Contribution of dead-space microdomains to tortuosity of brain extracellular space

The extracellular space (ECS) of the brain is a major channel for intercellular communication, nutrient and metabolite trafficking, and drug delivery. The dominant transport mechanism is diffusion, which is governed by two structural parameters, tortuosity and volume fraction. Tortuosity (lambda) represents the hindrance imposed on the diffusing molecules by the tissue in comparison with an obstacle-free medium, while volume fraction (alpha) is the proportion of tissue volume occupied by the ECS. Diffusion of small ECS markers can be exploited to measure lambda and alpha. In healthy brain tissue, lambda is about 1.6 but increases to 1.9-2.0 in pathologies that involve cellular swelling. Previously it was thought that lambda could be explained by the circumnavigation of diffusing molecules around cells. Numerical models of assemblies of convex cells, however, give an upper limit of about 1.23 for lambda. Therefore, additional factors must be responsible for lambda in brain. In principle, two mechanisms could account for the measured value: a more complex ECS geometry or an extracellular macromolecular matrix. Here we review recent work in ischemic tissue suggesting concave geometrical formations, dead-space microdomains, as a major determinant of extracellular tortuosity. A theoretical model of lambda based on diffusion dwell times supports this hypothesis and predicts that, in ischemia, dead spaces occupy approximately 60% of ECS volume fraction leaving only approximately 40% for well-connected channels. It is further proposed that dead spaces are present in healthy brain tissue where they constitute about 40% of alpha. The presence of dead-space microdomains in the ECS implies microscopic heterogeneity of extracellular channels with fundamental implications for molecular transport in brain.     

Extracellular space diffusion and extrasynaptic transmission

The diffusion of neuroactive substances in the extracellular space (ECS) plays an important role in short- and long-distance communication between nerve cells and is the underlying mechanism of extrasynaptic (volume) transmission. The diffusion properties of the ECS are described by three parameters: 1. ECS volume fraction alpha (alpha=ECS volume/total tissue volume), 2. tortuosity lambda (lambda2=free/apparent diffusion coefficient), reflecting the presence of diffusion barriers represented by, e.g., fine neuronal and glial processes or extracellular matrix molecules and 3. nonspecific uptake k'. These diffusion parameters differ in various brain regions, and diffusion in the CNS is therefore inhomogeneous. Moreover, diffusion barriers may channel the migration of molecules in the ECS, so that diffusion is facilitated in a certain direction, i.e. diffusion in certain brain regions is anisotropic. Changes in the diffusion parameters have been found in many physiological and pathological states in which cell swelling, glial remodeling and extracellular matrix changes are key factors influencing diffusion. Changes in ECS volume, tortuosity and anisotropy significantly affect the accumulation and diffusion of neuroactive substances in the CNS and thus extrasynaptic transmission, neuron-glia communication, transmitter "spillover" and synaptic cross-talk as well as cell migration, drug delivery and treatment.     

Extrasynaptic transmission and the diffusion parameters of the extracellular space

Extrasynaptic volume transmission, mediated by the diffusion of neuroactive substances in the extracellular space (ECS), plays an important role in short- and long-distance communication between nerve cells. The ability of a substance to reach extrasynaptic high-affinity receptors via diffusion depends on the ECS diffusion parameters, ECS volume fraction alpha (alpha=ECS volume/total tissue volume) and tortuosity lambda (lambda2=free/apparent diffusion coefficient), which reflects the presence of diffusion barriers represented by, e.g., fine astrocytic processes or extracellular matrix molecules. These barriers channel the migration of molecules in the ECS, so that diffusion may be facilitated in a certain direction, i.e. anisotropic. The diffusion parameters alpha and lambda differ in various brain regions, and diffusion in the CNS is therefore inhomogeneous. Changes in diffusion parameters have been found in many physiological and pathological states, such as development and aging, neuronal activity, lactation, ischemia, brain injury, degenerative diseases, tumor growth and others, in which cell swelling, glial remodeling and extracellular matrix changes are key factors influencing diffusion. Changes in ECS volume, tortuosity and anisotropy significantly affect the accumulation and diffusion of neuroactive substances and thus extrasynaptic transmission, neuron-glia communication, mediator "spillover" and synaptic crosstalk as well as, cell migration. The various changes occurring during pathological states can be important for diagnosis, drug delivery and treatment.     

