Computational Fluid Dynamics (CFD) is a computational science technique that analyzes fluid flow using numerical methods and algorithms based on the Navier-Stokes equations. By applying fluid dynamics laws to a computational model representing the structure, it is possible to infer flow patterns, pressure distributions, shear stress, and more.
The eye is an organ containing high-concentration fluids (aqueous humor, vitreous body), making it highly suitable as a model for CFD analysis. The main application areas in ophthalmology are as follows:
CFD has achieved significant results in the cardiovascular field (atherosclerosis, stent design). In recent years, collaboration with other medical fields including ophthalmology has progressed, and research involving multidisciplinary teams (physicians, mathematicians, physicists) is becoming more active.
As stages of simplification of the Navier-Stokes equations, removing the viscous term yields the Euler equations, further removing the vorticity term yields the full potential equation, and linearization yields the linearized potential equation. In the steady state of the anterior chamber, the maximum Reynolds number is very small, about 0.01, but for transient phenomena such as blinking, the full Navier-Stokes equations are required.
CFD (Computational Fluid Dynamics) is a technique for simulating fluid flow using computers. In ophthalmology, it is mainly applied to analyze abnormal aqueous humor flow that causes glaucoma, predict drug diffusion after intravitreal injection, and optimize fluid behavior during cataract surgery. Since the eye is an organ containing a large amount of fluid, it is very suitable as a model for CFD analysis.
Aqueous humor is secreted into the posterior chamber by the non-pigmented epithelium of the ciliary body. The daytime production rate is approximately 3.0 μL/min, and the aqueous humor in a standard anterior chamber volume (about 250 μL) is replaced every 1 to 2 hours. Aqueous humor flows through the pupil into the anterior chamber and is drained mainly via the trabecular meshwork-Schlemm’s canal pathway (primary pathway: 80-95%) and the uveoscleral outflow pathway (secondary pathway: 5-20%)2).
The main site of outflow resistance in the primary pathway is the region of the juxtacanalicular connective tissue where the extracellular matrix (ECM) is present4). Continuous turnover of the ECM is necessary for maintaining intraocular pressure regulation, and it has been experimentally shown that manipulating the ECM of the trabecular meshwork can alter the outflow rate4).
“The outflow pathway has a homeostatic mechanism that senses continuous pressure deviations and compensatorily adjusts outflow resistance to maintain intraocular pressure within the normal range”4)
The basement membrane of the inner wall endothelial cells of Schlemm’s canal (SCE) develops submicron discontinuities, through which aqueous humor is drained via giant vacuoles and pores4). A hypothesis that cells in the juxtacanalicular connective tissue (JCT) regulate outflow resistance by manipulating the orientation and concentration of versican has been tested4).
Intraocular pressure is a complex parameter that cannot be reduced to a single number3). It varies over time, differs depending on the location within the eye, and is also affected by the measurement method3).
| Characteristics of Intraocular Pressure | Description |
|---|---|
| Definition | Differential pressure from atmospheric pressure (mmHg) |
| Normal Intraocular Pressure | Approximately 15 mmHg (atmospheric pressure + 2 kPa) |
| Diurnal variation | Aqueous humor production is halved at night |
The mechanical strain generated by intraocular pressure affects axonal function at the optic nerve head (ONH), leading to local ECM remodeling and retinal ganglion cell (RGC) death3). The lamina cribrosa (LC) is a fenestrated structure covering the opening of the scleral canal and is considered the primary site of damage in glaucoma3).
In normal eyes, the maximum principal strain in the LC is approximately 3% under pressurization from 5 to 45 mmHg, with higher values in the periphery than in the center3). It has been reported that effective strain differs by disease type: 3.96% in ocular hypertensive eyes, 6.04% in primary open-angle glaucoma (POAG) eyes, and 4.05% in primary angle-closure glaucoma (PACG) eyes3).
Intraocular pressure-dependent factors
Mechanical stress: Intraocular pressure deforms the connective tissue beams of the lamina cribrosa. High IOP causes extensive remodeling and posterior displacement of the LC3)
Axonal transport impairment: IOP-related strain blocks anterograde and retrograde axonal transport at the LC3)
Mechanosensors: Deformation of the cell membrane → ion channel opening, integrin binding signaling → cellular response3)
Intraocular pressure-independent factors
Circulatory disturbance: Association with optic disc hemorrhage, peripapillary atrophy, low ocular perfusion pressure, low diastolic blood pressure
Risk factors: Older age, family history, large cup-to-disc ratio, thin cornea, low corneal hysteresis1)2)
RGC death: Apoptosis pathways, neurotrophic factor deprivation, mitochondrial accumulation
The main site of aqueous humor outflow resistance is the extracellular matrix of the juxtacanalicular connective tissue (JCT), the deepest layer of the trabecular meshwork. Continuous turnover of the ECM in this region maintains intraocular pressure within the normal range. In glaucoma, this regulatory mechanism fails, leading to abnormally increased outflow resistance. CFD contributes to understanding the pathology by numerically analyzing fluid behavior at this microstructural level.
Five physical mechanisms have been identified that drive aqueous humor flow in the anterior chamber:
Buoyancy-driven flow due to temperature gradient is the most dominant, with flow velocities orders of magnitude higher than those from other physical mechanisms. Shear stress calculations using CFD have shown that buoyancy-driven flow alone cannot explain the detachment of pigment particles from the iris.
Using CFD, the shear stress on corneal endothelial cells (CEC) due to changes in aqueous humor flow after laser iridotomy (LI) has been analyzed. Particularly in eyes with shallow anterior chambers, the shear stress on CECs after LI may reach levels sufficient to cause cell damage and loss.
CFD simulations of drug distribution in the posterior segment after intravitreal injection or implant show that injection time, needle gauge, and insertion angle affect the drug concentration profile. The location (anterior vs. posterior) and shape of the implant also influence intraocular drug concentration. Such models may contribute to optimizing therapeutic efficacy and reducing tissue toxicity.
Heat transfer models of the lens have shown that occupational heat exposure (e.g., in bakeries) can cause lens damage. Computational evaluation of the role of accommodation in pigmentary glaucoma has confirmed that accommodation causes posterior bowing of the iris, and the degree of bowing strongly depends on the amount of accommodation.
Attempts are also being made to investigate the hydrodynamic properties of aqueous humor in modified phakic posterior chamber intraocular lenses (ICL) with a central hole designed to improve aqueous humor circulation, using CFD.
CFD contributes to understanding the pathophysiology of glaucoma in many ways. Specifically, it is used for (1) analysis of aqueous humor flow patterns and temperature distribution in the anterior chamber, (2) quantitative evaluation of outflow resistance through the trabecular meshwork, (3) prediction of shear stress on corneal endothelial cells after laser treatment, (4) modeling of aqueous humor and iris interaction, and (5) analysis of pupillary block mechanisms. In the future, integration with clinical data is expected to enable the development of optimized treatment strategies for individual patients.
- European Glaucoma Society. European Glaucoma Society Terminology and Guidelines for Glaucoma, 5th Edition. Br J Ophthalmol. 2025.
- 日本緑内障学会. 緑内障診療ガイドライン（第5版）. 日眼会誌. 2022;126(2):85-177.
- Pitha IA, Du L, Nguyen TD, Quigley HA. 眼圧 and glaucoma damage: The essential role of optic nerve head and retinal mechanosensors. Prog Retin Eye Res. 2023;99:101232.
- Acott TS, Vranka JA, Keller KE, Raghunathan V, Kelley MJ. Normal and glaucomatous outflow regulation. Prog Retin Eye Res. 2021;82:100897.
