MULTISCALE BIOMECHANICAL RELATIONSHIPS IN LIGAMENT

by

Trevor Justin Lujan

A dissertation submitted to the faculty of The University of Utah

in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

Department of Bioengineering

The University of Utah

December 2007

Copyright © Trevor Justin Lujan 2007

All Rights Reserved

ABSTRACT

Healthy knee joints require structural stability through a full range of motion.

Knee stability is primarily provided by a network of ligaments that resist abnormal

forces and direct smooth articulations. Ligament malfunction has deleterious effects on

balance, agility, and knee laxity. Altered knee laxity redistributes the stress transmitted

across articulations, which may create regional stress concentrations that are potentially

damaging to articular cartilage. The high incidence of knee ligament injuries and

shortfalls of related treatments are thus adverse to knee joint health. As the function of

ligament is essentially mechanical, understanding the tissue-scale and molecular-scale

relationships that mechanically influence ligament are critical to functional restoration.

The aim of this dissertation was to strengthen the scientific knowledge of mechanical

relationships that impact ligament function in the knee. Toward this objective, a tissue-

scale relationship was investigated between the anterior cruciate ligament (ACL) and the

medial collateral ligament (MCL). These knee ligaments are frequently injured and

have inter-dependent functionality. At the molecular-scale, mechanical interactions

between glycosaminoglycans (GAGs) and collagen fibrils may impact gross ligament

function. Therefore, the influence of these molecular relationships on ligament material

behavior was inspected.

Experimental and numerical modeling techniques (finite element analysis) were

employed to fulfill these objectives. In an ACL-deficient knee, the MCL was more

susceptible to damage during anterior tibial translation, as strains reached values

v

corresponding to the threshold of microstructural failure. The MCL mid-substance and

insertions were functionally insensitive to ACL transection during valgus loading of the

knee. Interfibrillar GAGs were found to have negligible influence on tissue-scale

mechanics during tensile loading. Therefore, interfibrillar GAGs do not directly support

ligaments primary function of resisting tensile loads, which contradicts the popular

theory that GAGs transmit forces between adjacent collagen fibrils. By determining the

effect of multiscale relationships on ligament function, improvements are possible in the

innovation and evaluation of ligament treatment modalities.

To my loving wife and family.

They are my joy and inspiration.

TABLE OF CONTENTS

ABSTRACT..................................................................................................................... iv LIST OF TABLES..........................................................................................................viii LIST OF FIGURES..........................................................................................................ix ACKNOWLEDGEMENTS............................................................................................xiii CHAPTER 1. INTRODUCTION................................................................................................ 1

Motivation............................................................................................................. 1 Research Goals...................................................................................................... 3 Summary of Chapters............................................................................................ 3 References……………………..............................................................................6

2. BACKGROUND ................................................................................................ 10

Knee Joint Overview............................................................................................10 Composition and Structural Organization of Ligament...................................... 17 Ligament Contribution to Knee Joint Pathology................................................. 22 Experimental Biomechanics of Ligament........................................................... 26 Numerical Modeling of Ligament....................................................................... 28 References............................................................................................................ 34 3. SIMULTANEOUS MEASUREMENT OF THREE-DIMENSIONAL

JOINT KINEMATICS AND LIGAMENT STRAINS WITH OPTICAL METHODS. ........................................................................................................ 45

Abstract................................................................................................................ 45 Introduction.......................................................................................................... 46 Materials and Methods......................................................................................... 48

Results ................................................................................................................. 53 Discussion ........................................................................................................... 59 References............................................................................................................ 62

vii

4. EFFECT OF ACL DEFICIENCY ON MCL STRAINS AND JOINT KINEMATICS..................................................................................................... 64

Abstract................................................................................................................ 64 Introduction.......................................................................................................... 65 Materials and Methods......................................................................................... 67

Results ................................................................................................................. 73 Discussion ........................................................................................................... 80 References............................................................................................................ 85 5. MCL INSERTION SITE AND CONTACT FORCES

IN THE ACL-DEFICIENT KNEE...................................................................... 90 Abstract................................................................................................................ 90 Introduction......................................................................................................... 91 Materials and Methods........................................................................................ 93

Results ............................................................................................................... 100 Discussion ......................................................................................................... 106 References.......................................................................................................... 112 6. EFFECT OF DERMATAN SULFATE GLYCOSAMINOGLYCANS

ON THE QUASI-STATIC MATERIAL PROPERTIES OF THE HUMAN MEDIAL COLLATERAL LIGAMENT........................................... 116

Abstract.............................................................................................................. 116 Introduction........................................................................................................ 117 Materials and Methods....................................................................................... 121

Results ............................................................................................................... 127 Discussion ......................................................................................................... 132 References.......................................................................................................... 137 7. VISCOELASTIC TENSILE BEHAVIOR OF HUMAN LIGAMENT

AFTER INTERFIBRILLAR GLYCOSAMINOGLYCAN DIGESTION........ 143 Introduction........................................................................................................ 144 Materials and Methods...................................................................................... 146

Results ............................................................................................................... 154 Discussion ......................................................................................................... 163 References.......................................................................................................... 169 8. DISCUSSION.................................................................................................... 175

Summary............................................................................................................ 175 Limitations and Future Work............................................................................. 180

References.......................................................................................................... 187

LIST OF TABLES Table Page

3.1. Results for measurement of 3D precision.........................................................54 3.2. Accuracy of 3D simulated strain measurement along

the z- and x-axes for all four strain levels......................................................... 56 3.3. Accuracy of 3D kinematic measurements........................................................ 58 6.1. Physical dimensions of the MCL test specimens............................................ 122 7.1. Mechanical properties for all eight test groups before and after treatment.....154

LIST OF FIGURES Figure Page

2.1. X-ray picture of the medial knee...................................................................... 11 2.2. Illustration of the anterior knee joint. .............................................................. 13 2.3. Illustration of the posterior knee joint.............................................................. 14 2.4. Illustration of the quadricep and hamstring muscle groups............................. 16 2.5. Schematic of the structural hierarchy of tendon and ligament......................... 19 3.1. Plane view of the camera setup........................................................................ 50 3.2. Photograph of test setup for simultaneous measurement

of MCL strain and knee joint kinematics......................................................... 50 3.3. Simulated 3D strain error along the z-axis.and x-axis..................................... 57 3.4. Results for the measurement of 3D kinematics along the z-axis direction...... 58 4.1. Illustration of eighteen regions for strain measurement.................................. 69 4.2. Schematic of the structural testing system ...................................................... 70 4.3. Average anterior tibial translation at all flexion angles and

Average MCL strains at peak anterior tibial translation.................................. 75 4.4. Average valgus rotations at all flexion angles and

Average MCL strains at peak valgus............................................................... 76 4.5. MCL strain changes due to ACL transection at peak anterior translation

and valgus rotation........................................................................................... 77 4.6. Internal tibial axial rotation from neutral to peak anterior translation

and average MCL strains at peak anterior translation..................................... 79 5.1. FE predicted vs. experimental fiber stretch for all knees............................... 102

x

5.2. Representative fringe plots of FE predicted fiber strain................................. 103 5.3. FE predictions of insertion site forces for femoral and tibial insertion sites.. 105 5.4. FE predictions of contact forces between the MCL and femur

and between the MCL and tibia...................................................................... 107

6.1. Multiscale schematic of the proposed glycosaminoglycan interaction between collagen fibrils. ............................................................................... 119

6.2. Stress-Strain curves for tensile tests of control and

chondroitinase B treated ligament samples………........................................ 129 6.3. Stress-Strain curves for shear tests of control and

chondroitinase B treated ligament samples……………................................. 129 6.4. Specificity of Chondroitinase B...................................................................... 130 6.5. Decorin western blot of proteins extracted from 3 control

and 3 ChB treated ligament samples…………………................................... 131 6.6. Representative TEM images of tissue stained with

Cupromeroneic Blue after mechanical testing……........................................ 132 7.1. Illustration of specimen acquisition……………………................................ 148 7.2. Diagram of the viscoelastic protocol……………………............................... 149 7.3. Reduced relaxation curves for control and chondroitinase ABC treated samples in either standard buffer or PEG buffer............................................ 155 7.4. Dynamic modulus as a function of oscillatory frequency for control and

chondroitinase ABC treated in either standard buffer or PEG buffer............ 157 7.5. Phase shift as a function of oscillatory frequency for control and chondroitinase

ABC treated in either standard buffer or PEG buffer...................................... 159 7.6. Time history of the unloaded samples wet weight through the course of the experiment. ............................................................ 161 7.7 Water content of all tested samples after testing .......................................... 161

.

CHAPTER 1

INTRODUCTION

Motivation

The knee is the largest synovial joint in the human body and is also the most

vulnerable musculoskeletal structure [1]. In addition to transferring loads between the

femur and tibia of up to 7x body weight [2], the knee must functionally permit the broad

range of motion required for bipedal gait. To enable this mobility, a complex network

of tendons and ligaments primarily stabilize the knee and guide smooth articulations.

Through overuse, repetitive physical activity and abnormal loading, knee ligaments are

prone to tear and are responsible for over 6 million hospital visits a year [1, 3]. In the

short-term, knee ligament damage will restrict participation in certain sports and

activities [4-6], while in the long-term, ligament damage can predispose the knee to

debilitating osteoarthritis by altering gait patterns [7] [8, 9].

In order to return patients with knee ligament damage to normal activity levels

and to obstruct osteoarthritic progression, clinicians and scientists have developed both

surgical and nonsurgical treatment strategies. There are over 100,000 reconstructions of

knee ligaments performed annually in the United States [10]. Ligament reconstruction

vastly improves the gait and function of joints [11][12], however, reconstructed knees

are still beset with abnormal gait [13-15] and athletic performance is significantly

hampered post-surgery [16]. Even ligaments that are adept at healing with conservative

2

treatment experience reductions in mechanical properties [17, 18] that can alter knee

laxity [19, 20]. Moreover, ligament injury can cause physical [21, 22] and chemical

alterations [23] to intact ligaments that may hamper the effectiveness of clinical

treatments.

The inadequacies that exist in the present management of ligament injury can be

attributed to technological limitations and deficiencies in our underlying knowledge of

ligament function. It is self-evident that a ligaments function derives from molecular

interactions within its structure and is dependent on intrinsic relationships with other

joint stabilizers. Therefore, a fundamental understanding of these inter- and intra-

ligament relationships is absolutely necessary to develop strategies (drug therapy,

functional tissue engineering, novel reconstruction procedures) that restore or enhance

the native function of ligament Since the role of ligament is mechanical by nature,

mechanically based experimental and theoretical studies are appropriate to examine

these tissue and molecular scale (multi-scale) relationships.

Advances in experimental technologies, computational methods and

biochemistry have recently enabled multiscale relationships to be investigated in detail.

High resolution digital cameras have progressed to give an accurate and efficient means

to track tissue deformations for mechanical analysis [24]. The astounding growth of

computer power combined with improvements in medical imaging has propelled the

science of numerical modeling [25-27]. Moreover, burgeoning progress in molecular

biology has impelled the quantification and manipulation of tissue microstructure [28-

30]. By blending these tools, the multiscale relationships that define ligament function

3

can be comprehensively examined and applied to the treatment and prevention of

ligament injuries.

Research Goals

The overall objective of this research was to clarify multi-scale biomechanical

relationships in ligament. Advancement of the treatment and prevention of joint injury

and disease will be facilitated by a concise understanding of the mechanical

relationships within and between joint stabilizers. Experimental and theoretical

biomechanics, along with biochemical techniques, were utilized to accomplish the

research objective. At the tissue level, ex-vivo structural experiments were employed to

determine the functional interrelationship of primary knee stabilizers. Computational

finite element models were then generated to examine aspects of this interaction that

would otherwise be difficult or impossible to measure experimentally. At the molecular

level, the mechanical relationship of collagen molecules with ground substance

constituents was examined by performing a series of elastic and viscoelastic material

tests before and after enzymatic treatment. Finally, the solid-fluid phase interaction of

ligament was briefly examined both experimentally and computationally to investigate

the mechanical relevance of fluid flow during tensile deformation.

Summary of Chapters

The mechanical relationships investigated in this dissertation start at the tissue

scale and move to the molecular scale. The primary purpose of Chapter 2 was to

provide sufficient background on the topics that will be addressed in the later chapters.

This background information includes an overview of the structure and function of the

4

knee joint along with the pathologies of the knee joint associated with ligament injury.

The microstructural composition and organization of ligament is detailed along with

mathematical models and numerical methods that describe ligament material behavior.

To comprehensively study the structural interactions of ligaments, an

experimental technique was developed in Chapter 3 that simultaneously measures three-

dimensional joint kinematics and localized ligament strain. These coupled

measurements link specific movements to functional ligament regions. A high-

resolution optical tracking system was appropriate for this type of measurement, and

was rigorously validated. The excellent precision and accuracy of this system make it

an attractive tool for biomechanical experiments.

Chapter 4 describes the use of this validated technique to experimentally

examine the relationship between the anterior cruciate ligament (ACL) and the medial

collateral ligament (MCL). These two ligaments are primary knee stabilizers, have

overlapping roles and account for 70% of multi-ligament injuries in the knee [31]. The

objective of this study was to determine how ACL deficiency affects the local strain in

the MCL during loading configurations applicable to these ligaments. To meet this

objective, kinematic motions were applied to a prescribed force before and after ACL

transection under a variety of loading conditions. The results of this study provide

physiological and clinical insight into the interaction of these two primary knee

stabilizers.

Certain physical phenomena associated with ligament mechanics, such as

insertion and contact forces, are difficult or impossible to measure experimentally. One

method to approximate these inhomogeneous forces is by means of a validated finite

5

element model [32]. Therefore, to further examine the relationship between the ACL

and MCL, Chapter 5 focuses on using the experimental kinematics and strain

measurements from Chapter 4 to generate subject-specific finite element (FE) models

[26]. As a means of validation, the experimental strain values at peak load were

compared to the FE predictions. This study not only improved upon past advances in

subject-specific modeling, but helped clarify the specific tensile and compressive

stresses projected upon the MCL after ACL transection.

In Chapters 6 and 7, the focus of this dissertation shifts to the influence of

microstructure on tissue-scale mechanics. The chapter objectives are to determine

whether the mechanical interactions of non-collagenous constituents play a role in the

continuum material behavior of ligament. Understanding the origins of ligament

material behavior is applicable to functional tissue engineering and basic science. The

possible mechanical role of sulfated glycosaminoglycans (sGAGs) was investigated.

SGAGs include dermatan and chondroitin sulfate, which have been widely implicated as

contributors to the mechanical response of ligament. By performing experiments before

and after sGAG degradation, the mechanical influence of these noncollagenous

constituents was elucidated. Chapter 6 inspects the unique role of dermatan sulfate in

the elastic mechanics of ligament, while Chapter 7 researches the contribution of

dermatan and chondroitin sulfate on the viscoelastic material properties. Results are

related to relevant prior investigations, along with basic and applied science.

The final chapter highlights the major contributions that this dissertation has

made to the field of ligament biomechanics and comments on future work that is

necessary to expand upon this research. The discussion on future work includes

6

preliminary work looking at the roles of other non-collagenous constituents and

experimental factors that could be improved to better assess functionality of the ground

substance. In this section, a strong emphasis was placed on a biphasic mathematical

representation of ligament that describes the physical solid-fluid interaction that occurs

in soft-tissue. The current state of this work was included along with the long-term

perspective.

References

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[3] Miyasaka, K., et al., 1991, "The incidence of knee ligament injuries in the

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[5] Maquirriain, J., and Megey, P. J., 2006, "Tennis specific limitations in players

with an ACL deficient knee," Br J Sports Med, 40(5), pp. 451-453. [6] De Loes, M., Dahlstedt, L. J., and Thomee, R., 2000, "A 7-year study on risks

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[8] Andriacchi, T. P., Briant, P. L., Bevill, S. L., and Koo, S., 2006, "Rotational

changes at the knee after ACL injury cause cartilage thinning," Clin Orthop Relat Res, 442, pp. 39-44.

[9] Fink, C., Hoser, C., Hackl, W., Navarro, R. A., and Benedetto, K. P., 2001,

"Long-term outcome of operative or nonoperative treatment of anterior cruciate

7

ligament rupture--is sports activity a determining variable?," Int J Sports Med, 22(4), pp. 304-309.

[10] American board of orthopaedic surgery, 2004, "research committee report,"

diplomatic newsletter, Chapel hill, NC. [11] Nakayama, Y., Shirai, Y., Narita, T., Mori, A., and Kobayashi, K., 2000, "Knee

functions and a return to sports activity in competitive athletes following anterior cruciate ligament reconstruction," J Nippon Med Sch, 67(3), pp. 172-176.

[12] Bulgheroni, P., Bulgheroni, M. V., Andrini, L., Guffanti, P., and Giughello, A.,

1997, "Gait patterns after anterior cruciate ligament reconstruction," Knee Surg Sports Traumatol Arthrosc, 5(1), pp. 14-21.

[13] Jomha, N. M., Pinczewski, L. A., Clingeleffer, A., and Otto, D. D., 1999,

"Arthroscopic reconstruction of the anterior cruciate ligament with patellar-tendon autograft and interference screw fixation. The results at seven years," J Bone Joint Surg Br, 81(5), pp. 775-779.

[14] Laxdal, G., Kartus, J., Ejerhed, L., Sernert, N., Magnusson, L., Faxen, E., and

Karlsson, J., 2005, "Outcome and risk factors after anterior cruciate ligament reconstruction: a follow-up study of 948 patients," Arthroscopy, 21(8), pp. 958-964.

[15] Georgoulis, A. D., Ristanis, S., Chouliaras, V., Moraiti, C., and Stergiou, N.,

2007, "Tibial rotation is not restored after ACL reconstruction with a hamstring graft," Clin Orthop Relat Res, 454, pp. 89-94.

[16] Carey, J. L., Huffman, G. R., Parekh, S. G., and Sennett, B. J., 2006, "Outcomes

of anterior cruciate ligament injuries to running backs and wide receivers in the National Football League," Am J Sports Med, 34(12), pp. 1911-1917.

[17] Majima, T., Lo, I. K., Marchuk, L. L., Shrive, N. G., and Frank, C. B., 2006,

"Effects of ligament repair on laxity and creep behavior of an early healing ligament scar," J Orthop Sci, 11(3), pp. 272-277.

[18] Abramowitch, S. D., Woo, S. L., Clineff, T. D., and Debski, R. E., 2004, "An

evaluation of the quasi-linear viscoelastic properties of the healing medial collateral ligament in a goat model," Ann Biomed Eng, 32(3), pp. 329-335.

[19] Indelicato, P. A., 1983, "Non-operative treatment of complete tears of the medial

collateral ligament of the knee," J Bone Joint Surg (Am), 65(3), pp. 323-329. [20] Kannus, P., 1988, "Long-term results of conservatively treated medial collateral

ligament injuries of the knee joint," Clinical Orthopaedics and Related Research, 226, pp. 103-112.

8

[21] Markolf, K. L., Mensch, J. S., and Amstutz, H. C., 1976, "Stiffness and laxity of

the knee--the contributions of the supporting structures. A quantitative in vitro study," J Bone Joint Surg Am, 58(5), pp. 583-594.

[22] Yasuda, K., Erickson, A. R., Beynnon, B. D., Johnson, R. J., and Pope, M. H.,

1993, "Dynamic elongation behavior in the medial collateral and anterior cruciate ligaments during lateral impact loading," J Orthop Res, 11(2), pp. 190-198.

[23] Funakoshi, Y., Hariu, M., Tapper, J. E., Marchuk, L. L., Shrive, N. G., Kanaya,

F., Rattner, J. B., Hart, D. A., and Frank, C. B., 2007, "Periarticular ligament changes following ACL/MCL transection in an ovine stifle joint model of osteoarthritis," J Orthop Res.

[24] Zhang, D., and Arola, D. D., 2004, "Applications of digital image correlation to

biological tissues," J Biomed Opt, 9(4), pp. 691-699. [25] Elias, J. J., and Cosgarea, A. J., 2007, "Computational modeling: an alternative

approach for investigating patellofemoral mechanics," Sports Med Arthrosc, 15(2), pp. 89-94.

[26] Gardiner, J. C., and Weiss, J. A., 2003, "Subject-specific finite element analysis

of the human medial collateral ligament during valgus knee loading," J Orthop Res, 21(6), pp. 1098-1106.

[27] Anderson, A. E., Peters, C. L., Tuttle, B. D., and Weiss, J. A., 2005, "Subject-

specific finite element model of the pelvis: development, validation and sensitivity studies," J Biomech Eng, 127(3), pp. 364-373.

[28] Robinson, P. S., Huang, T. F., Kazam, E., Iozzo, R. V., Birk, D. E., and

Soslowsky, L. J., 2005, "Influence of decorin and biglycan on mechanical properties of multiple tendons in knockout mice," J Biomech Eng, 127(1), pp. 181-185.

[29] Puxkandl, R., Zizak, I., Paris, O., Keckes, J., Tesch, W., Bernstorff, S., Purslow,

P., and Fratzl, P., 2002, "Viscoelastic properties of collagen: synchrotron radiation investigations and structural model," Philos Trans R Soc Lond B Biol Sci, 357(1418), pp. 191-197.

[30] Screen, H. R., Shelton, J. C., Chhaya, V. H., Kayser, M. V., Bader, D. L., and

Lee, D. A., 2005, "The influence of noncollagenous matrix components on the micromechanical environment of tendon fascicles," Ann Biomed Eng, 33(8), pp. 1090-1099.

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[31] Kaeding, C. C., Pedroza, A. D., Parker, R. D., Spindler, K. P., McCarty, E. C., and Andrish, J. T., 2005, "Intra-articular findings in the reconstructed multiligament-injured knee," Arthroscopy, 21(4), pp. 424-430.

[32] Anderson, A., Ellis, B., Peters, C., and Weiss, J., 2007, "Factors Influencing

Cartilage Thickness Measurements with Multi-Detector CT Arthrography: A Phantom Study.," Radiology.

CHAPTER 2

BACKGROUND

Knee Joint Overview The knee is the most complex synovial joint in the human body and is well-

designed to withstand large (~7x body weight) and repetitive loads [3]. For example,

the knee of an average jogger will retain 16,000 impacts per week, equivalent to 2400

tons of force [4]. The knee offers mobility in all six degrees of freedom, however, the

joint primarily functions in the sagittal plane, where it has a flexion range of 100

degrees. At full extension, the knee is highly stable due to a “screw home mechanism”

that locks the joint over the final 20 degrees of extension [5]. Uniform articulating

contact during flexion is maintained by a smooth sliding and rolling mechanism between

the tibial and femoral surfaces [6]. Although the knee is best suited to transfer

compressive loads, it must also resist large torques due to forces that twist the lower

extremity. At full extension, the knee is capable of resisting 90 N-m of valgus and 120

N-m of tibial axial torque [7]. The mobility and strength that is axiomatic to proper

knee function is provided by the articulating surfaces, musculature and ligaments.

Articulations

Synovial, or diarthrodial, joints are classified as having a synovial filled capsule

that surrounds the articulating bones. The knee has two separate articulations: the

11

patellofemoral joint and the tibiofemoral joint (Figure 2.1). These joints are technically

condyloid joints, where convex condyles articulate with concave surfaces; however,

since they mainly support motion in one planar direction (sagittal), they act more like

modified hinges. The convex articulations of the patellofemoral joint are the oval

medial and lateral condyles, while the trey-shaped tibial plateau provides the concave

surface. Lying between the femoral condyles, the intercondyler notch forms the patellar

groove where the patella slides, or tracks, upon during flexion and extension. The

specific motion of articulating bones can be quantified through kinematic measurements,

such as those performed in Chapter 4 and 5 of this dissertation.

The bony interfaces of these articulations are mediated by a ~2 mm layer of

articular or hyaline cartilage [8]. Articular cartilage is 80% water and has qualities in-

between bone and dense connective tissue. It is resilient, flexible, and in the

surrounding synovial fluid has a coefficient of friction 40x lower than Teflon [9, 10]. In

mature cartilage tissue, chondrocyte cells are sparsely distributed. The solid phase of

Femoro-Patellar Joint

Femoro-Tibial Joint

Femur

Tibia

Patella

Figure 2.1: An x-ray picture of the medial knee at 30 deg flexion.

12

the extracellular matrix is predominantly type II collagen (~60%) and proteoglycans

(~30%). The collagen interfibrillar space contains approximately 30% of the water,

while the proteoglycan solution domain holds 70% of the water [11]. The cartilage

surfaces are surrounded by a vascularized dense membrane called a perichondrium. The

cartilage structure itself is avascular and aneural. Therefore, nutrients must diffuse from

the perichondrium through the cartilage matrix to reach the cellular network of

chondrocytes. The extracellular matrix is responsible for the mechanical properties of

cartilage. Collagen provides tensile strength and grips aggregated proteoglycans

through physical entrapment and weak electrostatic and hydrogen-bonding [12].

Through dynamic and equilibrium factors, the keratin sulfate and chondrotin sulfate

glycosaminoglycans associated with the cartilage proteoglycans are able to retain water

under compression. The retention of nearly incompressible water provides a solid-fluid

dynamic modulus up to 50x higher than the equilibrium modulus [13-15], which is

measured after water exudation.

The load bearing and shock absorption capability of the tibiofemoral articulation

is augmented by the fibrocartilaginous semilunar menisci that sit on the medial and

lateral concavities of the tibial plateau (Figures 2.2, 2.3). The menisci transmit 50% and

85% of the joint load at full extension and 90 deg flexion, respectively [16]. The

menisci also increase the contact area of the proximal tibia by 50-70% [16] and attenuate

intermittent shock waves developed during gait [17]. Structurally, the menisci are fiber

reinforced composites (74% water by wet weight) that primarily insert into the anterior

and posterior meniscal horns (i.e., the points of the crescent shaped menisci). The solid

phase consists mostly of dense Type I collagen fibers with small amounts of

13

Figure 2.2: Illustration of the anterior knee joint. Adapted from [1].

14

Figure 2.3: Illustration of the posterior knee joint. Adapted from [1].

Lateral collateral ligament

Lateral meniscus Popliteus tendon

Anterior cruciate ligament Ligament of

Wrisberg Medial meniscus Medial collateral ligament

15

proteoglycans (<1% wet weight). The collagen has a circumferential orientation in the

interior and a radial orientation on the surface. These orientations are adept at

supporting the enormous hoop stresses that develop during joint compression [18, 19].

Muscles

The musculature provides passive (muscle tone) and dynamic support to the knee

joint via forces applied to the tendenous inserts from muscular contraction. Muscle

consists of a network of nerves and vessels, a muscle-specific extracellular matrix and

muscle cells that contain multiple nuclei. Two major muscle groups cross the knee and

enhance joint stability: the quadriceps muscle group (Figure 2.4A) and the hamstring

muscle group (Figure 2.4B). Coactivation of these muscle groups during gait aids the

ligaments in maintaining stability and equalizes the distribution of stress on the articular

cartilage [20]. Valgus and varus stability of the knee is increased by 28-35% when the

medial and lateral compartments are actively contracted [21], and Hughston et al. [22]

found that medial knee stability was 25% stiffer with contraction of the

semimembranosous muscle (Figure 2.4B). The hamstring group also reduces anterior

tibial translation during gait [23]. The joint position sense [24] that contributes to joint

stability and function is improved by stretching the muscles that surround the knee [25].

When muscle hypertrophies, the knee ligaments are at an increased risk of damage [20].

Ligaments

Ligaments are short bands of dense fibrous tissue that bind bone to bone. There

are four major ligaments of the knee that play a primary role in joint stability: The

anterior cruciate ligament (ACL), the posterior cruciate ligament (PCL), the medial

16

Figure 2.4: Illustration of the A) quadricep and B) hamstring muscle groups of the knee.

Gastrocnemious Muscle

Quadriceps and Patellar Tendons

Iliotibial Band

Semimembranosus Muscle

Semitendinosus Muscle

Biceps Femoris Muscle

A B

17

collateral ligament (MCL) or tibial collateral ligament, and the lateral collateral ligament

(LCL) or fibular collateral ligament (Figures 2.2, 2.3). The joint capsule and other knee

ligaments (e.g., posterior medial corner, medial and lateral retinacullum, the popliteal

ligament and the meniscofemoral and meniscotibial ligament) provide additional

stability. Individually, knee ligaments act as primary and/or secondary restraints to

specific motions, while collectively they limit and passively guide all six degrees of

freedom in the knee joint. This function is supported by an elastic modulus that is over

three hundred times greater than skin [26-28]. The MCL has an elastic modulus and

maximum stress of 332 MPa and 38 MPa [27], respectively, while the ACL has an

elastic modulus and maximum stress of 345 MPa and 36 MPa [29], respectively. These

mechanical characteristics of ligament are a function of their composition and molecular

organization.

Ligament composition and molecular organization

The structural organization of ligament follows a hierarchy. In general, ligament

can be described as a fiber reinforced matrix, where fibrous collagen fascicles provide

structural integrity to the extrafibrillar matrix. Fibroblasts are regularly distributed in

the extrafibrillar matrix and are responsible for maintaining the integrity of the collagen

fascicles. The orientation of the fascicles is tissue dependent and can be parallel,

oblique, and helical relative to the primary loading direction. When unloaded, collagen

fibers form a sinusoidal crimp pattern that gradually straightens when strained, which

forms the upwardly concave stress-strain behavior of ligament under tension [30].

Ligament is highly hydrated and 70% water by weight [31]. Of the dry weight fraction,

18

collagen accounts for 65-80% of the total solid phase [32]. The remaining constituents

include extracellular matrix proteins (e.g., elastin) and proteoglycans [33, 34].

The insertion sites of ligament have a dramatically different composition that has

adapted to reduce stress concentrations that occur between the ligament-bone interface.

