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The ability of a cell to keep its volume constant irrespective of intra- and extracellular conditions is essential for cellular homeostasis and survival. The purpose of this study is to elaborate a theoretical model of cell volume homeostasis and to apply it to a simulation of human aqueous humor (AH) production. The model assumes a cell with a spherical shape and only radial deformation satisfying the property that the cell volume in rest conditions equals that of the cell couplets constituting the ciliary epithelium of the human eye. The cytoplasm is described as a homogeneous mixture containing fluid, ions, and neutral solutes whose evolution is determined by net production mechanisms occurring in the intracellular volume and by water and solute exchange across the membrane. Averaging the balance equations over the cell volume leads to a coupled system of nonlinear ordinary differential equations (ODEs) which are solved using the θ-method and the Matlab function ode15s. Simulation tests are conducted to characterize the set of parameters corresponding to baseline conditions in AH production. The model is subsequently used to investigate the relative importance of (a) impermeant charged proteins; (b) sodium–potassium (Na+/K+) pumps; (c) carbonic anhydrase (CA) in the AH production process; and (d) intraocular pressure. Results suggest that (a) and (b) play a role; (c) lacks significant weight, at least for low carbon dioxide values; and (d) plays a role for the elevated values of intraocular pressure. Model results describe a higher impact from charged proteins and Na+/K+ ATPase than CA on AH production and cellular volume. The computational virtual laboratory provides a method to further test in vivo experiments and machine learning-based data analysis toward the prevention and cure of ocular diseases such as glaucoma. 

In this article, we propose a theoretical model leveraging the analogy between fluid and electric variables to investigate the relation among aqueous humor (AH) circulation and drainage and intraocular pressure (IOP), the principal established risk factor of severe neuropathologies of the optic nerve such as glaucoma. IOP is the steady-state result of the balance among AH secretion (AHs), circulation (AHc), and drainage (AHd). AHs are modeled as a given volumetric flow rate electrically corresponding to an input current source. AHc is modeled by the series of two linear hydraulic conductances (HCs) representing the posterior and anterior chambers. AHd is modeled by the parallel of three HCs: a linear HC for the conventional adaptive route (ConvAR), a nonlinear HC for the hydraulic component of the unconventional adaptive route (UncAR), and a nonlinear HC for the drug-dependent component of the UncAR. The proposed model is implemented in a computational virtual laboratory to study the value attained by the IOP under physiological and pathological conditions. Simulation results (i) confirm the conjecture that the UncAR acts as a relief valve under pathological conditions, (ii) indicate that the drug-dependent AR is the major opponent to IOP increase in the case of elevated trabecular meshwork resistance, and (iii) support the use of the model as a quantitative tool to complement in vivo studies and help design and optimize medications for ocular diseases. 

Abstract The retinal tissue is highly metabolically active and is responsible for translating the visual stimuli into electrical signals to be delivered to the brain. A complex vascular structure ensures an adequate supply of blood and oxygen, which is essential for the function and survival of the retinal tissue. To date, a complete understanding of the configuration of the retinal vascular structures is still lacking. Optical coherence tomography angiography has made available a huge amount of imaging data regarding the main retinal capillary plexuses, namely the superficial capillary plexuses (SCP), intermediate capillary plexuses (ICP) and deep capillary plexuses (DCP). However, the interpretation of these data is still controversial. In particular, the question of whether the three capillary plexuses are connected in series or in parallel remains a matter of debate. In this work, we address this question by utilizing a multi-scale/multi-physics mathematical model to quantify the impact of the two hypothesized vascular configurations on retinal hemodynamics and oxygenation. The response to central retinal vein occlusion (CRVO) and intraocular pressure (IOP) elevation is also simulated depending on whether the capillary plexuses are connected in series or in parallel. The simulation results show the following: (i) in the in series configuration, the plexuses exhibit a differential response, with DCP and ICP experiencing larger pressure drops than SCP; and (ii) in the in parallel configuration, the blood flow redistributes uniformly in the three plexuses. The different vascular configurations show different responses also in terms of oxygen profiles: (i) in the in series configuration, the outer nuclear layer, outer plexiform layer and inner nuclear layer (INL) are those most affected by CRVO and IOP elevation; and (ii) in the in parallel configuration the INL and ganglion cell layer are those most affected. The in series results are consistent with studies on paracentral acute middle maculopathy, secondary to CRVO and with studies on IOP elevation, in which DCP and ICP and the retinal tissues surrounding them are those most affected by ischemia. These findings seem to suggest that the in series configuration better describes the physiology of the vascular retinal capillary network in health and disease.