Dextran decreases extracellular tortuosity in thick-slice ischemia model

Brain extracellular space of the naked mole-rat expands and maintains normal diffusion under ischemic conditions

Brain extracellular space (ECS) forms a conduit for diffusion, an essential mode of molecular transport between brain vasculature, neurons and glia. ECS volume is reduced under conditions of hypoxia and ischemia, contributing to impaired extracellular diffusion and consequent neuronal dysfunction and death. We investigated the ECS volume fraction and diffusion permeability of the African naked mole-rat (NM-R; Heterocephalus Glaber), a rodent with a remarkably high tolerance for hypoxia and ischemia. Real-Time Iontophoretic and Integrative Optical Imaging methods were used to evaluate diffusion transport in cortical slices under normoxic and ischemic conditions, and results were compared to values previously collected in rats. NM-R brains under normoxic conditions had a smaller ECS volume fraction than rats, and a correspondingly decreased diffusion permeability for macromolecules. Surprisingly, and in sharp contrast to rats, the NM-R ECS responded to ischemic conditions at the center of thick brain slices by expanding, rather than shrinking, and preserving diffusion permeabilities for small and large molecules. The NM-R thick slices also showed a blunted accumulation of ECS potassium compared to rats. The remarkable dynamic response of the NM-R ECS to ischemia likely demonstrates an adaptation for NM-R to maintain brain function in their extreme nest environment.

The need for mathematical modelling of spatial drug distribution within the brain

The blood brain barrier (BBB) is the main barrier that separates the blood from the brain. Because of the BBB, the drug concentration-time profile in the brain may be substantially different from that in the blood. Within the brain, the drug is subject to distributional and elimination processes: diffusion, bulk flow of the brain extracellular fluid (ECF), extra-intracellular exchange, bulk flow of the cerebrospinal fluid (CSF), binding and metabolism. Drug effects are driven by the concentration of a drug at the site of its target and by drug-target interactions. Therefore, a quantitative understanding is needed of the distribution of a drug within the brain in order to predict its effect. Mathematical models can help in the understanding of drug distribution within the brain. The aim of this review is to provide a comprehensive overview of system-specific and drug-specific properties that affect the local distribution of drugs in the brain and of currently existing mathematical models that describe local drug distribution within the brain. Furthermore, we provide an overview on which processes have been addressed in these models and which have not. Altogether, we conclude that there is a need for a more comprehensive and integrated model that fills the current gaps in predicting the local drug distribution within the brain.

Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics

Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. The extracellular medium of neural tissue is an active medium of neuromodulators, ions, inflammatory cells, oxygen, NO and other gases, with additional physiological, pharmacological and pathological agents. These extracellular agents influence, and are influenced by, cellular electrophysiology, and cellular chemophysiology-the complex internal cellular milieu of second-messenger signaling and cascades. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction-the proportion of space in which species are able to diffuse, and tortuosity-the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke. Simulation results were verified against analytic results and against the extracellular portion of the simulation run under FiPy. The creation of this NEURON interface provides a pathway for interoperability that can be used to automatically export this class of models into complex intracellular/extracellular simulations and future cross-simulator standardization.

