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Tractive forces during rolling motion of the knee: Implications for wear in total knee replacement
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PII: SOO21-9290(96)00112-l
J. Biomechanirc. Vol. 30. No. 2, pp. 131-137. 1997 (0 1996 Elseviet Science Ltd. All rights reserved Printed in Great Britain 0021 9290197 517.00 + .W
ELSEVIER
TRACTIVE FORCES DURING ROLLING IMPLICATIONS FOR WEAR IN TOTAL
MOTION OF THE KNEE: KNEE REPLACEMENT
Markus A. Wimmer* and Thomas P. Andriacchit * Biomechanics Section, Technical University Hamburg-Harburg, Hamburg, Germany; and t Section of Orthopedic Research. Rush-Presbyterian St. Luke’s 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 concerns with these devices. The artificial bearing of a TKR has to sustain large forces while allowing the mobility for normal motion, typically, rolling, gliding and rotation. The tractive forces during the rolling motion at the knee joint were analyzed to determine which factors cause these forces to increase in TKR. The implications of these tractive forces to polyethylene wear were considered. Traction forces were calculated using a model of the knee to evaluate the effect of variations in the coefficient of friction, gait characteristics, antagonistic muscle contraction and patellofemoral mechanics. The model was limited to the sagittal plane motion of the femur on the tibia. The input for the model was the shape of the articulating surface, coefficient of friction. contact path, muscle anatomy and gait kinetics common to patients with a total knee replacement. The generation of tractive forces on the tibia1 polyethylene plateau was highly dependent on the static and dynamic coefficient of friction between the femur and the tibia. A peak tractive force of approximately 0.4 body weight was calculated with a peak normal force of 3.3 body weight. Tractive rolling occurred during most of stance phase when the static coefficient was 0.2. Alterations in gait patterns had a substantial effect on the generation of tractive forces at the knee joint. When an abnormal gait pattern (often seen following TKR) was input to the model the posteriorly directed tractive force on the tibia1 surface was reduced. It was also found that variations in muscle contractions associated with antagonistic muscle activity as well as the angle of pull of the patellar tendon affected the magnitude of tractive forces. The results of the study suggest that there are feasible conditions following total knee replacement which can lead to tractive forces during rolling motion at the tibiofemoral articulation that should be considered in the analysis of factors leading to polyethylene damage in total knee replacement. Copyright :F: 1996 Elsevier Science Ltd. Keywords: Knee; Arthroplasty; Polyethylene; Wear; Gait.
INTRODUCTION
Wear at the polyethylene-bearing surface of the tibiofemoral articulation in a total knee arthroplasty (TKR) is one of the critical factors limiting the long-term success of the device (Blunn et al., 1992; Hood et al., 1983; Landy and Walker, 1988). Today, total knee failures are caused by wear and consequences of wear such as osteolysis (Cadambi et a/., 1994; Dorr and Serocki, 1994; Peters et al., 1992). The problem represents a unique challenge in that the kinematics and dynamics differ from any other joint. The articulation must transmit large forces while allowing the mobility to permit normal function. Typically, the femoral rollback during knee flexion is a result of rolling, gliding, and rotation of the condyles over the tibia1 plateau (Kapandji, 1970), whereby rolling motion is predominant early in flexion (o-20”) as described by Andriacchi et al. (1986) and Nisell (1985). Retrieval analyses of polyethylene components from TKR reflect the complexity of the wear problem. Several authors (Blunn et al., 1992; Engh et al., 1992; Landy and Walker, 1988; Wasielewski et al., 1994) have described multiple modes of damage in retrieved components of different shapes and conformity. Cyclic sliding has been Received in final form 13 June 1996 Address correspondence to: Thomas P. Andriacchi, Section of Orthopedic Research, Rush-Presbyterian St. Luke’s Medical Center. 1653 W. Congress Parkway, Chicago, IL 60612, U.S.A.
suggested as the most damaging kipematic action (Blunn et al., 1991) and used for wear studies in different test setups (Blunn et al., 1994; Davidson et al., 1992); however, the wear patterns seen in simulator studies do not completely reflect the severity of damage seen in retrieved specimens. For example, the severe delamination failures (Engh et al., 1992) reported in some types of TKR have not been reproduced in knee simulators. Under conditions of pure rolling (instantaneous relative velocity of contact point is zero), tractive rolling occurs when the tangential surface loads are non-zero, while free rolling occurs when the tangential loads are zero (Johnson, 1985). The initiation or breaking of rolling motion would produce tractive rolling. In a metal-polyethylene knee articulation, the tractive force generated during tractive rolling can be substantial since it is governed by the static coefficient of friction, ps, which is approximately twice (Lloyd and NoEl, 1988) the dynamic coefficient of friction, pd. The dynamic coefficient would apply during pure sliding. Tractive forces produce stress, potentially damaging the polyethylene (Natarajan et al., 1995). Further, these may be influenced by differences in gait characteristics. The purpose of this study was to test for conditions that can increase the tractive forces at the tibiofemoral joint of a TKR. The influence of gait mechanics, coefficient of friction and patellar position was studied. The implications of the tractive forces to polyethylene wear were considered. 131
I?7
M. A. Wimmer MATERIALS
AND
and T. P. Andriacchl
METHODS
A model (Fig. I) of the knee was used to calculate the normal (F,) and the tractive forces (F,) at the knee from kinematic and kinetic measures taken during the stance phase of gait of patients following total knee replacement. The model was similar to the previously described models (Morrison. 1970: Schipplein and Andriacchi, 1991) with the following modifications: (a) the kinematic linkage (pure rolling or sliding) between the femur and the tibia was determined by the static or dynamic coefficient of friction and the angle of knee flexion; (b) the lines of action for each muscle group were approximated by force vectors that change direction as a function of knee flexion (Fig. 1); and (c) gait kinetics common to patients following TKR (Andriacchi et al., 1982) were used. Tibiofemoral contact movement was derived from cadaver studies of knees with the anterior cruciate ligament and menisci removed (Draganich et al., 1987). During rolling, the contact point between femur and tibia moves anterior-posterior as a function of the curvature of the articulating surfaces and the flexion angle. The curvature
of the femoral condyle was modeled as a cylinder (55 mm radius). The tibia1 component had a flat polyethylene tibia1 surface which followed the anatomical posterior slope of IO” of the tibia. Pure rolling between the two rigid body segments was simulated between ~- 10 and 18” of knee flexion. In addition, pure rolling was limited to the condition where the ratio F,/F,, was less than the static coefficient of friction, ,u~. The ratio F,;F, was defined as the tractive coefficient, ~1,.The maximum static coefficient of friction, ,u~, was twice the dynamic coefflcient, 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 than pcls= 0.2). The contact path was derived from a retrieval study of the same implant (Miller/Galante) simulated in this study (Wasielewski et al., 1994). Similar data have been published by Blunn et al. (1992). The contact point at full extension was 20 mm posterior from the anterior lip of the insert. The maximum femoral rollback was set to 17 mm. Rolling resistance was included with the introduction of a rolling lever f of the joint reaction force about the center of instantaneous motion (Fig. 1). The
Anode1 Description
and Variables
i
p@= ($) - a * OAT a = Flexion Angle
Input
a
Fz = Segmental
Joint
Force(Axial))
Fy = Segmental
Joint
Force
Mx = Segmental
Flexion-Extension
6
Angular
= Segmental
f = rolling
(Tangential) Moment
Acceleration
offset
0=-3+0,75a output bad
- Force
F-r
t = Force
Fnam. = Force
in Quadriceps in Gastrocnemius in Hamstrings
Group Group Group
Ft = Traction
Force
on Tibia1 Surface
Fn = 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 total knee prosthesis. Muscle groups crossing the joint are represented by force vectors. Here, the external forces and moments are shown acting about the center of curvature of the femoral condyles. Patellar ligament angle (p) changes with knee flexion angle (a). Two initial angles 22 and 30” were simulated to represent changes in patellar thickness following total knee replacement.
