Marcus Wimmer

8/7/2019 Marcus Wimmer

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PII: SOO21-9290(96)00112-lJ. Biomechanirc. Vol. 30. No. 2, pp. 131-137. 1997

Copyrighf (0 1996 Elseviet Science Ltd. All rights reservedPrinted in Great Britain

0021 9290197 517.00 + .W

ELSEVIERTRACTIVE FORCES DURING ROLLING MOTION OF THE KNEE:

IMPLICATIONS FOR WEAR IN TOTAL KNEE REPLACEMENTMarkus A. Wimmer* and Thomas P. Andriacchit

* Biomechanics Section, Technical University Hamburg-Harburg, Hamburg, Germany; and t Sectionof Orthopedic Research. Rush-Presbyterian St. Lukes Medical Center, Chicago, IL 60612, U.S.A.Abstract-Wear at the polyethylene tibia1 plateau in total knee arthroplasty (TKR) is one of the primary concernswith these devices. The artific ial bearing of a TKR has to sustain large forces while allowing the mobility fornormal motion, typically, rolling, gliding and rotation. The tractive forces during the rolling motion at the kneejoint were analyzed to determine which factors cause these forces to increase in TKR. The implications of thesetractive forces to polyethylene wear were considered.Traction forces were calculated using a model o f the knee to evaluate the effectof variations in the coefficient offriction, gait characteristics, antagonistic muscle contraction and patellofemoral mechanics. The model was limitedto the sagittal plane motion of the femur on the tibia. The input for the model was the shape of the articulatingsurface, coefficient of friction. contact path, muscle anatomy and gait kinetics common to patients with a total kneereplacement.The generation of tractive forces on the tibia1 polyethylene plateau was highly dependent on the static anddynamic coefficient of friction between the femur and the tibia. A peak tractive force of approximately 0.4 bodyweight was calculated with a peak normal force of 3.3 body weight. Tractive rolling occurred during most of stancephase when the static coefficient was 0.2. Alterations in gait patterns had a substantial effecton the generation oftractive forces at the knee joint. When an abnormal gait pattern (often seen following TKR) was input to the modelthe posteriorly directed tractive force on the tibia1 surface was reduced. It was also found that variations in musclecontractions associated with antagonistic muscle act ivit y as well as the angle of pull of the patellar tendon affec tedthe magnitude of tractive forces.The results of the study suggest that there are feasible conditions following total knee replacement whichcan lead to tractive forces during rolling motion at the tibiofemoral articulation that should be consideredin the analysis of factors leading to polyethylene damage in total knee replacement. Copyright :F: 1996 ElsevierScience Ltd.Keywords: Knee; Arthroplasty; Polyethylene; Wear; Gait.

INTRODUCTIONWear at the polyethylene-bearing surface of thetibiofemoral articulation in a total knee arthroplasty(TKR) is one of the critical factors limiting the long-termsuccess of the device (Blunn et al., 1992; Hood et al., 1983;Landy and Walker, 1988). Today, total knee failures arecaused by wear and consequences of wear such as os-teolysis (Cadambi et a/., 1994; Dorr and Serocki, 1994;Peters et al., 1992). The problem represents a uniquechallenge in that the kinematics and dynamics differ fromany other joint. The articulation must transmit largeforces while allowing the mobility to permit normal func-tion. Typically, the femoral rollback during knee flexionis a result of rolling, gliding, and rotation of the condylesover the tibia1 plateau (Kapandji, 1970), whereby rollingmotion is predominant early in flexion (o-20) as de-scribed by Andriacchi et al. (1986) and Nisell (1985).Retrieval analyses of polyethylene components fromTKR reflect the complexity of the wear problem. Severalauthors (Blunn et al., 1992; Engh et al., 1992; Landy andWalker, 1988; Wasielewski et al., 1994) have describedmultiple modes of damage in retrieved components ofdifferent shapes and conformity. Cyclic sliding has been

Received in final form 13 June 1996Address correspondence to: Thomas P. Andriacchi, Section ofOrthopedic Research, Rush-Presbyterian St. Lukes Medical Center.1653 W. Congress Parkway, Chicago, IL 60612, U.S.A.

