Mathematical modeling of aqueous humor flow and intraocular pressure under uncertainty: towards individualized glaucoma management

Marcela Szopos, Simone Cassani, Giovanna Guidoboni, Christophe Prud'homme, Riccardo Sacco, Brent Siesky, Alon Harris


Purpose: The aim of the proposed analysis is to provide both a qualitative description and a quantitative assessment of how variations in aqueous humor (AH) flow parameters influence intraocular pressure (IOP) and the outcome of IOP-lowering medications.

Methods: We developed a mathematical model that describes the steady-state value of IOP as the result of the balance between AH production and drainage. We performed stochastic simulations to assess the influence of different factors on the IOP distribution in ocular normotensive and ocular hypertensive subjects and on the IOP reduction following medications.

Results: The distribution of the relative frequency of a given IOP value for ocular normotensive subjects fits a right-skewed Gaussian curve with a frequency peak of 25% at 15.13 mmHg and a skewness of 0.2, in very good agreement with the results from a population-based study on approximately 12,000 individuals. The model also shows that the outcomes of IOP-lowering treatments depend on the levels of pre-treatment IOP and blood pressure. The model predicts mean IOP reductions of 2.55 mmHg and 4.31 mmHg when the pre-treatment IOP mean values are 15.13 mmHg and 20.12 mmHg, respectively; these predictions are in qualitative and quantitative agreement with clinical findings.

Conclusion: These findings may help identify patient-specific factors that influence the efficacy of IOP-lowering medications and aid the development of novel, effective, and individualized therapeutic approaches to glaucoma management.


aqueous humor flow, glaucoma management, intraocular pressure, mathematical modeling, sensitivity analysis

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