Frog tongue segmentation data for a realistic vascular structure in modelling

In the last decade, numerical models have been an increasingly important tool in biological and medical science both for the fundamental understanding of physiology as well as the potential for novel diagnostics and treatments tools in clinical application. In this paper, a nonlinear multi-scale model framework is developed for blood flow distribution in the full vascular system of an organ. We couple a quasi 1D vascular graph model to represent blood flow in larger vessels and a porous media model to describe flow in smaller vessels and capillary bed. The vascular model is based on Poiseuille's law, with pressure correction by elasticity and pressure drop estimation at vessels junctions. The porous capillary bed is modelled as a two-compartment domain (artery and venous) using Darcy's law. The fluid exchange between the artery and venous capillary bed compartments are defined as blood perfusion. The numerical experiments show that the proposed model for blood circulation: 1) is closely dependent on the structure and parameters of both the vascular vessels and of the capillary bed, and 2) it provides a realistic blood circulation in the organ. The advantage of the proposed model is that it is complex enough to reliably capture the main underlying physiological function, yet highly flexible as it offers the possibility of incorporating various local effects. Furthermore, the numerical implementation of the model is straightforward and allows for simulations on a regular desktop computer.近十年来，数值模型在生物医学领域的重要性与日俱增，既可为生理学的基础研究提供理论支撑，亦有望为临床应用中的新型诊断与治疗工具研发提供可行路径。本文针对器官完整脉管系统内的血流分布问题，构建了一套非线性多尺度模型框架。我们将准一维（quasi 1D）脉管图模型与多孔介质模型（porous media model）相结合：前者用于刻画大血管内的血流动力学过程，后者则用以描述微小血管与毛细血管床（capillary bed）内的流动特性。该脉管模型以泊肃叶定律（Poiseuille's law）为核心理论基础，引入血管弹性带来的压力校正项，并对血管分叉处的压降进行精准估算。研究采用达西定律（Darcy's law），将多孔毛细血管床建模为包含动脉与静脉两个隔室的域结构。动脉与静脉毛细血管床隔室之间的流体交换过程被定义为血液灌注。数值实验结果表明，本文提出的血液循环模型具备两大核心特性：其一，其性能紧密依赖于脉管系统与毛细血管床的结构与参数；其二，该模型可在器官层面还原出贴合生理实际的血液循环状态。本模型的优势在于，其复杂度足以可靠捕捉血液循环的核心生理功能本质，同时又具备高度灵活性，可兼容各类局部生理效应的嵌入。此外，该模型的数值实现流程简洁直观，仅需普通台式电脑即可完成模拟运算。