Diffusion In Brain Extracellular Space Research Articles

Gliotoxin‐induced swelling of astrocytes hinders diffusion in brain extracellular space via formation of dead‐space microdomains

One of the hallmarks of numerous life-threatening and debilitating brain diseases is cellular swelling that negatively impacts extracellular space (ECS) structure. The ECS structure is determined by two macroscopic parameters, namely tortuosity (λ) and volume fraction (α). Tortuosity represents hindrance imposed on the diffusing molecules by the tissue in comparison with an obstacle-free medium. Volume fraction is the proportion of tissue volume occupied by the ECS. From a clinical perspective, it is essential to recognize which factors determine the ECS parameters and how these factors change in brain diseases. Previous studies demonstrated that dead-space (DS) microdomains increased λ during ischemia and hypotonic stress, as these pocket-like structures transiently trapped diffusing molecules. We hypothesize that astrocytes play a key role in the formation of DS microdomains because their thin processes have concave shapes that may elongate as astrocytes swell in these pathologies. Here we selectively swelled astrocytes in the somatosensory neocortex of rat brain slices with a gliotoxin DL-α-Aminoadipic Acid (DL-AA), and we quantified the ECS parameters using Integrative Optical Imaging (IOI) and Real-Time Iontophoretic (RTI) diffusion methods. We found that α decreased and λ increased during DL-AA application. During recovery, α was restored whereas λ remained elevated. Increase in λ during astrocytic swelling and recovery is consistent with the formation of DS microdomains. Our data attribute to the astrocytes an important role in determining the ECS parameters, and indicate that extracellular diffusion can be improved not only by reducing the swelling but also by disrupting the DS microdomains.

Modeling Calcium Diffusion in Chondroitin Sulfate using a Bimolecular Reaction Scheme

Ca2+ diffusion in brain extracellular space (ECS) regulates local Ca2+ concentration and influences synaptic transmission and neuronal excitability. Ca2+ diffusion is controlled by ECS geometry and extracellular matrix, a major component of which is chondroitin sulfate (CS). Previous experiments (Hrabetova et al., J. Physiol. 2009, 587:4029) show that Ca2+ movement is reduced when interacting with CS, however the process still obeys the diffusion equation. This implies that Ca2+-CS interaction can be modeled as a fast equilibrium bimolecular reaction (FEBR; Nicholson et al. Comput. Visual Sci., 2012, 10.1007/s00791-012-0185-9). The FEBR would provide an alternative to solving the Poisson-Boltzmann equation for electrostatic interactions between negatively charged CS and mobile cations.Our objectives were 1) to test whether the FEBR model describes previous experimental data, 2) if so, to determine the dissociation constant Kd, (ratio between backward and forward rate constants), 3) to explore the effect of background Ca2+ and/or Na+ on Ca2+ diffusion and 4) use a Monte Carlo simulator (MCell; www.mcell.org) to verify results.We developed analytical expressions for the Ca2+ effective diffusion coefficient in the presence of CS and compared results to experimental data with different background Ca2+ and CS concentrations (Magdelenat et al., Biopolymers, 1974, 13:1535; Maroudas et al., Biophys. Chem., 1988, 32:257). This validated the FEBR approach and provided estimates of Kd (0.01 to 0.1 mM) in agreement with literature data. Kd values were resolved into forward and backward rate constants using the Damkohler formula and the results further tested with MCell. Finally, we extended the work to include additional background Na+.We conclude that the FEBR model captures the main features of Ca2+ diffusion in CS matrix and can be extended to interactions involving multiple cations. Supported by NIH/NINDS grant R01-NS-28642.

Random-Walk Model of Diffusion in Three Dimensions in Brain Extracellular Space: Comparison with Microfiberoptic Photobleaching Measurements

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 three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction ( α), 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 versus 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 after 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 α, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D o/ D for different solute sizes. Also, the modeling showed 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.

