Reduced modelling of pulse wave propagation in the cardiovascular system

A good understanding of pulse wave propagation in the cardiovascular system under normal conditions and the impact of disease and anatomical variations on the propagation patterns can provide valuable information for clinical diagnose and treatment. Despite the growing interest in three- dimensional simulations, the one- dimensional (1-D) equations of blood flow in compliant vessels offer a good compromise between accuracy and computational cost when a global assessment of the system can suffice, since arterial pulse wavelengths are significantly much longer than arterial diameters under physiological conditions.

The nonlinear, 1-D equations are solved in arterial networks and in the time domain using a discontinuous Galerkin scheme with a spectral/hp spatial discretisation. This formulation has been tested by comparison against a well-defined experimental 1:1 replica of the left heart and the largest 37 conduit systemic arteries in the human, in which most of the parameters required by the numerical algorithm can be easily measured. Several clinically relevant applications of the 1-D model are shown, including the study of pulse wave propagation in the arm and cerebral circulations, focusing on the effect of cross-connections between arteries on pulse waveforms, and on modelling cerebral flow auto-regulation using a lumped parameter model based on variables with a direct physiological meaning and parameters that can be obtained from human experimental data. Finally, I will show how to separate the pressure at an arbitrary arterial location into a reservoir pressure generated by the windkessel effect and a wave pressure generated by the arterial waves. This separation allows a better understanding of the mechanics behind the main features of arterial pulse waveforms observed in vivo.