Evaluation of knee joint muscle forces and tissue stresses-strains during gait in severe OA versus normal subjects



Osteoarthritis (OA) is the leading cause of pain and disability in the elderly with the knee being the most affected weight bearing joint. We used a musculoskeletal biomechanical model of the lower extremity including a detailed validated knee joint finite element model to compute lower extremity muscle forces and knee joint stresses-strains during the stance phase of gait. The model was driven by gait data on OA patients, and results were compared with those of the same model driven by data on normal controls. Additional analyses were performed with altered cartilage-menisci properties to evaluate the effects of deterioration during OA. In OA patients compared to normal subjects, muscle forces dropped at nearly all stance periods except mid-stance. Force in the anterior cruciate ligament remained overall the same. Total contact forces-stresses deceased by about 25%. Alterations in properties due to OA had negligible effects on muscle forces, but increased contact areas and cartilage strains and reduced contact pressures. Reductions in contact stresses and increases in tissue strains and transfer of load via menisci are partly due to the altered kinetics-kinematics of gait and partly due to deterioration in cartilage-menisci properties in OA patients. © 2013 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 32:69–78, 2014.

Due to the pain, disability, and costs, joint osteoarthritis (OA) is a major public health concern. The knee is the site most frequently affected among lower extremity joints.[1] The dramatic increase in the number of knee replacement operations (for advanced OA) in recent years especially among the younger patients is alarming.[2] With the aging population and obesity epidemic along with the expectation to remain physically as active at elder ages, the problem is expected to deteriorate. Hence, an urgent need exists for adequate interventions to better understand, control and reduce the associated risk factors.[3] Though the pathomechanics of OA is not well understood, mechanical parameters play an important role. To uncover biomechanical characteristics of knee OA initiation and progression, gait analyses have been conducted to quantify the ground reaction forces (GRF) and lower-extremity joint rotations. Some accordingly focused on differences in gait response between asymptomatic and OA subjects at different stages of the disease.[4-9] These studies often do not compute muscle forces and hence the internal joint loads essential for subsequent prediction of stresses-strains in soft tissues and articular cartilage in particular. Since direct in vivo measurements of muscle forces and tissue stresses are invasive and likely impossible, computational modeling is recognized as a vital complementary tool to improve knowledge of the joint response. Effective management of knee OA, from prevention to treatment should benefit from validated biomechanical model studies.

The stance phase of gait is used to identify differences in kinematics–kinetics and muscle activation between asymptomatic subjects and OA patients.[10-12] Many have focused on knee adduction moment as a surrogate measure of medial load and associated OA.[13] Increases in the moment in early stance occur in severe OA patients compared to controls.[9, 14] In contrast, Astephen et al.[10] reported a reduction in the peak adduction moment in early stance. Smaller flexion rotations during stance accompanied with diminished peak flexion moment in early stance and peak extension moment in late stance were recorded in knee OA patients.[10, 15] However, Heiden et al.[6] reported greater peak flexion in early stance and little difference in flexion–extension moments between OA patients and controls. These differences depend partly on walking speed.[6, 10, 12, 14] In general, larger normalized muscle activation and co-contraction occur in OA patients.[6, 12, 16-18]

OA affects articular tissues with morphological, structural, and biomechanical deterioration via softening, loss of fluid/swelling, fibrillation and destruction of cartilage and hardening in subchondral bone. Earlier investigations demonstrated substantial reductions in cartilage mechanical properties (dynamic and equilibrium moduli) in OA joints compared to healthy ones.[19, 20] Cartilage thickness also diminishes in OA.[21] Thus, the joint environment is influenced both at the macro level by alterations in joint kinematics–kinetics and at the micro level via deterioration in tissue properties. The relative effects of these changes in active musculature and passive joint properties at different stages of OA remain unknown.

