Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical Models of Retinal Degeneration
Paul Roberts, Helen Byrne, Alexander Foss, Phil Luthert, Eamonn Gaffney

Last modified: 2014-03-31


The retina is the layer of tissue at the back of the eye that is responsible for the detection of light. It contains numerous cell types, most notably the photoreceptors, which capture light, converting visual information into an electrical signal, which is transmitted to and interpreted by the brain. Photoreceptors can be characterised as either rods or cones. Rods provide achromatic vision under low light conditions, whilst cones provide high-acuity colour vision under well-lit conditions.


The term Retinitis Pigmentosa (RP) refers to a range of genetically mediated retinal diseases that cause the degeneration and subsequent loss of photoreceptors. RP most commonly occurs as a rod-cone dystrophy, with an initial degeneration of rod photoreceptors, followed by the degeneration of cone photoreceptors. Mutant RP genes are expressed in rods but not in cones, explaining why rods degenerate, but raising the question as to why this is followed by cone degeneration.


A number of (complementary) mechanisms have been suggested to explain the secondary loss of cone photoreceptors. Here we investigate the oxygen toxicity hypothesis, which suggests that cone loss is driven by hyperoxia, that is, excess oxygen. Following the loss of rod photoreceptors, the retinal oxygen demand is significantly decreased, resulting in an increase in retinal oxygen concentrations and bringing the remaining cones into a toxic oxygen environment. This results in a positive feedback loop, as high oxygen levels cause cone death, which in turn leads to an increase in oxygen levels. Thus, cone death is self-reinforcing and continues until all cones are lost. At the same time, the loss of photoreceptors leads to the degeneration of the capillaries supplying the retina, thus limiting the effect of hyperoxia. The balance between photoreceptor and capillary loss therefore modulates the rate of disease progression.

We test this hypothesis using mathematical models consisting of coupled systems of PDEs and ODEs for rod and cone density, oxygen concentration and capillary density in 1D and 2D. We use a combination of numerical simulations, steady-state and asymptotic analysis to examine to what degree this mechanism can explain the pattern of cone loss found in vivo and under what conditions the degeneration will spread or halt.


Retina; Retinal Degeneration; Retinitis Pigmentosa; Oxygen Toxicity; PDE; ODE