cartilage

66 Biomechanics of Cartilage JOSEPH M. MANSOUR, PH.D. COMPOSITION AND STRUCTURE OF ARTICULAR CARTILAGE . . . . . . . . . . . . . . . . . . . . . . .68 MECHANICAL BEHAVIOR AND MODELING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68 MATERIAL PROPERTIES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69RELATIONSHIP BETWEEN MECHANICAL PROPERTIES AND COMPOSITION . . . . . . . . . . . .72 MECHANICAL FAILURE OF CARTILAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 JOINT LUBRICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 MODELS OF OSTEOARTHROSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77 The materials classed as cartilage exist in various forms and perform a range of functions in the body. Depending on its composition, cartilage is classified as articular cartilage (also known as hyaline), fibrocartilage, or elastic cartilage. Elastic cartilage helps to maintain the shape of structures such as the ear and the trachea. In joints, cartilage functions as either a binder or a bearing surface between bones. The annulus fibrosus of the intervertebral disc is an example of a fibrocartilaginous joint with limited movement (an amphiarthrosis). In the freely moveable synovial joints (diarthroses) articular cartilage is the bearing surface that permits smooth motion between adjoining bony segments. Hip, knee, and elbow areexamples of synovial joints. This chapter is concerned with the mechanical behavior and function of the articular cartilage found in freely movable synovial (diarthroidal) joints. In a typical synovial joint, the ends of opposing bones are covered with a thin layer of ar- ticular cartilage (Fig. 5.1). On the medial femoral condyle of the knee, for example, thecartilage averages 0.41 mm in rabbit and 2.21 mm in humans [2]. Normal articular carti- lage is white, and its surface is smooth and glistening. Cartilage is aneural, and in normal mature animals, it does not have a blood supply. The entire joint is enclosed in a fibrous tissue capsule, the inner surface of which is lined with the synovial membrane that se- cretes a fluid known as synovial fluid . A relatively small amount of fluid is present in a normal joint: less than 1 mL, which is less than one fifth of a teaspoon. Synovial fluid is clear to yellowish and is stringy. Overall, synovial fluid resembles egg white, and it is thisresemblance that gives these joints their name, synovia, meaning “with egg.” Cartilage clearly performs a mechanical function. It provides a bearing surface with low friction and wear, and because of its compliance, it helps to distribute the loads between opposing bones in a synovial joint. If cartilage were a stiff material like bone, the contact stresses at a joint would be much higher, since the area of contact would be much smaller. These mechanical functions alone would probably not be sufficient to justify an in-depth study of cartilage biomechanics. However, the apparent link between osteoarthrosis and 5CHAPTER 67 Chapter 5 |BIOMECHANICS OF CARTILAGE mechanical factors in a joint adds a strong impetus for studying the mechanical behavior of articular cartilage. The specific goals of this chapter are to ■Describe the structure and composition of cartilage in relation to its mechanical behavior ■Examine the material properties of cartilage, what they mean physically, and howthey can be determined ■Describe modes of mechanical failure of cartilage ■Describe the current state of understanding of joint lubrication ■Describe the etiology of osteoarthrosis in terms of mechanical factors A comment on terminology seems appropriate. Osteoarthritis is the term commonly used to describe the apparent degeneration of articular cartilage. Radin has argued that this is a mis- nomer since osteoarthritis does not directly involve inflammation. He suggests the term os- teoarthrosis, which is defined as “loss of articular cartilage with eburnation of the underlying bone associated with a proliferative response [68,69].” In this chapter, the term osteoarthro- sisis used in place of osteoarthritis . Before proceeding through this chapter, the reader should be familiar with the basic concepts and terminology introduced in Chapters 1 and 2. Bone BoneArticular cartilageJoint capsule Synovial membrane Figure 5.1: Schematic representation of a synovial joint. Articular cartilageforms the bearing surface on theends of opposing bones. The spacebetween the capsule and bones is exaggerated in the figure for clarity. 68 Part I |BIOMECHANICAL PRINCIPLES COMPOSITION AND STRUCTURE OF ARTICULAR CARTILAGE Articular cartilage is a living material composed of a relatively small number of cells known as chondrocytes surrounded by a multicomponent matrix. Mechanically, articular cartilage isa composite of materials with widely differing properties. Ap-proximately 70 to 85% of the weight of the whole tissue iswater. The remainder of the tissue is composed primarily ofproteoglycans and collagen. Proteoglycans consist of a pro-tein core to which glycosaminoglycans (chondroitin sulfateand keratan sulfate) are attached to form a bottlebrush-likestructure. These proteoglycans can bind or aggregate to abackbone of hyaluronic acid to form a macromolecule with aweight up to 200 million [61] (Fig. 5.2). Approximately 30%of the dry weight of articular cartilage is composed of pro-teoglycans. Proteoglycan concentration and water contentvary through the depth of the tissue. Near the articular sur-face, proteoglycan concentration is relatively low, and thewater content is the highest in the tissue. In the deeper re-gions of the cartilage, near subchondral bone, the proteogly-can concentration is greatest, and the water content is thelowest [43,51,59]. Collagen is a fibrous protein that makes up60 to 70% of the dry weight of the tissue. Type II is the pre- dominant collagen