Musculotendon Parameters in Lower Limb Models: Simplifications, Uncertainties, and Muscle Force Estimation Sensitivity

Abstract

Objective: Musculotendon parameters are key factors in the Hill-type muscle contraction dynamics, determining the muscle force estimation accuracy of a musculoskeletal model. Their values are mostly derived from muscle architecture datasets, whose emergence has been a major impetus for model development. However, it is often not clear if such parameter update indeed improves simulation accuracy. Our goal is to explain to model users in which way and how accurate these parameters are derived, and to what extent errors in parameter values might influence force estimation. Methods: We examine in detail the derivation of musculotendon parameters in six muscle architecture datasets and four prominent OpenSim models of the lower limb, and then identify simplifications which could add uncertainties to the derived parameter values. Finally, we analyze the sensitivity of muscle force estimation to these parameters both numerically and analytically. Results: Nine typical simplifications in parameter derivation are identified. Partial derivatives of the Hill-type contraction dynamics are derived. Tendon slack length is determined as the musculotendon parameter that muscle force estimation is most sensitive to, whereas pennation angle is the least impactful. Conclusion: Anatomical measurements alone are not enough to calibrate musculotendon parameters, and the improvement on muscle force estimation accuracy will be limited if the source muscle architecture datasets are the only main update. Significance: Model users may check if a dataset or model is free of concerning factors for their research or application requirements. The derived partial derivatives may be used as gradients for musculotendon parameter calibration. For model development, we demonstrate that it is more promising to focus on other model parameters or components and seek alternative strategies to further increase simulation accuracy.

A registration strategy to characterize DTI-observed changes in skeletal muscle architecture due to passive shortening

“…Besides non-invasively reflecting anatomy, muscle fiber-tract architecture is also used to predict function (3,61) and to detect changes in architectural properties between conditions. Indeed, the PCSA ( 62) is considered one of the key predictors of muscle force production; therefore, not finding changes in PCSA between the transformed and original fiber-tracts is very relevant with respect to the use of this method in musculoskeletal modelling (25)(26)(27)(28)(29)(30). Additionally, we observed a smaller pennation angle in the full TA in the plantarflexed (+20°) compared to dorsiflexed (-10°) ankle position, which is consistent with physiological predictions based on the relative compliance of resting muscle vs. tendinous structures and previous observations (55,63,64).…”

“…From such measurements, the microstructural and architectural properties of resting muscle have been characterized, including following passive joint motions (14,16,24). Furthermore, these microstructural and architectural properties have been used as inputs to musculoskeletal models to predict changes in muscle function in healthy, diseased, and injured muscle (25)(26)(27)(28)(29)(30). DTI has intrinsic three-dimensional sensitivity, whole-muscle coverage, and the potential to be integrated with other forms of functionally relevant MRI contrast.…”