Eye-specific 3D modeling of factors influencing oxygen concentration in the lamina cribrosa

Abstract

Our goal was to identify the factors with the strongest influence on the minimum lamina cribrosa (LC) oxygen concentration as potentially indicative of conditions increasing hypoxia risk. Because direct measurement of LC hemodynamics and oxygenation is not yet possible, we developed 3D eye-specific LC vasculature models. The vasculature of a normal monkey eye was perfusion-labeled post-mortem. Serial cryosections through the optic nerve head were imaged using fluorescence and polarized light microscopy to visualize the vasculature and collagen, respectively. The vasculature within a 450 μm-thick region containing the LC - identified from the collagen, was segmented, skeletonized, and meshed for simulations. Using Monte Carlo sampling, 200 vascular network models were generated with varying vessel diameter, neural tissue oxygen consumption rate, inflow hematocrit, and blood pressures (arteriole, venule, anterior boundary, and posterior boundary). Factors were varied over ranges of baseline ±20% with uniform probability. For each model we first obtained the blood flow, and from this the neural tissue oxygen concentration. ANOVA was used to identify the factors with the strongest influence on the minimum (10th percentile) oxygen concentration in the LC. The three most influential factors were, in ranked order, vessel diameter, neural tissue oxygen consumption rate, and arteriole pressure. There was a strong interaction between vessel diameter and arteriole pressure whereby the impact of one factor was larger when the other factor was small. Our results show that, for the eye analyzed, conditions that reduce vessel diameter, such as vessel compression due to elevated intraocular pressure or gaze-induced tissue deformation, may particularly contribute to decreased LC oxygen concentration. More eyes must be analyzed before generalizing.

Keywords: Blood flow; Glaucoma; Hemodynamics; Lamina cribrosa; Oxygen; Vasculature.

Figure 1.

General approach for the reconstruction of a 3D eye-specific lamina cribrosa (LC) vascular network. (a) Vessels in the eye were labeled with a fluorescent dye, while IOP was set to 5 mmHg using a saline fluid column. (b) The ONH was sectioned coronally. Each section was imaged using fluorescence (FM) and polarized light microscopies (PLM) to visualize the vessels and collagen, respectively. Colors in the PLM image represent collagen fiber orientations. The LC region was defined based on the presence of collagen beams. (c) The vessel segmentations or “labels” were combined to create a 3D map of the vasculature. The vasculature covered a region larger than the LC. Vessels in the LC region were identified based on the LC segmentations.

Figure 2.

(a) A diagram of the ONH adapted from (Hayreh, 1969). Our model represents the vessels within the scleral canal, delimited at the periphery by the connective tissues of the sclera and/or pia mater, and at the center by the central retinal artery and vein. The anterior and posterior limits of the model are flat planes perpendicular to the central retinal artery and vein, located to ensure that the region modeled completely enclosed the LC. The black dashed lines represent the model boundaries. (b) Assignment of boundary blood pressure conditions. Four blood pressure conditions were assigned at the peripheral, central, anterior, and posterior boundaries of the model. The model periphery was assigned an arteriole pressure to represent blood flow from the circle of Zinn-Haller. The center was assigned a venule pressure to simulate blood drainage through the central retinal vein. The anterior and posterior boundaries were assigned blood pressures related to IOP and CSFP, respectively. See the main text for the rationale and details on how these pressures were assigned.

Figure 3.

Lamina cribrosa vascular network colored by blood flow (left column) and contour plots of oxygen concentration in the neural tissues (right column). The plots are for a model with baseline values of all input parameters. Notice that there are similarities in the regional distribution of high/low blood flow and oxygen concentration, but there are also regions of disagreement.

Figure 4.

Distributions of (a) blood pressure and (b) flow velocity through the baseline model. The model was split into three layers: anterior (100 μm thick), middle (300 μm thick), and posterior (100 μm thick). The pressure was highest at the periphery, decreasing gradually towards the center, indicating that the blood flow was driven from the periphery to the center. This is further evidenced by the distributions of flow velocity.

Figure 5.

A still of the animation showing blood flow converging and draining via the central retinal vein opening (Video 2). Colors indicate blood flow rate. We used spheres to illustrate the movement of red blood cells. The density of spheres corresponds to hematocrit. The white squares indicate the points of outflow.

Figure 6.

Scatter plots showing the factor influences on the minimum oxygen concentration in the lamina cribrosa. Each dot is one model. There was a clear association with the vessel diameter, O₂ consumption rate, and arteriole pressure, but the association with the other factors was not obvious.

Figure 7.

Bar chart showing the ranking of factors and interactions with respect to their influences on the minimum oxygen concentration in the lamina cribrosa, as determined by ANOVA. The vessel diameter, neural tissue oxygen consumption rate, and arteriole pressure were the three most influential factors, followed by the interactions between vessel diameter and arteriole pressure.

Figure 8.

Effects of the interactions between vessel diameter and arteriole pressure on the minimum oxygen concentration in the lamina cribrosa. Nonparallel lines indicate that the effects of one factor depends on the other factor (i.e., an interaction). Line endpoints are the mean responses for a given value of factors, whereas error bars depict the 95% least significant confidence interval. (Anderson and Whitcomb, 2017) Response range was chosen so as to make the interactions clearest. The interaction plot shows that the influence of the vessel diameter was more substantial when the arteriole pressure was low (d₁ > d₂). Similarly, the effect of arteriole pressure was more substantial when the vessel diameter was small (d₃ > d₄).

Figure 9.

The distributions of (a) blood flow and (b) oxygen concentration of nine models with various combinations of vessel diameter and oxygen consumption rate. Shown are results in a 300 μm-thick slab through the middle of the region modeled. Oxygen concentration was higher at the periphery than at the center. Both vessel diameter and oxygen consumption rate affected oxygen concentration.