Control of the extension–flexion cycle of human knees during bicycle riding by a synergy of solitary muscular excitations and contractions

Abstract

A Hill-type model is proposed for the extension-flexion cycle of human knees during bicycle riding. The extension-flexion cycle is controlled by a synergy of muscular excitations and contractions of the knee musculature. Muscular action potentials are modeled by Sine-Gordon kinks, while titin-influenced actomyosin contractions are modeled by Korteweg-de Vries solitons. As an application, the total knee arthroplasty is discussed.

Generation of soliton bubbles in a sine-Gordon system with localised inhomogeneities

“…The propagation of nonlinear waves in inhomogeneous media has captured much recent interest in physics and biophysics [1]. Nonlinear pulse excitations regulate the functioning in many physical models of biological systems, such as the Purkinje's fibres of the cardiac muscles [2,3], neural fibres [4], DNA chains [5,6] and muscular networks [7]. The study of the effects that can be produced on these regulatory signals by the presence of spatial inhomogeneities, such as localised injuries and necrotic sites, has gained major interest in recent works [3,8,9].…”