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.

我们开发了一个数学模型来描述黄斑氧合如何受到视网膜和脉络膜氧供应异常的影响。黄斑区域被建模为分层结构，包括：神经节细胞和神经纤维层、内丛状层、内核层、外丛状层、外核层、感光层内段和视网膜色素上皮。每一层都以特定的耗氧量为特征。玻璃体和脉络膜位于黄斑边界，通过狄利克雷型边界条件提供氧气。视网膜循环的三个毛细血管丛（浅层、中间层和深层）穿透黄斑层并通过依赖于视网膜血流的容积源提供氧气。通过模拟氧气供应、消耗和扩散之间的平衡来计算通过黄斑组织的氧气分布： (a) 生理基线条件；(b) 视网膜血流量相对于基线减少了 10%、30% 和 50%；(c) 脉络膜氧水平相对于基线降低了 10%、30% 和 50%。模型模拟预测：（1）中心凹无血管区的氧合不受视网膜血流减少的影响；(2) 脉络膜供氧的减少显着影响外层，尤其是光感受器和外核层；(3)脉络膜供氧减少的影响在更接近黄斑中心的区域更大；(4)视网膜血流量减少的影响在更接近黄斑周边的区域更大。所提出的数学模型表明，视网膜和脉络膜氧供应的变化对黄斑组织的氧合有不同的影响。这些结果可能有助于更好地了解黄斑变性的发病机制。