Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods

TL;DR

This paper introduces a flexible multiscale blood flow model that captures various propagation phenomena in arteries and veins, derived from asymptotic analysis and solved with an advanced numerical scheme, applicable to complex cardiovascular studies.

Contribution

It develops a novel multiscale hyperbolic blood flow model based on asymptotic limits and perturbation analysis, unifying existing models and introducing a new viscoelastic formulation.

Findings

The model recovers known blood flow models in asymptotic limits.

The numerical scheme is asymptotic-preserving and efficient.

Numerical tests validate the model's accuracy and applicability.

Abstract

In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it is shown that different types of blood propagation phenomena in arteries and veins can be described through an appropriate choice of scaling parameters, which are related to distinct characterizations of the fluid-structure interaction mechanism (whether elastic or viscoelastic) that exist between vessel walls and blood flow. In these asymptotic limits, well-known blood flow models from the literature are recovered. Additionally, by analyzing the perturbation of the local elastic equilibrium of the system, a new viscoelastic blood flow model is derived. The proposed approach is highly flexible and suitable for studying the human cardiovascular system, which is composed of vessels with high morphological and mechanical variability. The resulting multiscale hyperbolic model of blood flow is solved using an asymptotic-preserving Implicit-Explicit Runge-Kutta Finite Volume method, which ensures the consistency of the numerical scheme with the different asymptotic limits of the mathematical model without affecting the choice of the time step by restrictions related to the smallness of the scaling parameters. Several numerical tests confirm the validity of the proposed methodology, including a case study investigating the hemodynamics of a thoracic aorta in the presence of a stent.