A Mathematical Model of Aqueous Humor Production and Composition.

Purpose: We develop a mathematical model that predicts aqueous humor (AH) production rate by the ciliary processes and aqueous composition in the posterior chamber (PC), with the aim of estimating how the aqueous production rate depends on the controlling parameters and how it can be manipulated. Methods: We propose a compartmental mathematical model that considers the stromal region, ciliary epithelium, and PC. All domains contain an aqueous solution with different chemical species. We impose the concentration of all species on the stromal side and exploit the various ion channels present on the cell membrane to compute the water flux produced by osmosis, the solute concentrations in the AH and the transepithelial potential difference. Results: With a feasible set of parameters, the model predictions of water flux from the stroma to the PC and of the solute concentrations in the AH are in good agreement with measurements. Key parameters which impact the aqueous production rate are identified. A relevant role is predicted to be played by cell membrane permeability to \(\text{K}^+\) and \(\text{Cl}^-\), by the level of transport due to the Na+-H+ exchanger and to the co-transporter of Na+/K+/2Cl-; and by carbonic anhydrase. Conclusions: The mathematical model predicts the formation and composition of AH, based on the structure of the ciliary epithelium. The model provides insight into the physical processes underlying the functioning of drugs that are adopted to regulate the aqueous production. It also suggests ion channels and cell membrane properties that may be targeted to manipulate the aqueous production rate.

Predicting quality of life in AMD patients-insights on the new NICE classification and on a bolt-on vision dimension for the EQ-5D.

BACKGROUND/AIMS: Health-related quality of life (HRQoL) in age-related macular degeneration (AMD) is difficult to estimate as most generic tools underestimate vision. Our aim was to measure the effect of AMD on generic and visual quality of life and how it relates to handicap. We also aimed to validate the NG82 NICE AMD classification. Finally, we studied if a bolt-on visual domain increased the EQ-5D sensitivity to AMD. PATIENTS AND METHODS: Ninety-six patients with AMD participated in this observational cross-sectional study. Visual (VF-14) and generic questionnaires (EQ-5D) with VIS, and the London handicap scale (LHS) was used to quantify HRQoL and handicap. ANOVA and regression analysis were used to identify significant associations. RESULTS: Visual dysfunction in AMD has a significant effect in VF-14 (P < 0.001), LHS (p < 0.001), and EQ-5D (p = 0.015). The EQ-5D was less sensitive than the VF-14 and LHS and was not significantly correlated with the VIS bolt-on domain (p = 0.608). On the other hand, VIS was significantly associated with visual acuity (p < 0.001), AMD diagnosis (p = 0.005), VF-14 (p < 0.001), and LHS (p < 0.001). The new AMD classification was a good predictor of visual HRQoL and had an excellent association with visual acuity in the best eye. CONCLUSION: This article shows that visual impairment is associated with lower HRQoL and with an increased handicap. It also suggests that a visual dimension may increase the EQ-5D sensitivity in AMD. There was a relationship between visual impairment and handicap with the items of the new NICE AMD classification, which supports its use.

Fluid and solute transport across the retinal pigment epithelium: a theoretical model.

The retina is composed of two main layers-the neuroretina and the retinal pigment epithelium (RPE)-that are separated by a potential gap termed the sub-retinal space (SRS). Accumulation of fluid in the SRS may result in a retinal detachment. A key function of the RPE is to prevent fluid accumulation in the SRS by actively pumping fluid from this space to the choroid. We have developed a mathematical model of this process that incorporates the transport of seven chemical species: Na+, K+, Cl-, HCO3-, H+, CO2 and H2CO3. This allows us to estimate solute and water fluxes and to understand the role of the different membrane ion channels. We have performed a global sensitivity analysis using the extended Fourier amplitude sensitivity test to investigate the relative importance of parameters in generating the model outputs. The model predicts that flow across the RPE is driven by an osmotic gradient in the cleft gap between adjacent cells. Moreover, the model estimates how water flux is modified in response to inhibition of membrane ion channels and carbonic anhydrase (CA). It provides a possible explanation for how CA inhibitors, which are used clinically to prevent fluid accumulation in the SRS, may be acting.

Clinical investigation plan for the use of interactive binocular treatment (I-BiT) for the management of anisometropic, strabismic and mixed amblyopia in children aged 3.5-12 years: a randomised controlled trial.

