Cross-bridge model for predicting muscle short-range stiffness during movement

Musculoskeletal simulations can offer valuable insight into how the properties of our musculoskeletal system influence the biomechanics of our daily movements. One such property is muscle's initial resistance to stretch, also known as short-range stiffness, which is key to stabilizing movements in response to external perturbations. Short-range stiffness is poorly captured by existing musculoskeletal simulations since they employ phenomenological Hill-type models lacking activation-dependent stiffness properties. Existing simulations also do not capture the history-dependent reduction in short-range stiffness after muscle shortening, known as muscle thixotropy. While cross-bridge models can reproduce muscle short-range stiffness, it remains unclear which model properties are necessary to capture its history dependence. Here, we tested the ability of various cross-bridge models to reproduce empirical short-range stiffness and its history-dependent changes across a broad range of behaviorally relevant length changes and activation levels, using an existing dataset on 11 permeabilized rat soleus muscle fibers. We quantified muscle thixotropy using the ratio between the observed short-range stiffnesses after and before shortening. We computed the root-mean-square deviation (σSRS) between the predicted short-range stiffness ratio of various muscle models and the measured stiffness ratio. We found that cross-bridge models captured short-range stiffness changes across conditions with both small and large history-dependent stiffness reductions (σSRS ≤ 0.1), but only when including cooperative activation of both thin and thick myofilaments. In contrast, Hill-type models and a cross-bridge model without cooperative myofilament activation underestimated short-range stiffness and did not capture its change across conditions with large history-dependent stiffness reductions (σSRS > 0.2). Similar results were obtained when using a Gaussian-approximated solution method to simulate the cross-bridge distribution, but at an approximately eightfold lower computational cost. We therefore propose to implement Gaussian-approximated cross-bridge models with cooperative myofilament activation into musculoskeletal simulations to improve the prediction of short-range stiffness during movements.