Loads on the knee during gait were measured in vivo using instrumented implants.[22] These data along with gait kinematics–kinetics were employed in models to estimate muscle forces and joint contact loads.[13, 23-25] Similar investigations were also performed in asymptomatic subjects.[26-29] Following on our earlier studies on biodynamics of normal knees using a musculoskeletal finite element (FE) model of the lower extremity,[30, 31] we investigated the knee biomechanics in subjects with severe OA during the stance phase. The FE analyses were driven by kinematics–kinetics collected during gait.[16, 32] In the model, cartilage and menisci properties were either left unchanged or altered to represent the disease. We hypothesized that muscle activation levels and joint contact loads are altered in OA subjects and alterations in material properties simulating tissue destruction affect contact stresses/areas and tissue stresses/strains but not the estimated muscle forces and joint loads.


FE Mode

The hip and ankle were considered as 3D and 2D spherical joints, respectively, crossed by 31 muscles (27 around the hip and 4 around the ankle, Fig. 1).[30] The knee model, reconstructed from CT images of bony structures along with direct digitization of soft tissue bounding surfaces and ligament insertion points of a female cadaver specimen,[33] consisted of three bones (tibia, patella, femur) and their articular cartilage layers, menisci, six ligaments (ACL, PCL, LCL, MCL in TF and MPFL, and LPFL in PF), patellar tendon (PT), and quadriceps (four components), hamstrings (six components), and gastrocnemius (two components).

Figure 1.

(A) Schematic diagram with the 34 muscles incorporated into the lower extremity model (taken from OpenSim[42]). Quadriceps: vastus medialis obliqus (VMO), rectus femoris (RF), vastus intermidus medialis (VIM), and vastus lateralis (VL); Hamstrings: biceps femoris long head (BFLH), biceps femoris short head (BFSH), semimembranous (SM)and TRIPOD made of sartorius (SR), gracilis (GA) and semitendinosus (ST); Gastrocnemius: medial (MG) and lateral (LG). Tibialis posterior (TP) and soleus (SO) muscles are uni-articular ankle muscles. Hip joint muscles (not all shown) include adductor, long (ADL), mag (three components ADM), and brev (ADB); gluteus max (three components GMAX), med (three components GMED), and min (three components GMIN), iliacus (ILA), iliopsoas (PSOAS), quadriceps femoris, pectineus (PECT), tensor facia lata (TFL), periformis. (B) Knee FE model; tibiofemoral (TF) and patellofemoral (PF) cartilage layers, menisci and patellar Tendon (PT). Joint ligaments: lateral/medial patellofemorals (LPFL/MPFL), anterior/posterior cruciates (ACL/PCL) and lateral collateral/medial collaterals (LCL/MCL).

Cartilage and menisci were modeled as depth-dependent composites of an isotropic bulk reinforced by networks of collagen fibrils. In menisci, fibrils were oriented primarily circumferentially but with no preferred orientation on bounding surfaces. In the cartilage superficial zones, fibrils were oriented parallel to the surface but became random in the transitional zone and then turned perpendicular in the deep zone anchoring into the subchondral bone. Membrane elements were used to simulate fibril networks in the superficial and deep zones, while brick elements represented the transitional zone.[31, 34] Bony structures were simulated as rigid bodies.[35] Ligaments were modeled by uniaxial connector elements with different initial pre-strains, non-linear (tension-only) material properties, and initial cross-sectional areas of 42, 60, 18, 25, 99, 42.7, and 28.5 mm2 for ACL, PCL, LCL, MCL, PT, MPFL, and LPFL, respectively.[36-39]

Muscle fascicles were modeled by connector elements with orientations at full extension taken from the literature. The Q angle model (Q = 14°)[40] was used for quadriceps muscles; orientations relative to the femoral axis in frontal/sagittal planes were: RF-VIM 0°/4° anteriorly, VL 22° laterally/0°, and VMO 41° medially/0°. Orientations for hamstrings relative to the tibial axis, respectively for BF (BFLH, BFSH), SM, and TRIPOD (GA, SR, ST) were taken[41] as 11.8° medially, 7° laterally, and 7.1° medially in the frontal plane and 0, 16.1, and 18.7° posteriorly in the sagittal plane. Gastrocnemius fascicles were parallel to the tibial axis in the sagittal plane but oriented (GM) 5.3° medially or (GL) 4.8° laterally in the frontal plane.[42, 43] Tibialis posterior/Soleus were oriented 5.3°/4.1° laterally and 1.0°/4° anteriorly relative to the tibial axis.[42] The orientations of the remaining hip muscles were taken from Delp et al.[42] (Fig. 1).

