Computational Retinal Hemodynamics

视网膜的血流，也称为视网膜血流动力学，长期以来一直被认为会受到青光眼的影响。青光眼是一种神经退行性疾病，是导致不可逆转但可预防的失明的主要原因。视网膜血流动力学的改变也是其他几种疾病病理的指标，包括高血压和糖尿病等全身性疾病。因此，许多成像方式已经发展到非侵入性测量视网膜的血流动力学参数。例子包括彩色多普勒成像、激光多普勒血流测量、光学相干断层扫描和眼底摄影。虽然通过成像进行血流动力学分析已经有一个多世纪的历史，但高分辨率视网膜图像的出现结合了新的自动注释技术，创造了对视网膜微血管血流的精确数值模拟的需求。该项目的主要目标是开发稳定、高精度的优化算法，用于通过患者特定动脉图直接数值模拟颗粒血流。该项目通过参与研究为研究生提供培训。该项目解决了两个计算瓶颈，出现在大规模模拟颗粒流动使用边界积分方法。首先，利用外部微积分和调和多项式近似的概念，提出了一种新的三维高阶近奇异积分方案。这些方案的吸引人的特点是，它们直接在用户提供的边界网格（例如，三角动脉图）上工作。如果给定网格上的光滑线积分可以求出较高的精度，那么奇异积分和近奇异积分都可以求出较高的精度。这与通常需要预处理的现有方法形成了对比。其次，为了提高仿真的鲁棒性和准确性，而不会对网格尺寸施加过多的约束，将开发基于互补约束的接触分辨技术。虽然这个项目的主要重点是模拟视网膜血流动力学，但正在开发的计算方法将适用于更一般的微尺度颗粒流动，包括液滴，细菌和胶体的流动。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Blood flow in the retina, also termed retinal hemodynamics, has long been known to be affected by glaucoma, a neurodegenerative condition that is the leading cause of irreversible but preventable blindness. Alterations in retinal hemodynamics are also indicators of several other disease pathologies, including systemic diseases such as hypertension and diabetes. Consequently, numerous imaging modalities have been developed to non-invasively measure hemodynamic parameters in the retina. Examples include color Doppler imaging, laser Doppler flowmetry, optical coherence tomography, and fundus photography. While hemodynamic analysis via imaging has been available for more than a century, the advent of high-resolution retinal images combined with novel automated annotation techniques created the need for accurate numerical simulations of blood flow through retinal microvasculature. The primary goal of this project is to develop stable, high-accuracy, optimal algorithms for direct numerical simulation of particulate blood flow through patient-specific arterial graphs. The project provides training for graduate students through involvement in the research.This project addresses two computational bottlenecks that arise in large-scale simulations of particulate flows using boundary integral methods. First, a new high-order nearly-singular integration scheme in three dimensions using concepts from exterior calculus and harmonic polynomial approximations will be developed. The appealing feature of these schemes will be that they work directly on user-supplied boundary meshes (e.g., triangulated arterial graphs). If smooth line integrals on the given meshes can be evaluated to high accuracy, then singular and nearly singular integrals can both be computed to high accuracy. This contrasts with existing methods, which often require pre-processing. Second, to improve the robustness and accuracy of simulations without imposing excessive constraints on mesh sizes, complementarity constraint based contact resolution techniques will be developed. While the primary focus of this project is on simulating retinal hemodynamics, the computational methods under development will be applicable to more general microscale particulate flow, including flows of droplets, bacteria, and colloids.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.