Key result
Four numerical schemes for a 1D viscoelastic blood flow model were successfully verified against analytical solutions and clinical observations, with comparisons made across accuracy and speed.
This computational study provides a verified comparison of four numerical schemes for modeling 1D viscoelastic blood flow, guiding the selection of appropriate methods for vascular simulations.
Four schemes solve viscoelastic 1D blood flow systems; leaves open clinical translation pending validation.
A reliable and fast numerical scheme is crucial for the 1D simulation of blood flow in compliant vessels. In this paper, a 1D blood flow model is incorporated with a Kelvin-Voigt viscoelastic arterial wall. This leads to a nonlinear hyperbolic-parabolic system, which is then solved with four numerical schemes, namely: MacCormack, Taylor-Galerkin, MUSCL (monotonic upwind scheme for conservation law) and local discontinuous Galerkin. The numerical schemes are tested on a single vessel, a simple bifurcation and a network with 55 arteries. The numerical solutions are checked favorably against analytical, semi-analytical solutions or clinical observations. Among the numerical schemes, comparisons are made in four important aspects: accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. The suitable conditions for the application of each scheme are discussed.
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Wang et al. (2013) studied this question. Numerical schemes (MacCormack, Taylor-Galerkin, MUSCL, local discontinuous Galerkin) vs. Analytical, semi-analytical solutions or clinical observations was evaluated on Accuracy, ability to capture shock-like phenomena, computational speed and implementation complexity. Four numerical schemes for a 1D viscoelastic blood flow model were successfully verified against analytical solutions and clinical observations, with comparisons made across accuracy and speed.