Diffusion in the ECS obeys Fick’s law, subject to three important modifications. First, diffusion in the ECS is constrained by the restricted volume of the tissue available for diffusing particles, i.e. by the extracellular volume fraction (a). Second, the free diffusion coefficient, D, is reduced by the square of the tortuosity (l) to an apparent diffusion coefficient ADC = D/l², due to an increase in the path length for diffusion between two points and because the diffusing substance encounters membrane obstructions, glycoproteins, macromolecules of the extracellular matrix, charged molecules and glial cell processes. Third, the diffusion of substances may be affected by nonspecific uptake, k´, a factor describing the loss of a substance across cell membranes. If we incorporate factors a, l and k´ into Fick’s laws, diffusion in the CNS is described fairly satisfactorily.

Studies in our laboratories have shown that the extracellular volume fraction changes during development, being about twice as large in the cortex and corpus callosum of newborn rats as in adults. The large ECS in the developing CNS might allow for the more effective diffusion of macromolecules, such as growth factors and cytokines. The reduction in ECS volume fraction with increasing age correlates well with gliogenesis and myelination. Changes in the membrane currents of glial cells associated with myelination have also been correlated with ECS diffusion parameters.

Extracellular space diffusion parameters were studied during aging. Aged rats were classified according to their performance during place learning, and two groups, good and bad learners, were selected. Diffusion measurements were performed along three orthogonal axes. The volume fraction and nonspecific uptake were significantly lower in both aged groups than in young adults. In young adults and good learners, anisotropy was found in the hippocampus; the anisotropy was lost in bad learners. The loss of anisotropy in the hippocampus of aged bad learners corresponded to the disorganization of glial processes and a loss of extracellular matrix (fibronectin and chondroitin sulfate proteoglycan). The significant differences in diffusion parameters between good and bad learners in the CA3 and DG regions of the hippocampus may affect LTP, memory and learning.
 
 

GFAP staining in the hippocampus of a young adult and aged rat showing the disorganization of parallel glial processes during aging.

During hypoxia, our experiments have revealed that a dramatically decreases, while l significantly increases. The time course of the changes is about ten times slower in neonatal rats than in adults, correlating with the well-known resistance of the immature CNS to anoxia. These changes in diffusion parameters during and after ischemia enhance the accumulation of substances, contributing to brain damage and hindering the influx of metabolic substances during any subsequent reperfusion. Diffusion-weighted MRI studies  have shown that the apparent diffusion coefficient of water is dramatically reduced during anoxia and ischemia, with a time course that correlates well with the observed changes in a and l. Further experiments are aimed at elucidating the mechanism underlying these changes in water diffusion during anoxia.
 

Brain injury, with consequent neuronal death and astrogliosis, results in changes in CNS architecture. Changes in diffusion parameters in experimental models of injury and regeneration such as stab wounds and radiation necrosis have been compared with histopathological changes in order to elucidate their possible mechanisms. Experimental animal models have revealed that in the vicinity of the injury, ECS volume and the apparent diffusion coefficients of both water (ADC_w) and tetramethylammonium (ADC_TMA) are decreased due to cell death and astrogliosis. In the lateral region of the ipsilateral cortex, where no changes in ECS volume are found, prominent increases in extracellular matrix expression (chondroitin sulfate proteoglycan) are seen along with decreases of both ADC_w and ADC_TMA. This shows that the apparent diffusion coefficient of water is affected by diffusion barriers resulting from an increase in extracellular matrix.

Following intracerebral bacterial inoculation, acute inflammation and increased blood-brain barrier permeability occurs, resulting in moderate changes in ECS diffusion parameters. More dramatic changes, particularly an increase in extracellular space volume, were seen in our studies utilizing an animal model of the demyelinating disease multiple sclerosis, experimental autoimmune encephalomyelitis, induced by an injection of myelin basic protein.

Recent experiments in the Department have used the 6-OHDA-lesion rat model of Parkinson’s disease to study two different grafting techniques and their influence on ECS diffusion parameters. Micrografting involves the transplantation of fetal dopaminergic cells into a number of small deposits in the striatum, while macrografting uses a single, larger deposit. We found a functional recovery, good survival of tyrosine hydroxylase-positive cells and astrogliosis in rats 3-5 months after grafting. Grafts were localized by T2 or diffusion-weighted NMR, and ECS diffusion parameters were investigated in the striatum. Tortuosity increased in the grafts and the adjacent tissue. The increase in ECS diffusion barriers corresponded to the astrogliosis in and around the grafts. The increased extracellular tortuosity therefore suggests an impediment to dopamine diffusion from the grafts into the lesioned striatum.