Electro-fluid dynamics of aqueous humor production: simulations and new directions.

Purpose: to theoretically investigate the role of bicarbonate ion (HCO− 3 ) on the nonpigmented transepithelial potential di erence Vm, the sodium potassium pump (Na/K) and the active secretion of aqueous humor. Methods: a three-dimensional mathematical model is proposed to isolate the roles of HCO− 3 and Na+, which are di icult to investigate experimentally. The model combines the velocity-extended Poisson-Nernst-Planck equations to describe ion electrodi usion and the Stokes equations to describe aqueous humor flow into the basolateral space adjacent to the nonpigmented ephitelial cells. Results: Computations show that Vm is close to baseline experimental measurements (on monkeys) in the range [−2.7, −2.3]mV only if HCO− 3 is included in the simulation. The model is also capable of reproducing the flow of Na+ exiting the cell and the flow of K+ entering the cell, in accordance with the physiology of the Na/K pump. The simulated Na/K ratio is 1.53, which is in very good agreement with the theoretical value of 1.5. Conclusion: Model simulations suggest that HCO− 3 inhibition may prevent physiologically correct baseline values of the nonpigmented transepithelial potential di erence and Na/K ATPase function. This may provide useful indication in the design of medications that decrease the active secretion of aqueous humor, and supports the advantage of using mathematical models as a noninvasive complement of animal models

Analysis of IOP and CSF alterations on ocular biomechanics and lamina cribrosa hemodynamics

Purpose : Optic neuropathies such as normal-tension glaucoma(NTG) may be caused by pathogenic translaminar pressure difference(TLPd). This mechanistically may lead to an improper perfusion of lamina cribrosa(LC) and alter the natural biomechanics of the eye. LC perfusion parameters are difficult to estimate with non-invasive measurements and the interaction between hemodynamics and biomechanics is affected by many factors that cannot be easily isolated. We employ a mathematical virtual simulator(MVS) to disentangle biomechanical and hemodynamical factors, in particular the system response to intraocular pressure(IOP) and retrolaminar tissue pressure(RLTp) alterations. Methods : The MVS(Fig. 1b) combines i) a three-dimensional porous-media model for LC perfusion with ii) a circuit-based model for blood flow in retrobulbar and ocular posterior segments and iii) a three-dimensional elastic model to simulate the biomechanics of LC, retina, choroid, sclera and cornea. Systems i), ii) and iii) are solved using advanced computational and visualization methods (Feel++, OpenModelica). We simulate 5 different virtual situations: baseline(IOP=15,RLTp=7,TLPd=8 [mmHg]), patient1(P1,IOP=11,RLTp=10,TLPd=1 [mmHg]), patient2(P2,IOP=17,RLTp=10,TLPd=7 [mmHg]), patient3(P3,IOP=17,RLTp=3,TLPd=14 [mmHg]) and patient4(P4,IOP=11,RLTp=3,TLPd=8 [mmHg]). Results : Baseline, P2 and P4 have similar TLPd, however Fig. 1c shows a difference up to 10% in LC perfusion. Fig. 1a displays a 1.4% discrepancy in the blood pressure gradient, whereas Fig. 2 exhibits analogous LC displacements for these three cases. Thus, MVS suggests that this difference may be primarily due to hemodynamical factors. RLTp variations do not seem to have notable effects on the velocity of central retinal artery(CRA) and the central retinal vein(CRV) both pre- and post-lamina(Fig. 1d-e), whereas small fluctuations occur in the CRV velocity due to higher IOP(P2,P3). Conclusions : In the context of glaucoma, particularly NTG, the proposed MVS multi-scale approach may be employed to single out hemodynamic and/or biomechanical mechanisms involved in the pathophysiology of ocular disease. This innovation may also allow for novel findings in IOP regulation and RLTp effects in central retinal vein occlusion. This is an abstract that was submitted for the 2018 ARVO Annual Meeting, held in Honolulu, Hawaii, April 29 - May 3, 2018