Department of Civil and Environmental Engineering, Massacheusetts Institute of Technology, Cambridge, MA, 02139, USA.
Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX, 77843, USA.
Med Biol Eng Comput. 2018 Aug;56(8):1357-1366. doi: 10.1007/s11517-017-1775-y. Epub 2018 Jan 8.
We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-structure interactions. The phenomenon has its origin in an old-fashioned fire-fighting equipment where an air chamber serves to transform the intermittent influx from a pump to a more steady stream out of the hose. A similar mechanism exists in the cardiovascular system where blood injected intermittantly from the heart becomes rather smooth after passing through an elastic aorta. In existing haeodynamics literature, this mechanism is explained on the basis of electric circuit analogy with empirical impedances. We present a mechanistic theory based on the principles of fluid/structure interactions. Using a simple one-dimensional model, wave motion in the elastic aorta is coupled to the viscous flow in the rigid peripheral artery. Explicit formulas are derived that exhibit the role of material properties such as the blood density, viscosity, wall elasticity, and radii and lengths of the vessels. The current two-element model in haemodynamics is shown to be the limit of short aorta and low injection frequency and the impedance coefficients are derived theoretically. Numerical results for different aorta lengths and radii are discussed to demonstrate their effects on the time variations of blood pressure, wall shear stress, and discharge. Graphical Abstract A mechanistic analysis of Windkessel Effect is described which confirms theoretically the well-known feature that intermittent influx becomes continuous outflow. The theory depends only on the density and viscosity of the blood, the elasticity and dimensions of the vessel. Empirical impedence parameters are avoided.
我们描述了一种基于流固耦合线性动力学的血流动力学现象模型。这种现象起源于一种老式的消防设备，其中空气室用于将泵的间歇性流入转换为软管中更稳定的水流。在心血管系统中也存在类似的机制，血液从心脏间歇性注入，在经过弹性主动脉后变得更加平稳。在现有的血液动力学文献中，这种机制是基于电路类比和经验阻抗来解释的。我们提出了一种基于流固耦合原理的机械理论。使用简单的一维模型，弹性主动脉中的波动与刚性外周动脉中的粘性流动耦合。推导出了显式公式，展示了血液密度、粘度、壁弹性以及血管半径和长度等材料特性的作用。当前血液动力学中的两元件模型被证明是主动脉较短和注入频率较低的极限，并且理论上推导出了阻抗系数。讨论了不同主动脉长度和半径的数值结果，以演示它们对血压、壁面切应力和流量的时间变化的影响。
