A Mathematical Model of the Dynamic Force–length Relationship of Skeletal Muscle Operating on Ascending and Descending Limbs

Abstract

A new Hill-type model of skeletal muscle contraction referred to as the “SL/ST model” is proposed based on recent physiological findings: intact human skeletal muscles operate on the ascending limb (hereinafter referred to as the “as-limb”) and the descending limb (“ds-limb”) of the isometric force–length relationship; and stretch-evoked force enhancement (“ST-enhancement”) is found on the ds-limb. Dynamic behaviors differ remarkably between the two limbs. The model has two modes: a sliding filament mode (“SL mode”) and a stretch-evoked force enhancement mode (“ST mode”). The SL mode operates on the as-limb, and on the ds-limb when the muscle is shortening, while the ST mode operates when ST-enhancement occurs in the ds-limb. Transient force responses of the model to length perturbations were similar to those of frog semitendinosus muscles in vitro. Length responses to step change in load of the model suggest that the muscle is unstable and not static in SL mode on the ds-limb, while it is stable and static in SL mode on the as-limb and in ST mode on the ds-limb.