Mathematical Model of Cardiovascular System

Abstract

According to the most recent statistics, cardiovascular diseases are currently a major cause of mortality in developed countries. These diseases have important individual and social consequences, with a significant impact on the cost and overall health care situation. A growing demand by the medical community for quantitative and scientifically rigorous results on these diseases has given a great impetus to the development of mathematical models and numerical methods for the computational simulation of the circulatory system, both in healthy and pathological cases. However, this system is highly integrated and modeling its various functions is a major challenge, with many fundamental issues still to be resolved. Blood is a concentrated suspension of cellular elements in plasma media, with complex rheological characteristics. The geometric structure of the vascular network and the heterogeneous composition of blood, as well as the mechanical and biochemical interactions with vessel walls and the pulsatile movement of blood flow, are extremely complex physiological phenomena. Therefore, it is impossible to construct a three-dimensional mathematical model of the whole circulatory system that allows the simulation of these characteristics and their application to the study of the hemodynamic effects associated with cardiovascular system pathologies. One of the challenges of research in this area is the development of mathematical models that, taking into account the computational resources available, include the most relevant complexities of blood circulation.