Biomechanics Of Knee Ligaments.pdf

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Review

Biomechanics of knee ligaments: injury, healing, and repair

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Savio L.-Y. Woo , Steven D. Abramowitch, Robert Kilger, Rui Liang

Department of Bioengineering, Musculoskeletal Research Center, University of Pittsburgh, Pittsburgh, PA, 15219, USA

Accepted 20 October 2004

Abstract

Knee ligament injuries are common, particularly in sports and sports related activities. Rupture of these ligaments upsets the

balance between knee mobility and stability, resulting in abnormal knee kinematics and damage to other tissues in and around the

joint that lead to morbidity and pain. During the past three decades, signiﬁcant advances have been made in characterizing the

biomechanical and biochemical properties of knee ligaments as an individual component as well as their contribution to joint

function. Further, signiﬁcant knowledge on the healing process and replacement of ligaments after rupture have helped to evaluate

the effectiveness of various treatment procedures.

This review paper provides an overview of the current biological and biomechanical knowledge on normal knee ligaments, as well

as ligament healing and reconstruction following injury. Further, it deals with new and exciting functional tissue engineering

approaches (ex. growth factors, gene transfer and gene therapy, cell therapy, mechanical factors, and the use of scaffolding

materials) aimed at improving the healing of ligaments as well as the interface between a replacement graft and bone. In addition, it

explores the anatomical, biological and functional perspectives of current reconstruction procedures. Through the utilization of

robotics technology and computational modeling, there is a better understanding of the kinematics of the knee and the in situ forces

in knee ligaments and replacement grafts.

The research summarized here is multidisciplinary and cutting edge that will ultimately help improve the treatment of ligament

injuries. The material presented should serve as an inspiration to future investigators.

Keywords: Biomechanics; Knee ligaments; Tissue engineering; Healing

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Anatomy, histological appearance and biochemical constituents of normal ligaments. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3. Tensile properties of ligaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1. Ligament anisotropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2. Signiﬁcant biological factors on the properties of ligaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4. Viscoelastic properties of ligaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4.1. The quasi-linear viscoelastic theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.2. Continuum based viscoelastic models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Corresponding author. Department of Bioengineering, Musculoskeletal Research Center, 405 Center for Bioengineering, 300 Technology Drive,

P.O. Box 71199, Pittsburgh, PA 15219, USA. Tel.: +14126482000; Fax: +14126882001.

E-mail addresses: ddecenzo@pitt.edu, slyw@pitt.edu (S.L.-Y. Woo).

doi:10.1016/j.jbiomech.2004.10.025

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5. Healing of knee ligaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5.1. MCLhealing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5.2. Phases of ligament healing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5.3. New animal model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6. New approaches to improve healing of ligaments—functional tissue engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6.1. Growth factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6.2. Gene transfer and gene therapy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6.3. Cell therapy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6.4. Biological scaffolds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6.5. Mechanical factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7. ACLreconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7.1. Graft function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

7.2. Graft incorporation and remodeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

8. Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1. Introduction

majority of ligament reconstructions yield good short-

term clinical results, 20–25% of patients experience

complications including instability that could progres-

sively damage other knee structures ( Aglietti et al., 1997 ;

Bach et al., 1998 ; Daniel et al., 1994 ; Jomha et al., 1999 ;

Ritchie and Parker, 1996 ; Shelbourne et al., 1995 ; Yagi

et al., 2002 ).

Thus, there has been a tremendous quest for knowl-

edge to better understand ligament injuries, healing and

remodeling in hope to develop new and improved

treatment strategies. The needs in meeting this goal

have stimulated researchers to seek new and innovative

methods of investigation. Because of the complex

biological process, it has become clear that collabora-

tions from different disciplines rather than an indivi-

dualistic approach in research must be developed. In this

review, the properties of normal ligaments, including

their anatomical, biological, biochemical and mechan-

ical properties, as well as the changes that occur

following injury will be described. The MCLwill be

used as a model because of its uniform cross-sectional

area, large aspect ratio, and propensity for healing.

