Anisotropic and heterogeneous diffusion in the turtle cerebellum: implications for volume transmission

Structural Connectivity and Emotion Recognition Impairment in Children and Adolescents with Chromosome 22q11.2 Deletion Syndrome

Children with chromosome 22q11.2 deletion syndrome (22q11.2DS) exhibit impaired ability to process and understand emotions in others. We measured structural connectivity in children and adolescents with 22q11.2DS (n = 28) and healthy controls (n = 29). Compared to controls, those with 22q11.2DS had poorer social skills and more difficulty recognizing facial emotions. Children with 22q11.2DS also had higher fractional anisotropic diffusion in right amygdala to fusiform gyrus white matter pathways. Right amygdala to fusiform gyrus fractional anisotropy values partially mediated the relationship between 22q11.2DS and social skills, as well as the relationship between 22q11.2DS and emotion recognition accuracy. These findings provide insight into the neural origins of social skills deficits seen in 22q11.2DS and may serve as a biomarker for risk of future psychiatric problems.

Understanding Neuropeptide Transmission in the Brain by Optical Uncaging and Release

Neuropeptides are abundant and essential signaling molecules in the nervous system involved in modulating neural circuits and behavior. Neuropeptides are generally released extrasynaptically and signal via volume transmission through G-protein-coupled receptors (GPCR). Although substantive functional roles of neuropeptides have been discovered, many questions on neuropeptide transmission remain poorly understood, including the local diffusion and transmission properties in the brain extracellular space. To address this challenge, intensive efforts are required to develop advanced tools for releasing and detecting neuropeptides with high spatiotemporal resolution. Because of the rapid development of biosensors and materials science, emerging tools are beginning to provide a better understanding of neuropeptide transmission. In this perspective, we summarize the fundamental advances in understanding neuropeptide transmission over the past decade, highlight the tools for releasing neuropeptides with high spatiotemporal solution in the brain, and discuss open questions and future directions in the field.

Local diffusion in the extracellular space of the brain

The brain extracellular space (ECS) is a vast interstitial reticulum of extreme morphological complexity, composed of narrow gaps separated by local expansions, enabling interconnected highways between neural cells. Constituting on average 20% of brain volume, the ECS is key for intercellular communication, and understanding its diffusional properties is of paramount importance for understanding the brain. Within the ECS, neuroactive substances travel predominantly by diffusion, spreading through the interstitial fluid and the extracellular matrix scaffold after being focally released. The nanoscale dimensions of the ECS render it unresolvable by conventional live tissue compatible imaging methods, and historically diffusion of tracers has been used to indirectly infer its structure. Novel nanoscopic imaging techniques now show that the ECS is a highly dynamic compartment, and that diffusivity in the ECS is more heterogeneous than anticipated, with great variability across brain regions and physiological states. Diffusion is defined primarily by the local ECS geometry, and secondarily by the viscosity of the interstitial fluid, including the obstructive and binding properties of the extracellular matrix. ECS volume fraction and tortuosity both strongly determine diffusivity, and each can be independently regulated e.g. through alterations in glial morphology and the extracellular matrix composition. Here we aim to provide an overview of our current understanding of the ECS and its diffusional properties. We highlight emerging technological advances to respectively interrogate and model diffusion through the ECS, and point out how these may contribute in resolving the remaining enigmas of the ECS.

A noninvasive fluorescence imaging-based platform measures 3D anisotropic extracellular diffusion

Diffusion is a major molecular transport mechanism in biological systems. Quantifying direction-dependent (i.e., anisotropic) diffusion is vitally important to depicting how the three-dimensional (3D) tissue structure and composition affect the biochemical environment, and thus define tissue functions. However, a tool for noninvasively measuring the 3D anisotropic extracellular diffusion of biorelevant molecules is not yet available. Here, we present light-sheet imaging-based Fourier transform fluorescence recovery after photobleaching (LiFT-FRAP), which noninvasively determines 3D diffusion tensors of various biomolecules with diffusivities up to 51 µm2 s-1, reaching the physiological diffusivity range in most biological systems. Using cornea as an example, LiFT-FRAP reveals fundamental limitations of current invasive two-dimensional diffusion measurements, which have drawn controversial conclusions on extracellular diffusion in healthy and clinically treated tissues. Moreover, LiFT-FRAP demonstrates that tissue structural or compositional changes caused by diseases or scaffold fabrication yield direction-dependent diffusion changes. These results demonstrate LiFT-FRAP as a powerful platform technology for studying disease mechanisms, advancing clinical outcomes, and improving tissue engineering.

Current Techniques for Investigating the Brain Extracellular Space

The brain extracellular space (ECS) is a continuous reticular compartment that lies between the cells of the brain. It is vast in extent relative to its resident cells, yet, at the same time the nano- to micrometer dimensions of its channels and reservoirs are commonly finer than the smallest cellular structures. Our conventional view of this compartment as largely static and of secondary importance for brain function is rapidly changing, and its active dynamic roles in signaling and metabolite clearance have come to the fore. It is further emerging that ECS microarchitecture is highly heterogeneous and dynamic and that ECS geometry and diffusional properties directly modulate local diffusional transport, down to the nanoscale around individual synapses. The ECS can therefore be considered an extremely complex and diverse compartment, where numerous physiological events are unfolding in parallel on spatial and temporal scales that span orders of magnitude, from milliseconds to hours, and from nanometers to centimeters. To further understand the physiological roles of the ECS and identify new ones, researchers can choose from a wide array of experimental techniques, which differ greatly in their applicability to a given sample and the type of data they produce. Here, we aim to provide a basic introduction to the available experimental techniques that have been applied to address the brain ECS, highlighting their main characteristics. We include current gold-standard techniques, as well as emerging cutting-edge modalities based on recent super-resolution microscopy. It is clear that each technique comes with unique strengths and limitations and that no single experimental method can unravel the unknown physiological roles of the brain ECS on its own.