Vascular, glial, and lymphatic immune gateways of the central nervous system

Immune privilege of the central nervous system (CNS) has been ascribed to the presence of a blood–brain barrier and the lack of lymphatic vessels within the CNS parenchyma. However, immune reactions occur within the CNS and it is clear that the CNS has a unique relationship with the immune system. Recent developments in high-resolution imaging techniques have prompted a reassessment of the relationships between the CNS and the immune system. This review will take these developments into account in describing our present understanding of the anatomical connections of the CNS fluid drainage pathways towards regional lymph nodes and our current concept of immune cell trafficking into the CNS during immunosurveillance and neuroinflammation. Cerebrospinal fluid (CSF) and interstitial fluid are the two major components that drain from the CNS to regional lymph nodes. CSF drains via lymphatic vessels and appears to carry antigen-presenting cells. Interstitial fluid from the CNS parenchyma, on the other hand, drains to lymph nodes via narrow and restricted basement membrane pathways within the walls of cerebral capillaries and arteries that do not allow traffic of antigen-presenting cells. Lymphocytes targeting the CNS enter by a two-step process entailing receptor-mediated crossing of vascular endothelium and enzyme-mediated penetration of the glia limitans that covers the CNS. The contribution of the pathways into and out of the CNS as initiators or contributors to neurological disorders, such as multiple sclerosis and Alzheimer’s disease, will be discussed. Furthermore, we propose a clear nomenclature allowing improved precision when describing the CNS-specific communication pathways with the immune system.

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 dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 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.

The quest for a better insight into physiology of fluids and barriers of the brain: the exemplary career of Joseph D. Fenstermacher

In June 2014 Dr. Joseph D. Fenstermacher celebrated his 80th birthday, which was honored by the symposium held in New London, NH, USA. This review discusses Fenstermacher's contribution to the field of fluids and barriers of the CNS. Specifically, his fundamental work on diffusion of molecules within the brain extracellular space and the research on properties of the blood-brain barrier in health and disease are described. Fenstermacher's early research on cerebrospinal fluid dynamics and the regulation of cerebral blood flow is also reviewed, followed by the discussion of his more recent work involving the use of magnetic resonance imaging.

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.

Glutamine is required for persistent epileptiform activity in the disinhibited neocortical brain slice

The neurotransmitter glutamate is recycled through an astrocytic-neuronal glutamate-glutamine cycle in which synaptic glutamate is taken up by astrocytes, metabolized to glutamine, and transferred to neurons for conversion back to glutamate and subsequent release. The extent to which neuronal glutamate release is dependent upon this pathway remains unclear. Here we provide electrophysiological and biochemical evidence that in acutely disinhibited rat neocortical slices, robust release of glutamate during sustained epileptiform activity requires that neurons be provided a continuous source of glutamine. We demonstrate that the uptake of glutamine into neurons for synthesis of glutamate destined for synaptic release is not strongly dependent on the system A transporters, but requires another unidentified glutamine transporter or transporters. Finally, we find that the attenuation of network activity through inhibition of neuronal glutamine transport is associated with reduced frequency and amplitude of spontaneous events detected at the single-cell level. These results indicate that availability of glutamine influences neuronal release of glutamate during periods of intense network activity.

Extracellular diffusion parameters in the rat somatosensory cortex during recovery from transient global ischemia/hypoxia

Changes in the extracellular space diffusion parameters during ischemia are well known, but information about changes during the postischemic period is lacking. Extracellular volume fraction (alpha) and tortuosity (lambda) were determined in the rat somatosensory cortex using the real-time iontophoretic method; diffusion-weighted magnetic resonance imaging was used to determine the apparent diffusion coefficient of water. Transient ischemia was induced by bilateral common carotid artery clamping for 10 or 15 mins and concomitant ventilation with 6% O(2) in N(2). In both ischemia groups, a negative DC shift accompanied by increased potassium levels occurred after 1 to 2 mins of ischemia and recovered to preischemic values within 3 to 5 mins of reperfusion. During ischemia of 10 mins duration, alpha typically decreased to 0.07+/-0.01, whereas lambda increased to 1.80+/-0.02. In this group, normal values of alpha=0.20+/-0.01 and lambda=1.55+/-0.01 were registered within 5 to 10 mins of reperfusion. After 15 mins of ischemia, alpha increased within 40 to 50 mins of reperfusion to 0.29+/-0.03 and remained at this level. Tortuosity (lambda) increased to 1.81+/-0.02 during ischemia, recovered within 5 to 10 mins of reperfusion, and was increased to 1.62+/-0.01 at the end of the experiment. The observed changes can affect the diffusion of ions, neurotransmitters, metabolic substances, and drugs in the nervous system.