BACKGROUND: Amblyopia (lazy eye) affects the vision of approximately 2% of all children. Traditional treatment consists of wearing a patch over their 'good' eye for a number of hours daily, over several months. This treatment is unpopular and compliance is often low. Therefore, results can be poor. I-BiT is a system, based on stereo technology using shutter glasses, designed to treat amblyopia using dichoptic stimulation. This trial uses a redesigned system for home use and includes eye-tracking capability. METHODS/DESIGN: This is a randomised controlled trial involving three groups of 40 patients each, aged between 3.5 and 12 years, with a diagnosis of (1) anisometropic amblyopia, (2) mixed or strabismic amblyopia prior to strabismic surgery and (3) mixed or strabismic amblyopia who have just undergone strabismus surgery. They will be randomised in a 1:1 ratio between I-BiT and control and will receive treatment, at home over a 6-week period. Their visual acuity will be assessed independently at baseline, mid-treatment (week 3), at the end of treatment (week 6) and, for those receiving the active I-BiT treatment, 4 weeks after completing treatment (week 10). The primary endpoint will be the change in visual acuity from baseline to the end of treatment. Secondary endpoints will be additional visual acuity measures, patient acceptability, compliance and the incidence of adverse events. DISCUSSION: This is a randomised controlled trial using the redesigned I-BiT™ system to determine if this is a feasible treatment strategy for the management of anisometropic, strabismic and mixed amblyopia. TRIAL REGISTRATION: ISRCTN Number/Clinical trials.gov, ID: NCT02810847 . Registered on 23 June 2016.

A theory-driven qualitative study exploring issues relating to adherence to topical glaucoma medications.

PURPOSE: Investigating patients' perceptions of their illness can provide important insights into the experience and management of the illness and associated treatment, and enhance understanding of variations in adherence to prescribed medication. The Common-Sense Model of Self-Regulation (CSM) provides a theoretical framework for the study of illness cognitions, health behavior, and adherence to health recommendations. The aim of this study was to use the CSM to investigate the experience of glaucoma and its treatment from the patients' perspective, and to apply these insights to classify and clarify issues related to nonadherence with treatment. PATIENTS AND METHODS: A qualitative investigation using semi-structured interviews took place in two outpatient glaucoma clinics. Thirty-three patients with primary open-angle glaucoma using hypotensive eye drops participated in the study. Deductive content analysis was used to analyze the interview data. RESULTS: Issues relating to nonadherence with hypotensive eye drops and patients' experience with their glaucoma and treatment were identified. Treatment schedule and patient factors were classified as common barriers to adherence. Further themes include experienced symptoms of glaucoma, illness coherence, and the emotional and practical consequences of the illness. CONCLUSION: Findings provide important insights into the emotional and practical outcomes of glaucoma for patients, perceived symptoms of the illness, and insights into patient memory and cognition. These findings provide supporting evidence for the importance of conducting theoretically driven qualitative investigations of patients' experience with glaucoma and their treatment, and provide suggestions on key issues that need to be addressed in future multidimensional interventions aimed at improving adherence and patient quality of life.

Osmotic and electroosmotic fluid transport across the retinal pigment epithelium: A mathematical model.

The retinal pigment epithelium (RPE) is the outermost cell layer of the retina. It has several important physiological functions, among which is removal of excess fluid from the sub-retinal space by pumping it isotonically towards the choroid. Failure of this pumping leads to fluid accumulation, which is closely associated with several pathological conditions, such as age-related macular degeneration, macular oedema and retinal detachment. In the present work we study mechanisms responsible for fluid transport across the RPE with the aim of understanding how fluid accumulation can be prevented. We focus on two possible mechanisms, osmosis and electroosmosis, and develop a spatially resolved mathematical model that couples fluid and ion transport across the epithelium, accounting for the presence of Na+,K+ and Cl- ions. Our model predicts spatial variability of ion concentrations and the electrical potential along the cleft gap between two adjacent cells, which osmotically drives the flow across the lateral membranes. This flow is directed from the sub-retinal space to the choroid and has a magnitude close to measured values. Electroosmosis is subdominant by three orders of magnitude to osmosis and has an opposite direction, suggesting that local osmosis is the main driving mechanism for water transport across the RPE.

