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

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 rare 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 expres- * sions 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.

Arterial pulse wave propagation across stenoses and aneurysms: assessment of one-dimensional simulations against three-dimensional simulations andin vitromeasurements

“…In all those studies, pressure losses across stenoses were described in the 1-D formulation based on empirical data [34,35]. Papadakis & Raspaud [36] compared 1-D model pressure and flow velocity data obtained both analytically and computationally in an idealized stenotic carotid artery (with a 75% stenosis size) against corresponding data obtained using a 3-D model. They showed a very good agreement between 1-D and 3-D model flow waveforms, with relative errors smaller than 1.0%, though the 1-D model pressure wave was severely underpredicted at the inlet.…”

Accelerated simulation methodologies for computational vascular flow modelling

“…Acceleration is measured by comparing the time taken for one ROM evaluation with one FOM evaluation. This is the case for all tables presenting acceleration statistics, unless otherwise stated.referencemethodapplicationaccuracyacceleration factorGrinberg et al [47]1Dpulsatile intracranial blood flow—147 000 a Blanco et al [55]1DFFR calculation in coronary arteries98%WCT: 302NT: 2870Xiao et al [56]1Dbaseline CCA>99normal%—baseline aorta>98normal%—aortic bifurcation>98normal%—Papadakis & Raspaud [57]1D (extended for stenosis)wave propagation in stenotic vessels>99normal%—Jonášová et al [58]1Doutlet flow rate in hepatic vein network88%—AW: 99%—Mirramezani & Shadden [59]1Dflow rate and pressure calculations in various vascular domains>93normal%>1000Gashi et al […”

Analytic solution for pulse wave propagation in flexible tubes with application to a patient-specific arterial tree

“…2008). Last but not least, the current model cannot be applied directly to diseased arteries such as those with an aneurism or stenosis, but can potentially be expanded to model these anomalies (Papadakis & Raspaud 2019).…”

“…Experimental evidences have shown that there is hysteresis between pressure and lumen area (Valdez-Jasso et al 2009) and the viscoelasticity causes attenuation of pulse waves as they travel downstream (Bessems et al 2008). Last but not least, the current model cannot be applied directly to diseased arteries such as those with an aneurism or stenosis, but can potentially be expanded to model these anomalies (Papadakis & Raspaud 2019).…”