Effect of Posterior Tibial Slope on Knee Biomechanics during Functional Activity

Effect of Posterior Tibial Slope on Knee Biomechanics during Functional Activity Kevin B. Shelburne, 1,2 Hyung-Joo Kim, 3 William I. Sterett, 1 Marcus G. Pandy 3 1 Steadman Philippon Research Institute, Vail, Colorado, 2 Department of Mechanical and Materials Engineering, University of Denver, Denver, Colorado, 3 Department of Mechanical Engineering, University of Melbourne, Victoria, Australia Received 16 September 29; accepted 12 July 21 Published online 2 September 21 in Wiley Online Library (wileyonlinelibrary.com). DOI 1.12/jor.21242 ABSTRACT: Treatment of medial compartment knee osteoarthritis with high tibial osteotomy can produce an unintended change in the slope of the tibial plateau in the sagittal plane. The effect of changing posterior tibial slope (PTS) on cruciate ligament forces has not been quantified for knee loading in activities of daily living. The purpose of this study was to determine how changes in PTS affect tibial shear force, anterior tibial translation (ATT), and knee-ligament loading during daily physical activity. We hypothesized that tibial shear force, ATT, and ACL force all increase as PTS increases. A previously validated computer model was used to calculate ATT, tibial shear force, and cruciateligament forces for the normal knee during three common load-bearing tasks: standing, squatting, and walking. The model calculations were repeated with PTS altered in 18 increments up to a maximum change in tibial slope of 18. Tibial shear force and ATT increased as PTS was increased. For standing and walking, ACL force increased as tibial slope was increased; for squatting, PCL force decreased as tibial slope was increased. The effect of changing PTS on ACL force was greatest for walking. The true effect of changing tibial slope on knee-joint biomechanics may only be evident under physiologic loading conditions which include muscle forces. ß 21 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 29:223 231, 211 Keywords: gait; musculoskeletal modeling; HTO; ACL; PCL; knee osteoarthritis Tibial shear force is a major determinant of the force transmitted to the cruciate ligaments of the knee. 1 3 This force derives from three main sources: an external load arising from the presence of the ground reaction force; knee muscle activity; and the contact force acting between the femur and tibia. 1 3 The tibiofemoral contact force induces an anterior directed shear force on the tibia, caused by the posterior slope of the tibial plateau in the sagittal plane. 1 3 This anterior shear force can be substantial during daily physical activity. During walking, for example, the shear force created by the tibiofemoral contact force is as large as that produced by the ground reaction force and the knee muscles. 3 Meyer and Haut 4 demonstrated in a cadaver model that the combination of tibiofemoral force and PTS produced an anterior shear force that increased both the anterior translation of the tibia and the force transmitted to the ACL. Current interest in PTS arises from the changes in PTS that can accompany valgus high tibial osteotomy (HTO). Treatment of medial compartment osteoarthritis (OA) with HTO surgery is based on the premise that correcting a varus deformity will shift the tibiofemoral joint load away from the medial side of the knee. However, HTO can also produce an unintended change in the slope of the tibial plateau in the sagittal plane. 5 7 Marti et al. 7 reported an average increase in the tibial plateau angle of 2.78, with a range of 88 to 18. This change is substantial given that the normal slope of the tibial plateau on the medial side of the knee averages 1 38 in the sagittal plane. 