Reverse-engineering and modeling the 3D passive and active responses of skeletal muscle using a data-driven, non-parametric, spline-based procedure

Abstract

In this work we present a non-parametric data-driven approach to reverse-engineer and model the 3D passive and active responses of skeletal muscle, applied to tibialis anterior muscle of Wistar rats. We assume a Hill-type additive relation for the stored energy into passive and active contributions. The terms of the stored energy have no upfront assumed shape, nor material parameters. These terms are determined directly from experimental data in spline form solving numerically the functional equations of the tests from which experimental data is available. To characterize typical longitudinal-to-transverse behavior in rodent's muscle, experiments from Morrow et al. (J. Mech. Beh. Biomed. Mater. 2010; 3: 124-129) are employed. Then, the passive and active behaviors of Wistar rats are determined from the experiments of Calvo et al. (J. Bomech. 2010; 43:318-325) and Ramirez et al. (J. Theor. Biol. 2010; 267:546-553). The twitch shape is not assumed, but reverse-engineered from experimental data. The influence of the strain and the stimulus voltage and frequency in the active response, are also modeled. A convenient stimulus power-related variable is proposed to comprise both voltage and frequency dependencies in the active response. Then, the behavior of the resulting muscle model depends only on the muscle strain maintained during isometric tests in the muscle and the stimulus power variable, along the time from initiation of the tetanus state.

Keywords: Active muscle response; B-splines; Hyperelasticity; Muscle model; WYPiWYG hyperelasticity.