A mathematical study of a continuum‐state cross‐bridge model of muscle contraction

Abstract

Communicated by K. P. HadelerIn the framework of the sliding-filament theory of muscle contraction, we develop a model which describes physiological cross-bridge activity with a continuum of states, from those which are detached and refractory to those which are attached. The latter are kinetically more important.An analytical study of the non-linear partial differential equations of the mathematical model shows existence and uniqueness of the solution.

A mathematical study of the plasticity effects in muscle contraction

“…Since the main interest of this paper is focused on the introduction of plasticity, in order to describe the contractile element we consider a simple sliding-filament model; other more sophisticated models (such as those introduced in [10], [12], [23], [25], and [27]) could be used without great additional difficulty. For the 3 same reasons we assume the muscle structures to be elastoplastic (with work hardening, i.e., the threshold separating two types of behavior can depend on the history of the deformation) instead of viscoelastoplastic, as may be more reasonable (see [11] for viscoelastic properties).…”