Material Properties

Depth-dependent isotropic hyperelastic (Ogden-Compressible) material properties were considered for the non-fibrillar solid matrix of cartilage layers with the elastic modulus varying linearly from 10 MPa at the surface to 18 MPa at the deep zone and a Poisson's ratio of 0.49.[44] This model that was used due to convergence difficulties was initially verified to yield global displacements and stresses/strains in different components nearly identical to an earlier one having a nearly-incompressible matrix with much lower moduli (∼1 MPa) and higher Poisson's ratio.[34] The matrix of menisci (apart from reinforcing nonlinear collagen fibrils in different locations/directions) was similarly taken as isotropic with 10 MPa for the modulus and 0.45 for the Poisson's ratio. To simulate their horns at tibial insertions, meniscus matrices were stiffened at a higher modulus of 18 MPa at both ends (∼5 mm length).[34]

The collagen content in the menisci was 14% circumferentially and 2.5% radially along with 12% in the outer surfaces in both directions. For cartilage, collagen fibril volume fractions were 15% in the superficial zone, 18% in the transitional zone, and 21% in the deep zone. Respective thicknesses were 15%, 22.5%, and 62.5% of the total height at each point.[34, 45]

To simulate deterioration in cartilage layers and menisci with OA,[19] three other cases were analyzed at 5% and 50% of stance:(OA + E) with matrix modulus and fibril stiffness in the cartilage decreased by 25% to simulate a drop in dynamic response (OA + E + P); with an additional reduction in Poisson's ratio of the cartilage from 0.49 to 0.45 to simulate increased compliance, compressibility, and fluid loss; and (OA + M + C) with combined drops in moduli (by 25%) and Poisson's ratio (to 0.45 in cartilage and 0.35 in menisci) in cartilage and menisci. Larger reductions were also attempted but aborted due to convergence problems.

Muscle Force Estimation

Static optimization with moment equilibrium equations (3 at the knee, 3 at the hip, and 1 at the ankle) (Equation (2)) and inequality equations on muscle forces remaining positive and larger than their passive forces, but smaller than the sum of their passive and maximum active forces (Equation (3)) as constraints were used along with a cost function of the sum of cubed muscle stresses of the entire lower extremity (Equation (1)).[46]

display math(1)
display math(2)
display math(3)

with Fi, Fpi, rij, σimax, PCSA1 being the force, passive force component, lever arms in different planes j, maximum stress, and physiological cross-sectional areas of a muscle i,[42] respectively. Mj are moments resisted by muscles; they were iteratively computed at the knee and were reported[16] at the hip and ankle in accordance with gait kinematics.

Loading, Kinematics, and Boundary Conditions

Iterative kinematics-driven FE analyses that account for passive structures and active musculature of the knee were conducted at six times corresponding to HS (heel strike), 5%, 25%, 50%, 75%, and TO (toe-off) of stance phase (Fig. 2). At each time, the femur was initially fixed in its instantaneous position while the patella was free. The hip/knee/ankle rotations/moments were taken from mean data of in vivo measurements on severe OA subjects (Fig. 2).[16, 32] Due to small differences between asymptomatic and severe OA subjects,[12, 47] GRFs were taken from mean data measurements on normal subjects.[32] Since our model was constructed based on a female knee, a body weight 606.6 N was considered.[48] The location of the resultant GRF at each instant is determined so as to generate reported joint moments[10] accounting for the leg/foot weights (29.78 N/7.98 N). Non-orthogonal local joint coordinate systems[49] were considered in compliance with prescribed rotations/moments.[10]

Figure 2.

Knee joint rotations (R) and moments (M) reported as mean of normal (N) and severe OA subjects during stance.[16] (a) Felxion/extension, (b) adduction/abduction, and (c) internal/external, (d) vertical, anterior, and lateral GRF components.[32] Six instances (heel strike, HS 0%), 5%, 25%, 50%, 75%, and end (toe off, TO 100%) of stance phase are indicated. Loads were normalized to BW of 606.6 N for a female subject.

