Aqueous humour flow in the posterior chamber of the eye and its modifications due to pupillary block and iridotomy

A Mechanistic Model of Aqueous Humor Flow to Study Effects of Angle Closure on Intraocular Pressure

Purpose

To study the relationship between the circumferential extent of angle closure and elevation in intraocular pressure (IOP) using a novel mechanistic model of aqueous humor (AH) flow.

Methods

AH flow through conventional and unconventional outflow pathways was modeled using the unified Stokes and Darcy equations, which were solved using the finite element method. The severity and circumferential extent of angle closure were modeled by lowering the permeability of the outflow pathways. The IOP predicted by the model was compared with biometric and IOP data from the Chinese American Eye Study, wherein the circumferential extent of angle closure was determined using anterior segment OCT measurements of angle opening distance.

Results

The mechanistic model predicted an initial linear rise in IOP with increasing extent of angle closure which became nonlinear when the extent of closure exceeded around one-half of the circumference. The nonlinear rise in IOP was associated with a nonlinear increase in AH outflow velocity in the open regions of the angle. These predictions were consistent with the nonlinear relationship between angle closure and IOP observed in the clinical data.

Conclusions

IOP increases rapidly when the circumferential extent of angle closure exceeds 180°. Residual AH outflow may explain why not all angle closure eyes develop elevated IOP when angle closure is extensive.

Translational Relevance

This study provides insight into the extent of angle closure that is clinically relevant and confers increased risk of elevated IOP. The proposed model can be utilized to study other mechanisms of impaired aqueous outflow.

Predicting a reduction in intraocular pressure in glaucoma patients in the early period after a trabeculectomy: Development and assessment of a new predictive nomogram

Purpose

To identify the factors associated with a reduction in intraocular pressure (IOP) in the early postoperative period after a trabeculectomy and to develop a predictive nomogram to guide clinical care.

Methods

This study included clinical data on 588 glaucoma patients (N = 588 eyes) who underwent a trabeculectomy in our hospital between January 2016 and December 2021. There were 412 eyes in a training cohort and 176 eyes in a validation cohort. We used logistic regression analysis to evaluate whether these factors were related to a decrease in IOP in the early period postsurgery and established a predictive model by combining features selected in a univariate analysis. We used external validation for evaluation. The standard for IOP reduction was that the IOP decreased to the normal range (10-21 mmHg) 1 month after the trabeculectomy.

Results

Among the patients in the training cohort, 82.8% met the standard for IOP lowering. There were 11 meaningful differences among the enrolled predictors, but the logistic regression analysis only showed significant differences with anterior chamber angle closed, age, preoperative IOP, axial length, and visual field mean sensitivity (MS). The C-index of the model was 0.910 (95% confidence interval [CI]: 0.869-0.951). The C-index was 0.956 for external validation of the model.

Conclusion

This new nomogram can be used to predict whether the IOP will reach the standard in the early stages after a trabeculectomy. The anterior chamber angle closed, age, preoperative IOP, axial length, and visual field MS are independent risk factors.

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.

Numerical study of aqueous humor flow and iris deformation with pupillary block and the efficacy of laser peripheral iridotomy

BACKGROUND

Disclosing the mechanism of primary angle closure glaucoma with pupillary block is important to the diagnosis as well as treatments, such as the laser peripheral iridotomy. Comparing with abundant clinical researches, there have been fewer quantitative studies of the aqueous humor flows with synechia iris configurations, and the efficacy of laser peripheral iridotomy in treating glaucoma.

METHODS

Based on the mathematical models of aqueous humor flow and iris deformation, the flow fields were simulated by computational fluid dynamics with normal and synechia iris configurations (iris-lens gap of 30, 5 and 2 μm, respectively), and through one-way fluid-structure coupling technique the deformations of the iris under the flow field pressure were calculated by finite element analysis. The efficacy of glaucoma treatment with different orifice sizes was also investigated.

FINDINGS

Results show that the pressure difference between anterior and posterior chambers and iris deformation increase dramatically with the iris-lens gap distance less than 5 μm, and when further decreasing this gap may lead the iris touch the cornea causing angle closure glaucoma with noticeable iris bombé. Laser peripheral iridotomy simulation results show that iridotomy size of 0.2 mm can effectively decrease the pressure difference across the iris and relieve iris bombé.

