Optimal Control in the Treatment of Retinitis Pigmentosa

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

doi:10.1007/s11538-013-9919-1

Cited by 21 publications

(18 citation statements)

References 27 publications

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“…Colón Vélez et al (2003); Camacho et al (2010); Camacho and Wirkus (2013);Camacho et al (2014Camacho et al ( , 2016a and Camacho et al (2016c) have produced a series of spatially-averaged ordinary differential equation (ODE) models examining the rod trophic factor hypothesis. Their work suggests the importance of rod trophic factor to the survival of both rods and cones.…”

Section: Introductionmentioning

confidence: 99%

Mathematical models of retinitis pigmentosa: The oxygen toxicity hypothesis

Roberts

Gaffney

Luthert

et al. 2017

Journal of Theoretical Biology

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The group of genetically mediated diseases, known collectively as retinitis pigmentosa (RP), cause retinal degeneration and, hence, loss of vision. The most common inherited retinal degeneration, RP is currently untreatable. The retina detects light using cells known as photoreceptors, of which there are two types: rods and cones. In RP, genetic mutations cause patches of photoreceptors to degenerate and typically directly affect either rods or cones, but not both. During disease progression, degenerate patches spread and the unaffected photoreceptor type also begins to degenerate. The cause underlying these phenomena is currently unknown.The oxygen toxicity hypothesis proposes that secondary photoreceptor loss is due to hyperoxia (toxically high oxygen levels), which results from the decrease in oxygen uptake following the initial loss of photoreceptors. In this paper, we construct mathematical models, formulated as 1D systems of partial differential equations, to investigate this hypothesis. Using a combination of numerical simulations, asymptotic analysis and travelling wave analysis, we find that degeneration may spread due to hyperoxia, and generate spatiotemporal patterns of degeneration similar to those seen in vivo. We determine the conditions under which a degenerate patch will spread and show that the wave speed of degeneration is a monotone decreasing function of the local photoreceptor density. Lastly, the effects of treatment with antioxidants and trophic factors, and of capillary loss, upon the dynamics of photoreceptor loss and recovery are considered.

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Section: Introductionmentioning

confidence: 99%

Mathematical models of retinitis pigmentosa: The oxygen toxicity hypothesis

Roberts

Gaffney

Luthert

et al. 2017

Journal of Theoretical Biology

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“…Experimental studies in mouse models have shown that cone death often commenced after the end of the major phase of rod death (occurring many months after rod degeneration) challenging the hypothesis of the liberation of a toxic factor [23-24]. Finally, the model incorporates the role of the RdCVF as a direct connection from rods to cones [3,20,45]. RdCVF is produced by both types of rods, R n and R s , and its presence and release by the rods does not hinder or benefit the functionality or viability of rods [46-47].…”

Section: Methodsmentioning

confidence: 99%

“…A second theory that gathered a lot of popularity comes from the idea that rods produce some kind of signal/protein that is essential for keeping cones alive. Consequently, the disappearance of rods would deprive the cones of this signal/protein and trigger their degeneration [3,18-20]. This theory is supported by various experiments on mice and rats and led to the discovery of the Rod-derived Cone Viability Factor (RdCVF).…”

Section: Introductionmentioning

confidence: 99%

“…This theory is supported by various experiments on mice and rats and led to the discovery of the Rod-derived Cone Viability Factor (RdCVF). Other known growth and neuroprotective factors such as PEDF, bFGF, and CNTF that are normally produced in the eye or upon injury, have also been tested by intravitreal injections (with various degrees of successes) for their ability to delay cone death [20-22]. Finally, a third theory proposes that the massive loss of rods, which outnumber cones at a ratio >20:1, leads to a disruption of the interactions between the photoreceptors and retinal-pigment epithelium (RPE) preventing cones from receiving enough nutrients and glucose needed to function properly [23-24].…”

Section: Introductionmentioning

confidence: 99%

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Quantifying the metabolic contribution to photoreceptor death in retinitis pigmentosa via a mathematical model

