Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

MIDIT                               OFD                           CATS
Modelling, Nonlinear Dynamics       Optics and Fluid Dynamics     Chaos and Turbulence Studies
and Irreversible Thermodynamics     Risø National Laboratory      Niels Bohr Institute and 
Technical University of Denmark     Building 128                  Department of Chemistry
Building 321                        P.O. Box 49                   University of Copenhagen 
DK-2800 Lyngby                      DK-4000 Roskilde              DK-2100 Copenhagen Ø
Denmark                             Denmark                       Denmark


by Robert M. Miura
Department of Mathematics,
University of British Columbia
Vancouver, B.C.

MIDIT-seminar 460

Thursday July 22, 1999, 15.00 h
at MIDIT, IMM Building 305, room 027

Abstract: In the brain-cell microenvironment, ions move by diffusion in the intra- and extracellular spaces and by passive and active transport mechanisms when passing through membranes in the absence of macroscopic electrical effects. 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; therefore, we build a simple microscopic level lattice Boltzmann equation 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 ions are incorporated into the model by suitable choices of the injection and 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. Mimicking some experiments on brain tissue, numerical simulations on this model are performed, and the numerical results on the artificial brain as a porous medium reproduce qualitatively the behavior of ion movements obtained from experiments. As applications of the model, we study the effects of each specific mechanism on potassium movement by artificially turning it on or off and the effects of geometrical factors on the potassium movement by varying the geometrical properties of the medium.