Probabilistic Modeling of Knee Muscle Moment Arms: Effects of Methods, Origin–Insertion, and Kinematic Variability

In musculoskeletal modeling, reliable estimates of muscle moment arms are an important step in accurately predicting muscle forces and joint moments. The degree of agreement between the two common methods of calculating moment arms—tendon excursion (TE) and geometric origin–insertion, is currently unknown for the muscles crossing the knee joint. Further, measured moment arm data are subject to variability in estimation of attachment sites as points from irregular surfaces on the bones, and due to differences in joint kinematics observed in vivo. Thus, the objectives of the present study were to compare moment arms of major muscles crossing the knee joint obtained from TE and geometric methods using a finite element-based lower extremity model, and to quantify the effects of potential muscle origin–insertion and tibiofemoral kinematic variability on the predicted moment arms using probabilistic methods. A semiconstrained, fixed bearing, posterior cruciate-retaining total knee arthroplasty was included due to available in vivo kinematic data. In this study, muscle origin and insertion locations and kinematic variables were represented as normal distributions with standard deviations of 5 mm for origin–insertion locations and up to 1.6 mm and 3.0° for the kinematic parameters. Agreement between the deterministic moment arm calculations from the two methods was excellent for the flexors, while differences in trends and magnitudes were observed for the extensor muscles. Model-predicted deterministic moment arms from both methods agreed reasonably with the experimental values from available literature. The uncertainty in input parameters resulted in substantial variability in predicted moment arms, with the size of 1–99% confidence interval being up to 41.3 and 35.8 mm for the TE and geometric methods, respectively. The sizeable range of moment arm predictions and associated excursions has the potential to affect a muscle’s operating range on the force–length curve, thus affecting joint moments. In this study, moment arm predictions were more dependent on muscle origin–insertion locations than the kinematic variables. The important parameters from the TE method were the origin and insertion locations in the sagittal plane, while the insertion location in the sagittal plane was the dominant parameter using the geometric method.