in articular cartilage, although other typesare present in smaller amounts [16]. Collagen architecturevaries through the depth of the tissue. The structure of articular cartilage is often described in terms of four zones between the articular surface and the sub-chondral bone: the surface or superficial tangential zone, theintermediate or middle zone, the deep or radiate zone, andthe calcified zone (Fig. 5.3). The calcified cartilage is theboundary between the cartilage and the underlying sub-chondral bone. The interface between the deep zone and cal-cified cartilage is known as the tidemark . Optical microscopy (e.g., polarized light), scanning electron microscopy, andtransmission electron microscopy have been used to revealthe structure of articular cartilage [6,7,26,27,61,85]. Whileeach of these methods suggests somewhat similar collagenorientation for the superficial and deep zones, the orientationof fibers in the middle zone remains controversial. Using scanning electron microscopy to investigate the structure of cartilage in planes parallel and perpendicular tosplit lines, Jeffery and coworkers [27] have given some newinsights into the collagen structure (Fig. 5.3). Split lines are formed by puncturing the cartilage surface at multiple siteswith a circular awl. The resulting holes are elliptical, not cir-cular, and the long axes of the ellipses are aligned in whatis called the split line direction . In the plane parallel to a split line, the collagen is organized in broad layers or leaves,while in the plane orthogonal to the split lines the structurehas a ridged pattern that is interpreted as the edges of theleaves (Fig. 5.3). In the calcified and deep zones, collagenfibers are oriented radially and are arranged in tightlypacked bundles. The bundles are linked by numerous fib-rils. From the upper deep zone into the middle zone, theradial orientation becomes less distinct, and collagen fibrilsform a network that surrounds the chondrocytes. In the su-perficial zone, the fibers are finer than in the deeper zones,and the collagen structure is organized into several layers.An amorphous layer that does not appear to contain anyfibers is found on the articular surface. The mechanical be-havior of articular cartilage is determined by the interactionof its predominant components: collagen, proteoglycans,and interstitial fluid. MECHANICAL BEHAVIOR AND MODELING In an aqueous environment, proteoglycans are polyanionic;that is, the molecule has negatively charged sites that arisefrom its sulfate and carboxyl groups. In solution, the mutualrepulsion of these negative charges causes an aggregated pro-teoglycan molecule to spread out and occupy a large volume.In the cartilage matrix, the volume occupied by proteoglycanaggregates is limited by the entangling collagen framework.The swelling of the aggregated molecule against the collagenHyaluronic acidKeratan sulfate Chondroitinsulfate Figure 5.2: A proteoglycan aggregate showing a collection of proteoglycans bound to a hyaluronic backbone. Proteoglycansare the bottlebrush-like structures consisting of a protein corewith side chains of chondroitin sulfate and keratan sulfate.Negatively charged sites on the chondroitin and keratan sulfatechains cause this aggregate to spread out and occupy a large domain when placed in an aqueous solution. 69 Chapter 5 |BIOMECHANICS OF CARTILAGE framework is an essential element in the mechanical response of cartilage. When cartilage is compressed, the negativelycharged sites on aggrecan are pushed closer together, whichincreases their mutual repulsive force and adds to the com-pressive stiffness of the cartilage. Nonaggregated proteogly-cans would not be as effective in resisting compressive loads,since they are not as easily trapped in the collagen matrix.Damage to the collagen framework also reduces the com-pressive stiffness of the tissue, since the aggregated proteo-glycans are contained less efficiently. The mechanical response of cartilage is also strongly tied to the flow of fluid through the tissue. When deformed, fluidflows through the cartilage and across the articular surface[42]. If a pressure difference is applied across a section of car-tilage, fluid also flows through the tissue [51]. These obser-vations suggest that cartilage behaves like a sponge, albeit onethat does not allow fluid to flow through it easily. Recognizing that fluid flow and deformation are interde- pendent has led to the modeling of cartilage as a mixture offluid and solid components [59–61]. This is referred to as thebiphasic model of cartilage . In this modeling, all of the solid- like components of the cartilage, proteoglycans, collagen,cells, and lipids are lumped together to constitute the solidphase of the mixture. The interstitial fluid that is free to movethrough the matrix constitutes the fluid phase. Typically, thesolid phase is modeled as an incompressible elastic material, and the fluid phase is modeled as incompressible and invis-cid, that is, it has no viscosity [60]. Under impact loads, car-tilage behaves as a single-phase, incompressible, elastic solid;there simply isn’t time for the fluid to flow relative to the solidmatrix under rapidly applied loads. For some applications, aviscoelastic model is used to describe the behavior of carti-lage in creep, stress relaxation, or oscillating shear. Althoughthe mathematics of modeling cartilage is outside the scope of this chapter, some examples illustrate the fundamental fluid– solid interaction in cartilage. MATERIAL PROPERTIES A confined compression test is one of the commonly used methods for determining material properties of cartilage (Fig. 5.4). A disc of tissue is cut from the joint and placed inan impervious well. Confined compression is used in eithera “creep” mode or a “relaxation” mode. In the creep mode,a constant load is