Inverse problem reveals conditions for characteristic retinal degeneration patterns in retinitis pigmentosa under the trophic factor hypothesis

Retinitis pigmentosa (RP) is the most common inherited retinal dystrophy with a prevalence of about 1 in 4000, affecting approximately 1.5 million people worldwide. Patients with RP experience progressive visual field loss as the retina degenerates, destroying light-sensitive photoreceptor cells (rods and cones), with rods affected earlier and more severely than cones. Spatio-temporal patterns of retinal degeneration in human RP have been well characterised; however, the mechanism(s) giving rise to these patterns have not been conclusively determined. One such mechanism, which has received a wealth of experimental support, is described by the trophic factor hypothesis. This hypothesis suggests that rods produce a trophic factor necessary for cone survival; the loss of rods depletes this factor, leading to cone degeneration. In this paper we formulate a partial differential equation mathematical model of RP in one spatial dimension, spanning the region between the retinal centre (fovea) and the retinal edge (ora serrata). Using this model we derive and solve an inverse problem, revealing for the first time experimentally testable conditions under which the trophic factor mechanism will qualitatively recapitulate the spatio-temporal patterns or retinal regeneration observed in human RP.