suggested as the most damaging kipematic action (Blunnet al., 1991) and used for wear studies in different testsetups (Blunn et al., 1994; Davidson et al., 1992); however,the wear patterns seen in simulator studies do not com-pletely reflect the severity of damage seen in retrievedspecimens. For example, the severe delamination failures(Engh et al., 1992) reported in some types of TKR havenot been reproduced in knee simulators.Under conditions of pure rolling (instantaneous rela-tive velocity of contact point is zero), tractive rollingoccurs when the tangential surface loads are non-zero,while free rolling occurs when the tangential loads arezero (Johnson, 1985). The initiation or breaking of rollingmotion would produce tractive rolling. In a metal-poly-ethylene knee articulation, the tractive force generatedduring tractive rolling can be substantial since it is gov-erned by the static coefficient of friction, ps, which isapproximately twice (Lloyd and NoEl, 1988) the dynamiccoefficient of friction, pd. The dynamic coefficient wouldapply during pure sliding. Tractive forces produce stress,potentially damaging the polyethylene (Natarajan et al.,1995). Further, these may be influenced by differences ingait characteristics.The purpose of this study was to test for conditionsthat can increase the tractive forces at the tibiofemoraljoint of a TKR. The influence of gait mechanics, coeffi-cient of friction and patellar position was studied. Theimplications of the tractive forces to polyethylene wearwere considered.

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I?7 M. A. Wimmer and T. P. Andriacchl

MATERIALS AND METHODS

A model (Fig. I) of the knee was used to calculate thenormal (F,) and the tractive forces (F,) at the knee fromkinematic and kinetic measures taken during the stancephase of gait of patients following total knee replace-ment. The model was similar to the previously describedmodels (Morrison. 1970: Schipplein and Andriacchi,1991) with the following modifications: (a) the kinematiclinkage (pure rolling or sliding) between the femur andthe tibia was determined by the static or dynamic coeffi-cient of friction and the angle of knee flexion; (b) the linesof action for each muscle group were approximated byforce vectors that change direction as a function of kneeflexion (Fig. 1); and (c) gait kinetics common to patientsfollowing TKR (Andriacchi et al., 1982) were used.Tibiofemoral contact movement was derived from ca-daver studies of knees with the anterior cruciate ligamentand menisci removed (Draganich et al., 1987). Duringrolling, the contact point between femur and tibia movesanterior-posterior as a function of the curvature of thearticulating surfaces and the flexion angle. The curvature

of the femoral condyle was modeled as a cylinder (55 mmradius). The tibia1 component had a flat polyethylenetibia1 surface which followed the anatomical posteriorslope of IO of the tibia. Pure rolling between the tworigid body segments was simulated between ~- 10 and18 of knee flexion. In addition, pure rolling was limitedto the condition where the ratio F,/F,, was less than thestatic coefficient of friction, ,u~. The ratio F,;F, was de-fined as the tractive coefficient, ~1,.The maximum staticcoefficient of friction, ,u~, was twice the dynamic coeff l-cient, c(,, (Lloyd and NoEl, 1988). Pure sliding with,,& = 0.1 (Davidson et al.. 1992; McKellop et a/.. 1978)occurred beyond 18 (or any time F,/F, was greater thanpcls= 0.2). The contact path w as derived from a retrievalstudy of the same implant (Miller/Galante) simulated inthis study (Wasielewski et al., 1994). Similar data havebeen published by Blunn et al. (1992). The contact pointat full extension was 20 mm posterior from the anteriorlip of the insert. The maximum femoral rollback was setto 17 mm. Rolling resistance was included with the intro-duction of a rolling lever f of the joint reaction forceabout the center of instantaneous motion (Fig. 1). The

Anode1 Description and Variables

i

a

p@= ($) - a * OATa = Flexion Angle

InputFz = Segm ental Joint Force(Axial))Fy = Segmental Joint Force (Tangential)Mx = Segm ental Flexion-Exten sion Moment6 = Segmental Angular Accelerationf = rolling offset

0=-3+0,75aoutput

bad - Force in Quadrice ps GroupF-r t = Force in Gastrocn emius GroupFnam. = Force in Hamstrings Group

Ft = Traction Force on Tibia1 SurfaceFn = Normal Force on Tibia1 Surface

Fig. 1. Sagittal view of the proximal portion of the tibia and the distal part of the femur with attached totalknee prost hesis. Muscle groups cross ing the joint are represented by force vectors. Here, the external forcesand moments are shown a cting about the center of curvature of the femoral condyles. Patellar ligamentangle (p) changes with knee flexion angle (a). Two initial angles 22 and 30 were simulated to representchanges in patellar thickness following total knee replacement.