applied to the cartilage through a porousplate, and the displacement of the tissue is measured as afunction of time. In relaxation mode, a constant displacementis applied to the tissue, and the force needed to maintain thedisplacement is measured. Axis of split line BoneSuperficial Intermediate Radiate Calcified SubchondalCalcified cartilageCollagen leaves Figure 5.3: Cross sections cut through the thickness of articular cartilage on two mutually orthogonal planes. These planes are oriented parallel and perpendicular to split lines on the cartilage surface. The backgroundshows the four zones of the cartilage: superficial, intermediate, radiate, and calcified. The foreground shows theorganization of collagen fibers into “leaves” with varying structure and organization through the thickness of the cartilage. The leaves of collagen are connected by small fibers not shown in the figure. 70 Part I |BIOMECHANICAL PRINCIPLES In creep mode, the cartilage deforms under a constant load, but the deformation is not instantaneous, as it would bein a single-phase elastic material such as a spring. The dis-placement of the cartilage is a function of time, since the fluid cannot escape from the matrix instantaneously (Fig. 5.5). Ini- tially, the displacement is rapid. This corresponds to a rela-tively large flow of fluid out of the cartilage. As the rate ofdisplacement slows and the displacement approaches a con-stant value, the flow of fluid likewise slows. At equilibrium,the displacement is constant and fluid flow has stopped. In general, it takes several thousand seconds to reach the equi-librium displacement. By fitting the mathematical biphasic model to the meas- ured displacement, two material properties of the cartilageare determined: the aggregate modulus and permeability.The aggregate modulus is a measure of the stiffness of thetissue at equilibrium when all fluid flow has ceased. Thehigher the aggregate modulus, the less the tissue deformsunder a given load. The aggregate modulus of cartilage istypically in the range of 0.5 to 0.9 MPa [2]. There is no anal-ogous material constant for solid materials, but using theaggregate modulus and representative values of Poisson’sratio (described below), the Young’s modulus of cartilage isin the range of 0.45 to 0.80 MPa. For comparison, theYoung’s modulus of steel is 200 GPa and for many woods isabout 10 GPa parallel to the grain. These numbers showthat cartilage has a much lower stiffness (modulus) than mostengineering materials. In addition to the aggregate modulus, the permeability of the cartilage is also determined from a confined compressiontest. The permeability indicates the resistance to fluid flowthrough the cartilage matrix. Permeability was first introducedin the study of flow through soils. The average fluid velocitythrough a soil sample (v ave) is proportional to the pressure gradient ( /H11612p) (Fig. 5.6). The constant of proportionality (k) is called the permeability . This relationship is expressed by Darcy’s law, vave/H11005 k/H11612p (Equation 5.1)Constant load Porous plateArticular cartilage Impervious container Figure 5.4: Schematic drawing of an apparatus used to perform a confined compression test of cartilage. A slice of cartilage isplaced in an impervious, fluid-filled well. The tissue is loadedthrough a porous plate. In the configuration shown, the load isconstant throughout the test, which can last for several thousandseconds. Since the well is impervious, flow through the cartilage will only be in the vertical direction and out of the cartilage. Displacement Time Figure 5.5: Typical displacement of cartilage tested in a confined compression test. A constant load is applied to the cartilage,and the displacement is measured over time. Initially, thedeformation is rapid, as relatively large amounts of fluid areexuded from the cartilage. As the displacement reaches aconstant value, the flow slows to zero. Two material properties are determined from this test.Low pressure (P1)High pressure (P2) Porous plateFluid filled chamber Fluid filled chamber Direction of fluid flowArticular cartilage h Figure 5.6: Schematic representation of a device used to measure the permeability of cartilage. A slice of cartilage issupported on a porous plate in a fluid-filled chamber. Highpressure applied to one side of the cartilage drives fluid flow.The average fluid velocity through the cartilage is proportionalto the pressure gradient, and the constant of proportionality is called the permeability . 71 Chapter 5 |BIOMECHANICS OF CARTILAGE where the pressure gradient is approximated by /H11612p/H33360 (Equation 5.2) In SI units, the permeability of cartilage is typically in the range of 10/H1100215to 10/H1100216m4/Ns. If a pressure difference of 210,000 Pa (about the same pressure as in an automobile tire)is applied across a slice of cartilage 1 mm thick, the averagefluid velocity will be only 1 /H1108010 /H110028m/s, which is about 100 million times slower than normal walking speed. Permeability is not constant through the tissue. The per- meability of articular cartilage is highest near the joint sur-face (making fluid flow relatively easy) and lowest in the deepzone (making fluid flow relatively difficult) [50–52]. Perme-ability also varies with deformation of the tissue. As cartilageis compressed, its permeability decreases [37, 47]. Therefore,as a joint is loaded, most of the fluid that crosses the articularsurface comes from the cartilage closest to the joint surface.Under increasing load, fluid flow will decrease because of thedecrease in permeability that accompanies compression. CLINICAL RELEVANCE: VARIABLE PERMEABILITY Deformation-dependent permeability may be a valuablemechanism for maintaining load sharing between the solid and fluid phases of cartilage. If the fluid flowed eas- ily out of the tissue, then