Contributions of Muscles, Ligaments, and the Ground-Reaction Force to Tibiofemoral Joint Loading During Normal Gait

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1 Contributions of Muscles, Ligaments, and the Ground-Reaction Force to Tibiofemoral Joint Loading During Normal Gait Kevin B. Shelburne, 1 Michael R. Torry, 1 Marcus G. Pandy 2,3 1 Steadman-Hawkins Research Foundation, Vail, Colorado 2 Department of Mechanical & Manufacturing Engineering, University of Melbourne, Australia 3 Departent of Biomedical Engineering, University of Texas, Austin, Texas Received 10 September 2005; accepted 14 May 2006 Published online 9 August 2006 in Wiley InterScience ( DOI /jor ABSTRACT: The aim of this study was twofold: first, to determine which muscles and ligaments resist the adduction moment at the knee during normal walking; and second, to describe and explain the contributions of muscles, ligaments, and the ground reaction force to medial and lateral compartment loading. Muscle forces, ground reaction forces, and joint motions obtained from a dynamic optimization solution for normal walking were used as input to a three-dimensional model of the lower limb. A static equilibrium problem was solved at each instant of the gait cycle to determine tibiofemoral joint loading at the knee. Medial compartment loading was determined mainly by the orientation of the ground reaction force. Because this force vector passed medial to the knee, it applied an adduction moment about the joint during stance. In contrast, all of the force transmitted by the lateral compartment was due to muscle and ligament action. The muscles that contributed most to support and forward propulsion during normal walking (quadriceps and gastrocnemius) also contributed most to knee stability in the frontal plane. The knee ligaments, particularly those of the posterior lateral corner, provided stability to the knee at certain periods of the stance phase, when activity of the important stabilizing muscles was low. ß 2006 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 24: , 2006 Keywords: walking; model; optimization; adduction moment; knee osteoarthritis INTRODUCTION The onset and progression of knee osteoarthritis (OA) is often attributed to an injury or pathology that alters load distribution between the medial and lateral compartments of the tibiofemoral joint. A change in normal joint loading may be due to damage to the soft tissues, such as the knee igaments 1 and menisci, 2,3 abnormal alignment of the tibia relative to the femur, 4 musculoskeletal weakness, 5,6 or some combination thereof. A number of studies have reported that surgical treatment of soft tissue injuries and correction of tibiofemoral alignment may decrease the progression of knee OA. 4,5 However, the outcomes of these surgeries remain uncertain, as little is known about the way muscles, ligaments, and external forces contribute to loading of the tibiofemoral joint during activities of daily living. Correspondence to: Kevin B. Shelburne (Telephone: ; Fax: ; kevin.shelburne@shsmf.org) ß 2006 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. The distribution of force between the medial and lateral compartments depends on two factors: the magnitude of the external varus or valgus moment acting about the knee, 7,8 and the contributions that the muscles and ligaments make to support this moment. In walking, the moment acting in the frontal plane (the adduction moment) bends the leg inward, causing most of the tibiofemoral joint load to be transmitted by the medial compartment. 8 The location of the resultant tibiofemoral force in normal walking was first predicted by Morrison 9 and Harrington. 10 Schipplein and Andriacchi 8 later showed that the adduction moment not only shifts tibiofemoral load to the medial side, but that it also acts to open the joint laterally. Their analysis demonstrated that some combination of muscle and ligament forces is needed to resist the external adduction moment and prevent lateral joint opening when humans walk at their natural speeds. Many researchers have used cadaver experiments to demonstrate the capacity of specific ligaments to support static adduction moments at the knee These studies have shown that the ligaments of the posterior lateral corner of the JOURNAL OF ORTHOPAEDIC RESEARCH OCTOBER

