Tortuosity of the extracellular space describes hindrance posed to the diffusion process by a geometrically complex medium in comparison to an environment free of any obstacles. Calculating tortuosity in biologically relevant geometries is difficult. Yet this parameter has proved very important for many processes in the brain, ranging from ischemia and osmotic stress to delivery of nutrients and drugs. It is also significant for interpretation of the diffusion-weighted magnetic resonance data. We use a volume-averaging procedure to obtain a general expression for tortuosity in a complex environment. A simple approximation then leads to tortuosity estimates in a number of two-dimensional (2D) and three-dimensional (3D) geometries characterized by narrow pathways between the cellular elements. It also explains the counterintuitive fact of lower diffusion hindrance in a 3D environment. Comparison with Monte Carlo numerical simulations shows that the model gives reasonable tortuosity estimates for a number of regular and randomized 2D and 3D geometries. Importantly, it is shown that addition of dead-end pores increases tortuosity in proportion to the square root of enlarged total extracellular volume fraction. This conclusion is further supported by the previously described tortuosity decrease in ischemic brain slices where dead-end pores were partially occluded by large macromolecules introduced into the extracellular space.
Hyaluronan (HA), a large anionic polysaccharide (glycosaminoglycan), is a major constituent of the extracellular matrix of the adult brain. To address its function, we examined the neurophysiology of knock-out mice deficient in hyaluronan synthase (Has) genes. Here we report that these Has mutant mice are prone to epileptic seizures, and that in Has3 Ϫ/Ϫ mice, this phenotype is likely derived from a reduction in the size of the brain extracellular space (ECS). Among the three Has knock-out models, namely Has3, and Has2 CKO , the seizures were most prevalent in Has3 Ϫ/Ϫ mice, which also showed the greatest HA reduction in the hippocampus. Electrophysiology in Has3Ϫ/Ϫ brain slices demonstrated spontaneous epileptiform activity in CA1 pyramidal neurons, while histological analysis revealed an increase in cell packing in the CA1 stratum pyramidale. Imaging of the diffusion of a fluorescent marker revealed that the transit of molecules through the ECS of this layer was reduced. Quantitative analysis of ECS by the real-time iontophoretic method demonstrated that ECS volume was selectively reduced in the stratum pyramidale by ϳ40% in Has3 Ϫ/Ϫ mice. Finally, osmotic manipulation experiments in brain slices from Has3 Ϫ/Ϫ and wild-type mice provided evidence for a causal link between ECS volume and epileptiform activity. Our results provide the first direct evidence for the physiological role of HA in the regulation of ECS volume, and suggest that HA-based preservation of ECS volume may offer a novel avenue for development of antiepileptogenic treatments.
During ischemia, the transport of molecules in the extracellular space (ECS) is obstructed in comparison with healthy brain tissue, but the cause is unknown. Extracellular tortuosity (lambda), normally 1.6, increases to 1.9 in ischemic thick brain slices (1000 microm), but drops to 1.5 when 70,000 Mr dextran (dex70) is added to the tissue as a background macromolecule. We hypothesized that the ischemic increase in lambda arises from diffusion delays in newly formed dead-space microdomains of the ECS. Accordingly, lambda decreases when dead-space diffusion is eliminated by trapping dex70 in these microdomains. We tested our hypothesis by analyzing the diffusion of several molecules in neocortical slices. First we showed that diffusion of fluorescent dex70 in thick slices declined over time, indicating the entrapment of background macromolecules. Next, we measured diffusion of tetramethylammonium (TMA+) (74 Mr) to show that the reduction of lambda depended on the size of the background macromolecule. The synthetic polymer, 40,000 Mr polyvinylpyrrolidone, reduced lambda in thick slices, whereas 10,000 Mr dextran did not. The dex70 was also effective in normoxic slices (400 microm) after hypoosmotic stress altered the ECS to mimic ischemia. Finally, the dex70 effect was confirmed independently of TMA+ using fluorescent 3000 Mr dextran as a diffusion marker in thick slices: lambda decreased from 3.29 to 2.44. Taken together, these data support our hypothesis and offer a novel explanation for the origin of the large lambda observed in ischemic brain. A semiquantitative model of dead-space diffusion corroborates this new interpretation of lambda.
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