the solid matrix would bear thefull contact stress, and under this increased stress, it might be more prone to failure. An indentation test provides an attractive alternative to confined compression [20, 21,33,45,58,82] (Fig. 5.7). Usingan indentation test, cartilage is tested in situ. Since discs ofcartilage are not removed from underlying bone, as must beP 2/H11002 P1/H5007hdone when using confined compression, indentation may be used to test cartilage from small joints. In addition, threeindependent material properties are obtained from one in-dentation test, but only two are obtained from confined com-pression. Typically, an indentation test is performed under aconstant load. The diameter of the indenter varies depend-ing on the curvature of the joint surface, but generally is nosmaller than 0.8 mm. Under a constant load, the displacementof the indenter resembles that for confined compression andrequires several thousand seconds to reach equilibrium. Byfitting the biphasic model of the test to the measured inden-tation, the aggregate modulus, Poisson’s ratio, and perme-ability are determined. Poisson’s ratio is typically less than0.4 and often approaches zero. This finding is a significantdeparture from earlier studies, which assumed that cartilagewas incompressible and, therefore, had a Poisson’s ratio of0.5. This assumption was based on cartilage being mostlywater, and water may often be modeled as an incompressiblematerial. However, when cartilage is loaded, fluid flows outof the solid matrix, which reduces the volume of the wholecartilage. Recognizing that cartilage is a mixture of a solid andfluid leads to the whole tissue behaving as a compressiblematerial, although its components are incompressible. The equilibrium displacement is determined by the ag- gregate modulus and Poisson’s ratio. The permeability influ-ences the rate of deformation. If the permeability is high, fluidcan flow out of the matrix easily, and the equilibrium isreached quickly. A lower permeability causes a more gradualtransition from the rapid early displacement to the equilib-rium. These qualitative results are helpful for interpretingdata from tests of normal and osteoarthrotic cartilage. CLINICAL RELEVANCE: PERMEABILITY OF OSTEOARTHROTIC CARTILAGEThe lower modulus and increased permeability of osteo- arthrotic cartilage result in greater and more-rapid defor- mation of the tissue than normal. These changes mayinfluence the synthetic activity of the chondrocytes, whichare known to respond to their mechanical environment. [8,87,96] Pure shear provides a means for evaluating the intrinsic properties of the solid matrix. Small torsional displacementsof cylindrical samples (which produce pure shear), result inno volume change of the cartilage to drive fluid flow. Fur-thermore, the interstitial fluid is water. It has low viscosity anddoes not make an appreciable contribution to resisting shear.Therefore, the resistance to shear is due to the solid matrix.Tests of cartilage in shear show that the matrix behaves as aviscoelastic solid [18–20,80]. Mathematical models of carti-lage deformation also suggest that the matrix may behave asa viscoelastic solid [44,80,83]. Studying the tensile properties of cartilage illustrates its anisotropy, inhomogeneity, some surprising age-dependentConstant force Rigid porous indenter Displacement of cartilage surface Fluid filled chamber BoneArticular cartilage Figure 5.7: Schematic representation of an apparatus used to perform an indentation test on articular cartilage. Unlike theconfined compression and most permeability tests, the cartilageremains attached to its underlying bone, which provides a morenatural environment for testing. A constant load is applied toa small area of the cartilage through a porous indenter. Thedisplacement of the cartilage is similar to that shown in Figure 5.6. Three material properties are determined from this test. 72 Part I |BIOMECHANICAL PRINCIPLES changes in mechanical behavior, and additional collagen– proteoglycan interaction. Tensile tests of cartilage are per-formed by first removing the cartilage from its underlyingbone. This sheet of cartilage is sometimes cut into thin slices(200–500 /H9262m thick) parallel to the articular surface, using a microtome. Dumbbell-shaped specimens are cut from eachslice with a custom-made cookie cutter. A particularly thorough study of the tensile properties of cartilage shows that samples oriented parallel to split lineshave a higher tensile strength and stiffness than those per-pendicular to the split lines. In skeletally mature animals(closed physis), tensile strength and stiffness decrease fromthe surface to the deep zone. In contrast, tensile strength andstiffness increase with depth from the articular surface inskeletally immature (open physis) animals [76]. The relative influence of the collagen network and pro- teoglycans on the tensile behavior of cartilage depends on therate of loading [77]. When pulled at a slow rate, the collagennetwork alone is responsible for the tensile strength and stiff-ness of cartilage. At high rates of loading, interaction of thecollagen and proteoglycans is responsible for the tensile be-havior; proteoglycans restrain the rotation of the collagenfibers when the tissue is loaded rapidly. RELATIONSHIP BETWEEN MECHANICAL PROPERTIES AND COMPOSITION In addition to the qualitative descriptions given above, quan-titative correlations between the mechanical properties of car-tilage and glycosaminoglycan content, collagen content, andwater content have been established. The compressive stiff-ness of cartilage increases as a function of the total gly-cosaminoglycan content [35] (Fig. 5.8). In contrast, there isno correlation of compressive stiffness with collagen content. In these cases, compressive stiffness is measured in creep,2 seconds after