Optimal control with MANF treatment of photoreceptor degeneration

Camacho, E.; Lenhart, Suzanne; Melara, Luis A.; Villalobos, María Cristina; Wirkus, Stephen

doi:10.1093/imammb/dqz003

Cited by 9 publications

(10 citation statements)

References 42 publications

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“…Camacho et al . have developed a series of (non-spatial) dynamical systems ordinary differential equation models to describe the role of RdCVF in health and RP (Colón Vélez et al, 2003; Camacho et al, 2010; Camacho and Wirkus, 2013; Camacho et al, 2014, Camacho 2016a,b,c, 2019, 2020, 2021; Wifvat et al, 2021). In Roberts (2021), we developed the first partial differential equation (PDE) models of the TF mechanism in RP, predicting the spatial spread of retinal degeneration (see also Roberts et al, 2017, 2018, for our work on the oxygen toxicity mechanism, together with Roberts et al, 2016b; Burns et al, 2002, for a mathematical model of the toxic substance mechanism; and Roberts et al, 2016a, for a review on mathematical models of the retina).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inverse Problem Reveals Conditions for Characteristic Retinal Degeneration Patterns in Retinitis Pigmentosa under the Trophic Factor Hypothesis

Roberts

2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Inverse Problem Reveals Conditions for Characteristic Retinal Degeneration Patterns in Retinitis Pigmentosa under the Trophic Factor Hypothesis

Roberts

2021

Preprint

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“…In this regard, we propose some control policies and implement them in the mathematical model to reduce or minimize the number of infected people. The design of control policies and solving the proposed control problems allow us to decide the optimal control strategies considering limited resources and economic costs 29‐34 . To design the strategies against diseases, it is appropriate to solve optimal control problems 35‐37 .…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling to design public health policies for Chikungunya epidemic using optimal control

González-Parra

Díaz‐Rodríguez

Arenas

2020

Optim Control Appl Methods

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Summary In this article, we study the control of a Chikungunya epidemic model solving several optimal control problems. We implement three strategies to control the spread of the Chikungunya virus in the human and vector population. The first control strategy is an educational campaign promoting the use bednets, avoiding water stagnation, wearing long sleeved shirts, among others. The second is treatment of the infected individual, and the third relies on spraying insecticide. The optimal control problem that we solve has a mathematical model for Chikungunya representing the control system. We rely on Pontryagin's maximum principle to solve the optimal control problem. For the mathematical model of the Chikungunya epidemic, we use the incidence data from Colombia corresponding to the year 2015. An additional aim of this study is to investigate which control measures are more efficient and suggest policies to health institutions to reduce the number of infected individuals. Although the mathematical model fits real data of the Colombian case, the policies and insights presented in this article might be extrapolated to different countries.

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“…The models developed and analysed in this paper are the first trophic factor hypothesis models to be spatially-resolved, or to account for photoreceptor distribution. As such, these are the first trophic factor models capable of answering the three key questions posed above (though we note that Camacho et al's work considers spatially-uniform analogues of questions (i) and (ii), see especially, Camacho et al, 2014Camacho et al, , 2020.…”

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confidence: 96%

“…Lastly, Camacho et al have produced a series of ordinary differential equation models of the trophic factor hypothesis, which focus on the biochemical details, rather than the spatial spread, of retinal degeneration (Colón Vélez et al, 2003;Camacho et al, 2010;Camacho and Wirkus, 2013;Camacho et al, 2014Camacho et al, , 2016aCamacho et al, ,b,c, 2019Camacho et al, , 2020Camacho et al, , 2021Wifvat et al, 2021). Their models replicate the rhythmic shedding and renewal of photoreceptor OSs; predict possible disease stages through which a retina may pass towards total blindness, recapitulating known RP phenotypes; identify key reactions and processes; and predict optimum treatment strategies.…”

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confidence: 99%

Mathematical models of retinitis pigmentosa: The trophic factor hypothesis

Roberts

2022

Journal of Theoretical Biology

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Optimal control with MANF treatment of photoreceptor degeneration

Cited by 9 publications

References 42 publications

Inverse Problem Reveals Conditions for Characteristic Retinal Degeneration Patterns in Retinitis Pigmentosa under the Trophic Factor Hypothesis

Inverse Problem Reveals Conditions for Characteristic Retinal Degeneration Patterns in Retinitis Pigmentosa under the Trophic Factor Hypothesis

Mathematical modeling to design public health policies for Chikungunya epidemic using optimal control

Mathematical models of retinitis pigmentosa: The trophic factor hypothesis

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