Microfiberoptic fluorescence photobleaching reveals size‐dependent macromolecule diffusion in extracellular space deep in brain

Diffusion in brain extracellular space (ECS) is important for nonsynaptic intercellular communication, extracellular ionic buffering, and delivery of drugs and metabolites. We measured macromolecular diffusion in normally light-inaccessible regions of mouse brain by microfiberoptic epifluorescence photobleaching, in which a fiberoptic with a micron-size tip is introduced deep in brain tissue. In brain cortex, the diffusion of a noninteracting molecule [fluorescein isothiocyanate (FITC)-dextran, 70 kDa] was slowed 4.5 +/- 0.5-fold compared with its diffusion in water (D(o)/D), and was depth-independent down to 800 microm from the brain surface. Diffusion was significantly accelerated (D(o)/D of 2.9+/-0.3) in mice lacking the glial water channel aquaporin-4. FITC-dextran diffusion varied greatly in different regions of brain, with D(o)/D of 3.5 +/- 0.3 in hippocampus and 7.4 +/- 0.3 in thalamus. Remarkably, D(o)/D in deep brain was strongly dependent on solute size, whereas diffusion in cortex changed little with solute size. Mathematical modeling of ECS diffusion required nonuniform ECS dimensions in deep brain, which we call "heterometricity," to account for the size-dependent diffusion. Our results provide the first data on molecular diffusion in ECS deep in brain in vivo and demonstrate previously unrecognized hindrance and heterometricity for diffusion of large macromolecules in deep brain.

Enhanced macromolecular diffusion in brain extracellular space in mouse models of vasogenic edema measured by cortical surface photobleaching

Diffusion of solutes and macromolecules in brain extracellular space (ECS) is important for normal brain function and efficient drug delivery, and is thought to be impaired in edematous brain. Here we measured the diffusion of an inert macromolecular fluorescent marker (FITC-dextran, 70 kDa) in the ECS by fluorescence recovery after photobleaching after staining the exposed cerebral cortex in vivo. In a brain tumor model of vasogenic (leaky capillary) edema, FITC-dextran diffusion was reduced more than fourfold in hypercellular tumor and surrounding astrogliotic tissue; however, diffusion in brain away from the tumor was approximately 30% faster than in normal contralateral brain. The increased diffusion was abolished by dexamethasone pretreatment. Enhanced ECS diffusion was also found in uninjured brain near a region of leaky brain vessels produced by focal cortical freeze injury. In contrast, ECS diffusion was slowed more than sixfold in cytotoxic brain edema caused by anoxia. Diffusion results were related semiquantitatively to ECS volume fraction and matrix viscosity from in vitro photobleaching studies in a model system consisting of silica particles in a fluorescent water/glycerol matrix. Our data provide in vivo evidence for enhanced ECS diffusion in vasogenic brain edema, yet greatly slowed diffusion in cytotoxic edema and in and around tumors.

Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells

Brain extracellular space (ECS) constitutes a porous medium in which diffusion is subject to hindrance, described by tortuosity, λ=( D/ D *) 1/2, where D is the free diffusion coefficient and D * is the effective diffusion coefficient in brain. Experiments show that λ is typically 1.6 in normal brain tissue although variations occur in specialized brain regions. In contrast, different theoretical models of cellular assemblies give ambiguous results: they either predict λ-values similar to experimental data or indicate values of about 1.2. Here we constructed three different ECS geometries involving tens of thousands of cells and performed Monte Carlo simulation of 3-D diffusion. We conclude that the geometrical hindrance in the ECS surrounding uniformly spaced convex cells is independent of the cell shape and only depends on the volume fraction α (the ratio of the ECS volume to the whole tissue volume). This dependence can be described by the relation λ=((3− α)/2) 1/2, indicating that the geometrical hindrance in such ECS cannot account for λ>1.225. Reasons for the discrepancy between the theoretical and experimental tortuosity values are discussed.

Maximum geometrical hindrance to diffusion in brain extracellular space surrounding uniformly spaced convex cells

Brain extracellular space (ECS) constitutes a porous medium in which diffusion is subject to hindrance, described by tortuosity, λ =( D / D * ) 1/2 , where D is the free diffusion coefficient and D * is the effective diffusion coefficient in brain. Experiments show that λ is typically 1.6 in normal brain tissue although variations occur in specialized brain regions. In contrast, different theoretical models of cellular assemblies give ambiguous results: they either predict λ -values similar to experimental data or indicate values of about 1.2. Here we constructed three different ECS geometries involving tens of thousands of cells and performed Monte Carlo simulation of 3-D diffusion. We conclude that the geometrical hindrance in the ECS surrounding uniformly spaced convex cells is independent of the cell shape and only depends on the volume fraction α (the ratio of the ECS volume to the whole tissue volume). This dependence can be described by the relation λ =((3− α )/2) 1/2 , indicating that the geometrical hindrance in such ECS cannot account for λ >1.225. Reasons for the discrepancy between the theoretical and experimental tortuosity values are discussed.