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Erika T. Camacho, Stephen Wirkus; Modeling Photoreceptor Interactions in the Presence of Retinitis Pigmentosa. Invest. Ophthalmol. Vis. Sci. 2012;53(14):6438.
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Retinitis pigmentosa (RP) is a heterogeneous group of inherited degenerative eye diseases characterized by mutations in the genetic structure of the photoreceptors that lead to the premature death of both rod and cone photoreceptors. The mechanisms and factors involved in the development of the different types of RP and the photoreceptor death are not well understood nor have researchers been able to provide more than a limited number of short-term therapies to slow the progression of the disease. Therefore we propose a mathematical model to better understand the photoreceptor interactions and factors that may be involved in RP.
Using nonlinear ordinary differential equations, we create a mathematical model of photoreceptor interactions in the presence of mutated rods. We examine the long-term behavior of the solutions and investigate their qualitative changes via dynamical systems bifurcation theory. Through analysis and numerical simulation, we investigate various scenarios (by varying certain parameters) and the resulting outcome in the overall system.
The mathematical solutions trace the progression of RP from the early stages to complete blindness in the various subtypes of RP. In particular, the following progressions of RP have been observed and transition in the various stages depends only on the parameter that is varied: rod death precedes cone death, rods and cones die off simultaneously, and cone death precedes rod death. In addition, our model demonstrates that halting the progression of RP depends on maintaining a delicate balance between renewal and shedding necessary to support the processes essential to the vision cycle.
The results from our mechanistic model, which considers only some of the intricate detail of the photoreceptor interactions in the presence of RP, give the counterintuitive result that an increase in the renewal rate or a decrease in the shedding rate of the outer segments leads to an overall decrease in the number of photoreceptors. While counterintuitive, our results suggest a possible link between some of the various hypotheses leading to photoreceptor death in RP and opens the door for new experimental research and theory that may ultimately lead to long-term therapies.
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