a load is applied to the tissue. Permeabilityand compressive stiffness, as measured by the aggregate mod-ulus, are both highly correlated with water content. As thewater content increases, cartilage becomes less stiff and morepermeable [1] (Fig. 5.9). Note that the inverse of permeabil-ity is plotted in Figure 5.9 B. This is done for convenience,Two-second creep stiffness x 10-6 (MPa) 6020 0406080120140160 100 80 100 120 140 160 Total glycosaminoglycan content (µg/mg dry weight) Figure 5.8: Correlation of compressive stiffness with the total glycosaminoglycan concentration. As the total glycosaminoglycan concentration decreases, the compressive stiffness also decreases. Aggregate modulus (MPa) 700.2 00.40.61.01.21.4 0.8 75 80 85 90 Water content (%) A 1/Permeability x 10-14 (Ns/m4) 701 023567 4 75 80 85 90 Water content (%) B Figure 5.9: A.Correlation of the aggregate modulus with water content of articular cartilage. A regression line obtained from testsof a large number of samples is plotted. As the water contentincreases, the aggregate modulus decreases. B.Correlation of the inverse of permeability with water content. A regression lineobtained from tests of a large number of samples is plotted. As the water content increases, the permeability increases. 73 Chapter 5 |BIOMECHANICS OF CARTILAGE since the permeability becomes very large as the water con- tent increases. CLINICAL RELEVANCE: MATERIAL PROPERTIES OF CARTILAGEThe relationships between material properties and watercontent help to explain early cartilage changes in animal models of osteoarthrosis. Proteoglycan content and equi- librium stiffness decrease and the rate of deformation andwater content increases in these models [38,56]. De- creasing proteoglycan content allows more space in the tissue for fluid. An increase in water content correlateswith an increase in permeability. Increasing permeability allows fluid to flow out of the tissue more easily, resulting in a more rapid rate of deformation. Using confined compression, indentation, tension, and shear tests, the mechanical properties of cartilage can be determined. These properties are necessary for any analy-sis of stress in the tissue. However, material properties donot give any indication of the failure of cartilage. For example, simply knowing the value of aggregate modulus or Poisson’s ratio is not sufficient to predict if cartilage willdevelop the cracks, fissures, and general wear that is char- acteristic of osteoarthrosis. Various loading conditions have been used to gain better insight into the failure properties of cartilage. MECHANICAL FAILURE OF CARTILAGE A characteristic feature of osteoarthrosis is cracking, fibrilla- tion, and wear of cartilage. This appears to be a mechanicallydriven process, and it motivates numerous investigationsaimed at identifying the stresses and deformations responsi-ble for the failure of articular cartilage. Since cartilage is ananisotropic material, we expect that it has greater resistanceto some components of stress than to others. For example,it could be relatively strong in tension parallel to collagenfibers, but weaker in shear along planes between leaves ofcollagen. Tensile failure of cartilage has been of particular interest, since it was generally believed that vertical cracks in cartilagewere initiated by relatively high tensile stresses on the artic-ular surface. More-recent computational models of joint con-tact show that the tensile stress on the surface is lower thanoriginally thought, although tensile stress still exists within thecartilage [13–15]. It now appears that failure by shear stressmay dominate. Studies of the tensile failure of cartilage areprimarily concerned with variations in properties amongjoints, the effects of repeated load, and age. Kempson and coworkers report a decrease in failure stress with age for cartilage from hip and knee [30–32, 34]. How-ever, they find no appreciable age-dependent decrease in ten-sile failure stress for cartilage from the talus (Fig. 5.10). CLINICAL RELEVANCE: INCIDENCE OF OSTEOARTHROSIS AT THE ANKLE There is a low incidence of osteoarthrosis in the ankle com- pared with the hip or knee. The maintenance of tensilestrength of cartilage from the ankle may play a role in the reduced likelihood of degeneration in this joint. Repeated tensile loading (fatigue) lowers the tensile strength of cartilage as it does in many other materials. As thepeak tensile stress increases, the number of cycles to failuredecreases (Fig. 5.11) [93–95]. For any value of peak stress,the number of cycles to failure is lower for cartilage fromolder than younger individuals. Repeated compressive loads applied to the cartilage sur- face in situ also cause a decrease in tensile strength, if a suf-ficient number of load cycles are applied [53]. Following64,800 cycles of compressive loading there is no change in thetensile strength of cartilage, but after 97,200 cycles, tensilestrength is reduced significantly. Surface damage is not foundin any sample. This shows that damage may be induced withinthe tissue before any signs of surface fibrillation are apparent. Some caution must be exercised when interpreting the re- sults of tests in which a large strain is applied to cause failureof samples removed from the joint. The strain to failure may be greater than that experienced in vivo. In addition, the prop- erties of most biological materials change with the appliedstrain; the collagen network becomes aligned with the direc-tion of the tensile strain, and the material becomes stronglyanisotropic. Tensile failure stress (MPa) 15 01015203035 25 20 40 60 80 100 Age in yearsFemoral head 40 Talus Figure 5.10: Comparison of the tensile failure stress of cartilage from the hip and talus. There is a statistically significant drop inthe failure stress, as a function of age, for cartilage from thehip, but not for cartilage from the talus. Interestingly, there is arelatively high occurrence of osteoarthrosis in the hip compared with that in the ankle (talus). 