Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

Abstract

Thistleton, W. (2016Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational modelReceived: date / Accepted: date Abstract 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

Advancing treatment of retinal disease through in silico trials

“…However, the effects of curvature have been assumed insignificant in most haemodynamics models to date. Dziubek et al modelled this curvature by representing the retina as a thin, curved surface, within which an artificial network of vessels is embedded [83]. The tissue is considered a porous medium-with the embedded vessels acting as pores-with pressure in the tissue described by Darcy's law.…”

“…The model confirms clinical suspicions of a change in retinal haemodynamics due to ocular curvature. Furthermore it highlighted the non-uniform effects on the retina, with the temporal region being less affected by ocular shape [83]. However, in the absence of data, tissue properties were assumed and, though the predicted pressure and velocity fields are within physiological ranges, model validation is limited.…”

“…However, when modelling certain diseases or interventions, incorporating additional details may be required, e.g. details of the haemodynamics in capillaries (see figure 3) and physiology [60,115] or retinal morphology [83,239].…”

Premature Infant Blood Vessel Segmentation of Retinal Images Based on Hybrid Method for the Determination of Tortuosity

“…Morphological close was used in the next step. This operation represents dilation followed by a morphological erosion operation with the same structural element [13,14]. In the second step, binary skeletonization was implemented.…”

Mimetic Spectral Element Method for Anisotropic Diffusion

“…Focussing on generalized diffusion equations we highlight [13, 69, 74, 76-78, 102, 107, 108, 111, 113, 114] for a finitedifference/finite-volume setting, [23,[36][37][38] for polyhedral discretizations, and [19,21,96,106,121] for a finite element/mixed finite element setting. For applications to Darcy flow equations and reservoir modelling see for example [1,6,7,55,73,83,89].…”