At each stance period and subject to GRFs and leg/foot weights, muscle forces at the hip, knee and ankle were predicted. This was done iteratively by counterbalancing required moments in deformed configurations at each step. These forces were subsequently applied as external loads and the procedure was repeated (8–10 iterations) till convergence (unbalanced moments <0.1 Nm). Matlab (Optimization Toolbox, genetic algorithms) and ABAQUS 6.10.1 (Static Analysis, SIMULIA, Providence, RI) programs were used.


In the reference OA case as compared to the intact case N, muscle forces in the lateral hamstrings (BFLH, BFSH) dropped except at 0% and 50% periods with their peak at the 5% period (Fig. 3). Results of earlier analyses for case N[30] are presented for comparison. Except at the 50% period, medial hamstrings (SM, GR, ST, and SR) decreased significantly (Fig. 3). Quadriceps forces substantially dropped at the 25% period where they reached their peak but increased at the 50% and 75% periods. Forces in gastrocnemius fascicles increased by 27% at the 50% period, but decreased by 18% at the 75% period (Fig. 3). Alterations in material properties in the OA group had negligible effects on muscle forces.

Figure 3.

Muscle forces at different periods, (a) quadriceps, (b) lateral hamstrings, (c) medial hamstrings, and (d) gastrocnemius. OA: Severe OA with intact material properties, N: results[30] in normal subjects, OA + E, OA + E + P, and OA + M + C present to different degrees the OA deterioration in cartilage and menisci properties.

In the reference OA case, ACL force reached a peak of 342 N at the 75% period and, in comparison to case N, increased except at the 0% and 25% periods (Fig. 4). This force was affected slightly by changes in material properties. Forces in the remaining ligaments were smaller and decreased compared to the case N with peaks of 47 N at HS in MCL and 80 N at TO in LCL.

Figure 4.

Predicted ACL forces at different stance periods. See caption of Figure 3.

Large total TF contact forces transferred through medial/lateral plateaus, via covered and uncovered areas of articulation, followed from variations in muscle forces. They were much larger in the medial plateau starting at the 25% period and peaked at 25% and 75% periods. Compared to the case N, contact forces in OA were lower except at the 50% stance period. Moreover, the proportion of load transmitted via menisci increased in the OA case and did so in cases simulating damaged material properties. The PF contact force dropped substantially at the 5%, 25%, and HS periods, but increased at the 50% and 75% periods due to changes in quadriceps forces in the OA group. The TF and PF contact areas followed the same trends as their respective contact forces. Changes in material properties in the OA group negligibly affected total contact forces, but markedly increased contact areas; for example, at the 50% period, the total TF medial contact area increased from 615 mm2 in OA case to 698 mm2 in OA + M + C case. As a consequence, the average contact pressure noticeably dropped in OA cases, especially with simulated OA material properties (Fig. 5).

Figure 5.

Predicted total TF contact forces (covered: via menisci, uncovered: via cartilage, M: medial plateau, L: lateral). See caption of Figure 3.

In the OA case compared to case N, the peak tibial articular contact pressure decreased throughout stance except at the 50% period (Fig. 6). However, the patterns in contact pressure distribution remained the same. In accordance with the increases in contact areas, the peak contact pressure dropped in cases with deteriorated material properties (Fig. 7). The maximum tensile strain in the cartilage occurred at the deep layers in all cases. These values decreased in the OA case compared with case N, except at the 50% period. In contrast to contact pressures, maximum tensile strains increased in cases with altered material properties (Fig. 8).

Figure 6.

Predicted contact pressure distributions and max values at articular surfaces of tibial plateaus at different periods in normal and OA (with no change in material properties) models. Note that a common legend is used for ease in comparisons. The greater contact stresses on the medial plateau after the 25% stance period and absence of articulation at the lateral plateau at TO are evident. Stresses are smaller in the OA model at all periods except at mid-stance.

Figure 7.

