A Phenomenological Theory of Muscular Contraction

Abstract

In part I of this series, the theory of irreversible thermodynamics was applied to the sliding filament model to obtain rate equations for a contracting muscle at the in situ length l(o). In this paper we extend the theory to include length variations derived from the sliding filament model of contracting muscle using the work of Gordon, Huxley, and Julian (1). Accepting the validity of Hill's forcevelocity relation (2) at the in situ length, we show that Hill's equation is valid for any length provided that the values of the parameters, a, b, and V(m) vary with length as derived herein. The predicted variation with length of the velocity for a lightly loaded isotonic contraction is shown to agree well with that measured by Gordon, Huxley, and Julian (1). Chemical rates are derived as functions of length using parameters that can be obtained experimentally.

A Simulation of Human Heart Function

“…Using the methods of irreversible thermodynamics, Caplan (23), Wilkie and Woledge (24), and Bornhorst and Minardi (25) studied not only the mechanics but also the energy conversion processes in muscle. In 1970, Bornhorst and Minardi (26,27) developed a phenomenological theory of muscular contraction and applied it to skeletal muscle experimental data. An important result of this theory is a set of phenomenological equations which describe the force-length-velocity relationship between force and the rate of the chemical reaction driving the contraction.…”

“…2 is essentially Eq. 20 of Bornhorst and Minardi's development (27). The parameters a, and uj are defined in terms of two dimensionless functions of length Ft and F,.…”