Diffusion of molecules in brain extracellular space: theory and experiment

Shadow imaging for panoptical visualization of brain tissue in vivo

Progress in neuroscience research hinges on technical advances in visualizing living brain tissue with high fidelity and facility. Current neuroanatomical imaging approaches either require tissue fixation (electron microscopy), do not have cellular resolution (magnetic resonance imaging) or only give a fragmented view (fluorescence microscopy). Here, we show how regular light microscopy together with fluorescence labeling of the interstitial fluid in the extracellular space provide comprehensive optical access in real-time to the anatomical complexity and dynamics of living brain tissue at submicron scale. Using several common fluorescence microscopy modalities (confocal, light-sheet and 2-photon microscopy) in mouse organotypic and acute brain slices and the intact mouse brain in vivo, we demonstrate the value of this straightforward 'shadow imaging' approach by revealing neurons, microglia, tumor cells and blood capillaries together with their complete anatomical tissue contexts. In addition, we provide quantifications of perivascular spaces and the volume fraction of the extracellular space of brain tissue in vivo.

A spatially distributed model of brain metabolism highlights the role of diffusion in brain energy metabolism

The different active roles of neurons and astrocytes during neuronal activation are associated with the metabolic processes necessary to supply the energy needed for their respective tasks at rest and during neuronal activation. Metabolism, in turn, relies on the delivery of metabolites and removal of toxic byproducts through diffusion processes and the cerebral blood flow. A comprehensive mathematical model of brain metabolism should account not only for the biochemical processes and the interaction of neurons and astrocytes, but also the diffusion of metabolites. In the present article, we present a computational methodology based on a multidomain model of the brain tissue and a homogenization argument for the diffusion processes. In our spatially distributed compartment model, communication between compartments occur both through local transport fluxes, as is the case within local astrocyte-neuron complexes, and through diffusion of some substances in some of the compartments. The model assumes that diffusion takes place in the extracellular space (ECS) and in the astrocyte compartment. In the astrocyte compartment, the diffusion across the syncytium network is implemented as a function of gap junction strength. The diffusion process is implemented numerically by means of a finite element method (FEM) based spatial discretization, and robust stiff solvers are used to time integrate the resulting large system. Computed experiments show the effects of ECS tortuosity, gap junction strength and spatial anisotropy in the astrocyte network on the brain energy metabolism.

Nanoscale and functional heterogeneity of the hippocampal extracellular space

The extracellular space (ECS) and its constituents play a crucial role in brain development, plasticity, circadian rhythm, and behavior, as well as brain diseases. Yet, since this compartment has an intricate geometry and nanoscale dimensions, its detailed exploration in live tissue has remained an unmet challenge. Here, we used a combination of single-nanoparticle tracking and super-resolution microscopy approaches to map the nanoscale dimensions of the ECS across the rodent hippocampus. We report that these dimensions are heterogeneous between hippocampal areas. Notably, stratum radiatum CA1 and CA3 ECS differ in several characteristics, a difference that gets abolished after digestion of the extracellular matrix. The dynamics of extracellular immunoglobulins vary within these areas, consistent with their distinct ECS characteristics. Altogether, we demonstrate that ECS nanoscale anatomy and diffusion properties are widely heterogeneous across hippocampal areas, impacting the dynamics and distribution of extracellular molecules.

Modeling the Effect of Binding Kinetics in Spatial Drug Distribution in the Brain

A 3-dimensional mathematical model is developed to determine the effect of drug binding kinetics on the spatial distribution of a drug within the brain. The key components, namely, transport across the blood-brain barrier (BBB), drug distribution in the brain extracellular fluid (ECF), and drug binding kinetics are coupled with the bidirectional bulk flow of the brain ECF to enhance the visualization of drug concentration in the brain. The model is developed based on the cubical volume of a brain unit, which is a union of three subdomains: the brain ECF, the BBB, and the blood plasma. The model is a set of partial differential equations and the associated initial and boundary conditions through which the drug distribution process in the mentioned subdomains is described. Effects of drug binding kinetics are investigated by varying the binding parameter values for both nonspecific and specific binding sites. All variations of binding parameter values are discussed, and the results show the improved visualization of the effect of binding kinetics in the drug distribution within the brain. For more realistic visualization, we suggest incorporating more brain components that make up the large volume of the brain tissue.