74 Part I |BIOMECHANICAL PRINCIPLES Rather than assume that tensile stress is responsible for fibrillation of the articular surface, the feasibility of severalcriteria is considered in a combined experimental and com-putational approach to cartilage failure [3–5]. Dropping threedifferent-sized spherical indenters (2, 4, and 8 mm) onto thearticular surface produces three different states of stress and,in some instances, a crack through the surface. Based on thestresses in the cartilage in each test and the presence orabsence of a crack, a regression is used to determine the con-dition that is most likely to cause a crack to develop. The max-imum shear stress in the cartilage is the most likely predictorof crack formation based on the location of the crack with re-spect to the calculated stresses. Since cartilage is loaded incompression, the idea of failure by shear stress may seem un-realistic. Shear stresses do exist in cartilage, although the ori-entation of these stresses is not always obvious. To illustratethis, imagine a loading situation that is simpler than a joint,namely a straight bar loaded in compression (Fig. 5.12). If thebar is cut by a plane perpendicular to its length, then the re-sultant force on the cross section must also be compressiveand equal to the applied force to maintain equilibrium. Nowimagine the bar is cut at a 45 /H11034angle to its length (the exact angle is not important). The resultant force must still be equalto the applied force. Resolving the resultant force into com-ponents parallel and perpendicular to the cut surface givesrise to a shear force and a normal force. The shear stress (forceper unit area) comes from the shear force acting over the in-clined cut area of the bar. The same concept applies in anyloading situation, including the cartilage in a synovial joint.However, in a synovial joint the stresses are multiaxial, notuniaxial as in the bar. Radin and coworkers also show that cartilage failure could be induced by shear stress [69]. However, they are particularlyinterested in failure at the cartilage–bone interface, not the articular surface. Motivation for this investigation comes frompostmortem studies that show cracks at the cartilage–bone in-terface and the recognition that under rapid loading, cartilagebehaves as an incompressible elastic material, that is, its Pois-son’s ratio is 0.5. The relatively compliant, but incompressibleTensile failure stress (MPa) 15 010152030 25 10 100 1000 10,000 100,000 Number of cycles10 Y ears old 40 Y ears old 80 Y ears old Figure 5.11: The effects of repeated tensile loading on the tensile strength of cartilage. As the tensile loading stressincreases, fewer cycles of loading are needed to cause failure.Age is also an important factor. Cartilage from older individualsfails at a lower stress than that from younger people. Regression lines fit to multiple tests are plotted.Compressive force P PPCompressive force PCompressive force P Shear forceP ABC Figure 5.12: Illustration of shear stress in a simple loading condition. A.A free body diagram of a bar loaded in compression. B.A free body diagram of the same bar cut perpendicular to the load at an arbitrary location. On the cut surface, the resultantforce must be Pto maintain equilibrium. C.The same bar cut at an arbitrary angle. Again, to be in equilibrium the resultant forceparallel to the bar must be equal to P. This force can always be decomposed into components parallel and perpendicular to thecut. The component parallel to the cut is a shear force that gives rise to a shear stress on the inclined surface. HighstressshearatcartilageboneboundaryCancellous boneSubchondral bone Cartilage Lateral expansion of cartilage Subchondral bone restricts lateral expansion Compressive force Compressive forceHighstressshearatcartilageboneboundary Figure 5.13: Under impulsive compressive loads, the cartilage experiences a relatively large lateral displacement due to itshigh Poisson’s ratio. This expansion is restrained by the muchstiffer subchondral bone, causing a high shear stress at the cartilage bone interface. 75 Chapter 5 |BIOMECHANICS OF CARTILAGE cartilage experiences large lateral displacement (due to its high Poisson’s ratio) when loaded in compression, but this ex-pansion is constrained by the stiff underlying bone (Fig. 5.13).Under these conditions, high shear stress develops at thecartilage–bone boundary. Most studies of cartilage failure are based directly on the values of ultimate stress or strain. An alternative is to use pa-rameters that more directly represent the propagation of acrack in a loaded material sample. The feasibility of using twomethods to determine fracture parameters of cartilage is eval-uated extensively by Chin-Purcell and Lewis (Fig. 5.14) [9].The so-called J integral is a measure of the fracture energydissipated per unit of crack extension. As used, the J integralalso assumes that a crack propagates in the material, as op-posed to deformation or flow of the material, which resultsin a more ductile failure. Since cracks may not propagate insoft biological materials, a tear test is also evaluated. The teartest yields a fracture parameter similar to the J integral. Aswith tensile-stress-based ideas of failure, it is necessary toapply large strains to cause failure of the samples: these strainsmay be far greater than those found in any in vivo loadingconditions. To date, the application of these fracture param-eters is limited to the normal canine patella. JOINT LUBRICATION Normal synovial joints operate with a relatively low coeffi-cient of friction, about 0.001 [40,54,86]. For comparison,Teflon sliding on Teflon has a