Numerical simulation of the blood-wall interaction in the human left ventricle

This paper presents a contribution to the numerical simulation of the left ventricle taking into account simultaneously the fluid flow inside the cavity and the motion of the cardiac wall. One describes mathematical tools which are useful for such a problem of fluid-structure interaction. After having written the continuous mathematical problem and noted the difficulties which exist to solve such a problem, one makes two important simplifying assumptions: on the one hand, one builds a new problem which, on the mathematical viewpoint, can be distinguished from the continuous problem but which, on the physical and physiological viewpoints, can be considered as acceptable. One builds then a software which has to be considered just as a numerical investigation tool. It can be noted that it is necessary to impose, for the shape of the cardiac wall, a time-evolution. Such a bi-dimensional framework is sufficient to study the numerical aspect of this interaction, but is not sufficient to investigate the effects of major parameters governing the behavior of the left ventricle.