Characterization of Developmental Changes in Spontaneous Electrical Activity of Medial Superior Olivary Neurons Before Hearing Onset With a Combination of Injectable and Volatile Anesthesia

In this work the impact of two widely used anesthetics on the electrical activity of auditory brainstem neurons was studied during postnatal development. Spontaneous electrical activity in neonate rats of either sex was analyzed through a ventral craniotomy in mechanically ventilated pups to carry out patch clamp and multi-electrode electrophysiology recordings in the medial region of the superior olivary complex (SOC) between birth (postnatal day 0, P0) and P12. Recordings were obtained in pups anesthetized with the injectable mix of ketamine/xylazine (K/X mix), with the volatile anesthetic isoflurane (ISO), or in pups anesthetized with K/X mix that were also exposed to ISO. The results of patch clamp recordings demonstrate for the first time that olivary and periolivary neurons in the medial region of the SOC fire bursts of action potentials. The results of multielectrode recordings suggest that the firing pattern of single units recorded in K/X mix is similar to that recorded in ISO anesthetized rat pups. Taken together, the results of this study provide a framework to use injectable and volatile anesthetics for future studies to obtain functional information on the activity of medial superior olivary neurons in vivo.

Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

A 3D brain unit model to further improve prediction of local drug distribution within the brain

The development of drugs targeting the brain still faces a high failure rate. One of the reasons is a lack of quantitative understanding of the complex processes that govern the pharmacokinetics (PK) of a drug within the brain. While a number of models on drug distribution into and within the brain is available, none of these addresses the combination of factors that affect local drug concentrations in brain extracellular fluid (brain ECF). Here, we develop a 3D brain unit model, which builds on our previous proof-of-concept 2D brain unit model, to understand the factors that govern local unbound and bound drug PK within the brain. The 3D brain unit is a cube, in which the brain capillaries surround the brain ECF. Drug concentration-time profiles are described in both a blood-plasma-domain and a brain-ECF-domain by a set of differential equations. The model includes descriptions of blood plasma PK, transport through the blood-brain barrier (BBB), by passive transport via paracellular and transcellular routes, and by active transport, and drug binding kinetics. The impact of all these factors on ultimate local brain ECF unbound and bound drug concentrations is assessed. In this article we show that all the above mentioned factors affect brain ECF PK in an interdependent manner. This indicates that for a quantitative understanding of local drug concentrations within the brain ECF, interdependencies of all transport and binding processes should be understood. To that end, the 3D brain unit model is an excellent tool, and can be used to build a larger network of 3D brain units, in which the properties for each unit can be defined independently to reflect local differences in characteristics of the brain.

A mathematical model for persistent post-CSD vasoconstriction

Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.

Magnetic Resonance Imaging and Modeling of the Glymphatic System

The glymphatic system is a newly discovered waste drainage pathway in the brain; it plays an important role in many neurological diseases. Ongoing research utilizing various cerebrospinal fluid tracer infusions, either directly or indirectly into the brain parenchyma, is investigating clearance pathways by using distinct imaging techniques. In the present review, we discuss the role of the glymphatic system in various neurological diseases and efflux pathways of brain waste clearance based on current evidence and controversies. We mainly focus on new magnetic resonance imaging (MRI) modeling techniques, along with traditional computational modeling, for a better understanding of the glymphatic system function. Future sophisticated modeling techniques hold the potential to generate quantitative maps for glymphatic system parameters that could contribute to the diagnosis, monitoring, and prognosis of neurological diseases. The non-invasive nature of MRI may provide a safe and effective way to translate glymphatic system measurements from bench-to-bedside.

