Computer simulation of arterial blood flow
Thomas R. Rogge
Computer models have been widely used to simulate pressure and flow propagation in the arterial system. While experimentation involving the human arterial system is difficult and impractical, computer models offer an attractive alternative for the study of arterial hemodynamics. The purpose of the present study was to develop a computer model of the whole systemic circulation and to use this model to study pressure and flow propagation under normal flow conditions, as well as under conditions of arterial disease;The mathematical model used to describe flow in an arterial segment was based on the one-dimensional continuity and momentum equations. The model includes nonlinearities arising from the convective acceleration term and the pressure-area relationship. The mathematical model also includes a seepage term for the modeling of small branches, as well as a body force term for the modeling of gravitational and external acceleration forces. Arterial segments that do not branch are terminated using modified windkessel lumped impedances. Arterial stenoses are modeled using an empirical pressure drop-flow relationship. The problem was solved numerically by employing either an explicit finite difference scheme, or a finite element scheme based on the Galerkin method;The physiological model consisted of 55 arterial segments and included most major arteries. The majority of the parameter data were obtained from the literature. Under normal flow conditions, the model predicted satisfactorily the major characteristics of pressure and flow throughout the arterial system. Tests were also run to assess the influence of model parameters, such as those related to boundary conditions, nonlinearities, and the wall shear stress model, on the model predictions;Finally, the model was used to study cases of medical interest, such as the effect of various forms of cardiovascular disease on pressure and flow waveforms. The cases studied include the effect of arterial stenoses on the mean flow and the pulsatility of the flow, the effect of heart valvular disease on central and peripheral pressure waveforms, as well as the effect of arteriosclerosis and hypertension on peripheral pressure pulse formation. The results were in reasonably good agreement with published experimental findings, suggesting that the computer model can be used to gain valuable information on the hemodynamics of the human arterial system.