A non-linear hierarchical model of stretch -induced injury to skeletal muscle fibers.

Abstract

Muscle is a unique material that converts chemical energy into mechanical work. Additionally, skeletal muscle in the passive state can undergo strains of 50% without damage to the microstructure. In contrast, when skeletal muscle is maximally activated, repetitive strains of 10% or single strains of 20% produce injury to the basic functional unit of skeletal muscle, the sarcomere. Current evaluations of contraction-induced injury do not permit rigorous testing of hypotheses because the number of sarcomeres injured does not correlate well with global strains applied to whole fibers, and current techniques do not permit visualization of the induction of injury. The purposes of this study were to: (1) describe the architecture of skeletal muscle tissue detailing the structure-function relationships and the mechanical properties of the constituent proteins, (2) characterize the non-linear active force generation and passive elastic material response based on the anatomy and physiology of skeletal muscle, (3) develop a hierarchical model for multi-scale analysis based on the homogenization method for modeling large deformation of a non-linear material with an active stress component, (4) formulate a method of analysis that accurately maps displacements across multiple spatial scales, (5) implement the hierarchical computational model to evaluate existing theories regarding the etiology of contraction-induced injury by estimating strains of myofibrillar proteins. Skeletal muscle has a hierarchical structure that requires a multi-scale modeling approach. The structural analyses were performed at two levels. First, representative volume elements (RVE's) were constructed to model the organization of structural and contractile proteins. These RVE's were then used to determine the mechanical response of global elements that represent regions within a muscle fiber. The displacement boundary conditions were applied at the level of the global elements. The responses of the global elements were in turn used to calculate protein level displacements, stresses, and strains. The results from this study demonstrate that in addition to reproducing the active and passive behavior of skeletal muscle, the analysis supports the hypothesis that contraction-induced injury is the result of heterogeneity in active force generation between sarcomeres in series rather than degradation of passive stiffness.