Spatial Organization and Dynamics of the Extracellular Space in the Mouse Retina

The extracellular space (ECS) plays an important role in the physiology of neural circuits. Despite our detailed understanding of the cellular architecture of the mammalian retina, little is known about the organization and dynamics of the retinal ECS. We developed an optical technique based on two-photon imaging of fluorescently labeled extracellular fluid to measure the ECS volume fraction (α) in the ex vivo retina of male and female mice. This method has high spatial resolution and can detect rapid changes in α evoked by osmotic challenge and neuronal activity. The measured ECS α varied dramatically in different layers of the adult mouse retina, with α equaling ∼0.050 in the ganglion cell layer, ∼0.122 in the inner plexiform layer (IPL), ∼0.025 in the inner nuclear layer (INL), ∼0.087 in the outer plexiform layer, and ∼0.026 in the outer nuclear layer (ONL). ECS α was significantly larger early in retinal development; α was 67% larger in the IPL and 100% larger in the INL in neonatal mice compared with adults. In adult retinas, light stimulation evoked rapid decreases in ECS α. Light-driven reductions in ECS α were largest in the IPL, where visual stimuli decreased α values ∼10%. These light-evoked decreases demonstrate that a physiological stimulus can lead to rapid changes in ECS α and indicate that activity-dependent regulation of extracellular space may contribute to visual processing in the retina.SIGNIFICANCE STATEMENT The volume fraction of the extracellular space (ECS α), that portion of CNS tissue occupied by interstitial space, influences the diffusion of neurotransmitters from the synaptic cleft and the volume transmission of transmitters. However, ECS α has never been measured in live retina, and little is known about how ECS α varies following physiological stimulation. Here we show that ECS α values vary dramatically between different retinal layers and decrease by 10% following light stimulation. ECS α differences within the retina will influence volume transmission and light-evoked α variations may modulate synaptic transmission and visual processing in the retina. Activity-dependent ECS α variations may represent a mechanism of synaptic modulation throughout the CNS.

The Effect of Hapln4 Link Protein Deficiency on Extracellular Space Diffusion Parameters and Perineuronal Nets in the Auditory System During Aging

Hapln4 is a link protein which stabilizes the binding between lecticans and hyaluronan in perineuronal nets (PNNs) in specific brain regions, including the medial nucleus of the trapezoid body (MNTB). The aim of this study was: (1) to reveal possible age-related alterations in the extracellular matrix composition in the MNTB and inferior colliculus, which was devoid of Hapln4 and served as a negative control, (2) to determine the impact of the Hapln4 deletion on the values of the ECS diffusion parameters in young and aged animals and (3) to verify that PNNs moderate age-related changes in the ECS diffusion, and that Hapln4-brevican complex is indispensable for the correct protective function of the PNNs. To achieve this, we evaluated the ECS diffusion parameters using the real-time iontophoretic method in the selected region in young adult (3 to 6-months-old) and aged (12 to 18-months-old) wild type and Hapln4 knock-out (KO) mice. The results were correlated with an immunohistochemical analysis of the ECM composition and astrocyte morphology. We report that the ECM composition is altered in the aged MNTB and aging is a critical point, revealing the effect of Hapln4 deficiency on the ECS diffusion. All of our findings support the hypothesis that the ECM changes in the MNTB of aged KO animals affect the ECS parameters indirectly, via morphological changes of astrocytes, which are in direct contact with synapses and can be influenced by the ongoing synaptic transmission altered by shifts in the ECM composition.

Uncertainty quantification of parenchymal tracer distribution using random diffusion and convective velocity fields

Background

Influx and clearance of substances in the brain parenchyma occur by a combination of diffusion and convection, but the relative importance of these mechanisms is unclear. Accurate modeling of tracer distributions in the brain relies on parameters that are partially unknown and with literature values varying by several orders of magnitude. In this work, we rigorously quantified the variability of tracer distribution in the brain resulting from uncertainty in diffusion and convection model parameters.

Methods

Using the convection–diffusion–reaction equation, we simulated tracer distribution in the brain parenchyma after intrathecal injection. Several models were tested to assess the uncertainty both in type of diffusion and velocity fields and also the importance of their magnitude. Our results were compared with experimental MRI results of tracer enhancement.

Results

In models of pure diffusion, the expected amount of tracer in the gray matter reached peak value after 15 h, while the white matter did not reach peak within 24 h with high likelihood. Models of the glymphatic system were similar qualitatively to the models of pure diffusion with respect to expected time to peak but displayed less variability. However, the expected time to peak was reduced to 11 h when an additional directionality was prescribed for the glymphatic circulation. In a model including drainage directly from the brain parenchyma, time to peak occured after 6–8 h for the gray matter.

Conclusion

Even when uncertainties are taken into account, we find that diffusion alone is not sufficient to explain transport of tracer deep into the white matter as seen in experimental data. A glymphatic velocity field may increase transport if a large-scale directional structure is included in the glymphatic circulation.

Time-Resolved Integrative Optical Imaging of Diffusion during Spreading Depression

An improved version of the integrative optical imaging method has been developed that substantially increases the time resolution of diffusion measurements. We present a theory for time-resolved integrative optical imaging that incorporates a time-dependent effective diffusion coefficient in homogeneous anisotropic media and a time-dependent nonspecific linear clearance. The method was applied to measure the very fast changes in extracellular diffusion that occur during spreading depression in rat hippocampal slices. We were able to achieve a time resolution of approximately 1 s, an improvement of at least 10 times compared to the standard methods for extracellular diffusion measurement. We have found that diffusion of a small fluorescent extracellular marker (MW 3000) completely stopped during the maximum direct current shift associated with the spreading depression wave, then gradually resumed over several minutes afterward. The effect of spreading depression on extracellular space is much larger than previously estimated by other methods with lower time resolution.