Predictive Mathematical Models for the Spread and Treatment of Hyperoxia-induced Photoreceptor Degeneration in Retinitis Pigmentosa.

Purpose: To determine whether the oxygen toxicity hypothesis can explain the distinctive spatio-temporal patterns of retinal degeneration associated with human retinitis pigmentosa (RP) and to predict the effects of antioxidant and trophic factor treatments under this hypothesis. Methods: Three mathematical models were derived to describe the evolution of the retinal oxygen concentration and photoreceptor density over time. The first model considers only hyperoxia-induced degeneration, while the second and third models include mutation-induced rod and cone loss respectively. The models were formulated as systems of partial differential equations, defined on a two-dimensional domain spanning the region between the foveal center and the ora serrata, and were solved numerically using the finite element method. Results: The mathematical models recapitulate patterns of retinal degeneration which involve preferential loss of photoreceptors in the parafoveal/perifoveal and far-peripheral retina, while those which involve a preferential loss of midperipheral photoreceptors cannot be reproduced. Treatment with antioxidants or trophic factors is predicted to delay, halt, or partially reverse retinal degeneration, depending upon the strength and timing of treatment and disease severity. Conclusions: The model simulations indicate that while the oxygen toxicity hypothesis is sufficient to explain some of the patterns of retinal degeneration observed in human RP, additional mechanisms are necessary to explain the full range of behaviors. The models further suggest that antioxidant and trophic factor treatments have the potential to reduce hyperoxia-induced disease severity and that, where possible, these treatments should be targeted at retinal regions with low photoreceptor density to maximize their efficacy.

Mathematical models of retinitis pigmentosa: The oxygen toxicity hypothesis.

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 spatio-temporal 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.

Use of video games for the treatment of amblyopia.

PURPOSE OF REVIEW: To review the literature up to recent for the use of videos, videogames and dichoptic stimulation as a treatment for amblyopia. RECENT FINDINGS: There have been three strategies explored. The first is to use videos and videogames monocularly with the normal eye covered. The second is dichoptic stimulation with a common background presented to both eyes and an enriched foreground to the amblyopic eye. The third are games specifically designed to generate stereopsis. Most work has focused on the second of these approaches but both of the first two approaches seem to give a similar improvement of 0.1-0.2 logMAR. One large randomized control trial (RCT) has published showing that dichoptic stimulation is not inferior to patching but no evidence that it was superior. It also showed that video games have their own compliance problems and a second smaller RCT did suggest that videogames, with a game designed by a gaming company, was superior. Most of the work done has had methodological issues and should be considered exploratory rather than definitive. SUMMARY: Dichoptic stimulation is a viable treatment option for the treatment of amblyopia. The first trial results have shown results that are not superior to patching but they are not without methodological issues. There is sufficient encouragement to justify further research in this area.

Mathematical and computational models of the retina in health, development and disease.

The retina confers upon us the gift of vision, enabling us to perceive the world in a manner unparalleled by any other tissue. Experimental and clinical studies have provided great insight into the physiology and biochemistry of the retina; however, there are questions which cannot be answered using these methods alone. Mathematical and computational techniques can provide complementary insight into this inherently complex and nonlinear system. They allow us to characterise and predict the behaviour of the retina, as well as to test hypotheses which are experimentally intractable. In this review, we survey some of the key theoretical models of the retina in the healthy, developmental and diseased states. The main insights derived from each of these modelling studies are highlighted, as are model predictions which have yet to be tested, and data which need to be gathered to inform future modelling work. Possible directions for future research are also discussed. Whilst the present modelling studies have achieved great success in unravelling the workings of the retina, they have yet to achieve their full potential. For this to happen, greater involvement with the modelling community is required, and stronger collaborations forged between experimentalists, clinicians and theoreticians. It is hoped that, in addition to bringing the fruits of current modelling studies to the attention of the ophthalmological community, this review will encourage many such future collaborations.

Changes in intraocular pressure in study and fellow eyes in the IVAN trial.