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Tractive forces during rolling motion of the knee 133rolling lever was defined such that it resists the rollingmovement. The calculation of this lever was based on thematerial constants of UHMWPE and cobalt-chromium(Johnson, 1985). The magnitude of f was 0.4 mm andremained constant for all joint angles.The assumptions for modeling muscle and ligamentforces were based on previous studies. It was assumed(Mahoney et al., 1994) that the retained posterior cruciateligament following TKR did not tighten during the rangeof knee flexion ( - 10-18 knee flexion) where tractiverolling took place. The anterior cruciate ligament wassacrificed at the time of surgery and therefore was notincluded in this analysis. Muscle attachments and lines ofaction were derived from previously reported studies(Draganich et al., 1987; Schipplein and Andriacchi, 1991).The quadriceps group (Fouad) included the rectus femorisand vasti muscles. The hamstrings group (FHams) formeda single vector consisting of the semimembranous, se-mitendinosus, biceps femoris and gracilis muscles. Themedial and lateral heads of the gastrocnemius muscleswith the plantaris muscles formed the gastrocnemiusgroup (FGast), Using a straight-line assumption, the ac-tion lines of these muscle groups were approximated byforce vectors acting on the tibia. The lines of action ofF Hams and Fast were dependent on the angle of kneeflexion (Fig. 1). The hamstring vector inserted as a singlepoint 40 mm below the tibia1 plateau (Draganich, 1984).The medial and lateral head of the gastrocnemius orig-inated proximally with respect to the medial and lateralfemoral condyles. Due to the femoral rollback, the angleof the FGast varied from - 3 to + 9, with respect to thetibia axis during knee flexion.Patellofemoral mechanics were defined in termsof angular change of the patellar ligament. The direc-tional change /I of FQuadfollowed the angular change ofthe patellar ligament with flexion. The angle /I was lin-early dependent (Matthews et al., 1977; Van Eijdenet al., 1985) on the flexion angle CIas illustrated in Fig. 1.The initial orientation (Fig. 1) of FQuad at full extension(c( = 0) was simulated at 22 and 30 to represent a patel-la of nominal thickness and the situation where thenominal thickness was increased by approximately6 mm, respectively.The traction, F,, and normal, F,, forces were calculatedbased on a statically determinate model (Morrison, 1970;Schipplein and Andriacchi, 1991) using the musclegroupings described above. While only one agonistgroup was active at a time (based on EMG), the ap-proach described by Schipplein and Andriacchi (1991),permitted the evaluation of the influence of antagonisticmuscle activity. Antagonistic muscle activity wassimulated based on a proportion of the externalflexion-extension moment, M,, needed to balance the netmoment at the knee. EMG measurements were used todetermine on-off activity of muscle groups. The effects ofantagonistic muscle work were investigated paramet-rically by simulating antagonistic levels of 0, 10,30, and45% of the moment created by the agonists. The externalabduction or adduction moment was balanced by lateralor medial soft tissue tension (Schipplein and Andriacchi,1991). However, the forces were not distributed betweenthe medial and lateral plateau, since the focus of thisstudy was to evaluate tractive forces in the sagittal plane.

-3 Stance Phase (%)Fig. 2. The two patterns of flexion-extension moment M, used forinput to the model. A positive moment is balanced by net quadricepsmuscle contraction and a negative moment is balanced by net kneeflexor contract ion. The quadriceps avoidance pattern is common topatients following total knee replacement.