Integrity of White Matter is Compromised in Mice with Hyaluronan Deficiency

Brain white matter is the means of efficient signal propagation in brain and its dysfunction is associated with many neurological disorders. We studied the effect of hyaluronan deficiency on the integrity of myelin in murine corpus callosum. Conditional knockout mice lacking the hyaluronan synthase 2 were compared with control mice. Ultrastructural analysis by electron microscopy revealed a higher proportion of myelin lamellae intruding into axons of knockout mice, along with significantly slimmer axons (excluding myelin sheath thickness), lower g-ratios, and frequent loosening of the myelin wrappings, even though the myelin thickness was similar across the genotypes. Analysis of extracellular diffusion of a small marker molecule tetramethylammonium (74 MW) in brain slices prepared from corpus callosum showed that the extracellular space volume increased significantly in the knockout animals. Despite this vastly enlarged volume, extracellular diffusion rates were significantly reduced, indicating that the compromised myelin wrappings expose more complex geometric structure than the healthy ones. This finding was confirmed in vivo by diffusion-weighted magnetic resonance imaging. Magnetic resonance spectroscopy suggested that water was released from within the myelin sheaths. Our results indicate that hyaluronan is essential for the correct formation of tight myelin wrappings around the axons in white matter.

Time-resolved quantification of the dynamic extracellular space in the brain during short-lived event: methodology and simulations

Two macroscopic parameters describe the interstitial diffusion of substances in the extracellular space (ECS) of the brain, the ECS volume fraction α and the diffusion tortuosity λ. Past methods based on sampling the extracellular concentration of a membrane-impermeable ion tracer, such as tetramethylammonium (TMA⁺), can characterize either the dynamic α(t) alone or the constant α and λ in resting state but never the dynamic α(t) and λ(t) simultaneously in short-lived brain events. In this work, we propose to use a sinusoidal method of TMA⁺ to provide time-resolved quantification of α(t) and λ(t) in acute brain events. This method iontophoretically injects TMA⁺ in the brain ECS by a sinusoidal time pattern, samples the resulting TMA⁺ diffusion waveform at a distance, and analyzes the transient modulations of the amplitude and phase lag of the sampled TMA⁺ waveform to infer α(t) and λ(t). Applicability of the sinusoidal method was verified through computer simulations of the sinusoidal TMA⁺ diffusion waveform in cortical spreading depression. Parameter sensitivity analysis identified the sinusoidal frequency and the interelectrode distance as two key operating parameters. Compared with other TMA⁺-based methods, the sinusoidal method can more accurately capture the dynamic α(t) and λ(t) in acute brain events and is equally applicable to other pathological episodes such as epilepsy, transient ischemic attack, and brain injury. Future improvement of the method should focus on high-fidelity extraction of the waveform amplitude and phase angle. NEW & NOTEWORTHY An iontophoretic sinusoidal method of tetramethylammonium is described to capture the dynamic brain extracellular space volume fraction α and diffusion tortuosity λ. The sinusoidal frequency and interelectrode distance are two key operating parameters affecting the method's accuracy in capturing α(t) and λ(t). High-fidelity extraction of the waveform amplitude and phase lag is critical to successful sinusoidal analyses.

A deficiency of the link protein Bral2 affects the size of the extracellular space in the thalamus of aged mice

Bral2 is a link protein stabilizing the binding between lecticans and hyaluronan in perineuronal nets and axonal coats (ACs) in specific brain regions. Using the real-time iontophoretic method and diffusion-weighted magnetic resonance, we determined the extracellular space (ECS) volume fraction (α), tortuosity (λ), and apparent diffusion coefficient of water (ADC_W ) in the thalamic ventral posteromedial nucleus (VPM) and sensorimotor cortex of young adult (3-6 months) and aged (14-20 months) Bral2-deficient (Bral2^-/- ) mice and age-matched wild-type (wt) controls. The results were correlated with an analysis of extracellular matrix composition. In the cortex, no changes between wt and Bral2^-/- were detected, either in the young or aged mice. In the VPM of aged but not in young Bral2^-/- mice, we observed a significant decrease in α and ADC_W in comparison with age-matched controls. Bral2 deficiency led to a reduction of both aggrecan- and brevican-associated perineuronal nets and a complete disruption of brevican-based ACs in young as well as aged VPM. Our data suggest that aging is a critical point that reveals the effect of Bral2 deficiency on VPM diffusion. This effect is probably mediated through the enhanced age-related damage of neurons lacking protective ACs, or the exhausting of compensatory mechanisms maintaining unchanged diffusion parameters in young Bral2^-/- animals. A decreased ECS volume in aged Bral2^-/- mice may influence the diffusion of neuroactive substances, and thus extrasynaptic and also indirectly synaptic transmission in this important nucleus of the somatosensory pathway.

Real-time Iontophoresis with Tetramethylammonium to Quantify Volume Fraction and Tortuosity of Brain Extracellular Space

This review describes the basic concepts and protocol to perform the real-time iontophoresis (RTI) method, the gold-standard to explore and quantify the extracellular space (ECS) of the living brain. The ECS surrounds all brain cells and contains both interstitial fluid and extracellular matrix. The transport of many substances required for brain activity, including neurotransmitters, hormones, and nutrients, occurs by diffusion through the ECS. Changes in the volume and geometry of this space occur during normal brain processes, like sleep, and pathological conditions, like ischemia. However, the structure and regulation of brain ECS, particularly in diseased states, remains largely unexplored. The RTI method measures two physical parameters of living brain: volume fraction and tortuosity. Volume fraction is the proportion of tissue volume occupied by ECS. Tortuosity is a measure of the relative hindrance a substance encounters when diffusing through a brain region as compared to a medium with no obstructions. In RTI, an inert molecule is pulsed from a source microelectrode into the brain ECS. As molecules diffuse away from this source, the changing concentration of the ion is measured over time using an ion-selective microelectrode positioned roughly 100 µm away. From the resulting diffusion curve, both volume fraction and tortuosity can be calculated. This technique has been used in brain slices from multiple species (including humans) and in vivo to study acute and chronic changes to ECS. Unlike other methods, RTI can be used to examine both reversible and irreversible changes to the brain ECS in real time.