Camacho

Punzo

Wirkus

2016

Journal of Theoretical Biology

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Retinitis Pigmentosa (RP) is a family of inherited retinal degenerative diseases that leads to blindness. In many cases the disease-causing allele encodes for a gene exclusively expressed in the night active rod photoreceptors. However, because rod death always leads to cone death affected individuals eventually lose their sight. Many theories have been proposed to explain the secondary loss of cones in RP; however, most fail to fully explain the different pathological transition stages seen in humans. Incorporating experimental data of rod and cone death kinetics from two mouse models of RP, we use a mathematical model to investigate the interplay and role of energy consumption and uptake of the photoreceptors as well as nutrient availability supplied through the retinal pigment epithelium (RPE) throughout the progression of RP. Our data driven mathematical model predicts that the system requires a total reduction of approximately 27% to 31% in nutrients available to result in the complete demise of all cones. Simulations utilizing retinal degeneration 1 (rd1) mouse cell count data in which cone death was delayed by altering cell metabolism in cones show that preventing a 1-2% decrease in nutrients available can permanently halt cone death even when 90% have already died. Our results also indicate that the ratio of energy consumption to uptake of cones, Dc, is mainly disrupted during the death wave of the rods with negligible changes thereafter and that the subsequent nutrient decrease is mainly responsible for the demise of the cones. The change in this ratio Dc highlights the compensation that the cones must undergo during rod death to meet the high metabolic demands of the entire photoreceptor population. Global sensitivity analysis confirms the results and suggests areas of focus for halting RP, even at later stages of the disease, through feasible therapeutic interventions.

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“…Thus, the sufficient conditions for the existence of optimal control are satisfied (see Theorem 4.1 in [Fleming and Rishel, 1976]). The similar exercises of proving the existence of optimal control based on Theorem 4.1 in [Fleming and Rishel, 1976] are referred to [de Pillis et al, 2008], [Jang et al, 2011], [Camacho et al, 2014], and [Blayneh et al, 2009].…”

Section: Preliminariesmentioning

confidence: 99%

Optimizing the Timing and Composition of Therapeutic Phage Cocktails: A Control-theoretic Approach

Leung

Wardi

et al. 2019

Preprint

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Viruses that infect bacteria, i.e., bacteriophage or 'phage', are increasingly considered as treatment options for the control and clearance of bacterial infections, particularly as compassionate use therapy for multi-drug resistant infections. In practice, clinical use of phage often involves the application of multiple therapeutic phage, either together or sequentially. However, the selection and timing of therapeutic phage delivery remains largely ad hoc. In this study, we evaluate principles underlying why careful application of multiple phage (i.e., a 'cocktail') might lead to therapeutic success in contrast to the failure of single-strain phage therapy to control an infection. First, we use a nonlinear dynamics model of within-host interactions to show that a combination of fast intra-host phage decay, evolution of phage resistance amongst bacteria, and/or compromised immune response might limit the effectiveness of single-strain phage therapy. To resolve these problems, we combine dynamical modeling of phage, bacteria, and host immune cell populations with control-theoretic principles (via optimal control theory) to devise evolutionarily robust phage cocktails and delivery schedules to control the bacterial populations. Our numerical results suggest that optimal administration of single-strain phage therapy may be sufficient for curative outcomes in immunocompetent patients, but may fail in immunodeficient hosts due to phage resistance. We show that optimized treatment with a two-phage cocktail that includes a counter-resistant phage can restore therapeutic efficacy in immunodeficient hosts.

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Optimal Control in the Treatment of Retinitis Pigmentosa

Cited by 21 publications

References 27 publications

Mathematical models of retinitis pigmentosa: The oxygen toxicity hypothesis

Mathematical models of retinitis pigmentosa: The oxygen toxicity hypothesis

Quantifying the metabolic contribution to photoreceptor death in retinitis pigmentosa via a mathematical model

Optimizing the Timing and Composition of Therapeutic Phage Cocktails: A Control-theoretic Approach

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