Is my musculoskeletal model complex enough? The implications of six degree of freedom lower limb joints for dynamic consistency and biomechanical relevance

Abstract

Studies have shown that modeling errors due to unaccounted for soft-tissue deformations – known as soft-tissue artifact (STA) – can reduce the efficacy and usefulness of musculoskeletal simulations. Recent work has proven that adding degrees of freedom (DOF) to the joint definitions of a musculoskeletal model’s lower limbs can significantly change the prediction of an individual’s kinematics and dynamics while simultaneously improving estimates of their mechanical work. This indicates that additional modeling complexity may mitigate the effects of STA. However, it remains to be determined whether adding DOF to the lower limb joints can impact a model’s satisfaction of Newton’s Second Law of Motion, or whether a specific number of DOF must be incorporated in order to produce the most biomechanically accurate simulations. To investigate these unknowns, I recruited ten subjects of variable body-mass-indices (BMI) and recorded subject walking data at three speeds normalized by Froude number (Fr) using optical motion capture and an instrumented treadmill (eight male, two females; mean ± s.d.; age 21.6 ± 2.87 years; BMI 25.1 ± 5.1). Then, I added DOF to the lower limb joints of OpenSim’s 23 DOF lower body and torso model until it minimized the magnitude of the pelvis residual forces and moments for a single, representative subject trial (BMI = 24.0, Fr = 0.15). These artificial residual forces and moments are applied at the pelvis to maintain the model’s orientation in space by satisfying Newton’s Second Law. Finally, I simulated all 30 trials with both the original and the edited model and observed how the biomechanical predictions of the two models differed over the range of subject BMIs and walking speeds. After applying both the original and the edited model to the entire data set, I found that the edited model resulted in statistically lower (α = 0.05) residual forces and moments in four of the six directions. Then, after investigating the impact of changes in BMI and Froude number on these residual reductions, I found that two of the six directions exhibited statistically significant correlations with Froude number while none of the six possessed correlations with BMI. Therefore, adding DOF to the lower limb joints can improve a model’s dynamic consistency and combat the effects of STA, and simulations of higher speed behaviors may benefit more from additional DOF. For BMI, it remains to be determined if a higher BMI indicates greater potential for residual reduction, but it was shown that this method of tuning the model for one representative subject was agnostic to BMI. Overall, the method of tuning the model for one representative subject was found to be quite limited. There were multiple subject trials for which reduced residuals corresponded to drastic changes in kinematic and dynamic estimates until they were no longer representative of normal human walking. Therefore, it is possible to improve dynamic consistency by adding DOF to the lower limb joints. But, for biomechanically relevant estimates to be consistently preserved and soft-tissue artifact to be completely minimized, subject-specific model tuning is likely necessary.