Feasibility study of a two dimensional functional heart model based on a single fiber contraction in an anatomical array of myocytes

Mathematical models became an important research tool, allowing scientists to explore biological systems and study mechanisms operating in pathological conditions that are often difficult to create in animal models. A model of the contracting two-dimensional myocardium was developed to analyze various pathological conditions and to optimize resynchronization therapy. The model was based on a single contracting myofiber situated in a complex anatomical structure of fibers. A matrix-based system was developed to compute deformation of the structure representing the myocardium. It was built of three types of trusses according to the characteristics of each element. The model will account for the propagation of the electrical activity within the myocardium, the mechanical behavior of the single fiber and the interaction between anatomically organized muscle arrays representing the entire cardiac muscle, and will interact with the vascular system. To validate the feasibility of our modeling approach, we applied these theoretical concepts in a small-scale two-dimensional model that is based on the anatomy of the contracting ventricle. Using arbitrary values of model parameters, we were able to obtain mathematically sound simulations, which predict physiological behavior. The model is expected to contribute to knowledge on pathophysiological states of heart failures, specifically on contraction patterns and on the effect of electrical wave velocity and delays on cardiac contraction patterns, and on resulting pressure and flow.