Two types of insertions sites exist: direct insertions and indirect insertions. Direct

insertions are found at the femoral insertion in the MCL, and have fibrocartilage and

mineralized fibrocartilage zones between deep ligament fibers and bone. Indirect

insertions are found at the tibial insertion of the MCL, and are characterized by

superficial fiber fixation directly to the bone without fibrocartilagenous transitional

zones. At both the insertions and mid-substance, collagen is the molecular constituent

most responsible for resisting tensile loads [35-37].

Collagen

Collagen proteins provide the “connective” ability of connective tissue and

therefore, not surprisingly, constitute 25% of the total protein mass in mammals. Type I

collagen represents the largest dry-weight fraction in ligament (~70%)[32]. The

assembly of collagen fascicles in ligament begins with the secretion of Type I collagen

molecules by fibroblast cells. A collagen molecule, or tropocollagen unit (300 nm in

length and 1.5 nm in diameter), is a tightly wound triple helix of polypeptide chains, or

alpha chains, that contain about 1000 amino acids each. In the extracellular matrix,

tropocollagens covalently cross-link into a quarter stagger pattern to make collagen

microfibrils (10-300 nm in diameter)( Figure 2.5). Structural stability of collagen is a

product of the covalent crosslinks formed between alpha chains and between adjacent

19

tropocollagen units. Microfibrils amass to form collagen fibrils, and fibrils aggregate to

form collagen fibers. Round or spindle shaped fibroblasts sparsely occupy the spaces

between these fibers. Fibers group to form fiber bundles, or fascicles, which measure

many micrometers in diameter and can be seen without a microscope.

Other types of collagen in ligament, such as types XII, are fibril-associated

collagens. These collagens are formed similarly to type I collagen, but do not aggregate

to form fibrils in the extracellular matrix. Instead, they bind periodically to the existing

fibrils. It is hypothesized that these collagens mediate the inter-fibril interactions along

with fibril-macromolecular interactions [38], however, this subgroup of collagen has not

been specifically identified with any tissue-level mechanical function.

Figure 2.5: Schematic of the structural hierarchy of tendon and ligament. Adapted from Kasterlic [2].

20

Extrafibrillar Matrix

The extrafibrillar matrix represents the non-collagenous components of the

extracellular matrix. These components include proteins such as elastin and fibronectin,

along with proteoglycans and water. Elastin is a highly extensible protein that is a

composite of single elastin molecules covalently cross-linked. In ligament, elastin

accounts for less than 1% of ligament dry weight [39] and is found in abundance as

longitudinal oriented fibers that run in parallel to collagen fibrils. Elastin mechanically

contributes to the toe-region of the stress response at low strains when the collagen

fibers are still partially crimped [40]. The glycoprotein fibronectin constitutes 1-2

µg/mg of dry tissue in the major knee ligaments [41]. Fibronectins function by coupling

normal and growing tissue elements, and are required in-vitro for collagen organization

and fibroblast deposition [42].

Proteoglycans account for less than 1% of ligament dry weight and consist of a

protein core covalently bonded to one or numerous glycosaminoglycans. Proteoglycans

expressed in ligament include the small leucine-rich proteoglycans decorin and biglycan,

and the hyalectan proteoglycans versican and aggrecan [43]. Decorin accounts for 90%

of total proteoglycan content in ligament [43]. The high presence of decorin is likely

due to its role in controlling the diameter and integrity of Type I collagen [43]. Decorin

is secreted in the fibroblasts and “decorates” the collagen fibrils by attaching to gap

spaces between longitudinally adjacent tropocollagen units [44]. The number of GAG

side chains depends on the proteoglycan. Decorin has a single GAG side chain,

dermatan sulfate, and biglycan has two GAG side chains that are chiefly dermatan

21

sulfate [45]. Versican binds 10-30 GAGs and aggrecan 100 GAGs of chondroitin and

keratan sulfate [45].

Glycosaminoglycans play a significant role in the association of water with the

extrafibrillar matrix and may contribute to the mechanical response of ligament [46, 47].

Biochemically, GAGs are sulfated polysaccharides, which mediate tissue hydration

through electrostatic and non-electrostatic interactions. Hydration from electrostatic

interactions has been termed “charge effect”, and it occurs when the negative fixed

charge density of sulfated GAGs attract cations, and thus create a concentration

imbalance that swells the tissue through osmotic gradients [48]. This charge effect is

reduced as the negative fixed charges become neutralized in hypertonic solution. Non-

electrostatic swelling is represented by configurational entropy of the GAG chains in

solution. When the solution is hypotonic, the negative charges within the GAGs repulse

each other, leading to stiff GAG formations that have low entropy. In hypertonic

solution (i.e., 1 M of NaCl,), the charge effect is neutralized and increased flexibility of

GAG chain configurations leads to higher entropy and water intake [49]. The charge

and configuration effects have an inverse relationship that oppositely influences swelling

depending on the tonicity of the solution [49]. These water retention mechanisms of

GAGs enhance the ability of articular cartilage to bear substantial loads in compression

[50, 51], and may similarly affect the mechanics of ligament. Further, GAG to GAG

interactions may act as a mechanical link between discontinuous collagen fibrils [46, 52]

and are a principle topic of Chapters 6 and 7.

22

Ligament Contribution to Knee Joint Pathology

Although the characteristic crimp pattern and molecular organization of ligament

is highly adapted to control tension, irreversible damage occurs when the mechanical

limits of the tissue is exceeded [53]. In 2004, there were 14.2 million visits to the

hospital due to knee pain [54], and an estimated 45% of those visits were related to

ligament injury [55]. One major reason for the prevalence of knee ligament injuries is

due to the non-conforming articular surfaces. For example, a healthy hip is primarily

stabilized from the deep “ball and socket” geometry of the femoral head and acetabulum

cup, whereas the knee is minimally stabilized from the shallow “modified hinge”

geometry of the tibial plateau and femoral condyles. Therefore, the connective tissues

of the knee are burdened with stabilizing a highly mobile joint.

The MCL and ACL are the most commonly injured ligaments of the knee [55].

The MCL primarily restricts medial joint opening, and overstretching of the MCL

typically occurs during participation is sports such as football and soccer due to a direct

blow to the lateral side of the knee [56]. The MCL also restrains external rotation.

Sports that rigidly-fix elongated equipment on the foot, such as alpine skiing, are

exceptionally well suited at applying large external rotational torques on the knee. For

this reason, the MCL is the most common injury during alpine skiing and accounts for

18% of all ski related injuries [57]. The ACL primarily restricts anterior tibial

translation and internal tibial rotation. Injury to the ACL occurs in pivot sports and

nearly 70% of all ACL injuries are non-contact [58]. In skiing, ACL tears account for

16% of injuries [57], and frequently occur when the skier falls back, a motion that places

tremendous stress on the ACL as the tibia translates in the anterior direction. Females

23

have a higher incidence of ACL injuries compared to males, which has been related to

measurably lower yield strength and modulus of elasticity in the female ACL [59] along

with biochemical changes related to hormone fluctuations [60]. Combined MCL and

ACL injuries are also common and account for 70% of all multiligament injuries [61].

The interdependent functions of the ACL and MCL relates to their frequent and

associated injuries, consequently the relationship between these ligaments is the focus of

Chapters 4 and 5.

When ligaments are torn, the failure typically occurs through the tissue

substance, but can also occur by bony avulsion and in rare occurrences at the insertion

junction [62, 63]. In general, bony avulsion and junction failures have better outcomes

than when the tissue substance is disrupted [64]. Tissue substance failures in the MCL

most frequently occur near the femoral or superior insertion [65]. The extra-articular

MCL receives adequate blood supply, and after an initial inflammatory phase, matrix

and cellular proliferation begins. By the time remodeling and maturation is completed

after 12 months, however, the MCL has only 50-70% of its original strength [66, 67].

The two synergistic bundles of the ACL most commonly tear near the femoral insertion,

although the rupture pattern of the two bundles differs in 44% of patients [68]. The

intraarticular ACL receives significantly less blood than the MCL [69] and therefore,

unlike the MCL, a mid-substance rupture can not heal [70].

The dissimilar healing mechanisms of the MCL and ACL have warranted

different treatment regiments. The widespread opinion with MCL injuries is that non-

operative treatment is equally as effective as surgical intervention and that exercise

accelerates recovery [71]. Biomechanical analysis has shown that conservative

24

treatment of transected canine MCLs yields better biomechanical properties than

surgical treatment [67]. Avulsion injuries to the MCL, when minimally displaced, can

be treated non-surgically, but otherwise are recommended for surgical reattachment of

the soft tissue to the denuded bone with sutures or screws [72].

While MCL surgery is uncommon, ACL surgery is extremely prevalent. 75,000

– 100,000 ACL reconstructions are preformed each year in the United States [73].

Complete ACL ruptures do not heal spontaneously and can cause gross instabililty due

to knee subluxation. The ACL reconstruction procedure typically involves removing the

ruptured ACL and replacing the ligament with an autograft or allograft from the

semitendinousus tendon or patellar ligament by fixing the grafts in reamed femoral and

tibial channels. There are also strong advocates of nonsurgical treatment, which focuses

on improving joint stability through muscular conditioning [74]. However, reports have

revealed that 60-80% of patients treated non-surgically experience unsatisfactory

outcomes in high-risk populations [75, 76]. Unfortunately, even ACL reconstruction

often does not completely restore pre-injury gait [77] or joint stability and studies have

shown a large percentage of knees with reconstructed ACLs have unsatisfactory athletic

performance [78-80].

In the short-term, knee instability due to ligament injury limits participation in

certain sports and activities [81], but in the long-term, these injuries can lead to the more

severe and debilitating pathology of osteoarthritis. Osteoarthritis is a joint disease that

results in the breakdown and eventual loss of the protective layer of hyaline cartilage

between the articulating bones. This condition affects 21 million people in the United

States and accounts for 25% of visits to the primary care physicians [82]. The only

25

treatment for this painful disease is total knee replacement. In 2002, 350000 primary

total knee replacements were performed in the United States [83]. Although this

operation has been extremely successful at relieving painful osteoarthritic symptoms,

there is an extensive recovery period and normal joint motion and function is

permanently restricted. Therefore, considerable research has focused on preventing the

necessity of knee replacement. Along with developing technology to regenerate

cartilage through tissue-engineering methods [84, 85], an emphasis has been placed on

identifying the etiology of this disease. Osteoarthritis has been connected to age-related

water loss in articular cartilage [86, 87] and recent studies have shown that ligament

injury can result in early progression of this disease [88].

The link between ligament pathology and osteoarthritis resides with altered gait

and biological adaptations that occur after ligament trauma. For example, the movement

patterns in the ACL deficient knee will exhibit increased flexion during the swing phase

and a greater hip extensor moment to reduce anterior tibial translation [77, 80] . These

gait changes are identified with redistribution of stresses on the articular cartilage. A

study by Andriacchi et al. [88] correlated a shift in the normal load bearing regions of

the knee joint after ACL rupture with increased cartilage thinning and Maffulli et al.

[89] found that 42% of ACL-deficient patients had a lesion on weight bearing regions of

the articular cartilage. The mechanoreceptors that protect the knee through

proprioreceptive mechanisms are also damaged during ligament rupture [90].

Mechanoreceptors give afferent signals of the spacial limb position to dynamically

control muscle and are most active at the limits of motion where joint supports are

susceptible to injury [91]. Elimination of these receptors disrupts ligament-muscle

26

communication. Further, injury to one ligament in the knee can result in histological,

biochemical and molecular changes to the other knee ligaments, even if they do not

share functional roles [92]. One can conclude that joints behave like an integrated organ

system, and it is not surprising that ligament damage and cartilage wear are related. It is

therefore imperative to restore ligament mechanical function for long-term health of the

knee. Proof of ligament restoration in meaningful terms of joint structural stability and

ligament material properties is cardinal, and thus biomechanical experimentation is an

indispensable tool for evaluating the efficacy of repair and reconstruction techniques.

Experimental Biomechanics of Ligament

The function of joint stabilizers is mechanical in nature and understanding the

mechanical characteristics of ligament has many clinical impacts. Biomechanical

studies have improved the prevention of ligament injury through intelligent design of

athletic equipment [7], playing surface interfaces [93] and prophylactic braces [94].

Quantifying ligament mechanical behavior is necessary to assess surgical techniques and

verify the efficacy of harvested or engineered grafts [95, 96]. The mechanisms of tissue

repair and structural integrity can be elucidated to improve wound healing modalities

and tissue engineering constructs [97, 98]. Finally, biomechanical studies of ligament

can be used to define constitutive models that mathematically describe experimental

observations. Constitutive models are essential in using computational techniques to

comprehensively analyze the complex relationships of joints and provide treatment

strategies [99]. Experimental mechanic studies in ligament can be grouped into

structural and material tests.

27

Structural tests involve the physiological manipulation of whole or partial joints

while kinematic and force data is collected. These experiments determine joint motion

limits and the role of and interaction between joint stabilizers. The first structural

experiments on cadaveric knees were performed by Brantigan in 1941 [100]. Brantigan

fixed the femur and applied torques and forces to the tibia at various flexion angles. The

simplification of these early experiments has evolved into modern systems that better

mimic physiological loading configurations. One such system is the Oxford Rig, which

permits 6 degrees of freedom (DOF) by simulating a flexed knee stance through tension

of the quadircieps tendon [101]. Another recent system is a robotic arm that can operate

in force and displacement mode in up to 6 DOF by finding the passive knee flexion path

in joints [102]. These and other structural testing systems have been used to discern the

primary and secondary ligamentous restraints in knees and the forces that ligaments

transfer from bone-to-bone. Limitations of structural knee tests include problems

inherent with in-vitro experiments as well as misrepresentation of passive residual forces

in muscle. Structural tests are also unable to characterize the behavior of a specific

tissue substance; however, this can be accomplished with material tests.

Material tests are used to characterize the fundamental relationship between

stress, strain and other state variables. This relationship may behave in an elastic or

viscoelastic manner and may depend on material symmetries. Like all biological tissue,

ligaments have elastic and viscous attributes. Elastic materials lose no energy during

deformation and behave independent of time, while viscoelastic materials dissipate

energy during deformation and have time dependent characteristics such as relaxation,

28

creep, and strain-rate sensitivity. Material symmetry classifies whether a certain tissue

has any preferred directions for a given loading configuration.

To perform a material test the tissue must be isolated and inserted into a material

testing system where tensile, compressive or shear loads are applied. Loads are applied

along one axis, or along multiple axes to better represent physiological loading patterns.

Ligaments can be isolated at their bony insertions [103] or be punched from the tissue

substance [27]. Material symmetry is determined by testing a material in various cutting

planes. In ligament, when tensile testing is aligned with visible collagen fascicles the

material is much stiffer than when tensile testing is aligned transverse to these fibers

[27]. This type of material symmetry has one preferred direction and is termed

transverse isotropy. The elastic material properties can be tested by 1) loading the

material to different strain-levels and allowing equilibration and 2) loading in a quasi-

static manner to reduce inertial effects and time-dependent viscoelastic effects. The

viscoelastic relaxation and creep properties are determined by deforming the tissue to a

constant displacement or force, respectively. Strain-rate sensitivity is measured by

varying loading rates. Finally, damping or energy dissipation can be measured by

determining the hysteresis or energy dissipation during a loading-unloading cycle. The

phase shift that occurs between sinusoidal displacements and the oscillatory force

response also reflects this damping behavior [104].

Numerical Modeling of Ligament

Constitutive Models

Once the material properties of a tissue are determined, it is useful to represent

the observed response mathematically for predictive modeling. The mathematical

29

interpretation of the material is a constitutive relationship that objectively describes the

interaction of stress, strain and other state variables such as strain rate and time.

Constitutive models contain coefficients that are fit to the experimental results through

numerical methods such as curve fitting [105], which can be supplemented with inverse

finite element methods [106]. Soft tissues experience large nonlinear deformations during

normal activity and therefore the constitutive relationship must be a function of variables

that are independent of rotation and have a nonlinear response to strain.

One constitutive model that can accommodate this tissue response is a

hyperelastic strain energy model. The strain energy W represents the stored energy in

the system, and the hyperelastic model permits large deformations by being a function of

the right Cauchy-Green deformation tensor C, which is unaffected by rigid body

rotation. For ligament under tension, the material behavior can be described reasonably

well by a transversely isotropic strain energy [107]:

2

1 1 2( ) ( ) (ln( ))2KW F I F Jλ= + + (1)

Here F1 is the matrix strain energy and F2 is the collagen fiber strain energy. These two

terms represent the stored energy due to deviatoric deformation. The matrix strain

energy is a function of the first deviatoric invariant, I1. The collagen fiber strain energy

is a function of the deviatoric part of the stretch ratio along the fiber direction, λ. The

dilational, or pressure response, is a function of the determinant of the deformation

gradient (i.e., volume change), J, and the bulk modulus, K. The mathematical functions

for each of these components are selected to best describe the tissue being modeled. In

ligament, a neo-Hookean model is commonly chosen to represent the matrix strain

30

energy [108]. With this simple model, the matrix function is only a dependent on the I1

invariant. The collagen fibers are given piecewise continuous functions for stress that

have physical interpretations [109]. Under compression, the fiber strain energy equation

is zero, because collagen structures tend to buckle under small compressive forces.

During initial tension, ligament will exhibit non-linear toe region as collagen fibers

uncrimp until the fibers are uniformly straightened at some stretch threshold, λ* This is

mathematically represented by including an exponential function from the start of tensile

stretch to λ*. After the tissue is stretched past this threshold, the fiber strain energy is

linearly governed by the modulus of the straightened fibers.

The stress is derived from the strain energy (energy per unit volume):

2 W∂=

∂S

C, (2)

where S is the 2nd Piola-Kirchhoff stress and C is the right Cauchy-Green deformation

tensor. The 2nd Piola-Kirchhoff stress can easily be converted to other stress forms such

as engineering stress (1st Piola-Kirchhoff Stress) and Cauchy stress.

A limitation of this hyperelastic strain energy material is that it does not

represent the innate viscoelasticity in ligament. Y-C Fung introduced the quasilinear

viscoelastic (QLV) model in 1973 [110] to better represent the strain-history dependent

characteristics of biological tissue. In the QLV theory, the tensile stress is the product of

a reduced relaxation function (3A) and an elastic stress function (3B):

( )[ ( )] ( )( ) ( )

t eTT t G t dλ τ λ ττ τλ τ−∞

∂ ∂= −

∂ ∂∫ , (3)

(A) (B)

31

where T is the Cauchy stress, G is the reduced relaxation function, τ denotes time, t

denotes time limit, and λ is stretch. The mechanism of this equation is that the reduced

relaxation function (3A) decays for increasing values of t-τ. This decaying function

introduces time-history dependence and acts to scale the elastic stress. The chain rule is

used to express the instantaneous change in elastic stress (3B). Thus, these two terms

scale stress at an instant in time, and the total stress T is calculated by superposing the

instantaneous stresses over the entire stress history of the response.

The QLV model can accommodate any well posed elastic (e.g., hyperelasticity)

and reduced relaxation function (e.g. continuous spectrum of kelvin models).

Limitations of the QLV model include the non-physical meaning of the parameter inputs

and its inability to model the experimentally observed dependence of damping on strain-

level [111]. Poroelasticity theory is an alternative constitutive model that has physically

meaningful inputs and can possibly support strain-dependent damping in ligament.

The poroelastic constitutive model was first implemented in biological tissue by

Mow et al. [112] to account for the deformation of the solid matrix and interstitial fluid

flow in articular cartilage. The force interface between these two phases is a function of

fluid pressure and solid/fluid velocity, therefore, a transitory response exists and the

theory captures viscoelastic attributes. The poroelastic model is formulated from

fundamental principles, which includes the equations of motion for the solid and fluid

phase:

+div( ) =sπ T 0 (4)

f+div( ) =-π T 0 (5)

32

where Tf and Ts are the stress tensors of the solid and fluid phase, respectively. An extra

reaction force, π, is present in both equations from the phase interaction. The

constitutive model specified for the solid-phase stress tensor can be any well constructed

constitutive model, including equations from hyperelastic strain energy and QLV

theories. The constitutive model specified for the fluid-phase can be a Newtonian

viscous fluid, however, an ideal non-viscous fluid is often assumed and hence the stress

tensor for the fluid phase equates to the fluid pressure. A constitutive relation is also

specified for the frictional force vector, π. This drag force is typically a function of

relative phase velocity, fluid pressure and permeability (constant or strain dependent).

The conservation of mass for the mixture requires:

s fdiv(φ φ ) 0+ =s fv v (6)

where vs and vf are the respective solid-phase and fluid-phase velocities, and φs and φf

are the respective solid-phase and fluid-phase volume fractions. The coefficient inputs

to the poroelastic model include parameters (e.g. permeability) that can be

experimentally measured [113]. The physical meaning of the coefficients has inherent

advantage over more phenomenological based models such as the QLV theory. The

poroelastic model has traditionally been used to describe compression-loaded tissues

such as cartilage [114], but theoretically it can also predict material behavior under any

loading configuration. The ability of the biphasic model to predict stress-relaxation and

harmonic oscillation behavior in ligament is briefly explored in the final chapter.

33

Finite Element Models

The background of this dissertation concludes with a brief dialogue on the finite

element method. The finite element method was developed to calculate how force and

displacements influence the stress and strain continuum in single or multiple bodies. For

3D finite element analysis, the stress and strain continuum is solved over the volume of

the object(s) being analyzed. The basic rationale is that calculations are greatly

simplified for repeated geometric shapes, such as tetrahedrals and hexahedrals.

Therefore, complex geometries are first discretized into a large group of simplified

shapes that can be aggregated to solve for the system. After discretization, boundary

conditions are applied (pre-processing) and the analysis is initiated. The vector

displacements are determined at each node by minimizing the systems potential energy

(internal strain energy + external forces) with a quasi-Newton method. Specified

constitutive models and the associated coefficients are necessary for this calculation.

Since the potential energy needs to be integrated over the volume of the system,

discontinuous nodal displacements can not be used and it is necessary to evaluate

differentiable shape functions. Once the total potential energy has been minimized at a

load step, the process starts again for the next load step until the analysis is complete.

Post-processing is performed to visualize predictions.

Finite element methods are well established in traditional engineering disciplines

and are becoming increasingly pervasive in biological sciences as their utility becomes

recognized [99, 115]. To bridge the gap between clinician and engineer, however, it is

critical to rigorously validate an FE model by coupling experimental and theoretical

work. Strong advances by Gardiner et al. [109] in validating FE models of knee

34

ligaments have paved the way for a clinically relevant injury model of the knee to be

simulated in this dissertation. A validated FE model grants access to a full continuum of

mechanical data and represents a successful synergy between experimental

biomechanics, mathematical constitutive relations, and numerical methods.

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44

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CHAPTER 3

SIMULTANEOUS MEASUREMENT OF THREE-DIMENSIONAL JOINT

KINEMATICS AND LIGAMENT STRAINS WITH OPTICAL METHODS1

Abstract The objective of this study was to assess the precision and accuracy of a non-

proprietary, optical three-dimensional (3D) motion analysis system for the simultaneous

measurement of soft tissue strains and joint kinematics. The system consisted of two

high-resolution digital cameras and software for calculating the 3D coordinates of

contrast markers. System precision was assessed by examining the variation in the

coordinates of static markers over time. 3D strain measurement accuracy was assessed

by moving contrast markers fixed distances in the field of view and calculating the error

in predicted strain. 3D accuracy for kinematic measurements was assessed by

simulating the measurements that are required for recording joint kinematics. The field

of view (190 mm) was chosen to allow simultaneous recording of markers for soft tissue

strain measurement and knee joint kinematics. Average system precision was between

±0.004 mm and ±0.035 mm, depending on marker size and camera angle. Absolute

___________________ 1 Reprinted from Journal of Biomechanical Engineering, Vol. 127, No. 1, Trevor J. Lujan, Spencer P. Lake, Timothy A. Plaizier, Benjamin J. Ellis, Jeffrey A. Weiss, “Simultaneous Measurement of Three-dimensional Joint Kinematics and Ligament Strains with Optical Methods”, pp: 193-197, 2005, with kind permission from the ASME.

46

error in strain measurement varied from a minimum of ±0.025% to a maximum of

±0.142%, depending on the angle between cameras and the direction of strain with

respect to the camera axes. Kinematic accuracy for translations was between ±0.008 and

±0.034 mm, while rotational accuracy was ±0.082 to ±0.160 degrees. These results

demonstrate that simultaneous measurement of 3D soft tissue strain and 3D joint

kinematics can be performed while achieving excellent accuracy for both sets of

measurements.

Introduction

The measurement of strain is of fundamental interest in the study of soft tissue

mechanics. In studies of musculoskeletal joint mechanics, the accurate measurement of

three-dimensional joint kinematics is equally important. By simultaneously quantifying

the strains in soft tissues such as ligaments and the joint kinematics in response to

externally applied loads, it is possible to elucidate the role of these structures in guiding

and restraining joint motion and to identify potential injury methods and clinical

treatments [1-3]. Further, simultaneous acquisition of joint kinematics and strain fields

can be used to drive and validate subject-specific models of ligament and joint

mechanics [4].

The simultaneous measurement of joint kinematics and soft tissue strain is

typically accomplished by using a combination of two or more different technologies.

Joint kinematics are commonly quantified using video-based techniques [5,6],

instrumented spatial linkages (ISLs) [7,8] or electromagnetic tracking systems [9-11].

ISL systems require the attachment of a bulky mechanical linkage across the joint, while

electromagnetic tracking systems are often plagued by interference from ferrous

47

materials, limiting their applicability. In contrast, there are relatively few techniques

that are capable of measurement of three-dimensional (3D) soft tissue strains.

Alternatives include the use of one-dimensional measurements from contact devices

such as DVRTs [12, 13]. Optical methods are currently considered to be the best option

for 3D strain measurement on visible soft tissues. These methods use the direct linear

transformation to calculate 3D strain measurements from two or more cameras [4,14].

Previous optical systems were primarily based on super VHS video, yielding an

effective vertical resolution of 400 lines. This limited resolution requires the use of

extremely small fields of view to achieve accuracies of ±0.1-0.5% error in percent strain

[14]. This precludes the simultaneous tracking of markers for kinematic measurements,

since a larger field of view is needed to see both the strain and kinematic markers.

Currently available systems based on digital cameras typically use vendor-supplied

proprietary cameras and/or framegrabbers. These systems primarily use digital cameras

that have much better resolution and sensitivity than video-based systems. However, the

use of proprietary vendor-supplied hardware is often costly and ties the support and

upgrade of the system to a particular vendor or system integrator.

Due to ongoing improvements in the sensitivity and resolution of charge-coupled

devices (CCDs), modern progressive-scan digital cameras can provide images with very

high quality and resolution. The improved spatial resolution (typically at least

1024x1024) opens up the possibility of using a field of view that is large enough to track

markers for both soft tissue strain and joint kinematics. The use of cameras and

framegrabbers from individual vendors is especially attractive since it eliminates the

need for proprietary, vendor-specific hardware and software. The objective of this study

48

was to develop a methodology for simultaneous measurement of 3D soft tissue strain

and joint kinematics using a non-proprietary digital camera system, and to quantify the

errors associated with these measurements in a test setup that mimicked the study of

knee ligament biomechanics.

Materials and Methods

Measurement Systems

The measurement system consisted of two high-resolution digital cameras

(Pulnix TM-1040, 1024x1024x30 frames per second (fps), Sunnyvale, CA) equipped

with 50 mm 1:1.8 lenses and extension tubes, two frame grabbers (Bitflow, Woburn,

MA) and Digital Motion Analysis Software (DMAS, Spica Technology Corporation,

Maui, HI). The cameras were configured to record 6 fps directly to computer memory,

requiring 2.1 MB of memory per frame. The cameras were focused at a target with a

190 mm diagonal field of view (FOV). The DMAS software tracked marker centroids

in both camera views automatically and applied the modified direct linear

transformation (DLT) to calculate the 3D centroid coordinates [15]. Preliminary tests

demonstrated that black markers against a white background provided superior contrast

and therefore system accuracy in comparison to markers covered with reflective tape,

while two 100 W incandescent lights provided better contrast than halogen or

fluorescent lighting. In the following sections, all instrument accuracy values are per the

manufacturer.

A 3D calibration frame was manufactured. Twenty-seven white Delrin spherical

markers (4.75 mm dia.) were arranged in three horizontal planes, with a 3x3 grid pattern

on each plane and 60 mm marker spacing. The exact coordinates of each marker

49

centroid were determined with a coordinate measuring machine (Zeiss Eclipse 4040,

accuracy ±0.0004 mm). These coordinates were used for DLT calibration.

Precision

The precision was determined by examining the variation of the 3D positions of

stationary markers over time. After calibration, two different frames with twelve 4.75

and 2.38 mm dia. spherical markers were recorded for 25 seconds. The dimensions of

these markers were chosen to be the exact same size as the kinematic markers (4.75 mm

dia) and the strain markers (2.38 mm dia) used during actual biomechanical testing in

our laboratory. The variation in marker position was determined by computing two

standard deviations of the length of their position vector and the individual x, y and z

coordinates over time. Experiments were repeated at camera angles of 30, 60 and 90

degrees (Figure 3.1). To evaluate the precision of the system in actual test conditions,

the variation of kinematic (4.75 mm dia) and strain (2.38 mm dia) marker positions were

determined for four-sets of three-second passive recordings taken at a 30° camera angle

during biomechanical testing of a human medial collateral ligament (MCL) (Figure 3.2).

Complete details of this test configuration and marker placement can be found in our

previous publications [4,14].

Accuracy of Simulated Strain Measurement

Accuracy tests were performed dynamically to determine the ability of the

system to measure simulated 3D changes in strain. The effects of strain magnitude and

camera angle were assessed. A 2.38 mm dia. marker was adhered to a fixed location,

while a similar marker was adhered 13.5 mm apart (Linitial) to a linear actuator (Tol-O-

50

Medial Meniscus

Proximal Tibia

Distal Femur

Femoral Kinematic Block

Tibial Kinematic Block

Figure 3.1. Plan view of the camera setup. The z-axis is directed out of the page. To assess system sensitivity to camera angle, angles of 30, 60 and 90 degrees were used during testing.

