Dziubek Andrea, Guidoboni Giovanna, Harris Alon, Hirani Anil N, Rusjan Edmond, Thistleton William
Department of Mathematics and Sciences, State University of New York Polytechnic Institute, 100 Seymour Rd, Utica, NY, 13502, USA.
Department of Mathematical Sciences, Indiana University Purdue University Indianapolis, Indianapolis, IN, 46202, USA.
Biomech Model Mechanobiol. 2016 Aug;15(4):893-907. doi: 10.1007/s10237-015-0731-8. Epub 2015 Oct 7.
A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method, we use an exterior calculus-based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how retinal hemodynamics is influenced by the ocular shape (sphere, oblate spheroid, prolate spheroid and barrel are compared) and vascular architecture (four vascular arcs and a branching vascular tree are compared). The model predictions show that changes in ocular shape induce non-uniform alterations of blood pressure and velocity in the retina. In particular, we found that (i) the temporal region is affected the least by changes in ocular shape, and (ii) the barrel shape departs the most from the hemispherical reference geometry in terms of associated pressure and velocity distributions in the retinal microvasculature. These results support the clinical hypothesis that alterations in ocular shape, such as those occurring in myopic eyes, might be associated with pathological alterations in retinal hemodynamics.
提出了一种考虑眼球曲率的视网膜血液动力学计算模型。该模型结合了：（i）一个分层达西模型，用于描述视网膜组织中小动脉、毛细血管和小静脉内的血流，其中不同大小的血管包含在多孔介质的不同分层级别中；以及（ii）一个一维网络模型，用于描述通过较大尺寸视网膜小动脉和小静脉的血流。通过以下方式纳入非平面眼球形状：（i）在嵌入三维空间的二维曲面上定义分层达西流模型；以及（ii）将简化的一维网络模型映射到曲面上。该模型使用有限元方法进行数值求解，其中空间域和分层级别分别离散化。对于有限元方法，我们使用基于外微积分的实现方式，这使得对非平面域的处理更加容易。数值解通过适当构建的解析解进行验证。进行数值实验以研究视网膜血液动力学如何受到眼球形状（比较球体、扁球体、长球体和桶状体）和血管结构（比较四条血管弧和一个分支血管树）的影响。模型预测表明，眼球形状的变化会引起视网膜内血压和速度的不均匀改变。特别是，我们发现：（i）颞侧区域受眼球形状变化的影响最小；以及（ii）就视网膜微血管中的相关压力和速度分布而言，桶状体形状与半球形参考几何形状的差异最大。这些结果支持了临床假设，即眼球形状的改变，如近视眼所发生的那些改变，可能与视网膜血液动力学的病理改变有关。