8 Changes in PTS may be a cause for concern because an increase in PTS has been associated with an increase in anterior tibial translation (ATT). Using sagittal plane Correspondence to: Kevin B. Shelburne (T: 33-92-1249; F: 33-871-445; E-mail: kevin.shelburne@du.edu) ß 21 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. radiographs of ACL-deficient knees, Dejour and Bonnin 8 reported that subjects with higher PTS experienced a greater amount of ATT during single-limb stance; specifically, for every 18 increase in PTS, ATT increased by 6 mm. Agneskirchner et al., 9 Rodner et al., 1 and Giffin et al. 11 obtained similar results when they applied a tibiofemoral joint force to cadaver knees with surgically altered PTS, although Giffin et al. 11 did not measure a corresponding increase in ACL force when PTS was increased by as much as 4.58. In contrast, clinical and in vivo biomechanical studies suggest that increased values of PTS may increase the risk of ACL injury by increasing the force transmitted to the ACL. 4,5,12 For example, Brandon et al. 12 found that subjects with ACL insufficiency had greater average values of PTS than controls. The disparity between the results reported by Giffin et al. and Brandon et al. may be due to the fact that the tibiofemoral compressive forces applied in cadaver experiments are much lower than those present in vivo. In particular, Giffin et al. applied a tibiofemoral joint force of 2 N in their cadaver experiments, which is only one-tenth of the peak force present in normal walking, 13,14 and one-fifth of that present in standing. 15 Furthermore, the cadaver experiments of Giffin et al. did not include the effects of the forces applied by the knee muscles. Concern for the effect of PTS on knee-joint loading has led to the development of surgical methods aimed at precisely controlling PTS during HTO surgery. 16 Indeed, some studies have shown that a deliberate surgical change in PTS may be beneficial in the treatment of knee pathology. 6,17 19 Lobenhoffer and Agneskirchner 6 suggested that a decrease in PTS may benefit patients with a naturally high PTS and anterior knee instability or a presurgery knee extension deficit. Conversely, an increase in PTS may be used to address disorders associated with posterior knee laxity 18 and genu recurvatum. 17 While the influence of PTS in knee surgery has 223

224 SHELBURNE ET AL. received a good deal of attention, no clear guidelines exist for defining the change in PTS needed to obtain a desired treatment effect. This is because the effect of PTS on knee-joint loading during daily physical activity is not well understood. The impact of PTS may be particularly important when a surgery that alters PTS is combined with ACL reconstruction, 2,21 because an increase in PTS may place excessive force on a healing graft. 5,12 The aim of this study was to quantify the effects of PTS on knee-joint loading and cruciate-ligament forces during functional activity. A previously published and validated musculoskeletal computer model of the lower limb 3,13,22 was used to determine changes in ATT, tibial shear force, and cruciate-ligament forces that result from a change in PTS in three common weight-bearing tasks: standing, squatting, and walking. We hypothesized that ATT, tibial shear force, and ACL force all increase with an increase in PTS. METHODS A two-stage procedure was used to calculate knee-joint loading for standing, squatting, and walking. In stage 1, leg-muscle forces and ground reaction forces for each task were found by solving an optimization problem using a three-dimensional (3D) musculoskeletal model of the body. In stage 2, the muscle and ground reaction forces calculated in stage 1 were input into another 3D lower limb model that included a detailed representation of the knee. The lower limb model was used to calculate the effect of altering PTS on ATT, tibial shear force, and cruciate-ligament forces at the knee. In stage 1, a 3D musculoskeletal model of the whole body was used to calculate leg-muscle forces for standing, squatting, and walking (Fig. 1). Details of this model are given by Anderson and Pandy, 23,24 so only a brief description is provided here. The skeleton was modeled as a 1-segment, 23 degree-of-freedom (dof) articulated chain. 23,24 The inertial properties of the segments were based on anthropometric measures obtained from five healthy adult males (age 26 3 years, height 177 3 cm, and mass 7.1 7.8 kg). The model was actuated by 54 musculotendinous units: 24 muscles actuated each leg and 6 abdominal and back muscles controlled the relative movements of the pelvis and upper body. Each musculotendon actuator was represented as a three-element muscle in series with tendon. 23 Parameters defining the force-producing properties of each actuator are given by Anderson and Pandy. 