Figure 3.2. Photograph of test setup for simultaneous measurement of MCL strain and knee joint kinematics. Eighteen markers (2.38 mm diameter) were adhered to the MCL for strain measurement. Femoral and tibial kinematic blocks, each with three kinematic markers (4.75 mm diameter), were affixed to the cortical bone.

Z-Axis

X-Axis

Y-Axis

Objective Camera

Angle (θ)

51

Matic, Inc, Hamel, MN, accuracy ±0.0025 mm). The Linitial was chosen to replicate the

spacing between markers used to calculate 3D strains in the human MCL [4,14]. In two

separate tests, the actuator was translated (∆L) along either the z- or x-axis in Figure 1 to

simulate strains of 1, 2, 5 and 20%. Tests were performed four times for each

displacement. Accuracy was calculated as the difference between the predicted

displacement and the known actuator displacement. The error in simulated strain

measurement was computed by determining the absolute difference between actuator

strain and DMAS strain (∆L/Linitial).

Accuracy of Kinematic Measurements

When tracking joint kinematics, it is desirable to establish “embedded”

coordinate systems within the bones using a convention such as the one described by

Grood and Suntay [16]. The transformation matrix between embedded coordinate

systems is established by tracking markers on the bones that define separate “marker”

coordinate systems. The transformation between one marker coordinate system and the

corresponding embedded coordinate system on a bone does not change during testing.

By establishing these transformations before testing and then tracking the transformation

between marker coordinate systems during testing, the transformation between

embedded coordinate systems can be determined [4,14]. To assess kinematic

measurement accuracy, the setup and calculations necessary to record knee joint

kinematics were simulated. Two L-shaped white blocks (the “kinematic blocks”, Figure

3.2) with three 4.75 mm dia. black markers that formed a 90 degree angle were used to

establish marker coordinate systems. The following tests were repeated four times for

each translation or rotation, at camera angles of 30, 60 and 90 degrees.

52

To measure accuracy of translations along the z-axis in Figure 3.1 from

kinematic calculations, one kinematic block was adhered to a static fixture and a second

one was attached to the linear actuator. An Inscribe 3D Digitizer (Immersion Corp, San

Jose, CA accuracy ±0.085 mm) was used to determine the centroids of the markers by

digitizing points on the marker surface and then fitting the coordinates to the equation of

a sphere. To simulate the use of embedded coordinate systems, three points on both the

static fixture and the actuator were digitized and used to establish orthonormal

coordinate systems. The transformation matrices were calculated between the kinematic

blocks and their respective embedded coordinate systems. The actuator was displaced

0.500, 1.000, 5.000 and 50.000 mm and an overall transformation matrix between the

embedded systems was calculated by concatenation. The ratio of the calculated

translations to the known translations was computed.

To measure accuracy of translation measurements along the x-axis in Figure 3.1

from kinematic calculations, a kinematic block was adhered to an x-y table and the table

was moved 0.50, 1.00, 5.00, and 50.00 mm, measured with digital calipers (Mitutoyo,

San Jose, accuracy ±0.02 mm). Error was calculated as the ratio of translation predicted

from the motion analysis data to the known translation.

To determine accuracy of rotations about the z-axis in Figure 3.1, a rotational

actuator (Tol-O-Matic, Inc, Hamel, MN, accuracy ±0.002°) was used to rotate one of the

kinematic blocks through angles of 2.00° and 20.00°. The transformation matrix

between the two embedded coordinate systems was calculated and the rotation between

the two systems was resolved using the method of Grood and Suntay [16]. The ratio of

the rotation angle from the motion analysis data to the known angle was determined.

53

Statistical Analysis

The effects of camera angle and marker size on 3D precision were assessed using

a two-way ANOVA with repeated measures. The effects of camera angle and strain

magnitudes on x-axis and z-axis strain accuracy were assessed using two separate two-

way ANOVAs with repeated measures. The effects of camera angle on x-axis and z-

axis translational kinematic accuracy and z-axis rotational kinematic accuracy were

assessed using two separate two-way ANOVAs with repeated measures. Statistical

significance was set at p<0.05 for all analyses.

Results

Precision

Results for precision were excellent for both marker sizes (Table 3.1). The

larger markers exhibited significantly better precision than the smaller markers

(p=0.005). There was no effect of camera angle on marker precision (p=0.089). The

best results (±0.004 mm, 0.0020 % FOV) were obtained for the larger markers using a

30-degree camera angle. Precision did not vary considerably between the x, y and z

coordinates of the markers. For example, at a 60 degree camera angle, the larger

markers had x, y and z coordinate precisions of 0.019, 0.019 and 0.012 mm,

respectively. The precisions for both marker sizes obtained with a MCL biomechanical

test setup were comparable to precisions for the controlled tests (Table 3.1, 4th row).

54

Table 3.1. Results for measurement of 3D precision. The first three rows of data were obtained by recording stationary markers for 25 seconds with a FOV of 190 mm. The fourth row was obtained from passive recording acquired during biomechanical testing of a human MCL. Each passive recording was approximately 3 seconds long, with a camera angle of 30°, and a FOV of 190 mm. Absolute precision was calculated as two standard deviations of the position measurement, while Percent FOV was calculated as the precision divided by the FOV multiplied by 100.

4.75 mm dia. Markers 2.38 mm dia. Markers

Camera Angle (θ) Precision (mm)

Percent FOV (%)

Precision (mm)

Percent FOV (%)

30° 0.004 0.0020% 0.035 0.0163% 60° 0.011 0.0049% 0.025 0.0117% 90° 0.006 0.0026% 0.012 0.0048%

MCL Study (30°) .009 0.0044% 0.011 0.0054%

55

Accuracy of Simulated Strain Measurement

The optical system delivered excellent results for strain error (Table 3.2). There

was a significant effect of camera angle on accuracy for z- and x-axis strain accuracy

(p=0.004 and p<0.001, respectively, Figure 3.3). The most accurate camera angle for

strains along the z-axis was 30°, having an average accuracy of ±0.005 mm with a strain

error of ±0.035%. Conversely, the most accurate camera angle when strains were

measured along the x-axis was 90°, having average accuracies of ±0.003 resulting in a

strain error of ±0.025%. There was a significant effect of strain magnitude on accuracy

for z- and x-axis strain accuracy (p=0.008 and p<0.001, respectively). The condition

conferring the least accuracy occurred for both the z-axis and x-axis cases at 90° and

30°, respectively, when a 20% strain was applied.

Accuracy of Kinematic Measurements

The optical system delivered very good results for kinematic accuracy (Table

3.3). Data for z-axis kinematic accuracy are shown as an example (Figure 3.4). The

average x- and z-axis translational accuracies across all three camera angles and all four

actuator displacements were ±0.025 and ±0.016 mm, respectively. Average accuracy for

rotation was ±0.124° (Table 3.3). There was a significant effect of camera angle on

accuracy of kinematic measurements of translation along the z- and x-axes (p=0.029 and

p<0.001, respectively), but there was no effect of camera angle on kinematic rotational

accuracy (p=0.378). The effect of camera angle on the kinematic translational

accuracies was similar to that for the strain accuracies. There was a significant effect of

the magnitude of translation/rotation on accuracy of kinematic measurements of

Table 3.2. Accuracy of 3D simulated strain measurement along the z- and x-axes for all four strain levels. Accuracy (mm) was calculated as the difference between the actuator-based value and the value calculated from the optical system data. Strain error (%) is the accuracy divided by the gauge length (13.5 mm) multiplied by 100.

Camera

Angle (θ) 1.0% Strain

2.0% Strain

5.0% Strain

20.0% Strain

Averages across all Strains

Accuracy (mm) 0.004 ± 0.007 0.011 ± 0.003 0.003 ± 0.004 0.001 ± 0.007 0.005 ± 0.005 30°

Strain Error (%) 0.028 ± 0.052 0.084 ± 0.018 0.019 ± 0.030 0.010 ± 0.052 0.035 ± 0.033

Accuracy (mm) 0.002 ± 0.001 0.013 ± 0.005 0.005 ± 0.005 0.009 ± 0.012 0.007 ± 0.006 60° Strain Error (%) 0.014 ± 0.009 0.099 ± 0.037 0.040 ± 0.035 0.067 ± 0.091 0.055 ± 0.037

Accuracy (mm) 0.009 ± 0.001 0.016 ± 0.003 0.011 ± 0.004 0.024 ± 0.005 0.015 ± 0.003

z axis

90° Strain Error (%) 0.065 ± 0.006 0.115 ± 0.025 0.081 ± 0.027 0.175 ± 0.034 0.109 ± 0.049

Accuracy (mm) 0.011 ± 0.002 0.011 ± 0.002 0.019 ± 0.002 0.036 ± 0.003 0.019 ± 0.012 30°

Strain Error (%) 0.081 ± 0.018 0.082 ± 0.014 0.138 ± 0.017 0.267 ± 0.024 0.142 ± 0.088

Accuracy (mm) 0.002 ± 0.002 0.018 ± 0.002 0.006 ± 0.011 0.003 ± 0.002 0.007 ± 0.007 60°

Strain Error (%) 0.015 ± 0.015 0.130 ± 0.017 0.045 ± 0.082 0.021 ± 0.011 0.053 ± 0.053

Accuracy (mm) 0.002 ± 0.001 0.006 ± 0.001 0.003 ± 0.007 0.003 ± 0.001 0.003 ± 0.002

x axis

90° Strain Error (%) 0.017 ± 0.008 0.045 ± 0.007 0.022 ± 0.049 0.018 ± 0.006 0.025 ± 0.013

56

57

Figure 3.3. A - Simulated 3D strain error along the z-axis. B – Simulated 3D strain error along the x-axes. Strain Error was computed as the difference between the actuator-based strain and the strain calculated by the motion analysis system, divided by the gauge length.

30° Camera Angle 60° Camera Angle 90° Camera Angle

1.0 2.0 5.0 20.0 Z-Axis Strain (%)

Abs

olut

e St

rain

Err

or (%

stra

in)

Abs

olut

e St

rain

Err

or (%

stra

in)

0.05

0.10

0.15

0.20

0.25

1.0 2.0 5.0 20.0 X-Axis Strain (%)

0.05

0.10

0.15

0.20

0.25 30° Camera Angle 60° Camera Angle 90° Camera Angle

A

B

58

Table 3.3. Accuracy of 3D kinematic measurements. Accuracy is the difference between the actuator translation/rotation and the value calculated from the optical system data. Accuracy in terms of Percent FOV is the accuracy divided by FOV multiplied by 100. Results are the average across all translations/rotations descibed in the Methods section.

Translation (x-axis) Translation (z-axis) Rotation (z-axis)

Camera Angle (θ)

Accuracy (mm) % FOV Accuracy

(mm) % FOV Accuracy (deg) % FOV

30 deg 0.034 ± 0.031 0.012 ± 0.004 0.008 ± 0.011 0.005 ± 0.006 0.132 ± 0.162 0.074 ± 0.091

60 deg 0.018 ± 0.005 0.009 ± 0.006 0.019 ± 0.023 0.009 ± 0.010 0.082 ± 0.069 0.043 ± 0.036

90 deg 0.021 ± 0.002 0.009 ± 0.008 0.020 ± 0.017 0.006 ± 0.005 0.160 ± 0.218 0.074 ± 0.101

Figure 3.4. Results for the measurement of 3D kinematics along the z-axis direction. Accuracy was measured as the difference between the actuator based translation and the value calculated by the motion analysis system, divided by the actuator translation.

Z-Axis Translation (mm)

Acc

urac

y (m

m)

30° Camera Angle 60° Camera Angle 90° Camera Angle

0.5 1.0 5.0

0.01

0.05

0.04

0.03

0.02

59

translation along the z- and x-axes and rotation about the z-axis (p<0.001, p<0.001 and

p=0.033, respectively). Larger translations/rotations reduced kinematic accuracy.

Discussion

This study demonstrated that the 3D system can accurately measure simulated

strain and kinematics using physical and optical conditions that accommodate

simultaneous tracking of markers for both measurements. A reduced camera angle

significantly improved accuracy for frontal plane (z-axis) displacements, while an

increased camera angle significantly improved accuracies of displacements along the

intersection of the saggital and transverse planes (x-axis). Moreover, in comparison to

similar systems using proprietary vendor-specific hardware, this system is a small

fraction of the cost.

Accuracy and precision of the system were determined using a testing

environment that was specifically designed to mimic the physical and optical conditions

for experiments on the human MCL in intact knees. For actual testing of the human

MCL, only precision was determined. It is not possible to determine strain accuracy

during an actual biomechanical test since a gold standard for strain measurements is

difficult if not impossible to establish. However, by setting all testing variables (i.e.,

FOV, marker size, marker spacing, lighting) appropriately, the controlled tests faithfully

reproduced the physical and optical conditions of actual biomechanical tests for the

MCL. Results for precision from the controlled tests and from actual measurements on

the MCL were similar (Table 3.1), supporting the notion that the controlled tests

provided a good surrogate for the physical and optical conditions that are encountered

during actual tests on the MCL.

60

System precision (Table 3.1) was calculated using the length of the position

vectors of the markers, and thus these measurements should be considered average

errors that take into account the precision in all three spatial directions. For the

simulated strain measurements, the major spatial directions were accounted for by

testing along the x- and z-axes. By positioning the cameras at an angle that permitted

the most marker motion perpendicular to the cameras, therefore reducing the

incremental distances that each pixel in the video system represents, the strain error was

significantly decreased. For z-axis strains this occurred at a 30° camera angle, and for x-

axis strains this occurred at a 90° camera angle. Based upon the accuracy results (Figure

3), it is recommended that these camera angles be optimized accordingly, especially if

large strains are predicted. The measurements of strain accuracy should be considered a

best case when considering general measurements in 3D using comparable camera

angles. Although a similar argument applies to the kinematic measurements, the “gold

standard” for these measurements was based on a combination of digitizer, actuator

encoder, or digital caliper measurements. Because of differences in the accuracy of

these measurement techniques and the propagation of errors in the kinematic

measurements, the results for translational and rotational kinematic accuracies likely

represent worst cases. This error propagation is likely responsible for the reduction of

accuracy with increased axial translation (Figure 3.4).

As with any system based on video or digital cameras, the most important

determinants of precision and accuracy are the resolution of the CCD and the FOV used

for measurements. This assumes that an accurate DLT calibration has been performed

and that this calibration has taken into account errors associated with lens distortion. In

61

this study, the FOV was chosen to allow simultaneous tracking of markers for strain and

kinematic measurements in the context of studying the human MCL [4,14]. Limitations

on the rate of data transfer from the camera to the framegrabber cards and then to

computer memory, primarily imposed by the bandwidth of the computer system’s bus,

result in a tradeoff between the frame rate and spatial resolution of the CCD. Cameras

with higher resolution CCDs typically have slower frame rates. This limitation will

likely be eliminated with improvements in computer architecture. Marker contrast is

also very important, with improved contrast yielding better system precision and thus

accuracy. During actual biomechanical testing, contrast may become reduced by

extraneous objects in the foreground and background. Draping the testing backdrop and

fixtures with white material, and applying white gauze to any uninvolved tissue that may

darken the captured image will alleviate this problem. Extreme specimen discoloration

could similarly reduce marker contrast. Affixing the strain markers to the tissue with

adhesives may cause local strain abnormalities; therefore a minimal amount of adhesive

should be applied. Finally, the physical size of a CCD affects the sensitivity through its

responsivity and dynamic range, with larger CCDs yielding better sensitivity and thus

better image quality (see, e.g., [17]). The cameras used in this study had 1” CCDs, the

largest size that was available.

In summary, the 3D measurement system provided excellent accuracy for

simulated strain measurement and very good accuracy for kinematic measurements. The

absolute and percent errors are considered to be more than acceptable for simultaneous

3D measurements of ligament strain and joint kinematics.

62

References

[1] Mazzocca, A. D., Nissen, C. W., Geary, M., and Adams, D. J., 2003, "Valgus Medial Collateral Ligament Rupture Causes Concomitant Loading and Damage of the Anterior Cruciate Ligament," J Knee Surg, 16, pp. 148-51.

[2] Hull, M. L., Berns, G. S., Varma, H., and Patterson, H. A., 1996, "Strain in the

Medial Collateral Ligament of the Human Knee under Single and Combined Loads," J Biomech, 29, pp. 199-206.

[3] Saeki, K., Mihalko, W. M., Patel, V., Conway, J., Naito, M., Thrum, H.,

Vandenneuker, H., and Whiteside, L. A., 2001, "Stability after Medial Collateral Ligament Release in Total Knee Arthroplasty," Clin Orthop, pp. 184-9.

[4] Gardiner, J. C. and Weiss, J. A., 2003, "Subject-Specific Finite Element Analysis

of the Human Medial Collateral Ligament During Valgus Knee Loading," J Orthop Res, 21, pp. 1098-106.

[5] Kuo, L. C., Su, F. C., Chiu, H. Y., and Yu, C. Y., 2002, "Feasibility of Using a

Video-Based Motion Analysis System for Measuring Thumb Kinematics," J Biomech, 35, pp. 1499-506.

[6] An, K. N., Growney, E., and Chao, E. Y., 1991, "Measurement of Joint

Kinematics Using Expertvision System," Biomed Sci Instrum, 27, pp. 245-52. [7] Kovaleski, J. E., Hollis, J., Heitman, R. J., Gurchiek, L. R., and Pearsall, A. W.

t., 2002, "Assessment of Ankle-Subtalar-Joint-Complex Laxity Using an Instrumented Ankle Arthrometer: An Experimental Cadaveric Investigation," J Athl Train, 37, pp. 467-474.

[8] Kirstukas, S. J., Lewis, J. L., and Erdman, A. G., 1992, "6r Instrumented Spatial

Linkages for Anatomical Joint Motion Measurement--Part 2: Calibration," J Biomech Eng, 114, pp. 101-10.

[9] Hefzy, M. S., Ebraheim, N., Mekhail, A., Caruntu, D., Lin, H., and Yeasting, R.,

2003, "Kinematics of the Human Pelvis Following Open Book Injury," Med Eng Phys, 25, pp. 259-74.

[10] Ezzet, K. A., Hershey, A. L., D'Lima, D. D., Irby, S. E., Kaufman, K. R., and

Colwell, C. W., Jr., 2001, "Patellar Tracking in Total Knee Arthroplasty: Inset Versus Onset Design," J Arthroplasty, 16, pp. 838-43.

[11] Meskers, C. G., Fraterman, H., van der Helm, F. C., Vermeulen, H. M., and

Rozing, P. M., 1999, "Calibration of the "Flock of Birds" Electromagnetic Tracking Device and Its Application in Shoulder Motion Studies," J Biomech, 32, pp. 629-33.

63

[12] Cerulli, G., Benoit, D. L., Lamontagne, M., Caraffa, A., and Liti, A., 2003, "In

Vivo Anterior Cruciate Ligament Strain Behaviour During a Rapid Deceleration Movement: Case Report," Knee Surg Sports Traumatol Arthrosc, 11, pp. 307-11.

[13] Fleming, B. C., and Beynnon, B. D., 2004, "In Vivo Measurement of

Ligament/Tendon Strains and Forces: A Review," Ann. Biomed. Eng., 32, pp. 318-328.

[13] Gardiner, J. C., Weiss, J. A., and Rosenberg, T. D., 2001, "Strain in the Human

Medial Collateral Ligament During Valgus Loading of the Knee," Clin Orthop, pp. 266-74.

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[16] Anonymous, "Ccd Performance and the Pixel Size (Chip Size)," TH-1084, 1998.

CHAPTER 4

EFFECT OF ACL DEFICIENCY ON MCL STRAINS

AND JOINT KINEMATICS1

Abstract

The knee joint is partially stabilized by the interaction of multiple ligament

structures. This study tested the interdependent functions of the anterior cruciate

ligament (ACL) and the medial collateral ligament (MCL) by evaluating the effects of

ACL deficiency on local MCL strain while simultaneously measuring joint kinematics

under specific loading scenarios. A structural testing machine applied anterior

translation and valgus rotation (limits 100 N and 10 N m, respectively) to the tibia of ten

human cadaveric knees with the ACL intact or severed. A three dimensional motion

analysis system measured joint kinematics and MCL tissue strain in 18 regions of the

superficial MCL. ACL deficiency significantly increased MCL strains by 1.8%

(p<0.05) during anterior translation, bringing ligament fibers to strain levels

characteristic of microtrauma. In contrast, ACL transection had no effect on MCL

strains during valgus rotation (increase of only 0.1%). Therefore, isolated valgus

________________________ 1 Reprinted from Journal of Biomechanical Engineering, Vol. 129, No. 3, Trevor J. Lujan, Michelle S. Dalton, Brent M. Thompson, Benjamin J. Ellis, Jeffrey A. Weiss, “Effect of ACL Deficiency on MCL Strains and Joint Kinematics”, pp: 386-92, 2007, with kind permission from the ASME.

65

rotation in the ACL-deficient knee was non-detrimental to the MCL. The ACL was also

found to promote internal tibial rotation during anterior translation, which in turn

decreased strains near the femoral insertion of the MCL. These data advance the basic

structure-function understanding of the MCL, and may benefit the treatment of ACL

injuries by improving the knowledge of ACL function and clarifying motions that are

potentially harmful to secondary stabilizers.

Introduction

The mechanical functions of knee ligaments are interrelated, with multiple soft

tissue structures contributing to joint stability under externally applied loading

conditions [1, 2]. The overlapping function of the anterior cruciate ligament (ACL) and

medial collateral ligament (MCL) is a prime example of this concept, as these ligaments

share responsibility in stabilizing anterior translation of the tibia and valgus joint

opening [3]. Injuries to the ACL and MCL account for 26% of knee trauma [4], with

combined ACL/MCL injuries comprising 70% of all multiligament knee injuries [5].

Isolated MCL injuries often adequately heal without surgical intervention, however,

conservatively treated ACL injuries have a high incidence of unsatisfactory outcomes [6,

7]. Even ACL reconstructed knees exhibit abnormal kinematics [8-10] that may lead to

cartilage degeneration [11]. Due to the relationship between the ACL and MCL,

treatment of combined or isolated ACL injuries may be improved by an understanding

of the mechanical effects of ACL deficiency on MCL function.

The current knowledge of ligament function in the knee joint is largely based on

ligament cutting studies that measured changes in laxity after dissecting a specific

structure. Experimental studies in cadaveric knees have demonstrated that the

66

superficial MCL is the primary restraint to valgus rotation, and a secondary restraint to

anterior translation [3, 12-16], while the ACL is the primary restraint to anterior

translation, and a secondary restraint to valgus rotation [3, 13, 14, 17-19]. In addition,

the MCL and ACL both resist internal tibial rotation [20-22], with the MCL also

resisting external tibial rotation [22, 23]. Recent experiments have investigated local

tissue strains and overall force in the ligament during applied loading conditions. Local

MCL strains have been measured for single or combined loading conditions, and with

the exception of studies by Fischer et al. [24] and Yasuda et al. [25], all MCL strain

studies have focused on intact knees [26-31]. Fischer utilized strain measurement

techniques to determine if function of the superficial MCL was affected when the

posterior aspect of the longitudinal parallel fibers was severed. Significant changes in

strain were only seen in an ACL deficient knee, prompting future research to look into

the interaction between the superficial MCL and the ACL. Yasuda found that the ACL

has minimal affect on the dynamic strain behavior of the MCL when a lateral impact

load is applied to the knee, and kinematic studies determined that when the MCL is

intact, the ACL has only a small influence on valgus laxity near full knee extension [12,

22]. Nevertheless, force measurement studies found that when the MCL is intact, ACL

tension significantly increases with the application of a valgus load over a range of

flexion angles [20, 32]. These results leave the role of the ACL in resisting valgus

rotation in an MCL-intact knee unclear; moreover, it is unknown how ACL deficiency

quantitatively affects regional MCL strain under specific loading conditions.

Interpretation of these interactions may be aided by investigating how ACL

deficiency alters localized MCL strains and joint kinematics. Local measurement of

67

ligament strain provides insight into regional function and the values of strain directly

relate to the propensity of the tissue to damage, tear or rupture [33]. Further, local strain

measurements on heterogeneous tissue structures are necessary to understand how

externally applied kinematic motions are resisted by specific regions [26, 34]. This

information would provide a broad visualization of MCL structural behavior and would

identify the loading configurations that the MCL resists actively. Finally, studying MCL

strain patterns in normal and ACL-deficient knees can afford a physiological baseline to

compare the in vitro efficacy of ACL reconstruction techniques. The objective of this

research was to quantify regional MCL strains and joint kinematics in the normal and

ACL deficient knee during anterior translation and valgus rotation at varying flexion

angles and tibial axial constraint. Two hypotheses were tested: (1) Strains in the MCL

increase following ACL transection during application of anterior translation, and (2)

strains in the MCL increase following ACL transection during application of valgus

rotation.

Materials and Methods

Experimental Design

Kinematic tests were performed on human knees before and after ACL

transection. Briefly, the tibia of each knee was subjected to cyclic anterior-posterior (A-

P) translation and varus-valgus (V-V) rotation at flexion angles of 0, 30, 60, and 90 deg

with tibial axial rotation constrained or unconstrained. MCL tissue strains and joint

kinematics were recorded during the entire application of anterior translation and valgus

rotation to the tibia. Following testing, the MCL was dissected free from the joint to

68

measure the stress-free strain pattern of the MCL. All tissues were kept moist with 0.9%

saline solution throughout dissection and testing.

Specimen Preparation

Ten cadaveric right knees were acquired fresh-frozen from male donors (donor

age = 56±7 y, range 18-65). Each knee was from mid-tibia to mid-femur and was

allowed to thaw for 16 h prior to dissection. All skin, fascia, muscle, and other

periarticular soft tissue surrounding the knee joint was removed, including the patella

and patellar tendon. One knee was eliminated from testing due to the absence of a

medial meniscus, otherwise all knees showed no sign of arthritis or previous soft tissue

injury. The fibula was secured to the tibia with a stainless steel screw to ensure an

anatomical position was maintained. The femur and tibia were potted in mounting tubes

using catalyzed polymer resin (Bondo, Mar-Hyde, Atlanta, GA). Two L-shaped white

blocks (the “kinematic blocks”) with three black acrylic markers (4.75 mm dia.) were

fastened to the anterior femoral condyle and the posterior aspect of the tibia using nylon

screws. Kinematic blocks were used to record the three-dimensional kinematic motions

of the tibia and femur during testing.

A 3 x 7 grid of markers (2.3 mm dia.) was adhered to the MCL using

cynoacrylate (Figure 4.1). These markers formed 18 gauge lengths for strain

measurement, with each gauge length spanning approximately 15 mm along the collagen

fiber direction. The markers were teased with tweezers after adhesion to verify that they

were attached to the superficial MCL fibers and not to the fascia. The markers in the

first and second rows were arranged along the anterior and posterior longitudinal parallel

fibers of the superficial MCL, respectively (Figure 4.1). Distal to the joint line, the

69

123

33

33

33

1 11

1 1 12 2 2 2 2 2

Marker in Row 1Marker in Row 2

1

2

3

MeniscusFemur

Tibia

Marker in Row 3112233

3333

3333

3333

11 1111

11 11 1122 22 22 22 22 22

Marker in Row 1Marker in Row 2

11

22

33

MeniscusFemur

Tibia

Marker in Row 3

Figure 4.1. Twenty-one markers defined eighteen regions for strain measurement. The markers in row 1 and row 2 were affixed to the anterior and posterior longitudinal fibers of the superficial MCL. Markers in row 3 inferior to the joint line were considered affixed to the distal oblique fibers of the superficial MCL. Markers in row 3 superior to the joint line were considered affixed to the anterior posteromedial corner. markers in the third row were affixed to the distal oblique fibers of the superficial MCL.

Proximal to the joint line, the markers in the third row were affixed to the anterior

portion of the posteromedial corner. These naming conventions are consistent with

Robinson et al. [35] and Warren and Marshall [36].

Testing Procedure

Each knee was mounted in fixtures on a custom testing machine. The machine

and fixtures allowed up to four degrees of freedom (DOF) through a combination of

linear and rotary bearings and actuators (Figure 4.2). Flexion was fixed, and either A-P

displacement during V-V rotation or V-V rotation during A-P displacement was fixed.

The tibial fixture permitted tibial axial rotation to be either constrained or unconstrained.

70

Figure 4.2. Schematic of the loading apparatus, depicting a medial view of the knee at 0 deg flexion. Kinematic blocks are rigidly attached to the tibia and femur for 3-D motion measurement. A – applied anterior-posterior tibial translation. B - applied varus-valgus rotation. C – adjustable flexion angle. D - constrained or unconstrained tibial axial rotation. E - unconstrained medial-lateral translation and joint distraction. F – load/torque cell. Thirty-two tests were performed on each knee. A-P displacements were applied to a set

force limit and V-V rotations were applied to a set torque limit (limits of ±100 N and

±10 N m, respectively [22, 26, 37]). Both A-P and V-V tests were performed at four

flexion angles (0, 30, 60, and 90 deg), with tibial rotation either unconstrained or

constrained, and the ACL either intact or deficient. Ten cycles were run for each test to

precondition the soft tissue structures of the knee. Data were analyzed at the tenth cycle

during anterior translation and valgus rotation. Linear and angular velocities (1.5 mm/s

and 1 deg/s, respectively) were selected to achieve quasi-static test conditions, thus

minimizing tissue viscoelastic and inertial effects. A bus cable (RTSI, Plano, TX) was

integrated with LabView software to enable real-time capture of boththe loading data

from the multiaxial load cell (Futek T5105, Irvine, CA, accuracy ±2.2 N and ±0.056 N

F

D

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71

m) and the positional data from the linear or rotary actuators (Tol-O-Matic, Inc, Hamel,

MN, linear accuracy ±0.0025 mm, rotational accuracy ±0.002 deg).

