Electro-Mechanical Activity of Cardiac Tissue: Mathematical andNumerical Modelling

Some basic aspects of the mathematical models used to describe the cardiac tissue will be presented considering, in particular, the electrophysiology and the myocardium mechanics, as well as the methods used for their coupling. The origins of the electrical activity in the cardiomyocytes will be shown, entering into the cell physiology. During a normal heart beat, the electrical signal propagates throughout the tissue and it generates internal forces which are the main responsible of the muscle contraction. The presentation will focus on the constitutive relations that are used to describe cardiac mechanics and on two possible approaches for the description of the active forces induced by the $\left[Ca\right]^{2+}$ ions during a contraction cycle. Some simple simulations will be shown for a better understanding of the subject.