coefficient of friction of about0.04, an order of magnitude higher than that for synovialjoints. Identifying the mechanisms responsible for the lowfriction in synovial joints has been an area of ongoing researchfor decades. Both fluid film and boundary lubrication mech-anisms have been investigated. For a fluid film to lubricate moving surfaces effectively, it must be thicker than the roughness of the opposing surfaces.The thickness of the film depends on the viscosity of the fluid,the shape of the gap between the parts, and their relative ve- locity, as well as the stiffness of the surfaces. A low coefficientof friction can also be achieved without a fluid film througha mechanism known as boundary lubrication. In this case,molecules adhered to the surfaces are sheared rather than afluid film. It now appears that a combination of boundary lubrication (at low loads) and fluid film lubrication (at high loads) isresponsible for the low friction in synovial joints [41,74,75].This conclusion is based on several important observations.First, at low loads, synovial fluid is a better lubricant thanbuffer solution, but synovial fluid’s lubricating ability doesnot depend on its viscosity. Digesting synovial fluid withhyaluronidase, which greatly reduces its viscosity, has no ef-fect on friction. This shows that a fluid film is not the pre-dominant lubrication mechanism, since viscosity is needed togenerate a fluid film. In contrast, digesting the protein com-ponents in synovial fluid (which does not change its viscosity)causes the coefficient of friction to increase. This resultsuggests that boundary lubrication contributes to the overalllubrication of synovial joints. A glycoprotein that is effectiveas a boundary lubricant has been isolated from synovial fluid[84]. Newer evidence suggests that phospholipids may be im-portant boundary lubricant molecules for articular cartilage[17,65,78]. At high loads, the coefficient of friction with syn-ovial fluid increases, but there is no difference in frictionbetween buffer and synovial fluid. This suggests that theboundary mechanism is less effective at high loads and thata fluid film is augmenting the lubrication process. Numerousmechanisms for developing this film have been postulated[12,28,48,54,89,91,92]. If cartilage is treated as a rigid mate- rial, it is not possible to generate a fluid film of sufficient thick- ness to separate the cartilage surface roughness. Treating thecartilage as a deformable material leads to a greater film thick-ness. This is known as elastohydrodynamic lubrication: the pressure in the fluid film causes the surfaces to deform. How-ever, as the surfaces deform, the roughness on the surfacealso deforms and becomes smaller. Models, which include de-formation of the cartilage and its surface roughness, haveshown that a sufficiently thick film can be developed [28].This is known as microelastohydrodynamic lubrication . De- formation also causes fluid flow across the cartilage surface,which modifies the film thickness, although there is somequestion as to the practical importance of flow across the sur-face [22,23,28]. MODELS OF OSTEOARTHROSIS Animal models are used to provide a controlled environmentfor studying the progression of osteoarthrosis. Althoughosteoarthrosis may be induced by numerous means, modelsbased on disruption of the mechanical environment ofthe joint, either by surgical alteration of periarticular struc-tures or by abnormal joint load, are commonly used[24,25,57,66,72,73,81].Cartilage Modified single edge notch testTrouser tear testCartilageForceForceBone Figure 5.14: Sample shape and load application for the modified single-edge notch and trouser tear tests. Each test yields aspecific measure of fracture, the energy required to propagate a crack in the material. 76 Part I |BIOMECHANICAL PRINCIPLES Surgical resection of one or combinations of the anterior cruciate ligament, the medial collateral ligament, and a par-tial medial meniscectomy produce osteoarthrosis of the knee.These models are thought to produce an unstable joint, butkinematic studies show varying degrees of deviation fromnormal joint kinematics. Small differences in kinematics between control and op- erated knees (anterior cruciate ligament release and partialmedial meniscectomy) are reported in rabbit [49] . At 4 weeksafter surgery, there is a statistically significant change in themaximum anterior displacement of the knee, but anterior dis-placement is not significantly different from normal at 8 or12 weeks after surgery. The most notable kinematic changesare in external rotation at 8 weeks and adduction at 4, 8, and12 weeks after surgery. In dog, which has a more extendedknee, greater anterior-posterior drawer is found after anterior(cranial) cruciate ligament release [36,88]. The relatively smallchanges in kinematics in unstable joints (particularly in rab-bit) suggests that altered forces and possibly sensory inputmay be more important than joint displacements in the de-velopment of osteoarthrosis [29]. Repetitive impulse loading also produces osteoarthrosis in animal joints [70,72,73,81]. An advantage of this model is thatit is more controlled than surgical models; the force appliedto the limb is known and can be altered. This model hasdemonstrated the effect of loading rate on the developmentof osteoarthrosis. Impulsively applied loads were found to pro-duce osteoarthrosis, while higher loads applied at a lower ratedo not. The importance of impulsive loading to the develop-ment of osteoarthrosis also appears in humans; persons withknee pain, but no history to suggest its origin, load their legsmore rapidly at heel strike than persons without knee pain. Although biochemical, metabolic, and mechanical assays have been used to evaluate the properties of cartilage fromanimal models of osteoarthrosis, this chapter