An improved model for reduced-order physiological fluid flows

TL;DR

This paper introduces an improved one-dimensional model for physiological fluid flows that integrates dynamic coefficients, providing more accurate and computationally efficient simulations of arterial networks compared to classical steady-state models.

Contribution

The paper develops a novel reduced-order model based on Pulsed Flow Equations with smoothly varying coefficients, enhancing accuracy over traditional steady-state theories.

Findings

Model accurately simulates arterial flow dynamics.

Compared to classical models, it captures transient effects more effectively.

Efficiently solves complex network flows with the Lax-Wendroff scheme.

Abstract

An improved one-dimensional mathematical model based on Pulsed Flow Equations (PFE) is derived by integrating the axial component of the momentum equation over the transient Womersley velocity profile, providing a dynamic momentum equation whose coefficients are smoothly varying functions of the spatial variable. The resulting momentum equation along with the continuity equation and pressure-area relation form our reduced-order model for physiological fluid flows in one dimension, and are aimed at providing accurate and fast-to-compute global models for physiological systems represented as networks of quasi one-dimensional fluid flows. The consequent nonlinear coupled system of equations is solved by the Lax-Wendroff scheme and is then applied to an open model arterial network of the human vascular system containing the largest fifty-five arteries. The proposed model with functional coefficients is compared with current classical one-dimensional theories which assume steady state Hagen-Poiseuille velocity profiles, either parabolic or plug-like, throughout the whole arterial tree. The effects of the nonlinear term in the momentum equation and different strategies for bifurcation points in the network, as well as the various lumped parameter outflow boundary conditions for distal terminal points are also analyzed. The results show that the proposed model can be used as an efficient tool for investigating the dynamics of reduced-order models of flows in physiological systems and would, in particular, be a good candidate for the one-dimensional, system-level component of geometric multiscale models of physiological systems.