Predicted contact pressure distributions and max values at articular surfaces of tibial plateaus at 50% of stance phase for normal and OA (with different material properties) models (see caption of Fig. 3). OA-associated deterioration in the articular tissues tended to increase contact areas and decrease contact pressures. Large stresses occurred at the medial plateau on the cartilage-cartilage (uncovered) areas.

Figure 8.

Maximum (tensile) principal strain distributions and max values at superficial and deep layers of femoral cartilage at the 50% stance phase for normal and OA (with different material properties) models (see caption of Fig. 3). Strains were much larger in the lower most layers compared to the superficial layers and on the medial condyle compared to the lateral one.


We investigated changes in the knee mechanical environment during gait in the presence of severe OA using kinematics–kinetics collected on asymptomatic and severe OA subjects[16, 32] to drive a lower-extremity iterative kinematics-driven active-passive FE model during stance. The likely effects of OA on articular cartilage and menisci tissues were incorporated by reducing elastic modulus and Poisson's ratio of the bulk and collagen fibrils at 5% and 50% periods. To our knowledge, no previous study investigated this passive-active response in gait of OA patients. Predictions supported the hypotheses that muscle forces and joint response changed markedly with OA and changes in material properties influenced contact stresses-areas and tissue stresses-strains but not the muscle, total contact and ligament forces.

The GRF was taken based on the measurements of normal subjects.[32] Studies that investigated differences between asymptomatic and OA subjects indicated a relatively small reduction in the peak GRF in OA.[12] Hunt et al.[11] argued, however, that the differences in the recorded external moments at the knee in OA patients are due to marked alterations in GRF lever arm and not in GRF magnitude. By using joint moments estimated for OA subjects in gait,[16] we automatically accounted for alterations in GRF magnitude and lever arm as far as joint moments are concerned. Any changes in GRF absolute magnitude can hence only negligibly influence the forces at the foot in our model of the OA group and not the resulting joint moments.

In accordance with the marked reduction in the knee flexion moment/rotation during early stance (Fig. 2),[16, 32] quadriceps forces dropped substantially from their peak of 1,087 N in the normal group at the 25% period to 525 N in the OA case (Fig. 3a). This could reflect quadriceps avoidance in early stance in OA patients. The quadriceps are also more efficient in generating flexion moments at smaller knee flexion angles as in the OA case.[36] These trends reversed, however, later in stance resulting in significantly greater quadriceps forces in the OA case (Fig. 3). At TO and despite slightly larger flexion moment, much smaller quadriceps forces were computed in the OA case likely due to much lower forces in medial hamstrings (acting as antagonists in flexion).

Large forces were generated in lateral hamstrings (Fig. 2b) in response to the knee adduction moments.[10] In association with the moments, lateral hamstrings (BFLH, BFSH) forces decreased in the OA case during stance except at HS and mid-stance. The latter increase is due to the augmented adduction moment associated with severe OA.[8-10] Forces in medial hamstrings (SM, ST, SR, and GA) decreased at almost all periods. Lower hip flexion moments in OA patients also acted to reduce hamstrings forces in early stance. In conjunction with variations in the knee adduction moment and the disappearance of the large extension moment at the 2nd half of stance, forces in the lateral and medial hamstrings dropped after mid-stance. At final stance, lateral hamstrings were completely unloaded, which along with the negligible activity in the lateral gastrocnemius, resulted in the transfer of the entire joint load via the medial compartment. This finding agrees with earlier studies indicating small or no loads on the lateral compartment at terminal stance.[27, 50-52] The lateral unloading at mid-stance in some OA patients computed in an EMG-driven model is likely associated with larger adduction rotations.[25]

In both normal and OA groups and despite substantial knee adduction moments, larger activity was predicted in the MG compared to the LG (Fig. 3d). To counterbalance this antagonistic activity, large forces occurred in lateral hamstrings. The deeper short-head component of biceps femoris was hence carrying most of the force in lateral hamstrings at 25% to 75% stance (Fig. 3d). This activity is hardly detectable by surface EMG measurements.