concentrateson the mechanical properties of cartilage. Following resec-tion of the anterior cruciate ligament in dog, tensile stiff-ness, aggregate modulus, and shear modulus are lower thanthose in cartilage from unoperated control joints [79]. Per-meability increases significantly 12 weeks after surgery.There is a significant increase in water content of samplesfrom the medial tibial plateau and the lateral condyle andfemoral groove. In summary, various mechanical alterations of a joint lead to the development of osteoarthrosis. The kinematic instabil-ity induced by surgical alterations may be small, suggestingthat altered forces are primarily responsible for the develop-ing osteoarthrosis. Models based solely on abnormal jointloading support the view that alterations in force can lead toosteoarthrosis. Following resection of the anterior cruciate lig-ament, cartilage is less stiff in both compression and shear,and fluid flows more easily through the tissue in joints withosteoarthrosis. This implies greater displacement of os-teoarthrotic cartilage than normal (decreased stiffness) and agreater rate of deformation (increased permeability).CLINICAL RELEVANCE: OSTEOARTHROSIS Osteoarthrosis is a leading cause of disability in devel-oped countries [10]. In the United States, it is second tocardiovascular disease as the most common cause of dis-ability [63]. Despite the widespread occurrence of osteo- arthrosis, it is difficult to study in human populations. Early physical symptoms such as fibrillation and crackingof the articular surface cannot be detected by an individ-ual, since cartilage is aneural. Insults to the cartilage may take years to progress to the point where symptoms are detected by the surrounding joint structures and underly-ing bone. Although numerous epidemiological studies of osteoarthrosis have been performed, they have been described as “disappointing,” since they have not lead toan explanation of the mechanisms underlying the devel- opment of osteoarthrosis [63]. However, what seems to be clear is that the development of osteoarthrosisdepends on a combination of factors including age, sex,heredity, joint mechanics, and cartilage biology and bio- chemistry [11,46,55]. Although it is not an inescapable consequence of aging, osteoarthrosis is more prevalent in the elderly [62,64]. In the United States, approximately 80% of people over the age of 65 and essentially everyone over the age of 80 hasosteoarthrosis, although it is uncommon before the age of 40. After 55 years of age, osteoarthrosis is more common in women than in men. Typically the interphalangeal, firstcarpometacarpal and knees are the first joints that are affected [62]. However, specific links between aging and osteoarthrosis are not known. Excessive mechanical load-ing may also predispose joints to osteoarthrosis. Somestudies have shown workers in physically strenuous occupa- tions (coal miners) have a higher incidence of osteoarthrosis than those in less strenuous lines of work (office workers)[63]. Interestingly, osteoarthrosis of the shoulder and elbow have been found in relatively young individuals in ancient populations who depended on hunting [63].However, strenuous work may not be the only risk factor for osteoarthrosis, since persons who use pneumatic drills or physical education teachers do not have an increasedrisk of osteoarthrosis [63]. Obesity has also been found to increase the risk of osteoarthrosis, particularly in the tibiofemoral, patellofem-oral, and carpometacarpal joints [10]. Although increased weight would be expected to increase the load on joints of the lower extremity and possibly predispose an individualto osteoarthrosis, obesity would have no direct mechanical effect on the carpometacarpal joint. Injuries to the anterior cruciate ligament, collateral ligament, or meniscus have been implicated in the devel-opment of osteoarthrosis in the knee [39]. Loss of theanterior cruciate ligament may impair sensory function andprotective mechanisms at the knee. Disruption of internaljoint structures may alter joint alignment and the areas of 77 Chapter 5 |BIOMECHANICS OF CARTILAGE cartilage that are loaded. If ligament damage results in a loss of joint stability, then joint loads may be increased by active muscle contraction trying to stabilize the joint. Partial or total meniscectomy can also be expected toincrease the stress on the joint, since the joint force is concentrated over a smaller area [90]. While there appears to be an increased risk of osteoarthrosis in situations that entail abnormal or exces-sive loading this is clearly not universal. Radin has argued that it is not the magnitude of the load, but the loadingrate that is the determining factor in the development of osteoarthrosis. Osteoarthrosis develops only when impul- sive loads are applied; that is, the load reaches its maxi- mum value over a relatively short time. This has beenclearly demonstrated in animal models by use of externally applied loads and in sheep walking on soft and hard sur- faces [67,71–73,75,81]. The role of impulsive rather thanmore-slowly applied loads is also supported by tests inhumans. Individuals with knee pain who are diagnosed as “prearthrotic” have a higher loading rate at heel strike than normal subjects [69]. These studies suggest that par-ticular activities alone do not necessarily predispose an individual to osteoarthrosis. Rather, the way in which the activity is performed may be the factor that determines if osteoarthrosis will develop. SUMMARY In summary, articular cartilage provides an efficient load- bearing surface for synovial joints that is capable of function-ing for the lifetime of an individual. The mechanical behav-ior of this tissue depends on the interaction of its fluid andsolid components. 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