Diffusion properties of the brain in health and disease

Extrasynaptic transmission between neurons and communication between neurons and glia are mediated by the diffusion of neuroactive substances in the extracellular space (ECS)--volume transmission. Diffusion in the CNS is inhomogeneous and often not uniform in all directions (anisotropic). Ionic changes and amino acid release result in cellular (particularly glial) swelling, compensated for by ECS shrinkage and a decrease in the apparent diffusion coefficients of neuroactive substances or water (ADCW). The diffusion parameters of the CNS in adult mammals (including humans), ECS volume fraction alpha (alpha = ECS volume/total tissue volume; normally 0.20-0.25) and tortuosity lambda (lambda2 = D/ADC; normally 1.5-1.6), hinder the diffusion of neuroactive substances and water. A significant decrease in ECS volume and an increase in diffusion barriers (tortuosity) and anisoptropy have been observed during stimulation, lactation or learning deficits during aging, due to structural changes such as astrogliosis, the re-arrangement of astrocytic processes and a loss of extracellular matrix. Decreases in the apparent diffusion coefficient of tetramethylammonium (ADCTMA) and ADCW due to astrogliosis and increased proteoglycan expression were found in the brain after injury and in grafts of fetal tissue. Tenascin-R and tenascin C-deficient mice also showed significant changes in ADCTMA and ADCW, suggesting an important role for extracellular matrix molecules in ECS diffusion. Changes in ECS volume, tortuosity and anisotropy significantly affect neuron-glia communication, the spatial relation of glial processes towards synapses, the efficacy of glutamate or GABA 'spillover' and synaptic crosstalk, the migration of cells, the action of hormones and the toxic effects of neuroactive substances and can be important for diagnosis, drug delivery and new treatment strategies.     

Changes in extracellular space volume and geometry induced by cortical spreading depression in immature and adult rats

Changes in extracellular space (ECS) diffusion parameters, DC potentials and extracellular potassium concentration were studied during single and repeated cortical spreading depressions (SD) in 13-15 (P13-15), 21 (P21) and 90-day-old (adult) Wistar rats. The real-time iontophoretic method using tetramethylammonium (TMA+)-selective microelectrodes was employed to measure three ECS parameters in the somatosensory cortex: the ECS volume fraction alpha (alpha = ECS volume/total tissue volume), ECS tortuosity lambda (increase in diffusion path length) and the nonspecific TMA+ uptake k'. SD was elicited by needle prick. SD was significantly longer at P13-15 than at P21 and in adults. During SD, alpha in all age groups decreased from 0.21-0.23 to 0.05-0.09; lambda increased from 1.55-1.65 to 1.95-2.07. Ten minutes after SD, alpha (in adults) and lambda (all age groups) increased compared to controls. This increase persisted even 1 hour after SD. When SD was repeated at 1 hour intervals, both alpha and lambda showed a gradual cumulative increase with SD repetition. Our study also shows that cortical SD is, as early as P13, accompanied by severe ECS shrinkage and increased diffusion path length (tortuosity) with values similar to adults, followed by a long-lasting increase in ECS volume and tortuosity when compared to pre-SD values.     

Cell cavities increase tortuosity in brain extracellular space

Brain extracellular space (ECS) forms hindered pathways for molecular diffusion in chemical signaling and drug delivery. Hindrance is quantified by the tortuosity lambda; the tortuosity obtained from simulations using uniformly spaced convex cells is significantly lower than that measured experimentally. To attempt to account for the difference in results, this study employed a variety of ECS models based on an array of cubic cells containing open rectangular cavities that provided the ECS with dead-space microdomains. Monte Carlo simulations demonstrated that, in such ECS models, lambda can equal or exceed the typical experimental value of about 1.6. The simulations further revealed that lambda is relatively independent of cavity shape and the number of cavities per cell. It mainly depends on the total ECS volume fraction alpha, the cavity volume fraction alpha(c), and whether the cavity is located at the center of a cell face or formed at the junction of multiple cells. To describe the results from the different ECS models, an expression was obtained that related lambda to alpha, alpha(c), and an empirical exit factor beta that correlated with the ease with which a molecule could leave a cavity and its vicinity.     