Evaluation of Drug Concentrations Delivered by Microiontophoresis

Microiontophoresis uses an electric current to eject a drug solution from a glass capillary and is often utilized for targeted delivery in neurochemical investigations. The amount of drug ejected, and its effective concentration at the tip, has historically been difficult to determine, which has precluded its use in quantitative studies. To address this, a method called controlled iontophoresis was developed which employs a carbon-fiber microelectrode incorporated into a multibarreled iontophoretic probe to detect the ejection of electroactive species. Here, we evaluate the accuracy of this method. To do this, we eject different concentrations of quinpirole, a D2 receptor agonist, into a brain slice containing the dorsal striatum, a brain region with a high density of dopamine terminals. Local electrical stimulation was used to evoke dopamine release, and inhibitory actions of quinpirole on this release were examined. The amount of drug ejected was estimated by detection of a coejected electrochemical marker. Dose response curves generated in this manner were compared to curves generated by conventional perfusion of quinpirole through the slice. We find several experimental conditions must be optimized for accurate results. First, selection of a marker with an identical charge was necessary to mimic the ejection of the cationic agonist. Next, evoked responses were more precise following longer periods between the end of the ejection and stimulation. Lastly, the accuracy of concentration evaluations was improved by longer ejections. Incorporation of these factors into existing protocols allows for greater certainty of concentrations delivered by controlled iontophoresis.

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.

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.

An excitatory GABA loop operating in vivo

While it has been proposed that the conventional inhibitory neurotransmitter GABA can be excitatory in the mammalian brain, much remains to be learned concerning the circumstances and the cellular mechanisms governing potential excitatory GABA action. Using a combination of optogenetics and two-photon calcium imaging in vivo, we find that activation of chloride-permeable GABA_A receptors in parallel fibers (PFs) of the cerebellar molecular layer of adult mice causes parallel fiber excitation. Stimulation of PFs at submaximal stimulus intensities leads to GABA release from molecular layer interneurons (MLIs), thus creating a positive feedback loop that enhances excitation near the center of an activated PF bundle. Our results imply that elevated chloride concentration can occur in specific intracellular compartments of mature mammalian neurons and suggest an excitatory role for GABA_A receptors in the cerebellar cortex of adult mice.

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.

Revealing neuronal function through microelectrode array recordings

Microelectrode arrays and microprobes have been widely utilized to measure neuronal activity, both in vitro and in vivo. The key advantage is the capability to record and stimulate neurons at multiple sites simultaneously. However, unlike the single-cell or single-channel resolution of intracellular recording, microelectrodes detect signals from all possible sources around every sensor. Here, we review the current understanding of microelectrode signals and the techniques for analyzing them. We introduce the ongoing advancements in microelectrode technology, with focus on achieving higher resolution and quality of recordings by means of monolithic integration with on-chip circuitry. We show how recent advanced microelectrode array measurement methods facilitate the understanding of single neurons as well as network function.

Multiscale vision model highlights spontaneous glial calcium waves recorded by 2-photon imaging in brain tissue

Intercellular glial calcium waves (GCW) constitute a signaling pathway which can be visualized by fluorescence imaging of cytosolic Ca(2+) changes. Reliable detection of calcium waves in multiphoton imaging data is challenging because of low signal-to-noise ratio. We modified the multiscale vision model (MVM), originally employed to detect faint objects in astronomy data to process stacks of fluorescent images. We demonstrate that the MVM identified and characterized GCWs with much higher sensitivity and detail than pixel thresholding. Origins of GCWs were often associated with prolonged secondary Ca(2+) elevations. The GCWs had variable shapes, and secondary GCWs were observed to bud from the primary, larger GCW. GCWs evaded areas shortly before occupied by a preceding GCW instead circulating around the refractory area. Blood vessels uniquely reshaped GCWs and were associated with secondary GCW events. We conclude that the MVM provides unique possibilities to study spatiotemporally correlated Ca(2+) signaling in brain tissue.

Brain Extracellular Space as a Diffusion Barrier

The extracellular space (ECS) consists of the narrow channels between brain cells together with their geometrical configuration and contents. Despite being only 20-60 nm in width, the ECS typically occupies 20% of the brain volume. Numerous experiments over the last 50 years have established that molecules moving through the ECS obey the laws of diffusion but with an effective diffusion coefficient reduced by a factor of about 2.6 compared to free diffusion. This review considers the origins of the diffusion barrier arising from the ECS and its properties. The paper presents a brief overview of software for implementing two point-source paradigms for measurements of localized diffusion properties: the real-time iontophoresis or pressure method for small ions and the integrative optical imaging method for macromolecules. Selected results are presented. This is followed by a discussion of the application of the MCell Monte Carlo simulation program to determining the importance of geometrical constraints, especially dead-space microdomains, and the possible role of interaction with the extracellular matrix. It is concluded that we can predict the impediment to diffusion of many molecules of practical importance and also use studies of the diffusion of selected molecular probes to reveal the barrier properties of the ECS.

An evaluation of the conductivity profile in the somatosensory barrel cortex of Wistar rats

Microelectrode arrays used to record local field potentials from the brain are being built with increasingly more spatial resolution, ranging from the initially developed laminar arrays to those with planar and three-dimensional (3D) formats. In parallel with such development in recording techniques, current source density (CSD) analyses have recently been expanded up to the continuous-3D form. Unfortunately, the effect of the conductivity profile on the CSD analysis performed with contemporary microelectrode arrays has not yet been evaluated and most of the studies assumed it was homogeneous and isotropic. In this study, we measured the conductivity profile in the somatosensory barrel cortex of Wistar rats. To that end, we combined multisite electrophysiological data recorded with a homemade assembly of silicon-based probes and a nonlinear least-squares algorithm that implicitly assumed that the cerebral cortex of rodents could be locally approximated as a layered anisotropic spherical volume conductor. The eccentricity of the six cortical layers in the somatosensory barrel cortex was evaluated from postmortem histological images. We provided evidence for the local spherical character of the entire barrels field, with concentric cortical layers. We found significant laminar dependencies in the conductivity values with radial/tangential anisotropies. These results were in agreement with the layer-dependent orientations of myelinated axons, but hardly related to densities of cells. Finally, we demonstrated through simulations that ignoring the real conductivity profile in the somatosensory barrel cortex of rats caused considerable errors in the CSD reconstruction, with pronounced effects on the continuous-3D form and charge-unbalanced CSD. We concluded that the conductivity profile must be included in future developments of CSD analysis, especially for rodents.

