Concurrent Prediction of Muscle and Tibiofemoral Contact Forces During Treadmill Gait

The knee joint is at the center of a kinetic chain that includes the foot, ankle joint, lower and upper leg, hip joint, and pelvis. The complexity of the knee, the fact that it bears most of the body's weight, and its centrality to human movement make the knee vulnerable to acute and chronic injuries. Contact loading is a contributing factor in the onset and progression of osteoarthritis [1], and it is equally important in artificial knee replacement wear [2,3], which leads to failure of total knee prostheses. Knowledge of in vivo joint loads and motions during activities of daily living is also crucial in tissue engineering, injury prevention, and in developing, evaluating, and optimizing therapeutic strategies. Instrumented knee prostheses capable of measuring joint loading during dynamic activities have been implanted in patients [4,5–7]. But implementing these devices is expensive, invasive, and the results may not necessarily transfer to other patients and healthy adults. Thus, in vivo joint loads must be predicted using computational models. Estimation of the in vivo knee loads under dynamic conditions is highly dependent on correct prediction of muscle forces. This requires resolution of the muscle redundancy problem, which occurs because the muscle force solutions to create a certain motion are not unique. A number of studies addressed the muscle redundancy problem by using optimization methods to converge to a set of muscle forces that recreate the kinematics [8–14]. This approach involves two stages. In the first stage the muscle and net joint torques are estimated by inverse dynamics (static optimization) or by forward dynamic optimization. Static optimization uses the ground reaction forces as an input and solves the dynamics equations at each time frame. Muscle forces are predicted at each time step such that the kinematics are consistent with the experimentally measured motions. In dynamic optimization, the dynamics equations are numerically integrated across all time frames; thus, the muscle forces and kinematics are predicted concurrently. Typically, articular contact models are not included in the first stage, and the computed forces are applied to an articular contact model of the knee to estimate the joint contact forces. There are several limitations in this approach. Because articular contacts are not included in the first stage and the knee is often modeled as a one degree-of-freedom idealized joint, the contact forces do not affect the predicted muscle forces. Implicitly, the assumption is that muscle forces do not contribute to motions outside of knee flexion-extension. In a study by Lin et al. [14], it was demonstrated that muscle forces are affected by the number of constraints included in the knee model. In the case of static optimization, the accuracy of the available motion and ground reaction force data influences the muscle force predictions [9]. Moreover, since the ground reaction forces are used as an input, they cannot be used to evaluate the performance of the model. Finally, optimization methods assume that human movement is bound by minimizing some cost function such as sum of squares of muscle activation or metabolic energy, but it is unknown if the nervous system produces motion in such a way. Another major challenge in estimating the in vivo joint loads is the correct resolution of the tibiofemoral contact force into the medial and lateral compartment contact forces. The two regions of contact between the femur and the tibia create a contact force redundancy issue, as well [4]. Most musculoskeletal modeling studies tend to overestimate the tibial contact forces during gait [2,15–18] when compared to in vivo measurements collected by instrumented implants [5–7,19]. The discrepancies between model predictions and measured joint loads are even greater when the medial to lateral compartment load distributions are considered. The distribution of the tibiofemoral contact forces depends on the magnitude of the moments acting about the knee joint and the individual contributions of the muscles and ligaments [15,18]. In this paper, we present a two stage modeling method to predict tibiofemoral contact loads during treadmill walking. Our work is distinguished from previous published studies in a number of ways. In the first stage of our method, kinematic data is the only input into the multibody model while the knee joint (including both the tibiofemoral and patellofemoral joints) is allowed 12 degrees-of-freedom. The tibiofemoral and patellofemoral joints are constrained by contact between articulating surfaces as well as ligament forces. In the second stage, muscle forces and joint torques are predicted by using a proportional integral derivative (PID) controller, and the contact forces are predicted concurrently. Moreover, the ground reaction forces, as well as electromyography (EMG) and segment kinematics are used to validate the performance of the forward simulation. Because the ground reaction forces are never used as an input to the model, a detailed model of the foot-shoe-floor is created. Our specific aims are (a) to develop a full body, musculoskeletal model with subject specific lower extremity geometries that includes a detailed model of the foot/floor interactions that can concurrently predict muscle, ligament, and contact forces and (b) to evaluate the tibiofemoral joint load predictions with measured tibial loads for two different cycles of treadmill gait.