A model of effective diffusion and tortuosity in the extracellular space of the brain

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.     

Quantitative dual-probe microdialysis: evaluation of [3H]mannitol diffusion in agar and rat striatum

Dual-probe microdialysis was used to study interstitial diffusion in the rat brain. A radiolabelled tracer, (3H]mannitol, was continuously infused at different concentrations via a probe acutely implanted into the striatum of an anaesthetized male rat or into a dilute agar gel. Samples were collected by a second probe placed 1 mm away from the first, and the recovered [3H]mannitol was measured by liquid scintillation counting. In the striatum, the delivery of [3H]mannitol was counteracted by its removal from the extracellular space by passive uptake into cells and clearance into the microcirculation, causing the diffusion profile to approach quasi steady-state levels within 2 h. Diffusion data from brain and agar were analysed using a mathematical model. The apparent (effective) diffusion coefficient for [3H]mannitol was D* = 2.9 x 10(-6) cm2/s, the effective volume fraction alpha* = 0.30 and the clearance rate constant kappa= 2.3 x 10(-5)/s. A tortuosity, lambda = 1.81, and penetration distance r = 4.2 mm, were calculated. We conclude that, using dual-probe microdialysis, parameters reflecting geometric and dynamic tissue properties may be obtained using appropriate mathematical analysis. Quantitative dual-probe microdialysis will be valuable in characterizing interstitial diffusion and the clearance processes underpinning volume transmission in the brain.     

Extracellular space diffusion in central nervous system: anisotropic diffusion measured by elliptical surface photobleaching

Diffusion in the extracellular space (ECS) is crucial for normal central nervous system physiology. The determinants of ECS diffusion include viscous interactions with extracellular matrix/plasma membranes ("viscosity") and ECS geometry ("tortuosity"). To resolve viscosity versus tortuosity effects, we measured direction-dependent (anisotropic) diffusion in ECS in mouse spinal cord by photobleaching using an elliptical spot produced by a cylindrical lens in the excitation path. Anisotropic diffusion slowed fluorescence recovery when the long axis of the ellipse was parallel versus perpendicular to the direction of faster diffusion. A mathematical model was constructed to deduce diffusion coefficients (D(x), D(y)) from fluorescence recovery measured for parallel and perpendicular orientations of the long axis of the ellipse. Elliptical spot photobleaching was validated by photobleaching aqueous-phase fluorophores on a diffraction grating, where diffusion is one-dimensional. Measurement of the diffusion of 70 kDa FITC-dextran in spinal cord in living mice indicated that viscosity slows diffusion by approximately 1.8-fold compared with its diffusion in solution. ECS geometry hinders diffusion across (but not along) axonal fibers in spinal cord further by approximately fivefold. In cerebral cortex, however, approximately 50% of the hindrance to ECS diffusion comes from viscosity and approximately 50% from tortuosity. We suggest that the extracellular matrix might have evolved to facilitate rather than hinder diffusion even for large molecules.     

Hindered diffusion of high molecular weight compounds in brain extracellular microenvironment measured with integrative optical imaging.

This paper describes the theory of an integrative optical imaging system and its application to the analysis of the diffusion of 3-, 10-, 40-, and 70-kDa fluorescent dextran molecules in agarose gel and brain extracellular microenvironment. The method uses a precisely defined source of fluorescent molecules pressure ejected from a micropipette, and a detailed theory of the intensity contributions from out-of-focus molecules in a three-dimensional medium to a two-dimensional image. Dextrans tagged with either tetramethylrhodamine or Texas Red were ejected into 0.3% agarose gel or rat cortical slices maintained in a perfused chamber at 34 degrees C and imaged using a compound epifluorescent microscope with a 10 x water-immersion objective. About 20 images were taken at 2-10-s intervals, recorded with a cooled CCD camera, then transferred to a 486 PC for quantitative analysis. The diffusion coefficient in agarose gel, D, and the apparent diffusion coefficient, D*, in brain tissue were determined by fitting an integral expression relating the measured two-dimensional image intensity to the theoretical three-dimensional dextran concentration. The measurements in dilute agarose gel provided a reference value of D and validated the method. Values of the tortuosity, lambda = (D/D*)1/2, for the 3- and 10-kDa dextrans were 1.70 and 1.63, respectively, which were consistent with previous values derived from tetramethylammonium measurements in cortex. Tortuosities for the 40- and 70-kDa dextrans had significantly larger values of 2.16 and 2.25, respectively. This suggests that the extracellular space may have local constrictions that hinder the diffusion of molecules above a critical size that lies in the range of many neurotrophic compounds.     