Bral1: its role in diffusion barrier formation and conduction velocity in the CNS

At the nodes of Ranvier, excitable axon membranes are exposed directly to the extracellular fluid. Cations are accumulated and depleted in the local extracellular nodal region during action potential propagation, but the impact of the extranodal micromilieu on signal propagation still remains unclear. Brain-specific hyaluronan-binding link protein, Bral1, colocalizes and forms complexes with negatively charged extracellular matrix (ECM) proteins, such as versican V2 and brevican, at the nodes of Ranvier in the myelinated white matter. The link protein family, including Bral1, appears to be the linchpin of these hyaluronan-bound ECM complexes. Here we report that the hyaluronan-associated ECM no longer shows a nodal pattern and that CNS nerve conduction is markedly decreased in Bral1-deficient mice even though there were no differences between wild-type and mutant mice in the clustering or transition of ion channels at the nodes or in the tissue morphology around the nodes of Ranvier. However, changes in the extracellular space diffusion parameters, measured by the real-time iontophoretic method and diffusion-weighted magnetic resonance imaging (MRI), suggest a reduction in the diffusion hindrances in the white matter of mutant mice. These findings provide a better understanding of the mechanisms underlying the accumulation of cations due to diffusion barriers around the nodes during saltatory conduction, which further implies the importance of the Bral1-based extramilieu for neuronal conductivity.

Radially expanding transglial calcium waves in the intact cerebellum

Multicellular glial calcium waves may locally regulate neural activity or brain energetics. Here, we report a diffusion-driven astrocytic signal in the normal, intact brain that spans many astrocytic processes in a confined volume without fully encompassing any one cell. By using 2-photon microscopy in rodent cerebellar cortex labeled with fluorescent indicator dyes or the calcium-sensor protein G-CaMP2, we discovered spontaneous calcium waves that filled approximately ellipsoidal domains of Bergmann glia processes. Waves spread in 3 dimensions at a speed of 4-11 microm/s to a diameter of approximately 50 microm, slowed during expansion, and were reversibly blocked by P2 receptor antagonists. Consistent with the hypothesis that ATP acts as a diffusible trigger of calcium release waves, local ejection of ATP triggered P2 receptor-mediated waves that were refractory to repeated activation. Transglial waves represent a means for purinergic signals to act with local specificity to modulate activity or energetics in local neural circuits.

Measuring diffusion parameters in the brain: comparing the real-time iontophoretic method and diffusion-weighted magnetic resonance

The extracellular space (ECS) diffusion parameters influence the movement of ions, neuroactive substances, hormones and metabolites in the nervous tissue. They also affect extrasynaptic transmission, a mode of signal transmission dependent solely on diffusion. This review compares in detail two methods for studying diffusion in the brain: the real-time iontophoretic tetramethylammonium method for ECS volume fraction and tortuosity measurements and diffusion weighted-magnetic resonance imaging for measuring the apparent diffusion coefficient of water. The results obtained using both methods under physiological conditions (post-natal development, ageing) or in pathologies (brain injury, ischaemia) and their similarities and differences are discussed.

Rigorous mathematical modeling techniques for optimal delivery of macromolecules to the brain

Several treatment modalities for neurodegenerative diseases or tumors of the central nervous system involve invasive delivery of large molecular weight drugs to the brain. Despite the ample record of experimental studies, accurate drug targeting for the human brain remains a challenge. This paper proposes a systematic design method of administering drugs to specific locations in the human brain based on first principles transport in porous media. The proposed mathematical framework predicts achievable treatment volumes in target regions as a function of brain anatomy and infusion catheter position. A systematic procedure to determine the optimal infusion and catheter design parameters that maximize the penetration depth and volumes of distribution will be discussed. The computer simulations are validated with agarose gel phantom experiments and rat data. The rigorous computational approach will allow physicians and scientists to better plan the administration of therapeutic drugs to the central 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.

Computational methods for predicting drug transport in anisotropic and heterogeneous brain tissue

Effective drug delivery for many neurodegenerative diseases or tumors of the central nervous system is challenging. Targeted invasive delivery of large macromolecules such as trophic factors to desired locations inside the brain is difficult due to anisotropy and heterogeneity of the brain tissue. Despite much experimental research, prediction of bio-transport phenomena inside the brain remains unreliable. This article proposes a rigorous computational approach for accurately predicting the fate of infused therapeutic agents inside the brain. Geometric and physiological properties of anisotropic and heterogeneous brain tissue affecting drug transport are accounted for by in-vivo diffusion tensor magnetic resonance imaging data. The three-dimensional brain anatomy is reconstructed accurately from subject-specific medical images. Tissue anisotropy and heterogeneity are quantified with the help of diffusion tensor imaging (DTI). Rigorous first principles physical transport phenomena are applied to predict the fate of a high molecular weight trophic factor infused into the midbrain. Computer prediction of drug distribution in humans accounting for heterogeneous and anisotropic brain tissue properties have not been adequately researched in open literature before.

