Carr Russell T, Geddes John B, Wu Fan
Department of Chemical Engineering, University of New Hampshire, Durham, NH 03824, USA.
Ann Biomed Eng. 2005 Jun;33(6):764-71. doi: 10.1007/s10439-005-2345-2.
We have identified the simplest topology that will permit spontaneous oscillations in a model of microvascular blood flow that includes the plasma skimming effect and the Fahraeus-Lindqvist effect and assumes that the flow can be described by a first-order wave equation in blood hematocrit. Our analysis is based on transforming the governing partial differential equations into delay differential equations and analyzing the associated linear stability problem. In doing so we have discovered three dimensionless parameters, which can be used to predict the occurrence of nonlinear oscillations. Two of these parameters are related to the response of the hydraulic resistances in the branches to perturbations. The other parameter is related to the amount of time necessary for the blood to pass through each of the branches. The simple topology used in this study is much simpler than networks found in vivo. However, we believe our analysis will form the basis for understanding more complex networks.
我们已经确定了最简单的拓扑结构，该结构能使包含血浆撇取效应和法厄-林德奎斯特效应的微血管血流模型产生自发振荡，并假设血流可用血细胞比容的一阶波动方程来描述。我们的分析基于将控制偏微分方程转化为延迟微分方程，并分析相关的线性稳定性问题。在此过程中，我们发现了三个无量纲参数，可用于预测非线性振荡的发生。其中两个参数与分支中水力阻力对扰动的响应有关。另一个参数与血液通过每个分支所需的时间量有关。本研究中使用的简单拓扑结构比体内发现的网络要简单得多。然而，我们相信我们的分析将为理解更复杂的网络奠定基础。