Subsequently, novel functional tissue engineering meth-

odologies and some of the early ﬁndings will be

presented. The challenging problems which remain to

be solved and the potential of new treatment strategies

will be explored. In terms of ligament reconstruction, the

biomechanics of surgical reconstruction of the ACLand

the utilization of robotics technology to study some of

the key surgical parameters that affect the performance

of the replacement grafts will be reviewed. It is hoped

that these creative research approaches will inspire many

to join this course of investigation and ultimately help

improve the treatment of ligament injuries.

Injuries to knee ligaments are very common. It has

been estimated that the incidence could be at 2/1000

people per year in the general population ( Miyasaka et

al., 1991 ) and a much higher rate for those involved in

sports activities ( Bruesch and Holzach, 1993 ). Ninety

percent of knee ligament injuries involve the anterior

cruciate ligament (ACL) and the medial collateral

ligament (MCL) ( Miyasaka et al., 1991 ). In fact, recent

studies have documented that ACLinjuries in females

are reaching epidemic proportions with the frequency of

rupture more than 3 times greater than that of their male

counterparts ( Anderson et al., 2001 ; Arendt and Dick,

1995 ; Powell and Barber-Foss, 2000 ). The results of

ligament injuries can be devastating. Frequently, surgery

is required, but the outcomes are variable. Further,

post-surgical rehabilitation could require an extended

absence from work or athletic competition.

Basic science and clinical studies have revealed that a

ruptured MCLcan heal spontaneously ( Frank et al.,

1983 ; Indelicato, 1983 ; Jokl et al., 1984 ; Kannus, 1988 ).

However, laboratory studies have shown that its

ultrastructure and biochemical composition remain

signiﬁcantly altered ( Frank et al., 1983 ; Niyibizi et al.,

2000 ; Weiss et al., 1991 ). Furthermore, the mechanical

properties of the ligament substance remain substan-

tially inferior to those of normal ligaments even after

years of remodeling ( Loitz-Ramage et al., 1997 ; Ohland

et al., 1991 ). On the other hand, midsubstance tears of

the ACLand posterior cruciate ligament (PCL) would

not heal spontaneously and surgical reconstruction

using a replacement graft is often required ( Hirshman

et al., 1990 ; Kannus and Jarvinen, 1987 ). While the

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2. Anatomy, histological appearance and biochemical

constituents of normal ligaments

bone

Ligaments are composed of closely packed collagen

ﬁber bundles oriented in a parallel fashion to provide for

stability of joints in the musculoskeletal system. The

major cell type is the ﬁbroblast and they are interspersed

in the parallel bundles of collagen.

In the human knee, the MCLis approximately 80mm

long and runs from the medial femoral epicondyle

distally and anteriorly to the posteromedial margin of

the metaphysis of the tibia. The lateral collateral

ligament (LCL) originates from the lateral femoral

epicondyle and passes postero-distally to the top of the

ﬁbular head. The cruciate ligaments, which are named

anterior and posterior according to their site of

attachment to the tibia, are located within the capsule

and cross each other obliquely. The anterior cruciate

ligament (ACL) arises from the anterior part of the

intercondylar eminentia of the tibia and extends to

the posterolateral aspect of the intercondylar fossa of

the femur. The posterior cruciate ligament (PCL) arises

from the posterior part of the intercondylar eminentia of

the tibia and passes to the anterolateral aspect of the

intercondylar fossa of the femur. Although morpholo-

gically intraarticular, the cruciate ligaments are sur-

rounded by a synovial layer. The ACLconsists of two

bundles, an anteromedial (AM) and a posterolateral

(PL) bundle. The AM bundle is thought to be important

as a restraint to anterior–posterior translation of the

knee, while the PLbundle is thought to be an important

restraint to rotational moments about the knee ( Yagi

et al., 2002 ). This anatomic division of these bundles is

based on the gross tensioning pattern of the ACLduring

passive ﬂexion-extension of the knee, with the AM

bundle being tauter in ﬂexion and the PLbundle tauter

in extension. The PCLis also composed of two distinct

bundles, the antero-lateral (AL) and the postero-medial

(PM) bundle. Additionally, ligaments are sometimes

found anterior and posterior to the PCLin some people.

