RANDOM-WALK MODEL OF DIFFUSION IN 3-DIMENSIONS IN BRAIN EXTRACELLULAR SPACE: COMPARISON WITH MICROFIBEROPTIC PHOTOBLEACHING MEASUREMENTS

¹ University of California-San Francisco
² UCSF
³ Univ. of California - SF

^* To whom correspondence should be addressed. E-mail: verkman{at}itsa.ucsf.edu.

Submitted on February 14, 2008
Revised on March 12, 2008
Accepted on 25 March 2008

	Abstract

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises ~20% of brain parenchymal volume and contains cell-cell gaps ~50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in 3-dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (), cell size, cell-cell gap geometry, intercellular 'lake' (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water vs. brain ECS (D_o/D). Experimental D_o/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D_o/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling following water intoxication. D_o/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D_o/D using realistic , cell size and cell-cell gap required the presence of intercellular 'lakes' at multi-cell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted Do/D for different solute sizes. Also, the modeling revealed unanticipated effects on D_o/D of changing ECS and cell dimensions that implicated 'solute trapping' by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.

Key Words: 3D modeling, Brain ECS diffusion, intracellular lake, microfiberoptic epifluorescence photobleaching, tortuosity