2 1984 SHELBURNE ET AL. knee, the lateral collateral ligament (LCL), and the popliteofibular ligament (PFL) offer the greatest resistance to the adduction moment. Some investigators have also quantified the capacity of specific muscles to resist knee adduction moments during activity Lloyd and Buchanan 19 found that the muscles that produce most of the flexion extension moment at the knee during isometric exercise (i.e., quadriceps, gastrocnemius, and hamstrings) also produce most of the moment needed to resist pure adduction. No study has identified the muscles and ligaments that stabilize the knee in the frontal plane during gait. The major aim of the present study was twofold: first, to determine which muscles and ligaments resist the external adduction moment applied at the knee during normal walking; and second, to describe and explain the contributions of muscles and ligaments, as well that of the ground reaction force, to medial and lateral compartment loading. Based on the results of previous studies, 8 10,19 we hypothesized that the resultant force transmitted by the tibiofemoral joint remains on the medial side of the knee during stance and that the knee adduction moment is resisted by the quadriceps, gastrocnemius, and hamstrings muscles, which act synergistically with the ligaments of the posterior lateral corner of the knee. MATERIALS AND METHODS Tibiofemoral joint loading was calculated using a 3D model of the lower limb. Joint angles, ground reaction forces, and muscle forces obtained from a dynamic optimization solution of normal walking 20 were applied to the lower limb model, and a static equilibrium problem was solved at each instant during the gait cycle to find the anterior posterior and medial lateral translations, varus valgus orientation, joint-contact forces, and ligament forces at the knee. A detailed description of the solution procedure is given by Shelburne et al. 21 The lower limb model was comprised of six segments: pelvis, thigh, shank, patella, hindfoot, and toes. These segments were connected together by a 3-degree-offreedom (dof) hip joint, a 6-dof tibiofemoral joint, a 6-dof patellofemoral joint, a 2-dof ankle joint, and a 1-dof metatarsal joint (Fig. 1A). The models of the hip, ankle, and metatarsal joints are described by Anderson and Pandy. 20 The hip and ankle joints were included in the lower limb model to account for the changing lines of action of the biarticular muscles crossing the knee. The metatarsal joint was included to allow the ground reaction force obtained from the walking simulation to be applied in the same way to the lower limb model as it was in the original walking model. The knee model is described by Pandy et al. 22 The geometries of the distal femur, proximal tibia, and Figure 1. (A) The muscles of the leg were modeled by 13 actuators: 21 vastus medialis (VasMed), vastus intermedius (VasInt), and vastus lateralis (VasLat), rectus femoris (RF), biceps femoris long head (BFLH), biceps femoris short head (BFSH), semimembranosus (MEM), semitendinosus (TEN), medial gastrocnemius (GasMed), lateral gastrocnemius (GasLat), and tensor fascia latae (TFL). Also included, but not shown, were sartorius and gracilis. (B) The knee ligaments were modeled by fourteen elastic bundles: 21 anterior (aacl) and posterior (pacl) bundles of the anterior cruciate ligament, the anterior (apcl) and posterior (ppcl) bundles of the posterior cruciate ligament, the anterior (amcl), central (cmcl), and posterior (pmcl) bundles of the superficial medial collateral ligament, the anterior (acm) and posterior (pcm) bundles of the deep medial collateral ligament, the lateral collateral ligament (LCL), the popliteofibular ligament (PFL), the anterolateral structures (ALS), and the medial (MCap) and lateral (LCap) posterior capsule. patella were based on cadaver data reported for an average-size knee. The contacting surfaces of the femur and tibia were modeled as deformable, while those of the femur and patella were assumed to be rigid. Compressibility of the articular surfaces was based on mechanical measurements obtained from cadaver specimens. Fourteen elastic elements were used to describe the geometry and mechanical behavior of the anterior and posterior cruciate ligaments, medial and lateral collateral ligaments, popliteofibular ligament, and joint capsule (Fig. 1B). The stiffness properties of the ligaments were adjusted to match measurements of knee joint laxity obtained from cadaver studies. 21,22 The reference lengths JOURNAL OF ORTHOPAEDIC RESEARCH OCTOBER 2006 DOI /jor