MCL strains and joint kinematics were measured simultaneously using a 3D

motion analysis system that tracked the centroids of the markers attached to the MCL

and kinematic blocks (Figure 4.2) [34]. The associated software used the modified

direct linear transformation method to calculate the 3D spatial coordinates of the

markers [34]. The 3D motion analysis system consisted of two high-resolution digital

cameras (Pulnix TM-1040, 1024x1024x30 fps, Sunnyvale, CA) equipped with 50 mm

1:1.8 lenses and extension tubes, two frame grabbers (Bitflow, Woburn, MA) and digital

motion analysis software (DMAS, Spica Technology Corp, Maui, HI). The extra-

capsular location of the MCL and its planar geometry facilitated the use of this motion

analysis system for strain measurement. Unconstrained tibial axial rotation of the knee

was calculated using the established kinematic conventions of Grood and Suntay [38].

Prior to testing, a mechanical digitizer (Immersion Corp, San Jose, CA accuracy ±0.085

mm) was used to create “embedded” coordinate systems based on anatomical landmarks

[39, 40]. The centroids of the markers on the kinematic blocks were determined by

averaging four digitized points around the circumference of each marker. These

centroids were used to create marker coordinate systems. The transformation matrix

between the femur and tibia could then be calculated by using the transformation

matrices formed between the embedded and marker coordinate systems and the video-

tracked kinematic block systems [34].

A testing methodology was developed to initiate ACL-deficient tests from the

ACL-intact neutral position. This neutral position was defined for each flexion angle by

72

finding the inflection point of the force response resulting from small cyclic A-P and V-

V displacements, with tibial axial rotation unconstrained. Actuator translation and

rotation positions were logged so that the original neutral positions could be restored

after ACL transection. To mimic ACL deficiency, the ACL was transected through its

mid-substance without removing the knee from the fixture. Care was taken to avoid

damage to the PCL. To verify that the ACL-intact testing position was reproduced for

the ACL-deficient knee, kinematic block positions were measured in relation to each

other and the multiaxial test frame for each flexion angle. After ACL transection,

positional information was compared at each flexion angle and adjustments were made

if necessary.

Establishment of Reference Configuration for Strain Measurement

Following testing, the MCL was dissected from its femoral and tibial

attachments to measure the stress-free reference length (lo) between all 18 marker pairs.

Using validated procedures [26, 37], the motion analysis system measured the stress-free

configuration after the isolated ligament relaxed for 10 min on a saline covered glass

plate. This was an important step for the calculation of absolute strain, as force exists in

the ligament when it is attached to its insertion sites. Material properties of ligament,

including ultimate and substructural failure limits, have been quantified in the literature

using stress-free configurations [33, 41]. Accurate interpretation of strain data therefore

required the use of stress-free reference lengths. In this study, it was found that basing

strain results on in situ gauge lengths measured at 0 and 30 deg passive knee flexion, on

average significantly underpredicted strain by 2.7±0.1% (p<0.001) and 1.1±0.1%

(p<0.001), respectively.

73

Data and Statistical Analysis

The lengths between marker pairs were measured in the previously described

stress-free reference state (lo) and during kinematic tests (l) at peak valgus rotation, peak

anterior translation, and in the neutral position. Tensile strain along the fiber direction

was calculated as ε = (l - lo) / lo. Repeated measures ANOVA analysis with three

within-subject factors (ACL state, knee flexion angle, tibial axial constraint) was used in

conjunction with Bonferroni adjusted pair-wise comparisons to measure significance of

factors, factor interactions and between factor levels. If significance was found

(p≤0.05), adjusted paired t-tests were used for case by case comparisons. A similar

analysis was performed for the kinematic data. A power analysis demonstrated that a

sample size of 10 was sufficient to obtain a power of 0.8 when detecting a 1.0% change

in the strain, a 1.0 deg kinematic rotation, and 1.5 mm kinematic displacement. Data are

reported as mean±standard error, unless otherwise stated.

To represent MCL strains graphically, mean values of regional fiber strain were

applied to a finite element mesh of a MCL constructed from one of the specimens [37].

This mesh was input to TOPAZ3D (LLNL, Livermore, CA) to perform a least squares

interpolation of fiber strain values between discrete measurement locations, which

yielded a continuous spatial representation of the results.

Results

Effect of ACL Transection

ACL deficiency significantly increased anterior translation by an average 10.0 ± 1.1

mm (p<0.001, Figure 4.3A), and MCL strains were significantly greater for ACL-

deficient cases at peak anterior translation (Figure 4.3B). ACL deficiency did not

74

significantly affect valgus rotation (p=0.12, Figure 4.4A), and MCL strains were not

significantly affected by ACL deficiency at peak valgus rotation (Figure 4.4B). ACL

transection increased MCL strains by an average 1.8 ± 0.5% at peak anterior translation.

In contrast, ACL transection increased MCL strains by only 0.1 ± 0.1% at peak valgus

rotation (Figure 4.5). The significant strain increases at peak anterior translation

(p<0.05) occurred along every region of the superficial longitudinal MCL and the region

representing the anterior fibers of the posteromedial corner.

ACL transection caused the largest increase in MCL strain during anterior

translation at 30 deg of knee flexion (2.0 ± 1.5%), corresponding with the greatest

increase in anterior laxity (12.4 ± 1.3 mm). During anterior translation, the lowest

aggregate strain increases due to ACL transection occurred at 0 deg of knee flexion (1.4

± 0.7%); however, even with these lower strain increases, 0 deg flexion had the greatest

absolute strain in both ACL intact and ACL-deficient cases. For all anterior translation

cases, the region with the largest overall strain increase due to ACL transection was near

the femoral insertion (3.8 ± 1.1%), while the region with the least overall increase was

along the distal oblique fibers of the superficial MCL (0.3 ± 0.4%) (Figure 4.5).

Effect of Knee Flexion Angle

Knee flexion angle had a significant effect on both anterior translation and

valgus rotation (p<0.001 and p=0.01, respectively). Flexing or extending the knee to 30

degrees from all other flexion angles significantly increased anterior translation (average

of 3.1 ± 0.5 mm for all cases, Figure 4.3A). Extending the knee to 0 deg from all other

angles significantly decreased valgus rotation (average of 1.5 ± 0.3 deg for all cases,

Figure 4.3. A) Anterior tibial translation at all flexion angles, with unconstrained tibial axial rotation, before and after ACL transection. B) Average MCL strains at ATT as a function of knee flexion angle, with unconstrained tibial axial rotation, before and after ACL transection. ACL transection had no significant effect on valgus laxity or MCL strains. Error bars = SD.

75

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Figure 4.4. A) Valgus rotation at all flexion angles, with unconstrained tibial axial rotation, before and after ACL transection. B) Average MCL strains at peak valgus rotation as a function of knee flexion angle, with unconstrained tibial axial rotation, before and after ACL transection. ACL transection had no significant effect on valgus laxity or MCL strains. Error bars = SD.

76

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Figure 4.5. MCL strain changes due to ACL transection at peak anterior translation and valgus rotation, averaged over all cases. Transection significantly increased MCL strains during anterior translation, but had no effect on MCL strains during valgus rotation. * p < 0.05 (within a region).

Overall Differences in % Strain from ACL Transection

Peak Anterior Translation

Peak Valgus Rotation

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78

Figure 4.4A). Medial collateral ligament strains in most measurement regions were also

significantly affected by flexion angle for all test cases. Interestingly, MCL strain

patterns were changed in a nearly uniform manner with each successive 30 deg flexion,

for both loading configurations. This uniform change in strain followed a pattern of

small yet significant strain increases along the most anterior row distal to the joint line

(0.3 ± 0.2%), coupled with larger and significant decreases in change around the

posteromedial corner (-3.5 ± 0.6%). Both ACL-intact knees and ACL-deficient knees

exhibited this trend in MCL strain behavior.

Effect of Tibial Axial Constraint

Unconstraining tibial axial rotation significantly increased anterior translation by

an average of 0.6 ± 0.1 mm and valgus rotation by an average of 0.7 ± 0.2 deg (p<0.001

and p=0.001, respectively), under all test conditions. Overall increases in laxity

corresponded with overall decreases in MCL strains of 0.45 ± 0.24% during anterior

translation and 0.10 ± 0.17% during valgus rotation. These strain decreases were

significant across the majority of longitudinal parallel fibers during anterior translation

and near the femoral insertion during valgus rotation.

When tibial axial rotation was unconstrained for the ACL-intact cases, an

average internal tibial rotation (ITR) of 9.3 ± 3.8 deg occurred during anterior

translation. Transecting the ACL significantly reduced ITR during anterior translation at

30, 60 and 90 deg flexion by an average 6.9 ± 3.8 deg (Figure 4.6A). When tibial

rotation was unconstrained, the larger ITR in knees with an intact ACL resulted in

Figure 4.6. A) Internal tibial axial rotation from neutral to peak anterior translation, 30 deg knee flexion, before and after ACL transection. B) Average MCL strains at peak anterior translation, 30 deg knee flexion, with fixed and unconstrained tibial axial rotation, before and after ACL transection. In the ACL-intact knee, unconstraining tibia axial rotation significantly reduced strain along the anterior MCL. After ACL transection, internal tibial rotation was significantly decreased and MCL strain was unaffected when tibial axial rotation was unconstrained. Thus, in the intact knee, the ACL promoted internal tibial rotation during anterior translation, which relieved strain in the MCL. This also occurred at 60 and 90 deg flexion. * p < 0.05

79

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significantly lower MCL strains in the longitudinal fibers near the femoral insertion (2.5

± 0.4%, Figure 4.6B). In contrast, for ACL deficient knees, ITR was reduced and the

decreases in strain near the femoral insertion were insignificant (0.6 ± 0.2%, Figure

4.6B). This illustrates that decreased ITR after ACL transection results in increased

MCL strains in the longitudinal fibers near the femoral insertion. Statistical analysis

further supported this observation, as there was a significant interaction between tibial

axial constraint and ACL transection along strain regions near the femoral insertion at

peak anterior translation (p<0.05).

Discussion

Understanding the interdependent functions of the ACL and MCL can clarify the

structure-function relationship of both ligaments. This study found that ACL deficiency

significantly increased MCL strains during anterior translation, but had no effect on

MCL strains during valgus rotation. Joint kinematics measured simultaneously with

MCL strains were consistent with comparable studies [19, 22, 26]. The results support

our hypothesis that ACL deficiency increases MCL strain during anterior translation,

which is logical considering the respective primary and secondary roles of the ACL and

MCL in restraining anterior translation. Conversely, our hypothesis that ACL deficiency

would increase MCL strain during valgus rotation was rejected. This means that

application of a valgus rotation to 10 N m in the ACL-deficient knee was non-

detrimental to the MCL.

The finding that strains in the superficial MCL are insensitive to ACL transection

during valgus rotation was surprising considering that the ACL has been shown to be an

active stabilizer to valgus rotation when the MCL is healthy [20, 32]. Studies by Fukuda

81

et al. [32] and Miyasaka et al. [20] used force superimposition techniques and strain

gauges, respectively, determining that the ACL resists valgus rotation from full

extension to 90 deg flexion. Our results showed that ACL transection produced small,

insignificant increases in valgus laxity, yet this increased valgus rotation minimally

impacted MCL strains at all flexion angles (average increase was 0.1%, average

p=0.64). A few explanations on this discrepancy are offered. First, it is possible that the

reported ACL force contributions during valgus rotation in an intact knee are easily

accommodated by the MCL after ACL transection. Therefore, MCL strain changes are

imperceptible and the integrity of the MCL is unaltered. Another possibility is that other

secondary stabilizers might increase their contribution to resisting valgus rotation after

ACL transection, allowing the MCL to continue to function normally. Yet, the most

likely explanation involves differences in degrees of freedom between testing systems.

The testing machine and fixtures in this study permitted up to 4 DOF, while experiments

by Fukuda et al. [32] used a 5 DOF system. The 5 DOF system permitted A-P

translation during V-V rotation, and demonstrated that coupled A-P translation during

V-V rotation increases after ACL transection. Therefore, in an intact knee, the function

of the ACL during valgus rotation may be to resist coupled anterior translation, and the

ACL only resists pure valgus rotation after the MCL is compromised.

To make clinical interpretations, it was necessary to identify loading conditions

that generate damaging strains, which was feasible since a stress-free reference was used

for strain calculation. A stress-free reference allows direct comparison with material

properties reported in the literature. Ligament rupture typically occurs at ~18% strain

[41], and the onset of microtrauma or substructural failure in ligament occurs at 5.2%

82

strain [33]. During valgus rotation, maximum absolute strains in the mid-longitudinal

MCL fibers remained around 4.4% in both the intact and ACL-deficient knee, below the

microtrauma threshold. During anterior translation, ACL transection significantly

increased maximum absolute strains along the mid-longitudinal fibers from 2.9% to

5.7%, a strain level that could induce microtrauma. These results show evidence that

longitudinal MCL fibers in ACL-deficient knees are initially predisposed to damage

from anterior translation. This finding is useful in interpreting results from a study by

Tashman et al. [42] who measured kinematic gait changes over two years in ACL-

deficient and ACL-intact canines. Consistent with our results and the literature [19, 22,

43], ACL transection immediately caused large translational increases during anterior

translation and small rotational increases during valgus rotation. In the ACL-deficient

knee, anterior translation significantly escalated with time. Our data suggest that the

MCL initially assisted in stabilizing anterior translation; however, the MCL became

strained over time leading to increased anterior tibial displacements. This potential

increase in MCL laxity may be one factor in the unsatisfactory outcomes characteristic

of conservatively treated ACL injuries [44].

Interestingly, the strains of around 10% in the anterior posteromedial corner

during both loading conditions greatly exceed the reported substructure failure threshold.

However, these results are deceiving. The material tests that defined damaging strains

[33, 41] were tested along the mid-longitudinal MCL fibers and therefore are not

directly comparable with regions of the posteromedial corner. Considering that the

posteromedial corner has been shown to play a limited role in resisting valgus rotation

83

[22], this tissue is likely less stiff with greater failure strain thresholds than the adjoining

longitudinal fibers.

Relating joint kinematics and local strains has enabled a better understanding of

functional MCL regions and is applicable to clinical diagnosis. Following ACL

transection, increased anterior laxity was resisted by fibers near the femoral insertion

and along the mid-substance of the parallel longitudinal fibers. The greatest average

increase in MCL strain following ACL transection occurred at 30 deg flexion, consistent

with the largest increase in anterior translation. Yet, 0 deg flexion held the distinguished

position of having the greatest absolute strains both before and after ACL transection.

Increasing the flexion angle, for both loading conditions, slightly stretched the fibers

distal to the joint line along the anterior superficial MCL. Meanwhile, the posterior

regions of the superficial MCL and anterior posteromedial corner uniformly slackened

with this increased flexion. This behavioral pattern and the corresponding magnitude of

the strain changes were unaffected by ACL transection, and were insensitive to the

discrepancies between anterior translation and valgus subluxation patterns observed at

different flexion angles. Therefore, regardless of directional loading or ACL condition,

progressive flexing of the knee will reduce overall MCL strain. These findings support

using a knee flexion angle of 15-30 deg when administering the Lachman test rather

than performing the test at full extension [45]. At a slightly flexed angle, the MCL will

not be overstressed, and deviations in joint laxity with the contralateral knee are

maximized.

The relationship between tibial axial rotation and the MCL and ACL was further

developed in this study. When tibial axial rotation was constrained, knee laxity

84

decreased under both loading conditions. This was at least partially due to increased

resistance along the longitudinal fibers of the MCL, which experienced significantly

higher strains, particularly during anterior translation. Unconstraining tibial axial

rotation permitted internal tibial rotation, which in turn decreased MCL strains. Internal

tibial rotation during anterior translation was reduced after the ACL was transected.

Thus, the ACL encourages internal rotation, perhaps by “unwinding” during anterior

translation [46]. In summary, in an intact knee, the ACL promotes internal tibial

rotation, which in turn reduces MCL strains along the longitudinal parallel fibers of the

superficial MCL near the femoral insertion.

The specific limitations of the methods used in this study deserve discussion.

Joint kinematics may have been altered due to the dissection necessary for strain

measurement or because joint compressive forces and stabilizing muscle activity were

not represented. Muscle activity has been shown to reduce knee laxity [47]. Therefore,

to reproduce the magnitudes of strains from this study in vivo, greater force and torque

limits would likely be required. Removing the patella may have also influenced MCL

strain patterns and joint kinematics. Tests were performed in a controlled environment,

and did not undergo high speed motions or combined loading configurations that would

have been more analogous to injury causing mechanisms. Strain measurement was

based on changes to gauge length between marker pairs. This assumed that strain was

homogeneous over the length of these discrete regions. For graphical representation,

MCL strain values were interpolated between marker rows, which may not accurately

account for inhomogeneities orthogonal to the fiber direction. Finally, strains in the

deep MCL were not measured, although previous studies have shown that the deep MCL

85

is half as stiff as the superficial MCL [48] and has a minimal contribution to valgus

restraint when the superficial MCL is intact [49].

Through measurement of tissue strain and joint kinematics, this research has

improved the understanding of how the ACL and MCL interact. Additionally, results

from this study can be used to validate finite element models and improve the governing

constitutive equations. The present results and methods can also serve as a baseline to

verify that a specific ACL reconstruction technique not only returns the knee to regular

joint kinematics, but is capable of returning normal functionality to the intact MCL.

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[28] Monahan, J. J., Grigg, P., Pappas, A. M., Leclair, W. J., Marks, T., Fowler, D. P.,

and Sullivan, T. J., 1984, "In vivo strain patterns in the four major canine knee ligaments," J Orthop Res, 2(4), pp. 408-418.

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[29] Hull, M. L., Berns, G. S., Varma, H., and Patterson, H. A., 1996, "Strain in the medial collateral ligament of the human knee under single and combined loads," J Biomech, 29(2), pp. 199-206.

[30] Kennedy, J. C., Hawkins, R. J., and Willis, R. B., 1977, "Strain gauge analysis of

knee ligaments," Clin Orthop Relat Res(129), pp. 225-229. [31] White, A. A., 3rd, and Raphael, I. G., 1972, "The effect of quadriceps loads and

knee position on strain measurements of the tibial collateral ligament. An experimental study on human amputation specimens," Acta Orthop Scand, 43(3), pp. 176-187.

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Debski, R. E., 2003, "A quantitative analysis of valgus torque on the ACL: a human cadaveric study," J Orthop Res, 21(6), pp. 1107-1112.

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2002, "Subfailure damage in ligament: a structural and cellular evaluation," J Appl Physiol, 92(1), pp. 362-371.

[34] Lujan, T. J., Lake, S. P., Plaizier, T. A., Ellis, B. J., and Weiss, J. A., 2005,

"Simultaneous measurement of three-dimensional joint kinematics and ligament strains with optical methods," ASME Journal of Biomechanical Engineering, 127, pp. 193-197.

[35] Robinson, J. R., Sanchez-Ballester, J., Bull, A. M., Thomas Rde, W., and Amis,

A. A., 2004, "The posteromedial corner revisited. An anatomical description of the passive restraining structures of the medial aspect of the human knee," J Bone Joint Surg Br, 86(5), pp. 674-681.

[36] Warren, L. F., and Marshall, J. L., 1979, "The supporting structures and layers on

the medial side of the knee: an anatomical analysis," J Bone Joint Surg Am, 61(1), pp. 56-62.

[37] Gardiner, J. C., and Weiss, J. A., 2003, "Subject-specific finite element analysis

of the human medial collateral ligament during valgus knee loading," J Orthop Res, 21(6), pp. 1098-1106.

[38] Grood, E. S., and Suntay, W. J., 1983, "A joint coordinate system for the clinical

description of three- dimensional motions: application to the knee," J Biomech Eng, 105(2), pp. 136-144.

[39] Lafortune, M. A., 1984, "The use of intra-cortical pins to measure the motion of

the knee joint during walking.," Ph.D thesis, Pennsylvania State University.

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[40] Pennock, G. R., and Clark, K. J., 1990, "An anatomy-based coordinate system for the description of the kinematic displacements in the human knee," J Biomech, 23(12), pp. 1209-1218.

[41] Quapp, K. M., and Weiss, J. A., 1998, "Material characterization of human

medial collateral ligament," J Biomech Eng, 120(6), pp. 757-763. [42] Tashman, S., Anderst, W., Kolowich, P., Havstad, S., and Arnoczky, S., 2004,

"Kinematics of the ACL-deficient canine knee during gait: serial changes over two years," J Orthop Res, 22(5), pp. 931-941.

[43] Markolf, K. L., Kochan, A., and Amstutz, H. C., 1984, "Measurement of knee

stiffness and laxity in patients with documented absence of the anterior cruciate ligament," J Bone Joint Surg Am, 66(2), pp. 242-252.

[44] Fink, C., Hoser, C., Hackl, W., Navarro, R. A., and Benedetto, K. P., 2001,

"Long-term outcome of operative or nonoperative treatment of anterior cruciate ligament rupture--is sports activity a determining variable?," Int J Sports Med, 22(4), pp. 304-309.

[45] Malanga, G. A., Andrus, S., Nadler, S. F., and McLean, J., 2003, "Physical

examination of the knee: a review of the original test description and scientific validity of common orthopedic tests," Arch Phys Med Rehabil, 84(4), pp. 592-603.

[46] Shoemaker, S. C., and Daniel, D. M., 1990, "The Limits of Knee Motion," Knee

ligaments: Structure, function, injury, and repair, Raven Press, p. 157. [47] Schipplein, O. D., and Andriacchi, T. P., 1991, "Interaction between active and

passive knee stabilizers during level walking," J Orthop Res, 9(1), pp. 113-119. [48] Robinson, J. R., Bull, A. M., and Amis, A. A., 2005, "Structural properties of the

medial collateral ligament complex of the human knee," J Biomech, 38(5), pp. 1067-1074.

[49] Robinson, J. R., Bull, A. M., Thomas, R. R., and Amis, A. A., 2006, "The role of

the medial collateral ligament and posteromedial capsule in controlling knee laxity," Am J Sports Med, 34(11), pp. 1815-1823.

CHAPTER 5

MCL INSERTION SITE AND CONTACT FORCES

IN THE ACL-DEFICIENT KNEE

Abstract

The objectives of this research were to determine the effects of ACL deficiency

on MCL insertion site and contact forces during anterior tibial loading and valgus

loading using a combined experimental-finite element (FE) approach. Our hypothesis

was that ACL deficiency would increase MCL insertion site forces at its attachment to

the tibia and femur and increase contact forces between the MCL and these bones. Six

male knees were subjected to varus-valgus and anterior-posterior loading at flexion

angles of 0° and 30°. Three-dimensional joint kinematics and MCL strains were

recorded during kinematic testing. Following testing, the MCL of each knee was

removed to establish a stress-free reference configuration. A FE model of the femur-

MCL-tibia complex was constructed for each knee to simulate valgus rotation and

anterior translation at 0 and 30°, using subject-specific bone and ligament geometry and

joint kinematics. A transversely isotropic hyperelastic material model with average

material coefficients taken from a previous study was used to represent the MCL.

___________________ Reprinted by kind permission of Wiley-liss Inc. a subsidiary of John Wiley & Sons Inc. Journal of Orthopaedic Research, Vol. 24, No. 4, Benjamin J. Ellis, Trevor J. Lujan, Michelle S. Dalton, Jeffrey A. Weiss, “MCL Insertion Site and Contact Forces in the ACL-Deficient Knee”, pp: 800-10, 2007.

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Subject-specific MCL in-situ strain distributions were used in each model. Insertion site

and contact forces were determined from the FE analyses. FE predictions were

validated by comparing MCL fiber strains to experimental measurements. The subject-

specific FE predictions of MCL fiber stretch correlated well with the experimentally

measured values (R2 = 0.953). ACL deficiency caused a significant increase in MCL

insertion site and contact forces in response to anterior tibial loading. In contrast, ACL

deficiency did not significantly increase MCL insertion site and contact forces in

response to valgus loading, demonstrating that the ACL is not a restraint to valgus

rotation in knees that have an intact MCL. When evaluating valgus laxity in the ACL-

deficient knee, increased valgus laxity indicates a compromised MCL.

Introduction

The effect of anterior cruciate ligament (ACL) deficiency on the mechanical

function of other knee ligaments remains unclear, although it is known that even knees

with reconstructed ACLs often exhibit abnormal knee kinematics [1]. The ACL is a

primary restraint to anterior tibial translation and a secondary restraint to valgus rotation

[2-12], while the medial collateral ligament (MCL) is a primary restraint to valgus

rotation [3-14] and a secondary restraint to anterior tibial translation [2, 4-6, 11, 14-18].

The MCL is involved in approximately 40% of all severe knee injuries [19], while

approximately 50% of partial MCL tears and 80% of complete MCL tears occur in

conjunction with injury to other knee ligaments [20]. In alpine skiing, the most common

ligament that is injured in conjunction with the MCL is the ACL [21].

Animal studies have shown that MCL healing is substantially poorer in the case

of a combined MCL/ACL injury than for an isolated MCL injury [2, 5-7, 11, 12]. After

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12 weeks of healing, MCLs from knees with combined MCL/ACL injuries had a tensile

strength of only 10% of control values [12]. It has been proposed that the healing MCL

in the ACL-deficient knee is subjected to increased strains and forces as a result of ACL

deficiency [6]. An ACL graft acts as a stabilizer initially, but as it heals, forces are

transferred to the MCL that hinder healing and result in a hypertrophy of the MCL with

tissue of lower quality. As long as two years after injury, healing MCLs still had

“significantly different biological composition, biomechanical properties, and matrix

organization” [11].

Although animal studies have shown that the MCL may be at risk for injury in an

ACL deficient knee, conclusions in the literature as to the exact contributions of the

MCL and ACL to valgus stability vary within and between studies of ligament healing

in animal models and joint kinematics in cadaver models. In animal models, the

variation in results is confounded by the variation in the type of injury model used.

Results from a rabbit healing study showed that valgus rotation does not increase over

time in response to healing of the ACL graft after an O'Donoghue triad injury (rupture of

the medial collateral ligament with removal of the anterior cruciate ligament and part of

the medial meniscus) although anterior translation did significantly increase over the

same healing period [2]. The conclusions of this animal study that created an

O'Donoghue triad injury are in contrast to other animal studies that have shown that

there are higher ACL forces and increased valgus laxity in response to a valgus load in a

MCL deficient knee [3-6, 9, 10]. Two previous cadaver studies concluded that valgus

laxity is relatively unaffected by ACL deficiency [13, 14] and Mazzocca et al. concluded

that, “the ACL can be compromised in isolated grade III MCL injuries” caused by a

93

valgus load [10]. The actual insertion site and contact forces in the MCL in response to

a valgus torque in the intact and ACL-deficient knee, which arguably are the most

relevant data for interpretation of ligament contribution to joint function, are unknown.

The aim of this study was to examine the effects of ACL deficiency on MCL

insertion site and contact forces when the knee is subjected to anterior tibial loading and

valgus torque. It was hypothesized that ACL deficiency would cause an increase in

MCL insertion site and contact forces in response to both loading conditions.

Materials and Methods

Overview

This study combined experimental and computational methods to determine the

effect of ACL injury on MCL insertion site and contact forces during anterior tibial

loading and valgus loading. Computed tomography (CT) images were used to obtain the

subject-specific geometry of the femur, tibia and MCL in a series of six cadaveric knees.

Each knee was tested with the ACL intact and the ACL completely severed. For each

injury state the knee was subjected to anterior-posterior (A-P) translation and varus-

valgus (V-V) rotation at two flexion angles (0° and 30°) with tibial rotation constrained

and unconstrained while knee kinematics and MCL strains were recorded. Polygonal

surfaces were extracted from the CT data and were used to generate subject-specific FE

models of each knee. The FE models were analyzed under the experimentally measured

kinematics to determine MCL strains, contact forces, and insertion site forces. FE

predicted fiber stretches were compared to experimental values as a means of validation

and the effect of injury state, flexion angle, and tibial constraint on MCL insertion site

and contact forces was determined.

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Specimen preparation and CT scan Six intact human male cadaver knees were used (donor age 60 ± 8.3 years).

Preparation for testing followed the same protocol as Gardiner et al. [22], with the

exception that additional contrast markers were used to define gauge lengths for

measurement of MCL fiber strain. Markers were distributed along the visible fiber

direction of the MCL in a 3x7 grid pattern, forming 18 gauge lengths (Figure 4.1). Each

gauge length was approximately 15 mm long. The position of the markers was chosen

based on anatomical landmarks. The boundaries of the MCL insertion sites on the femur

and tibia were marked with copper wires to aid with identification of their geometry in

the volumetric CT images. Nylon kinematic blocks were fastened to the distal femur

and proximal tibia (shown in Figure 3.2), while positioning blocks with three beveled

cavities (not shown in figure), forming a right angle, were fastened to the proximal

femur and distal tibia [23]. After dissection, a volumetric CT scan was obtained for each

knee at 0º flexion (slice thickness = 1.3 mm with 1.0 mm overlap, 142-168 mm field of

view, 512 512× acquisition matrix).

