People afflicted with diseases such as retinitis pigmentosa and age-related macular degeneration experience a decline in vision due to photoreceptor degeneration, which is currently unstoppable and irreversible. Currently there is no cure for diseases linked to photoreceptor degeneration. Recent experimental work showed that mesencephalic astrocyte-derived neurotrophic factor (MANF) can reduce neuron death and, in particular, photoreceptor death by reducing the number of cells that undergo apoptosis. In this work, we build on an existing system of ordinary differential equations that represent photoreceptor interactions and incorporate MANF treatment for three experimental mouse models having undergone varying degrees of photoreceptor degeneration. Using MANF treatment levels as controls, we investigate optimal control results in the three mouse models. In addition, our numerical solutions match the experimentally observed surviving percentage of photoreceptors and our uncertainty and sensitivity analysis identifies significant parameters in the math model both with and without MANF treatment.
Erika T Camacho, Suzanne Lenhart, Luis A Melara, M Cristina Villalobos, Stephen Wirkus, Optimal control with MANF treatment of photoreceptor degeneration, Mathematical Medicine and Biology: A Journal of the IMA, Volume 37, Issue 1, March 2020, Pages 1–21, https://doi.org/10.1093/imammb/dqz003
Mathematical Medicine and Biology