Improved fibre dispersion estimation using b-tensor encoding

Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i.e., the diffusion anisotropy expected for a single fibre orientation). This means that estimates of fibre dispersion rely on strong assumptions, such as constant microscopic anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. To test the accuracy of the fibre dispersion when our microstructural model is only an approximation of the true tissue structure, we simulate multi-compartment data and fit this with a single-compartment model. For such overly simplistic tissue assumptions, we show that the bias in fibre dispersion is greatly reduced (~5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data. In in-vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1.5 ms/μm², increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions of the tissue microstructure.

Distribution and Diffusion of Macromolecule Delivery to the Brain via Focused Ultrasound using Magnetic Resonance and Multispectral Fluorescence Imaging

Focused ultrasound (FUS), in combination with microbubble contrast agents, can be used to transiently open the blood-brain barrier (BBB) to allow intravascular agents to cross into the brain. Often, FUS is carried out in conjunction with magnetic resonance imaging (MRI) to evaluate BBB opening to gadolinium-based MRI contrast agents. Although MRI allows direct visualization of the distribution of gadolinium-based contrast agents in the brain parenchyma, it does not allow measurements of the distribution of other molecules crossing the BBB. Therapeutic molecules (e.g., monoclonal antibodies) are much different in size than MRI contrast agents and have been found to have different distributions in the brain after FUS-mediated BBB opening. In the work described here, we combined in vivo MRI and ex vivo multispectral fluorescence imaging to compare the distributions of MRI contrast and dextran molecules of different molecular weights (3, 70 and 500 kDa) after FUS-mediated BBB opening through a range of ultrasound pressures (0.18-0.46 MPa) in laboratory mice. The volume of brain exposed was calculated from the MRI and fluorescence images and was significantly dependent on both molecular weight and ultrasound pressure. Diffusion coefficients of the different-molecular-weight dextran molecules in the brain parenchyma were also calculated from the fluorescence images and were negatively correlated with the molecular weight of the dextran molecules. The results of this work build on a body of knowledge that is critically important for the FUS technique to be used in clinical delivery of therapeutics to the brain.

Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome

The prion-like hypothesis of neurodegenerative diseases states that the accumulation of misfolded proteins in the form of aggregates is responsible for tissue death and its associated neurodegenerative pathology and cognitive decline. Some disease-specific misfolded proteins can interact with healthy proteins to form long chains that are transported through the brain along axonal pathways. Since aggregates of different sizes have different transport properties and toxicity, it is important to follow independently their evolution in space and time. Here, we model the spreading and propagation of aggregates of misfolded proteins in the brain using the general Smoluchowski theory of nucleation, aggregation, and fragmentation. The transport processes considered here are either anisotropic diffusion along axonal bundles or discrete Laplacian transport along a network. In particular, we model the spreading and aggregation of both amyloid-β and τ molecules in the brain connectome. We show that these two models lead to different size distributions and different propagation along the network. A detailed analysis of these two models also reveals the existence of four different stages with different dynamics and invasive properties.

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.

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.

Improving the Prediction of Local Drug Distribution Profiles in the Brain with a New 2D Mathematical Model

The development of drugs that target the brain is very challenging. A quantitative understanding is needed of the complex processes that govern the concentration–time profile of a drug (pharmacokinetics) within the brain. So far, there are no studies on predicting the drug concentration within the brain that focus not only on the transport of drugs to the brain through the blood–brain barrier (BBB), but also on drug transport and binding within the brain. Here, we develop a new model for a 2D square brain tissue unit, consisting of brain extracellular fluid (ECF) that is surrounded by the brain capillaries. We describe the change in free drug concentration within the brain ECF, by a partial differential equation (PDE). To include drug binding, we couple this PDE to two ordinary differential equations that describe the concentration–time profile of drug bound to specific as well as non-specific binding sites that we assume to be evenly distributed over the brain ECF. The model boundary conditions reflect how free drug enters and leaves the brain ECF by passing the BBB, located at the level of the brain capillaries. We study the influence of parameter values for BBB permeability, brain ECF bulk flow, drug diffusion through the brain ECF and drug binding kinetics, on the concentration–time profiles of free and bound drug.

