# The application of the Lattice Boltzmann method to the one-dimensional blood flow dynamics in elastic vessels

## TL;DR

This paper demonstrates that the Lattice Boltzmann method can effectively model one-dimensional blood flow in elastic vessels, capturing nonlinear wave propagation and vessel stiffening with high accuracy.

## Contribution

It introduces a Lattice Boltzmann model for blood flow in elastic vessels, linking kinetic theory with cardiovascular dynamics, and validates it through various test problems.

## Key findings

- Accurate modeling of nonlinear wave propagation in elastic vessels
- Effective simulation of artery stiffening effects
- Good agreement with previous results in test cases

## Abstract

The one-dimensional nonlinear equations for the blood flow motion in distensible vessels are considered using the kinetic approach. It is shown that the Lattice Boltzmann (LB) model for non-ideal gas is asymptotically equivalent to the blood flow equations for compliant vessels at the limit of low Knudsen numbers. The equations of state for non-ideal gas are transformed to the pressure-luminal area response. This property allows to model arbitrary pressure-luminal area relations. Several test problems are considered: the propagation of a sole nonlinear wave in an elastic vessel, the propagation of a pulse wave in a vessel with varying mechanical properties (artery stiffening) and in an artery bifurcation, in the last problem Resistor-Capacitor-Resistor (RCR) boundary conditions are considered. The comparison with the previous results show a good precision.