Astrocytes and extracellular matrix in extrasynaptic volume transmission

Volume transmission is a form of intercellular communication that does not require synapses; it is based on the diffusion of neuroactive substances across the brain extracellular space (ECS) and their binding to extrasynaptic high-affinity receptors on neurons or glia. Extracellular diffusion is restricted by the limited volume of the ECS, which is described by the ECS volume fraction α, and the presence of diffusion barriers, reflected by tortuosity λ, that are created, for example, by fine astrocytic processes or extracellular matrix (ECM) molecules. Organized astrocytic processes, ECM scaffolds or myelin sheets channel the extracellular diffusion so that it is facilitated in a certain direction, i.e. anisotropic. The diffusion properties of the ECS are profoundly influenced by various processes such as the swelling and morphological rebuilding of astrocytes during either transient or persisting physiological or pathological states, or the remodelling of the ECM in tumorous or epileptogenic tissue, during Alzheimer''s disease, after enzymatic treatment or in transgenic animals. The changing diffusion properties of the ECM influence neuron–glia interaction, learning abilities, the extent of neuronal damage and even cell migration. From a clinical point of view, diffusion parameter changes occurring during pathological states could be important for diagnosis, drug delivery and treatment.     

Determination of Brain Interstitial Concentrations by Microdialysis

Microdialysis is an extensively used technique for the study of solutes in brain interstitial space. The method is based on collection of substances by diffusion across a dialysis membrane positioned in the brain. The outflow concentration reflects the interstitial concentration of the substance of interest, but the relationship between these two entities is at present unclear. So far, most evaluations have been based solely on calibrations in saline. This procedure is misleading, because the ease by which molecules in saline diffuse into the probe is different from that of tissue. We describe here a mathematical analysis of mass transport into the dialysis probe in tissue based on diffusion equations in complex media. The main finding is that diffusion characteristics of a given substance have to be included in the formula. These include the tortuosity factor (lambda) and the extracellular volume fraction (alpha). We have substantiated this by studies in a well-defined complex medium (red blood cell suspensions) as well as in brain. We conclude that the traditional calculation procedure results in interstitial concentrations that are too low by a factor of lambda 2/alpha for a given compound.     

Glial cells and volume transmission in the CNS

Although synaptic transmission is an important means of communication between neurons, neurons themselves and neurons and glia also communicate by extrasynaptic "volume" transmission, which is mediated by diffusion in the extracellular space (ECS). The ECS of the central nervous system (CNS) is the microenvironment of neurons and glial cells. The composition and size of ECS change dynamically during neuronal activity as well as during pathological states. Following their release, a number of neuroactive substances, including ions, mediators, metabolites and neurotransmitters, diffuse via the ECS to targets distant from their release sites. Glial cells affect the composition and volume of the ECS and therefore also extracellular diffusion, particularly during development, aging and pathological states such as ischemia, injury, X-irradiation, gliosis, demyelination and often in grafted tissue. Recent studies also indicate that diffusion in the ECS is affected by ECS volume inhomogeneities, which are the result of a more compacted space in certain regions, e.g. in the vicinity of oligodendrocytes. Besides glial cells, the extracellular matrix also changes ECS geometry and forms diffusion barriers, which may also result in diffusion anisotropy. Glial cells therefore play an important role in extrasynaptic transmission, for example in functions such as vigilance, sleep, depression, chronic pain, LTP, LTD, memory formation and other plastic changes in the CNS. In turn, ECS diffusion parameters affect neuron-glia communication, ionic homeostasis and movement and/or accumulation of neuroactive substances in the brain.     

