Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics
Boundary Conditions by Schwarz-Christoffel Mapping in Anatomically Accurate Hemodynamics
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DOI：
10.1007/s10439-008-9571-3
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发表时间：
2008-12-01
影响因子：
3.8
通讯作者：
Poulikakos, Dimos
中科院分区：
文献类型：
--
作者：
Boutsianis, Evangelos;Gupta, Sumeet;Poulikakos, Dimos
合适的速度边界条件是计算血流动力学的前提条件。提出了一种在解剖学上逼真的边界截面上绘制解析或实验速度剖面的方法。由于计算域和实验域很少对齐，因此需要进行内插。在缺乏速度信息的情况下，一种替代方法是基于体积通量约束的分析轮廓的调整。所提出的算法是基于单连通或双连通多边形到单位圆或具有一元外半径的环的Schwarz-Christoffel(S-C)映射。结合S-C变换，构造了目标表面与测量域或源解析轮廓支撑之间的一对一可逆映射。建议的技术允许我们单独分割每个空间，并将一个空间映射到另一个空间的整体。试验是在正常速度边界条件下进行的，用于计算模拟升主动脉中的血液流动和脊椎中的脑脊液流动。考虑了通过简单连接的圆管和通过双连接的圆环的Woersley型的轴对称速度分布的映射，以及在瞬时体积流量约束下的在体相衬磁共振成像速度测量的内插。
Appropriate velocity boundary conditions are a prerequisite in computational hemodynamics. A method for mapping analytical or experimental velocity profiles on anatomically realistic boundary cross-sections is presented. Interpolation is required because the computational and experimental domains are seldom aligned. In the absence of velocity information one alternative is the adaptation of analytical profiles based on volumetric flux constraints. The presented algorithms are based on the Schwarz-Christoffel (S-C) mapping of singly or doubly connected polygons to the unit circle or an annulus with unary external radius. S-C transformations are combined to construct a one-to-one invertible map between the target surface and the measurement domain or the support of the source analytical profile. The proposed technique permits us to segment each space separately and map one onto the other in its entirety. Tests are performed with normal velocity boundary conditions for computational simulations of blood flow in the ascending aorta and cerebrospinal fluid flow in the spinal cavity. Mappings of axisymmetric velocity profiles of the Womersley type through a simply connected circular pipe as well as through a doubly connected circular annulus, and interpolations from in-vivo phase-contrast magnetic resonance imaging velocity measurements under instantaneous volumetric flux constraints are considered.