Purpose

Atherosclerosis preferentially occurs near the junction of branching vessels, where blood recirculation tends to occur (Malek et al. in J Am Med Assoc 282(21):2035–2042, 1999, https://doi.org/10.1001/jama.282.21.2035). For decades, CFD has been used to predict flow patterns such as separation and recirculation zones in hemodynamic models, but those predictions have rarely been validated with experimental data. In the context of verification and validation (V&V), we first conduct a CFD benchmark calculation that reproduces the vortex detection experiments of Karino and Goldsmith (1980) with idealised branching blood vessels (Karino and Goldsmith in Trans. Am. Soc. Artif. Internal Organs 26:500–506, 1980). The critical conditions for the formation of recirculation vortices, the so-called critical Reynolds numbers, are the main parameters for comparison with the experimental data to demonstrate the credibility of the CFD workflow. We then characterise the wall shear stresses and develop a surrogate model for the size of formed vortices.

Methods

An automated parametric study generating more than 12,000 CFD simulations was performed, sweeping the geometries and flow conditions found in the experiments by Karino and Goldsmith. The flow conditions were restricted to steady-state laminar flow, with a range of inflow Reynolds numbers up to 350, with various flow ratios between the main branch outlet and side branch outlet. The side branch diameter was scaled relative to the main branch diameter, ranging from 1.05/3 to 3/3; and the branching angles ranged in size from \({45}^\circ\) to \(135^\circ\). Recirculation vortices were detected by the inversion of the velocity vector at certain locations, as well as by the inversion of the wall shear stress (WSS) vector.

Results

The CFD simulations demonstrated good agreement with the experimental data on the critical Reynolds numbers. The spatial distributions of WSS on each branch were analysed to identify potential regions of disease. Once a vortex is formed, the size of the vortex increases by the square root of the Reynolds number. The CFD data was fitted to a surrogate model that accurately predicts the vortex size without the need to run computationally more expensive CFD simulations.

Conclusions

This benchmark study validates the CFD simulation of vortex detection in idealised branching vessels under comprehensive flow conditions. This work also proposes a surrogate model for the size of the vortex, which could reduce the computational requirements in the studies related to branching vessels and complex vascular systems.

中文翻译：

---

理想分支支管中涡流的形成：CFD基准研究。

目的

动脉粥样硬化优先发生在分支血管的交界处，那里容易发生血液再循环（Malek等。参见J Am Med Assoc 282（21）：2035–2042，1999，https://doi.org/10.1001/jama.282.21.2035）。几十年来，CFD已被用于预测血流动力学模型中的流动模式，例如分离和再循环区域，但这些预测很少得到实验数据的证实。在验证和确认（V＆V）的背景下，我们首先进行CFD基准计算，该模拟计算重现了具有理想分支血管的Karino和Goldsmith（1980）的涡流检测实验（Kar。and Goldsmith in Trans。Am。Soc。Artif。Internal器官26：500-506，1980）。形成再循环涡旋的关键条件，即所谓的关键雷诺数，是与实验数据进行比较以证明CFD工作流程可信性的主要参数。

方法

进行了自动参数研究，生成了超过12,000个CFD模拟，扫描了Karino和Goldsmith在实验中发现的几何形状和流动条件。流动条件仅限于稳态层流，其流入雷诺数范围高达350，主分支出口和侧分支出口之间的流量比也不同。侧分支直径相对于主分支直径按比例缩放，范围为1.05 / 3至3/3；分支角的大小范围从\（{45} ^ \ circ \）到\（135 ^ \ circ \）。通过在某些位置对速度矢量进行反演，以及对壁切应力（WSS）矢量进行反演，可以检测到回旋涡。

结果

CFD模拟表明与关于雷诺临界数的实验数据吻合良好。分析了WSS在每个分支上的空间分布，以确定潜在的疾病区域。形成涡旋后，涡旋的大小会增加雷诺数的平方根。将CFD数据拟合到可以准确预测涡旋大小的替代模型，而无需运行计算上更昂贵的CFD模拟。

结论

这项基准研究验证了在理想流动条件下理想化分支容器中涡流检测的CFD模拟。这项工作还提出了漩涡大小的替代模型，可以减少与分支血管和复杂血管系统有关的研究中的计算要求。