Anomalous Extracellular Diffusion in Rat Cerebellum

Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent d_w from the IOI records. Diffusion was significantly anomalous in rat GL, where d_w reached 4.8. In the geometrically simpler turtle GL, d_w was elevated but not robustly anomalous (d_w = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures.     

Diffusion of water in cat ventricular myocardium

The rates of diffusion of tritiated water (THO) and [14C]sucrose across cat right ventricular myocardium were studied at 23 degrees C in an Ussing-type diffusion cell, recording the time-course of increase in concentration of tracer in one chamber over 4--6 h after adding tracers to the other. Sucrose data were fitted with a model for a homogeneous sheet of uneven thickness in which the tissue is considered to be an array of parallel independent pathways (parallel pathway model) of varying length. The volume of the sucrose diffusion space, presumably a wholly extracellular pathway, was 23% of the tissue or 27.4 +/-1.7% (mean +/- SEM; n=11) of the tissue water. The effective intramyocardial sucrose diffusion coefficient, D8, was 1.51 +/- 0.19 X 10(-6)cm2.s-1 (n=11). Combining these data with earlier data, D8 was 22.6 +/- 1.1% (n=95) of the free diffusion coefficient in aqueous solution D degrees 8. The parallel pathway model and a dead-end pore model, which might have accounted for intracellular sequestration of water, gave estimates of DW/D degrees W (observed/free) of 15%. Because hindrance to water diffusion must be less than for sucrose (where D8/D degrees 8=22.6%), this showed the inadequacy of these models to account simultaneously for the diffusional resistance and the tissue water content. The third or cell-matrix model, a heterogeneous system of permeable cells arrayed in the extracellular matrix, allowed logical and geometrically reasonable interpretations of the steady-state data and implied estimates of DW in the cellular and extracellular fluid of approximately 25% of the aqueous diffusion coefficient.     

Diffusion of nerve growth factor in rat striatum as determined by multiphoton microscopy

Neurotrophins such as nerve growth factor (NGF) may be useful for treating diseases in the central nervous system; our ability to harness the potential therapeutic benefit of NGF is directly related to our understanding of the fate of exogenously supplied factors in brain tissue. We utilized multiphoton microscopy to quantify the dynamic behavior of NGF in coronal, 400- micro m thick, fresh rat brain tissue slices. We administered a solution containing bioactive rhodamine nerve growth factor conjugate via pressure injection and monitored the dispersion in the striatal region of the coronal slices. Multiphoton microscopy facilitated repeated imaging deep ( approximately 200 micro m) into tissue slices with minimal photodamage of tissue and photobleaching of label. The pressure injection paradigm approximated diffusion from a point source, and we therefore used the corresponding solution to the diffusion equation to estimate an apparent diffusion coefficient in brain tissue (D(b)(34 degrees C)) of 2.75 +/- 0.24 x 10(-7) cm(2)/s (average +/- SE). In contrast, we determined a corresponding free diffusion coefficient in buffered solution (D(f)(34 degrees C)) of 12.6 +/- 0.9 x 10(-7) cm(2)/s using multiphoton fluorescence photobleaching recovery. The tortuosity, defined as the square root of the ratio of D(f) to D(b), was 2.14 and moderate in magnitude.     

Effects of microorganisms on effective oxygen diffusion coefficients and solubilities in fermentation media

Effective oxygen diffusion coefficients and solubilities were measured for submerged cultures of Saccharomyces cerevisiae, Escherichia coli, and Penicillium chrysogenum. Both effective oxygen diffusion coefficients and solubilities were found to decrease with increasing cell concentrations in the fermentation media. Comparison of the experimental results of effective oxygen diffusion coefficients in fermentation media with values theoretically predicted on the assumption of unpenetrable microbial cells indicates that oxygen molecules diffuse through the cells during the diffusion process. Within the cell concentration range of typical submerged fermentations, the effective oxygen diffusion coefficient of the fermentation media can be described as D(e) = A(1)f + A(2)f(2). In this equation, fis the cell volume fraction and both A(1) and A(2) are functions of the shape of the cells and the ratio of effective oxygen diffusion coefficient in microbial cells to that in the medium.     