Tractive forces during rolling motion of the knee
rolling lever was defined such that it resists the rolling movement. The calculation of this lever was based on the material constants of UHMWPE and cobalt-chromium (Johnson, 1985). The magnitude off was 0.4 mm and remained constant for all joint angles. The assumptions for modeling muscle and ligament forces were based on previous studies. It was assumed (Mahoney et al., 1994) that the retained posterior cruciate ligament following TKR did not tighten during the range of knee flexion ( - 10-18” knee flexion) where tractive rolling took place. The anterior cruciate ligament was sacrificed at the time of surgery and therefore was not included in this analysis. Muscle attachments and lines of action were derived from previously reported studies (Draganich et al., 1987; Schipplein and Andriacchi, 1991). The quadriceps group (Fouad) included the rectus femoris and vasti muscles. The hamstrings group (FHams) formed a single vector consisting of the semimembranous, semitendinosus, biceps femoris and gracilis muscles. The medial and lateral heads of the gastrocnemius muscles with the plantaris muscles formed the gastrocnemius group (FGast), Using a straight-line assumption, the action lines of these muscle groups were approximated by force vectors acting on the tibia. The lines of action of F Hams and Fast were dependent on the angle of knee flexion (Fig. 1). The hamstring vector inserted as a single point 40 mm below the tibia1 plateau (Draganich, 1984). The medial and lateral head of the gastrocnemius originated proximally with respect to the medial and lateral femoral condyles. Due to the femoral rollback, the angle of the FGast varied from - 3 to + 9”, with respect to the tibia axis during knee flexion. Patellofemoral mechanics were defined in terms of angular change of the patellar ligament. The directional change /I of FQuad followed the angular change of the patellar ligament with flexion. The angle /I was linearly dependent (Matthews et al., 1977; Van Eijden et 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 patella of nominal thickness and the situation where the nominal thickness was increased by approximately 6 mm, respectively. The traction, F,, and normal, F,, forces were calculated based on a statically determinate model (Morrison, 1970; Schipplein and Andriacchi, 1991) using the muscle groupings described above. While only one agonist group was active at a time (based on EMG), the approach described by Schipplein and Andriacchi (1991), permitted the evaluation of the influence of antagonistic muscle activity. Antagonistic muscle activity was simulated based on a proportion of the external flexion-extension moment, M,, needed to balance the net moment at the knee. EMG measurements were used to determine on-off activity of muscle groups. The effects of antagonistic muscle work were investigated parametrically by simulating antagonistic levels of 0, 10,30, and 45% of the moment created by the agonists. The external abduction or adduction moment was balanced by lateral or medial soft tissue tension (Schipplein and Andriacchi, 1991). However, the forces were not distributed between the medial and lateral plateau, since the focus of this study was to evaluate tractive forces in the sagittal plane.
-3 ’
133
Stance Phase (%)
Fig. 2. The two patterns of flexion-extension moment M, used for input to the model. A positive moment is balanced by net quadriceps muscle contraction and a negative moment is balanced by net knee flexor contraction. The quadriceps avoidance pattern is common to patients following total knee replacement.
Two gait patterns (Fig. 2) common to patients following TKR (Andriacchi et al., 1982) were used as input to the model. The first pattern was characterized by a normal net flexion/extension moment (‘normal’) while the second had a distinct reduction in the external flexion moment (‘quadriceps avoidance’). These patterns were compared without the assumption of antagonistic muscle activity. The external forces obtained in the sagittal plane included the effect of acceleration of the lower limb segments, and the external moments took the inertia moments into account. The external mediolateral force component and the internal-external moment were neglected, since the focus of this analysis was in the sagittal plane. The output of the model F, and F, were the sum of the forces acting on the medial and lateral plateaux. RESULTS
The coefficient of friction had a substantial effect on the generation of tractive force, F,. During rolling of the femoral condyles on the tibia1 plateau, the transfer of F, 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 rolling was possible during most of stance phase when ,LL~= 0.2, since tractive rolling occurs only when IF,/F,I < ps. In late stance the knee flexion angle a exceeded 18” and sliding was initiated with a dynamic coefficient of friction of pd = 0.1. As a result the tangential force was reduced. While the magnitude and pattern of the compression force, F, (Fig. 3) for normal gait were similar to the previously published results, it was interesting to examine the variation of F, and F, along the tibia1 contact region (Fig. 4). In the anterior region of the tibia1 plateau, F, reached a peak producing a posterior pull on the tibia1 surface. A second peak occurred in the posterior region as the femoral condyles rolled backwards with a relative angular acceleration as high as 50 rad s-‘. In contrast to sliding, the direction of the tangential force during tractive rolling is not necessarily in the direction of relative motion between the first and second body. A reversal of
M. A. Wimmer and T. P. Andriacchi
134
Forces Distribution
Normal
(Fn)
l?zz Traction
0.2
Force
Force
Along Tibia1 Surface
(Ft)
\ I
“Quadriceps Avoidance”
-
Nomal
---__-
Position
Along
\
4’
0.1 0.0
-0.1
-0.2 -0.6
-“.3w Stance Phasll
(%)
1
100 Anterior
Fig. 3. Traction, F,, and compression force, F,, for a normal walking pattern (0% antagonistic muscle activity). Note the biphasic shape of the traction force with its sign change around midstance. At about 85% of stance, rolling motion comes to an end and sliding takes place. Note that the traction coefficient F,/F, between the cobalt-chromium condyle and polyethylene liner during normal walking remains between + 0.2.
the tractive force occurred at the posterior end of the contact region. The knee rolled forward with knee extension following midstance flexion and F, did not change its posterior-anterior direction till the end of stance. There was a substantial change in the traction force when the gait characteristics were changed to the ‘quadriceps avoidance’ gait pattern. The posteriorly directed peak traction force in the posterior region of the tibia1 surface was reduced (Fig. 4). The reduction was primarily a result of the reduced quadriceps activity, diminishing the tractive pull of the patellar ligament. The anteriorly directed traction force was not affected by the different gait characteristics. An increase in antagonistic muscle activity in the quadriceps group had the largest influence on the peak traction force on the anterior portion of the tibia1 surface for the normal gait pattern (Fig. 5). Even a 10% antagonistic level doubled the magnitude of the initial peak of the traction force. Only the initial tractive pull at heel strike was affected by antagonistic extensor muscle force. Antagonistic flexor muscle activity occurring later in stance had a small effect on the tractive force. For the ‘quadriceps avoidance’ gait pattern the influence was similar. A change in the initial patellar ligament angle /3 (from 22 to 30”) increased the second relative maximum of the traction curve. The results for the ‘normal’ gait pattern
Posterior
Tibial
Surface
Fig. 4. Sagittal view of a polyethylene component with loading history (no antagonistic muscle activity) for the normal (dashed) and quadriceps avoidance (solid) gait patterns (Fig. 2). The normal and traction forces are shown with respect to their location on the articulating surface. The traction force in the posterior portion of the contact surface was largest for the normal gait pattern. There was also reversal in the direction of the tractive force in the posterior portion of the contact region for the traction force associated with normal gait. The quadriceps avoidance gait produced lower tractive forces than the normal gait pattern.
