Modelling mechanically stable muscle architectures

Abstract

This paper presents a planar architectural model for an activated skeletal muscle, with mechanical equilibrium throughout the muscle belly. The model can predict the shape of the muscle fibres and tendinous sheets as well as the internal pressure distribution in the central longitudinal plane (perpendicular to the tendinous sheets) of uni- and bipennate muscle bellies. Mechanically stable solutions for muscle architectures were calculated by equating the pressure developed by curved muscle fibres with the pressure under a curved tendinous sheet. The pressure distribution under a tendinous sheet is determined by its tension, its curvature and the tensile stress of the attached muscle fibres. Dissections showed a good resemblance of the architecture of embalmed muscles with those from our simulations. Calculated maximum pressures are in the same order of magnitude as pressure measurements from the literature. Our model predicts that intramuscular blood flow can be blocked during sustained contraction, as several experimental studies have indeed demonstrated. The volume fractions of muscle fibres and interfibre space in the muscle belly were also calculated. The planar models predict a too low volume fraction for the muscle fibres (about 45% for the bipennate models with a straight central aponeurosis, and about 60% for the simulated unipennate muscle). It is discussed how, in a real muscle, this volume problem can be solved by a special three-dimensional arrangement of muscle fibres in combination with varying widths of the tendinous sheets.