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

作者：Ji Chang Jin; Sugiyama Kazuyasu; Noda Shigeho; He Ying^*; Himeno Ryutaro

来源：Acta Mechanica Sinica, 2015, 31(1): 122-131.

DOI：10.1007/s10409-015-0010-z

• Lorentz's reciprocal theorem
• Theoretical relation
• Stenosis artery
• VOF method
• Lubrication theory

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.

• 出版日期2015-2
• 单位RIKEN; 中国科学技术大学