Digital computer simulation of human systemic arterial pulse wave transmission: A nonlinear model

Abstract

The transmission of pressure and flow pulse waves in human systemic arteries is modeled using one-dimensional, nonlinear transient analysis on a system of branching, nonuniform tubes. Nonlinearity results from the retention of the vessel cross-sectional area as a dependent variable and from an approximation to the convective acceleration terms.Coupling the momentum and continuity equations with a linear elastic membrane equation describing the vessel wall yields a system of quasi-linear, hyperbolic partial differential equations, solvable on a digital computer using the method fo characteristics and finite difference techniques. Appropriate boundary conditions enabling the application of the model to whole vascular beds are introduced.Using published data, a reference state for the human arterial system is defined in terms of vessel geometrical and physical parameters. Model behavior in this state is documented at 14 locations corresponding to vascular regions most frequently investigated clinically. Pressure and flow waveforms, and impedances from the model show reasonable agreement with clinical data reported in the literature.The model is found to reproduce the mechanical behavior of the real system with greater fidelity than previous models. Comparison of the nonlinear model with a linearized, lumped parameter model shows significant differences in performance. These differences are attributed mainly to the nonlinear interaction of vessel transverse and longitudinal impedance. It is concluded that the nonlinear effects of finite vessel wall displacements are of importance in determining arterial pulse propagation behavior, at least in the more distensible central vessels. Fluid friction and convective acceleration effects were found to be of lesser importance in determining overall pulse wave behavior.