling dimension goes into the page on the figure; it is a representation of meniscal thickness. Scaling a meniscus around a set axis allowed the menisci to be sized while keeping the desired position in the knee constant. The first scaling factors evaluated were 90% of the original size (small) and 110% of the original size (large). However, in some of the trials the knee would dislocate because of the lack of support from the menisci. The next attempt used scaling factors of 95% and 105% with similar results. Finally, scaling factors of 97.5% and 102.5% were successfully used, as shown in Table 5.3. Here, there are three control factors (medial-lateral size,

93 anterior-posterior size, and proximal-distal size) and three levels (small, original, large) to each control factor.

Medial-lateral

Anterior-posterior A

L M P Figure 5.13 Meniscal origins and scaling dimensions

Control Factors Small Original Large Medial-lateral scaling 97.5% 100% 102.5% Anterior-posterior scaling 97.5% 100% 102.5% Proximal-distal scaling 97.5% 100% 102.5%

Table 5.3 DOE control factors

The scaling of the menisci resulted in the changing in size of the menisci, as shown in

Table 5.4. In this table, the sizes given are the maximum lengths in each dimension.

Lateral meniscus (mm) Medial meniscus (mm) Medial-lateral size 24.7 ± 0.6175 24.75 ± 0.61875 Anterior-posterior size 17.86 ± 0.4465 23.87 ± 0.59675 Proximal-distal size 8.61 ± 0.21525 8.87 ± 0.22175

Table 5.4 Effects of scaling on meniscal sizing

There are three control factors (medial-lateral size, anterior-posterior size, and proximal-distal size) and three levels for each (small, original, large). Running every variation of these factors would lead to 33 or 27 experiments, as shown in Table 5.5.

Test Number Medial-lateral Anterior-posterior Proximal-distal 1 Original Original Original 2 Original Original Small 3 Original Original Large 4 Original Small Original 5 Original Small Small 6 Original Small Large 7 Original Large Original 8 Original Large Small 9 Original Large Large 10 Small Original Original 11 Small Original Small 12 Small Original Large 13 Small Small Original 14 Small Small Small 15 Small Small Large 16 Small Large Original 17 Small Large Small 18 Small Large Large 19 Large Original Original 20 Large Original Small 21 Large Original Large 22 Large Small Original 23 Large Small Small 24 Large Small Large 25 Large Large Original 26 Large Large Small 27 Large Large Large

Table 5.5 Full factorial experimental design

Running 27 experiments would be very time consuming. Instead, a partial factorial approach, as shown in Table 5.6, was used. This required only 33-1 or 9 experimental runs. There are three possible choices for partial fractional setups [102]. This setup design was chosen because one of the experiments analyzed the behavior of the knee with its normal sizing as shown in test number five in the following table.

Test Number Medial-lateral Anterior-posterior Proximal-distal 1 Small Small Original 2 Small Original Small 3 Small Large Large 4 Original Small Large 5 Original Original Original 6 Original Large Small 7 Large Small Small 8 Large Original Large 9 Large Large Original

Table 5.6 Partial factorial experimental design

CHAPTER 6 RESULTS AND CONCLUSIONS

The goal of this dissertation was to study the effects of meniscal sizing on stress distributions in the knee joint. This chapter will present results for both the stress distribution of the tibial plateau, which are also the maximum stresses in the joint, and the stress distribution of the menisci. The stresses on the tibial plateau are most significant because they represent the likelihood of developing osteoarthritis. The larger the maximum stress value, the more likely osteoarthritis will develop.

As explained in the design of experiment (DOE) section of Chapter 5, nine experimental runs were evaluated according to predetermined configurations. The results of these experimental runs are shown in Table 6.1. The second column of the table depicts the configuration of each test by assigning an “S” (small), “O” (original), or “L”

(large) to each of the three dimensions (medial-lateral, anterior-posterior, and proximal- distal), respectively. For example, the configuration of SSO, as shown in the first test, represents a small scaling in the medial-lateral dimension, a small scaling in the anterior- posterior dimension, and an original scaling in the proximal-distal dimension. This notation is used throughout this chapter. The third column of the table shows the maximum stresses on the tibial plateau. In this column, the values for the maximum stress vary greatly; and the largest stress of 188.5 MPa is more than thirty-five (35) times larger than the smallest stress of 5.24 MPa. The third and fourth columns show the maximum stresses on the medial and lateral menisci. Here, the stresses remain more constant than with the tibia.