Fluid outflow in the rat spinal cord: the role of perivascular and paravascular pathways

BACKGROUND

Cerebrospinal fluid (CSF) is thought to flow into the brain via perivascular spaces around arteries, where it mixes with interstitial fluid. The precise details concerning fluid outflow remain controversial. Although fluid dynamics have been studied in the brain, little is known about spinal cord fluid inflow and outflow. Understanding the normal fluid physiology of the spinal cord may give insight into the pathogenesis of spinal cord oedema and CSF disorders such as syringomyelia. We therefore aimed to determine the fluid outflow pathways in the rat spinal cord.

METHODS

A fluorescent tracer, Alexa-Fluor^®-647 Ovalbumin, was injected into the extracellular space of either the cervicothoracic lateral white matter or the grey matter in twenty-two Sprague-Dawley rats over 250 s. The rats were sacrificed at 20 or 60 min post injection. Spinal cord segments were sectioned and labelled with vascular antibodies for immunohistochemistry.

RESULTS

Fluorescent tracer was distributed over two to three spinal levels adjacent to the injection site. In grey matter injections, tracer spread radially into the white matter. In white matter injections, tracer was confined to and redistributed along the longitudinal axonal fibres. Tracer was conducted towards the pial and ependymal surfaces along vascular structures. There was accumulation of tracer around the adventitia of the intramedullary arteries, veins and capillaries, as well as the extramedullary vessels. A distinct layer of tracer was deposited in the internal basement membrane of the tunica media of arteries. In half the grey matter injections, tracer was detected in the central canal.

CONCLUSIONS

These results suggest that in the spinal cord interstitial fluid movement is modulated by tissue diffusivity of grey and white matter. The central canal, and the compartments around or within blood vessels appear to be dominant pathways for fluid drainage in these experiments. There may be regional variations in fluid outflow capacity due to vascular and other anatomical differences between the grey and white matter.

Role of the dorsomedial medulla in suppression of cough by codeine in cats

The modulation of cough by microinjections of codeine in 3 medullary regions, the solitary tract nucleus rostral to the obex (rNTS), caudal to the obex (cNTS) and the lateral tegmental field (FTL) was studied. Experiments were performed on 27 anesthetized spontaneously breathing cats. Electromyograms (EMG) were recorded from the sternal diaphragm and expiratory muscles (transversus abdominis and/or obliquus externus; ABD). Repetitive coughing was elicited by mechanical stimulation of the intrathoracic airways. Bilateral microinjections of codeine (3.3 or 33mM, 54±16nl per injection) in the cNTS had no effect on cough, while those in the rNTS and in the FTL reduced coughing. Bilateral microinjections into the rNTS (3.3mM codeine, 34±1 nl per injection) reduced the number of cough responses by 24% (P<0.05), amplitudes of diaphragm EMG by 19% (P<0.01), of ABD EMG by 49% (P<0.001) and of expiratory esophageal pressure by 56% (P<0.001). Bilateral microinjections into the FTL (33mM codeine, 33±3 nl per injection) induced reductions in cough expiratory as well as inspiratory EMG amplitudes (ABD by 60% and diaphragm by 34%; P<0.01) and esophageal pressure amplitudes (expiratory by 55% and inspiratory by 26%; P<0.001 and 0.01, respectively). Microinjections of vehicle did not significantly alter coughing. Breathing was not affected by microinjections of codeine. These results suggest that: 1) codeine acts within the rNTS and the FTL to reduce cough in the cat, 2) the neuronal circuits in these target areas have unequal sensitivity to codeine and/or they have differential effects on spatiotemporal control of cough, 3) the cNTS has a limited role in the cough suppression induced by codeine in cats.

