June 2020
Volume 61, Issue 7
Open Access
ARVO Annual Meeting Abstract  |   June 2020
A mathematically-based virtual laboratory for the study of the role of electroneutrality in aqueous humor production
Author Affiliations & Notes
  • Riccardo Sacco
    Mathematics, Politecnico di Milano, Italy, Milan, Italy
  • Alon Harris
    Department of Ophthalmology, Mount Sinai Hospital, New York, New York, United States
  • Giovanna Guidoboni
    Mathematics, University of Missouri, Columbia, Missouri, United States
  • Brent A Siesky
    Department of Ophthalmology, Mount Sinai Hospital, New York, New York, United States
  • Joseph W. Jerome
    Mathematics, George Washington University, Washington, District of Columbia, United States
  • Giulio Bonifazi
    Basque Center for Applied Mathematics, Bilbao, Spain
  • Nicholas Marazzi
    Mathematics, University of Missouri, Columbia, Missouri, United States
  • Matthew Lang
    Indiana University, School of Medicine, Columbia, Missouri, United States
  • Alice Verticchio Vercellin
    Department of Ophthalmology, Mount Sinai Hospital, New York, New York, United States
  • Footnotes
    Commercial Relationships   Riccardo Sacco, None; Alon Harris, AdOM (C), AdOM (I), AdOM (S), AdOM (R), LuSeed (I), Oxymap (I), Thea (R); Giovanna Guidoboni, Foresite LLC (C), Gspace LLC (I); Brent Siesky, None; Joseph Jerome, None; Giulio Bonifazi, None; Nicholas Marazzi, None; Matthew Lang, None; Alice Verticchio Vercellin, None
  • Footnotes
    Support  None
Investigative Ophthalmology & Visual Science June 2020, Vol.61, 4632. doi:
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      Riccardo Sacco, Alon Harris, Giovanna Guidoboni, Brent A Siesky, Joseph W. Jerome, Giulio Bonifazi, Nicholas Marazzi, Matthew Lang, Alice Verticchio Vercellin; A mathematically-based virtual laboratory for the study of the role of electroneutrality in aqueous humor production. Invest. Ophthalmol. Vis. Sci. 2020;61(7):4632.

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      © ARVO (1962-2015); The Authors (2016-present)

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Abstract

Purpose :
Elevated intraocular pressure (IOP) is an established risk factor for glaucoma. Steady-state IOP is determined by aqueous humor (AH) production (AHp) and drainage. AHp is mainly due to passive fluid motion resulting from ion osmotic gradient into the basolateral (BL) space between nonpigmented epithelial cells (NPECs). Electrochemical conditions in NPE and BL are difficult to access experimentally, thus, we propose a mathematical model to investigate to which extent deviations from solution electroneutrality may affect AHp.

Methods :
AHp is described by the Velocity-Extended Poisson-Nernst-Planck model for ion and fluid mass and momentum in the BL space. Ions are subject to injection sources distributed along BL walls. AH is subject to osmotic pressure difference across the BL walls. Na+ and Cl- ion motion is studied, whereas K+, HCO3- and a buffer X (cation in NPE, anion in BL) are added to enforce electroneutrality at baseline. Simulations are performed to assess the effect of (a) K+ = HCO3- = 0; (b) HCO3- = 0; (c) K+ = 0, and (d) including both K+ and HCO3-. In all cases, contribution of X is accounted for in the model.

Results :
Fig.1 shows the spatial distribution of AH volumetric flow rate Q as a function of the fixed ions. Model seems to indicate that K+ plays a crucial role in reducing Q. Results also show an interval in the BL with backward AH flow when HCO3- is included. Fig. 2 shows the spatial distribution of total space charge density ρ as a function of the fixed ions. Results seem to indicate that the solution deviates more significantly from local electroneutrality when AH flow is reduced.

Conclusions :
Model predictions suggest that inhibition of HCO3- ion secretion into the BL space of ciliary epithelium may prevent AH overproduction. while K+ secretion into the BL space seems to favor AH reduction. These results may help design IOP lowering medications to decrease AHp and support the advantage of a mathematical virual laboratory as a noninvasive complement of the animal model.

This is a 2020 ARVO Annual Meeting abstract.

 

Fig. 1. AH volumetric flow rate. AH continuously flows from stroma to posterior chamber only if K+ is included (yellow and red dashed lines). If HCO3- is included (blue line), AH backward flow occurs for 0 < x < 3.5 μm.

Fig. 1. AH volumetric flow rate. AH continuously flows from stroma to posterior chamber only if K+ is included (yellow and red dashed lines). If HCO3- is included (blue line), AH backward flow occurs for 0 < x < 3.5 μm.

 

Fig. 2. Space charge density ρ. A larger ρ means a larger deviation from local electroneutrality. AHp is reduced when the BL solution is far from electroneutrality.

Fig. 2. Space charge density ρ. A larger ρ means a larger deviation from local electroneutrality. AHp is reduced when the BL solution is far from electroneutrality.

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