A Mathematical Model of Aqueous Humor Production and Composition

Dvoriashyna, Mariia; Foss, Alexander J.E.; Gaffney, Eamonn A.; Repetto, Rodolfo

doi:10.1167/iovs.63.9.1

Cited by 5 publications

(6 citation statements)

References 38 publications

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“…However, given there is a concentration drop across the ciliary epithelium, one might anticipate that the osmotic flux is the primary mechanism for aqueous humour inflow. In particular, this is indirectly supported by an a posteriori consideration of the predictions of Dvoriashyna et al 24 which, for baseline models and physiological parameters, aligns with measured inflow rates without the need to consider additional transport mechanisms. This is in distinct contrast to the RPE, where at least one mechanism of local osmosis and electro-osmosis is indicated as active, as discussed in Section 2.…”

Section: Mathematical Expressionsmentioning

confidence: 74%

“…22 In turn, this has motivated modeling studies analyzing ion channels, transporters, exchangers, and the Na + -K + pump, that regulate the inflow from the ciliary processes via the secretory ciliary epithelium, together with the associated osmotic, oncotic, and hydraulic pressures. 21,23,24 In particular, the ciliary epithelium lining the ciliary processes of the ciliary body (Fig. 3A-C) consists of a double layer of epithelial cells, with the pigmented epithelium adjacent to the stroma and the nonpigmented epithelium facing the posterior chamber, as illustrated in Figure 3D.…”

Section: Aqueous Humor Production In the Ciliary Processesmentioning

confidence: 99%

“…Recent models based on these principles have been constructed by Sacco et al 23 and Dvoriashyna et al, 24 together with a lumping of the 2 epithelial layers into a sin- gle cellular compartment, as may be motivated by noting that the 2 epithelial layers are connected by gap junctions, thus forming a functional syncytium. In addition, both Sacco et al 23 and Dvoriashyna et al 24 neglected the additional transport mechanisms discussed in the previous sections, for instance, local osmosis. However, given there is a concentration drop across the ciliary epithelium, one might anticipate that the osmotic flux is the primary mechanism for aqueous humour inflow.…”

Section: Mathematical Expressionsmentioning

confidence: 99%

“…Dvoriashyna et al 24 thus constructed a steady-state model without fixing the posterior chamber concentrations and including the Na + -HCO − 3 cotransporter, resulting in 18 algebraic equations for the same number of unknowns. After confirming model consistency with the current understanding, a subsequent sensitivity analysis was conducted.…”

Section: Mathematical Expressionsmentioning

confidence: 99%

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Mathematical modelling of ocular epithelial transport: a review

Dvoriashyna,

Foss,

Gaffney

et al. 2023

MAIO

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Purpose: Ocular epithelial layers are fundamental for the physiology of the eye as they regulate water transport. The purpose of this review is to discuss the existing mathematical models of water transport across these layers. Methods: We detail the physical mechanisms that can induce water transport across epithelial layers and describe how they can be mathematically modelled. Results: We consider 3 ocular epithelial layers. The first is the epithelium of the ciliary processes, which is responsible for aqueous humour production. The second is the corneal endothelium (functionally an epithelium), which plays a key role in maintaining the delicate hydration state of the cornea. The third is the retinal pigment epithelium, which actively removes water from the retina by pumping it into the choroid. Conclusion: Owing to the difficulty of obtaining direct measurements of water fluxes across epithelial layers, mathematical models can significantly improve our understanding of this field. For instance, they can help develop insight and predictive capability concerning the role of different ion channels, transporters, exchangers, and pumps, as well as carbon dioxide hydrolysis, in ocular water transport processes. Likewise, they can elucidate the importance of the various mechanisms and associated parameters that are involved.

