IEEE Trans Biomed Eng. 2024 Apr;71(4):1345-1354. doi: 10.1109/TBME.2023.3334758. Epub 2024 Mar 20.
The branching behavior of vascular trees is often characterized using Murray's law. We investigate its validity using synthetic vascular trees generated under global optimization criteria.
Our synthetic tree model does not incorporate Murray's law explicitly. Instead, we show that its validity depends on properties of the optimization model and investigate the effects of different physical constraints and optimization goals on the branching exponent that is now allowed to vary locally. In particular, we include variable blood viscosity due to the Fåhræus-Lindqvist effect and enforce an equal pressure drop between inflow and the micro-circulation. Using our global optimization framework, we generate vascular trees with over one million terminal vessels and compare them against a detailed corrosion cast of the portal venous tree of a human liver.
Murray's law is fulfilled when no additional constraints are enforced, indicating its validity in this setting. Variable blood viscosity or equal pressure drop lead to different optima but with the branching exponent inside the experimentally predicted range between 2.0 and 3.0. The validation against the corrosion cast shows good agreement from the portal vein down to the venules.
Not enforcing Murray's law increases the predictive capabilities of synthetic vascular trees, and in addition reduces the computational cost.
The ability to study optimal branching exponents across different scales can improve the functional assessment of organs.
血管树的分支行为通常采用 Murray 定律进行描述。我们使用在全局优化标准下生成的合成血管树来研究其有效性。
我们的合成树模型并未明确纳入 Murray 定律。相反，我们证明其有效性取决于优化模型的属性，并研究不同物理约束和优化目标对允许局部变化的分支指数的影响。具体而言，我们包括由于 Fåhræus-Lindqvist 效应而导致的可变血液粘度，并在流入和微循环之间强制实现相等的压降。使用我们的全局优化框架，我们生成了具有超过一百万个终端血管的血管树，并将其与人类肝脏门静脉的详细腐蚀铸件进行了比较。
在不施加其他约束的情况下，Murray 定律得到满足，表明其在这种情况下是有效的。可变血液粘度或相等的压降会导致不同的最优解，但分支指数在实验预测的 2.0 到 3.0 范围内。与腐蚀铸件的验证显示，从门静脉到小静脉都具有良好的一致性。
不强制实施 Murray 定律可以提高合成血管树的预测能力，并降低计算成本。
研究不同尺度下最佳分支指数的能力可以改善器官的功能评估。