Diffusion of flexible random-coil dextran polymers measured in anisotropic brain extracellular space by integrative optical imaging

There are a limited number of methods available to quantify the extracellular diffusion of macromolecules in an anisotropic brain region, e.g., an area containing numerous aligned fibers where diffusion is faster along the fibers than across. We applied the integrative optical imaging method to measure diffusion of the fluorophore Alexa Fluor 488 (molecular weight (MW) 547) and fluorophore-labeled flexible random-coil dextran polymers (dex3, MW 3000; dex75, MW 75,000; dex282, MW 282,000; dex525, MW 525,000) in the extracellular space (ECS) of the anisotropic molecular layer of the isolated turtle cerebellum. For all molecules, two-dimensional images acquired an elliptical shape with major and minor axes oriented along and across, respectively, the unmyelinated parallel fibers. The effective diffusion coefficients, D*(major) and D*(minor), decreased with molecular size. The diffusion anisotropy ratio (DAR = D*(major)/D*(minor)) increased for Alexa Fluor 488 through dex75 but then unexpectedly reached a plateau. We argue that dex282 and dex525 approach the ECS width and deform to diffuse. In support of this concept, scaling theory shows the diffusion behavior of dex282 and dex525 to be consistent with transition to a reptation regime, and estimates the average ECS width at approximately 31 nm. These findings have implications for the interstitial transport of molecules and drugs, and for modeling neurotransmitter diffusion during ectopic release and spillover.

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.

Extracellular space in mouse cerebellar cortex revealed by in vivo cryotechnique

Conventional methods of preparing tissue specimens for morphological investigation of the central nervous system suffer from inevitable artifacts caused by anoxia during the processing. In the present study we performed ultrastructural analyses of mouse cerebellar cortex using the in vivo cryotechnique (IVCr), which minimizes ischemic artifacts of target organs through direct cryofixation in vivo. In molecular and Purkinje cell layers of the mouse cerebellum prepared with IVCr, considerably large extracellular spaces (ECS) were detected among cellular profiles and synaptic clefts. The ECS obtained with IVCr without ischemia were larger than those obtained with IVCr after 8-minute ischemia or a conventional quick-freezing method with fresh resected tissues (FQF), but did not decrease with IVCr after 30-second ischemia. By contrast, the parallel fibers observed with IVCr without ischemia were slightly smaller than those after 30-second ischemia, and significantly smaller than those prepared with IVCr after 8-minute ischemia or FQF. ECS were frequently preserved around synaptic clefts, although the rest were totally or partially enclosed with closely apposed glial processes. The estimated sizes of the ECS around synaptic clefts did not differ between the opened and enclosed synapses, suggesting that the opened synapses might be temporarily surrounded by glial sheaths dynamically extending or retracting throughout the perisynaptic ECS. These findings indicate IVCr to be useful for some morphological analyses of ECS in the central nervous system. The appreciable ECS around synapses would allow morphological and functional changes of neuronal and glial cells dynamically involved in synaptic remodeling or signal transduction.

Serotonin concentrations in the lumbosacral spinal cord of the adult rat following microinjection or dorsal surface application

Application of neuroactive substances, including monoamines, is common in studies examining the spinal mechanisms of sensation and behavior. However, affected regions and time courses of transmitter activity are uncertain. We measured the spatial and temporal distribution of serotonin [5-hydroxytryptamine (5-HT)] in the lumbosacral spinal cord of halothane-anesthetized adult rats, following its intraspinal microinjection or surface application. Carbon fiber microelectrodes (CFMEs) were positioned at various locations in the spinal cord and oxidation currents corresponding to extracellular 5-HT were measured by fast cyclic voltammetry. Intraspinal microinjection of 5-HT (100 microM, 1-3 microl) produced responses that were most pronounced at CFMEs positioned <or=800 microm from the drug micropipette: 5-HT concentration was significantly higher (1.43 vs. <0.28% of initial concentration) and response latency was shorter (67.1 vs. 598.2 s) compared with more distantly positioned CFMEs. Treatment with the selective 5-HT reuptake inhibitor clomipramine only slightly affected the spread of microinjected 5-HT. Surface application over several segments led to a transient rise in concentration that was usually apparent within 30 s and was dramatically attenuated with increasing depth: 0.25% of initial concentration (1 mM) within 400 microm of the dorsal surface and <0.001% between 1,170 and 2,000 microm. This initial response to superfusion was sometimes followed by a gradual increase to a new concentration plateau. In sum, compared with bath application, microinjection can deliver about tenfold higher transmitter concentrations, but to much more restricted areas of the spinal cord.

Contrast-modulated Nonlinear Diffusion for X-ray Angiogram Images

In this paper, we present a new method for X-ray angiogram images enhancement using a contrast-modulated nonlinear diffusion. The original nonlinear diffusion is gradient driven, which leads into much dependence on the accurate estimation of the edge. However, it is very difficult to get the accurate estimation of edges for X-ray angiogram images, which are characterized with complex background. So it is necessary to do some improvements to this model. By designing a new concept of contrast space according to the characteristics of these images, we change the original nonlinear diffusion into contrast-modulated nonlinear diffusion. Compared with the traditional method, this new approach is proved to have a better performance of enhancement.

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.

Extrasynaptic volume transmission and diffusion parameters of the extracellular space

Extrasynaptic communication between neurons or neurons and glia is mediated by the diffusion of neuroactive substances in the volume of the extracellular space (ECS). The size and irregular geometry of the diffusion channels in the ECS substantially differ not only around individual cells but also in different CNS regions and thus affect and direct the movement of various neuroactive substances in the ECS. Diffusion in the CNS is therefore not only inhomogeneous, but often also anisotropic. The diffusion parameters in adult mammals (including humans), ECS volume fraction alpha (alpha=ECS volume/total tissue volume) and tortuosity lambda (lambda(2)=free/apparent diffusion coefficient), are typically 0.20-0.25 and 1.5-1.6, respectively, and as such hinder the diffusion of neuroactive substances and water. These diffusion parameters modulate neuronal signaling, neuron-glia communication and extrasynaptic "volume" transmission. A significant decrease in ECS volume fraction and an increase in diffusion barriers (tortuosity) occur during neuronal activity and pathological states. The changes are often related to cell swelling, cell loss, astrogliosis, the rearrangement of neuronal and astrocytic processes and changes in the extracellular matrix. They are also altered during physiological states such as development, lactation and aging. Plastic changes in ECS volume, tortuosity and anisotropy significantly affect neuron-glia communication, the spatial relation of glial processes toward synapses, glutamate or GABA "spillover" and synaptic crosstalk. The various changes in tissue diffusivity occurring during many pathological states are 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.

