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Giovanna Guidoboni, Alon Harris, Brent Siesky, Christophe Prud'homme, Riccardo Sacco, Marcela Szopos; Influence of blood pressure and vascular resistance on the response to medications lowering intraocular pressure: a mathematical model. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):5820.
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© ARVO (1962-2015); The Authors (2016-present)
Elevated intraocular pressure (IOP) can be reduced via medications modulating aqueous humor (AH) flow, but the drug efficacy varies significantly among patients. Many factors may influence drug efficacy, including mean arterial pressure (MAP) and systemic vascular resistance (sVR). Here we propose a mathematical model to theoretically investigate the individual roles played by MAP and sVR on the response to IOP-lowering medications.
Two models for retinal circulation and AH flow are combined to compute IOP, retinal vascular resistance (Rret) and retinal blood flow (RBF) given inflow permeability (Lin) and outflow resistance (Rout) to AH flow. In the model, changes in Lin and Rout lead to changes in IOP, which, in turn, alter Rret directly (IOP compression on the retinal vessels) and indirectly (IOP-induced compression of the lamina cribrosa on the central retinal vessels), ultimately leading to changes in RBF (Fig1). Blood pressure in the ciliary body (Pcb) and in the ophthalmic artery (Poa) are defined as Pcb = α MAP and Poa = β MAP, α and β being reduction factors accounting for sVR.
At baseline, Lin = 0.3 (mmHg min)-1 mm3, Rout = 3.5 mmHg min mm-3, α = 1/3 and β = 2/3. Conditions of low, normal and high blood pressure (LBP, NBP and HBP) are modeled by setting MAP = 80, 93.3 and 106.7 mmHg. Fig1 shows IOP, Rret and RBF computed for LBP, NBP and HBP cases as Lin varies between 0.1 and 0.5 (mmHg min)-1 mm3 and Rout varies between 2.5 and 5.5 mmHg min mm-3. Fig2 shows the first-order indices quantifying the sensitivity of Rret α and β treated as random variables with uniform distribution. The model predicts that: 1) IOP reductions are steeper when Lin is reduced (rather than Rout) for all the MAP levels; 2) the higher is the MAP the larger are the IOP reductions; 3) the sensitivity of Rret to changes in α and β, thus sVR, is not always monotone and its magnitude depends on MAP.
The model suggests that: 1) overall reducing AH inflow seems more effective than increasing AH outflow; 2) drug efficacy depends on MAP; and 3) changes in retinal hemodynamics following IOP-lowering medications differ depending on the patient-specific MAP and sVR. These findings are clinically important as MAP and sVR may be altered in patients with systemic hypertension, a highly prevalent disease within the glaucomatous population worldwide.
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