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.
