VW Applied Sciences, Volume: 1, Issue: 1, 25-31
Received: Sept. 09, 2019
Accepted: Sept. 16, 2019
Published online: Sept. 28, 2019
Fisal Asiri1
1Department of Mathematics, College of Science, Taibah University, Medina, Saudi Arabia
Author Email: fasiri@taibahu.edu.sa.
Research publication from M.S. Thesis, submitted at School of Mathematics and Statistics, University of Glasgow, United Kingdom
Abstract: The paper presents the mathematical modeling of the excitation contraction phenomena in single cardiac cells. Particular emphasis was placed on three models: the Hill model, the Huxley model and the Land model. Further literature was reviewed concerning the mathematical modeling of the myocyte cardiac cells. This included the Hunter model, which presented the passive active mechanics of the cardiac muscle suitable for use in the continuum mechanics models of the entire heart; the Rice Filament model, which approximated the activation and generation of force in cardiac myofilaments and; Vasileiou’s work, which described the coupling between mechanical contraction and electrical excitation in cardiac cells. As a starting point, descriptions of fundamental models were obtained along with their underlying mathematical modelling 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.