Where are we? The anatomy of the murine cortical meninges revisited for intravital imaging, immunology, and clearance of waste from the brain

Rapid progress is being made in understanding the roles of the cerebral meninges in the maintenance of normal brain function, in immune surveillance, and as a site of disease. Most basic research on the meninges and the neural brain is now done on mice, major attractions being the availability of reporter mice with fluorescent cells, and of a huge range of antibodies useful for immunocytochemistry and the characterization of isolated cells. In addition, two-photon microscopy through the unperforated calvaria allows intravital imaging of the undisturbed meninges with sub-micron resolution. The anatomy of the dorsal meninges of the mouse (and, indeed, of all mammals) differs considerably from that shown in many published diagrams: over cortical convexities, the outer layer, the dura, is usually thicker than the inner layer, the leptomeninx, and both layers are richly vascularized and innervated, and communicate with the lymphatic system. A membrane barrier separates them and, in disease, inflammation can be localized to one layer or the other, so experimentalists must be able to identify the compartment they are studying. Here, we present current knowledge of the functional anatomy of the meninges, particularly as it appears in intravital imaging, and review their role as a gateway between the brain, blood, and lymphatics, drawing on information that is scattered among works on different pathologies.

Extracellular space diffusion analysis in the infant and adult rat striatum using magnetic resonance imaging

The extracellular space (ECS) in the brain provides an extrasynaptic transfer channel among neurons, axons and glial cells. It is particularly important in the early stage after birth, when angiogenesis is not yet complete and the ECS may provide the main pathway for metabolite transport. However, the characteristics of extracellular transport remain unclear. In this study, a novel magnetic resonance imaging (MRI) method was used to perform real-time visualization and quantification of diffusion in the brain ECS of infant (postnatal day 10 (P10)) and adult rats. Using a modified diffusion equation and the linear relationship between the signal intensity and the gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) concentration, diffusion parameters were obtained; these parameters include the effective diffusion coefficient (D*), clearance rate (k'), tortuosity (λ) and the volume fraction of distribution (Vd%). There were significant differences in the diffusion parameters between P10 and adult rats. This finding provides a reference for future treatment of brain diseases using drugs administered via interstitial pathways.

A model of space-fractional-order diffusion in the glial scar

Implantation of neuroprosthetic electrodes induces a stereotypical state of neuroinflammation, which is thought to be detrimental for the neurons surrounding the electrode. Mechanisms of this type of neuroinflammation are still poorly understood. Recent experimental and theoretical results point to a possible role of the diffusing species in this process. The paper considers a model of anomalous diffusion occurring in the glial scar around a chronic implant in two simple geometries - a separable rectilinear electrode and a cylindrical electrode, which are solvable exactly. We describe a hypothetical extended source of diffusing species and study its concentration profile in steady-state conditions. Diffusion transport is assumed to obey a fractional-order Fick law, derivable from physically realistic assumptions using a fractional calculus approach. Presented fractional-order distribution morphs into integer-order diffusion in the case of integral fractional exponents. The model demonstrates that accumulation of diffusing species can occur and the scar properties (i.e. tortuosity, fractional order, scar thickness) and boundary conditions can influence such accumulation. The observed shape of the concentration profile corresponds qualitatively with GFAP profiles reported in the literature. The main difference with respect to the previous studies is the explicit incorporation of the apparatus of fractional calculus without assumption of an ad hoc tortuosity parameter. The approach can be adapted to other studies of diffusion in biological tissues, for example of biomolecules or small drug molecules.

A Simulation Model of Periarterial Clearance of Amyloid-β from the Brain

The accumulation of soluble and insoluble amyloid-β (Aβ) in the brain indicates failure of elimination of Aβ from the brain with age and Alzheimer's disease (AD). There is a variety of mechanisms for elimination of Aβ from the brain. They include the action of microglia and enzymes together with receptor-mediated absorption of Aβ into the blood and periarterial lymphatic drainage of Aβ. Although the brain possesses no conventional lymphatics, experimental studies have shown that fluid and solutes, such as Aβ, are eliminated from the brain along 100 nm wide basement membranes in the walls of cerebral capillaries and arteries. This lymphatic drainage pathway is reflected in the deposition of Aβ in the walls of human arteries with age and AD as cerebral amyloid angiopathy (CAA). Initially, Aβ diffuses through the extracellular spaces of gray matter in the brain and then enters basement membranes in capillaries and arteries to flow out of the brain. Although diffusion through the extracellular spaces of the brain has been well characterized, the exact mechanism whereby perivascular elimination of Aβ occurs has not been resolved. Here we use a computational model to describe the process of periarterial drainage in the context of diffusion in the brain, demonstrating that periarterial drainage along basement membranes is very rapid compared with diffusion. Our results are a validation of experimental data and are significant in the context of failure of periarterial drainage as a mechanism underlying the pathogenesis of AD as well as complications associated with its immunotherapy.

