Department of Mathematical and Computer Sciences, Metropolitan State University of Denver, P.O. Box 173362, Campus Box 38, Denver, CO 80217, USA.
Department of Mathematical Sciences, Indiana University-Purdue University-Indianapolis, 402 N. Blackford St, LD 270, Indianapolis, IN 46202, USA.
Math Biosci. 2018 Nov;305:1-9. doi: 10.1016/j.mbs.2018.08.005. Epub 2018 Aug 24.
Impaired oxygen delivery and tissue perfusion have been identified as significant factors that contribute to the loss of retinal ganglion cells in glaucoma patients. This study predicts retinal blood and tissue oxygenation using a theoretical model of the retinal vasculature based on confocal microscopy images of the mouse retina. These images reveal a complex and heterogeneous geometry of vessels that are distributed non-uniformly into multiple distinct retinal layers at varying depths. Predicting oxygen delivery and distribution in this irregular arrangement of retinal microvessels requires the use of an efficient theoretical model. The model employed in this work utilizes numerical methods based on a Green's function approach to simulate the spatial distribution of oxygen levels in a network of retinal blood vessels and the tissue surrounding them. Model simulations also predict the blood flow rates and pressures in each of the microvessels throughout the entire network. As expected, the model predicts that average vessel PO decreases as oxygen demand is increased. However, the standard deviation of PO in the vessels nearly doubles as oxygen demand is increased from 1 to 8 cm O/100 cm/min, indicating a very wide spread in the predicted PO levels, suggesting that average PO is not a sufficient indicator of oxygenation in a heterogeneous vascular network. Ultimately, the development of this mathematical model will help to elucidate the important factors associated with blood flow and metabolism that contribute to the vision loss characteristic of glaucoma.
已确定氧输送和组织灌注受损是导致青光眼患者视网膜神经节细胞丧失的重要因素。本研究使用基于小鼠视网膜共聚焦显微镜图像的视网膜血管理论模型来预测视网膜血液和组织的氧合作用。这些图像揭示了血管的复杂和异质几何形状，这些血管不均匀地分布在多个不同的视网膜层中，深度不同。在这种不规则的视网膜微血管排列中预测氧输送和分布需要使用有效的理论模型。这项工作中使用的模型利用基于格林函数方法的数值方法来模拟视网膜血管网络及其周围组织中氧水平的空间分布。模型模拟还预测了整个网络中每个微血管中的血流速度和压力。正如预期的那样，模型预测平均血管 PO 随着氧需求的增加而降低。然而，当氧需求从 1 增加到 8 cm O/100 cm/min 时，PO 的标准偏差几乎增加了一倍，这表明预测的 PO 水平有很大的差异，这表明平均 PO 不是异质血管网络中氧合作用的充分指标。最终，这种数学模型的发展将有助于阐明与血流和代谢有关的重要因素，这些因素导致青光眼的视力丧失特征。