They are the anterior meniscofemoral ligament (MFL;

i.e. ligamentum Humphrey) and the posterior menisco-

femoral ligament (i.e. ligamentum Wrisberg) ( Girgis

et al., 1975 ).

Generally, ligaments are inserted to bone in two ways;

direct and indirect ( Fig. 1 ). For direct insertions (e.g. the

femoral insertion of MCL), ﬁbers attach directly into

the bone and the transition of ligament to bone occurs in

four zones: ligament, ﬁbrocartilage, mineralized ﬁbro-

cartilage and bone ( Woo et al., 1987 ). For an indirect

insertion (e.g. the tibial insertion of MCL) superﬁcial

ﬁbers are attached to periosteum while the deeper ﬁbers

are directly attached to the bone at acute angles ( Woo

et al., 1987 ). The tibial insertion of the MCLcrosses the

epiphyseal plate so that it can be lengthened in

synchrony with the bone growth.

mineralized

fibrocartilage

ligament

(A)

deep fibers

bone

superficial

fibers

connects to

periosteum

(B)

Fig. 1. (A) Photomicrograph demonstrating direct insertion, i.e. the

femoral insertion of rabbit medial collateral ligament (MCL). (B)

Photomicrograph demonstrating indirect insertion, i.e. the tibial

insertion of rabbit MCL. (Hematoxylin and eosin, x50) (permission

requested from ( Woo et al., 1987 )).

Between 65 and 70% of a ligament’s total weight is

composed of water. On a fat-free basis, Type I collagen

is the major constituent (70–80% dry weight) and is

primarily responsible for a ligament’s tensile strength.

Type III collagen (8% dry weight) and Type V collagen

(12% dry weight) are other major components ( Birk and

Mayne, 1997 ; Linsenmayer et al., 1993 ). Collagen Types

II, IX, X, XI, and XII have also been found to be

present ( Fukuta et al., 1998 ; Niyibizi et al., 1996 ;

Sagarriga Visconti et al., 1996 ).

Variations in the concentrations of these basic

constituents lead to a diverse array of mechanical

behaviors of knee ligaments that are suitable for their

respective functions. A comparative study showed that

the tangent modulus and tensile strength of the rabbit

MCLis higher than the ACL( Woo et al., 1992 ) which

correlates with a larger mean ﬁbril diameter for the

MCL( Hart et al., 1992 ). In addition, the ﬁbroblasts of

the MCLare more spindle shaped ( Lyon et al., 1991 )

and produce a higher level of procollagen type I mRNA

( Wiig et al., 1991 ) and a lower collagen type III to type I

ratio in culture ( Ross et al., 1990 ). Further, mechanical

loading has been found to regulate the gene expression

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of collagens in ligaments ( Hsieh et al., 2002 ). Therefore,

each ligament’s composition is directly correlated with

its mechanical properties.

the human ACLwas larger than that for the PLbundle

( Butler et al., 1992 ). In a separate study, the mechanical

properties of the bundles of the human PCLwere found

to be different as well ( Harner et al., 1995 ). The tangent

modulus of the ALbundle (294

115MPa) was almost

twice that of the PM bundle (150

3. Tensile properties of ligaments

69MPa). The fact

that different bundles have different properties suggests

that each bundle contributes to knee joint stability

differently, which may have important ramiﬁcations on

their replacements ( Table 1 ).

Ligaments are best suited to transfer load from bone

to bone along the longitudinal direction of the ligament.