Maximum Maximum stress on Maximum stress Test Configuration stress on tibia lateral meniscus on medial Number (MPa) (MPa) meniscus (MPa) 1 SSO 51.12 3.53 3.99 2 SOS 12.83 3.83 4.80 3 SLL 17.02 5.73 3.83 4 OSL 5.24 2.76 3.79 5 OOO 5.96 3.68 5.00 6 OLS 13.95 3.09 3.12 7 LSS 146.50 2.23 2.25 8 LOL 14.60 2.44 3.17 9 LLO 188.50 2.85 2.64

Table 6.1 Results of partial factorial study

The results for maximum stresses on the tibia are shown again in a different format in

Table 6.2. This format demonstrates how the design of the experiment was used to test all factors without using all 27 possible test configurations.

Medial-lateral scaling

Proximal- Small Original Large distal scaling Anterior-posterior scaling

Small Original Large Small Original Large Small Original Large Small 12.83 13.95 146.50 Original 51.12 5.96 188.50 Large 17.02 5.24 14.60

Table 6.2 Maximum stresses on the tibia

Each experiment was evaluated over a time interval of 0.25 seconds. Figure 6.1 shows five snapshots of stress contours on the knee over that time period. The first

99 column shows the knee with all of the tissues: the femur, the tibia, and the medial and lateral menisci. The view of this figure looks at the anterior of the left knee. Therefore, in this figure, the top tissue is the femur, the bottom tissue is the tibia, the left meniscus is the medial meniscus, and the right meniscus is the lateral meniscus. In the second column, the femur is removed, showing stresses on only the tibia and the menisci. The third column shows only the tibia, and the fourth column displays only the menisci, showing the stress contours on each. Displacements in all of the following figures throughout this chapter are shown in full scale, which means you are looking at the actual displacement. An attempt to simulate the response of the knee with no menisci present for comparison failed because the knee dislocated before the full load could be applied.

100

0 s

.25 s

Figure 6.1 Stress contours on knee over time

101

The magnitude of stress values on the tibia are shown in Figure 6.2 for each of the nine cases. The maximum stress, as shown in yellow, is 188.5 MPa or 1.885 x 109 dynes/cm2. This maximum stress was found in the LLO configuration (test number nine). Although it is not the situation, in this figure, some configurations may appear to have no stress due to the large difference between the high maximum stress on the tibia in one case and the lower maximum stresses on the tibia in other cases.

102

SSO OLS

SOS LSS

SLL LOL

LLO OSL

Medial-lateral Anterior-posterior Proximal-distal Small Small Original A Small Original Small Small Large Large L M Original Small Large Original Original Original P Original Large Small OOO Large Small Small Large Original Large Large Larg e Original Figure 6.2 Stresses on the tibia (in dynes/cm2)

103

In order to more clearly illustrate the stress contours for each individual case,

Figure 6.3 uses automatic contouring specific to each test case. For example, the yellow contour in the SSO configuration represents a maximum stress of 51.12 MPa while the yellow contour in the SOS configuration represents a maximum stress of only 12.83

MPa. The advantage of using this depiction is the capability to visualize how stress is distributed on the tibia for each individual case. However, the limitation is that the magnitudes of the contours cannot be compared to one another. Yellow represents higher levels of stress, and blue represents lower levels of stress.

104

SSO OLS

SOS LSS

SLL LOL

LLO OSL

Medial-lateral Anterior-posterior Proximal-distal Small Small Original Small Original Small Small Large Large Original Small Large Original Original Original A Original Large Small Large Small Small L M OOO Large Original Large P Large Larg e Original Figure 6.3 Stresses on the tibia with automatic contouring

105

The magnitude of stress values for the menisci without the tibia are shown in

Figure 6.4. The maximum stress value, as depicted by yellow, is 5.73 MPa, or 5.73 x 107 dynes/cm2, and was found in the SLL configuration of the lateral meniscus.

106

SSO OLS

SOS LSS

SLL LOL

OSL LLO

Medial-lateral Anterior-posterior Proximal-distal Small Small Original Small Original Small Small Large Large Original Small Large

Original Original Original OOO A Original Large Small

Large Small Small L M Large Original Large Large Larg e Original P

Figure 6.4 Stresses on the menisci (in dynes/cm2)

107

To more clearly depict the stress contours of the menisci, Figure 6.5 is shown with automatic contouring specific to each test case. In each of the cases, the higher levels of stress are found on the anterior portion of the menisci. In this figure, yellow represents higher levels of stress, and blue represents lower levels of stress.

