On Using Model Populations to Determine Mechanical Properties of Skeletal Muscle. Application to Concentric Contraction Simulation

Abstract

In the field of computational biomechanics, the experimental evaluation of the material properties is crucial for the development of computational models that closely reproduce real organ systems. When simulations of muscle tissue are concerned, stress/strain relations for both passive and active behavior are required. These experimental relations usually exhibit certain variability. In this study, a set of material parameters involved in a 3D skeletal muscle model are determined by using a system biology approach in which the parameters are randomly varied leading to a population of models. Using a set of experimental results from an animal model, a subset of the entire population of models was selected. This reduced population predicted the mechanical response within the window of experimental observations. Hence, a range of model parameters, instead of a single set of them, was determined. Rat Tibialis Anterior muscle was selected for this study. Muscles ($n=6$) were activated through the sciatic nerve and during contraction the tissue pulled a weight fixed to the distal tendon (concentric contraction). Three different weights 1, 2 and 3 N were used and the time course of muscle stretch was analyzed obtaining values of (mean $\pm$ standard deviation): $0.714\pm 0.01$, $0.808\pm 0.060$ and $0.851\pm 0.033$ respectively. A paired two-sided sign rank test showed significant differences between the muscle response for the three weights ($p<0.01$). This study shows that the Monte Carlo method could be used for determine muscle characteristic parameters considering the variability of the experimental population.