Diffusion in brain extracellular space

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules in the brain. Deviations from the equation reveal loss of molecules across the blood-brain barrier, through cellular uptake, binding, or other mechanisms. Early diffusion measurements used radiolabeled sucrose and other tracers. Presently, the real-time iontophoresis (RTI) method is employed for small ions and the integrative optical imaging (IOI) method for fluorescent macromolecules, including dextrans or proteins. Theoretical models and simulations of the ECS have explored the influence of ECS geometry, effects of dead-space microdomains, extracellular matrix, and interaction of macromolecules with ECS channels. Extensive experimental studies with the RTI method employing the cation tetramethylammonium (TMA) in normal brain tissue show that the volume fraction of the ECS typically is approximately 20% and the tortuosity is approximately 1.6 (i.e., free diffusion coefficient of TMA is reduced by 2.6), although there are regional variations. These parameters change during development and aging. Diffusion properties have been characterized in several interventions, including brain stimulation, osmotic challenge, and knockout of extracellular matrix components. Measurements have also been made during ischemia, in models of Alzheimer's and Parkinson's diseases, and in human gliomas. Overall, these studies improve our conception of ECS structure and the roles of glia and extracellular matrix in modulating the ECS microenvironment. Knowledge of ECS diffusion properties is valuable in contexts ranging from understanding extrasynaptic volume transmission to the development of paradigms for drug delivery to the brain.

Tortuosity and anomalous diffusion in the neuromuscular junction

The signal transfer from nerve to muscle occurs by diffusion across the neuromuscular junction. The continuum level analysis of diffusion processes is based on the diffusion equation, which in one dimension is partial differential c/partial differential t=D(partial differential(2)c/partial differential x(2)) , where c is the molecular concentration and D is the diffusivity. However, in confined systems such as the neuromuscular junction, the diffusion equation may not be valid, and even if valid the value of D may be altered by the confinement. In this paper, Monte Carlo simulations are used to probe diffusion at the molecular level in a realistic model of a neuromuscular junction. The results show that diffusion is anomalous (i.e., not described by the diffusion equation) for time scales less than approximately 0.01 s, which is the time scale relevant for signaling processes in the synapse. At longer time scales, the diffusion is normal (i.e., described by the diffusion equation), but with a value of D that is reduced by a factor of approximately 5 times compared to the value for diffusion in open space. As the width of the synaptic cleft decreases, these effects become even more pronounced. The physical basis of these results is described in terms of the structure of the neuromuscular junction.

Characterizing molecular probes for diffusion measurements in the brain

Brain diffusion properties are at present most commonly evaluated by magnetic resonance (MR) diffusion imaging. MR cannot easily distinguish between the extracellular and intracellular signal components, but the older technique of real-time iontophoresis (RTI) detects exclusively extracellular diffusion. Interpretation of the MR results would therefore benefit from auxiliary RTI measurements. This requires a molecular probe detectable by both techniques. Our aim was to specify a minimum set of requirements that such a diffusion probe should fulfill and apply it to two candidate probes: the cation tetramethylammonium (TMA(+)), used routinely in the RTI experiments, and the anion hexafluoroantimonate (SbF(6)(-)). Desirable characteristics of a molecular diffusion probe include predictable diffusion properties, stability, minimum interaction with cellular physiology, very slow penetration into the cells, and sufficiently strong and selective MR and RTI signals. These properties were evaluated using preparations of rat neocortical slices under normal and ischemic conditions, as well as solutions and agarose gel. While both molecules can be detected by MR and RTI, neither proved an ideal candidate. TMA(+) was very stable but it penetrated into the cells and accumulated there within tens of minutes. SbF(6)(-) did not enter the cells as readily but it was not stable, particularly in ischemic tissue and at higher temperatures. Its presence also resulted in a decreased extracellular volume. These probe properties help to interpret previously published MR data on TMA(+) diffusion and might play a role in other diffusion experiments obtained with them.

