Painter Page R
Office of Environmental Health Hazard Assessment, California Environmental Protection Agency, P, O, Box 4010, Sacramento, CA 95812, USA.
Theor Biol Med Model. 2008 Jul 29;5:15. doi: 10.1186/1742-4682-5-15.
The arterial pulse is a viscous-fluid shock wave that is initiated by blood ejected from the heart. This wave travels away from the heart at a speed termed the pulse wave velocity (PWV). The PWV increases during the course of a number of diseases, and this increase is often attributed to arterial stiffness. As the pulse wave approaches a point in an artery, the pressure rises as does the pressure gradient. This pressure gradient increases the rate of blood flow ahead of the wave. The rate of blood flow ahead of the wave decreases with distance because the pressure gradient also decreases with distance ahead of the wave. Consequently, the amount of blood per unit length in a segment of an artery increases ahead of the wave, and this increase stretches the wall of the artery. As a result, the tension in the wall increases, and this results in an increase in the pressure of blood in the artery.
An expression for the PWV is derived from an equation describing the flow-pressure coupling (FPC) for a pulse wave in an incompressible, viscous fluid in an elastic tube. The initial increase in force of the fluid in the tube is described by an increasing exponential function of time. The relationship between force gradient and fluid flow is approximated by an expression known to hold for a rigid tube.
For large arteries, the PWV derived by this method agrees with the Korteweg-Moens equation for the PWV in a non-viscous fluid. For small arteries, the PWV is approximately proportional to the Korteweg-Moens velocity divided by the radius of the artery. The PWV in small arteries is also predicted to increase when the specific rate of increase in pressure as a function of time decreases. This rate decreases with increasing myocardial ischemia, suggesting an explanation for the observation that an increase in the PWV is a predictor of future myocardial infarction. The derivation of the equation for the PWV that has been used for more than fifty years is analyzed and shown to yield predictions that do not appear to be correct.
Contrary to the theory used for more than fifty years to predict the PWV, it speeds up as arteries become smaller and smaller. Furthermore, an increase in the PWV in some cases may be due to decreasing force of myocardial contraction rather than arterial stiffness.
动脉脉搏是一种粘性流体冲击波，由心脏射出的血液引发。该波以称为脉搏波速度（PWV）的速度远离心脏传播。在许多疾病过程中，PWV会增加，这种增加通常归因于动脉僵硬。当脉搏波接近动脉中的某一点时，压力会上升，压力梯度也会上升。这个压力梯度会增加波前方的血流速度。波前方的血流速度会随着距离的增加而降低，因为压力梯度也会随着波前方距离的增加而降低。因此，在波前方的一段动脉中，单位长度的血液量会增加，这种增加会拉伸动脉壁。结果，动脉壁中的张力增加，这导致动脉中血液压力升高。
从描述弹性管中不可压缩粘性流体中脉搏波的流压耦合（FPC）的方程中推导出PWV的表达式。管中流体力的初始增加由时间的指数增长函数描述。力梯度与流体流动之间的关系通过一个已知适用于刚性管的表达式近似。
对于大动脉，用这种方法得出的PWV与非粘性流体中PWV的科特韦格 - 莫恩斯方程一致。对于小动脉，PWV大约与科特韦格 - 莫恩斯速度除以动脉半径成正比。当压力随时间的特定增加率降低时，小动脉中的PWV预计也会增加。这个速率会随着心肌缺血的增加而降低，这为观察到的PWV增加是未来心肌梗死的预测指标提供了一种解释。对已使用五十多年的PWV方程的推导进行了分析，结果表明其预测似乎不正确。
与用于预测PWV五十多年的理论相反，随着动脉变得越来越小，PWV会加快。此外，在某些情况下，PWV的增加可能是由于心肌收缩力下降而不是动脉僵硬。
