Physics-based modeling of Age-related Macular Degeneration—A theoretical approach to quantify retinal and choroidal contributions to macular oxygenation

Abstract

We developed a mathematical model to characterize how macular oxygenation may be affected by abnormalities in the retinal and choroidal oxygen supplies. The macular region is modeled as a layered structure including: ganglion cell and nerve fiber layers, inner plexiform layer, inner nuclear layer, outer plexiform layer, outer nuclear layer, inner segment of photoreceptors layer and retinal pigmented epithelium. Each layer is characterized by specific levels of oxygen consumption. The vitreous and the choroid are located at the macula boundary and provide oxygen via boundary conditions of Dirichlet type. The three capillary plexi (superficial, intermediate, and deep) of the retinal circulation pierce the macular layers and provide oxygen via a volumetric source that depends on the retinal blood flow. Oxygen profiles through the macular tissue are calculated by simulating the balance among oxygen supply, consumption and diffusion in: (a) physiological baseline conditions; (b) retinal blood flow reduced by 10%, 30% and 50% with respect to baseline; (c) choroidal oxygen level diminished by 10%, 30% and 50% with respect to baseline. Model simulations predict that: (1) the oxygenation of the foveal avascular zone is not affected by reduction in retinal blood flow; (2) a reduction in choroidal oxygen supply significantly affects the outer layers, especially the photoreceptors and outer nuclear layers; (3) the impact of reduction in choroidal oxygen supply is larger in the region more proximal to the macular center; (4) the impact of reduction in retinal blood flow is larger in the region more proximal to the macular periphery. The proposed mathematical model suggests that changes in retinal and choroidal oxygen supplies impact the oxygenation of the macular tissue differentially. These results may help better understand the pathogenesis of macular degeneration.