Effect of ocular curvature and myopia on retinal blood flow: a theoretical study

Abstract

 

Purpose

 

Alterations of ocular curvature are involved in myopia, which is considered a risk factor for glaucoma. The mechanism by which myopia contributes to glaucoma remains unclear. In this study we test the hypothesis that blood flow alterations secondary to myopia contribute to glaucomatous optic neuropathy.

 

Methods

 

We use a mathematical model describing the blood flow in the retina as the flow of a fluid (blood) through a porous medium (retinal tissue). Distributions of blood velocity and pressure are obtained as the solutions of Darcy's equations via finite elements exterior calculus. Four main arterioles/veins are included as sources/sinks for the flow. We compare the pressure distributions obtained for the case of (1) a flat circular surface and (2) a hemispherical surface, when the same level of blood flow is imposed through the tissue.

 

Results

 

Figure 1 shows the pressure distribution in case (1). The pressure distributions looks similar in both cases, but absolute pressure values differ. For a tissue permeability of 4.165 mms^-1kPa^-1 and overall blood flow of 0.68 mm³s^-1, maximal pressures are 5.0 kPa in case (1) and 7.4 kPa in case (2). Thus, the curved case needs higher pressures than the flat case to attain the same blood flow in the tissue. Also, for the same artero/venous pressure difference, area of higher curvature experiences reduced blood flow. Figure 2 shows the pressure difference between case (1) and case (2) projected on the two-dimensional plane. The difference is larger when the distance to the arteries/veins is smaller and is least when the distance to the arteries and veins is equal. The maximal pressure difference reaches 32.4%, namely 2.4 kPa.

 

Conclusions

 

We computed and compared pressure distributions for retinal blood flow on flat and hemispherical surfaces. Ocular curvature has a noticeable effect in pressure distribution, with differences up to 32.4%. Our model suggests that alterations in ocular curvature, such as those occurring in myopic eyes, might contribute to glaucomatous damage by reducing retinal blood flow.

 

 

Pressure distribution in case (2)

 

 

Pressure difference between case (1) and case (2)

 

Keywords: 473 computational modeling • 436 blood supply • 605 myopia