Spatially-dependent model for rods and cones in the retina.

We develop a mathematical model for photoreceptors in the retina. We focus on rod and cone outer segment dynamics and interactions with a nutrient source associated with the retinal pigment epithelium cells. Rod and cone densities (number per unit area of retinal surface) are known to have significant spatial dependence in the retina with cones located primarily near the fovea and the rods located primarily away from the fovea. Our model accounts for this spatial dependence of the rod and cone photoreceptor density as well as for the possibility of nutrient diffusion. We present equilibrium and dynamic solutions, discuss their relation to existing models, and estimate model parameters through comparisons with available experimental measurements of both spatial and temporal photoreceptor characteristics. Our model compares well with existing data on spatially-dependent regrowth of photoreceptor outer segments in the macular region of Rhesus Monkeys. Our predictions are also consistent with existing data on the spatial dependence of photoreceptor outer segment length near the fovea in healthy human subjects. We focus primarily on the healthy eye but our model could be the basis for future efforts designed to explore various retinal pathologies, eye-related injuries, and treatments of these conditions.

A Mathematical Analysis of Aerobic Glycolysis Triggered by Glucose Uptake in Cones.

Patients affected by retinitis pigmentosa, an inherited retinal disease, experience a decline in vision due to photoreceptor degeneration leading to irreversible blindness. Rod-derived cone viability factor (RdCVF) is the most promising mutation-independent treatment today. To identify pathologic processes leading to secondary cone photoreceptor dysfunction triggering central vision loss of these patients, we model the stimulation by RdCVF of glucose uptake in cones and glucose metabolism by aerobic glycolysis. We develop a nonlinear system of enzymatic functions and differential equations to mathematically model molecular and cellular interactions in a cone. We use uncertainty and sensitivity analysis to identify processes that have the largest effect on the system and their timeframes. We consider the case of a healthy cone, a cone with low levels of glucose, and a cone with low and no RdCVF. The three key processes identified are metabolism of fructose-1,6-bisphosphate, production of glycerol-3-phosphate and competition that rods exert on cone resources. The first two processes are proportional to the partition of the carbon flux between glycolysis and the pentose phosphate pathway or the Kennedy pathway, respectively. The last process is the rods' competition for glucose, which may explain why rods also provide the RdCVF signal to compensate.

Simulating long-term human weight-loss dynamics in response to calorie restriction.

Background: Mathematical models have been developed to predict body weight (BW) and composition changes in response to lifestyle interventions, but these models have not been adequately validated over the long term. Objective: We compared mathematical models of human BW dynamics underlying 2 popular web-based weight-loss prediction tools, the National Institutes of Health Body Weight Planner (NIH BWP) and the Pennington Biomedical Research Center Weight Loss Predictor (PBRC WLP), with data from the 2-year Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy (CALERIE) study. Design: Mathematical models were initialized using baseline CALERIE data, and changes in body weight (ΔBW), fat mass (ΔFM), and energy expenditure (ΔEE) were simulated in response to time-varying changes in energy intake (ΔEI) objectively measured using the intake-balance method. No model parameters were adjusted from their previously published values. Results: The PBRC WLP model simulated an exaggerated early decrease in EE in response to calorie restriction, resulting in substantial underestimation of the observed mean (95% CI) BW losses by 3.8 (3.5, 4.2) kg. The NIH WLP simulations were much closer to the data, with an overall mean ΔBW bias of -0.47 (-0.92, -0.015) kg. Linearized model analysis revealed that the main reason for the PBRC WLP model bias was a parameter value defining how spontaneous physical activity expenditure decreased with caloric restriction. Both models exhibited substantial variability in their ability to simulate individual results in response to calorie restriction. Monte Carlo simulations demonstrated that ΔEI measurement uncertainties were a major contributor to the individual variability in NIH BWP model simulations. Conclusions: The NIH BWP outperformed the PBRC WLP and accurately simulated average weight-loss and energy balance dynamics in response to long-term calorie restriction. However, the substantial variability in the NIH BWP model predictions at the individual level suggests cautious interpretation of individual-level simulations. This trial was registered at clinicaltrials.gov as NCT00427193.