Kinematic testing

Following the CT scan, each knee was mounted in fixtures on a custom materials

testing machine, which allowed both A-P translation and V-V rotation to be applied at

fixed flexion angles with constrained or unconstrained tibial axial rotation and

unconstrained medial-lateral translation and joint distraction (Figure 4.2). During

testing, ten cycles of A-P translation (load limits of ±100 N at 1.5 mm/sec) and ten

cycles of V-V rotation (torque limits of ±10 N-m at 1 degree/sec) were independently

applied to the tibia. The A-P load and V-V torque limits were established so that they

95

were large enough to achieve the terminal stiffness of the ligament without inflicting

injury to the tissue and thereby allowing multiple tests with the same specimen [24]. A-

P and V-V loading were conducted at 0° and 30° flexion. The tests were repeated with

tibial axial rotation constrained and unconstrained at each flexion angle. The load and

torque were measured with a multi-axis load cell (Futek T5105, Irvine, CA, accuracy

±2.2 N and ±0.056 N-m). Following the eight ACL intact tests, the ACL was transected

through the mid-substance without damage to the PCL or removal of the knee from the

fixture and all the tests were repeated. Finally, following ACL transection, the

attachment of the medial meniscus to the MCL was transected. This test was performed

to verify that the attachment did not influence joint kinematics and MCL strains under

A-P and V-V loading; a similar conclusion was reached for the effect of the meniscus

attachment on MCL strains in the intact knee in our previous study [22]. To minimize

hysteresis effects, data from the 10th cycle of loading were analyzed for all tests.

Care was taken to ensure that the relative kinematic positions of the bones were

duplicated for a given flexion angle and tibial axial rotation constraint for both injury

states. When testing the intact knee, a neutral A-P and V-V position was determined at

each flexion angle with tibial axial rotation unconstrained. The neutral A-P and V-V

positions were determined by iteratively adjusting the starting position and running A-P

and V-V motion cycles until the given load (±100 N) and torque (±10 N-m) limits

produced equal anterior and posterior translation and equal varus and valgus rotations,

respectively. Once these reference positions were established, actuator translation and

rotation positions were logged so the positions could be restored after ACL transection.

The three-dimensional kinematic position of the femur relative to the tibia was verified

96

through the use of a Microscribe digitizer (Immersion Corp, San Jose, CA, accuracy

±0.085 mm) in combination with the positioning blocks. The digitizer and positioning

blocks were used to precisely determine the relative three dimensional kinematics of the

femur and tibia [25]. In this manner, positional repeatability between the different injury

states was insured.

Measurement of Joint Kinematics and Ligament Strains

A digital motion analysis system consisting of two high-resolution digital

cameras (Pulnix TM-1040, 1024x1024x30 fps, Sunnyvale, CA) and Digital Motion

Analysis Software (DMAS, Spica Technology Corporation, Maui, HI) was used to

record MCL strain in the 18 measurement regions and joint kinematics simultaneously

(strain measurement accuracy: ±0.035 percent; joint kinematic translational accuracy:

±0.025 mm; joint kinematic rotational accuracy: ±0.124 degrees) [23].

In situ strain

At the conclusion of testing, the MCL was dissected from the bones and placed

in a buffered saline bath for 10 minutes to allow the ligament to achieve a stress-free

reference configuration. The 3D coordinates of the fiducial markers on the MCL were

determined using the digital motion analysis system. This provided reference (zero-

load) lengths for each strain region, 0l [12, 22, 26]. These values were combined with

length measurements taken during the kinematic testing to calculate in situ fiber strain

between marker pairs. These data were used as input to the subject-specific FE models

[22, 27].

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CT scan, surface reconstruction and FE mesh generation

Using the copper insertion site wires and MCL strain contrast markers as guides,

cross-sectional contours of the MCL, femur, and tibia were extracted from the CT

dataset (SurfDriver, Kailua, Hawaii). Polygonal surfaces were generated by stacking

and lacing together the contours [28] and smoothing was applied [29]. The polygons

composing the surfaces of the femur and tibia were converted directly to shell elements

and used to represent the bones as rigid bodies [30]. The MCL surface was imported

into FE preprocessing software (TrueGrid, XYZ Scientific, Livermore, CA) and a

hexahedral mesh was created.

Constitutive model

The MCL was represented as transversely isotropic hyperelastic, with the strain

energy (W) [22]:

( ) ( ) ( )( )2211 ln

2~~ JKFIFW +λ+= . (1)

Here, 1I is the first deviatoric invariant, λ is the deviatoric part of the stretch

ratio along the local fiber direction, and J is the determinant of the deformation gradient,

F. The matrix strain energy ( )1 1F I was chosen so that 111~ CIF =∂∂ , yielding the neo-

Hookean constitutive model. The derivatives of the fiber strain energy function ( )2F λ

were defined as a function of the fiber stretch:

0~ 2 =λ∂

∂λ

F , 1λ ≤ ;

98

( )( )[ ]11~exp~43

2 −−λ=λ∂

∂λ CC

F , *~1 λλ << ; (2)

652 ~~ CC

F+λ=

λ∂∂

λ , *~ λλ ≥ .

C3 scales the exponential stress, C4 specifies the rate of collagen uncrimping, C5 is the

modulus of straightened collagen fibers, and λ* is the stretch at which the collagen is

straightened. The third term in Eq (1) represents the bulk (volumetric) response, with

the bulk modulus K controlling the entire volumetric response of the material. The

population-average material coefficients from Gardiner et al. were used [22]:

1 1.44 MPaC = , * 1.062 (no units)λ = , 3 0.57 MPaC = , 4 48.0 (no units)C = ,

5 467.1 MPaC = . Population average material coefficients were used based on the

finding that using average coefficients versus subject specific coefficients yielded no

significant difference in the accuracy of FE strain predictions [31]. Due to a lack of

experimental data describing ligament bulk behavior, the bulk modulus was specified to

be two orders of magnitude greater than C1, yielding nearly incompressible material

behavior [22].

Boundary Conditions

The experimentally measured kinematic dataset was used to prescribe the motion

of the tibia relative to the femur in the FE analyses [22]. The coordinates of the

kinematic blocks in both the CT and kinematic datasets allowed for correlation of the

two datasets. The entire FE model was transformed so that the global coordinate system

was aligned with the coordinate system of the femur kinematic block. Motion of the

tibia was described using incremental translations and rotations referenced to the femur

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kinematic block [30, 32]. The MCL mesh was attached to the bones by defining node

sets, based on the area within the copper wires, at the proximal and distal ends of the

MCL as the same rigid material as the femur and tibia, respectively. Contact was

enforced using the penalty method.

Finite Element Analysis

The implicitly integrated FE code NIKE3D was used for all analyses [32]. An

automatic time stepping strategy was employed, with iterations based on a quasi-Newton

method. Each analysis was performed in three parts. In the first part, the knee was

moved from the position in which it was placed at the time of the CT scan to the initial

testing position (either 0 or 30 degrees of flexion). During the second part, the

experimentally measured in situ strains for a given flexion angle and injury state were

applied to the MCL. During the third part the experimental kinematic motion was

applied (either anterior translation or valgus rotation). FE results were analyzed with

GRIZ [33].

Regional strains, insertion site and contact forces

FE predicted fiber stretches for nodes within each measurement region were

averaged. Average FE predicted fiber stretches were compared to the experimentally

measured values. The magnitude of ligament forces at the insertion sites and the

magnitude of the resultant forces due to MCL-bone contact were obtained from the

NIKE3D output.

100

Statistical Analysis

Regression analyses were used to evaluate the ability of the FE models to predict

experimentally measured values of MCL fiber stretch. FE predictions of regional fiber

stretch were determined as a function of location along the length of the MCL. The

predicted stretches were calculated and tabulated for all six knees according to test case

and compared to experimental results. Coefficients of determination (R2), regression

lines, and p-values were determined.

The effect of tibial axial rotation constraint on insertion site and contact forces

was assessed with a paired t-test using all the force data (insertion site and contact forces

for both injury states at both angles and both loading conditions). The effects of within-

subject treatment (injury state and flexion angle) in response to anterior and valgus

loading on insertion site and contact forces were assessed using 2-way repeated

measures ANOVAs. The results of the paired t-test showed no significant effect of tibial

constraint on insertion site and contact forces (see results section below), so only the

force data for the tests with constrained tibial axial rotation were used in the 2-way

ANOVAs. In cases when significance was found (p<0.05), multiple comparisons were

performed using the Tukey procedure.

Results

Experimental Kinematics

Before ACL resection, the average anterior displacements at 0º and 30º knee

flexion in response to a 100 N anterior tibial load were 6.8 ± 2.6 mm and 6.7 ± 2.2 mm,

respectively. ACL transection significantly increased anterior displacement in response

to a 100 N anterior tibial load (16.5 ± 6.1 mm and 20.8 ± 4.4 mm at 0º and 30º,

101

respectively) (p<0.001 for both flexion angles). Before ACL transection, the average

valgus rotation at 0º and 30º knee flexion in response to a 10 N-m valgus torque were

3.6 º ± 1.8 º and 5.1 º ± 2.0 º, respectively. ACL deficiency did not significantly change

valgus rotation in response to a 10 N-m valgus torque (4.3 º ± 1.9 º and 5.3 º ± 1.7 º at 0º

and 30º, respectively). Subsequent separation of the medial meniscus attachment had no

significant effect on knee joint kinematics for both A-P and V-V loading (data not

shown). Because there was no change in joint kinematics following separation of the

medial meniscus from the MCL in the ACL-deficient knee, these data were not

subsequently analyzed via FE analysis.

FE Predictions of Regional Fiber Stretch

The FE values for fiber stretch were excellent predictors of experimental fiber

stretch. Regression analysis of FE predicted fiber stretch versus experimentally

measured fiber stretch for all regions, knees and test cases of intact and ACL-deficient

knees yielded a coefficient of determination of R2 = 0.953 (p=0.001) (Figure 5.1).

Fringe plots of the FE fiber strain illustrate the MCL strain patterns and increases in

strain caused by ACL-deficiency in response to anterior and valgus loading (Figure 5.2).

In response to both types of load and regardless of injury state, the highest MCL strains

were found in the posterior-proximal region [34]. MCL strain increased significantly in

response to anterior loading when the ACL was injured, but the increase was not

significantly different in response to a valgus load. Higher MCL strains tended to be

more distributed in response to valgus loading than anterior loading regardless of injury

102

Experimental Stretch

0.95 1.00 1.05 1.10 1.15 1.20 1.25

FE S

tret

ch

0.95

1.00

1.05

1.10

1.15

1.20

1.25y = 0.919x + 0.084(R2 = 0.953)

Figure 5.1. FE predicted vs. experimental fiber stretch for all knees, test conditions, and measurement regions (N=1632).

Figure 5.2. Representative fringe plots of FE predicted fiber strain for a 100 N anterior load (top row) and a 10 N-m valgus load (bottom row) for the uninjured knee and the ACL-deficient knee. MCL strains increased in response to anterior tibial loading when the ACL was injured. MCL strains also increased locally in the ACL-deficient knee in response to a valgus torque, but these local increases did not result in significant changes in insertion site or contact forces.

0%

8%

100 N anterior tibial load, ACL deficient

10 N-m valgus torque, ACL intact 10 N-m valgus torque, ACL deficient

100 N anterior tibial load, ACL intact

103

104

state. A comprehensive set of MCL strain data as well as the kinematic data from this

testing can be found in Lujan et. al. [34].

Tibial Axial Rotation Constraint

A paired t-test using all insertion site and contact forces for both flexion angles

and loading conditions showed that there was no effect of tibial axial rotation constraint

on the predicted forces (p = 0.154).

Insertion Site Force

ACL deficiency caused significant increases in MCL insertion site forces at both

the femur and tibia during anterior tibial translation. The forces at both insertion sites

were significantly higher at 0º than at 30º in ACL-deficient knees in response to the 100

N anterior tibial load. The MCL femoral insertion site forces corresponding to the in

situ strains in the intact knee (before application of the experimental kinematics) at 0º

and 30º were 39.7 ± 38.1 N and 6.0 ± 5.4 N, respectively. The MCL tibial insertion site

forces due to in situ strain in the intact knee at 0º and 30º were 42.9 ± 43.1 N and 6.0 ±

5.5 N, respectively. Before ACL resection, the MCL femoral insertion site forces

during anterior translation at 0º and 30º were 55.9 ± 38.2 N and 8.3 ± 5.4 N,

respectively. Before ACL resection, the MCL tibial insertion site force during anterior

tibial translation at 0º and 30º were 58.7 ± 42.0 N and 8.3 ± 5.5 N, respectively (Figure

5.3, left panel). ACL-deficiency significantly increased MCL insertion site forces at the

femur (126.6 ± 84.8 N and 74.1 ± 57.8 N at 0º and 30º, respectively) and tibia (133.9 ±

88.5 N and 80.9 ± 62.4 N at 0º and 30º, respectively) during anterior tibial translation

105

(p<0.05 for all cases). Insertion site forces were significantly higher at 0° than at 30°

during anterior tibial translation (p=0.012 for both insertions).

In contrast to the anterior loading results, ACL deficiency did not significantly

affect insertion site forces during application of valgus torque (Figure 5.3, right panel).

This was true at both the femoral and tibial insertion sites and for both flexion angles.

Although the increases caused by ACL deficiency were not statistically significant in

response to a valgus load, the results followed the same trend as the anterior loading

results, with higher forces and increases in forces at the tibial insertion and at 0° flexion.

Before ACL resection, the MCL femoral insertion site forces during valgus rotation at 0º

and 30º were 72.8 ± 49.9 N and 46.0 ± 34.4 N, respectively. Before ACL resection, the

MCL tibial insertion site forces during valgus rotation at 0º and 30º were 77.8 ± 55.6 N

Figure 5.3. FE predictions of insertion site forces for femoral and tibial insertion sites as a function of flexion angle and ACL state. Left panel - anterior tibial translation. Right panel – valgus rotation. Asterisks indicate statistically significant comparisons. There was a significant increase in MCL insertion site forces at the femur and tibia during anterior tibial translation after ACL injury at both 0º and 30º. In contrast, there was no significant effect of ACL deficiency on MCL insertion site forces in response to valgus loading. Both tibial and femoral insertion site forces were significantly higher at 0º than at 30º in the ACL-deficient knee during anterior tibial translation. (mean ± standard deviation).

Flexion Angle (Degrees)0 30

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250

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)

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150

200

250ACL intact, femur ACL cut, femur ACL intact, tibia ACL cut, tibia

* *

* *

Flexion Angle (Degrees)0 30

Inse

rtion

Site

For

ce (N

)

0

50

100

150

200

250

Flexion Angle (Degrees)0 30

Inse

rtion

Site

For

ce (N

)

0

50

100

150

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250ACL intact, femur ACL cut, femur ACL intact, tibia ACL cut, tibia

Flexion Angle (Degrees)0 30

Inse

rtion

Site

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ce (N

)

0

50

100

150

200

250

Flexion Angle (Degrees)0 30

Inse

rtion

Site

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)

0

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250ACL intact, femur ACL cut, femur ACL intact, tibia ACL cut, tibia

** **

** **

Anterior Loading Valgus Loading

106

and 47.9 ± 37.9 N, respectively. After the ACL was transected, the MCL femoral

insertion site forces during valgus rotation at 0º and 30º were 92.0 ± 64.0 N and 57.5 ±

45.0 N, respectively. After the ACL was transected, the MCL tibial insertion site forces

during valgus rotation at 0º and 30º were 99.0 ± 72.2 N and 60.7 ± 49.3 N, respectively.

Contact Forces

ACL deficiency resulted in significantly increased MCL contact forces on the

tibia during anterior tibial translation at both flexion angles, and MCL contact forces on

the tibia were significantly higher at 0º than at 30º in the ACL-deficient knee. Before

ACL resection, the MCL contact forces on the tibia during anterior translation at 0º and

30º were 11.6 ± 11.9 N and 0.7 ± 0.9 N, respectively (Figure 5.4, left panel). ACL

deficiency significantly increased MCL contact forces on the tibia (28.4 ± 18.9 N and

21.1 ± 15.8 N at 0º and 30º, respectively) during anterior translation (p=0.001 at both

angles). MCL contact forces on the tibia in the ACL-deficient knee were significantly

higher at 0º than at 30º in response to anterior tibial loading (p=0.044). ACL deficiency

did not significantly affect contact forces during application of valgus torque (Figure

5.4, right panel).

Discussion

The hypothesis of this research was that ACL deficiency would increase MCL

insertion site forces at the femur and tibia and increase contact forces between the MCL

and the bones in response to both anterior and valgus loading. This hypothesis was

partially disproved. In the ACL-deficient knee, the MCL is indeed subjected to higher

insertion site and contact forces in response to an anterior load. However, MCL forces

107

Figure 5.4. FE predictions of contact forces between the MCL and femur and between the MCL and tibia as a function of flexion angle and ACL injury state. Left - anterior tibial translation. Right – valgus rotation. Asterisks indicate statistically significant comparisons. ACL deficiency significantly increased tibial contact forces at both flexion angles during anterior tibial translation. Further, tibial contact forces in the ACL-deficient knee at 0º were significantly higher than at 30º during anterior loading. In contrast, there was no significant effect of ACL deficiency on MCL contact forces during valgus loading (mean ± standard deviation).

due to a valgus torque are not significantly increased in the ACL-deficient knee. It

follows that the MCL resists anterior tibial translation in knees with intact ACLs, but the

ACL is not a restraint to valgus rotation when a healthy MCL is present.

ACL deficiency caused a significant increase in MCL insertion site and contact

forces in response to anterior tibial loading. This result is supported by a FE study that

examined MCL insertion site and contact forces in the ACL-deficient knee [35] and by

cadaver studies that have utilized a robotic/universal force-moment sensor system to

calculate MCL insertion site forces in the ACL-deficient knee [16, 17]. Moglo et al.

created a single FE model of the knee including the MCL, ACL, posterior cruciate

ligament, lateral collateral ligament, menisci, and cartilage [35]. A 100 N posterior load

Flexion Angle (Degrees)0 30

Con

tact

For

ce (N

)

0

10

20

30

40

50

Flexion Angle (Degrees)0 30

Con

tact

For

ce (N

)

0

10

20

30

40

50ACL intact, femur ACL cut, femur ACL intact, tibia ACL cut, tibia

**

Flexion Angle (Degrees)0 30

Con

tact

For

ce (N

)

0

10

20

30

40

50

Flexion Angle (Degrees)0 30

Con

tact

For

ce (N

)

0

10

20

30

40

50ACL intact, femur ACL cut, femur ACL intact, tibia ACL cut, tibia

***

Anterior Loading

Valgus Loading

108

was applied to the femur at a range of flexion angles from 0 to 90 degrees to study the

forces in the remaining structures after removing the ACL. At full extension, forces in

collateral ligaments increased in the ACL-deficient knee. Better support for our findings

can be found in two studies that used a robotic/universal force-moment sensor system to

calculate MCL insertion site forces in the intact and ACL-deficient knee [16, 17]. In

each study, anterior loads were applied to intact and ACL-deficient cadaver knees and

the resulting MCL insertion site forces were measured. Both studies found a significant

increase in MCL insertion site forces during anterior tibial loading in the ACL-deficient

knee.

In vivo studies of MCL healing have demonstrated that MCL healing is inferior

when injured in conjunction with the ACL [2, 5, 6, 12]. Each of these studies found

increased knee laxity and decreased MCL material properties when the MCL is injured

in conjunction with the ACL as compared to MCL injury with intact ACL, but only one

of these studies measured MCL forces. Using a goat model, the insertion site forces in

healing MCLs in response to an anterior tibial load in knees with reconstructed ACLs

were measured by Abramowitch et al. using a robotic/universal force-moment sensor

system [6]. It was their conclusion that “the healing MCL may have been required to

take on excessive loads and was unable to heal sufficiently as compared to an isolated

MCL injury.” Although these conclusions were reached based on healing studies in

animal models, application of the results of the present study suggest that differences in

MCL healing between knees with intact ACLs and those with transected ACLs could be

due to either anterior or valgus loading. The insertion site forces in response to a valgus

torque were generally of the same magnitude for a given flexion angle as the insertion

109

site forces in response to an anterior tibial load, although they did not significantly

increase with ACL deficiency, and the types and magnitudes of loads that hinder MCL

healing are unknown.

The ACL is not a restraint to valgus rotation if the MCL is intact (Figures 4 and

5, right panels). At first this may seem contradictory to the widely held notion that the

ACL is a secondary restraint to valgus rotation [3-8, 11]. However, upon closer

examination, these studies reached this conclusion based on the results of MCL

transection. Specifically, when the MCL was injured or transected, the ACL

experienced increased loading during application of a valgus torque. Although our

conclusion has not been reported previously in the literature, the results of other studies

support the conclusions indirectly. Engle et al. examined the effect of ACL repair and

graft restructuring on MCL healing after an O'Donoghue triad injury [2]. At 0, 6, and 12

weeks postoperatively, the anterior translation and valgus rotation of the knees were

tested. From time point zero to twelve weeks anterior laxity significantly increased, but

valgus laxity did not. Markolf et al. found that valgus knee laxity was relatively

unaffected by sectioning of the cruciate ligaments [14]. This idea is further supported by

a study looking at medial and lateral laxity in intact cadaver knees [13]. Using a six

degree of freedom linkage attached to six different knees with applied varus-valgus

loading, Grood et al. found that the ACL and PCL combined accounted for only 14.8%

of the medial restraining moment at 5 degrees knee flexion and only 13.4% of the

restraining moment at 25 degrees knee flexion. Thus, when evaluating valgus laxity in

the ACL-injured knee, any increase in valgus laxity indicates a compromised MCL.

110

Applying the in situ strain to the MCL during the second part of the FE analysis

creates insertion site forces. These forces represent the contribution of the MCL to knee

stability when there is little or no muscle activation or external loading. The insertion

site forces caused by the in situ strain were smaller than the insertion site forces present

after anterior or valgus loading in the intact knee, although not always significantly

smaller. This result is reflective of the relatively low load limits used in this study. In

the ACL-deficient knee, insertion site forces significantly increased in response to an

anterior tibial load, but not a valgus load, from the insertion site forces caused by the in

situ strain. This followed the trend of the results comparing the insertion site forces in

the ACL-deficient knee to the intact knee.

Changes in MCL contact forces followed the trend of MCL insertion site forces

in that there was a significant increase in contact forces between the MCL and tibia

following ACL transection in response to an anterior tibial load, but not a valgus torque.

Contact forces were generated between the MCL and tibia during anterior tibial

translation as the MCL slid over the convex surface of the tibia. These forces were

relatively small in knees with intact ACL. Contact forces increased when the ACL was

transected, and on average anterior tibial translation was more than doubled, forcing the

MCL to slide over parts of the bone that have increased curvature. To our knowledge

this is the first study to examine ligament contact forces using subject-specific FE

modeling.

The attachment of the medial meniscus to the MCL was not represented in the

FE analyses. This approach was justified by the results of our previous study, which

demonstrated that transection of the attachment had no effect on knee kinematics under

111

valgus loading in the intact knee [22]. In the present study, it was confirmed that

separation of the attachment of the medial meniscus to the MCL had no significant

effect on joint kinematics for both A-P and V-V loading in the ACL-deficient knee. Of

course, it is possible that other soft tissue structures that were dissected away from the

knees may contribute to knee stability under A-P and V-V loading, and thus as with any

cadaveric study, caution should be taken when extrapolating results to other situations.

Improvements in the experimental methods that were used in the present study

resulted in substantially better agreement between FE predictions and experimental

measurements of fiber stretch than was obtained in our previous study [22].

Improvements included the use of a more accurate digital motion analysis system,

placement of wires around the MCL insertion sites to aid in identifying their locations in

the CT images, and the placement of additional strain markers along and across the

MCL [23]. The excellent correlation between experimental and FE predicted fiber

strains (R2 = 0.953) provides confidence in the fidelity of the subject-specific FE model

predictions. Data such as insertion site forces and contact forces, which elucidate other

injury mechanisms and risks, can be evaluated using subject-specific FE methods.

Further, the combination of results available through a combined experimental and

computational protocol can be used to determine the likely location of injury and to what

extent it may occur.

Several assumptions were made in the constitutive model used for the MCL to

decrease both the experimental and computational time it took to conduct the study.

Average MCL material coefficients from a previous study [22] were used. In the

previous study, results from FE simulations using subject-specific material properties

112

were compared to those using average material properties and no statistical differences

were found. The MCL was assumed to have homogenous material properties. This

assumption was used in our previous study [22] that yielded good correlations between

experimental and FE strain results so the assumption was used again for this study which

yielded an even better correlation.

It should be noted that the A-P and V-V mechanical testing performed for this

research simulated an ideal clinical exam for knee laxity and no attempt was made to

simulate weight bearing or muscle forces. Caution should be use when extrapolating the

results reported here to a knee under muscle activation forces and/or ground contact

forces. The anterior load and valgus torque limits for this research were specifically

chosen to allow multiple tests on a single knee. Future research examining other loading

conditions including muscle and body weight forces during regular daily activities is still

needed.

In summary, ACL deficiency significantly increases MCL insertion site and

contact forces in response to an anterior tibial load, and the largest increases occur at full

extension. In contrast, ACL deficiency does not significantly increase MCL insertion

site and contact forces in response to a valgus torque. Since it was demonstrated that the

ACL is not a restraint to valgus rotation if the MCL is intact, increased valgus laxity in

the ACL-deficient knee indicates a compromised MCL.

References

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113

[2] Engle, C. P., Noguchi, M., Ohland, K. J., Shelley, F. J., and Woo, S. L., 1994, "Healing of the rabbit medial collateral ligament following an O'Donoghue triad injury: effects of anterior cruciate ligament reconstruction," J Orthop Res, 12(3), pp. 357-364.

[3] Inoue, M., McGurk-Burleson, E., Hollis, J. M., and Woo, S. L., 1987,

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between the ACL graft and MCL in a combined ACL+MCL knee injury using a goat model," Acta Orthop Scand, 71(4), pp. 387-393.

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"Healing of the medial collateral ligament following a triad injury: a biomechanical and histological study of the knee in rabbits," J Orthop Res, 10(4), pp. 485-495.

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[7] Loitz-Ramage, B. J., Frank, C. B., and Shrive, N. G., 1997, "Injury size affects

long-term strength of the rabbit medial collateral ligament," Clin Orthop(337), pp. 272-280.

[8] Norwood, L. A., and Cross, M. J., 1979, "Anterior cruciate ligament: functional

anatomy of its bundles in rotatory instabilities," Am J Sports Med, 7(1), pp. 23-26.

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collateral ligament insufficiency on the reconstructed anterior cruciate ligament: a study in the rabbit," Acta Orthop Scand, 74(2), pp. 196-200.

[10] Mazzocca, A. D., Nissen, C. W., Geary, M., and Adams, D. J., 2003, "Valgus

medial collateral ligament rupture causes concomitant loading and damage of the anterior cruciate ligament," J Knee Surg, 16(3), pp. 148-151.

[11] Woo, S. L., Jia, F., Zou, L., and Gabriel, M. T., 2004, "Functional tissue

engineering for ligament healing: potential of antisense gene therapy," Ann Biomed Eng, 32(3), pp. 342-351.

[12] Woo, S. L., Young, E. P., Ohland, K. J., Marcin, J. P., Horibe, S., and Lin, H. C.,

1990, "The effects of transection of the anterior cruciate ligament on healing of

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the medial collateral ligament. A biomechanical study of the knee in dogs," J Bone Joint Surg Am, 72(3), pp. 382-392.

[13] Grood, E. S., Noyes, F. R., Butler, D. L., and Suntay, W. J., 1981, "Ligamentous

and capsular restraints preventing straight medial and lateral laxity in intact human cadaver knees," J Bone Joint Surg Am, 63(8), pp. 1257-1269.

[14] Markolf, K. L., Mensch, J. S., and Amstutz, H. C., 1976, "Stiffness and laxity of

the knee--the contributions of the supporting structures. A quantitative in vitro study," J Bone Joint Surg Am, 58(5), pp. 583-594.

[15] Seering, W. P., Piziali, R. L., Nagel, D. A., and Schurman, D. J., 1980, "The

function of the primary ligaments of the knee in varus-valgus and axial rotation," J Biomech, 13(9), pp. 785-794.

[16] Kanamori, A., Sakane, M., Zeminski, J., Rudy, T. W., and Woo, S. L., 2000, "In-

situ force in the medial and lateral structures of intact and ACL-deficient knees," J Orthop Sci, 5(6), pp. 567-571.

[17] Sakane, M., Livesay, G. A., Fox, R. J., Rudy, T. W., Runco, T. J., and Woo, S.

L., 1999, "Relative contribution of the ACL, MCL, and bony contact to the anterior stability of the knee," Knee Surg Sports Traumatol Arthrosc, 7(2), pp. 93-97.

[18] Butler, D. L., Noyes, F. R., and Grood, E. S., 1980, "Ligamentous restraints to

anterior-posterior drawer in the human knee. A biomechanical study," J Bone Joint Surg Am, 62(2), pp. 259-270.

[19] Miyasaka, K., et al., 1991, "The incidence of knee ligament injuries in the

general population.," Am J Knee Surg, 4(1), pp. 3-8. [20] Fetto, J. F., and Marshall, J. L., 1978, "Medial collateral ligament injuries of the

knee: a rationale for treatment," Clin Orthop(132), pp. 206-218. [21] Hull, M. L., 1997, "Analysis of skiing accidents involving combined injuries to

the medial collateral and anterior cruciate ligaments," Am J Sports Med, 25(1), pp. 35-40.

[22] Gardiner, J. C., and Weiss, J. A., 2003, "Subject-specific finite element analysis

of the human medial collateral ligament during valgus knee loading," J Orthop Res, 21(6), pp. 1098-1106.

[23] Lujan, T. J., Lake, S. P., Plaizier, T. A., Ellis, B. J., and Weiss, J. A., 2005,

"Simultaneous measurement of three-dimensional joint kinematics and ligament strains with optical methods," ASME Journal of Biomechanical Engineering, 127, pp. 193-197.

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[24] Gardiner, J. C., 2002, "Computational Modeling of Ligament Mechanics,"

University of Utah, Salt Lake City. [25] Grood, E. S., Suntay, W.J., 1983, "A joint coordinate system for the clinical

description of the three-dimensional motions: application to the knee.," J Biomech Eng, 105, pp. 136-144.

