Voltairas P A, Fotiadis D I, Massalas C V, Michalis L K
Department of Computer Science, University of Ioannina, GR451 10 Ioannina, Greece; Biomedical Research Institute-FORTH, GR 451 10 Ioannina, Greece.
J Biomech. 2005 Jul;38(7):1423-31. doi: 10.1016/j.jbiomech.2004.06.023. Epub 2004 Oct 7.
Fourier analysis is usually employed for the computation of blood flow in arteries. Although the orthogonality of Fourier eigenfunctions guarantees the accurate mathematical modeling of the blood pressure and flow waveforms, the physics behind this objective function is frequently missing. We propose a new method to account for the blood pressure and flow, single-cycle (systole-diastole) waveforms. It is based on the one dimensional hydrodynamic mass and momentum conservation equations for viscous flow. The similarity of the linear problem, under discussion, with related transmission line theory in electromagnetic wave propagation, permits expansion in anharmonic, non-separable eigenfunctions. In some cases one term in the expansion is adequate to fit the main peak of the observed waveforms. Analytical formulas are derived for the dependence of the pressure and flow main peaks on whole blood viscosity and distance from the heart, which interpret observations related to hypertension.
傅里叶分析通常用于计算动脉中的血流。尽管傅里叶本征函数的正交性保证了血压和血流波形的精确数学建模，但该目标函数背后的物理原理常常缺失。我们提出了一种新方法来处理血压和血流的单周期（收缩期 - 舒张期）波形。它基于一维粘性流动的流体动力学质量和动量守恒方程。正在讨论的线性问题与电磁波传播中相关传输线理论的相似性，允许用非谐波、不可分离的本征函数展开。在某些情况下，展开式中的一项就足以拟合观测波形的主峰。推导了压力和血流主峰与全血粘度以及距心脏距离的依赖关系的解析公式，这些公式解释了与高血压相关的观测结果。