Passive immunotherapy targeting amyloid-β reduces cerebral amyloid angiopathy and improves vascular reactivity

Prominent cerebral amyloid angiopathy is often observed in the brains of elderly individuals and is almost universally found in patients with Alzheimer’s disease. Cerebral amyloid angiopathy is characterized by accumulation of the shorter amyloid-β isoform(s) (predominantly amyloid-β40) in the walls of leptomeningeal and cortical arterioles and is likely a contributory factor to vascular dysfunction leading to stroke and dementia in the elderly. We used transgenic mice with prominent cerebral amyloid angiopathy to investigate the ability of ponezumab, an anti-amyloid-β40 selective antibody, to attenuate amyloid-β accrual in cerebral vessels and to acutely restore vascular reactivity. Chronic administration of ponezumab to transgenic mice led to a significant reduction in amyloid and amyloid-β accumulation both in leptomeningeal and brain vessels when measured by intravital multiphoton imaging and immunohistochemistry. By enriching for cerebral vascular elements, we also measured a significant reduction in the levels of soluble amyloid-β biochemically. We hypothesized that the reduction in vascular amyloid-β40 after ponezumab administration may reflect the ability of ponezumab to mobilize an interstitial fluid pool of amyloid-β40 in brain. Acutely, ponezumab triggered a significant and transient increase in interstitial fluid amyloid-β40 levels in old plaque-bearing transgenic mice but not in young animals. We also measured a beneficial effect on vascular reactivity following acute administration of ponezumab, even in vessels where there was a severe cerebral amyloid angiopathy burden. Taken together, the beneficial effects ponezumab administration has on reducing the rate of cerebral amyloid angiopathy deposition and restoring cerebral vascular health favours a mechanism that involves rapid removal and/or neutralization of amyloid-β species that may otherwise be detrimental to normal vessel function.

Hematocrit distribution and tissue oxygenation in large microcirculatory networks

OBJECTIVE

Oxygen tension in the brain is controlled by the microcirculatory supply of RBC, but the effect of non-Newtonian blood flow rheology on tissue oxygenation is not well characterized. This study assesses different biphasic blood flow models for predicting tissue oxygen tension as a function of microcirculatory hemodynamics.

METHODS

Two existing plasma-skimming laws are compared against measured RBC distributions in rat and hamster microcirculatory networks. A novel biphasic blood flow model is introduced. The computational models predict tissue oxygenation in the mesentery, cremaster muscle, and the human secondary cortex.

RESULTS

This investigation shows deficiencies in prior models, including inconsistent plasma-skimming trends and insufficient oxygen perfusion due to the high prevalence (33%) of RBC-free microvessels. Our novel method yields physiologically sound RBC distributions and tissue oxygen tensions within one standard deviation of experimental measurements.

CONCLUSIONS

A simple, novel biphasic blood flow model is introduced with equal or better predictive power when applied to historic raw data sets. It can overcome limitations of prior models pertaining to trifurcations, anastomoses, and loops. This new plasma-skimming law eases the computations of bulk blood flow and hematocrit fields in large microcirculatory networks and converges faster than prior procedures.