(0% antagonistic muscle activity) are illustrated in Fig. 6. The second relative traction peak increased by about 40% with the initial patellar ligament angle increase for the case of normal gait. Changing the initial patellar ligament angle had no influence on the peak traction force for the quadriceps avoidance gait, since the second relative traction maximum was absent for this gait pattern. It should also be noted that the increase in the initial patellar ligament caused an increase in the range of the force reversal in the posterior region of the tibia1 surface. The combination of a normal gait pattern with antagonistic muscle activity and an increased patellar ligament angle produced the highest tractive forces on the tibia1 surface. DISCUSSION
This study suggests that there are conditions following TKR that can increase the magnitude of the tractive force acting at the knee. The coefficient of friction is probably the single most important factor influencing the magnitude of the tractive force at the tibia1 femoral articulation.
Tractive
Traction
Force vs Antagonistic
forces during
Muscle
rolling
Activity
Anterior
Posterior
Position Along Tibia1 Surface Fig. 5. Antagonistic muscle activity produced the largest increase tractive force in the anterior portion of the contact region.
Traction b +i
; a
0.3
Force vs Patellar -
/'
--
0.2
0.1
c
--
-rt 1:
0
b -0.1 -0.2
(3 --
-0.3
--
p -0.4
--
j
-0.5 -0.6
Ligament
10
;;\,', 40,
“\;] \i \ j
30
\ \
'1, )
mm
40
$ '\
--
Angle (p)
\
\.
, 3
in
\
.--;-\
,'
0)-d O)-3o"
Anterior
Posterior
Position Along Tibia1 Surface Fig. 6. The initial patella ligament angle at full extension influences the traction force on the tibia1 surface. The anterior-posterior pull is reduced with smaller patella tendon angles.
If the coefficient of friction increases, the articulation becomes vulnerable to other factors such as gait mechanics or patellofemoral mechanics which can also increase tractive forces. The large variations of the coefficient of friction reported in the literature have been attributed to a variety of conditions. Davidson et al. (1992) found that the dynamic coefficient of friction can start as low as 0.03, but rise to 0.1 after 200,000 load cycles. Similar observations have been made by others (McKellop et al., 1978; Wright et af., 1982). Many have related these variable coefficients of friction to changes in the interface, such as the creation
motion
of the knee
135
of a polymer transfer film to the metal counterface. Lloyd and Noel (1988) reported a static coefficient of friction approximately twice the dynamic coefficient of friction (between 0.2 and 0.3) for stainless steel against polyethylene with water lubrication. Evans and Kennedy (1987) found even higher coefficients of friction, but in a dry environment, An increased coefficient of friction will allow the tibia1 femoral articulation to sustain a larger traction force associated with different gait characteristics or variations in surgical technique. Large variation in the tractive forces at the knee can result from different patterns of walking. For example, the ‘quadriceps avoidance’ type of gait reduced the tractive forces on the joint. Surgical factors can also influence tractive forces. The natural orientation of the patellar ligament creates a force component which can add to the traction force on the tibiofemoral articulation. The angle of the patellar ligament will increase with a thicker patella. While there are other important factors, like patella wear and breakage, that should be considered in deciding on the thickness of the patella, this study suggests that a thicker patella could increase tractive forces at the tibiofemoral articulation. Rolling and sliding kinematics of the knee joint can influence polyethylene damage mechanisms (Andriacchi and Galante, 1988; Blunn et al., 1991; White et al., 1994; Whiteside and Nagamine, 1994). In the study by Blunn et al. (1991) the highest damage occurred when normal forces acted coincidentally with tangential forces, mainly in the sliding cyclic load combinations. In the present study, the tractive forces generated during pure rolling could produce higher tangential forces than those possibly occurring during sliding since the tractive forces are dependent upon the static coefficient of friction rather than the lower dynamic coefficient of friction. tt is important to consider the scope and the limitation of the methodology used to conduct this investigation. The analysis only considers the generation of tractive forces in the sagittal plane, and no attempt was made to distribute those forces between the medial and lateral tibia1 plateau. Femoral rotation and the internal/external torque can also contribute to the tangential forces generated at the knee joint. The choice of muscle lines of action as well as the ligament approximation could influence the tangential component of the resultant force and, thus, may affect variations in the predicted tractive forces. The assumed fixed kinematic linkage of pure rolling and sliding during knee flexion, based on passive knee kinematic studies, could dramatically vary from subject to subject. The model assumed that the retained posterior cruciate ligament following TKR did not tighten earlier than 18” of flexion based on previous studies. A PCL that functioned earlier in flexion could reduce the traction force along the articular surface which normally occurs later in stance phase. The presence of antagonistic muscle activity alters both the normal and some components of the tractive forces. We have attempted to select the appropriate combination of agonistic and antagonistic muscles based on patterns of flexion-extension moments and EMG measurements from patients in the gait laboratory. The parametric approach of investigating the effect of antagonistic muscle activity (Schipplein and
M. A. Wimmer and T. P. Andriacchl
Andriacchi, 199 1) allowed us to estimate the contribution of antagonistic muscle activity. It is also important to note that this model focused only on the generation of tractive forces under conditions of normal alignment. Wasielewski et al. (1994) reported that rotational or varus malalignment can lead to severe damage modes. In spite of the model limitations, the model predictions seem consistent with retrieval analysis. Retrieval studies (Wasielewski et al., 1994) of the type of implant modeled in this study show that the wear pattern is associated with anterior and posterior regions of pitting surrounding a shiny, burnished section on the polyethylene surface. The distribution of the normal and tractive forces predicted by this model (Fig. 4) would increase the tensile stresses (Natarajan er al., 1995) from those generated from purely compressive contact (Pappas et al., 1987). Pitting is the most predominant and frequently occurring form of damage seen in retrieved specimens (Collier et al., 1991; Engh et al., 1992; Hood et al., 1983; Landy and Walker, 1988; Wright et al., 1988, 1992). Although pitting has often been associated with a third body such as PMMA particles, it is possible for pitting to occur without third-body debris (Pappas et al., 1987; Wright and Bartel, 1986; Wright et al., 1982). A moving contact area between articulating surfaces will cause portions of the surface to be subjected to cyclic stresses that would provide the necessary conditions leading to pitting (Bartel et al., 1986). Tangential forces can produce regions of higher (maximum shear) stresses near the surface and initiate surface cracking (Rullkoetter et al., 1994). Thus, the tractive forces should be considered with other factors such as contamination, lubrication and the cyclic fatigue due to contact movement in the analysis of wear in TKR. Acknowledyements-The authors would like to thank the German exchange organization DAAD and the National Institute of Health for financial support through grant AR-20702, and helpful suggestions of Dr Raghu Natarajan. REFERENCES
Ahmed, A. M., Burke, D. L. and Hyder, A. (1987) Force analysis of the patellar mechanism. J. orthop. Res. 5, 69-85. Andriacchi, T. P. and Galante, J. 0. (1988) Retention of the posterior cruciate ligament in total knee arthroplasty. J. Arthroplusty (Suppl.) 13-19. Andriacchi, T. P., Galante, J. 0. and Fermier, R. W. (1982) The influence of total knee replacement design on function during walking and stair climbing. J. Bone Jt Surg. 64, 1328-1335. Andriacchi, T. P., Stanwick, T. S. and Galante, J. 0. (1986) Knee biomechanics and total knee replacement. J. Arthroplasty 1,211-219. Bartel, D. L., Bicknell, V. L. and Wright, T. M. (1986) The effect of conformity, thickness and material on stresses in ultra-high molecular weight components for total joint replacement. J. Bone Jt Surg. 68-A, 104-1051. Blunn, G. W., Joshi, A. B., Lilley, A. P., Engelbrecht, E., Ryd, L., Lidgren, L. and Walker, P. S. (1992) Polyethylene wear in unicondylar knee prostheses. Acta orthop. Stand. 63, 247-255. Blunn, G. W., Lilley, P. A. and Walker, P. S. (1994) Variability of the wear of ultra high molecular weight polyethylene in simulated TKR. Trans. orthop. Res. Sot. 40, 177. Blunn, G. W., Walker, P. S., Joshi, A. and Hardinge, K. (1991) The dominance of cyclic sliding in producing wear in total knee replacements. Clin. Orthop. 273, 253-260. Cadambi, A., Engh, G. A., Dwyer, K. A. and Vinh, T. N. (1994) Osteolysis of the distal femur after total knee arthroplasty. J. Arthroplasty
9. 579-594.
