Are the maximum shortening velocity and the shape parameter in a Hill-type model of whole muscle related to activation?

Mathematical models of the inter-relationship of muscle force, velocity, and activation are useful in forward dynamic simulations of human movement tasks. The objective of this work was to determine whether the parameters (maximum shortening velocity V(max) and shape parameter k) of a Hill-type muscle model, interrelating muscle force, velocity, and activation, are themselves dependent on the activation. To fulfill this objective, surface EMG signals from four muscles, as well as the kinematics and kinetics of the arm, were recorded from 14 subjects who performed rapid-release elbow extension tasks at 25%, 50%, 75%, and 100% activation (MVC). The experimental elbow flexion angle was tracked by a forward dynamic simulation of the task in which V(max) and k of the triceps brachii were varied at each activation level to minimize the difference between the simulated and experimental elbow flexion angle. Because a preliminary analysis demonstrated no dependency of k on activation, additional simulations were performed with constant k values of 0.15, 0.20, and 0.25. The optimized values of V(max) normalized to the average value within a subject were then regressed onto the activation. Normalized V(max) depended significantly on the activation (p<0.001) for all values of k. Furthermore, the estimated V(max) values were not sensitive to the selected k value. The results support the use of Hill-type models in which V(max) depends on activation in forward dynamic simulations modeling muscles with mixed fiber-type composition recruited in the range of 25-100% activation. The use of more accurate models will lend greater confidence to the results of forward dynamic simulations.