双极截面管内脉动流的血流动力学分析
Hemodynamic analysis of the Pulsatile Flow in Tubes of Bipolar Cross Sections
AI总结：
本研究推导了双极截面管内脉动流和泊肃叶流控制方程的解析解，分析了不同脉动频率和几何参数对速度场、流量及壁面剪切应力的影响，为心血管疾病进展和诊断模型改进提供了重要见解。
摘要：
脉动流通过受压或有缺陷的血管是血流动力学中一个极其重要的课题，特别是在心血管研究中。本研究考察了双极截面管内的流体动力学，该截面可能代表二叶主动脉瓣（BAV）、主动脉分叉和主动脉弓区域的几何形状，在这些区域，非均匀的血管形状会显著影响血流动力学行为。本文推导了双极截面管中脉动流和泊肃叶流控制方程的解析解。分析侧重于不同脉动频率和几何参数下的速度场、流量和壁面剪切应力（WSS），突出了这些因素如何相互作用以塑造流动特性。在低频下，速度剖面保持平滑，具有平缓的加速和减速阶段。相比之下，在较高频率下，振荡效应变得更加显著，最初出现在 $ωt=0$ 和 $ωt=π$ 附近的峰值体积流量，在周期内向更早的阶段（$ωt=0$ 到 $ωt=π/2$）移动，随后在极高频率下趋于稳定。剪切应力行为也表现出依赖于频率的变化。在低频下，流体平滑地响应压力梯度，产生类似于稳态流的剪切应力分布。然而，随着频率增加，惯性和非稳态效应引入了相位滞后，导致更复杂的剪切应力模式。这些发现为血管几何形状与脉动力之间的相互作用提供了有价值的见解，对理解疾病进展和改进心血管医学中的诊断模型具有重要意义。
英文摘要：
Pulsatile flow through compressed or defective blood vessels is a topic of fundamental importance in hemodynamics, particularly in cardiovascular research. This study examines flow dynamics within a tube with a bipolar cross section, possibly representing the geometry of bicuspid aortic valves (BAV), aortic bifurcations, and the aortic arch regions where non-uniform vessel shapes significantly influence hemodynamic behavior. An analytical solution is derived for the governing equations of pulsatile and poiseuille flow in a bipolar cross-sectional tube. The analysis focuses on the velocity field, flow rate, and wall shear stress (WSS) across different pulsation frequencies and geometric parameters, highlighting how these factors interact to shape flow characteristics. At low frequencies, the velocity profile remains smooth, with gradual acceleration and deceleration phases. In contrast, at higher frequencies, oscillatory effects become more pronounced, and the peak volume flow, initially occurring near $ωt=0$ and $ωt$=$π$, shifts toward an earlier phase in the cycle $ωt=0$ to $ωt=π/2)$ before stabilizing at very high frequencies. Shear stress behavior also exhibits frequency-dependent variations. At low frequencies, the fluid responds smoothly to pressure gradients, producing a shear stress distribution similar to steady flow. However, as frequency increases, inertial and unsteady effects introduce phase lags, leading to more complex shear stress patterns. These findings provide valuable insights into the interplay between vessel geometry and pulsatile forces, with implications for understanding disease progression and refining diagnostic models in cardiovascular medicine.
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