Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem Abstract A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxel-based simulator V-FLOW VOF3D, where the vessel geometry is expressed by using volume of fluid (VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

An improved correlation of the pressure drop in stenotic vessels using Lorentz’s reciprocal theorem

Download PDF
10 pages

Loading next page...
 
/lp/springer-journals/an-improved-correlation-of-the-pressure-drop-in-stenotic-vessels-using-hXiYQL3vyL

References (30)

Publisher
Springer Journals
Copyright
2015 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-015-0010-z
Publisher site
See Article on Publisher Site

Abstract

Abstract A mathematical model of the human cardiovascular system in conjunction with an accurate lumped model for a stenosis can provide better insights into the pressure wave propagation at pathological conditions. In this study, a theoretical relation between pressure drop and flow rate based on Lorentz’s reciprocal theorem is derived, which offers an identity to describe the relevance of the geometry and the convective momentum transport to the drag force. A voxel-based simulator V-FLOW VOF3D, where the vessel geometry is expressed by using volume of fluid (VOF) functions, is employed to find the flow distribution in an idealized stenosis vessel and the identity was validated numerically. It is revealed from the correlation that the pressure drop of NS flow in a stenosis vessel can be decomposed into a linear term caused by Stokes flow with the same boundary conditions, and two nonlinear terms. Furthermore, the linear term for the pressure drop of Stokes flow can be summarized as a correlation by using a modified equation of lubrication theory, which gives favorable results compared to the numerical ones. The contribution of the nonlinear terms to the pressure drop was analyzed numerically, and it is found that geometric shape and momentum transport are the primary factors for the enhancement of drag force. This work paves a way to simulate the blood flow and pressure propagation under different stenosis conditions by using 1D mathematical model.

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: Feb 1, 2015

There are no references for this article.