A novel Fourier-based (pseudo)spectral framework for 1D hemodynamics and wave propagation in the entire human circulatory system

Fast and accurate numerical simulation of blood flow is necessary to study and identify important physical and physiological quantities as well as their relationships to cardiovascular functions. Comprehensive analysis requires simulating pressure and flow waves that travel, reflect and attenuate through a complex vascular network that is also coupled to organs. This work introduces a new numerical framework for modeling such wave propagation in the complete circulation, employing a (pseudo)spectral approach for resolving the reduced-order (1D) Navier-Stokes PDEs that govern the corresponding fluid-structure dynamics in each vascular segment. The solver has a number of appealing properties: it is high-order in both space and time; it faithfully preserves the diffusion/dispersion characteristics of the underlying continuous problems (errors do not compound as waves propagate through vasculature); it has mild CFL constraints on explicit time integrators; it is parallelizable; and it incorporates the nonlinear and nonstationary coupling of other cardiovascular system components (a hybrid ODE heart model). The physiological accuracy and computational performance of this framework is demonstrated by a variety of well-established benchmarks.