A fast algorithm for the simulation of arterial pulse waves

Abstract

One-dimensional models have been widely used in studies of the propagation of blood pulse waves in large arterial trees. Under a periodic driving of the heartbeat, traditional numerical methods, such as the Lax-Wendroff method, are employed to obtain asymptotic periodic solutions at large times. However, * I am corresponding author.

Virtual Lobule Models Are the Key for Multiscale Biomechanical and Pharmacological Modeling for the Liver

“…In addition, errors in biomechanical models may arise from the choice of numerical schemes. For example, when solving arterial flow equations, the selection of mesh sizes and temporal steps must meet the Courant–Friedrichs–Lewy (CFL) condition to avoid numerical instabilities and errors (Du et al, 2016 ).…”

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

“…Several numerical methodologies have been constructed for the various formulations (e.g., area-velocity, area-flow, pressure-flow). These include characteristic methods [12] as well as finite element (FE) [13,14,15,16,17], finite volume (FV) [18] and finite difference (FD) [19,20,21,22,23] methods. A number of these tools have been successfully utilized for blood flow analysis and are wellestablished.…”

Wave propagation in stenotic vessels; theoretical analysis and comparison between 3D and 1D fluid–structure-interaction models

“…The most significant advantage of the proposed analytical, frequency domain, solution method is that it is very fast. When the equations are formulated in space-time variables, the large speed of blood pulse waves and short lengths of vessels, restricts the time step to very small values, to the order of 10 −4 s (Du et al (2016)) or even less. Furthermore, one needs to evolve the solution for a sufficient number of cardiac cycles (each with period around 0.8s − 1s) to obtain an asymptotic periodic result.…”