Two gait patterns (Fig. 2) common to patients follow-ing TKR (Andriacchi et al., 1982) were used as input tothe model. The first pattern was characterized by a nor-mal net flexion/extension moment (normal) while thesecond had a distinct reduction in the external flexionmoment (quadriceps avoidance). These patterns werecompared without the assumption of antagonistic muscleactivity. The external forces obtained in the sagittal planeincluded the effect of acceleration of the lower limbsegments, and the external moments took the inertiamoments into account. The external mediolateral forcecomponent and the internal-external moment were ne-glected, since the focus of this analysis was in the sagittalplane. The output of the model F, and F, were the sum ofthe forces acting on the medial and lateral plateaux.

RESULTSThe coefficient of friction had a substantial effect onthe generation of tractive force, F,. During rolling of thefemoral condyles on the tibia1 plateau, the transfer ofF, may occur only below the limiting static friction, Pi;otherwise sliding takes place. The traction coefficient,u, = FJFn varied between f 0.2. Thus, tractive rollingwas possible during most of stance phase when ,LL~= 0.2,

since tractive rolling occurs only when IF,/F,I < ps. Inlate stance the knee flexion angle a exceeded 18 andsliding was initiated with a dynamic coefficient of frictionof pd = 0.1. As a result the tangential force was reduced.While the magnitude and pattern of the compressionforce, F, (Fig. 3) for normal gait were similar to thepreviously published results, it was interesting to exam-ine the variation of F, and F, along the tibia1 contactregion (Fig. 4). In the anterior region of the tibia1 plateau,F, reached a peak producing a posterior pull on the tibia1surface. A second peak occurred in the posterior regionas the femoral condyles rolled backwards with a relativeangular acceleration as high as 50 rad s-. In contrast tosliding, the direction of the tangential force during trac-tive rolling is not necessarily in the direction of relativemotion between the first and second body. A reversal of


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134 M. A. Wimmer and T. P. Andriacchi

Normal Force (Fn)

Traction Force (Ft)l?zz0.2

0.1

0.0

-0.1

-0.2

-.3w 100Stance Phasll (%)

Fig. 3. Traction, F,, and compression force, F,, for a normal walkingpattern (0% antagonistic muscle acti vity ). Note the biphasic shape ofthe traction force with its sign change around midstance. At about 85%of stance, rolling motion comes to an end and sliding takes place. Notethat the traction coeffic ient F,/F, between the cobalt-chromium con-dyle and polyethylene liner during normal walking remains between+ 0.2.

the tractive force occurred at the posterior end of thecontact region. The knee rolled forward with knee exten-sion following midstance flexion and F, did not changeits posterior-anterior direction till the end of stance.There was a substantial change in the traction forcewhen the gait characteristics were changed to the quad-riceps avoidance gait pattern. The posteriorly directedpeak traction force in the posterior region of the tibia1surface was reduced (Fig. 4). The reduction was primarilya result of the reduced quadriceps activity, diminishingthe tractive pull of the patellar ligament. The anteriorlydirected traction force was not affected by the differentgait characteristics.An increase in antagonistic muscle activity in thequadriceps group had the largest influence on the peaktraction force on the anterior portion of the tibia1 surfacefor the normal gait pattern (Fig. 5). Even a 10% antagon-istic level doubled the magnitude of the initial peak of thetraction force. Only the initial tractive pull at heel strikewas affected by antagonistic extensor muscle force. An-tagonistic flexor muscle activity occurring later in stancehad a small effect on the tractive force. For the quad-riceps avoidance gait pattern the influence was similar.A change in the initial patellar ligament angle /3 (from22 to 30) increased the second relative maximum of thetraction curve. The results for the normal gait pattern

Forces Distribution Along Tibia1 Surface

\ IQuadriceps \- 4Avoidance

Nomal ---__-

-0.6 1Anterior PosteriorPosition Along Tibial Surface

Fig. 4. Sagittal view of a polyethylene component with loading history(no antagonistic muscle activity ) for the normal (dashed) and quad-riceps avoidance (solid) gait patterns (Fig. 2). The normal and tractionforces are shown with respect to their location on the articulatingsurface. The traction force in the posterior portion of the contactsurface was largest for the normal gait pattern. There was also reversalin the direction of the tractive force in the posterior portion of thecontact region fo r the traction force associated with normal gait. Thequadriceps avoidance gait produced lower tractive forces than thenormal gait pattern.

