Mathematical Modeling of General Muscle Contraction

Abstract

Mathematical modeling of the Hill model, the Huxley model for excitation-contraction phenomena in single cardiac cells have been studied. The functionality of the heart is enabled by the cardiac muscles that contract to promote the flow of blood to diff t parts of the body. As a starting point, descriptions of fundamental models were obtained along with their underlying mathematical modeling describing the processes behind excitation and contraction in cardiac cells. The Hill model representing muscle behavior, as well as the Hodgkin-Huxley model representing excitation, are fully considered due to their significance in mathematical physiology literature and as the basis for many models of cells. The Hill model was examined based on the outcome of the mathematical analysis of the contraction of the cardiac muscle. The Hill model establishes the relation- ship between force and velocity in the cardiac myocytes. However, the Hill model is limited by the absence of the interaction of the sarcomere elements in its development. The Hill model was developed before the details of the sarcomere anatomy were known, and was based on Hill’s observations that when a muscle contracts against a constant load, the relationship between the constant rate of shortening velocity and the load is well described by the force-velocity equation.