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Section: Mathematical Expressionsmentioning

confidence: 74%

Section: Aqueous Humor Production In the Ciliary Processesmentioning

confidence: 99%

Section: Mathematical Expressionsmentioning

confidence: 99%

Section: Mathematical Expressionsmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical modelling of ocular epithelial transport: a review

Dvoriashyna,

Foss,

Gaffney

et al. 2023

MAIO

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“…The eye is a pressurized organ and the intraocular pressure (IOP) is responsible for the main mechanical loads acting on the corneo-scleral shell under physiological conditions. IOP is regulated by a delicate balance between the rate of aqueous production by the ciliary body [ 2 ] and resistance to its drainage at the junction between the cornea and the iris, mostly through a spongy tissue named trabecular meshwork [ 3 ]. IOP has a significant impact on the functioning of the eye and is involved in the onset and development of various pathological conditions.…”

Section: Introductionmentioning

confidence: 99%

A mechanical model of ocular bulb vibrations and implications for acoustic tonometry

Tambroni,

Tomassetti,

Lombardi

et al. 2024

PLoS ONE

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In this study, we propose a comprehensive mechanical model of ocular bulb vibrations and discuss its implications for acoustic tonometry. The model describes the eye wall as a spherical, pre-stressed elastic shell containing a viscoelastic material and accounts for the interaction between the elastic corneoscleral shell and the viscoelastic vitreous humor. We investigate the natural frequencies of the system and the corresponding vibration modes, expanding the solution in terms of scalar and vector spherical harmonics. From a quantitative point of view, our findings reveal that the eyebulb vibration frequencies significantly depend on IOP. This dependency has two origins: “geometric” stiffening, due to an increase of the pre-stress, and “material” stiffening, due to the nonlinearity of the stress-strain curve of the sclera. The model shows that the second effect is by far dominant. We also find that the oscillation frequencies depend on ocular rigidity, but this dependency is important only at relatively large values of IOP. Thus close to physiological conditions, IOP is the main determinant of ocular vibration frequencies. The vitreous rheological properties are found to mostly influence vibration damping. This study contributes to the understanding of the mechanical behavior of the eye under dynamic conditions and thus has implications for non-contact intraocular pressure measurement techniques, such as acoustic tonometry. The model can also be relevant for other ocular pathological conditions, such as traumatic retinal detachment, which are believed to be influenced by the dynamic behavior of the eye.

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Numerical simulation of aqueous flow in a novel posterior chamber phakic intraocular lens versus its counterparts

2023

Physics of Fluids

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Phakic intraocular lenses (pIOLs), particularly posterior chamber pIOLs, are becoming important for patients with high myopia and thin corneas. By phakic intraocular, we mean the ocular environmental conditions, where the natural lens is unremoved. A new posterior chamber pIOL, the sine wave phakic refractive lens (SW-PRL), is in the development stage, and its aqueous humor (AH) dynamics and the effects of intraocular geometry on the flow characteristics are not well understood. To analyze the adaptability and functionality of SW-PRL, a comparison study is made with its counterparts, the posterior chamber phakic refractive lens (PC-PRL), PC-PRL combined with peripheral iridotomy [PC-PRL(PI)], and implantable collamer lens with a central hole (ICL V4c). The result demonstrates that SW-PRL has a positive effect on AH flow circulation. Interestingly, there is a relationship between a posterior chamber flow and the type of pIOLs with vault variation. With an increase in vault, the flow between the lens and pIOLs slowed down after ICL V4C implantation but accelerated after PC-PRL (PI) implantation with little change after SW-PRL implantation. On the rear surface of the iris, the wall shear stress (WSS) was lower for PC-PRL(PI), SW-PRL, and ICL V4c (5.6 × 10−4, 6 × 10−3, and 8.2 × 10−3 Pa, respectively) compared to the PC-PRL (0.14 Pa), and on the front surface of lens, the WSS was lower for PC-PRL and SW-PRL (1.16 × 10−5 and 9.7 × 10−6 Pa, respectively) compared to the ICL V4c (8.2 × 10−4 Pa). WSS on the cornea surface was similar for each pIOL. These might provide a fresh viewpoint on the clinical decision of different intraocular lenses.

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A Mathematical Model of Aqueous Humor Production and Composition

Cited by 5 publications

References 38 publications

Mathematical modelling of ocular epithelial transport: a review

Mathematical modelling of ocular epithelial transport: a review

A mechanical model of ocular bulb vibrations and implications for acoustic tonometry

Numerical simulation of aqueous flow in a novel posterior chamber phakic intraocular lens versus its counterparts

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