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Three-Dimensional Modeling of the Brain's ECS by Minimum Configurational Energy Packing of Fluid Vesicles

Ravi K. Nandigam ^* and Daniel M. Kroll 

^* School of Chemical Engineering, Purdue University, West Lafayette, Indiana; and Department of Physics, North Dakota State University, Fargo, North Dakota

Correspondence: Address reprint requests to D. M. Kroll, Tel.: 701-231-8968 or 231-8974; E-mail: daniel.kroll{at}ndsu.edu.

The extracellular space of the brain is the heterogeneous porous medium formed by the spaces between the brain cells. Diffusion in this interstitial space is the mechanism by which glucose and oxygen are delivered to the brain cells from the vascular system. It is also a medium for the transport of certain informational substances between the cells (called volume transmission), and for drug delivery. This work involves three-dimensional modeling of the extracellular space as void space in close-packed arrays of fluid membrane vesicles. These packings are generated by minimizing the configurational energy using a Monte Carlo procedure. Both regular and random packs of vesicles are considered. A random walk algorithm is then used to compute the geometric tortuosities, and the results are compared with published experimental data. For the random packings, it is found that although the absolute values for the tortuosities differ, the dependence of the tortuosity on pore volume fraction is very similar to that observed in experiment. The tortuosities we measure are larger than those computed in previous studies of packings of convex polytopes, and modeling improvements, which require higher resolution studies and an improved modeling of brain cell shapes and mechanical properties, could help resolve remaining discrepancies between model simulations and experiment. It is also shown that the specular reflection scheme is the appropriate technique for implementing zero-flux boundary conditions in random walk simulations commonly encountered in diffusion problems.

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