INTERPRETATION

This is a biomechanical numerical study, and the results are reasonable compare to those of published works. It may shed additional light on the diagnosis and treatment of angle closure glaucoma with pupillary block.

Ocular Fluid Mechanics and Drug Delivery: A Review of Mathematical and Computational Models

The human eye is a complex biomechanical structure with a range of biomechanical processes involved in various physiological as well as pathological conditions. Fluid flow inside different domains of the eye is one of the most significant biomechanical processes that tend to perform a wide variety of functions and when combined with other biophysical processes play a crucial role in ocular drug delivery. However, it is quite difficult to comprehend the effect of these processes on drug transport and associated treatment experimentally because of ethical constraints and economic feasibility. Computational modeling on the other hand is an excellent means to understand the associated complexity between these aforementioned processes and drug delivery. A wide range of computational models specific to different types of fluids present in different domains of the eye as well as varying drug delivery modes has been established to understand the fluid flow behavior and drug transport phenomenon in an insilico manner. These computational models have been used as a non-invasive tool to aid ophthalmologists in identifying the challenges associated with a particular drug delivery mode while treating particular eye diseases and to advance the understanding of the biomechanical behavior of the eye. In this regard, the author attempts to summarize the existing computational and mathematical approaches proposed in the last two decades for understanding the fluid mechanics and drug transport associated with different domains of the eye, together with their application to modify the existing treatment processes.

Dynamic volume-rendered optical coherence tomography pupillometry

PURPOSE

To assess intrapupillary space (IPS) changes in healthy subjects with regard to decreased iris motility in patients with pseudoexfoliation glaucoma (PEXG) or non-arteritic anterior ischaemic optic neuropathy (NAION) in a feasibility study in a clinical environment.

METHODS

Scotopic and photopic IPS measurements using three-dimensionally rendered swept-source optical coherence tomography (SS-OCT) data were obtained and compared for all subjects. Intrapupillary space (IPS) parameters were evaluated such as absolute volumetric differences, relative light response for volumetric ratios and pupillary ejection fraction (PEF) for functional contraction measurements.

RESULTS

From a total of 122 IPS from 66 subjects, 106 IPS were eligible for comparison providing values for 72 normal, 30 PEXG and 4 NAION eyes. In healthy, PEXG and NAION subjects, scotopic overall mean IPS was 8.90, 3.45 and 4.16 mm³ , and photopic overall mean IPS was 0.87, 0.74 and 1.13 mm³ , respectively. Three-dimensional contractility showed a mean absolute difference of 8.03 mm³ for normals (defined as 100% contractility), 2.72 mm³ for PEXG (33.88% of normal) and 3.03 mm³ for NAION (38.50% of normal) with a relative light response ratio between scotopic and photopic volumes of 10.26 (100%), 4.69 (45.70%) and 3.67 (35.78%), respectively. Pupillary ejection fraction (PEF) showed a contractile pupillary emptying of 88.11% for normals, 76.92% for PEXG and 70.91% for NAION patients.

CONCLUSION

This 3D pupillometry OCT assessment allows for quantitative measurements of pupil function, contractility and response to light. More specifically, PEF is presented as a potential (neuro)-pupillary outcome measure that could be useful in the monitoring of ophthalmic disorders that affect pupillary function.

Computational Study on the Biomechanics of Pupil Block Phenomenon

Pupil blocking force (PBF) can indicate the potential risk of pupil block (PB), which is considered as a main pathogenic factor of primary angle-closure glaucoma (PACG). However, the effect of PB on the PBF under different pupil diameters and iris-lens channel (ILC) distance was unknown. Besides, a simple and practical method to assess PBF has not been reported yet. In this study, 21 finite element models of eyes with various pupil diameters (2.4 mm–2.6 mm) and ILC (2 μm–20 μm) were constructed and were conducted to simulate aqueous humor flow by fluid-solid coupling numerical simulation. PBF in each model was calculated based on the numerical simulation results and was fitted using response surface methodology. The results demonstrated that ILC distance had a more significant effect than pupil diameter on PBF. With the decrease of ILC distance, the PBF increased exponentially. When the reduced distance was lower than 5 μm, the PBF exploded quickly, resulting in a high risk of iris bomb. The PBF also varied with pupil diameter, especially under the condition of narrow ILC. Both ILC distance and pupil diameter could explain more than 97% variation in PBF, and a second-order empirical model has been developed to be a good predictor of PBF. Based on the linear relationship between anterior chamber deformation and PBF, a threshold value of PBF was given to guide clinical decisions. This study could be used to investigate PACG pathological correlation and its pathogenesis, so as to provide a reference value for clinical diagnosis of PACG.

