Parker K H, Jones C J
Physiological Flow Studies Unit, Imperial College of Science, Technology and Medicine, London, England.
J Biomech Eng. 1990 Aug;112(3):322-6. doi: 10.1115/1.2891191.
The one-dimensional equations of flow in the elastic arteries are hyperbolic and admit nonlinear, wavelike solutions for the mean velocity, U, and the pressure, P. Neglecting dissipation, the solutions can be written in terms of wavelets defined as differences of the Riemann invariants across characteristics. This analysis shows that the product, dUdP, is positive definite for forward running wavelets and negative definite for backward running wavelets allowing the determination of the net magnitude and direction of propagating wavelets from pressure and velocity measured at a point in the artery. With the linearizing assumption that intersecting wavelets are additive, the forward and backward running wavelets can be separately calculated. This analysis, applied to measurements made in the ascending aorta of man, shows that forward running wavelets dominate during both the acceleration and deceleration phases of blood flow in the aorta. The forward and backward running waves calculated using the linearized analysis are similar to the results of an impedance analysis of the data. Unlike the impedance analysis, however, this is a time domain analysis which can be applied to nonperiodic or transient flow.
弹性动脉中一维流动方程是双曲型的，对于平均速度U和压力P允许有非线性的波状解。忽略耗散，解可以用定义为跨特征线的黎曼不变量之差的小波来表示。该分析表明，对于向前传播的小波，乘积dUdP是正定的，而对于向后传播的小波是负定的，这使得可以根据在动脉某一点处测量的压力和速度来确定传播小波的净大小和方向。在线性化假设即相交小波是可加的情况下，可以分别计算向前和向后传播的小波。将该分析应用于人体升主动脉的测量结果表明，在主动脉血流的加速和减速阶段，向前传播的小波都占主导。使用线性化分析计算得到的向前和向后传播的波与数据的阻抗分析结果相似。然而，与阻抗分析不同的是，这是一种时域分析，可应用于非周期性或瞬态流动。
