Biophysical 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 muscles history-dependent 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 muscle models that lack the mechanisms underlying short-range stiffness. While it has been previously shown that biophysical cross-bridge models can reproduce muscle short-range-stiffness, it is unclear which specific biophysical properties are necessary to capture history-dependent muscle force responses in behaviorally relevant conditions. Here, we tested the ability of various biophysical 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 permeabilized rat soleus muscle fibers (N = 11). We found that a biophysical cross-bridge model with cooperative myofilament activation reproduced the effects of muscle activation (R2 = 0.86), stretch amplitude (R2 = 0.71) and isometric recovery time (R2 = 0.79) on history-dependent changes in short-range stiffness after shortening. Similar results were obtained when the cross-bridge distribution of the biophysical model was approximated by a Gaussian (R2 = 0.73 - 0.88), but at a 20 times lower computational cost. These effects could not be reproduced by either a biophysical cross-bridge model without cooperative myofilament activation or a Hill-type model (R2 < 0.5). The reduced computational demand of the Gaussian-approximated models facilitates implementing biophysical cross-bridge models with cooperative myofilament activation in musculoskeletal simulations to improve the prediction of short-range stiffness during movements.