A high-order space-time Fourier continuation approach for one-dimensional hemodynamics and wave propagation in the entire human circulatory system

Accurate and robust numerical simulation of hemodynamics is of interest for the identification and investigation of important physical or physiological quantities and their relationships to various cardiac and vascular functions. Comprehensive analysis requires efficiently simulating pressure and flow waves that travel and reflect through a complex network of vessels with varying geometric/material properties. This work introduces a new numerical methodology for modeling such wave propagation throughout the (closed-loop) circulation, employing a fast high-order (pseudo)spectral approach for resolving the well-established reduced-order one-dimensional Navier-Stokes hemodynamics formulations (coupled to hyperelastic tube laws) that govern the corresponding fluid-structure dynamics in each vascular segment. The model includes both systemic and pulmonary circulations and four heart chambers and four heart valves. Together with a correspondingly high-order treatment of multiscale zero-dimensional boundary conditions based on time-dependent ordinary differential equations, the overall solver has a number of attractive qualities: high-order accuracy in time and space; fast Fourier transform (FFT)-level computational efficiency; little to no numerical pollution errors (faithfully preserving the diffusion and dispersion characteristics of the underlying continuous operators); relatively mild Courant-Friedrichs-Lewy constraints for explicit temporal integration methods; robustness to extreme physiological parameters; and stable incorporation of the nonlinear and nonstationary coupling to other cardiovascular system components (e.g., heart chambers, valves, and microvasculature). The convergence properties, computational performance, and physiological accuracy of the proposed framework are demonstrated through a variety of numerical experiments that include applications to community benchmark problems previously proposed for mutual validation with other solvers (and three-dimensional or in vitro reference solutions).