Three-Dimensional Modeling of Metabolic Species Transport in the Cornea With a Hydrogel Intrastromal Inlay

Pinsky, Peter M.

doi:10.1167/iovs.13-13844

Cited by 28 publications

(26 citation statements)

References 24 publications

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“…In order to gain insight into the behaviour of the cornea, several mechanisms have been modelled separately by means of numerical models e. g., the remarkable examples given by models of cornea transport and swelling [7] and aqueous flow around IOLs [8,9]. Computational mechanics has allowed for the simulation of the biomechanical responses of the eye to physiological actions [10], external actions [11][12][13], and geometric changes due to refractive surgery [14][15][16][17].…”

mentioning

confidence: 99%

Cornea modelling

Pandolfi

2020

Eye and Vis

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Background: Biomechanics introduces numerous technologies to support clinical practice in ophthalmology, with the goal of improving surgical outcomes and to develop new advanced technologies with minimum impact on clinical training. Unfortunately, a few misconceptions on the way that computational methods should be applied to living tissues contributes to a lack of confidence towards computer-based approaches. Methods: Corneal biomechanics relies on sound theories of mechanics, including concepts of equilibrium, geometrical measurements, and complex material behaviors. The peculiarities of biological tissues require the consideration of multi-physics, typical of the eye environment, and to adopt customized geometrical models constructed on the basis of advanced optical imaging and in-vivo testing. Results: Patient-specific models are able to predict the outcomes of refractive surgery and to exploit the results of in-vivo test to characterize the material properties of the corneal tissue. Conclusions: Corneal biomechanics can become an important support to clinical practice, provided that methods are based on the actual multi-physics and use customized geometrical and mechanical models.

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confidence: 99%

Cornea modelling

Pandolfi

2020

Eye and Vis

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“…For example, accumulation of lactate ions due to lack of oxygen tension leads to edema. 16,25 In this article, following Pinsky, 15 we only considered the following three metabolic species: oxygen, glucose, and lactate.…”

Section: Transport Equationsmentioning

confidence: 99%

“…Several mathematical models 8,[13][14][15][16] and experiments [17][18][19][20][21] have been proposed, aimed at describing corneal metabolism. Taking advantage of the fact that the thickness of the cornea is much smaller than its lateral dimension, in most cases onedimensional models have been adopted in which the transport of all species across the cornea is assumed to be much larger than in the other directions.…”

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confidence: 99%

“…Taking advantage of the fact that the thickness of the cornea is much smaller than its lateral dimension, in most cases onedimensional models have been adopted in which the transport of all species across the cornea is assumed to be much larger than in the other directions. Chhabra et al 14 have proposed a coupled reaction-diffusion model for nutrient and oxygen delivery to the cornea, which together with the model proposed by Pinsky, 15 is the basis of the model used in this work. None of the above works have considered the direct effect of aqueous flow in delivering nutrients to the cornea.…”

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confidence: 99%

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

Khongar

Pralits

Cheng

et al. 2019

Invest. Ophthalmol. Vis. Sci.

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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.

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“…While the pressure-driven Darcy flow inside a poroelastic skeleton is of great relevance in geophysics, biological poromechanical flows often involve the coupling between an exterior viscous fluid flow and an interior poroelastic flow, see work by Lai et al 13 . In these models, the viscous dissipation in the fluid phase may be comparable to the pressure gradient, and this poromechanical coupling is further complicated by ion transport in the porous medium flow, see work by Pinsky et al [14][15][16] . Cogan and Keener developed a two-phase flow model for cellular cytosol, with a dominant viscous dissipation of a deformable skeleton (that depends on the rate of strain) and no elastic energy (that depends on the strain) 17 .…”

Section: Introductionmentioning

confidence: 99%

Slightly deformable Darcy drop in linear flows

2019

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The small-deformation of a poroelastic drop due to an external linear flow field in the suspending medium is investigated. A two-phase flow model is developed to study the small-deformation of such a poroelastic drop under linear flows. Inside the drop a deformable porous network with a bending rigidity and a viscosity is fully immersed in a viscous fluid. When the viscous dissipation of the interior fluid phase is negligible (compared to the friction between the fluid and the skeleton), the two-phase flow is reduced to a poroelastic Darcy fluid with a deformable porous network. At the interface between the poroelastic drop and the exterior Stokesian fluid, a novel set of boundary conditions are derived by the free energy dissipation principle. Both slip and permeability are taken into account and the permeating flow induces dissipation that depends on the elastic stress of the interior solid. Assuming that the porous network is slightly deformed from its original spherical shape due to its large bending rigidity, a small-deformation analysis is conducted. A steady equilibrium is computed for two different linear flows: a uniaxial extensional flow and a planar shear flow. By exploring the interfacial slip, permeability and network elasticity various flow patterns are found at equilibrium of these slightly deformed poroelastic drops. Linear dynamics of the small-amplitude deviation of the poroelastic drop from the spherical shape is governed by a nonlinear eigenvalue problem, and the eigenvalues are determined numerically, and asymptotically in certain limits. These results lay the foundation for studying the rheology of a suspension of poroelastic spherical particles, and give insight to possible flow patterns of a system of selfpropelling swimmers with porous flow (such as intracellular cytosol) inside.

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Three-Dimensional Modeling of Metabolic Species Transport in the Cornea With a Hydrogel Intrastromal Inlay

Cited by 28 publications

References 24 publications

Cornea modelling

Cornea modelling

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

Slightly deformable Darcy drop in linear flows

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