Thus, their properties are commonly studied via a

uniaxial tensile test of a bone–ligament–bone complex

(e.g. femur-MCL-tibia complex). These tests result in a

load–elongation curve that is non-linear and concave

upward. This enables ligaments to help to maintain

smooth movement of joints under normal, physiologic

circumstances and to restrain excessive joint displace-

ments under high loads. The parameters describing the

structural properties of the bone–ligament–bone com-

plex include stiffness, ultimate load, ultimate elongation,

and energy absorbed at failure. With cross-sectional

area and strain measurements, a stress–strain curve

representing the mechanical properties (quality) of the

ligamentous tissue can be obtained. The parameters

describing the mechanical properties of the ligament

substance include tangent modulus, ultimate tensile

strength, ultimate strain, and strain energy density. A

large number of experimental methods have been

employed by investigators to overcome some of the

technical difﬁculties encountered in measuring the

mechanical properties of ligaments ( Beynnon et al.,

1992 ; Ellis, 1969 ; Lam et al., 1992 ; Lee and Woo, 1988 ;

Peterson et al., 1987 ; Peterson and Woo, 1986 ; Smutz et

al., 1996 ). Furthermore, environmental factors can also

cause large differences in the experimental data obtained

( Crowninshield and Pope, 1976 ; Figgie et al., 1986 ;

Haut, 1983 ; Haut and Powlison, 1990 ; Noyes et al.,

1974 ). For more information on these methodologies

and environmental factors, the readers are encouraged

to read the provided references and study the chapter

entitled: Biology, Healing and Repair of Ligaments in

Biology and Biomechanics of the Traumatized Synovial

Joint: The Knee as a Model, 1992 by the authors ( Woo

et al., 1992 ).

An equally important consideration is the geometry of

the ligament. Unlike the MCLwhose cross-section is

relatively uniform over its length, the ACLand PCL

have two functionally distinct bundles that are loaded

non-uniformly ( Fuss, 1989 ; Girgis et al., 1975 ; Sakane et

al., 1997 ). Thus, they need to be separated in order to

have a specimen with a more uniform cross-sectional

area for tensile testing. Using this approach, a study

performed at our center showed the tangent modulus of

a section of the rabbit ACL(516

3.1. Ligament anisotropy

Ligaments are three dimensional (3-D) anisotropic

structures. To describe the 3-D mechanical behavior of

the human MCL, investigators have developed a quasi-

static hyperelastic strain energy model based on the

assumption of transverse isotropy ( Quapp and Weiss,

1998 ). The total strain energy, W, in response to a

stretch along the collagen ﬁber direction, l; was deﬁned

to be equal to the sum of the strain energy resulting from

ground substance (F 1 ), collagen ﬁbers (F 2 ), and an

interaction component (F 3 ),

W ðI 1 ; I 2 ; lÞ¼F 1 ðI 1 ; I 2 ÞþF 2 ðlÞþF 3 ðI 1 ; I 2 ; lÞ (1)

where I 1 and I 2 are invariants of the right Cauchy stretch

tensor. For a uniaxial tensile test, F 1 was described with

a two coefﬁcient Mooney–Rivlin material model

F 1 ¼ 1=2½C 1 ðI 1 3ÞþC 2 ðI 2 3Þ; (2)

where C 1 and C 2 are constants, and F 2 was described by

separate exponential and linear functions. F 3 was

assumed to be zero.

The Cauchy stress, T, can then be written as

T ¼ 2fðW 1 þ I 1 W 2 ÞB W 2 B 2 gþlW l aaþ r1; (3)

where, B is the left deformation tensor, and W 1 , W 2 ,and

W l are the partial derivatives of strain energy with

respect to I 1 , I 2 , and l; respectively. The unit vector ﬁeld,

a, represents the ﬁber direction in the deformed state,

and r is the hydrostatic pressure required to enforce

incompressibility.

It was found that this constitutive model can ﬁt both

the data obtained from longitudinal and transverse

dumbbell shaped specimens cut from the human MCL

Table 1

Values for tangent modulus of the human MCL( Quapp and Weiss,

1998 ), AM and PLbundles of the human ACL( Butler et al., 1992 ),

and ALand PM bundles of the PCL( Harner et al., 1995 ).