PURPOSE: To describe changes in intraocular pressure (IOP) in the 'alternative treatments to Inhibit VEGF in Age-related choroidal Neovascularisation (IVAN)' trial (registered as ISRCTN92166560). DESIGN: Randomised controlled clinical trial with factorial design. PARTICIPANTS: Patients (n=610) with treatment naïve neovascular age-related macular degeneration were enrolled and randomly assigned to receive either ranibizumab or bevacizumab and to two regimens, namely monthly (continuous) or as needed (discontinuous) treatment. METHODS: At monthly visits, IOP was measured preinjection in both eyes, and postinjection in the study eye. OUTCOME MEASURES: The effects of 10 prespecified covariates on preinjection IOP, change in IOP (postinjection minus preinjection) and the difference in preinjection IOP between the two eyes were examined. RESULTS: For every month in trial, there was a statistically significant rise in both the preinjection IOP and the change in IOP postinjection during the time in the trial (estimate 0.02 mm Hg, 95% CI 0.01 to 0.03, p<0.001 and 0.03 mm Hg, 95% CI 0.01 to 0.04, p=0.002, respectively). There was also a small but significant increase during the time in trial in the difference in IOP between the two eyes (estimate 0.01 mm Hg, 95% CI 0.005 to 0.02, p<0.001). There were no differences between bevacizumab and ranibizumab for any of the three outcomes (p=0.93, p=0.22 and p=0.87, respectively). CONCLUSIONS: Anti-vascular endothelial growth factor agents induce increases in IOP of small and uncertain clinical significance. TRIAL REGISTRATION NUMBER: ISRCTN92166560.

Retinal oxygen distribution and the role of neuroglobin.

The retina is the tissue layer at the back of the eye that is responsible for light detection. Whilst equipped with a rich supply of oxygen, it has one of the highest oxygen demands of any tissue in the body and, as such, supply and demand are finely balanced. It has been suggested that the protein neuroglobin (Ngb), which is found in high concentrations within the retina, may help to maintain an adequate supply of oxygen via the processes of transport and storage. We construct mathematical models, formulated as systems of reaction-diffusion equations in one-dimension, to test this hypothesis. Numerical simulations show that Ngb may play an important role in oxygen transport, but not in storage. Our models predict that the retina is most susceptible to hypoxia in the regions of the photoreceptor inner segment and inner plexiform layers, where Ngb has the potential to prevent hypoxia and increase oxygen uptake by 30-40 %. Analysis of a simplified model confirms the utility of Ngb in transport and shows that its oxygen affinity ([Formula: see text] value) is near optimal for this process. Lastly, asymptotic analysis enables us to identify conditions under which the piecewise linear and quadratic approximations to the retinal oxygen profile, used in the literature, are valid.

Comparing different dosing regimens of bevacizumab in the treatment of neovascular macular degeneration: study protocol for a randomised controlled trial.

BACKGROUND: Bevacizumab (Avastin®) is as effective as ranibizumab (Lucentis®) in the treatment of neovascular age-related macular degeneration (nAMD). However it has two important structural differences. First, it has two active sites instead of one; second, it retains the Fc portion of the antibody which would be expected to confer a significantly longer half-life. These agents have been associated with systemic complications including strokes, so it is desirable to use the smallest effective dose. Furthermore, the standard dosing regimen requires monthly hospital visits, which present a significant challenge both to the hospital services and to the patients (who are elderly). METHODS/DESIGN: Patients ≥50 years who are eligible for anti-vascular endothelial growth factor (VEGF) treatment of nAMD in the NHS, who are either newly referred for treatment or have reactivation of nAMD and who have not received treatment to either eye for the previous six months. We have designed a factorial multi-centre masked randomised controlled trial using bevacizumab as the intervention, with patients randomised to one of four arms: to standard or low dose and to monthly or two-monthly patient review. The aim is to recruit sufficient patients (around 1,000) to obtain 304 patients meeting the endpoint over a four-year period. The primary endpoint is time to treatment failure to be analysed using Cox regression. DISCUSSION: This randomised control trial will show if half dose and two monthly as required is as effective as full dose and monthly regimes. A two monthly as required regimen of Bevacizumab would significantly reduce both the cost and the service delivery burden for the treatment of nAMD while a reduced dose would be expected to enhance the safety profile of this treatment regime. TRIAL REGISTRATION: International Standard Randomised Controlled Trial Number: ISRCTN95654194 , registered on 22 September 2009.

A theoretical model to allow prediction of the CSF pressure from observations of the retinal venous pulse.

