Research Interests
In the brain-cell microenvironment, the movements of ions such as TMA and TEA is by diffusion when there is neither any electrical activity in the cells nor externally applied electric field. In this complex medium, several factors can impose constraints on long-range diffusion. The primary constraints are due to the geometrical factors of the medium, especially tortuosity and volume fraction. The tortuosity and the volume fraction are lumped parameters that incorporate geometrical properties such as connectivity and pore size. First, we study the effects of these geometrical properties on the tortuosity and the volume fraction. In mimicking the real experimental situation in the brain. We build a lattice cellular automata model, called the lattice Boltzmann equation, for ion diffusion within the brain-cell microenvironment and perform numerical simulations on this model. In the model, particle injection is introduced to match the experimental situation of ion injection through a microelectrode. 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, and a possible relationship between the volume fraction and the tortuosity is also investigated. 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.
In the brain, many important ions, such as potassium, not only move by diffusion, but the movement of ions is constrained by many mechanisms such as extra- and intracellular diffusion, active and passive transport across the cell membrane. The movement of the electric charged potassium is also subject to the electric gradients and the spatial buffering mechanism. In addition, the geometrical factors of the brain-cell microenvironment can impose constraints on the diffusion process. It is difficult to study such a complex system using conventional methods such as the cable theory. Therefore, we build a lattice Boltzmann microscopic level model for this system. The evolution of the model consists of three successive operations, particle injection, collision and propagation. Those mechanisms affecting the movement of potassium are incorporated into the model by suitable choices of the injection and the collision operations, while the geometrical factors such as tortuosity and volume fraction are incorporated into the model by a suitable choice of the brain tissue as a porous medium based on our previous results on the calculation of tortuosity and volume fraction. Numerical simulations on this model are performed and the numerical results on the artificial brain as a porous medium reproduce quantitatively and qualitatively the behavior of the potassium obtained from the experiments within the brain tissue. As applications of the model, we study the effects of each specific mechanism on the potassium movement within the brain-cell microenvironment by artificially turning on or off the mechanism and the effects of geometrical factors on the potassium movement by varying the geometrical properties of the medium. which is hard to achieve by the experiment on the brain tissue.
The brain can be thought of as a porous medium, we study the migration of substances in the brain by using the volume-averaging theory developed for the flow of porous media.
The ICS calcium movement in the brain is very important, we will study the calcium waves in the brain by using the lattice Boltzmann equations.
All of those computations are intended to be done in both two- and three-dimensions and we wish to visualize the results. Many computations have been performed on an HP735/125 computer. However, the limitations in speed and storage size have prevented realistic computations. The use of the vector supercomputer will allow me to perform a lot of computations with large lattice size and use algorithms for the lattice gas and lattice Boltzmann methods in parallel form. This is also my dream.
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