A Master of Science thesis in Mathematics by Rana Itani entitled, "Study of the Electromechanical Models for Cardiac Activity," submitted in May 2017. Thesis advisor is Dr. Youssef Belhamadia. Soft and hard copy available.
The mathematical modeling of the complex physical phenomena occurring in the heart is an area of increasing interest, as it facilitates the better understanding of relevant mechanisms driving the behavior of the system in both physiological and pathological contexts. In this work, we are interested in the study of the interaction between the propagation of the electrical potential through the cardiac tissue and the related mechanical response. Two mathematical models for this electromechanical coupling will be presented: the first model is based on an active-stress approach that adds an active contribution to the stress of the material, and the second model is based on an active-strain approach that adopts a multiplicative decomposition of the tensor gradient of deformation. Comparison between these two models and numerical results will be presented illustrating some
important features of the cardiac electromechanical coupling.