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

Abstract

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.

Physiology-Enhanced Data Analytics to Evaluate the Effect of Altitude on Intraocular Pressure and Ocular Hemodynamics

“…Finally, no specific altitude was consistently utilized across studies, therefore complicating the understanding of what elevation level is required to significantly impact IOP and/or ocular hemodynamics. In order to overcome these limitations, in this study, we used an innovative methodological approach indicated as physiology-enhanced data analytics able to integrate experimental data-derived from the MBS [32]-with validated mathematical models [39,40] in order to shed further light on the physiologic relationships between IOP, BP, and ocular hemodynamics with altitude.…”

“…In addition, we also used the mathematical model validated in [40] on AH dynamics in combination with the experimental data from the MBS to shed further light on the physiological mechanisms between changes in IOP and BP with altitude through two sub-analyses. The pe-IOP analysis used the values of MAP derived from the MBS as individualized inputs and provided the corresponding IOP values at different altitudes as individualized outputs, which were then compared with the actual IOP values collected in the real word (Figure 2).…”

“…The mathematical model proposed and validated in [40] to study aqueous humor (AH) dynamics was also used in combination with the data from the MBS to gain insights into the relationship between altitude and IOP physiology. In the model, IOP is calculated as the result of the balance between AH inflow (J IN ) and outflow (J OUT ).…”

“…For each subject in the study, we computed the mean arterial pressure (MAP) as MAP = 1/3 SBP + 2/3 DBP, and we used it to set the value of cBP as an individualized input for the model. Following [39], we set cBP = α× MAP, with α = 0.29, and we kept other model parameters at their baseline values as listed in [40]. Upon utilizing cBP as an individualized input, the AH model was used to predict the corresponding IOP value as an individualized output, which was then compared with the actual IOP value measured on that specific subject at different altitudes (PV, CM, PH).…”

“…In this perspective, herein, we combined experimental measurements with mathematical modeling to better understand the relationships between altitude, IOP, and hemodynamic changes and the clinical significance of these alterations on ocular disease. Specifically, the data previously collected from the Mont Blanc Study (MBS) [32] were used as inputs for two mathematical models describing the physiology of ocular hemodynamics [39] and aqueous humor flow [40]. The outputs of these models provide estimates for variables that bear physiological interest but that cannot be measured directly.…”