3 TIBIOFEMORAL JOINT LOADING DURING NORMAL GAIT 1985 and stiffness values of the model ligaments are given in Shelburne et al. 21 Thirteen muscles were represented (Fig. 1A). The paths of all the muscles, except vasti, hamstrings, and gastrocnemius, were identical to those represented in the walking model described by Anderson and Pandy. 20 Whereas vasti, hamstrings, and gastrocnemius were each represented by a single muscle in the walking model, the separate portions of each of these muscles were included in the lower limb model (see ref. 21 for details). The attachment sites and path geometries of the muscles were based on data reported by Delp et al. 23 The muscle forces, ground reaction forces, and joint angles that were input into the lower limb model were obtained from a dynamic optimization solution of normal walking. 20 The inertial properties of the limb segments in the model were based on anthropometric measures obtained from five healthy adult males (26 3 years, cm, and kg) with no history of knee pathology. 20 The regression equations of McConville et al. 24 were used to estimate the values of the anthropometric parameters. Details of the 3D model of the body (178 cm, 71 kg) used in these calculations are given by Anderson and Pandy. 25 The optimization problem was to minimize the metabolic energy consumed per unit distance traveled on level ground subject to a set of initial states and terminal constraints. The initial states were found by averaging kinematic and force plate data obtained from gait measurements of the five subjects. Terminal constraints were applied to the joint angles, joint angular velocities, and muscle forces to enforce symmetry of the gait cycle. Details of the model used to estimate metabolic energy consumption are presented by Bhargava et al. 26 The solution to the dynamic optimization problem produced a forward dynamic simulation of a half cycle of normal gait. The excitation patterns of the muscles and the resulting joint angles and ground forces generated during the simulation compared favorably to muscle EMG, kinematic, and force plate measurements recorded for the five male subjects, each of whom walked at his self-selected speed. 20,27 Knee adduction moment was calculated in two ways. To compare our results with the adduction moment commonly reported in gait studies, 4,28,29 the external knee adduction moment was taken as the moment produced by the component of the ground reaction force in the frontal plane acting about the geometric center of the knee (Fig. 2A). To consider the individual contributions of the muscles, ligaments, and the ground reaction force to stability of the knee in the frontal plane, we defined the total knee adduction moment as the sum of all the internal and external moments that adduct the knee and compress the joint on the medial side. Total knee adduction moment was calculated as the sum of two moments taken about the center of pressure on the medial tibial condyle: 8 one produced by the component of the ground reaction force in the frontal plane and the other by the tibiofemoral force acting on the lateral tibial condyle (Fig. 2B). Stability of the knee in the frontal plane is maintained by equal and opposite adduction and abduction moments. The abduction moments produced by muscle and ligament forces were calculated as the frontal-plane components of these forces acting about the center of pressure on the medial tibial condyle; the net effect of these moments is equal and opposite to the total adduction moment, tending to compress the joint on the lateral side (see Fig. 2B). RESULTS The peak external knee adduction moment in the model (3.5 Nm/weight*height) was near the top of the normal range reported for normal gait in healthy adults 7,8,28,29 (Fig. 3A). The total knee adduction moment was balanced by the abduction moments applied by the muscles and ligaments crossing the knee (Fig. 3B). Muscles provided most of the resistance during single-leg stance; the knee ligaments contributed significantly during early stance and midstance (cf. gray solid and black dashed lines). The quadriceps and gastrocnemius muscles dominated the total abduction moment at the knee. The first peak in the abduction moment occurred at contralateral toe-off and was due to the force developed by the quadriceps; the second peak occurred at contralateral heel-strike and was caused by the force in gastrocnemius (Fig. 4A). The hamstrings contributed significantly only during early stance. The tensor fascia latae, sartorius, and gracilis contributed much less than the other muscles crossing the knee. The ligaments of the posterior lateral corner provided the primary passive resistance to knee adduction during early stance and midstance (Fig. 4B). The ACL and posterior capsule offered little resistance to knee adduction throughout stance. The resultant tibiofemoral force peaked at contralateral toe-off and was 2.7 times body weight (BW) or 2015 N (Fig. 5A). The contact force remained mainly on the medial side during single-leg stance. Peak force in the medial compartment was 2.4 BW or 1650 N, while that in the lateral compartment was much less (0.8 BW or 560 N). Only near toe-off were the magnitudes of the contact forces on the medial and lateral sides more or less the same. The force pattern in the medial compartment resembled that of the external knee adduction moment (cf. Fig. 3A with gray line in Fig. 5A). When the external knee adduction moment peaked just before contralateral toe-off, all of the force acting between the femur and tibia shifted to the medial side. The lateral compartment was unloaded just prior to single-leg stance and for a short period DOI /jor JOURNAL OF ORTHOPAEDIC RESEARCH OCTOBER 2006