[26] Gardiner, J. C., and Weiss, J. A., 2001, "Simple shear testing of parallel-fibered

planar soft tissues," J Biomech Eng, 123(2), pp. 170-175. [27] Weiss, J. A., Gardiner, J. C., Ellis, B. J., Lujan, T. J., and Phatak, N. S., 2005,

"Three-dimensional finite element modeling of ligaments: Technical aspects," Medical Engineering and Physics, In Press.

[28] Boissonnat, J. D., 1988, "Shape reconstruction from planar cross-sections,"

Computer Vision, Graphics and Image Processing, 44, pp. 1-29. [29] Schroeder, W. J., Zarge, J., and Lorensen, W. E., 1992, "Decimation of triangle

meshes," Computer Graphics (Proc SIGGRAPH), 25. [30] Maker, B. N., 1995, "Rigid bodies for metal forming analysis with NIKE3D,"

University of California, Lawrence Livermore Lab Rept, UCRL-JC-119862, pp. 1-8.

[31] Weiss, J. A., and Maker, B. N., 1996, "Finite element implementation of

incompressible, transversely isotropic hyperelasticity," Computer Methods in Applied Mechanics and Engineering(135), pp. 107-128.

[32] Maker, B. N., 1995, "NIKE3D: A nonlinear, implicit, three-dimensional finite

element code for solid and structural mechanics," Lawrence Livermore Lab Tech Rept, UCRL-MA-105268.

[33] Speck, D., 2001, "GRIZ - Finite Element analysis results visualization for

unstructured grids - user manual," Lawrence Livermore National Laboratory, UCRL-MA-115696 Rev.2.

[34] Lujan, T. J., Dalton, M. S., Thompson, B. M., Ellis, B. J., Rosenberg, T. D., and

Weiss, J. A., 2005, "MCL strains and joint kinematics in the ACL-deficient and posteromedial meniscus injured knee," American Journal of Sports Medicine, In Review.

[35] Moglo, K. E., and Shirazi-Adl, A., 2003, "Biomechanics of passive knee joint in

drawer: load transmission in intact and ACL-deficient joints," Knee, 10(3), pp. 265-276.

CHAPTER 6

EFFECT OF DERMATAN SULFATE GLYCOSAMINOGLYCANS ON

THE QUASI-STATIC MATERIAL PROPERTIES OF THE

HUMAN MEDIAL COLLATERAL LIGAMENT

Abstract

The glycosaminoglycan of decorin, dermatan sulfate (DS), has been suggested to

contribute to the mechanical properties of soft connective tissues such as ligaments and

tendons. This study investigated the mechanical function of DS in human medial

collateral ligaments (MCL) using non-destructive shear and tensile material tests

performed before and after targeted removal of DS with Chondroitinase B (ChB). The

quasi-static elastic material properties of human MCL were unchanged after DS

removal. At peak deformation, tensile and shear stresses in ChB treated tissue were

within 0.5% (p>0.70) and 2.0% (p>0.30) of pretreatment values, respectively. From

pre- to post-ChB treatment under tensile loading, the tensile tangent modulus went from

242 ± 64 to 233 ± 57 MPa (p=0.44), and tissue strain went from 4.3 ± 0.3% to 4.4 ±

___________________ 1 Reprinted by kind permission of Wiley-liss Inc. a subsidiary of John Wiley & Sons Inc. Journal of Orthopaedic Research, Vol. 25, No. 7, Trevor J. Lujan, Clayton J. Underwood, Heath B. Henninger, Brent M. Thompson, Jeffrey A. Weiss, “Effect of Dermatan Sulfate Glycosaminoglycans on the Quasi-Static Material Properties of the Human Medial Collateral Ligament”, pp: 894-903, 2007.

117

0.3% (p=0.54). Tissue hysteresis was unaffected by DS removal for both tensile and

shear loading. Biochemical analysis confirmed that 90% of DS was removed by ChB

treatment when compared to control samples, and TEM imaging further verified the

degradation of DS by showing an 88% reduction (p<.001) of sulfated

glycosaminoglycans in ChB treated tissue. These results demonstrate that DS in mature

knee MCL tissue does not resist tensile or shear deformation under quasi-static loading

conditions, challenging the theory that decorin proteoglycans contribute to the material

behavior of ligament.

Introduction

The mechanical characteristics of ligament and tendon are a function of their

composition and molecular organization. The major solid phase constituent of ligament

and tendon is type I collagen, which represents over 70% of the total solid phase [1, 2].

The remaining constituents include other collagens (III,V,VI,XI,XIV), extracellular

matrix proteins (e.g. elastin) and proteoglycans [3, 4]. The hierarchical organization of

type I collagen in ligament has been extensively studied; type I collagen fibrils form

parallel arrays of fibers that are the main contributors to ligament material properties [5].

However, there are very limited data on the mechanical influence of the non-collagenous

components of ligament. Understanding the contributions of these components to

connective tissue mechanics can clarify their roles and aid efforts to engineer

replacement tissues.

The primary proteoglycan in ligament [6, 7], decorin, and its single sulfated

glycosaminoglycan (GAG) have been the subject of numerous studies due to their

respective proven and theoretical roles in tissue-level organization and mechanics at the

118

molecular level. Dermatan sulfate (DS) is the GAG that associates with the decorin core

protein in nearly all mature tissues [8, 9](Figure 6.1, A). The concave face of decorin

has been modeled to straddle the D-period binding site of a single collagen triple helix

[10, 11] (Figure 6.1, B). Decorin appears to be excluded from the tightly tropocollagen

packed fibril interior [12], localizing to the surface of the collagen fibrils (Figure 6.1, C).

The highly charged DS GAG projects away from the decorin core protein [13];

generally orthogonally aligned to the fibril direction [8].

Scanning electron and atomic force microscopy of connective tissues

demonstrate that the majority of DS GAGs span the space between neighboring fibrils

[12, 15]. Several studies report that collagen fibrils in various species are short and

discontinuous [16-18], suggesting that a secondary microstructure could be involved in

transferring axial force between contiguous fibrils. This finding led to an appealing

hypothesis that decorin based DS GAGs on adjacent fibril surfaces interact, creating

functional “cross-links” that transfer forces between discontinuous fibrils [8, 15, 17, 19-

24] (Figure 6.1, C). Supporting this hypothesis, molecular dynamics predict that the

summation of GAG interaction forces in collagen-decorin networks are capable of

transferring inter-fibril stress [15, 25], and experiments confirm that DS does indeed

self-associate [26]. The proposed fibril-fibril link would prevent fibril sliding and

potentially contribute to quasi-static mechanical properties under both shear and tensile

loading.

Using knockout mice and competitive peptides, previous studies have

investigated the possible mechanical role of decorin indirectly. Knockout studies have

Figure 6.1. (A) Magnified schematic of decorin proteoglycan. The boxed domains “L” represent the Leucine-rich repeats of the protein core. “C” represents the cysteine rich domain. The dermatan sulfate GAG is attached to the protein core near the amino (NH2) terminus through a serine linked oligosaccharide (“LO”). On the macroscopic level, dermatan sulfate is made up of iduronic acid-containing regions “I” and glucuronic acid-containing regions “G”. Chondroitinase B will degrade the iduronic acid regions mainly into disaccharides. (B) Frontal view of collagen fibril assembly. Five quarter staggered tropocollagen units construct a microfibril. Decorin core proteins likely bind to tropocollagen triple helix units at the D-period gap region of the microfibril. Although decorin binds to collagen, the exact mechanism of this attachment is debated [14]. (C) Cross-sectional view of collagen fibril assembly. A fibril consists of a variable number of microfibrils, however decorin is only able to bind to tropocollagen units on the outer surface of the fibril. The proposed interaction between collagen fibrils involves the association of at least two dermatan sulfate GAG side-chains bonded to decorin core proteins on adjacent collagen fibrils.

D = 67nm

Micro Fibril

Fibril

Tropocollagenx

y

B C

z

y

Decorin Core Protein

Dermatan Sulfate GAG

A

LO

NH2

G

I

LL

LL

LL

C

L

LL

L

CLL

D = 67nm

Micro Fibril

Fibril

Tropocollagenx

y

x

y

B C

z

y

z

y

Decorin Core Protein

Dermatan Sulfate GAG

A

LO

NH2

G

I

LL

LL

LL

C

L

LL

L

CLL

LL

LL

LL

C

L

LL

L

CLCLL

119

120

reported that decorin deficiency decreases the tensile strength in the dermis [27], does

not affect tensile strength or modulus in tail tendon fascicles [28, 29], and increases

modulus in the patellar tendon [28, 29]. NKISK, a pentapeptide that inhibits the ability

of decorin to bind to collagen, caused fibril to fibril disassociation [18], and ultimately

greater tissue laxity without reduction in material strength [30]. The mechanical

behavior of connective tissues from knockout mice may be influenced by changes in

tissue development due to the absence of decorin, such as irregular collagen structure

[27] and regulatory activity that increases biglycan production as a compensatory

mechanism [31-33]. Lack of biochemical analyses in the NKISK studies has left the

molecular alterations in question. If NKISK specifically inhibits decorin binding,

observed changes may be due to the absence of the decorin core protein and not

necessarily the associated GAG. Altogether these studies have left the mechanical role

of DS under elastic tensile deformation unclear and controversial.

In this study, a new experimental model was developed to quantify the effects of

DS GAGs on the elastic material behavior of mature ligament tissue. The objective of

this study was to assess the role of DS in resisting quasi-static tensile and shear

deformation along the fiber direction in human ligament by targeted removal of DS

crosslinks with enzymatic degradation. Understanding the elastic contribution of DS

will clarify the structure-function relationships in ligament and address the validity of

the decorin cross-linking theory.

121

Materials and Methods

Experimental Design

The medial collateral ligament (MCL) of the human knee was chosen for study

due to the extensive prior mechanical test data available [34-37] and our well-developed

experimental protocols for mechanical characterization [34, 36, 38]. Knees were

acquired fresh-frozen and were allowed 16 hours to thaw prior to dissection. The freeze-

thaw cycle does not influence the quasi-static material properties of ligament [39, 40].

Knees with surgical scars, ligament injury or cartilage degeneration characteristic of

osteoarthritis were eliminated. To account for material symmetry characteristics of

ligament, two types of mechanical tests were performed – uniaxial tensile testing [34]

and shear testing [36]. For tensile testing, 16 specimens were harvested from 4 unpaired

human MCLs (donor age = 57±5 yrs). For shear testing, 16 specimens were harvested

from 5 unpaired human MCLs (donor age = 55±8 yrs). The specimens were divided

between two treatment groups: a control treatment group and a Chondroitinase B (ChB)

treatment group. ChB specifically degrades DS side chains of proteoglycans [41].

Mechanical testing was performed pre- and posttreatment on the same specimen.

Uniaxial Tensile Testing

Four unpaired human MCLs were used for tensile testing. A hardened steel

punch [34] was used to extract four samples from different locations in each superficial

MCL between the tibial and femoral insertions, for a total of 16 tested samples. The

punch shape included beveled ends for gripping and was oriented so that its long axis

was aligned with visible fiber bundles. Sample geometry met ASTM requirements for

fiber reinforced composite materials [42]. Samples were randomly divided between the

122

control and ChB treatment groups and loaded in a clamp assembly. A 0.1 N preload was

applied to establish a consistent reference length. Vertical position of the actuator (Tol-

O-Matic, Hamel, MN, accuracy ±1.0 µm) and high-resolution micrometer measurements

(Newport, Irvine, CA, accuracy ±0.5 µm) of the x-y table were logged so that the

reference configuration could be reproduced after treatment. Sample position was

further measured by tracking 4.75 mm dia acrylic white spheres adhered to each clamp

and to a fixed reference with a digital camera (Pulnix TM-1040, 1024x1024x30 fps,

Sunnyvale, CA) and digital motion analysis software (DMAS, Spica Technology Corp,

Maui, HI, accuracy ± 0.005 mm) [43]. This protocol verified that posttreatment clamp

positions were within 0.04 ± 0.01 mm of pretreatment clamp positions.

Specimen dimensions were measured using digital calipers (Mitutoyo, San Jose,

accuracy ±0.02 mm) by taking an average of three measurements (Table 1). Following

five minutes of relaxation, a triangular displacement profile was applied for ten cycles at

a strain rate of 1.0%/sec with a clamp-to-clamp strain amplitude of 8% of the specimen

length. Clamp-to-clamp strain was based on substructural failure limits of ligament,

reported to occur after 5% tissue strain [44]. Tissue tissue strain is approximately half

the clamp-to-clamp strain [37], so an 8% clamp-to-clamp strain was chosen to avoid

structural damage. The strain rate was selected to minimize viscoelastic and inertial

effects [34]. Tissue strain was measured by tracking 1 mm diameter contrast markers on

Table 6.1. Physical dimensions of the MCL test specimens (n=16).

Specimen type

Mean clamp-to-clamp length ± SD

Mean width ± SD

Mean thickness ± SD

Tensile 15.06 ± 1.84 1.81 ± 0.38 1.48 ± 0.58 Shear 6.93 ± 0.91 9.81 ± 0.93 1.84 ± 0.42

123

the specimen mid-substance using the DMAS system. Force and displacement were

monitored continuously, with peak stress calculations based on the 10th cycle. Tangent

modulus was calculated as the slope of the linear region of the stress-strain curve using

local tissue strain, and was standardized for each case by using linear regression to fit

the stress-strain data for the final 1% strain region. Hysteresis was determined from the

area enclosed by the loading and unloading stress-strain curves from the last loading

cycle.

Shear Testing

Five unpaired human MCLs were used. A rectangular punch (10 x 25 mm) was

used to extract up to four samples from each superficial, for a total of 16 tested samples.

Samples were randomly divided between the control and ChB treatment groups and

loaded in a clamp assembly so that visible fibers were along the direction of

displacement [36]. Load cells (Sensotec Inc, Columbus, OH, 1000 g, accuracy ±0.1 g)

monitored both transverse and longitudinal clamp reaction forces. After the specimen

was loaded and aligned in an unstrained state, a 1 g preload was applied in the transverse

direction. The vertical displacement was then set at a neutral position, defined as the

inflection point of the force response resulting from small cyclic up-down clamp

displacements. Clamp position and physical dimensions were recorded (Table 1) using

methods identical to the tensile mechanical protocol. Following a five minute

equilibration period, a triangular displacement profile was applied for ten cycles at a

strain rate of 6.5%/sec, with peak displacement based on tan(θ) = (peak displacement) /

(clamp-to-clamp length) = 0.4 [36]. Strain rate was chosen to minimize viscoelastic and

inertial effects and peak displacement was selected to maximize loading without

124

damaging the tissue. Transverse force, longitudinal force and vertical displacement

were monitored continuously, with peak stress calculations based on the 10th cycle.

Shear modulus was defined as the slope of the stress-strain curve over the final 0.1 shear

strain region. Hysteresis effect was measured using the previously mentioned methods.

Chondroitinase B Treatment Protocol

Following initial shear and tensile testing, each specimen was removed from the

test machine while still mounted in the clamps. The entire specimen and clamp

assembly was bathed for one hour at room temperature in 15 ml of buffer solution (15

ml of 20 mM Tris pH 7.5, 150 mM NaCl, 5 mM CaCl2) with protease inhibitors (1 tablet

of mini-complete per 10 ml of buffer). Samples were then bathed in 15 ml of either the

control buffer solution or the ChB (ChB, 1.0 IU/mL) for 6 hours at room temperature

with gentle agitation using an orbital shaker. Preliminary tests confirmed that all DS

was completely degraded using 0.25 IU/mL for 6 hours (data not shown). Immediately

after treatment, the clamp assembly was reattached to the test machine and returned to

the original testing position. The sample was allowed to equilibrate for five minutes.

Shear or tensile posttreatment testing was then performed with the same test parameters.

For the tensile test specimens, failure tests were performed subsequently using our

published protocol [34]. The sample was then removed from the clamps and placed in a

stop buffer (20 mM Tris, pH 7.5, 150 mM Sodium Chloride, and 10 mM EDTA) to

inhibit any further ChB activity. Samples were kept continuously moist by applying

0.9% saline solution through a nozzle.

125

Specificity of Chondroitinase B

A large quantity of ChB was required to treat all ligament specimens. ChB was

cloned into a prokaryotic expression vector as previously described [45]. ChB degrades

DS into disaccharides by cleaving regions that contain iduronic acid (Figure 6.1, A).

One international unit (IU) of ChB activity corresponds to the amount of enzyme

required to liberate 1 µM of unsaturated uronic acid from DS per minute at 30oC (pH

7.5, [DS] = 2 mg/mL).

The specificity of ChB was determined by incubating ChB with various sulfated

GAGs and then determining the GAG concentration remaining after digestion using the

dimethylmethylene blue (DMB) assay [46]. Individual reactions (30 µl, n=6 for each

condition) were set up containing 1.0 IU/mL ChB and 500 µg/mL of sulfated GAG (DS,

chondroitin sulfate A and C, heparan sulfate, or keratan sulfate). Control reactions

contained GAGs and buffer only: 20 mM Tris-HCl (pH 7.5), 150 mM NaCl, and 5 mM

CaCl2. The reaction was allowed to proceed for 6 hours at RT. Five µl of each reaction

(diluted 2 fold) was transferred to a 96 well plate in duplicate, along with GAG

standards. Two hundred µl of dimethylmethylene blue reagent were added to each well,

and the plate was immediately read in a plate reader at 530 and 590 nm. GAG

concentrations were expressed as a percentage of control reactions.

Verification of ChB Activity and Removal of DS

Following mechanical testing, the ligament tissue between the clamps was

isolated with a scalpel and cut into three pieces for GAG quantification, decorin Western

blot analysis and transmission electron microscopy (TEM). GAG quantification

followed established guidelines [47], which involved taking DMB assays from digested

126

papain extracts. These guidelines permitted DS content in control and ChB treated

samples to be calculated by subtracting the amount of GAG present in the papain extract

treated with additional ChB from the papain extract that was treated with additional

buffer only.

Western blot analysis examined the glycosylation state of decorin from extracted

proteoglycans. Wet weights were obtained and samples were then frozen in liquid

nitrogen and pulverized. Proteoglycans were extracted twice over 24 hours at 4oC in a

total of 25 volumes of 4 M GuHCl , 50 mM acetate buffer pH 6.0 plus protease

inhibitors. Two-hundred microliters of extract were precipitated overnight by the

addition of 1 ml of 100% ethanol. Following centrifugation at 14,100 g, the protein

pellet was washed with 70% ethanol and resuspended in 20 µl of 8 M urea, followed by

an additional 140 µl of 10 mM Tris pH 7.4. Twenty five microliters of this extract were

treated with and without additional ChB, as described above. Fifteen microliters of each

reaction was resolved by size on 4-16% gradient SDS-polyacrylamide gels. Proteins

were electrophoretically transferred to nitrocellulose membranes and blocked in 3%

BSA in 1X TBST (Tris-buffered saline plus 0.1% Tween 20) for 1 hr at RT. Blots were

incubated with 0.2 µg/ml biotinylated anti-human decorin antibody (BAF140, R&D

Systems, Minneapolis, MN) for 3 hours at RT on a nutator. Blots were washed and

incubated with 0.8 µg/ml with Neutravidin-HRP (Pierce, Rockford, IL) for 1 hour at RT.

Blots were developed using a chemiluminescent substrate (Bio-Rad, Hercules, CA) and

imaged with a gel documentation system with an integrated 12 bit camera.

TEM was used to investigate the presence of sulfated GAGs in the five control

and ChB treated MCL specimens that were tested in shear. Ligament sections were

127

fixed in 4% paraformaldehyde / 2% glutaraldehyde at 4°C overnight. Samples were

sectioned to 20 µm (cryostat, Leica CM3050S, Exton PA), mounted on slides, and

stained with Cupromeronic Blue [8, 48]. Ultrathin sections, approximately 70 nm, were

obtained via ultramicrotome (Leica Ultracut UCT, Exton, PA) and viewed using a

Hitachi H7100 TEM with a LAB6 filament. Digital images of a minimum of four fields

of view were obtained from each examined MCL. An image processing program was

used to determine the number of stained GAGs per image. All images from a sample

were averaged to produce a representative number of detected objects for each sample.

Statistical Analysis

The effects of control and ChB treatment on tensile and shear peak stresses,

tensile and shear tangent moduli and peak tissue strain were assessed using paired t-tests

to measure significance between pre- and posttreatment. Control versus ChB treatment

effect upon hysteresis was assessed using ANCOVA, controlling for pretreatment

results, with Bonferroni adjustment for multiple comparisons. TEM and biochemistry

results were assessed using independent t-tests to measure control versus ChB treatment

effect. A power analysis demonstrated that a sample size of 8 was sufficient to detect a

10% change with 80% confidence for all measured quasi-static mechanical results

(Power = 0.80). Unless otherwise noted, all results are reported with standard error.

Results

ChB and control treatments had no significant effect on tensile (Figure 6.2) or

shear (Figure 6.3) stress-strain response. At peak deformation, there were no significant

differences in the tensile peak stress due to control or ChB treatments (percent decreases

128

of 0.4 ± 1.3% (p=0.75) and 0.4 ± 0.9% (p=0.718) due to control and ChB treatments,

respectively). Similarly, there were no significant differences in the shear peak stress

due to control or ChB treatments (percent increases of 5.6 ± 3.3% (p=0.13) and 1.7 ±

1.6% (p=0.32) due to control and ChB treatments, respectively).

Tensile tangent modulus, shear modulus and tissue strain were unaffected by

ChB and control treatments. For tensile tests, an 8.0% clamp strain equated to 5.1 ±

0.4% tissue strain. Between time stages, tensile control specimens went from 5.8 ±

0.5% to 5.7 ± 0.6% (p=0.58) tissue strain, while tensile ChB treated specimens went

from 4.3 ± 0.3% to 4.4 ± 0.3% (p=0.54) tissue strain. The pre- and posttreatment tensile

moduli from the 8% cyclic tests were respectively 160 ± 56 and 159 ± 55 MPa for the

control (p=0.79), 242 ± 64 and 233 ± 57 MPa for the ChB treated (p=0.37). The tensile

tangent modulus data calculated from the 8% cyclic strain tests (198 ± 28 MPa) had a

high correlation with the tensile tangent modulus data calculated from the failure tests

(202 ± 37 MPa) (r2=0.8). The pre- and posttreatment shear moduli were respectively

133 ± 11 and 142 ± 14 KPa for the control (p=0.08), 146 ± 39 and 151 ± 41 KPa for the

ChB treated (p=0.08).

There were no significant differences in percent hysteresis between control and

ChB treatments for tensile (p=0.16) and shear (p=0.79) material tests. The pre- and

posttreatment percent hysteresis for tensile specimens were respectively 18.8 ± 0.9% and

20.4 ± 0.9% for control treated, and 20.0 ± 0.7% and 20.8 ± 0.9% for ChB treated. The

pre- and posttreatment percent hysteresis for shear specimens were respectively 21.2 ±

1.8% and 27.5 ± 1.5% for control, and 21.2 ± 1.1% and 28.0 ± 1.9% for ChB treated.

129

Figure 6.2. Stress-Strain curves for tensile tests of control (n=8) and chondroitinase B (n=8) treated ligament samples. (A) Tensile mechanical response immediately after dissection (pretreatment) and after 6 hours of control treatment (posttreatment). (B) Tensile mechanical response immediately after dissection (pretreatment) and after 6 hours of chondroitinase B treatment (posttreatment). Bars = standard error.

Figure 6.3. Stress-Strain curves for shear tests of control (n=8) and chondroitinase B (n=8) treated ligament samples. (A) Shear mechanical response immediately after dissection (pretreatment) and after 6 hours of control treatment (posttreatment). (B) Shear mechanical response immediately after dissection (pretreatment) and after 6 hours of chondroitinase B treatment (posttreatment). Bars = standard error.

2 4

6

2 4 6 8 0

Tens

ile S

tress

(MPa

)

Clamp Strain (%)

ChB Treatment

Pretreatment

Posttreatment 2

4 6

2 4 6 8 0

Pretreatment

Posttreatment

Tens

ile S

tress

(MPa

)

Clamp Strain (%)

Control TreatmentA BA B

tan (θ)

Shea

r Stre

ss (K

Pa)

8 16

24

0.1 0.2 0.3 0.40

Pretreatment

Posttreatment

Control TreatmentA

Shea

r Stre

ss (K

Pa)

8 16

24

tan (θ)

Pretreatment

Posttreatment

ChB TreatmentB

0.1 0.2 0.3 0.40

130

DS CS HS KS

Perc

ent o

f Con

trol

0

20

40

60

80

100

120

ChB reduced the concentration of the DS standard by 78% (Figure 6.4).

Concentrations of Chondroitin sulfates A and C, heparan sulfate and keratan sulfate

were unaffected by ChB treatment. A likely reason that the specificity test did not show

a complete degradation of DS is due to the presence of DMB detectable glucuronic acid-

containing regions in DS, which are not digested by ChB [49, 50]. Biochemical analysis

of the mechanically tested samples found that over 90% of the DS in ChB treated

ligament samples (0.1 ± 0.2 µg DS / mg dry tissue) were eliminated when compared to

control specimens (1.5 ± 0.5 µg DS / mg dry tissue) (p < 0.001). DS accounted for 44 ±

4% of all sulfated GAGs (3.6 ± 0.6 µg sulfated GAGs / mg dry tissue) in the

mechanically tested controls. Western blot results for three control and three treated

specimens are shown in Figure 6.5, but all shear samples and random tensile samples

were tested and yielded similar results. Control specimens (lanes 1, 3, and 5) had two

predominant species, a band at ~43 kDa and a smear from 50-100 kDa. When extracts

Figure 6.4. Specificity of Chondroitinase B. Chondroitinase B (1 U/ml) was incubated with glycosaminoglycans (500 µg/ml) for 6 hours. GAG concentration after six hours was determined using the DMB assay. Concentrations were normalized to control reactions which did not contain chondroitinase B. DS = dermatan sulfate, CS = equal mixture of chondroitin sulfates A and C, HS = heparan sulfate, KS = keratan sulfate. N = 6. Error bars = SD.

131

were treated with ChB (lanes 2, 4, and 6) the smear was eliminated and there were two

major bands at 45 and 90 kDa. The species are consistent with published results in the

literature - the 45 kDa band, which appears as a doublet with shorter exposure times,

represents decorin that has lost its glycosaminoglycan side chain, and the 90 kDa band is

a dimeric form of decorin [51, 52]. Protein extracts obtained from ChB treated ligament

samples (lanes 7, 9, and 11) did not show the smear pattern between 50 and 100 kDa,

suggesting that decorin obtained from these samples had already lost its DS side chain.

Additional ChB treatment did not cause any further changes (lanes 8, 10, and 12).

Figure 6.5. Decorin western blot of proteins extracted from 3 control and 3 ChB treated ligament samples. Each lane represents protein extracted from approximately 375 µg of wet tissue. Two tests were performed on each sample. They were either given an additional control buffer treatment (-) or given an additional treatment of ChB (+). Decorin core protein migrated as a doublet at ~45 kDa. Decorin containing its dermatan sulfate side-chain migrated as a smear from ~55 to 120 kDa.

-

Mol

ecul

ar W

eigh

t (K

Da)

115

82

64

49

37

182

Control Treatment ChB Treatment

---- - + + + + + + Additional ChB

3 Paired Samples 3 Paired Samples

1 9 7 5 3 11 2 10 8 6 4 12Lane

132

TEM images further verified degradation of sulfated GAGs. ChB treated

samples showed a significant reduction in the number of sulfated GAGs when compared

to controls (88% reduction, p<0.001). The quantity of stained GAGs was reasonably

uniform within groups having 47 ± 13 and 350 ± 40 stained GAGs per field for ChB

treated and control images, respectively. Stained GAGs remaining after ChB treatment

were preferentially aligned with the local collagen fibrils and generally larger than the

GAGs that were removed (Figure 6.6).

Discussion

The DS GAG of decorin has been implicated as a contributor to the material

behavior of connective tissue [27-29]. Our present findings do not support the theory

that sulfated GAG crosslinks influence continuum-level mechanical behavior during

Figure 6.6. Representative TEM images of tissue stained with Cupromeroneic Blue after mechanical testing. Large arrows indicate collagen fibril direction, small arrows indicate darkly stained sulfated GAGs. (A) Control treated specimen. (B) ChB treated specimen with 88% reduction in sulfated GAGs. Note the decrease in the overall number of fibril spanning GAGs and the preferred alignment of remaining sulfated GAGs along the collagen fibril direction. (Bar = 200 nm).

133

quasi-static tensile loading [8, 15, 17, 19-23]. Shear testing was conducted to determine

whether DS contributes to the mechanical behavior of mature human MCL when fibrils

are sheared relative to each other [29, 53]. This hypothesis was similarly rejected.

Therefore, DS in mature human medial collateral ligament does not resist quasi-static

tensile or shear loads.

Mathematical studies have hypothesized that GAG crosslinks contribute to the

resistance of loads along the fiber direction by transferring force between discontinuous

fibrils. For instance, Redaelli et al. [22] used a molecular dynamics model to explore the

ability of decorin GAG crosslinks to prevent sliding between discontinuous 100 µm

fibrils. Results suggested that interfibrillar GAGs could transfer force between adjacent

fibrils, with maximum load transfer and GAG strain occurring at 5% tissue strain. The

current study demonstrated that even near 5% tissue strain, interfibrillar GAG crosslinks

did not contribute to the tensile material response of mature human MCL. This result

does not negate the theory that DS may resist fibril motion, but it does confirm that any

interfibrillar resistance from DS interaction does not affect quasi-static mechanics at the

macro scale. Past studies support this conclusion. Cribb and Scott [8] demonstrated that

the orientation of sulfated GAGs does not change under tensile stretch along the

direction of the fibrils, indicating that there was no relative sliding of the fibrils.

