Musculoskeletal simulations of human movement are often used to estimate soft tissue and joint contact loads. However, traditional modeling approaches use a serial approach that does not account for knee joint laxity when simulating movement. In the traditional approach, a multibody dynamics model is used to calculate muscle forces needed to produce skeletal movement. Then, these muscle forces are applied as boundary conditions to a detailed joint model to solve for soft tissue loading. However, the dynamic musculoskeletal models often assume a one degree of freedom kinematic knee joint that behaves independent of load. The overall goal of this work was to investigate the coupling of multibody dynamics and soft tissue mechanics. This goal was achieved by completing the following three objectives.

Objective 1:​ Empirically assess how in vivo knee kinematics vary with quadriceps loading Rationale:​ Musculoskeletal models often assume that joints are simply kinematic constraints. However in reality, joint kinematics vary with loading, which can influence the line of action and moment arm of a muscle about the knee. Hypothesis:​ The in vivo tibiofemoral finite helical axis and patellar tendon moment arm will exhibit load‐dependent behavior. Methods:​ Dynamic MRI imaging techniques were used to measure three‐dimensional knee kinematics under controlled loading conditions. Eight subjects performed cyclic knee flexion/extension tasks against inertial and elastic loads, which induced quadriceps activity with knee flexion and extension, respectively. For both loading conditions, the tibiofemoral finite helical axis was calculated as well as the patellar tendon’s moment arm with respect to this axis. Results:​ Quadriceps loading in a flexed knee induced a significant inferior shift of the finite helical axis, which diminished the patellar tendon moment arm. Since the quadriceps load induced during flexion in the experiment was similar to that seen during the load‐acceptance phase of gait, this load‐dependence may be important to consider in gait simulations. Relevance:​ Since the quadriceps load induced during flexion in the experiment was similar to that seen during the load‐acceptance phase of gait, this load‐dependence may be important to consider in gait simulations.

Objective 2:​ Investigate whether a muscle‐actuated computational knee model that includes ligament compliance and tibiofemoral contact could emulate in vivo kinematic patterns. Rationale:​ Since the knee exhibits load‐dependent behavior in vivo, a framework should be developed to couple multibody dynamics and soft tissue loads. Hypothesis:​ Similar to what was seen in vivo, the finite helical axis will shift inferiorly when the quadriceps are loaded in flexion, thus diminishing the moment arm of the patellar tendon. Methods:​ We started with a generic lower extremity model with 44 muscles, 6 joints, and 18 degrees of freedom. The kinematic knee joint was replaced by a six degree of freedom tibiofemoral joint. This knee model included 19 ligaments represented by non‐linear springs as well as an elastic foundation model to calculate tibiofemoral cartilage contact loads. The one degree of freedom patellofemoral joint was constrained to move within a path relative to the femoral groove with patellar tendon and quadriceps forces acting on either end of the patella. A co‐simulation framework was implemented in which neuromusculokeletal dynamics and knee mechanics were simultaneously solved using a computed muscle control algorithm. Results:​ The co‐simulation framework predicted similar load‐dependent variations in knee kinematics as seen in vivo, specifically that quadriceps loading at flexed angles induces anterior tibial translation and superior patellar translation. The model predicted internal rotation with quadriceps loading, which was not seen experimentally. However, the model agrees with other ex vivo studies on quadriceps function. Relevance:​ These results demonstrate the relevance and potential for co‐simulating musculoskeletal dynamics and soft tissue loads.

Objective 3:​ Use the co‐simulation framework to investigate the influence of knee laxity on tibiofemoral kinematics and kinetics during walking. Rationale:​ The load‐dependent behavior of the knee is evident in intact healthy knees and may even more important to consider in pathological cases where injury can alter joint laxity and surgery can alter the properties of both reconstructed and donor tissues. These effects are particularly relevant when using models to characterize cartilage and muscle loads. Hypothesis:​ When the quadriceps are maximally loaded during stance, the models with laxity will exhibit an anteriorly translated and internally rotated tibia in comparison to a kinematic joint assumption. These will in turn affect the moment arm of the patellar tendon and thus predictions of quadriceps loading. Methods:​ Using the developed co‐simulation technique from objective 2, muscle activation patterns were computed that drove a lower extremity musculoskeletal model to track normal hip, knee, and ankle flexion patterns during gait. Results:​ During the load acceptance phase of gait, the models with laxity predicted increased anterior tibia translation and internal tibia rotation due to quadriceps loading. These variations in tibiofemoral kinematics resulted in a more inferior finite helical axis, a diminished patellar tendon moment arm, and increased quadriceps loading, relative to what would be computed using a traditional kinematic knee model. Simulating gait with an ACL‐deficient knee shifted tibia plateau cartilage contact posteriorly and laterally. Relevance:​ Shifts in cartilage loading after surgery are thought to contribute to early onset knee osteoarthritis.

We have shown that load‐dependent variations in secondary joint kinematics affect muscle actions by using a modified computed muscle control algorithm to co‐simulate soft tissue loads and musculoskeletal dynamics during gait. This is the first study to predict changes in cartilage contact loading between a healthy and ACL‐deficient knee. This framework could be further used to explore surgical and rehabilitative strategies to restore normal knee mechanics after injury and disease.