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.

Modulation of Glutamate Mobility Reveals the Mechanism Underlying Slow-Rising AMPAR EPSCs and the Diffusion Coefficient in the Synaptic Cleft

Fast- and slow-rising AMPA receptor-mediated EPSCs occur at central synapses. Fast-rising EPSCs are thought to be mediated by rapid local release of glutamate. However, two controversial mechanisms have been proposed to underlie slow-rising EPSCs: prolonged local release of transmitter via a fusion pore, and spillover of transmitter released rapidly from distant sites. We have investigated the mechanism underlying slow-rising EPSCs and the diffusion coefficient of glutamate in the synaptic cleft (Dglut) at cerebellar mossy fiber-granule cell synapses using a combination of diffusion modeling and patch-clamp recording. Simulations show that modulating Dglut has different effects on the peak amplitudes and time courses of EPSCs mediated by these two mechanisms. Slowing diffusion with the macromolecule dextran slowed slow-rising EPSCs and had little effect on their amplitude, indicating that glutamate spillover underlies these currents. Our results also suggest that under control conditions Dglut is approximately 3-fold lower than in free solution.

Significant shrinkage of extracellular space during global cerebral ischemia: differences in gray and white matter ischemia

Brain extracellular space (ECS) provides an important microenvironment for neurons and glial cells. In the present study, we investigated differences in ischemic changes of ECS in gray and white matter during global ischemia in cats (n = 8). Diffusion capacity of tetramethylammonium ion (TMA+, 74.1Da) was evaluated by measuring extracellular TMA+ concentration applied via microdialysis. In both gray and white matter, TMA+ concentration significantly increased within 10 minutes after the induction of ischemia, and sustained during 120 min of ischemia. The increase, however, was slower and smaller in white matter than in gray matter. In other two animals, volume fraction and tortuosity of ECS were determined by iontophoresis during global ischemia. After 30 min of ischemia induction, volume fraction was decreased and tortuosity was increased in both gray and white matter. In white matter, decrease in volume fraction and increase in tortuosity were smaller than in gray matter. The present study demonstrates that cerebral ischemia induces not only significant shrinkage of ECS volume but also restricts molecular diffusion within. Smaller changes of diffusion capacity within white matter ECS during ischemia may be relevant for lower ischemic vulnerability of the region.

Automatic segmentation of thalamic nuclei from diffusion tensor magnetic resonance imaging

The nuclei of the thalamus have traditionally been delineated by their distinct cyto/myeloarchitectural appearance on histology. Here, we show that diffusion tensor magnetic resonance imaging (DTI) can noninvasively resolve the major thalamic nuclei based on the characteristic fiber orientation of the corticothalamic/thalamocortical striations within each nucleus. Using an automatic clustering algorithm, we extracted the Talairach coordinates for the individual thalamic nuclei. The center-of-mass coordinates for the segmented nuclei were found to agree strongly with those obtained from a histological atlas. The ability to resolve thalamic nuclei with DTI will allow for morphometric analysis of specific nuclei and improved anatomical localization of functional activation in the thalamus.

Diffusion parameters of the extracellular space in human gliomas

Tumor cell migration through the extracellular space (ECS) might be affected by its pore size and extracellular matrix molecule content. ECS volume fraction alpha (alpha = ECS volume/total tissue volume), tortuosity lambda (lambda(2) = free/apparent diffusion coefficient) and nonspecific uptake k' were studied by the real-time tetramethylammonium method in acute slices of human tissue. The diffusion parameters in temporal cortical tissue resected during surgical treatment of temporal lobe epilepsy (control) were compared with those in brain tumors. Subsequently, tumor slices were histopathologically classified according to the grading system of the World Health Organization (WHO), and proliferative activity was assessed. The average values of alpha, lambda, and k' in control cortex were 0.24, 1.55, and 3.66 x 10(-3)s(-1), respectively. Values of alpha, lambda, and k' in oligodendrogliomas did not significantly differ from controls. In pilocytic astrogliomas (WHO grade I) as well as in ependymomas (WHO grade II), alpha was significantly higher, while lambda and k' were unchanged. Higher values of alpha as well as lambda were found in low-grade diffuse astrocytomas (WHO grade II). In cellular regions of high-grade astrocytomas (WHO grade III and IV), alpha and lambda were further increased, and k' was significantly larger than in controls. Classic medulloblastomas (WHO grade IV) had an increased alpha, but not lambda or k', while in the desmoplastic type alpha and k' remained unchanged, but lambda was greatly increased. Tumor malignancy grade strongly corresponds to an increase in ECS volume, which is accompanied by a change in ECS structure manifested by an increase in diffusion barriers for small molecules.

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.

Water ADC, extracellular space volume, and tortuosity in the rat cortex after traumatic injury

The diffusion parameters in rat cortex were studied 3-35 days following a cortical stab wound, using diffusion-weighted MR to determine the apparent diffusion coefficient of water (ADC(W)) in the tissue, and the real-time iontophoretic tetramethylammonium (TMA) method to measure the extracellular space (ECS) diffusion parameters: ECS volume fraction alpha and the ADC of TMA(+) (ADC(TMA)). Severe astrogliosis was found close to the wound, and mild astrogliosis was found in the ipsilateral but not the contralateral cortex. Chondroitin sulfate proteoglycan (CSPG) expression was increased throughout the ipsilateral cortex. In the hemisphere contralateral to the wound, alpha, ADC(TMA), and ADC(W) were not significantly different from control values. ECS volume fraction was increased only in the vicinity of the wound, in the region of cell death and severe astrogliosis, at 3 and 7 days after injury. However, both ADC(TMA) and ADC(W) were significantly decreased after lesion in the vicinity of the wound as well as in the rest of the ipsilateral hemisphere distant from the wound. Thus, both ADC(W) and ADC(TMA) decreased in regions wherein alpha did not change but CSPG increased. An increase in extracellular matrix expression may therefore impose diffusion barriers for water as well as for TMA molecules.