4 1986 SHELBURNE ET AL. Figure 2. Knee adduction moment was calculated in two ways. (A) The external adduction moment was calculated about the center of the knee to compare with measured values from the literature. (B) The total adduction moment was calculated about the center of pressure in the medial compartment of the tibiofemoral joint. Total adduction moment was the sum of all the moments that tended to adduct the knee. The total adduction moment was resisted by the actions of the muscles and ligaments that applied abduction moments about the knee. during midstance. During swing, the forces acting in the medial and lateral compartments were roughly the same (not shown). Muscles dominated the resultant force acting at the tibiofemoral joint during stance (Fig. 5B). The quadriceps and gastrocnemius contributed most to the resultant tibiofemoral force (dashed line at CTO and CHS). Except near heel strike, the knee ligaments contributed little. The ground reaction force dominated medial compartment loading during stance (Fig. 6A). Muscles contributed significantly only at the beginning and end of single-leg stance, as the quadriceps and gastrocnemius developed large forces at these times. The knee ligaments contributed little to the force transmitted by the medial condyle. The ground reaction force acted to unload the lateral compartment during stance (Fig. 6B). Muscles contributed significantly to lateral compartment loading when the forces developed by the quadriceps and gastrocnemius were highest (Fig. 6B, dashed line at CTO and CHS). The knee ligaments contributed significantly during early stance and for a short period in midstance. DISCUSSION Our predictions of tibiofemoral loading are similar to the results of others. 7 10,30,31 Using a modeling approach based on the reduction method, Morrison, 9 Harrington, 10 and Hurwitz et al. 7 calculated two peaks in the tibiofemoral contact force: the first peak corresponded to quadriceps muscle action at contralateral toe-off; the second, to gastrocnemius action at contralateral heel-strike. Our results (Fig. 5A) are in accord with these findings. Our model predicted a peak resultant joint contact JOURNAL OF ORTHOPAEDIC RESEARCH OCTOBER 2006 DOI /jor

5 TIBIOFEMORAL JOINT LOADING DURING NORMAL GAIT 1987 Moment A dduction Moment. x Height) (% BW x Height) Abduction (%BW HS FF CTO MS HO CHS TO A Total Muscle Ligament Gait Cycle (%) Figure 3. (A) The external adduction moment calculated for the stance phase of normal gait. This is the moment of the ground reaction force acting about the center of the knee in the frontal plane (see Fig. 2A). Symbols appearing at the top mark major events during the gait cycle: heel-strike (HS), foot-flat (FF), contralateral toe-off (CTO), midstance (MS), heel-off (HO), contralateral heel-strike (CHS), and toe-off (TO). (B) The resistance provided by the muscles and ligaments to the total adduction moment acting about the knee. The total adduction moment was the sum of the moments produced by the component of the ground reaction force in the frontal plane and the lateral compartment tibiofemoral force acting about the center of pressure in the medial compartment. Abduction moments are positive; adduction moments are negative. force of 2.7 BW at contralateral toe-off. Peak values measured by Taylor et al. 30 for a single patient wearing an instrumented knee prosthesis ranged from 2.3 to 2.5 BW. In a subsequent study, using computer modeling and gait measurements, Taylor et al. 31 reported an average peak resultant tibiofemoral force of 3.1 BW in four patients. Consistent with previous findings, 7 10 our analysis shows that the center of pressure of the resultant tibiofemoral force remains on the medial side of the knee during stance. Peak medial compartment load was 2.3 BW, which agrees closely with the results of Hurwitz et al. 7 (2.4 BW) and Schipplein and Andriacchi 8 (2.3 BW). Hurwitz et al. 7 also found that the lateral