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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. 

Recent data across the globe indicates a decline in stem competency among secondary education students. Despite persistent interest in STEM fields this decrease in preparedness could yield detrimental effects for both future scientists and engineers. To address this current trend, a collaborative partnership between a university and high school commenced. The goal was to create an advanced experiential engineering course focused primarily on ophthalmology principles, research, and hands-on solutions. Twenty-one high school students (grades 9-12) enrolled in the course. Their objective was to investigate research questions involving ocular physiology. These ranged from surveying intraocular pressure measurement methods, examining the nature of vitreous humor properties, and investigating the inherent connection between blood flow and fluid dynamics. Furthermore, students engaged in hands-on experimentation that resulted in a hydraulics-based model which attempted to link the correlation between blood pressure and intraocular pressure involved in glaucoma progression. Post-course interviews revealed three major themes: i) an increased appreciation for the utility of mathematics and its real-world use; ii) the importance of the mentor-mentee relationship and professional networking; and iii) increased access to resources beyond what is traditionally found in a high school classroom. These findings suggest that incorporating research into a high school classroom can foster positive outcomes and spark students’ interest in ophthalmology research and in STEM more broadly. This course can serve as a model in future development of project-based engineering curriculum and help broaden participation in STEM. 

In biomechanics, local phenomena, such as tissue perfusion, are strictly related to the global features of the surrounding blood circulation. In this paper, we propose a heterogeneous model where a local, accurate, 3D description of tissue perfusion by means of fluid flows through deformable porous media equations is coupled with a systemic, 0D, lumped model of the remainder of the circulation, where the fluid flow through a vascular network is described via its analog with a current flowing through an electric circuit. This represents a multiscale strategy, which couples an initial boundary value problem to be used in a specific tissue region with an initial value problem in the surrounding circulatory system. This PDE/ODE coupling leads to interface conditions enforcing the continuity of mass and the balance of stresses across models at different scales, and careful consideration is taken to address this interface mismatch. The resulting system involves PDEs of mixed type with interface conditions depending on nonlinear ODEs. A new result on local existence of solutions for this multiscale interface coupling is provided in this article.