Towards multi-scale modeling of muscle fibers with sarcomere non-uniformities

A theoretical framework for studying the collective behavior of a large ensemble of half sarcomeres in a myofibril is presented. The approach is based on transforming the large system of discrete elements (half-sarcomeres) into a continuum for which macro-behavior is dictated by micro-properties. Specifically, we consider statistical properties of the ensemble rather than solving for each degree of freedom. This enables a reasonable computational effort and provides important insights. We demonstrate that such a multi-scale approach is indispensable for studying quantitatively the role of sarcomere non-uniformities in muscle mechanics. Specifically, we illustrate that adopting a model with a non-physiological number of sarcomeres can lead to a non-realistic behavior and therefore to erroneous interpretation. Further, we demonstrate that the new modeling approach provides a suitable platform for addressing controversial phenomena, such as residual enhanced tension, creep, length redistribution, and damage due to eccentric contraction.