Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods

TL;DR

This paper systematically compares various reduced one-dimensional blood flow models, discretized with Runge-Kutta discontinuous Galerkin methods, to understand discrepancies based on model formulation, averaging, and velocity profile assumptions.

Contribution

It provides a comprehensive comparison of different blood flow models and their discretizations, highlighting the impact of formulation choices on results.

Findings

Discrepancies among models depend on averaging and velocity profile assumptions.

Runge-Kutta discontinuous Galerkin methods effectively discretize blood flow models.

Model differences influence predictions for physiologically relevant parameters.

Abstract

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we systematically compare several reduced models of blood flow for physiologically relevant vessel parameters, network topology, and boundary data. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.