Numeric models for supporting noninvasive investigation of the left atrium-ventricle system

The aim of this study was to analyze the physiological variables regarding the left ventricular filling pattern by means of two numerical models of th e diastolic atrial-ventricular flow. Diastolic dysfunction is an important cause of cardiac morbidity and, consequently, there is a need for developin g noninvasive techniques to evaluate the diastolic function in terms of pre ssure and volume interactions. Two complementary approaches have been devel oped. In the first one, the flow is assumed to be two-dimensional and the f luid Newtonian. In the second approach, the flow is assumed to be axisymmet rical and the fluid inviscid. By using a boundary integral formulation, num erical simulations of the solution of the Euler equations are performed. Th e M-color Doppler images have been obtained by the transthoracic echocardio graphic technique (apical four-chamber view) with a scan through the center of the mitral plane. The images have been transformed in a numerical matri x in which each pixel of color corresponds to a numerical value proportiona l to the brightness (corresponding in color Doppler code to a definite velo city). The resulting numerical field of velocities is used to compute the g radient of the pressure via the Navier-Stokes equation. In this way, a nume rical matrix that describes the instantaneous local gradient of pressure is obtained. For the axisymmetrical model, preliminary results show that the mitral opening is quite slower with respect to the real dynamics. This is d ue to the coarse time integration step that is used. Actually, with the pre sent integration procedure, the mass of the valve cannot be as small as nec essary. Moreover, we can see how the pressure gradient, which is favorable at the initial times (t = 0.04, 0.05), becomes adverse up to the beginning of a backflow. The dependence of such results on the heart wall motion (par ticularly on the mitral dynamics) is presently under investigation. Prelimi nary results indicate that the study of the course of the velocities and of the pressure gradient in space and time, by means of computerized analysis of the M-color images, furnishes useful information about the fluid dynami cs behavior of the left ventricle during diastole and provides indexes desc riptive of the diastolic function.