The Impact of Alpha-Syntrophin Deletion on the Changes in Tissue Structure and Extracellular Diffusion Associated with Cell Swelling under Physiological and Pathological Conditions

Aquaporin-4 (AQP4) is the primary cellular water channel in the brain and is abundantly expressed by astrocytes along the blood-brain barrier and brain-cerebrospinal fluid interfaces. Water transport via AQP4 contributes to the activity-dependent volume changes of the extracellular space (ECS), which affect extracellular solute concentrations and neuronal excitability. AQP4 is anchored by α-syntrophin (α-syn), the deletion of which leads to reduced AQP4 levels in perivascular and subpial membranes. We used the real-time iontophoretic method and/or diffusion-weighted magnetic resonance imaging to clarify the impact of α-syn deletion on astrocyte morphology and changes in extracellular diffusion associated with cell swelling in vitro and in vivo. In mice lacking α-syn, we found higher resting values of the apparent diffusion coefficient of water (ADC_W) and the extracellular volume fraction (α). No significant differences in tortuosity (λ) or non-specific uptake (k′), were found between α-syn-negative (α-syn −/−) and α-syn-positive (α-syn +/+) mice. The deletion of α-syn resulted in a significantly smaller relative decrease in α observed during elevated K⁺ (10 mM) and severe hypotonic stress (−100 mOsmol/l), but not during mild hypotonic stress (−50 mOsmol/l). After the induction of terminal ischemia/anoxia, the final values of ADC_W as well as of the ECS volume fraction α indicate milder cell swelling in α-syn −/− in comparison with α-syn +/+ mice. Shortly after terminal ischemia/anoxia induction, the onset of a steep rise in the extracellular potassium concentration and an increase in λ was faster in α-syn −/− mice, but the final values did not differ between α-syn −/− and α-syn +/+ mice. This study reveals that water transport through AQP4 channels enhances and accelerates astrocyte swelling. The substantially altered ECS diffusion parameters will likely affect the movement of neuroactive substances and/or trophic factors, which in turn may modulate the extent of tissue damage and/or drug distribution.     

Nuclear magnetic resonance (NMR) measurement of the apparent diffusion coefficient (ADC) of tissue water and its relationship to cell volume changes in pathological states

Diffusion-weighted nuclear magnetic resonance (NMR) imaging (DWI) is sensitive to the random translational motion of water molecules due to Brownian motion. Although the mechanism is still not completely understood, the cellular swelling that accompanies cell membrane depolarization results in a reduction in the net displacement of diffusing water molecules and thus a concomitant reduction in the apparent diffusion coefficient (ADC) of tissue water. Cerebral regions of reduced ADC appear hyperintense in a DWI and this technique has been used extensively to study acute stroke. In addition to cerebral ischemia, reductions in the ADC of cerebral water have been observed following cortical spreading depression, ischemic depolarizations (IDs), transient ischemic attack (TIA), status epilepticus, and hypoglycemia. Although the mechanism responsible for initiating membrane depolarization varies in each case, the ensuing cell volume changes follow a similar pattern. Water ADC values are also affected by the presence and orientation of barriers to translational motion (such as cell membranes and myelin fibers) and thus NMR measures of anisotropic diffusion are sensitive to more chronic pathological states where the integrity of these structures is modified by disease. Both theoretical prediction and experimental evidence suggest that the ADC of tissue water is related to the volume fraction of the interstitial space via the electrical conductivity of the tissue. The implication is that acute neurological disorders that exhibit electrical conductivity changes should also exhibit ADC changes that are detectable by DWI. A qualitative correlation between electrical conductivity and the ADC of water has been demonstrated in a number of animal model studies and the results indicate that reduced ADC values are associated with reductions in the extracellular volume fraction and increased extracellular tortuosity. The close relationship between ADC changes and cell volume changes in various pathological states suggests that NMR measurements are also sensitive to chemical communication between cells through the extracellular space (i.e., extrasynaptic or volume transmission, VT).