Reduced-Order Model for Cell Volume Homeostasis: Application to Aqueous Humor Production

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 the simulation of human aqueous humor (AH) production. The model assumes a cell with a spherical shape and only radial deformation. 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 (ODE) 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; and (c) carbonic anhydrase (CA) in the AH production process. Results suggest that (a) and (b) play a role whereas (c) does lack significant weight, at least for low carbon dioxide values. 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 towards the prevention and cure of ocular diseases such as glaucoma.