Mathematical analysis of transport and consumption of molecules in heterogeneous brain tissue (methodology)

A computer model of metabolite transport and consumption in heterogeneous brain tissue, using a combination of probabilistic and deterministic techniques is being developed. The metabolites are put into two separate classes: (I) those that have reached a membrane for the first time during a small time step, delta t, and (II) those that have not yet reached a cell membrane for the first time during that time step. The time dependent spatial distribution of class (I) molecules is determined using random walk theory, which takes into account the actual paths of the molecules. The variation of the spatial distribution of class (II) molecules with time is determined using the time dependent diffusion equation with a boundary condition of zero concentration on the enclosing membrane boundaries.