Further, the mathematical model used by Radaelli [22] assumed fibril length to be

discontinuous in 100 µm segments. Fibril discontinuity is debated in the literature, with

many investigators reporting that mature fibrils are continuous structures [53-56], with

tapered ends only present on embryonic and in-vitro fibrils [21, 57, 58]. It should be

noted that non-DS molecules, including other sulfated GAGs, may transfer forces

134

between shorter discontinuous fibrils or contribute to the mechanical properties of

ligaments in other test configurations.

Our findings aid the interpretation of results from studies using knockout mice

and competitive peptide techniques. Results of this study suggest that material

alterations reported for tendons from decorin knockouts [27] are likely due to genetic

compensation or developmental abnormalities inherent in decorin deficiency. In another

study, pentapeptide NKISK treatment [30] disrupted the decorin-collagen interaction in

mouse tendon, resulting in increased strain behavior. Since the current study found that

DS degradation did not influence strain behavior, another factor may have influenced

tissue mechanics in the NKISK study. Biochemical analyses are needed to understand

how NKISK alters molecular composition.

Since negatively charged GAGs have an affinity for water molecules, we

investigated hysteresis during both shear and tensile tests. There were no significant

changes in hysteresis following the control and ChB treatments. However, DS may still

contribute to the viscoelastic response when other loading rates or protocols are used. In

studies of decorin-deficient knockout mice, decorin content correlated with strain-rate

sensitivity [28] and stress-relaxation behavior [59]. As stated previously, knockout

models are unable to directly measure DS contribution. Thus to completely characterize

the possible role of DS in ligament mechanical behavior, viscoelastic testing in both

tensile and compressive configurations is necessary.

To have confidence in our results, the experiments needed to be performed in a

reproducible manner that provided data consistent with the literature. Ligament

mechanical behavior can vary between donors, and this can be especially problematic in

135

studies using cadaveric tissues. Measured mechanical response can also be influenced

by tissue heterogeneity, clamping, and specimen alignment in the material testing

system. These variables were controlled with the repeated measures design of the

experiments. Measured mechanical properties were also in good agreement with past

research. Peak shear stress for this experiment was 22 KPa, while published peak shear

stress using similar shear strains and loading configurations was 25 KPa [36]. Past

studies measured an average tangent modulus of 332 MPa in human MCL specimens

taken along the anterior portion of the superficial MCL between the tibial insertion and

the meniscal attachment [34]. Samples taken from this same region in the current study

had a similar average tangent modulus of 330 MPa.

Biochemical and TEM analysis verified selective degradation of DS and

elimination of interfibrillar crosslinks. Samples treated with ChB had 90% less DS than

control samples and an absence of the DS GAG side chain commonly associated with

decorin. TEM results demonstrated that ChB treatment removed the vast majority of

GAGs. Since the sulfated GAGs that remained after ChB treatment were oriented along

the fibrils, DS represented the majority of fibril-spanning sulfated GAGs in the mature

human MCL.

Since ChB degrades all DS chains, it likely degraded DS side chains on biglycan,

a small leucine rich proteoglycan that accounts for less than 10% of all proteoglycans in

ligament [7]. Biglycan has two associated GAG side chains and a core protein that

binds to collagen [60] and is highly homologous to decorin. Biglycan is another

proteoglycan that could contribute to the mechanical properties of tendon [29].

However, since biglycan side chains are predominantly DS, and DS was eliminated via

136

ChB treatment, biglycan proteoglycans similarly did not contribute to quasi-static

mechanical behavior of the human MCL.

Several limitations of this research must be mentioned. A quasi-static loading

rate was used and thus DS depletion could have an effect if mechanical testing was

performed using faster loading rates. Further, DS may contribute to ligament

mechanical properties in other test configurations such as compressive loading. Results

from this study are based on in-vitro tests and long-term effects of DS depletion were

not considered. The human MCL tissue used in this study came from relatively old

donors with several different causes of death. The exact time from death to postmortem

freezing was unknown but less than 24 hours. Although the experimental design utilized

pre-and posttreatment testing of the same sample (repeated measures design), which

controls for the effect of initial differences between samples, the posmortem conditions

and differences in cause of death may have affected the starting concentration of DS in

the tissues. Similar to previous studies that used a repeated measures design to assess

treatment [59, 61], multiple samples were taken from each donor. However, it should be

noted that the measured quasi-static mechanical parameters and GAG content had as

much variability between samples from a specific donor as between donors. Had

mechanical test data from each donor been averaged (n=4) to focus on variability

between donors, an acceptable change of 20% would be detected with 80% confidence

for all measured quasi-static mechanical results.

In summary, mechanical tests on the same mature human MCL specimens before

and after targeted DS removal demonstrated that DS does not contribute to the quasi-

static tensile or shear material properties of mature human MCL. Future studies should

137

examine how DS contributes to viscoelasticity, and if other GAGs influence tissue

mechanics. By continuing to examine microstructural influence on mechanical

properties of tissue, the origins of tissue material response can be elucidated and applied

to the improvement of tissue engineering and wound healing methods. Studies seeking

to engineer replacement tissues can use the results of this study and others like it to

understand the contribution of specific molecules to the mechanics of the tissue that is

being replaced.

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strain rate," J Biomech Eng, 107(2), pp. 166-174.

CHAPTER 7

VISCOELASTIC TENSILE BEHAVIOR OF HUMAN LIGAMENT AFTER

INTERFIBRILLAR GLYCOSAMINOGLYCAN DIGESTION

Abstract

The viscoelastic properties of human ligament potentially guard against structural

failure, yet the microstructural origins of these transient behaviors are unknown.

Glycosaminoglycans (GAGs) are widely suspected to affect ligament viscoelasticity by

forming molecular bridges between neighboring collagen fibrils. This study investigated

whether GAGs directly affect viscoelastic material behavior in human medial collateral

ligament (MCL) by using non-destructive tensile tests before and after degradation of

glycosaminoglycans with Chondroitinase ABC (ChABC). Control and ChABC treatment

(83% GAG removal) produced similar alterations to ligament viscoelasticity. This

finding was consistent at different levels of collagen fiber stretch and tissue hydration.

On average, stress relaxation increased after incubation by 2.2% (control) and 2.1%

(ChABC), dynamic modulus increased after incubation by 3.6% (control) and 3.8%

(ChABC), and phase shift increased after incubation by 8.5% (control) and 8.4%

(ChABC). The changes in viscoelastic behavior after treatment were significantly more

pronounced at lower clamp-to-clamp strain levels. A 10% difference in the water content

of tested specimens had minor influence on ligament viscoelastic properties. The major

finding of this study was that mechanical interactions between collagen fibrils and GAGs

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do not affect tissue-level viscoelastic mechanics in mature human MCL. These findings

narrow the number of extracellular matrix proteins that have a direct contribution to

ligament viscoelasticity.

Introduction

The intrinsic viscoelastic behavior of ligament originates from molecular

realignments that are neither infinitely slow (elastic) or instantaneous (viscous). This

transient response may guard against structural failure. In particular, ligament stiffness

and damping properties increase at greater rates of strain [1, 2], and ligament stress

reduces with time during cyclic loading [3, 4]. These mechanisms may brake excessive

joint loads and protect against ligament fatigue failure [5]. Although such functionally

significant behaviors in ligament are well-defined, the microstructural genesis of these

transient behaviors is unknown. Determination of microstructural influence on tissue-

scale viscoelasticity could improve the innovation and evaluation of ligament treatment

modalities (e.g. tissue engineering, drug therapy).

The origins of viscoelastic material behavior in ligament are certainly related to

its organization and composition. Ligament can be described as a hydrated (~70% water)

fiber-reinforced matrix, where collagen fibers provide structural integrity to the

extrafibrillar matrix [6, 7]. Collagen fibers are formed by arrays of fibrils that in turn are

composed of aggregating tropocollagen monomers. These tropocollagen units are tightly

wound Type I collagen helices, which represent 70% of the solid phase weight [8]. The

remaining constituents include other collagens (III, V, X, XII, and XIV), extracellular

matrix proteins and proteoglycans. Theories on the viscoelastic origin in ligament and

tendon include inherent viscoelasticy of the collagen fibers [6, 9], interaction of collagen

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fibers with the extracellular constituents [10, 11] and fluid movement through the solid

phase [10, 11]. One theory that has received considerable attention concerns the

interaction between collagen fibrils and sulfated glycosaminoglycans [6, 12, 13].

Sulfated glycosaminoglycans (sGAGs) are negatively-charged polysaccharide

macromolecules that covalently bind to proteoglycan core proteins. The sGAGs in

ligament include dermatan sulfate, chondroitin sulfate (A & C), and keratin sulfate.

Dermatan and chondroitin sulfate make up over 95% of all sGAGs in ligament [14], and

are the exclusive sGAG chains of the interfibrillar proteoglycans biglycan and decorin.

Biglycan attaches to collagen fibrils through its sGAG chains [15], while decorin, which

represents ~90% of all ligament proteoglycans [16], attaches to collagen fibrils through

the regular binding of its core protein on D-period sites [17]. The sGAG chains of

biglycan and decorin span fibrils [17, 18] and are preferentially distributed orthogonal to

the fibril direction [19]. Since sGAGs have been shown to self-associate [20],

interactions between sGAGs on neighboring fibrils have the capacity to influence the

fibril sliding that is attributed with tensile stretch [6]. Although it has been shown that

interfibrillar sGAGs do not appear to influence quasi-static ligaments mechanics [21],

sGAGs may still resist transient tensile loads [13, 22]. Further, sGAGs are highly

negatively charged and through collagen fibril interactions create a fixed charge density

that influences tissue hydration [23], and potentially viscoelastic behavior [24, 25].

Experimental and theoretical studies have investigated the viscoelastic mechanical

influence of sulfated GAGs during tensile deformation. Research by Robinson et al. [26]

and Elliot et al. [7] found that tendon tail fascicles in decorin-deficient mice were less

strain-rate sensitive and experienced faster stress relaxation than those of wild type mice,

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while tendon tail fascicles in young wild type mice with elevated levels of decorin were

more strain-rate sensitive and experienced slower stress relaxation than those of wild type

mice. These results indicate that decorin deficiency is strongly associated with altered

tensile viscoelastic properties in tendon. Further, degradation of sulfated GAGs

significantly altered tensile viscoelastic properties in lung parenchymal strips [27] and in

bovine cartilage [13, 22]. No studies have directly measured the influence of sGAGs in

ligament, but theoretical studies did successfully predict viscoelastic behavior of

structurally similar tendon with models that account for sGAG-fibril interactions [6, 13].

Collectively, these previous studies have identified sGAGs as a macromolecule

likely connected to viscoelastic tensile properties in ligament. Yet, the mechanical

alterations observed in decorin-deficient mice [7, 28] were not specific to sGAGs and

experimental results in parenchymal lung and cartilage tissue may not translate to

ligament, where sGAGs are more sparsely distributed [8, 29]. Therefore, the aim of this

study was to specifically determine whether interfibrilar sGAGs influence the viscoelastic

material behavior of ligament under tension. To meet this objective, it was necessary to

control for tissue hydration and collagen fiber stretch, which have been demonstrated to

independently impact ligament viscoelasticity [2, 24, 25].

Materials and Methods

Experimental Design

The medial collateral ligament (MCL) of the human knee was chosen as a model

ligament due to a relatively high distribution of sulfated GAGs [8, 14, 30] and our well

established experimental protocol for mechanical characterization [1, 31]. Samples

extracted from MCLs were subjected to tensile loading along the fiber direction on a

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material testing system. This configuration best represents the principle loading

orientation in ligament [32]. After tensile testing was completed, samples were removed

from the material testing system and incubated in either a control or chondroitinase ABC

(ChABC) treatment. ChABC degrades chondroitin sulfate (A+C) and dermatan sulfate

without affecting other proteoglycan macromolecules [33, 34] and has been reported to

remove 98% of interfibrillar sGAGss [14]. Mechanical testing was then repeated on each

specimen to determine the treatment effect. To measure whether this treatment effect

was affected by testing parameters, strain level and buffer solution were varied to make

eight groups, with n=5 samples in each group, for a total of 40 samples.

Viscoelastic Testing

Eleven unpaired human MCLs were used for this experiment (donor age = 54±10

yrs). Six MCLs were used for viscoelastic testing at a 4% strain level and five MCLs

were used for viscoelastic testing at a 6% strain level. Knees were acquired fresh-frozen

and were allowed 16 hours to thaw prior to dissection. Knees with ligament lacerations,

surgical scars, or cartilage wear characteristic of osteoarthritis were eliminated. During

dissection, the tissue was kept moist by applying a physiological 0.9% saline buffer

solution through a nozzle. A hardened steel punch was used to extract four tensile

samples from different locations in each superficial MCL between the tibial and femoral

insertions (Figure 7.1, A) [31]. Two strips of tissue immediately adjacent to the punched

tensile sample were retained to monitor the tissue hyrdration in an unloaded stated

(Figure 7.1, B). The punch shape included beveled ends for gripping and was oriented so

that its long axis was aligned with visible fiber bundles. Black optical markers were

adhered to the narrow central third of the tensile sample using cyanoacrylate. Samples

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were loaded in the clamping assembly and width and thickness dimensions were

determined by taking an average of three measurements with digital calipers (Mitutoyo,

San Jose, CA; accuracy ±0.02 mm). Mechanical testing was performed in a custom built

testing chamber that interfaced with a heating recirculator (PolyScience, Niles, IL;

accuracy ± 0.2°C) to maintain a solution temperature of 37°C [3, 35].

The testing protocol involved a series of preconditioning loads followed by a

period of recovery and then viscoelastic testing (Figure 7.2). This testing protocol

allowed the measurement of multiple viscoelastic characteristics while not permanently

altering the elastic tissue properties. To establish a consistent reference position for all

samples, a 0.1 N preload was applied (Sensotec Inc, Columbus, OH; 1,000 g, max range

2,900 grams, accuracy 0.3g). At this reference position, clamp-to-clamp specimen length

was determined. This was calculated by averaging three measurements (Mitutoyo, San

Jose, accuracy ±0.02 mm) of an inside calipers prong-to-prong distance after insertion

between the testing clamps. To precondition the samples, the tissue was first ramped at

1.0%/sec to 8% of the reference length, and held for 5 minutes. This was immediately

followed by a triangular displacement profile applied to 8% of the reference length for

Figure 7.1: Specimen acquisition. A) Up to four specimen sets were extracted from each MCL, with three samples to each set. Each set included one punched sample for viscoelastic tensile testing (dark grey) and two adjacent strips to monitor tissue hydration (light grey). B) Photograph of the specimen set.

Tibia Insert Femur

Insert

A B

MCL

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5 min St

rain

10 min

10 min

Time

8%6% or 4%

0.1, 1, 5, 10, and 15 Hz

Figure 7.2: Diagram of the viscoelastic protocol. After preloading to 0.1 N, specimens were preconditioned. Peak stress from 10th cycle (bold) was compared after incubation to verify that protocol did not cause elastic damage. Specimens were allowed to recover for 10 minutes prior to stress relaxation and sinusoidal displacements (amplitude = 0.125% strain).

ten cycles at a strain rate of 1%/sec. The 8% strain amplitude was selected to exceed the

highest strain level experienced during the testing protocol [36], while not elastically

damaging the tissue [21]. To verify that no elastic damage occurred between pre- and

post-treatment, the peak stress of the final preconditioning cycle was recorded (Figure

7.2).

After preconditioning, the sample was allowed to recover for 10 minutes at its

reference length. The specimen was then ramped at 1%/sec to a prescribed strain level of

4% or 6% clamp-to-clamp strain and allowed to stress-relax for 10 minutes (Figure 7.2).

At a 4% strain level, the stress-strain response is still in the toe region [21] and the

collagen fibers are not completely uncrimped [37]. At a 6% strain, the stress-strain

response is in the linear region and the collagen fibers are collectively straightened [37,

38]. Testing these two strain levels permitted the assessment of sulfated GAGs at

different states of collagen and extrafibrillar matrix contribution. Following stress

relaxation, sinusoidal displacement waves (0.1, 1, 5, 10, and 15 Hz) were applied to a

0.125% strain amplitude (Figure 7.2). The 15 HZ sinusoidal oscillation corresponds to a

Precondition Rest Viscoelastic Test

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max strain-rate of ~12%/s. Since the optical tracking system recorded at a maximum of

30 HZ, the local tissue strain during 0.1 HZ oscillations was used to predict the local

strain for all sinusoidal frequencies [1]. There was an average drop of 0.6% ± 0.4% (SD)

in the equilibrium stress level between the start and completion of the entire set of

oscillations. This small drop verified that 10 minutes of stress relaxation was sufficient

to allow equilibrium to be reached.

After completing the test protocol, each sample was removed from the material

testing system while still mounted in the clamps. The entire specimen and clamp

assembly was bathed for one hour at room temperature in the buffer solution (detailed in

the next section) with protease inhibitors (1 tablet of mini-complete per 10 ml of buffer).

This was followed by six hours of incubation in the buffer solution with or without

ChABC treatment (1.0 IU/mL, Sigma-Aldrich, Buchs, Switzerland). Following

incubation, the clamp assembly was reattached to the material testing system and

returned to the original testing position. Mechanical tests were then repeated using

parameters identical to the pre-treatment mechanical tests. Treatment and repeatability

protocols are described in greater detail in our previous publications [14, 21](Chapter. 6).

Tissue Swelling

To control tissue swelling, two testing solutions were used throughout the

experiment. One solution consisted of a physiological buffer mixture (15 ml of 20 mM

Tris pH 7.5, 150 mM NaCl, 5 mM CaCl2), and was designated the standard buffer. A

second solution was this buffer plus 7.5% polyethylene glycol (10 kDa; Sigma-Aldrich,

Buchs, Switzerland), and was designated the PEG buffer. Polyethylene glycol has been

previously used to control swelling in biological tissue [39, 40] and this concentration has

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been shown to maintain wet weight in ligament during prolonged immersion [41].

Samples were equilibrated in their respective buffer solutions for at least 2 hours prior to

pre-treatment mechanical tests. All mechanical tests and incubations were performed in

their respective buffer solutions.

Multiple techniques were employed to quantify tissue swelling during the course

of the experiment. Adjacent to each tensile sample, two strips were harvested to monitor

tissue hydration (Figure 7.1, B). One strip was weighed and immediately frozen to serve

as the time-zero control for water content. The second strip shadowed the testing

protocol of the mechanically tested specimen in an unloaded state. For example, this

sample was immersed in solution from the testing chamber during mechanical tests and

was included in the same incubation compartment as the mechanically tested sample. It

was therefore possible to assess whether the wet weight of the tissue had been altered

during mechanical testing and incubation. After the post-treatment mechanical tests,

tensile samples were excised from the clamps. Tensile samples and their adjacent strips

were then weighed, rinsed, frozen and lyophilized. Water content was calculated from

the ratio of dry weight to final wet weight (APX-60, Denver Instruments, Denver;

readability ±0.1 mg).

Verification of Sulfated GAG Removal

The efficacy of the ChABC treatment was determined by using

dimethylmethylene blue assays to first measure the concentration of sulfated GAGs in

papain digested samples before and after re-treatment with ChABC [21, 27]. The

percentage of non-degraded sGAGs in ChABC incubated samples was estimated by

subtracting the amount of sGAGs (µg of sGAG / mg of dry weight) in the papain digested

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sample from the sGAGs in the same sample after additional ChABC treatment. This

value, which represents the amount of sGAGs unsuccessfully digested during incubation,

was divided by the amount of sGAGs native to the sample. Native sGAG estimates were

calculated by averaging the amount of sGAGs in all the time-zero control specimens.

Since ChABC does not degrade keratin or heparin sulfate, this native sGAG estimate was

first reduced by the amount of sGAGs in the time-zero control after ChABC treatment.

An approximation of the efficacy of ChABC could thus be attained, along with the

percentage of sGAGs that could not be degraded by ChABC.

Data Reduction and Statistical Analysis

To generate stress-strain curves, the first Piola-Kirchhoff stress was determined

with tissue engineering strains approximated from the digital camera data ((l-lo) / lo,

where l is the current length and lo is the reference length). The stress–time curves from

the stress relaxation tests were normalized by the peak stress to obtain reduced relaxation

curves [42]. The cyclic strain–time and stress–time data from the final four cycles of

each frequency were fit to a four-parameter sine function in Matlab:

02sin ty y Abπ φ⎛ ⎞= + +⎜ ⎟

⎝ ⎠ (1)

Here, y and t represent the strain (or stress) and time data, respectively, y0 represents the

equilibrium strain (or stress) level and A denotes the amplitude of the sine wave. φ

represents the phase and f denotes the frequency (Hz). The final four cycles of each

frequency were chosen as input to give a sufficient number of preconditioning cycles,

while maintaining an excellent fit (average r2 = 0.998 ± 0.002). The fit parameters were

not significantly altered when the final two cycles were substituted as input (data not

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shown). Dynamic modulus M (MPa) and phase shift φ (radians) were calculated for all

frequencies:

; = AMAσ

σ εε

φ φ φ= − (2)

Aσ and Aε denote amplitudes of the cyclic stress–time and strain– time data, respectively,

while φσ and φε denote the corresponding phase angles [43].

Statistical analysis was performed in four parts. First, a repeated measures design

was used to determine the effect of incubation and frequency on material properties for

each of the eight test groups. The effect of incubation on peak stress, stress relaxation,

average dynamic modulus, and average phase shift was assessed using paired t-tests with

pre- and post-treatment data. The effect of frequency on dynamic modulus and phase

shift, along with factor interaction between frequency and time, was assessed using

repeated measures ANOVA with two within-subject factors (frequency, time), with

Bonferoni adjusted pair-wise comparisons to measure significance between levels.

Second, the effect of treatment, buffer solution and strain-level on mechanical changes

due to incubation was assessed using ANCOVA, by controlling for pre-treatment results,

with Bonferroni adjustment for multiple comparisons. Third, to determine whether the

pre-treatment material properties were different between the eight test groups, ANOVA

analysis was used with factors of treatment, buffer solution and strain-level. Lastly,

biochemistry results were assessed using independent t-tests to measure treatment effect

on sGAG content. A power analysis demonstrated that a sample size of 5 was sufficient

to minimally detect a 20% change in all measured mechanical properties with 80%

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confidence (Power = 0.80). Significance was set to p≤0.05, and all results are reported

with standard error unless otherwise noted.

Results

Reduced Relaxation Data

The reduced relaxation curves were unaffected by incubation for all combinations

of treatments, buffer solutions and strain-levels (Fig. 7.3, Table 7.1). The percent

relaxation for all tests was 30.0 ± 1.0% before incubation and 30.6 ± 1.0% after

incubation. The reduced relaxation of all samples tested at the lower strain-level, 31.8 ±

1.0%, was significantly greater than at the higher strain-level, 28.1 ± 1.0% (p=0.01). The

Table 7.1: Mechanical properties for all eight test groups (n=5) before and after treatment. SEM – “Standard error of the mean” for paired differences. Bolded SEM values represent statistically significant differences between related pre- and post-treatment mechanical properties (p<0.05).

4% Strain Level 6% Strain Level Standard buffer PEG Buffer Standard buffer PEG Buffer

Pre-Treat

Post-Treat SEM Pre-

Treat Post-Treat SEM Pre-

Treat Post-Treat SEM Pre-

Treat Post-Treat SEM

Control Treat

Avg. Peak Stress (MPa) 5.3 5.4 (0.05) 5.5 5.8 (0.11) 6.8 6.7 (0.11) 9.6 9.9 (0.15)

Avg. Stress Relax (%) 36.1 36.6 (0.9) 29.4 31.1 (1.0) 28.1 28.4 (0.3) 31.0 31.2 (0.6)

Avg. Dynamic Mod (MPa) 176 181 (4.6) 264 280 (8.5) 485 501 (2.3) 758 786 (11.7 )

Avg. Phase Shift (rad) 0.104 0.118 (0.004) 0.124 0.133 (0.004) 0.089 0.098 (0.002) 0.101 0.104 (0.002)

ChABC Treat

Avg. Peak Stress (MPa) 8.3 8.4 (0.11) 7.0 7.0 (0.11) 7.9 7.8 (0.06) 11.6 11.9 (0.09)

Avg. Stress Relax (%) 31.6 32.4 (0.8) 30.0 32.4 (1.8) 28.0 27.7 (0.4) 25.4 25.1 (0.3)

Avg. Dynamic Mod (MPa) 374 361 (24.8) 361 369 (9.9) 671 726 (23.1) 627 655 (7.4)

Avg. Phase Shift (rad) 0.106 0.120 (0.006) 0.116 0.126 (0.002) 0.091 0.098 (0.003) 0.099 0.104 (0.001)

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Figure 7.3: (top, right), and ChABC treated in either standard buffer (bottom, left) or PEG buffer (bottom, right). Legends indicate applied clamp-to-clamp strain for pre- and post-treatment results. Mean ± standard error.

Time (s)0.01 0.1 1 10 100 1000

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type of treatment and buffer solution did not affect the change in relaxation after

incubation (p=0.69 and p=0.41, respectively). However, the strain-level did indeed

influence the change in relaxation after incubation (p=0.02). The percent increase in

percent relaxation after incubation varied by 0.2% due to treatment, 3.2% due to buffer

solution (greater increase with PEG buffer), and 4.1% due to strain-level (greater increase

at a 4% strain level).

Dynamic Modulus

The average dynamic modulus (averaged over all frequencies) was significantly

affected by incubation in only two of the eight test groups (Fig. 7.4, Table 7.1). These

groups were both at a 6% clamp-to-clamp strain and had an average increase in dynamic

modulus of 4.0 ± 1.1% after treatment. The average dynamic modulus for all specimens

at 0.1 Hz was 424 ± 48 MPa before incubation and 434 ± 50 after incubation, while

average dynamic modulus at 15 Hz was 501 ± 55 before incubation and 522 ± 59 after

incubation. The samples tested at the higher strain level had a dynamic modulus 226%

greater than the lower strain level (p<0.001). Frequency only had a significant effect on

dynamic modulus for the two test groups control treated in standard buffer. The

frequency effect on dynamic modulus was not influenced by incubation. The type of

treatment, buffer solution, and strain-level did not affect the change in dynamic modulus

between pre- and post-treatment (p=0.86, p=0.20 and p=0.96, respectively). The percent

increase in dynamic modulus after incubation only varied by 0.3% due to treatment, 0.1%

due to buffer solution, and 4.2% due to strain-level (greater increase at the 6% strain-

level).

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Figure 7.4: Dynamic modulus as a function of oscillatory frequency for control treated in either standard buffer (top, left) or PEG buffer (top, right), and ChABC treated in either standard buffer (bottom, left) or PEG buffer (bottom, right). Legends indicate applied clamp-to-clamp strain for pre- and post-treatment results. Mean ± standard error.

Frequency (Hz)0.1 1 10

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Phase Shift

The average phase shift (averaged over all frequencies) was significantly affected

by incubation in four of the eight test groups (Fig. 7.5, Table 7.1). Groups significantly

affected had an increase in phase shift of 9.4 ± 2.6%, while groups not significantly

affected had an increase in phase shift of 7.5 ± 0.8%. The average phase shift for all

specimens at 0.1 Hz was 0.062 ± 0.004 radians before incubation and 0.069 ± 0.004

radians after incubation, while at 15 Hz was 0.155 ± 0.004 radians before incubation and

0.169 ± 0.005 radians after incubation. The average phase shift at the 4% strain-level,

0.114 ± 0.003 radians, was significantly greater than at the 6% strain-level, 0.095 ± 0.003

radians (p<0.001). Additionally, the average phase shift in PEG buffer, 0.111 ± 0.003,

was significantly greater than in standard buffer, 0.098 ± 0.003 radians (p=0.004).

Frequency had a significant effect on phase shift for all eight test groups. The frequency

effect on phase shift for all eight groups was not influenced by incubation. The type of

treatment and buffer solution did not affect the change in phase shift after incubation

(p=0.98 and p=0.32, respectively). The strain-level, however, did significantly influence

the change in phase shift after incubation (p=0.02). The percent increase in phase shift

after incubation varied by 0.1% due to treatment, 5.2% due to buffer solution (greater

increase in standard buffer), and 5.3% due to strain-level (greater increase at a 4% strain-

level).

Tissue Swelling

The wet weights of the unloaded samples were normalized to their initial weight

and graphed with respect to discrete measurement points during testing (Figure 7.6). On

average, the wet weight of unloaded samples increased by 18 ± 2% when tested in

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Figure 7.5: Phase shift as a function of oscillatory frequency for control treated in either standard buffer (top, left) or PEG buffer (top, right), and ChABC treated in either standard buffer (bottom, left) or PEG buffer (bottom, right). Legends indicate applied clamp-to-clamp strain for pre- and post-treatment results. Mean ± standard error.

Frequency (Hz)0.1 1 10

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0.20ChABC Treatment – Standard Buffer ChABC Treatment – PEG Buffer

Control Treatment – PEG Buffer Control Treatment – Standard Buffer

4% Pre-Treatment C4% Post-Treatment 6% Post-Treatment

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standard buffer and decreased by 11 ± 2% when tested in PEG buffer. The unloaded

samples tested in standard buffer had a significantly greater wet weight than those tested

in PEG buffer (p<0.001). There was no effect of treatment on the overall normalized wet

weight (p=0.68). During the incubation period, the average wet weight in the unloaded

samples decreased by 1.2 ± 1.7% (p=0.48) in the standard buffer and increased by 3.2 ±

1.4% (p=0.08) in the PEG buffers. The greatest change during the incubation period was

a 4.5 ± 2.8% decrease in wet weight in samples treated with ChABC in standard buffer

(p=0.15).

The native water content was consistent between treatment and buffer solution

groups, with an average range from 71.6% to 73.1% (Figure 7.7). All tested samples had

significantly different water content than the native samples, with the exception of the

mechanically loaded samples tested in standard buffer (average water content = 72.3,

p=0.24). Compared to the native samples, unloaded samples incubated in the PEG buffer

had a significantly decreased water content, and unloaded samples incubated in standard

buffer had a significantly increased water content (p<0.001 and p<0.001, respectively).

