Changes in brain cell shape create residual extracellular space volume and explain tortuosity behavior during osmotic challenge

Abstract

Diffusion of molecules in brain extracellular space is constrained by two macroscopic parameters, tortuosity factor and volume fraction ␣. Recent studies in brain slices show that when osmolarity is reduced, increases while ␣ decreases. In contrast, with increased osmolarity, ␣ increases, but attains a plateau. Using homogenization theory and a variety of lattice models, we found that the plateau behavior of can be explained if the shape of brain cells changes nonuniformly during the shrinking or swelling induced by osmotic challenge. The nonuniform cellular shrinkage creates residual extracellular space that temporarily traps diffusing molecules, thus impeding the macroscopic diffusion. The paper also discusses the definition of tortuosity and its independence of the measurement frame of reference.diffusion ͉ lattice ͉ volume transmission ͉ cell swelling and shrinkage ͉ numerical simulation M any biological processes involve diffusion of substances through a disordered heterogeneous medium. Diverse examples are intracellular signaling (1), intercellular signaling (2), volume transmission (3, 4), and drug delivery (5, 6). The rapid increase in the use of diffusion-weighted MRI has raised further issues about diffusion in tissues (7). In approaching such problems, two essential parameters are the extracellular space (ECS) volume fraction ␣, the volume ratio of the ECS compared to the whole tissue, and the tortuosity , a measure of how diffusing molecules are hindered by cellular obstructions. Recent studies by using osmotic challenge in brain tissue (8, 9) have shown a complex relation between these two parameters. In this paper, we apply the mathematical technique of homogenization to show that changes in cell shape provide an explanation for osmotic data and are likely to be applicable in a much wider context.To quantify diffusion in a complex biological medium, it is necessary to apply the diffusion equation through the use of some macroscopically effective properties, such as the local average concentration, ͗C͘, and the apparent (or effective) diffusion coefficient, D*. Such macroscopic formulations have been applied successfully in the ECS of brain tissues (8-15). When discussing the ECS, 2 is frequently defined as the ratio between the diffusion coefficient, D, of a given molecule in a bulk liquid and the apparent diffusion coefficient D* of the same molecule in the ECS,although other definitions have been used. Furthermore, some authors (16-18) include terms for viscosity of the ECS and hydrodynamic interaction of the diffusing molecule in their definition of ; we exclude such factors here, to focus on the relationship between geometry and tortuosity, but briefly discuss them later in the paper and in the Appendix, which also comments on the independence of tortuosity from its measurement frame of reference.The question of whether and ␣ are related has been explored in many contexts, but because it depends on the structure of the heterogeneous medium, no universal relationship is known. It is expected tha...

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