Collier, J. P., Mayor, M. B., McNamara, J. L., Surprenant, V. A. and Jensen, R. E. (1991) Analysis of the failure of I??. polyethylene insert5 from uncemented tibia1 knee components. C/i,i. 01~/1ctp. 273. 232-242. Davidson, J. A., Mishra, A. K., Poggie, R. A. and Werr. J. .I. ( 1992) Sliding friction and UHMWPE wear comparison between cobalt alloy and zirconia surfaces. Trtrns. orthop. Rrs. SOC,. 38, 404. Dorr, L. D. and Serocki, J. H. (I 994) Mechanisms of failure of total knee arthroplasty. In The Knee (Edited by Scott. W. N.), pp. 1239.-1249. Mosby, St. Louis. Draganich, L. F. (1984) The influence of the cruciate ligaments, knee musculature and anatomy on knee joint loading. Ph.D. thesis. University of Illinois at Chicago, Chicago. Draganich, L. F., Andriacchi, T. P. and Andersson, G. B. J. (1987) Interaction between intrinsic knee mechanics and the knee extensor mechanism. J. orthop. Res. 5, 539-547. Engh, G. A., Dwyer, K. A. and Hanes, C. K. (1992) Polyethylene wear of metal-backed tibia1 components in total and unicompartmental knee prostheses. J. Bone Jt Surg. 74-B, 9-17. Evans, V. R. and Kennedy, F. E. (1987) The effects of temperature on friction and wear in oscillatory motion of polyethylene against stainless steel. Wear Mater. 1, 427433. Hood, R. W., Wright, T. M. and Burstein, A. H. (1983) Retrieval analysis of total knee prostheses: a method and its application to 48 total condylar prostheses. J. biomed. Mater. Res. 17, 829-842. Johnson, K. L. (1985) Contact Mechanics. Cambridge University Press, Cambridge. Kapandji, I. A. (1970) The knee. In The Physiology of the Joints, tm. 72-106. Church Livinestone. London. Liidy, M. M. and Walker, p. S. (i988) Wear of ultra-high-molecularweight polyethylene components of 90 retrieved knee prostheses. J. Arthroplasty
(Suppl.)
73-85.
Lloyd, A. I. and Notl, R. E. (1988) The effect of counterface surface roughness on the wear of UHMWPE in water and oil-in-water emulsion. Tribal. Int. 21, 83-88. McKellop, H., Clarke, I. C., Markolf, K. L. and Amstutz, H. C. (1978) Wear characteristics of UHMW polyethylene: A method for accurately measuring extremely low wear rates. J. hiomed. Mater. Res. 12, 895-927.
Mahoney, 0. M., Noble, P. C., Rhoads, D. D., Alexander, J. W. and Tullos, H. S. (1994) Posterior cruciate function following total knee arthroplasty. J. Arthroplasty 9, 569-578. Matthews, L. S., Sonstegard, D. A. and Henke, J. A. (1977) Load bearing characteristics of the patello-femoral joint. Actu orthop. Stand. 48, 511-516. Morrison, J. B. (1970) The mechanics of the knee joint in relation to normal walking. J. Biomechanics 3, 51-61. Natarajan, R. N., Beard, B. and Andriacchi, T. P. (1995) Stresses in the polyethylene component of a total knee replacement during the stance phase of gait. ASME/AlChE/ASCE .&nmer Bioengineering Conf. Beaver Creek, CO, Paoer #OB4.1. Nisell; R. (1985) Mechanics’of t’he knee. Acta orthop. Stand. 56 (Suppl. 216) 442. Pappas, M. J., Makris, G. and Buechel, F. F. (1987) Evaluation of contact stresses in metal-plastic total knee replacement. In Biomaterials and Clinical Applications (Edited by Pizzoferrato et al.) Elsevier, Amsterdam. Peters, P. C., Engh, G. A., Dwyer, K. A. and Vinh, T. N. (1992) Osteolysis following cementless total knee arthroplasty. J. Bone Jr Surg. 74-A,
874884.
Rullkoetter, P. J. and Hillberry, B. M. (1994) Tibio-femoral contact under dynamic loading. Trans ORS 39, 425. Schipplein, 0. D. and Andriacchi, T. P. (1991) Interaction between active and passive knee stabilizers during level walking. J. orthop. Res. 9, 113-119. Van Eijden, T. M., De Boer, W. and Weijs, W. A. (1985) The orientation of the distal part of the quadriceps femoris muscle as a function of the knee flexion-extension angle. J. Biomechanics 18, 803-809. Wasielewski, R. C., Galante, J. O., Leighty, R. M., Natarajan, R. N. and Rosenberg, A. G. (1994) Wear patterns on retrieved polyethylene tibia1 inserts and their relationship to technical considerations during total knee arthroplasty. Cfin. orthop. 299, 31-43. White, S. E., Whiteside, L. A., McCarthy, D. S., Anthony, M. and Poggie, R. A. (1994) Simulated knee wear with cobalt chromium and oxidized zirconium knee femoral components. C/in. orthop. 309, 176-184.
Tractive forces during rolling motion of the knee Whiteside, L. A. and Nagamine, R. (1994) Biomechanical aspects of knee 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 on prosthetic materials using the pin-on-disk machine. Biomaterials 3, 4148. Wright, T. M. and Bartel, D. L. (1986) The problem of surface damage in polyethylene total knee components, Clin. orthop. 205, 67-74. Wright. T. M., Hood, R. W. and Burstein, A. H. (1982) Analysis of
137
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 and plain polyethylene tibia1 components from posterior stabilized total knee 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 total joint replacements: observations from retrieved PCA knee implants. C/in. Orthop. 276, 126-134.