108

SSO OLS

SOS LSS

SLL LOL

OSL LLO

Medial-lateral Anterior-posterior Proximal-distal Small Small Original Small Original Small Small Large Large Original Small Large Original Original Original A OOO Original Large Small Large Small Small L M Large Original Large Large Large Original P

Figure 6.5 Stresses on the menisci with automatic contouring

109

The statistical significances of meniscal sizing on the plateau stress levels are shown in Figure 6.6. Based on this figure, all meniscal dimensions are significant to the behavior of stresses in the knee, as shown by the significant differences between the maximum stress values for each factor at each level. The most significant dimension is the medial-lateral dimension, as represented by the blue line. This dimension is most significant because the range of stress is larger than either of the other two dimensions.

Table 6.3 shows the sum of the squares of the sources of variation. These calculations further show that all factors are statistically significant, with medial-lateral sizing being the most significant. All three dimensions showed nonlinear behavior with either a maximum or a minimum at original sizing.

140

120 ) a P 100 (M

s Medial-lateral scaling s

e 80 r Anteroir-posterior scaling t Proximal-distal scaling m S 60 u Mean m i

x 40 a M 20

0 Small Original Large Meniscal Size

Figure 6.6 Statistical significance of parameters on the tibial plateau

110

Source of variation Sum of squares Medial-lateral scaling 19706 Anterior-posterior scaling 6949 Proximal-distal scaling 7322

Table 6.3 Significance of sources of variation

To better understand the behavior of each sizing dimension, it is important to look at each one separately. Medial-lateral scaling had its lowest maximum stress at original sizing. As the sizes of the menisci were reduced, the maximum stress value for this dimension rose only moderately. On the other hand, when the sizes of the menisci were enlarged, the maximum stress value for this dimension rose dramatically. Therefore, when sizing in the medial-lateral dimension, the size of the menisci should err on the small side. This behavior was anticipated due to the wedge-shaped nature of the menisci.

In the original configuration, the wedge is in the optimal position. As the wedge is pushed in further, it still distributes the force, but the force is not as optimally focused.

When the wedge is pulled out, it has less effect on force distribution, resulting in higher stresses on the tibial plateau.

The red line in Figure 6.6 represents the effect of anterior-posterior scaling. The behavior in this dimension is similar to the behavior of the medial-lateral dimension. The lowest maximum stress value was found at original sizing as expected. When the sizes of the menisci were changed in either direction, larger or smaller, the stress rose to almost identical levels. When sizing the menisci for replacement, sizing in this dimension

111 should be as close to the original size of the tissue as possible, as incorrect sizing in either direction would results in similar levels of increased stress.

The green line in Figure 6.6 represents the effect of proximal-distal scaling.

Proximal-distal sizing closely approximates the thickness of the tissue. The lowest maximum stress value was exhibited in the large sizing. This was expected because the thickness of the tissue was increased. Surprisingly, the highest maximum stress value is shown in original sizing. This was contrary to the expectation that the highest maximum stress would be exhibited when the menisci are at their thinnest. These results could possibly be due to an interaction with one or both of the other scaling dimensions and could change if more experimental trials are performed.

To better understand the overall effect of meniscal sizing on stresses on the tibia, it is important to look at the scaling effects together. From looking at Figure 6.6, it is estimated that the lowest stress value would be found when the medial-lateral size is the same size as the original, the anterior-posterior size is also the same as the original, and the proximal-distal size is larger than originally sized. If you look at the meniscal size simply as small, original, and large (all directions are scaled the same) the original meniscal size would have the least stress followed by the smaller meniscal size. The greatest maximum stress would be found in the knee with larger sized menisci.

The statistical significances of meniscal sizing on the stresses of the lateral meniscus are shown in Figure 6.7. In contrast to the results for the tibial plateau, the results for the lateral meniscus appear to be linear. As the menisci increase in size, the level of stress increases in the medial-lateral dimension and decreases in both the

112 anterior-posterior and proximal-distal dimensions. Simplifications of the material properties of the menisci may distort these results. However, it is important to note that the fluctuations in stress levels in the lateral menisci are relatively minor to those observed on the tibial plateau.

5 4.5 )

a 4 P

M 3.5 (

s Medial-lateral scaling

s 3 e

r Anteroir-posterior scaling t 2.5 Proximal- distal scaling m S 2 Mean mu i

x 1.5 a

M 1 0.5 0 Small Original Large Meniscal Size

Figure 6.7 Statistical significance of parameters on the lateral meniscus

The statistical significances of meniscal sizing on the stresses of the medial meniscus are shown in Figure 6.8. The results for the medial meniscus indicate that the relationships may not be linear. As with the lateral meniscus, simplifications of the material properties of the medial meniscus may distort these results. Also similar to the lateral meniscus, the fluctuations in stress levels of the medial menisci were relatively small.

