A Bidomain Model for Lens Microcirculation

Abstract

There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the “brain.” Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.

Type
Publication
Biophysical Journal (116)
Shixin Xu
Shixin Xu
Assistant Professor

Shixin Xu is an Assistant Professor of Mathematics at Duke Kunshan University. His research interests are machine learning and data-driven models for diseases, multiscale modeling of complex fluids, homogenization theory, and numerical analysis. Xu has a B.Sc. in mathematics (honors) from Ocean University of China and a Ph.D. in mathematics from the University of Science and Technology China. From 2013 to 2017, he held postdoctoral positions at the National University of Singapore, the University of Notre Dame, the University of California, Riverside, and the Fields Institute for Research in Mathematical Sciences, Canada.

Huaxiong Huang
Huaxiong Huang
Professor

Huaxiong Huang is Professor of Mathematics at the York University. He is VP (Academic) and Executive Director of Research Center of Mathematics (Zhuhai, China). He has served as Deputy Director of the Fields Institute and Director of the Fields Centre for Quantitative Analysis and Modelling. His wide array of publications in applied mathematics focus on fluid mechanics and scientific computing, finance, biology, physiology, energy and medicine.