PII: SOO21-9290(96)00112-l
J. Biomechanirc. Vol. 30. No. 2, pp. 131-137. 1997 (0 1996 Elseviet Science Ltd. All rights reserved Printed in Great Britain 0021 9290197 517.00 + .W
ELSEVIER
TRACTIVE FORCES DURING ROLLING IMPLICATIONS FOR WEAR IN TOTAL
MOTION OF THE KNEE: KNEE REPLACEMENT
Markus A. Wimmer* and Thomas P. Andriacchit * Biomechanics Section, Technical University Hamburg-Harburg, Hamburg, Germany; and t Section of Orthopedic Research. Rush-Presbyterian St. Luke’s 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 concerns with these devices. The artificial bearing of a TKR has to sustain large forces while allowing the mobility for normal motion, typically, rolling, gliding and rotation. The tractive forces during the rolling motion at the knee joint were analyzed to determine which factors cause these forces to increase in TKR. The implications of these tractive forces to polyethylene wear were considered. Traction forces were calculated using a model of the knee to evaluate the effect of variations in the coefficient of friction, gait characteristics, antagonistic muscle contraction and patellofemoral mechanics. The model was limited to the sagittal plane motion of the femur on the tibia. The input for the model was the shape of the articulating surface, coefficient of friction. contact path, muscle anatomy and gait kinetics common to patients with a total knee replacement. The generation of tractive forces on the tibia1 polyethylene plateau was highly dependent on the static and dynamic coefficient of friction between the femur and the tibia. A peak tractive force of approximately 0.4 body weight was calculated with a peak normal force of 3.3 body weight. Tractive rolling occurred during most of stance phase when the static coefficient was 0.2. Alterations in gait patterns had a substantial effect on the generation of tractive forces at the knee joint. When an abnormal gait pattern (often seen following TKR) was input to the model the posteriorly directed tractive force on the tibia1 surface was reduced. It was also found that variations in muscle contractions associated with antagonistic muscle activity as well as the angle of pull of the patellar tendon affected the magnitude of tractive forces. The results of the study suggest that there are feasible conditions following total knee replacement which can lead to tractive forces during rolling motion at the tibiofemoral articulation that should be considered in the analysis of factors leading to polyethylene damage in total knee replacement. Copyright :F: 1996 Elsevier Science Ltd. Keywords: Knee; Arthroplasty; Polyethylene; Wear; Gait.
INTRODUCTION
Wear at the polyethylene-bearing surface of the tibiofemoral articulation in a total knee arthroplasty (TKR) is one of the critical factors limiting the long-term success of the device (Blunn et al., 1992; Hood et al., 1983; Landy and Walker, 1988). Today, total knee failures are caused by wear and consequences of wear such as osteolysis (Cadambi et a/., 1994; Dorr and Serocki, 1994; Peters et al., 1992). The problem represents a unique challenge in that the kinematics and dynamics differ from any other joint. The articulation must transmit large forces while allowing the mobility to permit normal function. Typically, the femoral rollback during knee flexion is a result of rolling, gliding, and rotation of the condyles over the tibia1 plateau (Kapandji, 1970), whereby rolling motion is predominant early in flexion (o-20”) as described by Andriacchi et al. (1986) and Nisell (1985). Retrieval analyses of polyethylene components from TKR reflect the complexity of the wear problem. Several authors (Blunn et al., 1992; Engh et al., 1992; Landy and Walker, 1988; Wasielewski et al., 1994) have described multiple modes of damage in retrieved components of different shapes and conformity. Cyclic sliding has been Received in final form 13 June 1996 Address correspondence to: Thomas P. Andriacchi, Section of Orthopedic Research, Rush-Presbyterian St. Luke’s Medical Center. 1653 W. Congress Parkway, Chicago, IL 60612, U.S.A.
suggested as the most damaging kipematic action (Blunn et al., 1991) and used for wear studies in different test setups (Blunn et al., 1994; Davidson et al., 1992); however, the wear patterns seen in simulator studies do not completely reflect the severity of damage seen in retrieved specimens. For example, the severe delamination failures (Engh et al., 1992) reported in some types of TKR have not been reproduced in knee simulators. Under conditions of pure rolling (instantaneous relative velocity of contact point is zero), tractive rolling occurs when the tangential surface loads are non-zero, while free rolling occurs when the tangential loads are zero (Johnson, 1985). The initiation or breaking of rolling motion would produce tractive rolling. In a metal-polyethylene knee articulation, the tractive force generated during tractive rolling can be substantial since it is governed by the static coefficient of friction, ps, which is approximately twice (Lloyd and NoEl, 1988) the dynamic coefficient of friction, pd. The dynamic coefficient would apply during pure sliding. Tractive forces produce stress, potentially damaging the polyethylene (Natarajan et al., 1995). Further, these may be influenced by differences in gait characteristics. The purpose of this study was to test for conditions that can increase the tractive forces at the tibiofemoral joint of a TKR. The influence of gait mechanics, coefficient of friction and patellar position was studied. The implications of the tractive forces to polyethylene wear were considered. 131
I?7
M. A. Wimmer MATERIALS
AND
and T. P. Andriacchl
METHODS
A model (Fig. I) of the knee was used to calculate the normal (F,) and the tractive forces (F,) at the knee from kinematic and kinetic measures taken during the stance phase of gait of patients following total knee replacement. The model was similar to the previously described models (Morrison. 1970: Schipplein and Andriacchi, 1991) with the following modifications: (a) the kinematic linkage (pure rolling or sliding) between the femur and the tibia was determined by the static or dynamic coefficient of friction and the angle of knee flexion; (b) the lines of action for each muscle group were approximated by force vectors that change direction as a function of knee flexion (Fig. 1); and (c) gait kinetics common to patients following TKR (Andriacchi et al., 1982) were used. Tibiofemoral contact movement was derived from cadaver studies of knees with the anterior cruciate ligament and menisci removed (Draganich et al., 1987). During rolling, the contact point between femur and tibia moves anterior-posterior as a function of the curvature of the articulating surfaces and the flexion angle. The curvature
of the femoral condyle was modeled as a cylinder (55 mm radius). The tibia1 component had a flat polyethylene tibia1 surface which followed the anatomical posterior slope of IO” of the tibia. Pure rolling between the two rigid body segments was simulated between ~- 10 and 18” of knee flexion. In addition, pure rolling was limited to the condition where the ratio F,/F,, was less than the static coefficient of friction, ,u~. The ratio F,;F, was defined as the tractive coefficient, ~1,.The maximum static coefficient of friction, ,u~, was twice the dynamic coefflcient, 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 than pcls= 0.2). The contact path was derived from a retrieval study of the same implant (Miller/Galante) simulated in this study (Wasielewski et al., 1994). Similar data have been published by Blunn et al. (1992). The contact point at full extension was 20 mm posterior from the anterior lip of the insert. The maximum femoral rollback was set to 17 mm. Rolling resistance was included with the introduction of a rolling lever f of the joint reaction force about the center of instantaneous motion (Fig. 1). The
Anode1 Description
and Variables
i
p@= ($) - a * OAT a = Flexion Angle
Input
a
Fz = Segmental
Joint
Force(Axial))
Fy = Segmental
Joint
Force
Mx = Segmental
Flexion-Extension
6
Angular
= Segmental
f = rolling
(Tangential) Moment
Acceleration
offset
0=-3+0,75a output bad
- Force
F-r
t = Force
Fnam. = Force
in Quadriceps in Gastrocnemius in Hamstrings
Group Group Group
Ft = Traction
Force
on Tibia1 Surface
Fn = 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 total knee prosthesis. Muscle groups crossing the joint are represented by force vectors. Here, the external forces and moments are shown acting about the center of curvature of the femoral condyles. Patellar ligament angle (p) changes with knee flexion angle (a). Two initial angles 22 and 30” were simulated to represent changes in patellar thickness following total knee replacement.
