Modeling the relation between intraocular pressure and human trabecular meshwork fluid-mechanical properties

Riccardo Sacco; Greta Chiaravalli; Giovanna Guidoboni; Anita Layton; Gal Antman; Alice Verticchio; Brent Siesky; Thomas A. Ciulla; Alon Harris; Riccardo Sacco; Greta Chiaravalli; Giovanna Guidoboni; Anita Layton; Gal Antman; Alice Verticchio; Brent Siesky; Thomas A. Ciulla; Alon Harris

doi:10.3934/mbe.2026075

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 7: 2055-2082. doi: 10.3934/mbe.2026075

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Research article

Modeling the relation between intraocular pressure and human trabecular meshwork fluid-mechanical properties

1.
Dipartimento di Matematica, Politecnico di Milano, Milano 20133, Italy
2.
Dipartimento di Fisica, Politecnico di Milano, Milano 20133, Italy
3.
Maine College of Engineering and Computing, University of Maine, Orono 04469, USA
4.
Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada
5.
Faculty of Medicine, Tel Aviv University, Tel Aviv 6997801, Israel
6.
Department of Ophthalmology, Icahn School of Medicine at Mount Sinai Hospital, New York 10029, USA
7.
School of Medicine, Indiana University, Indianapolis 46202, USA

Received: 30 January 2026 Revised: 27 May 2026 Accepted: 15 June 2026 Published: 10 July 2026

Elevated introcular pressure (IOP) is a major risk factor for primary open angle glaucoma (POAG), the second leading cause of blindness worldwide. In this article, we investigate the relation between IOP increase and fluid-mechanical properties of the trabecular meshwork (TM), which is the main pathway of aqueous humor (AH) outflow in the human eye. TM is represented as an axisymmetric deformable biphasic porous medium (solid and fluid) with hydraulic permeability nonlinearly depending on the local AH pressure. Solving Darcy's law provides a TM hydraulic resistance (TMR) depending on the radial pressure drop, while TM stiffness is included multiplying the TMR by a shape function of TM Young's modulus constructed using postmortem measurements of human eye outflow facility. Simulations of AH flow based on an electric equivalent scheme of the eye indicate that TMR increases with TM stiffness, leading to a progressive increase of IOP until over the upper limit of the normal IOP range. The obtained results shed light on the impact of microscopic properties of the eye on its macroscopic function, and support the integration of experimental studies, mathematical modeling, and data analysis to develop an optimized patient-specific therapy to cure POAG.
- mathematical modeling,
- simulation,
- glaucoma,
- aqueous humor,
- biphasic porous media,
- stiffness,
- hydraulic resistance
Citation: Riccardo Sacco, Greta Chiaravalli, Giovanna Guidoboni, Anita Layton, Gal Antman, Alice Verticchio, Brent Siesky, Thomas A. Ciulla, Alon Harris. Modeling the relation between intraocular pressure and human trabecular meshwork fluid-mechanical properties[J]. Mathematical Biosciences and Engineering, 2026, 23(7): 2055-2082. doi: 10.3934/mbe.2026075

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Abstract

Elevated introcular pressure (IOP) is a major risk factor for primary open angle glaucoma (POAG), the second leading cause of blindness worldwide. In this article, we investigate the relation between IOP increase and fluid-mechanical properties of the trabecular meshwork (TM), which is the main pathway of aqueous humor (AH) outflow in the human eye. TM is represented as an axisymmetric deformable biphasic porous medium (solid and fluid) with hydraulic permeability nonlinearly depending on the local AH pressure. Solving Darcy's law provides a TM hydraulic resistance (TMR) depending on the radial pressure drop, while TM stiffness is included multiplying the TMR by a shape function of TM Young's modulus constructed using postmortem measurements of human eye outflow facility. Simulations of AH flow based on an electric equivalent scheme of the eye indicate that TMR increases with TM stiffness, leading to a progressive increase of IOP until over the upper limit of the normal IOP range. The obtained results shed light on the impact of microscopic properties of the eye on its macroscopic function, and support the integration of experimental studies, mathematical modeling, and data analysis to develop an optimized patient-specific therapy to cure POAG.

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