Extracellular diffusion is fast and isotropic in the stratum radiatum of hippocampal CA1 region in rat brain slices

Molecular transport in brain extracellular space (ECS) is hindered by the structure of the tissue. Diffusion analysis of small extracellular markers quantifies tissue hindrance, expressed as tortuosity lambda = (D/D*)(1/2), where D is the free diffusion coefficient and D* is the effective diffusion coefficient in tissue. In healthy brain, lambda is approximately 1.6, but the nature of this parameter is poorly understood. We report that the stratum radiatum of the hippocampal CA1 region in vitro, previously shown to be anisotropic (i.e., different along the x-, y-, and z-axes) in in vivo study, is isotropic like somatosensory neocortex but has a reduced lambda. Diffusion of fluorophore-labeled dextran (f-dex, M(r) 3,000) and tetramethylammonium (TMA(+), M(r) 74) was measured in rat brain slices (400 mum) using integrative optical imaging (IOI) and real-time iontophoresis (RTI), respectively. In the stratum radiatum, diffusion of f-dex was similar along the x-, y-, and z-axes (lambda(x), lambda(y); lambda(z) were 1.55, 1.53, and 1.55), but the tortuosity was significantly lower than in the neocortex, where lambda = 1.81. This finding was confirmed by the RTI method, which measured lambda with TMA(+), a much smaller molecule, and determined volume fraction alpha, the proportion of tissue occupied by the ECS. In stratum radiatum, lambda(x), lambda(y), and lambda(z) were 1.47, 1.44, and 1.46, while in neocortex, lambda was 1.65. The ECS volume fraction was similar (0.24) in both regions. It is proposed that in the hippocampus, low lambda reflects a reduced occurrence of concave extracellular microdomains, referred to as dead spaces, which increase tortuosity by transient trapping of markers. Functionally, a low lambda may permit structural plasticity and facilitate extrasynaptic communication. It may also enhance the spread of neuroactive substances and thus contribute to the sensitivity of the hippocampal CA1 region to ischemia and epilepsy.

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.

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.

Diffusion of epidermal growth factor in rat brain extracellular space measured by integrative optical imaging

Epidermal growth factor (EGF) stimulates proliferation, process outgrowth, and survival in the CNS. Understanding the actions of EGF necessitates characterizing its distribution in brain tissue following drug delivery or release from cellular sources. We used the integrative optical imaging (IOI) method to measure diffusion of fluorescently labeled EGF (6,600 Mr; 4 microg/ml) in the presence of excess unlabeled EGF (90 microg/ml) to compete off specific receptor binding and reveal the "true" EGF diffusion coefficient following injection in rat brain slices (400 microm). The effective diffusion coefficient was 5.18 +/- 0.16 x 10(-7) (SE) cm2/s (n = 22) in rat somatosensory cortex and the free diffusion coefficient, determined in dilute agarose gel, was 16.6 +/- 0.12 x 10(-7) cm2/s (n = 27). Tortuosity (lambda), a parameter representing the hindrance imposed on EGF by the convoluted brain extracellular space (ECS), was 1.8, the lowest yet measured by IOI for a protein in brain. Control experiments with fluorescent dextran of similar molecular weight and tetramethylammonium confirmed EGF did not affect local ECS structure. We conclude that transport of smaller growth factors such as EGF through brain ECS is less hindered than that of larger proteins (>10,000 Mr, e.g., nerve growth factor) where typically lambda > 2.1. Modeling was used to predict that low lambda will allow EGF sources in the brain to be further from target cells and still elicit a biological response. High lambda values for larger growth factors imply more constrained local biological effects than with smaller proteins such as EGF.

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, lambda = (D/D*)1/2, where D is the free diffusion coefficient and D* is the effective diffusion coefficient in brain. Experiments show that lambda 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 lambda-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 alpha (the ratio of the ECS volume to the whole tissue volume). This dependence can be described by the relation lambda = ((3-alpha)/2)1/2, indicating that the geometrical hindrance in such ECS cannot account for lambda > 1.225. Reasons for the discrepancy between the theoretical and experimental tortuosity values are discussed.