Generally greater muscle activation and co-contraction levels were recorded via superficial EMG in OA patients compared to normal subjects.[6, 9, 12, 15-18] To qualitatively validate our predictions with reported normalized EMG measurements corresponding to the same input data used in our models,[15, 16] the computed muscle forces and the normalized EMG measurements were both normalized to their maximum values during stance (Fig. 9). The predictions in absolute terms plus their relative variations matched the reported trends. Estimated values in both OA and normal groups were, however, consistently smaller than measurements at HS (Fig. 9), which may be partly due to the absence of coactivity in our FE models. Moreover, the commonly used normalization of collected EMG data to their values recorded at isometric maximal voluntary exertion should be taken with caution when applied to OA patients, as pain avoidance may reduce peak muscle activity during maximum exertion by ∼50% compared with healthy subjects.[53] Finally, errors anticipated in superficial EMG measurements in larger and deeper muscles and in any attempt to correlate normalized EMG magnitude with active muscle force are additional factors that call for caution in such qualitative comparisons.

Figure 9.

Ensemble averaged EMG[15, 16] and estimated muscle forces (Model) normalized to their maximum values during the stance phase for various knee muscles.

Due to the marked drop in hamstrings activity at the 2nd half of stance, ACL forces substantially increased in OA patients (Fig. 4). With the significant reduction in quadriceps activation at the 25% period, however, ACL forces were slightly lower in the OA group. As expected, the PCL remained slack under all conditions. The decrease in the knee adduction angle at TO dropped LCL force from 206 N in the normal subjects to 80 N in the OA model.

In keeping with changes in muscle activation patterns, the TF contact load increased only at mid-stance in OA models when compared with the normal model. Due to substantial increases in contact areas in OA models at all instances, the mean and peak contact pressures on both tibial and femoral surfaces decreased at all periods except mid-stance when they increased slightly (2%) despite much larger contact forces. The medial compartment carried 70–100% of the joint load after initial stance periods, which agrees with reported estimates.[8, 25] Any varus alignment in OA subjects[8, 25] could further increase the medial share of joint loading. The disagreement with the estimate of equal lateral/medial load sharing by Mononen et al.[28, 29] is due partly to their valgus orientation during stance.

Deterioration in cartilage and menisci properties in OA models did not influence muscle, contact, and ligament forces, but substantially increased contact areas that further reduced mean and peak contact pressures. This effect was evident even in mid-stance when despite larger contact forces, peak and mean contact pressures dropped substantially (Fig. 7). In parallel, the portion of contact load transmitted via the menisci increased in OA models. Deterioration in material properties increased, as expected, the superficial and deep cartilage strains in OA models (Fig. 8). Markedly larger strains at the deep zone were predicted that could be related to the existing stiffness gradient.[54] This bone–cartilage junction is reported as the site of horizontal split fractures during daily activities[55] and impact loads.[56, 57] These results are in agreement with earlier FE model studies.[58, 59]

Our work has limitations. Co-activity in muscle exertions was not considered. Identical musculature (no atrophy) was also assumed in both OA and normal subjects. The material deterioration expected with OA[19, 21] was simulated sequentially by reductions in matrix and fibril dynamic moduli and tissue compressibility. Larger reductions in moduli[19] were attempted but aborted due to convergence problems in our simulations. The cartilage thickness in TF and PF joints were left unchanged in OA models. Identical lower-extremity geometry was used for both groups. Our results depended on the measured kinematics–kinetics used as input data. Despite disagreements in the literature on the effect of OA during gait,[6] the results of Astephen[16] were used due to the large number of subjects, the complete data on rotations and moments at the ankle, knee, and hip, and the collected EMG values.

In summary, OA-associated alterations in rotations and moments at lower extremity joints recorded during gait influenced activation levels in lower extremity musculature and contact forces-stresses and stresses-strains in knee articular cartilage. Reductions in mean and peak contact stresses and increases in tissue strains and load transfer via menisci are partly due to altered kinetics–kinematics of gait and partly due to deterioration in cartilage material properties in OA patients.


The work was supported by a grant from the Natural Sciences and Engineering Research Council of Canada (NSERC-Canada).