23 Leg-muscle forces for standing and squatting were found by assuming that the model remained in static equilibrium under the influence of gravity alone. The angles of the ankle, knee, and hip joints were obtained from motion analysis experiments reported by Shelburne and Pandy. 25 Because the number of muscles crossing each joint in the model was greater than the number of equilibrium equations, a static optimization problem was formulated to determine the unknown values of the legmuscle forces for each prescribed configuration of the model. The performance criterion was to minimize the sum of the squares of all muscle stresses. Leg-muscle forces for walking were found by solving a dynamic optimization problem, in which the performance criterion was to minimize the metabolic energy consumed per unit distance traveled. Quantitative comparisons of the model predictions with joint angles, ground reaction forces, and muscle activations obtained from experiment showed that the Figure 1. The effect of PTS on knee-joint biomechanics was calculated for three weight-bearing activities: standing, squatting, and the instant of contralateral toe-off in normal walking. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] simulation reproduced the salient features of normal walking. 24 Details of the dynamic optimization solution are given by Anderson and Pandy. 24 In stage 2, a 3D model of the right lower limb was used to calculate knee-joint loading for each task 3 (Fig. 2A). The model of the lower limb was the same as that included in the wholebody model described above, except that the tibiofemoral and patellofemoral joints were each modeled as a six degree-offreedom joint. 26 The contacting surfaces of the femur and tibia were modeled as deformable, while those of the femur and patella were assumed to be rigid. The geometries of the distal femur, proximal tibia, and patella were based on cadaver data reported for an average-size knee. 27 Using methods similar to those reported by Hashemi et al. 28 and Stijak et al., 29 the measured slope of the lateral tibial plateau in the cadaver data reported by Garg and Walker 27 was determined to be 78. Thus, the lateral tibial plateau of the knee model was represented as a flat surface sloping 78 posteriorly. 26 A flat surface is a reasonable representation for knee angles between full extension and 98 because the mid-sagittal contour of the bone and cartilage of the lateral plateau is essentially flat in the region where joint loading occurs. 3 The range of knee flexion utilized in our study was between 58 and 788. Again, using methods similar to those described by Hashemi et al. 28 and Stijak et al., 29 the measured slope between the anterior and posterior cortex of the medial tibial plateau in the cadaver specimens on which the knee model was based was 58. However, the medial articular surface in the cadaver specimens was concave, whilst the medial articular surface was represented by a flat surface in the model. The 28 slope for the surface in the model was measured from the center of the medial articular surface of the cadaver data. This is consistent with the suggestion of Hashemi et al. 28 that medial side measurements of tibial slope ought to be made at the center of the medial articular surface, where joint loading occurs, 31 rather than between the anterior posterior cortex. An elastic-foundation

EFFECT OF POSTERIOR TIBIAL SLOPE ON KNEE BIOMECHANICS 225 Table 1. Values of Knee Ligament Stiffnesses and Reference Strains Assumed in the Model Ligament Reference Strain Stiffness (N/Strain) aacl.93 1, pacl.83 1,5 apcl.39 2,6 ppcl.12 1,9 amcl.17 2,5 cmcl.44 3, pmcl.49 2,5 acm.274 2, pcm.61 4,5 LCL.56 4, Mcap.77 2,5 Lcap.64 2,5 ALS.275 1, Figure 2. (A) The lower limb model was actuated by 13 muscles: 3 vastus medialis (VasMed), intermedius (VasInt), and lateralis (VasLat), rectus femoris (RF), biceps femoris long head (BFLH) and short head (BFSH), semimembranosus (Mem), semitendinosus (Ten), medial and lateral gastrocnemius (GasMed, GasLat), and tensor fascia latae (TFL). Also included in the model but not shown were sartorius and gracilis. (B) The ligaments and capsule of the knee were represented by 14 elastic elements: 3 anterior (aacl) and posterior (pacl) bundles of the ACL, anterior (apcl) and posterior (ppcl) bundles of the PCL, anterior (amcl), central (cmcl), and posterior (pmcl) bundles of the superficial MCL, anterior (acm) and posterior (pcm) bundles of the deep MCL, lateral collateral ligament (LCL), the popliteofibular ligament (PFL), anterolateral structures (ALS), and medial (Mcap) and lateral (Lcap) posterior capsule. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] model was used to calculate the pressure distributions and resultant contact forces in the medial and lateral compartments of the tibiofemoral joint 32 (see Pandy et al. 26 for details). The elastic modulus and Poisson s ratio of cartilage were assumed to be 5 MPa and.45, respectively. 26,32 Fourteen elastic elements were used to describe the geometric and mechanical behavior of the knee ligaments and joint capsule (Fig. 2B). The attachment sites of each ligament, except those of the deep medial collateral ligament (MCL), joint capsule, and popliteofibular ligament (PFL), were based on the data set reported by Garg and Walker. 27 The attachment sites of the deep MCL and joint capsule were obtained from Blankevoort and Huiskes 33 and Reicher. 34 The attachment sites of the PFL were obtained from Shelburne et al. 22 The path of each ligament was approximated as a straight line, and the effects of ligament-bone contact were neglected. Each ligament was assumed to be elastic, and its properties were described by a nonlinear force strain curve. 26,33 The stiffness values and reference lengths of the model ligaments were based on the data reported by Blankevoort and Huiskes 33 and Shelburne and Pandy. 2 The properties of the model ligaments were adjusted to match measurements of knee-joint laxity in the intact and ACLdeficient knee obtained from cadaver studies. 3,26 The ligament stiffnesses and initial strains assumed in the model are given in Table 1. Thirteen muscles actuated the lower limb model. The paths of all the muscles, except vasti, hamstrings, and gastrocnemius, were identical with those represented in the whole-body model The elastic properties of the ligaments in the model were described by a nonlinear force strain curve. 26 All stiffness values are expressed in Newtons per unit strain. Symbols appearing in the table are as follows: anterior (aacl) and posterior (pacl) bundles of the ACL, anterior (apcl) and posterior (ppcl) bundles of the PCL, anterior (amcl), central (cmcl), and posterior (pmcl) bundles of the superficial MCL, anterior (acm) and posterior (pcm) bundles of the deep MCL, lateral collateral ligament (LCL), the popliteofibular ligament (PFL), anterolateral structures (ALS), and medial (Mcap) and lateral (Lcap) posterior capsule. See also Figure 2B. described by Anderson and Pandy. 24 Whereas vasti, hamstrings, and gastrocnemius were each represented by a single line of action in the whole-body model, the separate portions of each of these muscles were included in the lower limb model. 3 Inverse dynamics was used to calculate tibial shear force, ATT, and knee-ligament loading for each task (Fig. 1). Specifically, for each task, the joint angles, ground reaction forces, and leg-muscle forces obtained from the optimization calculations in stage 1 were input into the 3D lower limb model, and a static equilibrium problem was solved to find the corresponding anterior posterior shear force applied to the tibia, ATT, and knee-ligament forces. For walking, we focused on the instant of contralateral toe-off (CTO) because ACL force, tibiofemoral joint force, and ATT were maximum at this time. 3 Tibial shear force, ATT, and knee-ligament forces were first found using a nominal value of PTS of 78. This nominal value is the average value of the PTS of the lateral articular surface obtained from cadaver data on which the knee model was based. 27 The model calculations were then repeated for 18 increments in PTS ranging from 38 to þ178, which amounts to a 18 decrease and increase in PTS, respectively, relative to the nominal value. PTS was altered in the model by rotating the tibial plateau about an axis located above the tibial tuberosity, 2 cm distal to the tibial plateau and normal to the long axis of the tibia (see Fig. 3). This location was chosen because it is the approximate level of the tibia at which a medial-opening or lateral-closing wedge osteotomy is performed. 35 No change was made to the tibial slope in the frontal plane, because it was assumed that the HTO procedure would successfully restore or preserve normal frontal plane alignment at the knee. 35 The results given below are presented as a change in tibial shear force, ATT, and knee-ligament force calculated for a prescribed change in PTS. The effect of PTS on the absolute