Tractive forces during rolling motion of the knee
rolling lever was defined such that it resists the rolling movement. The calculation of this lever was based on the material constants of UHMWPE and cobalt-chromium (Johnson, 1985). The magnitude off was 0.4 mm and remained constant for all joint angles. The assumptions for modeling muscle and ligament forces were based on previous studies. It was assumed (Mahoney et al., 1994) that the retained posterior cruciate ligament following TKR did not tighten during the range of knee flexion ( - 10-18” knee flexion) where tractive rolling took place. The anterior cruciate ligament was sacrificed at the time of surgery and therefore was not included in this analysis. Muscle attachments and lines of action were derived from previously reported studies (Draganich et al., 1987; Schipplein and Andriacchi, 1991). The quadriceps group (Fouad) included the rectus femoris and vasti muscles. The hamstrings group (FHams) formed a single vector consisting of the semimembranous, semitendinosus, biceps femoris and gracilis muscles. The medial and lateral heads of the gastrocnemius muscles with the plantaris muscles formed the gastrocnemius group (FGast), Using a straight-line assumption, the action lines of these muscle groups were approximated by force vectors acting on the tibia. The lines of action of F Hams and Fast were dependent on the angle of knee flexion (Fig. 1). The hamstring vector inserted as a single point 40 mm below the tibia1 plateau (Draganich, 1984). The medial and lateral head of the gastrocnemius originated proximally with respect to the medial and lateral femoral condyles. Due to the femoral rollback, the angle of the FGast varied from - 3 to + 9”, with respect to the tibia axis during knee flexion. Patellofemoral mechanics were defined in terms of angular change of the patellar ligament. The directional change /I of FQuad followed the angular change of the patellar ligament with flexion. The angle /I was linearly dependent (Matthews et al., 1977; Van Eijden et 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 patella of nominal thickness and the situation where the nominal thickness was increased by approximately 6 mm, respectively. The traction, F,, and normal, F,, forces were calculated based on a statically determinate model (Morrison, 1970; Schipplein and Andriacchi, 1991) using the muscle groupings described above. While only one agonist group was active at a time (based on EMG), the approach described by Schipplein and Andriacchi (1991), permitted the evaluation of the influence of antagonistic muscle activity. Antagonistic muscle activity was simulated based on a proportion of the external flexion-extension moment, M,, needed to balance the net moment at the knee. EMG measurements were used to determine on-off activity of muscle groups. The effects of antagonistic muscle work were investigated parametrically by simulating antagonistic levels of 0, 10,30, and 45% of the moment created by the agonists. The external abduction or adduction moment was balanced by lateral or medial soft tissue tension (Schipplein and Andriacchi, 1991). However, the forces were not distributed between the medial and lateral plateau, since the focus of this study was to evaluate tractive forces in the sagittal plane.
-3 ’
133
Stance Phase (%)
Fig. 2. The two patterns of flexion-extension moment M, used for input to the model. A positive moment is balanced by net quadriceps muscle contraction and a negative moment is balanced by net knee flexor contraction. The quadriceps avoidance pattern is common to patients following total knee replacement.
Two gait patterns (Fig. 2) common to patients following TKR (Andriacchi et al., 1982) were used as input to the model. The first pattern was characterized by a normal net flexion/extension moment (‘normal’) while the second had a distinct reduction in the external flexion moment (‘quadriceps avoidance’). These patterns were compared without the assumption of antagonistic muscle activity. The external forces obtained in the sagittal plane included the effect of acceleration of the lower limb segments, and the external moments took the inertia moments into account. The external mediolateral force component and the internal-external moment were neglected, since the focus of this analysis was in the sagittal plane. The output of the model F, and F, were the sum of the forces acting on the medial and lateral plateaux. RESULTS
The coefficient of friction had a substantial effect on the generation of tractive force, F,. During rolling of the femoral condyles on the tibia1 plateau, the transfer of F, 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 rolling was possible during most of stance phase when ,LL~= 0.2, since tractive rolling occurs only when IF,/F,I < ps. In late stance the knee flexion angle a exceeded 18” and sliding was initiated with a dynamic coefficient of friction of pd = 0.1. As a result the tangential force was reduced. While the magnitude and pattern of the compression force, F, (Fig. 3) for normal gait were similar to the previously published results, it was interesting to examine the variation of F, and F, along the tibia1 contact region (Fig. 4). In the anterior region of the tibia1 plateau, F, reached a peak producing a posterior pull on the tibia1 surface. A second peak occurred in the posterior region as the femoral condyles rolled backwards with a relative angular acceleration as high as 50 rad s-‘. In contrast to sliding, the direction of the tangential force during tractive rolling is not necessarily in the direction of relative motion between the first and second body. A reversal of
M. A. Wimmer and T. P. Andriacchi
134
Forces Distribution
Normal
(Fn)
l?zz Traction
0.2
Force
Force
Along Tibia1 Surface
(Ft)
\ I
“Quadriceps Avoidance”
-
Nomal
---__-
Position
Along
\
4’
0.1 0.0
-0.1
-0.2 -0.6
-“.3w Stance Phasll
(%)
1
100 Anterior
Fig. 3. Traction, F,, and compression force, F,, for a normal walking pattern (0% antagonistic muscle activity). Note the biphasic shape of the traction force with its sign change around midstance. At about 85% of stance, rolling motion comes to an end and sliding takes place. Note that the traction coefficient F,/F, between the cobalt-chromium condyle and polyethylene liner during normal walking remains between + 0.2.
the tractive force occurred at the posterior end of the contact region. The knee rolled forward with knee extension following midstance flexion and F, did not change its posterior-anterior direction till the end of stance. There was a substantial change in the traction force when the gait characteristics were changed to the ‘quadriceps avoidance’ gait pattern. The posteriorly directed peak traction force in the posterior region of the tibia1 surface was reduced (Fig. 4). The reduction was primarily a result of the reduced quadriceps activity, diminishing the tractive pull of the patellar ligament. The anteriorly directed traction force was not affected by the different gait characteristics. An increase in antagonistic muscle activity in the quadriceps group had the largest influence on the peak traction force on the anterior portion of the tibia1 surface for the normal gait pattern (Fig. 5). Even a 10% antagonistic level doubled the magnitude of the initial peak of the traction force. Only the initial tractive pull at heel strike was affected by antagonistic extensor muscle force. Antagonistic flexor muscle activity occurring later in stance had a small effect on the tractive force. For the ‘quadriceps avoidance’ gait pattern the influence was similar. A change in the initial patellar ligament angle /3 (from 22 to 30”) increased the second relative maximum of the traction curve. The results for the ‘normal’ gait pattern
Posterior
Tibial
Surface
Fig. 4. Sagittal view of a polyethylene component with loading history (no antagonistic muscle activity) for the normal (dashed) and quadriceps avoidance (solid) gait patterns (Fig. 2). The normal and traction forces are shown with respect to their location on the articulating surface. The traction force in the posterior portion of the contact surface was largest for the normal gait pattern. There was also reversal in the direction of the tractive force in the posterior portion of the contact region for the traction force associated with normal gait. The quadriceps avoidance gait produced lower tractive forces than the normal gait pattern.