Tangent modulus (MPa)

64MPa) was less than

half of that for the rabbit MCL(1120

Human MCLHuman ACL

Human PCL

153MPa) ( Woo

et al., 1992 ). Further, the tangent modulus, tensile

strength, and strain energy density of the AM bundle in

332

283

114 154

120 294

115 150

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Transverse

Decrease

Stress

Increase

Stress

Longitudinal

Immobilization

Normal

Activity

Exercise

Strain (%)

In-vivo Loads and Activity Levels

Fig. 2. Stress–strain curves for human MCLs longitudinal and

transverse to the collagen ﬁber direction (permission requested from

Quapp and Weiss (1998) ).

Fig. 3. A schematic diagram describing the homeostatic responses of

ligaments and tendons in response to different levels of stress and

motion (permission requested from ( Woo et al., 1987 )).

( Fig. 2 ). The longitudinal specimens displayed a tangent

modulus of 332.2

58.3MPa and a tensile strength of

Based on the results of these and other related studies,

a highly non-linear representation of the relationship

between different levels of stress and ligament properties

is depicted in Fig. 3 . The normal range of physiological

activities is represented by the middle of the curve.

Immobilization results in a rapid reduction in tissue

properties and mass. In contrast, long term exercise

resulted in a slight increase in mechanical properties as

compared with those observed in normal physiological

activities.

Skeletal maturity also causes signiﬁcant changes

to ligaments whereby the stiffness and ultimate load

of the FMTC was shown to increased dramatically

from 6 to 12 months of age followed by insigniﬁcant

change from 1 to 4 years in the rabbit model ( Woo et al.,

1990 ). This corresponded with a change in failure

mode from the tibial insertion to the midsubstance

reﬂecting closure of the tibial epiphysis during matu-

ration ( Woo et al., 1986 ). On the other hand, the

human FATC demonstrated a signiﬁcant decrease in

the stiffness and ultimate load with increasing age

( Noyes and Grood, 1976 ; Woo et al., 1991 ). There-

fore, each ligament is unique in its growth, development,

and aging. Investigators should be cautious when

extrapolating age related changes from one ligament

(ex. ACLto PCL) or species (ex. rabbit to human) to

another.

4.8MPa, while the transverse specimens were an

order of magnitude lower with a tangent modulus of

11.0

0.9MPa and tensile strength of 1.7

0.5MPa

( Quapp and Weiss, 1998 ).

3.2. Signiﬁcant biological factors on the properties of

ligaments

The effects of immobilization and exercise on the

mechanical properties of ligaments has been investigated

by a number of laboratories ( Larsen et al., 1987 ;

Newton et al., 1990 ; Noyes, 1977 ; Woo et al., 1987 ).

When rabbit hind limbs were subjected to a few weeks of

immobilization, there were marked decreases in the

structural properties of the femur–MCL–tibia complex

(FMTC). These decreases occurred due to subperiosteal

bone resorption within the insertion sites, as well as

microstructural changes in the ligament substance.

Remobilization was found to reverse these negative

changes. However, up to one year of remobilization was

required for the properties of the ligament to return to

normal levels following 9 weeks of immobilization ( Woo

et al., 1987 ). Similar results were found for the

femur–ACL–tibia complex (FATC) of primates and

rabbits ( Newton et al., 1990 ; Noyes, 1977 ). Long periods

of exercise training, on the other hand, only showed

marginal increases in the structural properties of

ligaments with a 14% increase in linear stiffness of the

FMTC and a 38% increase in ultimate load/body weight

( Laros et al., 1971 ; Woo et al., 1982, 1979 ). There was

only a slight change in the mechanical properties of the

ligament substance.

4. Viscoelastic properties of ligaments

The complex interactions of collagen with elastin,

proteoglycans, ground substance, and water results in

the time- and history-dependent viscoelastic behaviors

of ligaments. In response to various tensile loading

38.6

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