不同孔径球冠上的多尺度视网膜血流
Multiscale retinal flow on a spherical cap of varying aperture
- Beijing Normal University（北京师范大学）
- Utah State University（犹他州立大学）
- Illinois Institute of Technology（伊利诺伊理工学院）
- Duke Kunshan University（杜克昆山大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究将视网膜血流模型从平面圆盘扩展到不同孔径的球冠，利用解析解耦合多尺度血流，发现孔径主要通过改变血管结构影响血流动力学，为解剖学上更真实的视网膜病理研究奠定基础。
AI中文摘要：
对视网膜血流动力学进行建模对于理解视网膜微循环至关重要，但由于其涉及血管系统与周围组织在多尺度上的耦合，计算成本很高。最近在平面圆盘上得到的解析解通过将毛细血管床和周围组织合并为一个有效电阻，大大减轻了这一计算负担。然而，该公式将视网膜视为平面，而视网膜实际上是一个具有有限前部孔径的曲面。在本工作中，我们开发了一个非平凡且生理上必要的扩展，将其应用于具有不同孔径的球冠组织域，其中表面曲率和有限孔径边界使得在弯曲流形上求解耦合的达西方程变得复杂。利用球极投影和解耦变换，我们推导出了球冠上毛细血管-组织系统的解析解，该解更真实地表示了毛细血管床和间质组织中的血流，同时保留了平面圆盘公式的一个关键优势——高效的电阻公式。该解与一维（1D）小动脉和小静脉血流耦合，以获得视网膜血流动力学的多尺度描述。使用一个旨在捕捉视网膜血管特征的血管模型，我们展示了多尺度模型的预测与实验数据一致。我们进一步使用固定的半球形血管系统和依赖于孔径的血管系统来探索孔径效应。孔径主要通过构建的血管系统本身的变化来影响视网膜血流动力学，而表面平均压力和相对末端血流分布几乎保持不变。该框架为在更符合解剖学的域上研究视网膜病理生理学提供了基础。
英文摘要：
Modelling retinal haemodynamics is crucial for understanding retinal microcirculation but is computationally demanding because it involves coupling between the vasculature and surrounding tissue across multiple scales. This computational burden has been substantially alleviated by a recent analytic solution on the planar disc that enables lumping the capillary bed and surrounding tissue into an effective resistor. However, that formulation treats the retina as a flat surface, whereas the retina is a curved surface with a finite anterior aperture. In this work, we develop a nontrivial and physiologically necessary extension to spherical-cap tissue domains with varying apertures, where surface curvature and finite-aperture boundaries complicate solving coupled Darcy equations on a curved manifold. Using a stereographic projection and a decoupling transformation, we derive an analytic solution for the capillary-tissue system on the spherical cap that represents flow in both the capillary bed and interstitial tissue more realistically while retaining the efficient resistor formulation, a key advantage of the planar-disc formulation. This solution is coupled to one-dimensional (1D) arteriolar and venular flows to obtain a multiscale description of retinal haemodynamics. Using a vasculature model designed to capture retinal vascular features, we show that the multiscale model's predictions are consistent with experimental data. We further explore aperture effects using both a fixed hemispherical vasculature and aperture-dependent vasculature. The aperture affects retinal haemodynamics mainly through changes in the constructed vasculature itself, whereas the surface-averaged pressures and relative terminal flow distributions remain nearly unchanged. This framework provides a foundation for studying retinal pathophysiology on more anatomically realistic domains.
