Frasch H F, Kresh J Y, Noordergraaf A
Department of Anesthesia, University of Pennsylvania, Philadelphia 19104-6392.
Ann Biomed Eng. 1994 Jan-Feb;22(1):45-57. doi: 10.1007/BF02368221.
We analyzed wave transmission properties and input impedance of a microvascular network model. The model, derived from rat spinotrapezius muscle and previously described and validated by other investigators for steady pressure-flow relations, was expanded to include pulsatile phenomena. Microvessels are considered purely elastic, with compliances a function of vessel type; viscous dissipation follows Poiseuille's law. Linear and nonlinear results are presented. In the nonlinear case, shear rate-dependent viscosity of blood and transmural pressure-dependent vascular diameters were calculated and small signal perturbations were imposed around several working points. We investigated effects on input impedance of physiological variability of network parameters and structure: distribution of capillary diameters, capillary segment length, and presence or absence of cross-connecting capillaries. Results show that although wave transmission properties are complex, input impedance is simple. Apparent wave speeds differ substantially from phase velocities and change markedly from branch to branch; pressure and flow waves appear to travel at different speeds. These features result from the mesh-like structure of the network and the prominence of reflection at branchpoints. Input impedance displays a similar form under all conditions: Magnitude is a monotonically decreasing function of frequency, and phase decreases from 0 to approximately -45 degrees. Consideration of the characteristic impedance of a microvessel leads to modification of the three-element Windkessel as a reduced model of the observed input impedance.
我们分析了一个微血管网络模型的波传播特性和输入阻抗。该模型源自大鼠斜方肌，先前已由其他研究人员针对稳定压力-流量关系进行了描述和验证，并扩展到包括脉动现象。微血管被视为纯弹性的，其顺应性是血管类型的函数；粘性耗散遵循泊肃叶定律。给出了线性和非线性结果。在非线性情况下，计算了血液的剪切速率依赖性粘度和跨壁压力依赖性血管直径，并在几个工作点周围施加了小信号扰动。我们研究了网络参数和结构的生理变异性对输入阻抗的影响：毛细血管直径的分布、毛细血管段长度以及交叉连接毛细血管的有无。结果表明，尽管波传播特性复杂，但输入阻抗却很简单。表观波速与相速度有很大差异，并且在不同分支之间变化显著；压力波和流量波似乎以不同速度传播。这些特征源于网络的网状结构以及分支点处反射的突出性。在所有条件下，输入阻抗都呈现出类似的形式：幅值是频率的单调递减函数，相位从0度减小到大约 -45度。对微血管特征阻抗的考虑导致对三元件Windkessel模型进行修改，作为观察到的输入阻抗的简化模型。
