A Bidomain Model for Lens Microcirculation

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 and 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. 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, like 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. convection to bring materials close enough to cells so diffusion to and across cell membranes can provide what the cell needs to live.The circulatory system of blood vessels-arteries, veins, and capillaries-provides the convection in almost all tissues. But there is one clear exception, the lens of the (mammalian) eye. The lens does not have blood vessels, presumably because even capillaries would so seriously interfere with transparency. The lens is large, much larger than the length scale on which diffusion itself is efficient. The lens must provide nutrients through another kind of convection, a microcirculation of water that moves nutrients into the lens and rinses wastes out of it. The microcirculation is in fact driven by the lens itself, without an external 'pump'. The lens is itself an osmotic pump.The lens is an asymmetrical electrical syncytium in which all cells are electrically coupled one to another, with a narrow extracellular space between the cells (see Fig.1). The extracellular space is filled with ionic solution in free diffusion with the plasma outside cells. It may also contain specialized more or less immobile proteins and specialized polysaccharides, as well as containing obstructions formed by the connexin proteins themselves. The intracellular space behaves very much as a large single cell would, with the bio-ions of classical electro-physiology (Na + , K + , Cl − ) free to move without much resistance from cell to cell, and many solutes of significant size (say with diameter less than 1.5 nm) able to move as well. The i...

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

“…The motion of water molecules, i.e., the osmosis of water [ 147 , 148 ] is directly controlled by the steric potential in our model and their distributions are expressed by . Nevertheless, this motion is still implicitly changed by the electric potential via the correlated motion of ions described by other in the void fraction function and hence in the charge density in ( 17 ).…”

Homogenization Theory of Ion Transportation in Multicellular Tissue

“…In this case, the intracellular could indirectly communicate through the connected extracellular space. Our macroscale model could be used to study some diseases induced by ion micro-circulation disorder, like spreading depression [11] and lens problems [49].…”

“…• The second part is the current induced by the active pumps on the membrane. Here we only consider the N a + /K + pumps [49].…”

Connexin Gap Junctions and Hemichannels in Modulating Lens Redox Homeostasis and Oxidative Stress in Cataractogenesis

“…Studies show that gap junction conductance plays an important role in the microcirculation of the lens and that GJIC modulates lens microcirculation through lens intracellular hydrostatic pressure. [ 30 , 31 , 32 ]. Ebihara et al [ 33 ] report that Cx46 HCs may play an important role in the lens internal circulation system by allowing the entry of sodium from the extracellular space into lens fiber cells.…”