A 3D-1D-0D Computational Model for the Entire Cardiovascular System

Abstract

In the present work a computational model of the entire closed cardiovascular system is established. This model stands for the integration of different levels of circulation. Indeed, the arterial tree is described by a one dimensional model in order to simulate the propagation phenomena that takes place at the larger arterial vessels. The inflow and outflow locations of this 1D model are coupled with proper lumped parameter descriptions (0D model) of the remainder part of the circulatory system. At each outflow point we incorporate the peripheral circulation in arterioles and capillaries by using a 0D three-component Windkessel models. In turn, the whole peripheral circulation converges to the venous system through the upper and lower parts of the body, for which we set two corresponding major venous circulation circuits (superior and inferior vena cava). Then, the right and left heart circulation, as well as the pulmonary circulation are accounted for also by means of 0D models. Particularly for the four cardiac valves we employ a valve model allowing for the regurgitation phenomenon during the valve closing. Finally, the 0D model of the left ventricle is coupled with the inflow boundary in the 1D model, closing the system. In addition, we consider the existence of 3D models accounting for the detailed aspects of blood flow in specific vessels of interest. The resulting integrated model (3D-1D-0D coupled model) forms a closed loop network capable of taking into account the interaction between the global circulation (1D-0D Models) and the local hemodynamics (3D models). Several situations of interest are presented showing the capabilities of the model.