compartment was unloaded for portions of the stance phase in some subjects. In our model, the force in the lateral B A bduction Moment. (% BW x Height) A bduction Moment. (% BW x Height) HS FF CTO MS HO CHS TO 3.0 Total Muscle Quadriceps A TFL 2.0 Gastrocnemius Hamstrings Total Ligament PLC = LCL + PFL ACL Posterior Capsule Gait Cycle (%) Figure 4. (A) Individual muscle contributions to the total abduction moment during normal gait. The black curve represents the total contributions from all muscles (the same as the gray curve in Fig. 3B). The contributions from sartorius and gracilis are not shown because they were much smaller than those in the diagram. (B) Individual ligament contributions to the total abduction moment. The black curve represents the total contributions from all ligaments (the same as the dashed curve in Fig. 3B). compartment was zero just before contralateral toe-off and for a brief period in midstance (Fig. 5A, dashed line). A potential limitation of our analysis was the assumption of static equilibrium during the simulated gait cycle. Specifically, the inertial contributions of the lower limb segments were neglected in the calculations of tibiofemoral joint loading. However, Anderson and Pandy 32 showed that muscle and gravitational forces dominate the forces transmitted by the lower limb joints throughout the stance phase of normal walking. We expect, therefore, that the pattern of tibiofemoral loading would look much the same as that shown in Figure 5A had the effects of centrifugal and inertial forces been included. A second limitation of our analysis was that some of the muscle forces input into the lower limb model did not come directly from the walking simulation. Specifically, the forces in the separate portions of vasti, hamstrings, and gastrocnemius were apportioned according to their size because their B DOI /jor JOURNAL OF ORTHOPAEDIC RESEARCH OCTOBER 2006

6 1988 SHELBURNE ET AL.. Force (BW) Tibiofemoral Force (BW) Tibiofemoral HS FF CTO MS HO CHS TO Total Medial Lateral Gait Cycle Total (%) GRF Muscle Ligament Gait Cycle (%) Figure 5. (A) Distribution of tibiofemoral joint load during the stance phase of normal gait. Most of the force acting between the femur and tibia was located in the medial compartment. (B) Contributions of muscles, ligaments, and the ground reaction force (GRF) to the resultant force (Total) transmitted by the tibiofemoral joint during stance. A B M edial Compartment. Force (BW) L ateral Compartment. Force (BW) HS FF CTO MS HO CHS TO Total Ligament Total GRF Ligament Muscle GRF Muscle Gait Cycle (%) Figure 6. (A) Contributions of muscles, ligaments, and the ground reaction force (GRF) to medial compartment load during stance. (B) Contributions of muscles, ligaments, and the ground force to lateral compartment load. In the model, the lateral compartment was unloaded for two brief periods during the stance phase of normal gait (at CTO and just prior to HO). A B separate portions were omitted in the original walking model. As a result, it is difficult to draw firm conclusions about the contributions that the separate portions of these muscles make to knee stability in the frontal plane. Even so, a sensitivity analysis was performed to quantify the change in knee load caused by a change in the amount of muscle force apportioned to the separate portions of vasti, hamstrings, and gastrocnemius. The apportionment of vasti had little effect on tibiofemoral load because these muscles insert similarly into the model patella. The apportionment of hamstrings had little effect because hamstrings force is low throughout stance. Although tibiofemoral load was sensitive to the apportionment of gastrocnemius force between its medial and lateral heads, we believe equal apportionment was reasonable considering that these muscles have similar size and are similarly activated during walking. 33 The muscles that contribute most to support and forward propulsion during normal walking also contribute most to knee stability in the frontal plane. Anderson and Pandy 32 identified five major muscle groups responsible for supporting the body against gravity during normal gait: quadriceps and gluteus maximus in early stance; gluteus medius during midstance; and gastrocnemius and soleus during late stance. Recently, Liu et al. 34 showed that these muscle groups also contribute most significantly to forward propulsion during normal walking. Among these muscles, only two, the quadriceps and gastrocnemius, cross the knee. The quadriceps contributed most of the muscular moment needed to resist knee adduction during the early portion of single-leg stance, whereas