113

5 4.5

) 4 a P 3.5 (M

s Medial-lateral scaling

s 3 e

r Anteroir-posterior scaling t 2.5 Proximal-distal scaling m S

u 2 Mean m i

x 1.5 a

M 1 0.5 0 Small Original Large Meniscal Size

Figure 6.8 Statistical significance of parameters on the medial meniscus

The changes in size of the menisci used for this study were very small. The largest change in size was 0.62 mm, and the smallest change in size was only 0.22 mm.

Even with these extremely small changes in meniscal size, the changes in stresses were dramatic. Trying to find a replacement meniscus that closely matches the original meniscus size close enough to preserve stress levels comparable to the original meniscus may be extremely difficult or unlikely. As a word of caution, this conclusion is based on a grossly simplified material model, and the use of a more accurate material may introduce contradictory results.

Another important conclusion was found when the results of the stresses on the menisci were examined: the stress levels between original and incorrectly sized menisci

114 were not significantly different. This indicates that it may be possible to develop osteoarthritis without any visual damage being present to the menisci.

115

CHAPTER 7 FUTURE RECOMMENDATIONS

This dissertation is a starting point, a foundation for further research. The purpose of this chapter is to present recommendations to further the current research.

The intent is not to limit future research to these areas but to provide some directions for future studies. The largest limitations of the current research were the material models that were used. The results presented in this dissertation were based on a linear isotropic material model, even though the menisci, in particular, actually exhibit more of a nonlinear anisotropic behavior. A new material model should be derived from experimental results from literature or from more advanced material testing techniques.

A design of experiments similar to that used in this dissertation could be used to evaluate the effect of different material properties on stresses in the knee.

The boundary conditions used for this dissertation were another limitation on the accuracy of the results. All of the boundary conditions used leave room for improvement. The first boundary condition discussed was the fixed constraint on the distal surface of the tibia. This needs to be examined to determine if adding springs that would mimic the behavior of the lower part of the limb would increase the accuracy of the results. The next boundary condition discussed was the fixed medial-lateral and anterior-posterior translations of the menisci at both the horn attachments and the peripheries of the tissues. Instead of a more simple fixed constraint, it is more likely that these attachments would behave more like multiple spring elements with an individual stiffness for each. The third boundary condition discussed was the medial-lateral and anterior-posterior transitional constraint of the femur. The current spring stiffness values

116 were chosen because they not only helped prevent dislocation but also allowed the femur to settle on the tibia. It is likely that a spring constraint is an accurate portrayal of this behavior but the values for these spring constants need to be more accurate. The final boundary condition discussed was the force on the femur. Studies need to address the magnitude of this force in the porcine. Additionally, new boundary conditions should be introduced to mimic the behavior of the four ligaments in the knee. These new boundary conditions will directly affect the amount of force applied to the femur.

After exploring the effects of the new boundary conditions, studies of the effects of the different methods of attachment in a meniscal allograft should be performed. For example, it would be useful to know the actual effect of the peripheral attachments on the menisci. For this type of research, it might be useful to take meniscal models from a source other than the knee from which the femur and tibia were constructed from to examine the results.

More testing trials should also be performed to expand the experimental design from three factors with three levels for each to three factors with five or more levels for each. This would help to explain the nonlinear behavior of stresses on the tibia more accurately. In addition, performing a full factorial design rather than the partial factorial design currently used, will further decipher the effects of interactions between the main factors.

Another useful study that could be performed based on this research is a study of the effect of friction on the knee joint. The knee is commonly thought to have a coefficient of friction of 0.002 (as assigned in this research). Most current models from

117 literature model the knee as frictionless, which may accurately portray the knee when it is in perfect working order. However, as the knee gradually wears down with age and use, the surfaces become less smooth and the coefficient of friction will increase. It would be beneficial to know what the effects of friction are on stresses in the knee.

The results produced within this dissertation, and all subsequent finite element simulations, need to be verified by experimental results. To do this, robotic equipment could be used to mimic the true behavior of the knee and compare these results to the simulation results.

Finally, this research must be expanded to human models. Ultimately, the goal of this research and all subsequent work is to improve the success of meniscal allograft surgery in humans, not in the porcine. In addition, using human models would afford the ability to compare the simulation results to pressure distributions of the human knee from literature.

118

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