Dead-space microdomains hinder extracellular diffusion in rat neocortex during ischemia

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.

Measurement of diffusion parameters using a sinusoidal iontophoretic source in rat cortex

A new method was developed to extract diffusion parameters in brain tissue using a sinusoidal iontophoretic point source of tetramethylammonium operated at different frequencies. The resulting steady state oscillating extracellular concentration of this probe molecule was continuously monitored using an ion-selective microelectrode located about 100 microm from the source. Because the probe molecules must diffuse through the extracellular space (ECS), the oscillating concentration at the recording location will develop a phase lag and an amplitude attenuation relative to the sinusoidal source. These two components of the signal can be analyzed to determine the tortuosity factor lambda and the ECS volume fraction alpha. The method also measures the nonspecific clearance rate constant kappa. In brain slices this reflects washout of diffusing molecules. Values of alpha (0.18+/-0.05) and lambda (1.67+/-0.08) obtained from this frequency method in rat cortical slices were similar to those obtained by the real-time iontophoretic method employing a square pulse source. The relative merits of the frequency method compared to the pulse method are discussed.

Independence of extracellular tortuosity and volume fraction during osmotic challenge in rat neocortex

The structural properties of brain extracellular space (ECS) are summarised by the tortuosity (lambda) and the volume fraction (alpha). To determine if these two parameters were independent, we varied the size of the ECS by changing the NaCl content to alter osmolality of bathing media for rat cortical slices. Values of lambda and alpha were extracted from diffusion measurements using the real-time ionophoretic method with tetramethylammonium (TMA+). In normal medium (305 mosmol kg(-1)), the average value of lambda was 1.69 and of alpha was 0.24. Reducing osmolality to 150 mosmol kg(-1), increased lambda to 1.86 and decreased alpha to 0.12. Increasing osmolality to 350 mosmol kg(-1), reduced lambda to about 1.67 where it remained unchanged even when osmolality increased further to 500 mosmol kg(-1). In contrast, alpha increased steadily to 0.42 as osmolality increased. Comparison with previously published experiments employing 3000 M(r) dextran to measure lambda, showed the same behaviour as for TMA+, including the same constant lambda in hypertonic media but with a steeper slope in the hypotonic solutions. These data show that lambda and alpha behave differently as the ECS geometry varies. When alpha decreases, lambda increases but when alpha increases, lambda rapidly attains a constant value. A previous model allowing cellular shape to alter during osmotic challenge can account qualitatively for the plateau behaviour of lambda.

Water compartmentalization and spread of ischemic injury in thick-slice ischemia model

Water compartmentalization was studied in a thick-slice (1000 microm) model of ischemia by combining water-content measurements with extracellular diffusion analysis. Thick slices bathed in artificial cerebrospinal fluid continually gained water. Total tissue water content was increased by 67% after 6 hours of the incubation. Diffusion measurements using the tetramethylammonium method showed that the extracellular space, typically occupying 20% of brain tissue in vivo, was decreased to 10% at 30 minutes and 15% at 6 hours in both deep and superficial layers of thick slices. Quantification of water compartmentalization revealed that water moved initially from the extracellular space into the cells. Later, however, both compartments gained water. The initial cell swelling was accompanied by dramatic shifts in potassium. An initial rise of extracellular potassium to about 50 mmol/L was measured with a potassium-selective microelectrode positioned in the center of the thick slice; the concentration decreased slowly afterwards. Potassium content analysis revealed a 63% loss of tissue potassium within two hours of the incubation. In thick slices, ionic shifts, water redistribution, and a loss of synaptic transmission occur in both deep and superficial layers, indicating the spread of ischemic conditions even to areas with an unrestricted supply of nutrients.