BB19: Mathematical models of retinitis pigmentosa

Background

The group of hereditary retinal diseases known as retinitis pigmentosa (RP) cause premature photoreceptor death. Degeneration is typically initiated at the peripheral retina and progresses towards the centre, leading to tunnel vision and eventual blindness.  At least 1 in 4,000 people suffer from RP, with over one million individuals affected worldwide. While several treatments are under development, including vitamin therapy and retinal implantation, there are currently no clinically available treatments that can halt RP or reverse its effects.

Techniques and Challenges

This project will involve the development and analysis of new mathematical models of the human retina in both healthy and diseased states. The models will be formulated as mixed systems of ordinary and partial differential equations (PDEs). They will be studied using a combination of analytical and numerical techniques (e.g. asymptotic analysis, bifurcation theory and finite element methods).

Results

So far, we have developed a one-dimensional PDE model in which disease progression is driven by oxygen toxicity. The model exhibits travelling wave solutions that correspond to either the loss, or recovery, of all photoreceptors.

The Future

We will extend this model to higher dimensions before considering alternative models and mechanisms. By using mathematical models to test current hypotheses about the evolution of RP, we aim to achieve a better understanding of the mechanisms that drive its evolution and to suggest more effective strategies for its treatment.

References

Hartong D.T., Berson E.L., Dryja T.P.: Retinitis pigmentosa, The Lancet, 368(9549): 1795 – 1809, 2006

Hamel C.: Retinitis pigmentosa, Orphanet J Rare Dis, 1:40, 2006

Images courtesy of Prof. Phil Luthert, UCL