A Bidomain Model for Lens Microcirculation

TL;DR

This paper introduces a comprehensive non-electro-neutral model for lens microcirculation, linking historical analytical models with recent computational approaches, and simplifies it while preserving key features.

Contribution

It presents a new general model for lens microcirculation that bridges older analytical models and modern computational models, validated through asymptotic analysis.

Findings

The simplified model aligns with recent computational results.

The full model is consistent with advanced computational models.

The simplified model captures main features of the full model.

Abstract

There exists a large body of research on the lens of mammalian eye over the past several decades. The objective of the current work is to provide a link between the most recent computational models to some of the pioneering work in the 1970s and 80s. We introduce a general non-electro-neutral model to study the microcirculation in lens of eyes. It describes the steady state relationships among ion fluxes, 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 while our full model is consistent with the most recent computational models. In addition, our simplified model captures the main features of the full model. Our results serve as a useful link intermediate between the computational models and the first generation analytical models.