A Mathematical Model of Corneal Metabolism in the Presence of an Iris-Fixated Phakic Intraocular Lens

Purpose

Corneal endothelial cell loss is one of the possible complications associated with phakic iris-fixated intraocular lens (PIOL) implantation. We postulate that this might be connected to the alteration of corneal metabolism secondary to the lens implantation.

Methods

A mathematical model of transport and consumption/production of metabolic species in the cornea is proposed, coupled with a model of aqueous flow and transport of metabolic species in the anterior chamber.

Results

Results are presented both for open and closed eyelids. We showed that, in the presence of a PIOL, glucose availability at the corneal endothelium decreases significantly during sleeping.

Conclusions

Implantation of a PIOL significantly affects nutrient transport processes to the corneal endothelium especially during sleep. It must still be verified whether this finding has a clinical relevance.

Time Course Changes of the Mechanical Properties of the Iris Pigment Epithelium in a Rat Chronic Ocular Hypertension Model

BACKGROUND

The flow field of aqueous humor correlates to the stiffness of iris pigment epithelium (IPE) which acts as a wall of posterior chamber. We focus on the variations of IPE stiffness in a rat ocular hypertension (OHT) model, so as to prepare for exploring the mechanism of duration of OHT.

METHODS

Episcleral venous cauterization (EVC) was applied on one eye of male adult Sprague-Dawley rats to induce chronic high intraocular pressure. According to the duration of OHT (0, 1, 2, 4, and 8 weeks), rats were randomly divided into Gw0, Gw1, Gw2, Gw4, and Gw8. Atomic force microscope (AFM) analysis was applied to test IPE stiffness in three regions: iris root, mid-periphery, and pupillary-margin in each group. Histological changes of IPE were also examined in Gw4 and Gw8.

RESULTS

There was an overall growing tendency of IPE stiffness in EVC eye. IPE in EVC eye was significantly stiffer than fellow eye in Gw2, Gw4, and Gw8 (in iris root, mid-periphery, and pupillary-margin, p<0.05). IPE in EVC eye in pupillary-margin was significantly stiffer than iris root in Gw4 and Gw8 (p<0.05). In EVC eye, IPE becomes thinner and IPE cell density decreases.

CONCLUSION

IPE stiffness increases gradually with the duration of chronic high intraocular pressure.

Computational simulation of aqueous humour dynamics in the presence of a posterior-chamber versus iris-fixed phakic intraocular lens

Purpose

To compare aqueous humour (AH) dynamics in the presence of a precrystalline (Implantable Collamer Lens^®; ICL) or iris-fixed (Artiflex^®) phakic intraocular lens (PIOL).

Methods

By computational fluid dynamics simulation, AH flow was modelled through a peripheral iridotomy (PI) or central lens hole (both 360 μm) in the presence of an Artiflex or ICL lens, respectively. The impacts of AH flow were then determined in terms of wall shear stress (WSS) produced on the endothelium or crystalline lens. Effects were also modelled for different scenarios of pupil diameter (PD 3.5 or 5.5 mm), ICL vault (100, 350, 800 μm) and number of Artiflex iridotomies (1 or 2) and location (12 or 6 o’clock).

Results

For a PD of 3.5 mm, AH volumes flowing from the posterior to the anterior chamber were 37.6% of total flow through the lens hole (ICL) and 84.2% through PI (Artiflex). For an enlarged PD (5.5 mm), corresponding values were 10.3% and 81.9% respectively, so PI constitutes a very efficient way of evacuating AH. Central endothelial WSS in Pa was lower for the large vault ICL and the Artiflex (1⁻⁰³ and 1.1⁻⁰³ respectively) compared to the PIOL-free eye (1.6⁻⁰³). Crystalline lens WSS was highest for the lowest vault ICL (1⁻⁰⁴).

Conclusions

AH flow varied according to the presence of a precrystalline or iris-fixed intraocular lens. Endothelial WSS was lower for an implanted ICL with large vault and Artiflex than in the PIOL-free eye, while highest crystalline WSS was recorded for the lowest vault ICL.