A stable high-order FC-based methodology for hemodynamic wave propagation

Abstract

A high-order numerical algorithm is proposed for the solution of one-dimensional arterial pulse wave propagation problems based on use of an accelerated “Fourier continuation” (FC) methodology for accurate Fourier expansion of non-periodic functions. The solver provides high-order accuracy, mild Courant-Friedrichs-Lewy (CFL) constraints on the time discretization and, importantly, results that are essentially free of spatial dispersion errors—enabling fast and accurate resolution of clinically-relevant problems requiring simulation of many cardiac cycles or vascular segments. The left ventricle-arterial model that is employed presents a particularly challenging case of ordinary differential equation (ODE)-governed boundary conditions that include a hybrid ODE-Dirichlet model for the left ventricle and an ODE-based Windkessel model for truncated vasculature. Results from FC-based simulations are shown to capture the important physiological features of pressure and flow waveforms in the systemic circulation. The robustness of the proposed solver is demonstrated through a number of numerical examples that include performance studies and a physiologically-accurate case study of the coupled left ventricle-arterial system. The results of this paper imply that the FC-based methodology is straightforwardly applicable to other biological and physical phenomena that are governed by similar hyperbolic partial differential equations (PDEs) and ODE-based time-dependent boundaries.