(0% antagonistic muscle activity) are illustrated in Fig. 6.The second relative traction peak increased by about40% with the initial patellar ligament angle increase forthe case of normal gait. Changing the initial patellarligament angle had no influence on the peak tractionforce for the quadriceps avoidance gait, since the secondrelative traction maximum was absent for this gait pat-tern. It should also be noted that the increase in the initialpatellar ligament caused an increase in the range o f theforce reversal in the posterior region of the tibia1 surface.The combination of a normal gait pattern with antagon-istic muscle activity and an increased patellar ligamentangle produced the highest tractive forces on the tibia1surface.DISCUSSION

This study suggests that there are conditions followingTKR that can increase the magnitude of the tractive forceacting at the knee. The coefficient of friction is probablythe single most important factor influencing the magni-tude of the tractive force at the tibia1 femoral articulation.


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Tractive forces during rolling motion of the knee 135

Traction Force vs Antagonistic Muscle Activity

Anterior PosteriorPosition Along Tibia1 Surface

Fig. 5. Antagonistic muscle activity produced the largest increase intractive force in the anterior portion of the contact region.

Traction Force vs Patellar Ligament Angle (p)0.3 -b /' \

+i 0.2 --; c0.1 -- \. \ \;]a 0 -rt , i1: 3 j-0.1 (3 10 ;; 40,

\\,', \ 30 40'1, ) mmb -0.2 --

j -0.3 -- \ $-p -0.4 -- \ 0)-d\

-0.5 ---0.6 -

'\ .--;- ,'

O)-3o"

Anterior PosteriorPosition Along Tibia1 Surface

Fig. 6. The initial patella ligament angle at full extension influences thetraction force on the tibia1 surface. The anterior-posterior pull isreduced with smaller patella tendon angles.

If the coefficient of friction increases, the articulationbecomes vulnerable to other factors such as gait mechan-ics or patellofemoral mechanics which can also increasetractive forces.The large variations of the coefficient of friction re-ported in the literature have been attributed to a varietyof conditions. Davidson et al. (1992) found that the dy-namic coefficient of friction can start as low as 0.03, butrise to 0.1 after 200,000 load cycles. Similar observationshave been made by others (McKellop et al., 1978; Wrightet af., 1982). Many have related these variable coefficientsof friction to changes in the interface, such as the creation

of a polymer transfer film to the metal counterface. Lloydand Noel (1988) reported a static coefficient of frictionapproximately twice the dynamic coefficient of friction(between 0.2 and 0.3) for stainless steel against polyethy-lene with water lubrication. Evans and Kennedy (1987)found even higher coefficients of friction, but in a dryenvironment,An increased coefficient of friction will allow the tibia1femoral articulation to sustain a larger traction forceassociated with different gait characteristics or variationsin surgical technique. Large variation in the tractiveforces at the knee can result from different patterns ofwalking. For example, the quadriceps avoidance type ofgait reduced the tractive forces on the joint. Surgicalfactors can also influence tractive forces. The naturalorientation of the patellar ligament creates a force com-ponent which can add to the traction force on thetibiofemoral articulation. The angle of the patellar liga-ment will increase with a thicker patella. While there areother important factors, like patella wear and breakage,that should be considered in deciding on the thickness ofthe patella, this study suggests that a thicker patellacould increase tractive forces at the tibiofemoral articula-tion.Rolling and sliding kinematics of the knee joint caninfluence polyethylene damage mechanisms (Andriacchiand Galante, 1988; Blunn et al., 1991; White et al., 1994;Whiteside and Nagamine, 1994). In the study by Blunnet al. (1991) the highest damage occurred when normalforces acted coincidentally with tangential forces, mainlyin the sliding cyclic load combinations. In the presentstudy, the tractive forces generated during pure rollingcould produce higher tangential forces than those pos-sibly occurring during sliding since the tractive forces aredependent upon the static coefficient of friction ratherthan the lower dynamic coefficient of friction.tt is important to consider the scope and the limitationof the methodology used to conduct this investigation.The analysis only considers the generation of tractiveforces in the sagittal plane, and no attempt was made todistribute those forces between the medial and lateraltibia1 plateau. Femoral rotation and the internal/externaltorque can also contribute to the tangential forces gener-ated at the knee joint. The choice of muscle lines of actionas well as the ligament approximation could influence thetangential component of the resultant force and, thus,may affect variations in the predicted tractive forces. Theassumed fixed kinematic linkage of pure rolling andsliding during knee flexion, based on passive knee kin-ematic studies, could dramatically vary from subject tosubject. The model assumed that the retained posteriorcruciate ligament following TKR did not tighten earlierthan 18 of flexion based on previous studies. A PCL thatfunctioned earlier in flexion could reduce the tractionforce along the articular surface which normally occurslater in stance phase. The presence of antagonistic muscleactivity alters both the normal and some components ofthe tractive forces. We have attempted to select the ap-propriate combination of agonistic and antagonisticmuscles based on patterns of flexion-extension momentsand EMG measurements from patients in the gait labor-atory. The parametric approach of investigating theeffect of antagonistic muscle activity (Schipplein and