226 SHELBURNE ET AL. Figure 3. Posterior tibial slope in the model was changed by rotating the tibial plateau about an axis 2 cm below the distal plateau and centered on the long axis of the tibia. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com] values of each of these quantities are presented as Supplementary Material available on the Journal of Orthopaedic Research website. RESULTS, squatting, and walking produced distinctly different loads at the knee. The total tibiofemoral compressive load for standing was half that for squatting and one-third that for walking at CTO (Table 2). In addition, these loads occurred at different knee flexion angles; specifically, at 58, 28, and 788 for standing, walking, and squatting, respectively. Tibial shear force was directed anteriorly in standing and walking and posteriorly in squatting (Table 2). ACL force was 119 N in standing and 33 N at CTO in walking. The posterior cruciate ligament (PCL) was unloaded in both standing and walking. In contrast, only the PCL was loaded in squatting with peak force being 274 N (Table 2). The change in the resultant shear force applied to the tibia was linearly related to a change in PTS (Fig. 4). The effect of PTS on tibial shear force was approximately the same for squatting and walking. A 58 change in PTS produced a 3% change in tibial shear force (Table 3). The effect of PTS on tibial shear force for standing was slightly less than that calculated for squatting and walking. In all three tasks, as the shear force induced by the tibiofemoral contact force increased in the model, the shear force created by the pull of the patellar tendon decreased in proportion (Fig. 5). Changing PTS had the greatest effect on the shear component of the patellar tendon force calculated for walking. The change in ATT was linearly related to a change in PTS and was similar for all three tasks (Fig. 6). A 58 increase in PTS resulted in a 2 mm increase in ATT (Table 3). The change in ACL force was also linearly related to a change in PTS, except when PTS was increased beyond 78 (Fig. 7). For standing and walking, ACL force increased as PTS was increased in the model (Fig. 7A). The change in ACL force was greatest for walking, with ACL force increasing by 16 N for each 18 increase in PTS. Thus, the model predicted a 26% increase in ACL force when PTS was increased by 58 relative to the nominal value (Table 3). For standing and walking, PTS had a smaller effect on MCL force than ACL force, except near the upper limit of PTS (i.e., 7 18) (Fig. 7B). In squatting, the ACL remained unloaded for the full range of values of PTS evaluated in the model. However, for each 18 increase in PTS, the model predicted a 6 N decrease in PCL force and a 15 N decrease in posterior-lateral corner (PLC) ligament force (Fig. 7A,C). Thus, the model predicted an 11% decrease in PCL force, and a 38% decrease in PLC force, when PTS was increased by 58 relative to the nominal value (Table 3). DISCUSSION The purpose of this study was to determine how changes in posterior tibial slope (PTS) affect tibial shear force, ATT, and knee-ligament loading during functional activity. The model calculations showed that changes in tibial shear force, ATT, and cruciate ligament loading are all linearly related to a change in PTS for standing, squatting, and walking. While the effects of PTS on tibial shear force and ATT were similar for all three tasks, the effect of PTS on ACL force was most noticeable in gait. There are a number of limitations of our analysis. The limitations related to the calculation of leg-muscle forces have been discussed in detail by Anderson and Pandy 24 Table 2. Tibiofemoral and Patellofemoral Compressive Joint Forces, Knee-Ligament Forces, and Tibial Shear Forces Calculated for the Nominal Value of PTS Assumed in the Model Knee Angle (deg) Tibio-Femoral (N) Patella-Femoral (N) ACL (N) PCL (N) MCL (N) PLC (N) Anterior Shear Force (N) þ5 þ663 (1.) þ78 (.1) þ119 (.2) þ39 (.1) þ17 þ83 (.1) þ78 þ1,279 (1.8) þ1,197 (1.7) þ274 (.4) þ12 (.2) 266 (.4) þ2 þ2,15 (2.9) þ935 (1.3) þ33 (.4) þ1 þ255 (.4) Force values normalized to body weight are shown in parentheses.

