A nonlinear finite-element model of arterial blood flow demonstrates significant differences from linear models during rapid pressure or flow changes and simulates the hemodynamic effects of arterial stenoses.
Nonlinear models may better capture dynamic arterial hemodynamics or stenoses; leaves open clinical translation of waveform differences.
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 alternations 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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Porenta et al. (1986) studied this question.