A one-dimensional model of blood flow in arteries with friction and convection based on the Womersley velocity profile.
A one-dimensional model of blood flow in arteries with friction and convection based on the Womersley velocity profile.
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DOI：
10.1007/s10558-007-9031-y
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发表时间：
2007-06-01
影响因子：
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通讯作者：
Peskin, Charles S
中科院分区：
文献类型：
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作者：
Azer, Karim;Peskin, Charles S
在本文中，我们提出了动脉血流的一维模型，没有假设动脉速度分布的先验形状（Azer 博士论文，纽约大学库朗研究所，2006 年）。我们以迭代方式将质量和动量守恒的一维方程与速度剖面的 Womersley 模型结合起来。一维模型的压力梯度驱动沃默斯利方程，然后计算出的速度分布反馈到一维模型的摩擦和非线性部分。除了使我们能够正确评估摩擦以及使用速度分布来校正非线性项之外，将速度分布作为输出在各种应用中应该很有用。我们使用结构化树和小动脉纯阻力模型进行流动模拟，并比较各种摩擦模型下产生的流动和压力波。此外，我们还展示了如何将一维方程与对流扩散方程的泰勒扩散极限（Azer, Int J Heat Mass Transfer 2005;48:2735-40; Taylor, Proc R Soc Lond Ser A 1953;219:186-203）耦合起来，以及时驱动溶质沿动脉的浓度。
In this paper, we present a one-dimensional model for blood flow in arteries, without assuming an a priori shape for the velocity profile across an artery (Azer, Ph.D. thesis, Courant Institute, New York University, 2006). We combine the one-dimensional equations for conservation of mass and momentum with the Womersley model for the velocity profile in an iterative way. The pressure gradient of the one-dimensional model drives the Womersley equations, and the velocity profiles calculated then feed back into both the friction and nonlinear parts of the one-dimensional model. Besides enabling us to evaluate the friction correctly and also to use the velocity profile to correct the nonlinear terms, having the velocity profile available as output should be useful in a variety of applications. We present flow simulations using both structured trees and pure resistance models for the small arteries, and compare the resulting flow and pressure waves under various friction models. Moreover, we show how to couple the one-dimensional equations with the Taylor diffusion limit (Azer, Int J Heat Mass Transfer 2005;48:2735-40; Taylor, Proc R Soc Lond Ser A 1953;219:186-203) of the convection-diffusion equations to drive the concentration of a solute along an artery in time.