EFFECT OF POSTERIOR TIBIAL SLOPE ON KNEE BIOMECHANICS 227 Change in Anterior Shear Force (N) 2 1-1 -2 Decreasing Slope Increasing Slope -1-8 -6-4 -2 2 4 6 8 1 Change in PTS (deg) Figure 4. Change in anterior tibial shear force relative to the nominal value of seven degrees plotted against change in PTS for standing, squatting, and contralateral toe-off produced during walking. Please note the data are presented as change relative to the nominal value, and not absolute values. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary. com] and Shelburne and Pandy. 25 The limitations of the knee model used to evaluate ligament and joint-contact loading have been described by Pandy et al. 26 and Shelburne et al. 3 Our predictions of ligament forces depend heavily on the muscle forces calculated for standing, squatting, and walking. While no data exist to validate the calculated values of muscle forces obtained for standing, squatting, and walking, the joint kinematics, net joint moments, and muscle activation patterns predicted for each of these tasks compare favorably with measurements of the same quantities obtained in vivo. 13,24,25 Perhaps the most significant limitation of the present analysis is that the results were obtained by altering a model of the intact knee. The model was developed to simulate knee-joint biomechanics in healthy subjects, and the model predictions were evaluated by comparing the calculated values of tibial shear forces, ATT, leg-muscle forces, and knee-ligament loading with in vivo and in vitro data reported in the literature. 3,13,23,24,26,36,37 However, the changes made to PTS at the time of surgery apply to knees that are affected by various pathologies. In an ACL-deficient knee, for example, it is likely that ATT will be more sensitive to changes in PTS. 37 Nonetheless, the effects of joint pathology were excluded in the present analysis as our aim was to quantify the influence of PTS alone. Further research is needed to address the effect of PTS on knee biomechanics in specific musculoskeletal disorders, such as knee-ligament deficiency. The calculations also did not explicitly account for the effects of internal external (I E) rotation of the knee. Although the 3D knee model allowed for axial rotation of the tibia relative to the femur, the value of I E rotation was constrained to be zero in the simulations in order to match the value of I E rotation assumed in the wholebody model that was used to calculate leg-muscle forces in standing, squatting, and walking. I E rotations during standing and during the stance phase of walking are reported to be small. 38 In squatting, however, internal rotation of the tibia relative to the femur can be significant (i.e., 88 on average in males at 758 of knee flexion 38 ). Because internal tibial rotation increases the force borne by the ACL, 39 and also because tibial rotation in the model was fixed to the value corresponding to that present at full knee extension, it is possible that the model calculations underestimate ACL forces in squatting. To examine the effect of I E rotation on the results obtained in the present study, we applied an internal rotation of 128 to the model knee and repeated the simulation of squatting. ACL force during squatting remained zero, consistent with the results given in Tables 2 and 3 and Figure 7A. This finding is consistent with experimental results reported by Ahmed et al. 4 In the cadaver experiments performed by Ahmed et al., 4 the ACL remained unloaded at higher flexion angles, despite internal and external knee rotation angles as large as 28. In agreement with these results, our calculations for ACL force during squatting were unaffected by the assumption of zero internal rotation. We note here that adding 128 of internal rotation at the knee in the simulations of squatting reduced the force transmitted to the posterior lateral corner ligaments, and shifted more of the burden of resisting the total tibial shear force to the PCL. Thus, PCL force increased by 94 N (34%) when the nominal value of PTS was assumed in the model. Even so, the change in PCL load elicited by a18 increase and decrease in PTS (Fig. 7A) remained approximately the same. Another potential limitation of the present analysis is that it did not address differences between PTS on the medial and lateral sides of the knee. In the model, the slope of the lateral tibial plateau was 58 greater than that assumed for the medial tibial plateau. This side-to-side Table 3. Changes in Anterior Tibial Translation (ATT), Knee-Ligament Forces, and Tibial Shear Force Calculated for a 58 Change in PTS ATT (mm) ACL (N) þ58 PCL (N) þ58 MCL (N) þ58 PLC (N) þ58 Anterior Shear Force (N) þ58 þ58 58 þ58 58 þ58 58 þ58 58 þ58 58 þ58 58 þ2. 2. þ45 (38) 35 (29) þ27 (69) 13 (33) 9 (53) þ13 (76) þ52 (63) 5 (6) þ1.6 1.7 3 (11) þ3 (11) 42 (35) þ38 (32) þ6 (23) 74 (28) þ2.4 2.3 þ8 (26) 75 (25) þ5 (>1) () þ75 (29) 76 (3) Values shown in parentheses indicate the percentage changes in these quantities relative to the nominal values given in Table 2.

