# Mathematical Modeling of Human Retinal Vascular Pattern Around the Foveal Avascular Zone

## TL;DR

This paper uses mathematical modeling to explain how human retinal vascular patterns form, focusing on the role of astrocytes and angiogenesis.

## Contribution

A novel mathematical model combining angiogenesis and astrocyte dynamics to explain human-specific retinal vascular patterns.

## Key findings

- The astrocyte-coupling model successfully recapitulates key features of human retinal vascular patterns.
- Other models failed to support alternative hypotheses for vascular formation.
- Astrocyte dynamics and timing of spreading are crucial for vascular pattern formation.

## Abstract

Human retinas have unique anatomical structures called the macula and an associated characteristic vascular pattern. Despite its clinical importance, the mechanism underlying the human-specific vascular pattern remains unknown because of limitations in experimental approaches using primate samples. This study aimed to elucidate such vascular formation process.

We first examined the effects of four hypothetical factors contributing to foveal avascular zone (FAZ) formation: inhibitory molecule secretion, chemoattractant depletion, tissue deformation (towing), and tip cell migration restriction. None reproduced the features of the human retinal vascular structure. Next, we developed a mathematical model of human retinal vascular development by considering endothelial cells and astrocytes. We assumed that retinal vessels form via angiogenesis according to the gradient of vascular endothelial growth factor and that astrocytes dynamically expand while avoiding the fovea, providing scaffolds for angiogenesis.

Our astrocyte-coupling model recapitulated various features of the human retinal vascular pattern, including a radially outward vascular pattern from the optic disc, inferior and superior temporal arcades, FAZ formation, a radially inward vascular pattern around FAZ, and a vertically facing pattern toward the horizontal vascular borderline in the temporal region of FAZ. Other models did not support the other four hypotheses.

Our model explained human-specific retinal vascular formation as the combination of angiogenesis and vascular growth restriction by retinal astrocytes. These results also suggest the importance of astrocyte dynamics, particularly their timing of spreading.

Our modeling framework can be extended to abnormal vascular patterns observed in diseases, including retinopathy of prematurity.