Simulation of pulsatile flow in arteries using the finite-element method

In this study, a computer model has been developed for the prediction of flow and pressure along segments of arteries. The model can account for important factors such as vessel taper, branching, nonlinear area pressure relationships for the vessel, and single and multiple stenoses. One-dimensional continuity and momentum equations for flow in flexible tubes are used to describe the main arterial flow, and a quadratic form of area variation with pressure is used for the vessel equation of state. A seepage term is included in the continuity equation to allow for flow through small branches. Large branches are modeled as arterial segments terminating as modified Windkessel lumped impedances. Arterial stenoses are modeled with a nonlinear equation relating flow and pressure drop. The method of finite-elements with semi-discrete shape functions is used to solve for pressure and flow variations along the arterial segment. The sensitivity of the model is specific values of lumped impedance parameters has been investigated in detail. Some validation studies were carried out based on pressure and flow measurements obtained from the hindlimbs of dogs. Reasonable agreement between observed and predicted flow waveforms were obtained;The suitability of the finite-element method for the study of arterial flow dynamics, and the importance of using the correct form of lumped impedance, has been demonstrated by simulating flow in two different arterial segments: (1) the human leg arteries containing stenoses, and (2) the bovine uterine artery;The predicted waveforms for the human femoral artery compared well with those published in past studies. In this study the effects of (1) multiple stenoses, and (2) compensation of peripheral beds to accommodate for stenosis induced loss of pressure were considered. The human leg artery model was also used to study the effects of approximating wall shear in the momentum equation;The bovine uterine artery is unique since flow and mechanical properties associated with the artery undergo marked changes during the estrous cycle. With proper selection of the lumped impedances and main arterial parameters, good agreement between predicted and measured flow waveforms was achieved