(0% antagonistic muscle activity) are illustrated in Fig. 6. The second relative traction peak increased by about 40% with the initial patellar ligament angle increase for the case of normal gait. Changing the initial patellar ligament angle had no influence on the peak traction force for the quadriceps avoidance gait, since the second relative traction maximum was absent for this gait pattern. It should also be noted that the increase in the initial patellar ligament caused an increase in the range of the force reversal in the posterior region of the tibia1 surface. The combination of a normal gait pattern with antagonistic muscle activity and an increased patellar ligament angle produced the highest tractive forces on the tibia1 surface. DISCUSSION
This study suggests that there are conditions following TKR that can increase the magnitude of the tractive force acting at the knee. The coefficient of friction is probably the single most important factor influencing the magnitude of the tractive force at the tibia1 femoral articulation.
Tractive
Traction
Force vs Antagonistic
forces during
Muscle
rolling
Activity
Anterior
Posterior
Position Along Tibia1 Surface Fig. 5. Antagonistic muscle activity produced the largest increase tractive force in the anterior portion of the contact region.
Traction b +i
; a
0.3
Force vs Patellar -
/'
--
0.2
0.1
c
--
-rt 1:
0
b -0.1 -0.2
(3 --
-0.3
--
p -0.4
--
j
-0.5 -0.6
Ligament
10
;;\,', 40,
“\;] \i \ j
30
\ \
'1, )
mm
40
$ '\
--
Angle (p)
\
\.
, 3
in
\
.--;-\
,'
0)-d O)-3o"
Anterior
Posterior
Position Along Tibia1 Surface Fig. 6. The initial patella ligament angle at full extension influences the traction force on the tibia1 surface. The anterior-posterior pull is reduced with smaller patella tendon angles.
If the coefficient of friction increases, the articulation becomes vulnerable to other factors such as gait mechanics or patellofemoral mechanics which can also increase tractive forces. The large variations of the coefficient of friction reported in the literature have been attributed to a variety of conditions. Davidson et al. (1992) found that the dynamic coefficient of friction can start as low as 0.03, but rise to 0.1 after 200,000 load cycles. Similar observations have been made by others (McKellop et al., 1978; Wright et af., 1982). Many have related these variable coefficients of friction to changes in the interface, such as the creation
motion
of the knee
135
of a polymer transfer film to the metal counterface. Lloyd and Noel (1988) reported a static coefficient of friction approximately twice the dynamic coefficient of friction (between 0.2 and 0.3) for stainless steel against polyethylene with water lubrication. Evans and Kennedy (1987) found even higher coefficients of friction, but in a dry environment, An increased coefficient of friction will allow the tibia1 femoral articulation to sustain a larger traction force associated with different gait characteristics or variations in surgical technique. Large variation in the tractive forces at the knee can result from different patterns of walking. For example, the ‘quadriceps avoidance’ type of gait reduced the tractive forces on the joint. Surgical factors can also influence tractive forces. The natural orientation of the patellar ligament creates a force component which can add to the traction force on the tibiofemoral articulation. The angle of the patellar ligament will increase with a thicker patella. While there are other important factors, like patella wear and breakage, that should be considered in deciding on the thickness of the patella, this study suggests that a thicker patella could increase tractive forces at the tibiofemoral articulation. Rolling and sliding kinematics of the knee joint can influence polyethylene damage mechanisms (Andriacchi and Galante, 1988; Blunn et al., 1991; White et al., 1994; Whiteside and Nagamine, 1994). In the study by Blunn et al. (1991) the highest damage occurred when normal forces acted coincidentally with tangential forces, mainly in the sliding cyclic load combinations. In the present study, the tractive forces generated during pure rolling could produce higher tangential forces than those possibly occurring during sliding since the tractive forces are dependent upon the static coefficient of friction rather than the lower dynamic coefficient of friction. tt is important to consider the scope and the limitation of the methodology used to conduct this investigation. The analysis only considers the generation of tractive forces in the sagittal plane, and no attempt was made to distribute those forces between the medial and lateral tibia1 plateau. Femoral rotation and the internal/external torque can also contribute to the tangential forces generated at the knee joint. The choice of muscle lines of action as well as the ligament approximation could influence the tangential component of the resultant force and, thus, may affect variations in the predicted tractive forces. The assumed fixed kinematic linkage of pure rolling and sliding during knee flexion, based on passive knee kinematic studies, could dramatically vary from subject to subject. The model assumed that the retained posterior cruciate ligament following TKR did not tighten earlier than 18” of flexion based on previous studies. A PCL that functioned earlier in flexion could reduce the traction force along the articular surface which normally occurs later in stance phase. The presence of antagonistic muscle activity alters both the normal and some components of the tractive forces. We have attempted to select the appropriate combination of agonistic and antagonistic muscles based on patterns of flexion-extension moments and EMG measurements from patients in the gait laboratory. The parametric approach of investigating the effect of antagonistic muscle activity (Schipplein and
M. A. Wimmer and T. P. Andriacchl
Andriacchi, 199 1) allowed us to estimate the contribution of antagonistic muscle activity. It is also important to note that this model focused only on the generation of tractive forces under conditions of normal alignment. Wasielewski et al. (1994) reported that rotational or varus malalignment can lead to severe damage modes. In spite of the model limitations, the model predictions seem consistent with retrieval analysis. Retrieval studies (Wasielewski et al., 1994) of the type of implant modeled in this study show that the wear pattern is associated with anterior and posterior regions of pitting surrounding a shiny, burnished section on the polyethylene surface. The distribution of the normal and tractive forces predicted by this model (Fig. 4) would increase the tensile stresses (Natarajan er al., 1995) from those generated from purely compressive contact (Pappas et al., 1987). Pitting is the most predominant and frequently occurring form of damage seen in retrieved specimens (Collier et al., 1991; Engh et al., 1992; Hood et al., 1983; Landy and Walker, 1988; Wright et al., 1988, 1992). Although pitting has often been associated with a third body such as PMMA particles, it is possible for pitting to occur without third-body debris (Pappas et al., 1987; Wright and Bartel, 1986; Wright et al., 1982). A moving contact area between articulating surfaces will cause portions of the surface to be subjected to cyclic stresses that would provide the necessary conditions leading to pitting (Bartel et al., 1986). Tangential forces can produce regions of higher (maximum shear) stresses near the surface and initiate surface cracking (Rullkoetter et al., 1994). Thus, the tractive forces should be considered with other factors such as contamination, lubrication and the cyclic fatigue due to contact movement in the analysis of wear in TKR. Acknowledyements-The authors would like to thank the German exchange organization DAAD and the National Institute of Health for financial support through grant AR-20702, and helpful suggestions of Dr Raghu Natarajan. REFERENCES
Ahmed, A. M., Burke, D. L. and Hyder, A. (1987) Force analysis of the patellar mechanism. J. orthop. Res. 5, 69-85. Andriacchi, T. P. and Galante, J. 0. (1988) Retention of the posterior cruciate ligament in total knee arthroplasty. J. Arthroplusty (Suppl.) 13-19. Andriacchi, T. P., Galante, J. 0. and Fermier, R. W. (1982) The influence of total knee replacement design on function during walking and stair climbing. J. Bone Jt Surg. 64, 1328-1335. Andriacchi, T. P., Stanwick, T. S. and Galante, J. 0. (1986) Knee biomechanics and total knee replacement. J. Arthroplasty 1,211-219. Bartel, D. L., Bicknell, V. L. and Wright, T. M. (1986) The effect of conformity, thickness and material on stresses in ultra-high molecular weight components for total joint replacement. J. Bone Jt Surg. 68-A, 104-1051. Blunn, G. W., Joshi, A. B., Lilley, A. P., Engelbrecht, E., Ryd, L., Lidgren, L. and Walker, P. S. (1992) Polyethylene wear in unicondylar knee prostheses. Acta orthop. Stand. 63, 247-255. Blunn, G. W., Lilley, P. A. and Walker, P. S. (1994) Variability of the wear of ultra high molecular weight polyethylene in simulated TKR. Trans. orthop. Res. Sot. 40, 177. Blunn, G. W., Walker, P. S., Joshi, A. and Hardinge, K. (1991) The dominance of cyclic sliding in producing wear in total knee replacements. Clin. Orthop. 273, 253-260. Cadambi, A., Engh, G. A., Dwyer, K. A. and Vinh, T. N. (1994) Osteolysis of the distal femur after total knee arthroplasty. J. Arthroplasty
9. 579-594.
