Muscles have hierarchical structure that spans several scales. The basic contraction unit is
the sarcomere, having a length of two microns. Myofibrils, typically of a few millimeters
long, are composed of thousands of sarcomeres connected in series. The muscle fiber is
made of a large number of parallel myofibrils coupled by a tissue.

Much is known about the overall mechanical response of an entire muscle fiber. Further,
recent technological advances have revealed the structure of the single sarcomere down
to the molecular level. Nevertheless, there is still a gap in understanding how the
collective behavior of the various scales gives rise to overall behavior. Importantly,
single-sarcomere models can not explain various experimental observations on the
macro-scale.

We present a theoretical framework for predicting the collective behavior of biologically
relevant ensembles of sarcomeres. The analysis is accomplished by transforming the non-
linear dynamics of an assemblage of sarcomeres into a partial differential equation for the
distribution of sarcomere lengths in the presence of stochastic fluctuations and biological
variability. It reproduces the results of previous experiments with no fitting parameters,
explains some puzzling observations and provides insights into damage under cyclic
eccentric loading.