228 SHELBURNE ET AL. A Change in Anterior Shear Force (N) B Change in Anterior Shear Force (N) C Change in Anterior Shear Force (N) 4 3 2 1-1 -2-3 -4 2 1-1 -2 3 2 1-1 Total Shear Patellar Tendon Shear TF Contact Shear Decreasing Slope Total Shear Patellar Tendon Shear TF Contact Shear Total Shear Patellar Tendon Shear TF Contact Shear Increasing Slope -2-3 -1-8 -6-4 -2 2 4 6 8 1 Change in PTS (deg) Figure 5. Change in the resultant tibial shear force (total shear) and in the anterior shear forces induced by the tibiofemoral joint force (TF contact shear) and the patellar tendon force (patellar tendon shear) plotted against change in PTS for (A) contralateral toe-off in walking, (B) standing, (C) squatting. difference was kept constant in the calculations as the overall angle of the tibial plateau was increased and decreased by 18. However, recent studies have shown that substantial side-to-side differences in articular ATT Change (mm) 6 4 2-2 -4-6 Decreasing Slope Increasing Slope -1-8 -6-4 -2 2 4 6 8 1 Change in PTS (deg) Figure 6. Change in anterior tibial translation (ATT) plotted against change in PTS for standing, squatting, and contralateral toe-off in walking. A B Change in Cruciate Ligament Force (N) Change in Medial Collateral Ligament Force (N) C Change in Lateral Collateral Ligament Force (N) 2 1-1 -2 125 1 75 5 25-25 -5-75 1 75 5 25-25 -5-75 -1 Decreasing Slope PLC ACL PCL Increasing Slope MCL -1-8 -6-4 -2 2 4 6 8 1 Change in PTS (deg) Figure 7. (A) Change in cruciate ligament forces plotted against change in PTS for standing, squatting, and contralateral toe-off in walking. The solid lines show the change in ACL force, while the dashed line shows the change in PCL force. PCL force was zero for standing and walking, whereas ACL force was zero for squatting. (B) Change in MCL force plotted against change in PTS. MCL force was zero for squatting. (C) Change in the force transmitted to the posterior lateral corner (PLC) ligaments plotted against change in PTS. slope can occur. 28 Because variations in the geometry of the medial and lateral articular surfaces may be a risk factor for ligament injury, 29,41 this issue warrants further investigation. The total anterior shear force applied the tibia (Table 2) was the resultant of the anterior shear forces produced by the muscles, ground reaction forces, and tibiofemoral joint load. In standing, the majority of the anterior shear force applied to the tibia was resisted by the ACL, and only small portions of the forces borne by the LCL and MCL assisted the ACL in resisting the anterior tibial shear force. ACL force was greater than the resultant anterior shear force during standing because the ACL was inclined at an angle relative to the tibial plateau. In walking, the total anterior shear force applied to the tibia was roughly three times higher than that calculated for standing (Table 2). This occurred

EFFECT OF POSTERIOR TIBIAL SLOPE ON KNEE BIOMECHANICS 229 mainly due to the increase in quadriceps force and the concomitant increase in anterior pull of the patellar tendon on the tibia. 3 As in standing, the majority of the tibial shear force present in walking was resisted by the ACL. In squatting, the total shear force applied the tibia was directed posteriorly ( 266 N in Table 2) because of the posterior pull of the hamstrings muscles and also because the ground reaction force vector passed posterior to the knee. 25 Although quadriceps force was higher in squatting than in walking, the anterior pull of the patellar tendon was less because the angle the patellar tendon made with the long axis of the tibia was smaller. 25 The model calculations showed that the resultant shear force applied to the tibia and resisted by the knee ligaments was sensitive to a change in PTS. Specifically, a18 increase in PTS resulted in a tibial shear force for standing that was comparable to the peak value present in normal walking. 3 Tibial shear force was dependent on PTS for two reasons. First, and most importantly, increasing or decreasing PTS altered the amount of shear force created by the tibiofemoral contact force (Fig. 5). Second, changing PTS in the model caused the forces in the soft tissues at the knee to change, particularly the shear component of the patellar tendon force. Specifically, a change in PTS caused ATT to change, which altered the line of action of the patellar tendon relative to the tibial plateau (Fig. 6), and hence, the line of action and shear component of the patellar tendon force. For each activity, as PTS increased in the model, the shear component of the patellar tendon force decreased (Fig. 5). In walking, when quadriceps force and the line of action of the patellar tendon relative to the tibial plateau were both relatively large (Fig. 5A), the resultant shear force applied to the tibia was due mainly to the shear force created by the patellar tendon. 