Collier, J. P., Mayor, M. B., McNamara, J. L., Surprenant, V. A. and Jensen, R. E. (1991) Analysis of the failure of I??. polyethylene insert5 from uncemented tibia1 knee components. C/i,i. 01~/1ctp. 273. 232-242. Davidson, J. A., Mishra, A. K., Poggie, R. A. and Werr. J. .I. ( 1992) Sliding friction and UHMWPE wear comparison between cobalt alloy and zirconia surfaces. Trtrns. orthop. Rrs. SOC,. 38, 404. Dorr, L. D. and Serocki, J. H. (I 994) Mechanisms of failure of total knee arthroplasty. In The Knee (Edited by Scott. W. N.), pp. 1239.-1249. Mosby, St. Louis. Draganich, L. F. (1984) The influence of the cruciate ligaments, knee musculature and anatomy on knee joint loading. Ph.D. thesis. University of Illinois at Chicago, Chicago. Draganich, L. F., Andriacchi, T. P. and Andersson, G. B. J. (1987) Interaction between intrinsic knee mechanics and the knee extensor mechanism. J. orthop. Res. 5, 539-547. Engh, G. A., Dwyer, K. A. and Hanes, C. K. (1992) Polyethylene wear of metal-backed tibia1 components in total and unicompartmental knee prostheses. J. Bone Jt Surg. 74-B, 9-17. Evans, V. R. and Kennedy, F. E. (1987) The effects of temperature on friction and wear in oscillatory motion of polyethylene against stainless steel. Wear Mater. 1, 427433. Hood, R. W., Wright, T. M. and Burstein, A. H. (1983) Retrieval analysis of total knee prostheses: a method and its application to 48 total condylar prostheses. J. biomed. Mater. Res. 17, 829-842. Johnson, K. L. (1985) Contact Mechanics. Cambridge University Press, Cambridge. Kapandji, I. A. (1970) The knee. In The Physiology of the Joints, tm. 72-106. Church Livinestone. London. Liidy, M. M. and Walker, p. S. (i988) Wear of ultra-high-molecularweight polyethylene components of 90 retrieved knee prostheses. J. Arthroplasty
(Suppl.)
73-85.
Lloyd, A. I. and Notl, R. E. (1988) The effect of counterface surface roughness on the wear of UHMWPE in water and oil-in-water emulsion. Tribal. Int. 21, 83-88. McKellop, H., Clarke, I. C., Markolf, K. L. and Amstutz, H. C. (1978) Wear characteristics of UHMW polyethylene: A method for accurately measuring extremely low wear rates. J. hiomed. Mater. Res. 12, 895-927.
Mahoney, 0. M., Noble, P. C., Rhoads, D. D., Alexander, J. W. and Tullos, H. S. (1994) Posterior cruciate function following total knee arthroplasty. J. Arthroplasty 9, 569-578. Matthews, L. S., Sonstegard, D. A. and Henke, J. A. (1977) Load bearing characteristics of the patello-femoral joint. Actu orthop. Stand. 48, 511-516. Morrison, J. B. (1970) The mechanics of the knee joint in relation to normal walking. J. Biomechanics 3, 51-61. Natarajan, R. N., Beard, B. and Andriacchi, T. P. (1995) Stresses in the polyethylene component of a total knee replacement during the stance phase of gait. ASME/AlChE/ASCE .&nmer Bioengineering Conf. Beaver Creek, CO, Paoer #OB4.1. Nisell; R. (1985) Mechanics’of t’he knee. Acta orthop. Stand. 56 (Suppl. 216) 442. Pappas, M. J., Makris, G. and Buechel, F. F. (1987) Evaluation of contact stresses in metal-plastic total knee replacement. In Biomaterials and Clinical Applications (Edited by Pizzoferrato et al.) Elsevier, Amsterdam. Peters, P. C., Engh, G. A., Dwyer, K. A. and Vinh, T. N. (1992) Osteolysis following cementless total knee arthroplasty. J. Bone Jr Surg. 74-A,
874884.
Rullkoetter, P. J. and Hillberry, B. M. (1994) Tibio-femoral contact under dynamic loading. Trans ORS 39, 425. Schipplein, 0. D. and Andriacchi, T. P. (1991) Interaction between active and passive knee stabilizers during level walking. J. orthop. Res. 9, 113-119. Van Eijden, T. M., De Boer, W. and Weijs, W. A. (1985) The orientation of the distal part of the quadriceps femoris muscle as a function of the knee flexion-extension angle. J. Biomechanics 18, 803-809. Wasielewski, R. C., Galante, J. O., Leighty, R. M., Natarajan, R. N. and Rosenberg, A. G. (1994) Wear patterns on retrieved polyethylene tibia1 inserts and their relationship to technical considerations during total knee arthroplasty. Cfin. orthop. 299, 31-43. White, S. E., Whiteside, L. A., McCarthy, D. S., Anthony, M. and Poggie, R. A. (1994) Simulated knee wear with cobalt chromium and oxidized zirconium knee femoral components. C/in. orthop. 309, 176-184.
Tractive forces during rolling motion of the knee Whiteside, L. A. and Nagamine, R. (1994) Biomechanical aspects of knee 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 on prosthetic materials using the pin-on-disk machine. Biomaterials 3, 4148. Wright, T. M. and Bartel, D. L. (1986) The problem of surface damage in polyethylene total knee components, Clin. orthop. 205, 67-74. Wright. T. M., Hood, R. W. and Burstein, A. H. (1982) Analysis of
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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 and plain polyethylene tibia1 components from posterior stabilized total knee 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 total joint replacements: observations from retrieved PCA knee implants. C/in. Orthop. 276, 126-134.