Ku D N, Zeigler M N, Downing J M
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta 30332-0405.
J Biomech Eng. 1990 Nov;112(4):444-50. doi: 10.1115/1.2891209.
A one-dimensional inviscid solution for flow through a compliant tube with a stenosis is presented. The model is used to represent an artery with an atherosclerotic plaque and to investigate a range of conditions for which arterial collapse may occur. The coupled equations for flow through collapsible tubes are solved using a Runge-Kutta finite difference scheme. Quantitative results are given for specific physiological parameters including inlet and outlet pressure, flow rate, stenosis size, length and stiffness. The results suggest that high-grade stenotic arteries may exhibit collapse with typical physiological pressures. Critical stenoses may cause choking of flow at the throat followed by a transition to supercritical flow with tube collapse downstream. Greater amounts of stenosis produced a linear reduction of flow rate and a shortening of the collapsed region. Changes in stenosis length created proportional changes in the length of collapse. Increasing the stiffness of the stenosis to a value greater than the nominal tube stiffness caused a greater amount of flow limitation and more negative pressures, compared to a stenosis with constant stiffness. These findings assist in understanding the clinical consequences of flow through atherosclerotic arteries.
本文给出了通过带有狭窄的顺应性血管的一维无粘流解。该模型用于表示具有动脉粥样硬化斑块的动脉，并研究一系列可能发生动脉塌陷的情况。使用龙格 - 库塔有限差分格式求解通过可塌陷血管的耦合方程。针对特定生理参数给出了定量结果，包括入口和出口压力、流量、狭窄尺寸、长度和刚度。结果表明，高度狭窄的动脉在典型生理压力下可能会发生塌陷。临界狭窄可能导致喉部血流阻塞，随后转变为下游血管塌陷的超临界流。更大程度的狭窄会导致流量线性减少和塌陷区域缩短。狭窄长度的变化会使塌陷长度产生成比例的变化。与具有恒定刚度的狭窄相比，将狭窄刚度增加到大于标称血管刚度的值会导致更大程度的流量限制和更负的压力。这些发现有助于理解通过动脉粥样硬化动脉的血流的临床后果。