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M. A. Wimmer and T. P. AndriacchlAndriacchi, 199 1) allowed us to estimate the contributionof antagonistic muscle activity. It is also important tonote that this model focused only on the generation oftractive forces under conditions of normal alignment.Wasielewski et al. (1994) reported that rotational orvarus malalignment can lead to severe damage modes.In spite of the model limitations, the model predictionsseem consistent with retrieval analysis. Retrieval studies(Wasielewski et al., 1994) of the type of implant modeledin this study show that the wear pattern is associatedwith anterior and posterior regions of pitting surround-ing a shiny, burnished section on the polyethylene sur-face. The distribution of the normal and tractive forcespredicted by this model (Fig. 4) would increase the tensilestresses (Natarajan er al., 1995) from those generatedfrom purely compressive contact (Pappas et al., 1987).Pitting is the most predominant and frequently occur-ring form of damage seen in retrieved specimens (Collieret al., 1991; Engh et al., 1992; Hood et al., 1983; Landyand Walker, 1988; Wright et al., 1988, 1992). Althoughpitting has often been associated with a third body suchas PMMA particles, it is possible for pitting to occurwithout third-body debris (Pappas et al., 1987; Wrightand Bartel, 1986; Wright et al., 1982). A moving contactarea between articulating surfaces will cause portions ofthe surface to be subjected to cyclic stresses that wouldprovide the necessary conditions leading to pitting (Bar-tel et al., 1986). Tangential forces can produce regions ofhigher (maximum shear) stresses near the surface andinitiate surface cracking (Rullkoetter et al., 1994). Thus,the tractive forces should be considered with other fac-tors such as contamination, lubrication and the cyclicfatigue due to contact movement in the analysis of wearin TKR.Acknowledyements-The authors would like to thank the Germanexchange organization DAAD and the National Insti tute o f Health forfinancial support through grant AR-20702, and helpful suggestions ofDr Raghu Natarajan.

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Tractive forces during rolling motion of the knee 137Whiteside, L. A. and Nagamine, R. (1994) Biomechanical aspects ofknee replacement design. In The Knee (Edited by Scott , W. N.).pp. 1079-1096. Mosby, St. Louis.Wright, K. W., Dobbs, H. S. and Scales, J. T. (1982) Wear studies onprosthetic materials using the pin-on-disk machine. Biomaterials 3,4148.Wright, T. M. and Bartel, D. L. (1986) The problem of surface damagein polyethylene total knee components, Clin. orthop. 205, 67-74.Wright. T. M., Hood, R. W. and Burstein, A. H. (1982) Analysis of

material failures. Whop. Clin. North Am . 13, 3344.Wright, T. M., Rimnac, C. M., Faris, P. M. and Bansal, M. (1988)Analysis of surface damage in retrieved carbon fiber-reinforced andplain polyethylene tibia1 components from posterior stabilized totalknee replacements. J. Bone Jr Surg. 70-A, 1312-1319.Wright, T. M., Rimnac, C. M., Stulberg, S. D., Mintz. L.. Tsao, A. K.,Klein, R. W. and McCrae, C. (1992) Wear of polyethylene in totaljoint replacements: observations f rom retrieved PCA knee implants.C/in. Orthop. 276, 126-134.

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