3 This result would not have been obtained if only a tibiofemoral joint force was applied to the model knee. This finding reinforces the important role that muscle forces play in determining knee-joint function in vivo. Our results support the argument that a surgical change in PTS produces a consistent shift of the tibia relative to the femur. 9 11 The linear relationship between a change in PTS and a change in ATT was consistent across all three tasks (Fig. 6), even though the joint angles, ground reaction forces, muscle forces, and joint contact forces were all significantly different for each task. Dejour and Bonnin 8 reported that ATT increased by 6 mm when PTS was increased by 18. The model calculations are in general agreement with these results; when PTS was increased by 18 in the model, ATT increased by 5 mm for walking, and by 4 and 3 mm for standing and squatting, respectively. The model predicted a smaller increase in ATT because the experimental results were obtained from ACL-deficient subjects, whereas the model analysis was performed on an intact knee. The model predictions are also in general agreement with results obtained from cadaver experiments. Agneskirchner et al., 9 Rodner et al., 1 and Giffin et al. 11 found that ATT increased significantly when quadriceps force and tibiofemoral joint load were applied to cadaver knees in which PTS was increased. Figure 6 indicates that a 58 increase in PTS in the model would produce a 2 mm increase in ATT for standing, squatting, and walking. The model calculations showed that a change in ACL force is linearly related to a change in PTS, except at the upper limit of PTS (Fig. 7A). These results do not concur with those of Giffin et al., 11 who found that ACL force (measured in situ) did not change as PTS was altered in cadaver specimens. The difference between model and experiment in this instance is most likely due to differences in the loading conditions employed in these two studies. The tibiofemoral joint forces applied in the cadaver experiments of Giffin et al. 11 were much lower than the forces used to simulate weight-bearing activity in the model. A smaller tibiofemoral joint force produces a smaller net change in the shear force applied to the tibia subsequent to an increase in PTS. This result further emphasizes the critical importance of using physiological loading conditions when attempting to quantify the effects of PTS on knee-joint biomechanics. The model calculations showed that ACL force was sensitive to a change in PTS. Specifically, a 58 increase in PTS resulted in an ACL force for walking that was 26% higher than the nominal value. Following combined ACL repair and HTO surgery, 42 an increase in PTS may cause the force transmitted to the newly reconstructed ACL graft to increase during daily physical activity and rehabilitation exercise. 5 While this may not contribute to failure of the graft, it may produce an effect analogous to accelerated rehabilitation, 43 as ACL graft forces during rehabilitation may be higher than expected. The model calculations also showed that a change in PTS alters the magnitude and location of the contact force acting between the femur and tibia. Changing the anterior posterior position of the tibia relative to the femur causes knee-joint loading to be altered, which may have implications for the progression of OA by shifting load to an area of cartilage unable to accommodate the applied load. 44 Conversely, precise control of PTS may ensure that knee-joint load during weight-bearing activity is directed away from an area of cartilage repair. In summary, our modeling results show that changes in knee-joint loading elicited by changes in PTS depend on tibiofemoral joint load as well as the forces developed by the knee muscles. Therefore, the effects of PTS on knee-joint function can only be fully assessed when physiologic loading conditions are applied to the knee. Our results support the premise that a surgical change in PTS can produce consistent changes in both tibial shear force and ATT. Specifically, we found that ATT, tibial shear force, and ACL force all increase with an increase in PTS. The results obtained in this study describe how a change in PTS affects the mechanics of the knee and also indicate how PTS may be changed to address knee instability.

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