# Wave propagation in stenotic vessels; theoretical analysis and comparison between 3D and 1D fluid-structure-interaction models

## TL;DR

This paper develops an analytical 1D model for wave propagation in stenotic vessels, accurately approximating 3D FSI results and enabling fast, large-scale simulations for cardiovascular studies.

## Contribution

The authors introduce a simple, analytically solvable 1D model using only two geometric parameters that closely matches complex 3D FSI simulations for stenotic vessels.

## Key findings

- Excellent agreement with 3D FSI volume flow rate (<1% error)
- Accurate pressure distribution prediction with small error
- Model is adaptable for arbitrary vessel shapes and large-scale simulations

## Abstract

Using analytical expressions for the pressure and velocity waveforms in tapered vessels, we construct a linear 1D model for wave propagation in stenotic vessels in the frequency domain. We demonstrate that using only two parameters to approximate the exact geometry of the constriction (length and degree of stenosis), we can construct a model that can be solved analytically and can approximate with excellent accuracy the response of the original vessel for a wide range of physiologically relevant frequencies. We then proceed to compare the 1D results with full 3D FSI results from the literature for parameters corresponding to an idealized stenotic carotid artery. We find excellent matching with the volume flow rate over the cardiac cycle (less than $1\%$ error). Using results from DNS simulations to parametrize the velocity profile in the stenotic region, we manage to predict also the pressure distribution with small error (a few percentage points). The method proposed in the paper can be used to approximate vessels of arbitrary shape profile and can be extended to cover the whole cardiovascular tree. Recursive expressions make the solution very fast and open the possibility of carrying out sensitivity and uncertainty quantification studies that require thousands (or even millions) of simulations with minimal cost.