There was no effect of treatment or strain-level on water content in incubated samples

(p=0.29 and p=0.52, respectively), although in samples incubated in standard buffer, the

ChABC treated samples had 2.2% less water content than control treated samples. The

mechanically loaded samples had 2.5% less water content than the unloaded samples

(p=0.002).

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Figure 7.6: Time history of the unloaded samples wet weight through the course of the experiment. Wet weight was normalized to the initial weight of the unloaded sample immediately after dissection. All samples equilibrated in buffer solution for at least 2 hours before pre-treatment test. The 4% and 6% strain-level groups were combined. Figure 7.7: Water content of the time-zero reference samples (native), the incubated samples that were not mechanically tested (unloaded), and the incubated samples that were mechanically tested (loaded). Data from 4% and 6% strain-levels were combined.

Incubation Pre-trt Test

Post-trt Test

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Experimental Repeatability and Efficacy

Repeatability of the pre-treatment mechanical tests was confirmed by optically

measuring post-treatment clamp positions to be within 0.03 ± 0.01 mm of the pre-

treatment clamp positions. To verify that the mechanical testing protocol did not

elastically damage the specimens, a comparison was made between pre-treatment and

post-treatment peak stress during the last preconditioning cycle (Table 1). For all

treatment, buffer solution and strain level combinations, incubation affected the average

peak stress by less than 5%. All changes to the peak stress after incubation were not

significant, with the exception of the group treated with ChABC in PEG buffer solution

at a 6% strain-level, which had a significant increase of only 2.7 ± 0.8% (Table

1)(p=0.03). A qualitative comparison validated that the 4% and 6% clamp-to-clamp

strains were indeed in the toe and linear stress-strain regions, respectively (data not

shown). This comparison was made by superimposing the 4% and 6% clamp-to-clamp

strains on the final cycle of their respective 8% clamp-to-clamp preconditioning loads.

The efficiency of ChABC digestion of sGAGs was dependent on the buffer

solution. ChABC treatment of the time-zero reference samples removed 90 ± 6% (SD) of

sulfated GAGs. The time-zero reference samples had 4.2 ± 0.4 and 4.4 ± 0.5 µg sulfated

gag / mg dry tissue in standard and PEG buffer groups, respectively. Samples that were

mechanically tested in the standard buffer and treated with ChABC had an average of 0.7

µg sulfated gag / mg dry tissue at the end of testing, a 91.8% reduction from the native

reference. Samples that were mechanically tested in the PEG buffer and treated with

ChABC had an average of 1.6 µg sulfated gag / mg dry tissue at the end of testing, a

68.4% reduction from the native reference. The sulfated GAG reduction in mechanically

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tested samples treated with ChABC was significantly less in the PEG buffer compared to

the standard buffer (p=0.03). The native samples had on average 20% more sulfated

GAGs than the unloaded samples that endured the lengthy testing protocol (p=0.23).

Discussion

The aim of this research was to determine the specific influence of interfibrillar

sGAGs on ligament viscoelasticity. Viscoelastic properties were measured before and

after incubation in either control or ChABC treatments. Control and ChABC treatments

had no effect on stress relaxation and strain-rate dependent behavior, and moderately

increased dynamic modulus and phase shift. Testing in either control or ChABC

treatment did not influence any of the observed viscoelastic changes after incubation.

This was consistent at different levels of collagen fiber stretch and tissue hydration.

Therefore, this study concludes that mechanical interactions between collagen fibrils and

interfibrillar sGAGss do not affect tissue-level viscoelastic mechanics in human MCL.

The mechanical property most impacted by incubation was phase shift. Phase

shift, which quantifies energy dissipation, increased by 8.4% in control treated samples

and 8.5% in ChABC samples. Although this increase was only significant in half the

tested groups (table 1), it was observed in 35 of the 40 tested samples. A similar time-

dependent effect occurs in articular cartilage. Cartilage tested after control-treated

incubation exhibited greater creep [22] and phase shift [44] than cartilage tested

immediately upon dissection. This effect may tie into the observed relationship between

strain-level and changes in viscoelastic properties after incubation. Samples tested at a

4% strain level were more apt to dissipate energy after incubation than samples tested at

the 6% strain level. This would indicate a time-dependent degradation of structures or

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networks that provide elastic function at low-strain rates, such as elastin [45].

Interestingly, in our final preliminary studies with the same test procedure (Fig. 2), the

phase shift increased by only 1.4 ± 3.3% after incubation (n=4). The only deviation in

the preliminary protocol was that tests were conducted on specimens that had been

thawed and refrozen multiple times. Therefore, this ex-vivo loss in energy storage

appears to equilibrate in time.

Although the specific contribution of sGAGss on viscoelastic properties has not

been tested previously in ligament or tendon, it has been examined in other connective

tissues. Enyzmatic degradation with ChABC has affirmed that sGAGS moderately

control the kinetics of the viscoelastic response in cartilage through sGAG-collagen

interactions [22, 44, 46, 47]. Based on the negligible effect of ChABC treatment on

ligament viscoelasticity, it can be concluded that sGAGs do not physically provide the

functional integrity in ligament that they do in cartilage. This may be due to the low

concentrations of sGAGs in ligament (<1% dry weight) relative to cartilage (15-30% dry

weight), and the differences in anisotropy and collagen organization. It is important to

note that although sGAGs did affect viscoelasticity in cartilage under tension and

compression, collagen is a more significant determinant of cartilage viscoelastic

properties than sGAG concentration [46]. Al Jamal et al. [27] used a repeated measures

design with ChABC on parenchymal lung tissue to show that dermatan and chondroitin

sulfate removal resulted in increased hysteresis. Compositional and structural differences

between ligament and lung tissue may again account for the conflicting results.

Additionally, the paranchymal lung study was unable to reproduce material properties

with the control group, which complicates their data interpretations.

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The primary function of ligament is to resist tensile loads. It is becoming clear

that interfibrillar sGAGs do not directly support this function, although they likely have

an indirect effect by modulating collagen fibrillogenesis [48, 49]. This inference is

supported by our previous study, which showed that sGAGs have no effect on ligament

quasi-static material behavior [14] and in other studies that examined decorin-deficiency.

Mice knockout studies identified decorin as a proteoglycan that influences elastic and

viscoelastic tensile behavior in tendon [7, 28]. Based the results of the present study, it

appears that these mechanical alterations were due to compensatory or developmental

abnormalities intrinsic to decorin deficient mice. For instance, histological studies have

shown decorin-deficiency to cause irregularly sized and spaced fibrils, which is likely

caused by the absence of interfibrillar GAGs that normally inhibit lateral fibril fusion

[50]. Although tendon and ligament have unique histological and biochemical

characteristics, they also exhibit gross compositional similarities and ligaments have

higher GAG concentrations than tendons [8]. Therefore, it is appropriate to extend the

results of the present study to tendon. Finally, the results of the present study are only

applicable to tensile loads, and it is still possible that sGAGs physically resist

compression in mature human ligament. Sulfated GAG-fibril networks have been shown

to resist compressive stresses by retarding fluid exudation [51], and the sGAG

concentrations in ligament are highest near the insertion sites, which experience the

highest compressive stresses [14, 30, 52].

The experimental protocol provided reproducible results and material properties

consistent with the literature. The protocol incorporated a repeated measures design to

reduce the inter- and intra-specimen variability that has been observed mechanically and

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chemically in ligament [21]. To test the reproducibility of the protocol, a quantitative

comparison of peak stress values was made to confirm that pre-treatment mechanical

tests did not damage the sample and cause a reduction in post-treatment mechanical

behaviors. Pre-treatment and post-treatment peak stress values were indeed verified to be

within 5% for all test groups. Several protocol revisions were required to achieve this

consistency. The viscoelastic results are consistent with previous research that defined

the viscoelastic properties of human MCL [1]. Variations in phase shift between these

studies may be due to different testing environments (fluid chamber versus humidity

chamber [1]). Since specimens were extracted from four distinct regions in the MCL, the

material properties and conclusions of this study are representative of the longitudinal

(proximal and distal) and oblique fiber zones of the superficial MCL.

Incubation in ChABC successfully removed the interfibriller sGAGs, chondroitin

and dermatan sulfate. In standard buffer, ChABC treated samples had a 92% reduction of

dermatan and chondroitin sulfates, while in PEG buffer, ChABC treated samples had a

69% reduction in chondroitin and dermatan sulfates. These degradation values are higher

or similar to those reported in other studies that used ChABC in connective tissue [27, 53,

54]. Our previous studies in human ligament used TEM imaging with cupromeronic blue

staining to determine that 80% removal of dermatan and chondroitin sulfate resulted in a

98% reduction in interfibrillar sGAGs [14]. Therefore, we are confident that the majority

of interfibrillar sGAGs were degraded. The PEG buffer significantly lessened the

effectiveness of ChABC, which is likely due to the increased viscosity of the buffer

solution and the inverse relationship between viscosity and diffusion (Stokes-Einstein

relation). ChABC will also degrade hyaluronic acid, a macromolecule that forms non-

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covalent bonds with aggrecan and is chemically similar to chondroitin sulfate. Based on

the effectiveness of ChABC in degrading hyaluronic acid [14], this acid does not appear

to influence viscoelasticity in human MCL. Biochemical assays showed that chondroitin

and dermatan sulfate represent 90% of total sGAGs in the MCL samples. The remaining

10% of sGAGs likely includes keratin sulfate and heparin sulfate. These sGAGs may

contribute to ligament viscoelasticity, but this is unlikely based on their low

concentrations and distribution near fibroblasts [55].

Tissue hydration was controlled by immersing samples in two types of treatment

buffer solutions throughout the entire testing protocol. One of the buffers included 7.5%

PEG to create a hypertonic solution that reduced tissue swelling. The philosophy behind

testing at varying states of hydration was to ensure that our results were not dependent on

a particular tissue hydration state or masked by tissue swelling. Previous research

indicated that concentrations of 0.9% saline and 7.5% PEG maintained initial wet weight

in ligament, with a 5% decrease in water content [41]. This study found that tissue

dehydration was more pronounced with these same concentrations, likely from the

addition of 5mM calcium chloride or surrounding temperature variations .

The minor effect of hydration on mechanical properties has implications for other

theoretical explanations on the origins of viscoelasticity in ligaments and tendons. Fluid

flow can contribute to viscoelasticity through solid-fluid interactions that results in

frictional drag [56, 57]. These biphasic interactions are dependent on permeability,

which is a function of sGAG concentration and water content [58]. Since sGAG

extraction and water content fluctuations had no effect on viscoelastic characteristics,

fluid flow appears to not contribute to viscoelastic effects in organized structures such as

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ligament that have low concentrations of sGAGs. Other studies have reached similar

conclusions [27, 59]. The present study, however, is limited in supporting this statement,

for two reasons. First, sulfate groups may have remained in the tissue after being cleaved

and continued to influence fluid permeability. Secondly, fluid flow mechanisms in

ligament may be insensitive to 10% fluctuations in gross water content. Future studies

that specifically examine fluid flow mechanisms in ligament through experimental or

theoretical approaches could better address this postulation.

A principle limitation of this research is that biochemical composition within the

ligaments may have been altered post-mortem. This concern is justified by research that

found freezing rabbit ligament caused significant changes in hysteresis during tensile

tests [3, 60], yet, the measured change was small and its relevance has been questioned

[3]. It is unlikely that the in-vivo conditions of the MCL were perfectly replicated in this

experiment, although every effort was made to provide a physiological testing

environment (e.g. temperature, hydration, protease inhibitors). Lastly, the prolonged

effect of sGAG deprivation was not investigated in this study.

In conclusion, this study demonstrated that mechanical interactions between

sGAGs and collagen fibrils insignificantly contribute to tissue-level viscoelastic behavior

in mature ligament. Although the origins of viscoelasticity in human ligament remains

unresolved, our findings have helped narrow the possible contributions of extracellular

matrix proteins. Future studies need to assess the inherent viscoelasticity of collagen by

determining the influence of inter- and intra-molecular collagen bonds and fibril-

associating collagens (i.e. Type XII) on transient ligament behavior. The findings of this

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study have progressed the structure-function knowledge of ligament, and are applicable

to research seeking to engineer and evaluate replacement tissues.

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postmortem storage by freezing on ligament tensile behavior," J Biomechanics, 19, pp. 399-404.

CHAPTER 8

DISCUSSION

Summary

The objective of this dissertation was to strengthen the scientific knowledge of

mechanical relationships that impact ligament function in the human knee. Two

mechanical relationships were studied in this dissertation: The first between the medial

collateral ligament (MCL) and the anterior cruciate ligament (ACL), the second between

sulfated glycosaminoglycans and collagen fibrils. This discussion will focus on

conclusions from these studies. The principle conclusions are first summarized:

• The MCL was more susceptible to damage after ACL transection. This finding

favors reconstruction of the ACL to minimize damage to interrelated ligaments.

• The ACL does not directly resist valgus torque. However, the ACL indirectly resists

valgus torques by limiting coupled anterior tibial translation during valgus rotation.

• The ACL promotes internal tibial rotation during anterior translation. This should be

considered for reconstructive surgery techniques that aim to restore ACL function.

• Sulfated glycosaminoglycans had negligible influence on tissue level mechanics of

ligament during tensile loading, and therefore do not directly support ligaments

primary function of resisting tensile loads.

• Ligament viscoelasticity was insensitive to tissue hydration, which questions the

theory that interstitial fluid flow controls the tensile time-dependent mechanics.

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The anterior cruciate ligament and medial collateral ligament have overlapping

functionality that results in a high incidence of multi-ligament injuries [1]. An

experimental and theoretical approach was used to study the inter-dependence between

these two primary knee stabilizers. Cadaveric joint kinematics and local strain

distributions upon the MCL were measured with the ACL intact and deficient for

specific loading configurations. Finite element models of the experimental tests were

generated from subject-specific geometries and kinematic measurements. Ligament

strain and joint kinematics were measured with a newly validated method of optical

tracking. For a field of view typical of cadaveric knee experiments (~190 mm), this

optical system had an accuracy of 0.04% for measuring strain and an accuracy better

than 0.07% for measuring three-dimensional joint kinematics. This optical technique

demonstrated superior accuracy and flexibility to previous methods [2, 3], and was

likely responsible for this studies improved correlation of experimental-theoretical strain

measurements (r2 = 0.95) compared to previous subject-specific studies of human knee

ligaments (r2=0.75)[4]. This optical measurement system has now been implemented in

other national labs for biomechanical experiments [5-7].

This research clarified the specific and inter-dependent function of the MCL. As

hypothesized, the MCL actively resists anterior tibial translation (ATT) and this

resistance increases in the ACL-deficient knee. ACL transection significantly increased

peak strain in the MCLs mid-longitudinal fibers from 2.9% to 5.7%. The 5.7% strain is

above the 5.2% threshold where microtrauma initiates [8]. This would indicate that the

MCL is sensitive to overuse in an ACL deficient knee. The FE model predicted peak

insertion site forces in the tibia and femur to increase after ACL transection by 54% and

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56%, respectively. The associated force values at the insertions (max=140 N) are

difficult to measure experimentally and provide parameters to evaluate fatigue

propensity in MCL reattachment surgeries and engineered replacement tissues. The FE

model also helped resolve a query on the source of strain heterogeneity in the MCL [9].

High contact gradients coincided with strain heterogeneity, while regions with consistent

bone contact had uniform strain fields. For example, the MCL substance between the

medial condyle of the tibia (high contact) and distal to the femoral insertion (low

contact) experienced elevated strain heterogeneity. Regions of uniform contact proximal

to the tibial insertion had homogenous localized strain.

The observations of this research also explicitly defined ACL function. In an

intact knee, the ACL was found to promote internal tibial rotation during anterior

translation. This “unwinding” [10] in turn reduced MCL strains along the longitudinal

parallel fibers of the superficial MCL near the femoral insertion, which is the region that

experiences the highest strains and is most prone to rupture [11]. Additionally, it is well

known that the ACL is the primary restraint to ATT, but controversy exists as to whether

the ACL is an active secondary restraint to valgus rotation when the MCL is intact [12-

15]. This study found that ACL-deficiency was non-detrimental to the MCLs ability to

restrain pure valgus rotation. The discrepancy between our results and previous reports,

in that the ACL actively resists valgus rotation [14, 15], can be logically explained. The

ACL and posterior cruciate ligament (PCL) counteract each other during valgus rotation

through respective application of posterior and anterior force on the tibia [16]. After

ACL transection, this force balance is disrupted and the tibia will slide anteriorly during

valgus rotation [15]. Since the tibia was constrained from anterior-posterior translation,

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this kinematic alteration manifested as a 121 ± 49% increase in posterior force during

peak valgus load at full knee extension. Coupled ATT thus likely explains the

previously measured ACL force response during valgus torque [15, 17]. Removing the

anterior-posterior constraint may have resulted in increased valgus rotation and MCL

strains in our study due to coupled ATT. However, based on the negligible increases in

MCL strains after ACL transection, it appears that the ACL does not directly resist

valgus torque, but serves its primary function of resisting ATT during valgus rotation.

These functional roles of the ACL should be considered when evaluating surgical

reconstructions, and may be helpful in diagnosing whether an ACL deficient patient has

a combined MCL injury.

The ability of the MCL and ACL to perform their functions of joint stabilization

is directly related to the molecular relationships that provide structural integrity. A

molecular relationship that has been widely implicated to contribute to tissue level

mechanics is between proteoglycans and collagen fibrils. This relationship has been

theoretically and experimentally shown to affect elastic and viscoelastic mechanical

behavior in ligament [18-22]. However, the sulfated glycosaminoglycans (GAG) that

would mediate this mechanical interaction have not been specifically studied.

Therefore, two experimental protocols were performed to test whether elastic and

viscoleastic material properties of ligament where affected by GAG degradation via

enzymatic treatments. A repeated measures design was utilized to afford a powerful

means of measuring treatment effect. Successful execution of these experiments

required the design and fabrication of a new material test system that utilized detailed

protocols to control experimental repeatability.

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The principle conclusion of these extensive mechanical tests was that sulfated

glycosaminoglycans have negligible influence on tissue level mechanics during tensile

loading. The degradation of interfibrillar GAGs had less than a 5% effect on almost all

mechanical properties. In comparison, removal of intermolecular collagen crosslinks in

tendon fascicles reduced peak stress by 90% [23], and removal of elastin in tendon and

aponeuroses significantly increased hysteresis [24]. Relative to these molecular

structures, it becomes quite clear that interfibrillar GAGs do not directly support

ligaments primary function of resisting tensile loads. Nonetheless, GAGs likely have an

indirect affect on tissue-level mechanics [19, 21] by modulating collagen fibrillogenesis

through inhibition of lateral fibril fusion [25].

The findings of this research are relevant to past studies. First, the results

contradict the popular theory that interfibrillar GAG interactions are responsible for

transmitting forces along discontinuous collagen fibrils [22, 26, 27], and support studies

that have predicted fibrils to be continuous [28, 29]. Additionally, the observed

insensitivity of viscoelastic material behavior to tissue hydration is inconsistent with the

theory that interstitial fluid flow [30] controls the time-dependent mechanical response

of ligament in tension. The removal of GAGs should have theoretically increased

permeability and therefore affected pressure gradients and time-dependent drag

interactions between the fluid and solid phases. This inference can be confirmed

through future experiments that measure the affect of GAG extraction on permeability

[31]. Lastly, the role of GAGs in ligament and cartilage is drastically different. In

cartilage, GAGs retard fluid flow through the porous solid phase to partially control

elastic and viscoelastic material properties in both tension and compression [32-34].

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The different mechanical roles of GAGs in ligament and cartilage may be due to the low

concentrations of GAGs in ligament (<1% dry weight) relative to cartilage (15-30% dry

weight), and the differences in anisotropy and collagen organization (Type I vs. Type

II). This body of work has expanded the structure-function knowledge of ligament and

the findings are applicable to research seeking to engineer and evaluate replacement

tissues.

Limitations and Future Work

An important limitation to the numerical analysis covered in Chapter 5, is the

inability of the material model to represent time-dependent effects. To negotiate this

limitation, it was necessary to apply quasi-static loads to the associated experimental

study, thus limiting the viscoelastic effects and permitting the finite element model to

make accurate predictions. These slow strain-rates are justified in the context of

simulating diagnostic exams, however, the applied strain-rates (1%/s) are not

appropriate for modeling ligament injury mechanisms, which occur at strain-rates in

excess of 28%/s [35]. To broaden the application of these subject-specific finite element

models, it is necessary to implement and validate a material that represents the intrinsic

viscoelastic behavior of ligament. The viscoelastic material model would have

enhanced functionality if it was physical, as opposed to phenomenological. A physical

model would not only permit further investigation into the structural mechanisms

contributing to mechanical integrity, but it would permit the study of compositional

inhomogeneities and pathologies (e.g. Ehlers-Danlos syndrome) that alter the physical

structure of ligament [36]. The concurrent validation of functional physical models with

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experiments examining structure-function relationships is a natural expansion of the

work covered in this dissertation.

Future work should immediately test the ability of a poroelastic material to

represent the time-dependent effects experimentally observed in Chapter 7. Poroelastic

constitutive equations are derived from first principles and physically represent water

transport through a porous solid medium [37]. Analytically, pressures at continuum

points are solved in addition to displacements. The pressure is a function of fluid flux

and tissue permeability. Through conservation of mass, fluid flux relates to the velocity

of the solid-fluid mixture. These relations provide a time-dependent material response.

Experimental studies support the supposition that water freely moves through the solid

phase of ligament. Hannafin and Arnoczky [38] determined that 6% of water in a canine

flexor tendon, which is compositionally similar to ligament [39], is exuded shortly after

application of small static loads. Additionally, MRI studies measured an increase in free

water molecules after tendon was exposed to axial stress, which suggests that previously

bound molecules were released [40]. In these studies, fluid transport was indicated by

higher concentrations of water molecules along the tissue periphery. The ability of

poroelastic theory to describe experimental behavior will allow conclusions to be drawn

about the solid-fluid mechanical relationship in ligament.

Preliminary studies in our lab have demonstrated that the poroelastic model is

able to accurately predict stress relaxation behavior using experimental permeability

coefficients [31] and validated bulk modulus values [4]. The poroelastic model,

however, was found to incorrectly predict how variations to strain-level and frequency

influence aspects of the mechanical response. For example, stress relaxation increased

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with strain-level, which conflicts with experimental results (Figure 7.3). Furthermore,

the poroelastic FE model incorrectly predicted a decrease in phase shift as oscillation

frequency increased, while experimentally the phase shift significantly increased

progressively at greater frequencies (Figure 7.5). This poroelastic behavior is in

agreement with a study by Ateshian et al. [41]. [41]. Ateshian et al. demonstrated that

with instantaneous loads the interstitial fluid pressure within a poroelastic model is

nearly identical to the hydrostatic pressure of an incompressible elastic material at every

point except near the fluid boundary. Hence, the poroelastic material will behave

elastically. It is important to note that the loading rate at which a poroelastic material

begins to behave elastically is dependent on permeability and bulk modulus. Alterations

to these parameters may result in model predictions that better represent experimental

behavior. This raises the question of whether the parameters used in this preliminary

study accurately represent ligament.

Experimental research supports a low bulk modulus by demonstrating that the

Poisson’s ratio (longitudinal vs. transverse) in ligament is greater than 1.5 [42]. This

high poisons ratio is indicative of significant volumetric deformation during tension,

which would require a value for bulk modulus lower than values commonly used in the

literature [4]. Furthermore, a Poissons ratio above 1.5 would indicate that fluid is

flowing out of the tissue during tension. Therefore, the model used in this preliminary

study, along with numerous studies in the literature [4, 43, 44], have been inaccurately

modeling the volumetric deformation of ligament during tensile loading. Although the

incorrect orientation of fluid flow will still model damping effects, it is not

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physiological. In the future, hyperelastic constitutive models should be emulated that

utilize strain energy functions permitting Poisson’s ratios greater than 0.5 [45].

Other inconsistencies exist between physical ligament mechanics and the

implemented poroelastic material. The permeability used in the current model is

isotropic and strain-independent. Experimentation has in fact shown that permeability is

anisotropic [30] and strain-dependent [31]. The isotropic permeability can be replaced

with an anisotropic tensor [50] that physiologically reduces permeability along the

collagen fiber direction [51]. This anisotropy should allow more realistic boundary

conditions to be applied at off-axis surfaces and will direct lateral fluid flow. The

permeability tensor can also be readily updated to be strain-dependent [52]. Due to the

high Poisson’s ratio for ligament, the permeability should decrease with tensile stress,

which could describe the experimental reduction in stress relaxation at higher strain

levels. Furthermore, based on the insensitivity of ligament viscoelastic behavior to

extraction of sulfated glycosaminoglycan macromolecules (Chapter 7), it would appear

that collagen networks mediate fluid flow and not constituents in the extrafibrillar

matrix. Overall, poroelastic theory may be an effective tool to describe ligament

material behavior and future investigations offer significant challenges and rewards.

Another principle limitation to this body of work is the in-vitro model used for

study. The structural cadaveric test employed for the MCL-ACL experiments have

inherent error associated with muscle excision, tissue swelling, chemical decay, and

motion constraints (i.e. limited degrees of freedom). For example, the removal of joint

stabilizing muscles would result in an over-estimation of the translations and rotations

associated with particular load limits. However, regardless of this over-estimation,

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ligament strains are still valid for the measured kinematics. All limitations inherent with

cadaveric models could be eliminated by using image registration to non-invasively

measure strain distribution in-vivo [49, 50]. For example, ligament strains and joint

kinematics in different population groups (e.g. normal, ACL-deficient) could be

measured with open MRI technology, which facilitates anatomical positions and joint

loads. The highly accurate data provided in this research would serve as an excellent

source for future studies that use such non-invasive methods.

In all experiments, ligament biochemical composition may have been altered

post-mortem. Although efforts were made to provide physiological testing

environments, it is unlikely that the in-vivo conditions of the MCL were perfectly

replicated. To remove this limitation, future studies of GAG interactions could be

performed on appropriate animal models [51, 52]. The observation made in Chapter 7

that viscoelastic energy dissipation is dependent on exposure time could be controlled

with this type of study. An animal model could also be used to examine the effect of

GAG degradation over long time periods. It is feasible that interfibrillar space

reductions from GAG extraction [25] could eventually cause fibril damage due to

interfibrillar friction. Lastly, gene alterations could be used to propagate interfibrillar

GAGs to determine if a certain concentration of GAGs influenced tissue mechanics.

Supplementary experiments were performed to test certain aspects of

biochemical alterations. One valid apprehension of the GAG studies was that

mechanical interaction of the GAGs is dependent on intermediary ions (e.g. calcium,

sodium) that neutralize the repulsion of negatively charged GAGs. To ensure that

calcium exudation was not masking the mechanical contributions from GAGs,

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supplementary experiments were performed. In these pilot studies, ligament tissue was

rinsed during dissection and mechanical testing with a solution that included high

concentrations of calcium (0.9% NaCl + 2mM Ca). Upon completion of testing, these

samples were soaked in normal saline (1 hr, 0.9% NaCl), retested, soaked again in the

calcium solution (1 hr) and retested. This sequential treatment minimally affected peak

stress in tensile (~2%) and shear (~4%) loading configurations. Even though these

experiments did not implicate calcium exudation as a cause of mechanical defect,

physiological calcium concentrations were always included in the testing buffer (5 mM

CaCl2). Supplementary studies were also conducted with elastase to test the sensitivity

of the testing system. Elastin was expected to contribute to the tensile response at low

strains [53]. Compared to the control group elastase treatment doubled the phase shift

and decreased the peak stress at a 4% clamp-to-clamp strain level by 35%. It is logical

that elastin provides mechanical support when fibers are crimped and loss of elastin

would reduce energy storage mechanisms. Considering the small sample size (n=2) and

lack of chemical verification of elastase efficacy and specificity, these results should be

interpreted with caution. Nonetheless, this pilot study confirmed that the testing

apparatus was sensitive to molecular alterations and it is recommended that elastin be

further investigated to quantify its contribution to the mechanical function of ligament.

Although the origins of elasticity and viscoelasticity in human ligament are

incomplete, future work can begin where this dissertation ends. First, to completely

characterize the mechanical effect of GAGs in ligament, compression and permeability

tests need to be performed. Theoretically, GAGs should contribute to compressive

stiffness [54] near insertions and articulations where compressive forces are innate. This

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theory is supported by regionally high GAG concentrations in these zones [55].

Experiments can be synchronized with an investigation of GAG influence on

permeability transverse to the fiber direction. By identifying mechanisms responsible

for resisting fluid exudation, these finding would be applicable to the poroelastic model.

Next, mounting evidence from this study and others [28, 40] suggest that the intrinsic

viscoelasticity in collagen and the fluid exudation from collagen controls the viscoelastic

response when ligament is tensioned. The effect of inter-collagen bonds on

viscoelastitcy can be examined in a rat model with β-APN [23] and the effect of intra-

collagen bonds on viscoelasticity may be tested with molecular dynamics models [56].

One postulation is that inter-collagen bonds primarily control viscoelasticity in ligament

through molecular realignments that originate from fluid interaction and tropocollagen

sliding [23].

In conclusion, continued investigations in the structure-function relationships of

ligament will drive the long-term goal of representing material behavior with physical

models and be applicable to treatment strategies. Implementing physical constitutive

relationships into finite element models may improve adaptability of the model to

anatomically distinct regions [21, 57] and facilitate representation of viscoelastic

mechanisms that guard against structural failure. Connective tissue is composed of

similar constituents that have diverse concentrations and organizations. Understanding

the akin and dissimilar functions of these constituents in specific tissues will aid

interpretations of mechanical alterations that occur from injury repair mechanisms and

disease states, as well as spur innovations in clinical treatments.

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