gastrocnemius provided most of the moment needed to resist adduction in late stance (Fig. 4A). These results are similar to those reported by Lloyd and Buchanan, 19 who found that the muscles that contribute most to knee flexion extension moments during isometric exercise also provide most of the moment needed to resist knee abduction and adduction. It is surprising that quadriceps and gastrocnemius offer the most resistance to knee adduction in normal walking, considering that these muscles have relatively small abduction moment arms at the knee. They can exert large abduction moments because they develop relatively large forces during the stance phase of normal gait. In contrast, tensor fascia latae has a much larger abduction moment arm, yet this muscle offers relatively little JOURNAL OF ORTHOPAEDIC RESEARCH OCTOBER 2006 DOI /jor

7 TIBIOFEMORAL JOINT LOADING DURING NORMAL GAIT 1989 resistance to knee adduction because it develops a much smaller force in the model. The hamstrings also offer little resistance to knee adduction in the model, because these muscles have relatively small abduction moment arms about the knee, and also because they develop relatively small forces during stance. Similar to the findings of Lloyd and Buchanan, 19 sartorius and gracilis contributed little to abduction and adduction moment, respectively, because these relatively small muscles produced much smaller forces than the prime movers of the leg in walking. The model simulation showed that the posterolateral corner provided the main passive resistance to adduction moment (Fig. 4B). In the model, the posterolateral corner was comprised of two structures: the LCL and the PFL. The forces borne by these structures were highest at foot-flat and heel-off, when the external knee adduction moment was high and the activation levels of all the muscles were relatively low. Nonetheless, the peak forces borne by the LCL (167 N) and PFL (15 N) remained well below the failure strengths for these tissues. 35 This prediction of the model is consistent with the results of a large number of in vitro studies, in which the LCL and PFL were found to be the key passive structures that resist knee adduction In their modeling study, Schipplein and Andriacchi 8 also found that the lateral supporting structures bear some force for 60% of the stance phase of normal gait. Muscles made the largest contribution to the resultant force acting between the femur and tibia (Fig. 5B). The reason is twofold. First, the muscles crossing the knee contributed almost equally to the forces acting in the medial and lateral compartments during stance (dashed lines in Fig. 6A and B). This was because the quadriceps and gastrocnemius were arranged symmetrically about the center of the knee in the frontal plane. Second, although the ground reaction force contributed significantly to medial compartment loading, it also acted to unload the lateral compartment, which meant that its contribution to the resultant tibiofemoral force was not as great. Our model clearly shows that the medial compartment transmits the majority of tibiofemoral joint load throughout the stance phase of normal walking. The resultant tibiofemoral force remained on the medial side because the ground reaction force applied an adduction moment about the knee (i.e., the ground force passed medial to the knee). As the ground force squeezed the femur and tibia together on the medial side, it also acted to unload the lateral compartment. Some force was nonetheless transmitted by the lateral condyle due to the resistance provided by the muscles and knee ligaments (Fig. 6B). In summary, medial compartment loading at the knee during normal walking is determined mainly by the orientation of the ground reaction force. Because this force passes medial to the knee, it applies an external adduction moment about the joint during stance. As a result, the center of pressure of the resultant tibiofemoral force remains on the medial side of the knee. In contrast, all of the force acting in the lateral compartment is due to the actions of the muscles and knee ligaments. The quadriceps and gastrocnemius muscles contribute most to knee stability in the frontal plane; these muscles act synergistically with the ligaments of the posterior lateral corner to resist knee adduction during stance. ACKNOWLEDGMENTS This work was supported in part by the Steadman- Hawkins Research Foundation and a VESKI Fellowship provided to M.G.P. REFERENCES 1. Noyes FR, Schipplein OD, Andriacchi TP, et al The anterior cruciate ligament-deficient knee with varus alignment. 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