PURPOSE: There is no easy way to estimate the intracranial pressure (ICP) noninvasively. The retinal vein can exhibit large amplitude oscillations at the level of the lamina cribrosa under certain circumstances. The aims of this study were to develop a theoretical understanding of the conditions required to establish this vigorous oscillatory behavior and to determine whether observations of it could lead to a noninvasive estimate of the ICP. METHODS: A mathematical model was constructed in which the central retinal vein was modeled as 2 Starling resistors in series, 1 located in the eye and the other in the cerebrospinal fluid (CSF) space, separated by a region where it was not collapsible, corresponding to its course within the optic nerve itself. Intraocular pressure (IOP) and ICP were modeled as sinusoidal wave forms. RESULTS: The model predicted an approximately linear relationship between the IOP and the ICP at the point of onset of oscillatory behavior. The predicted onset IOP also depended weakly on the retinal blood flow rate and on vein diameter and was only mildly sensitive to the phase difference between the two pressure waveforms. The predicted onset curve showed encouraging agreement with measurements in canines. CONCLUSIONS: The model suggested that it may be possible to estimate the ICP from observations of the retinal venous pulse by using a modified form of ophthalmodynamometry.

Basement membrane changes in capillaries of the ageing human retina.

OBJECTIVES: The ultrastructural appearance of retinal capillaries can yield important information about disease mechanisms, but is not well characterised in human post mortem samples. We therefore aimed to create a baseline for the appearance of capillaries and establish how this is influenced by post mortem fixation delays and donor age. METHODS: Electron microscopy was used to characterise retinal capillaries in 20 anonymous donors (with no known eye diseases) of various ages and with various post mortem fixation delays. In addition, samples from six patients with conditions that are known to affect the retinal vasculature (four cases of type 2 diabetes without diabetic retinopathy, one case of diabetic retinopathy and one case of macular telangiectasia type 2) were analysed. RESULTS: Vacuoles were found in capillary basement membranes at the vessel-glia interface in all samples, from both the normal and disease cases. Vacuole frequency increased with donor age but was not influenced by post mortem fixation delays. CONCLUSION: Vacuoles in the basement membrane are a normal feature of adult human retinal capillaries and do not indicate disease. Their incidence increases with age and might be a contributing factor to late-onset pathologies of the retinal vasculature.

Should there be a visual standard for ophthalmologists and other surgeons?

A number of professions have a visual standard but there is no standard for surgeons, including surgeons such as ophthalmologists who operate with the aid of a microscope. We review which professions do have a visual standard, the evidence addressing the issue of a visual standard in medicine and surgery, and an international survey of what visual standards other countries apply to ophthalmologists, and performed a survey of the views of the member of the British Royal College of Ophthalmologists. A number of professions, where public safety is an issue, do have a visual standard without compelling supporting evidence. By contrast, all but two countries do not have a visual standard for their ophthalmic surgeons. The survey of members of the British Royal College of Ophthalmologists supported the adoption of such a standard, which would include minimum requirements for both visual acuity and stereoacuity. Good vision is clearly essential for ophthalmologists, as well as for other surgeons and practioners of some other branches of medicine. While there is no evidence to support a specific visual standard, we conclude that one should be adopted until there is definitive evidence to settle the issue on the basis of the precautionary principle as patient safety is involved.

Intracellular flow in optic nerve axons: a mechanism for cell death in glaucoma.

PURPOSE: In glaucoma, elevated intraocular pressure causes a progressive loss of retinal ganglion cells and results in optic neuropathy. The authors propose a potential mechanism for cell death, whereby elevated intraocular pressure causes fluid to permeate axonal membranes, creating a passive intracellular fluid flow within the axons. It is hypothesized that this intracellular flow locally depletes the adenosine triphosphate (ATP) concentration, disrupting axonal transport and leading to cell death. METHODS: A mathematical model was developed that takes into account the biomechanical principles underpinning the proposed hypothesis, and was solved to determine the implications of the mechanism. RESULTS: The model suggests that the raised intraocular pressures present in glaucoma are adequate to produce significant intracellular fluid flow. In the periphery of the optic nerve head, this flow may be sufficient to disrupt the diffusion of ATP and hence interrupt active axonal transport. CONCLUSIONS: The mathematical model demonstrates that it is physically plausible that a passive intracellular fluid flow could significantly contribute to the pathophysiology of the retinal ganglion cell axon in glaucoma.