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 when there is not any electrical activity in either the cells or the externally 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 that incorporate local geometrical properties such as connectivity and pore size. In this paper, we study the effects of these geometrical properties in mimicking the experimental situation in the brain. We build a lattice cellular automata model for ion diffusion within the brain-cell microenvironment and perform numerical simulations using the corresponding lattice Boltzmann equation. In this model, particle injection mimics extracellular ion injection from a microelectrode in experiments. As an application of the model, we combine the results from the simulations with porous media theory to compute tortuosities and volume fractions for various regular and irregular porous media. Porous media theory previously had been combined with diffusion experiments in brain tissue to determine tortuosity and volume fraction. As in the case of the diffusion experiments, porous media theory gives a good approximation to the numerical simulations. We conclude that the lattice Boltzmann equation can accurately describe ion diffusion in the extracellular space of brain tissue.