视网膜微循环中一种新的多尺度建模方法及其毛细血管-组织耦合系统的解析解
A novel multiscale modelling for the hemodynamics in retinal microcirculation with an analytic solution for the capillary-tissue coupled system
AI总结：
本文提出一种新的多尺度建模方法，结合毛细血管和组织的耦合达西方程，通过解析解提高计算效率，验证了模型的预测准确性，并探讨了参数对视网膜血流动力学的影响。
摘要：
视网膜微循环血流动力学的数学建模是理解视网膜疾病的关键工具，但因视网膜血管的多尺度性质及其与周围组织的耦合而具有挑战性。为此，我们开发了一种多尺度模型，将视网膜血管跨尺度耦合到间质组织中。该模型结合了动脉和静脉的一维模型，以及毛细血管和组织的耦合达西方程。模型使用了毛细血管-组织耦合系统的解析解，提供了结果的简单解释并显著提高了计算速度。解析解表明了一种动态耦合条件，将毛细血管床与上游动脉和下游静脉的流动联系起来。该模型通过解的截断误差和收敛性分析证明了其数学稳健性。其预测准确性通过实验数据和其他模型验证，使其在解释实验结果中具有实用性。最后，探讨了各种参数在控制视网膜血流动力学中的作用。
英文摘要：
Mathematical modelling of the microcirculatory hemodynamics in the retina is an essential tool for understanding various diseases of the retina, yet remains challenging due to the multiscale nature of the retinal vasculature and its coupling to surrounding tissue. To address this, we develop a multiscale model that couples retinal vasculature across scales with interstitial tissue. Our model combines the one-dimensional (1D) model for arterioles and venules with the coupled Darcy equations for capillaries and tissue. The model uses an analytic solution for capillary-tissue coupled system that provides a simple interpretation of the results along with much faster computation. The analytic solution implies a dynamic coupling condition that links the capillary bed with upstream arteriolar and downstream venular flows. The model is mathematically robust, demonstrated through analysis of the solution's truncation error and convergence. Its predictive accuracy is validated against experimental data and other models, making it useful in interpreting experimental results. Finally, the role of various parameters in controlling retinal hemodynamics is explored.
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