Brain antioxidant regulation in mammals and anoxia-tolerant reptiles: balanced for neuroprotection and neuromodulation

Reactive oxygen species (ROS) generated by mitochondrial respiration and other processes are often viewed as hazardous substances. Indeed, oxidative stress, defined as an imbalance between oxidant production and antioxidant protection, has been linked to several neurological disorders, including cerebral ischemia-reperfusion and Parkinson's disease. Consequently, cells and organisms have evolved specialized antioxidant defenses to balance ROS production and prevent oxidative damage. Research in our laboratory has shown that neuronal levels of ascorbate, a low molecular weight antioxidant, are ten-fold higher than those in much less metabolically active glial cells. Ascorbate levels are also selectively elevated in the CNS of anoxia-tolerant reptiles compared to mammals; moreover, plasma and CSF ascorbate concentrations increase markedly in cold-adapted turtles and in hibernating squirrels. Levels of the related antioxidant, glutathione, vary much less between neurons and glia or among species. An added dimension to the role of the antioxidant network comes from recent evidence that ROS can act as neuromodulators. One example is modulation of dopamine release by endogenous hydrogen peroxide, which we describe here for several mammalian species. Together, these data indicate adaptations that prevent oxidative stress and suggest a particularly important role for ascorbate. Moreover, they show that the antioxidant network must be balanced precisely to provide functional levels of ROS, as well as neuroprotection.

The basis of anisotropic water diffusion in the nervous system - a technical review

Anisotropic water diffusion in neural fibres such as nerve, white matter in spinal cord, or white matter in brain forms the basis for the utilization of diffusion tensor imaging (DTI) to track fibre pathways. The fact that water diffusion is sensitive to the underlying tissue microstructure provides a unique method of assessing the orientation and integrity of these neural fibres, which may be useful in assessing a number of neurological disorders. The purpose of this review is to characterize the relationship of nuclear magnetic resonance measurements of water diffusion and its anisotropy (i.e. directional dependence) with the underlying microstructure of neural fibres. The emphasis of the review will be on model neurological systems both in vitro and in vivo. A systematic discussion of the possible sources of anisotropy and their evaluation will be presented followed by an overview of various studies of restricted diffusion and compartmentation as they relate to anisotropy. Pertinent pathological models, developmental studies and theoretical analyses provide further insight into the basis of anisotropic diffusion and its potential utility in the nervous system.

Learning deficits in aged rats related to decrease in extracellular volume and loss of diffusion anisotropy in hippocampus

The extracellular space (ECS) is the microenvironment of the nerve cells and an important communication channel, allowing for long-distance extrasynaptic communication between cells. Changes in ECS size, geometry, and composition have been reported in diverse (patho)physiological states, including aging. In the present study, real-time tetramethylammonium (TMA+) iontophoresis was used to quantify ECS diffusion parameters in different brain regions of adult and behaviorally characterized aged rats. Prior to ECS diffusion measurement, superior and inferior learners were selected from a large group of aged rats, according to their performance in the open-field water maze. The main finding was that the degree of impaired maze performance of old rats correlates, firstly, with decrease in ECS volume, loss of diffusion anisotropy in hippocampus, and degree of astrogliosis, and secondly, with disorganization of the astrocytic processes and reduction of hippocampal ECS matrix molecules. Importantly, no significant differences were found in the density of neurons in any region of the hippocampus or dentate gyrus. The alterations in hippocampal diffusion parameters evident in aged animals with severe learning deficits could account for the learning impairment, due to their effects on extrasynaptic volume transmission and/or on the "cross-talk" between synapses, which has been suggested to be involved in neural processes associated with learning and memory formation.

Activity-dependent changes of tissue resistivity in the CA1 region in vivo are layer-specific: modulation of evoked potentials

We have investigated the spatial map of tissue resistivity across CA1 layers in vivo, its modifications during repetitive orthodromic activity, and the influence of this factor on the shaping of population spikes. Measurement of tissue resistance was made by a high-spatial-resolution three-electrode method. A computer network of equivalent resistors aided theoretical analysis. Tissue resistivity was homogeneous within the basal and apical dendritic trees (260+/-4.5 and 287+/-2.6 Omega cm, respectively). In the stratum pyramidale we found a sharply delimited high-resistivity (643+/-35 Omega cm) band approximately 20 microm wide. Resistivity in slices was approximately 30% higher than in vivo. Computer analysis indicated that the high-resistance somatic layer has a strong influence on the somatic and proximal dendritic contribution to the shaping of population spikes, and reduces volume propagation of currents between dendritic trees. Repetitive orthodromic activation at the theta frequency (4-5 Hz, 20-30 s) caused a stereotyped cycle of field potentials and layer-specific changes of resistivity. Initially (approximately 10 s), long-lasting field excitatory postsynaptic potentials and multiple somatodendritic population spikes developed, and resistivity gradually increased in all layers at a similar rate (period average: 11%). Subsequently, the long-lasting field excitatory synaptic potential subsided and dendritic spike generators were strongly reduced, but multiple somatic spikes remained. Concurrently, the resistivity reached a plateau in all dendritic layers but continued to increase in the somatic layer for about 10-15 s (20% average and up to 50% maximum). Recovery required approximately 60 s. The orthodromic somatic population spike increased variably during stimulation (up to 60%). Using local resistivity changes for correction, supernormal increments of the population spikes were offset, but not totally, uncovering several sub- and supernormal phases that were partially related to changes in dendritic population spike. These resistivity-independent modulations of the somatic population spike are caused by variable volume spread from dendritic spike currents and changed somatic contribution of firing units. This report demonstrates that the strong heterogeneity in the stratum pyramidale is an important factor shaping and modulating the population spike. The different regional rates of resistivity variation force the independent correction of local evoked potentials. We show that not doing so may cause bulk errors in the interpretation of, for instance, field potential ratios widely used to measure the population excitability. The present results underscore the importance of checking variations in recording conditions, which are inherent in most experimental protocols.