A Finite-Element Model of Blood Flow in Arteries Including Taper, Branches, and Obstructions

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Abstract
A nonlinear mathematical model of arterial blood flow, which can account for tapering, branching, and the presence of stenosed segments, is presented. With the finite-element method, the model equations are transformed into a system of algebraic equations that can be solved on a high-speed digital computer to yield values of pressure and volume rate of flow as functions of time and arterial position. A model of the human femoral artery is used to compare the effects of linear and nonlinear modeling. During periods of rapid alterations in pressure or flow, the nonlinear model shows significantly different results than the linear model. The effect of a stenosis on pressure and flow waveforms is also simulated, and the results indicate that these waveforms are significantly altered by moderate and severe stenoses.

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