A lattice cellular automata model for ion diffusion in the brain-cell microenvironment and determination of tortuosity and volume fraction

In the brain-cell microenvironment, the movement of ions is by diffusion wh en there is not any electrical activity in either the cells or the external ly applied electric field. In this complex medium, the primary constraints on long-range diffusion are due to the geometrical properties of the medium , especially tortuosity and volume fraction, which are lumped parameters th at incorporate local geometrical properties such as connectivity and pore s ize. In this paper, we study the effects of these geometrical properties in mimicking the experimental situation in the brain. We build a lattice cell ular automata model for ion diffusion within the brain-cell microenvironmen t and perform numerical simulations using the corresponding lattice Boltzma nn equation. In this model, particle injection mimics extracellular ion inj ection from a microelectrode in experiments. As an application of the model , we combine the results from the simulations with porous media theory to c ompute tortuosities and volume fractions for various regular and irregular porous media. Porous media theory previously had been combined with diffusi on experiments in brain tissue to determine tortuosity and volume fraction. As in the case of the diffusion experiments, porous media theory gives a g ood approximation to the numerical simulations. We conclude that the lattic e Boltzmann equation can accurately describe ion diffusion in the extracell ular space of brain tissue.