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Simone Cassani, Giovanna Guidoboni, Marcela Szopos, Christophe Prud'homme, Riccardo Sacco, Brent A Siesky, Alon Harris; Mathematical modeling and statistical analysis of aqueous humor flow towards individualized glaucoma treatment. Invest. Ophthalmol. Vis. Sci. 2016;57(12):6404. doi: https://doi.org/.
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© ARVO (1962-2015); The Authors (2016-present)
Ocular hypertension (OHT), or elevated introcular pressure (IOP), is a risk factor for vision loss. IOP results from the balance between aqueous humor (AH) production and drainage (P/D) and is influenced by several factors such as blood pressure (BP), episcleral venous pressure (EVP) and blood/AH osmotic pressure difference (Δπ). Such factors influence disease risks and treatment outcomes, but are difficult to isolate experimentally. We use a theoretical approach to: (1) quantify the relative influence of these factors on IOP; (2) study the variability in the outcome of IOP-lowering medications.
The mathematical model describes P/D of AH in analogy with an electric circuit. AH production occurs via ultrafiltration from the ciliary circulation and via the Δπ generated by ionic active secretion, and is modulated by the total inflow facility (L). AH drainage occurs via the trabecular meshwork pathway (outflow facility C) and the uveoscleral pathway (outflow facility k). Steady-state IOP results from the balance between P/D of AH, and it solves a non-linear algebraic equation. A sensitivity analysis (SA) is performed to simulate healthy individuals (HI), OHT (C=0.3*Cref) and the effect of IOP-lowering medications (reduced Δπ).
The IOP frequency distribution, Fig1a, fits a right-skewed Gaussian curve as in a population-based study on 12.000 individuals (Carel 1984). Fig1c,d show the effect of a 25% Δπ reduction on HI and OHT. The model predicts an average IOP reduction of 2.6mmHg and 4.3mmHg, respectively. Fig2 shows the Sobol indexes for the SA. The indexes quantify the relative importance of each parameter in the variance of IOP. The results in Fig2a suggest that IOP is strongly influenced by BP and Δπ and mildly influenced by the level of L, C and EVP in HI. OHT patients, Fig2b, show a stronger dependence on BP and Δπ and a weaker dependence on L, C and EVP of IOP than HI.
The proposed model suggests that the outcomes of IOP lowering treatments might depend on the initial IOP level of the patient and on its individual clinical condition. The model identifies the strong influence of BP and Δπ and the mild influence of L, C and EVP on the level of IOP. Model predictions in synergy with clinical and animal studies could help unravel the complex relationship between the parameters involved and contribute to the formulation of patient specific treatments.
This is an abstract that was submitted for the 2016 ARVO Annual Meeting, held in Seattle, Wash., May 1-5, 2016.
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