Modeling localized delivery of Doxorubicin to the brain following focused ultrasound enhanced blood-brain barrier permeability

Doxorubicin (Dox) is a well-established chemotherapeutic agent, however it has limited efficacy in treating brain malignancies due to the presence of the blood-brain barrier (BBB). Recent preclinical studies have demonstrated that focused ultrasound induced BBB disruption (BBBD) enables efficient delivery of Dox to the brain. For future treatment planning of BBBD-based drug delivery, it is crucial to establish a mathematical framework to predict the effect of transient BBB permeability enhancement on the spatiotemporal distribution of Dox at the targeted area. The constructed model considers Dox concentrations within three compartments (plasma, extracellular, intracellular) that are governed by various transport processes (e.g. diffusion in interstitial space, exchange across vessel wall, clearance by cerebral spinal fluid, uptake by brain cells). By examining several clinical treatment aspects (e.g. sonication scheme, permeability enhancement, injection mode), our simulation results support the experimental findings of optimal interval delay between two consecutive sonications and therapeutically-sufficient intracellular concentration with respect to transfer constant Ktrans range of 0.01-0.03 min(-1). Finally, the model suggests that infusion over a short duration (20-60 min) should be employed along with single-sonication or multiple-sonication at 10 min interval to ensure maximum delivery to the intracellular compartment while attaining minimal cardiotoxicity via suppressing peak plasma concentration.

Emerging insights into barriers to effective brain tumor therapeutics

There is great promise that ongoing advances in the delivery of therapeutics to the central nervous system (CNS) combined with rapidly expanding knowledge of brain tumor patho-biology will provide new, more effective therapies. Brain tumors that form from brain cells, as opposed to those that come from other parts of the body, rarely metastasize outside of the CNS. Instead, the tumor cells invade deep into the brain itself, causing disruption in brain circuits, blood vessel and blood flow changes, and tissue swelling. Patients with the most common and deadly form, glioblastoma (GBM) rarely live more than 2 years even with the most aggressive treatments and often with devastating neurological consequences. Current treatments include maximal safe surgical removal or biopsy followed by radiation and chemotherapy to address the residual tumor mass and invading tumor cells. However, delivering effective and sustained treatments to these invading cells without damaging healthy brain tissue is a major challenge and focus of the emerging fields of nanomedicine and viral and cell-based therapies. New treatment strategies, particularly those directed against the invasive component of this devastating CNS disease, are sorely needed. In this review, we (1) discuss the history and evolution of treatments for GBM, (2) define and explore three critical barriers to improving therapeutic delivery to invasive brain tumors, specifically, the neuro-vascular unit as it relates to the blood brain barrier, the extra-cellular space in regard to the brain penetration barrier, and the tumor genetic heterogeneity and instability in association with the treatment efficacy barrier, and (3) identify promising new therapeutic delivery approaches that have the potential to address these barriers and create sustained, meaningful efficacy against GBM.

Diffusion in the extracellular space in brain and tumors

Diffusion of solutes and macromolecules in the extracellular space (ECS) in brain is important for non-synaptic intercellular communication, extracellular ionic buffering, and delivery of drugs and metabolites. Diffusion in tumor ECS is important for delivery of anti-tumor drugs. The ECS in brain comprises ∼20% of brain parenchymal volume and contains cell-cell gaps down to ∼50 nm. We have developed fluorescence methods to quantify solute diffusion in the ECS, allowing measurements deep in solid tissues using microfiberoptics with micron tip size. Diffusion through the tortuous ECS in brain is generally slowed by ∼3-5-fold compared with that in water, with approximately half of the slowing due to tortuous ECS geometry and half due to the mildly viscous extracellular matrix (ECM). Mathematical modeling of slowed diffusion in an ECS with reasonable anatomical accuracy is in good agreement with experiment. In tumor tissue, diffusion of small macromolecules is only mildly slowed (<3-fold slower than in water) in superficial tumor, but is greatly slowed (>10-fold) at a depth of few millimeters as the tumor tissue becomes more compact. Slowing by ECM components such as collagen contribute to the slowed diffusion. Therefore, as found within cells, cellular crowding and highly tortuous transport can produce only minor slowing of diffusion in the ECS.

Quantitative detection of thrombin activity in an ischemic stroke model

Thrombin, a central factor in thrombogenesis, affects cells in the brain through protease activated receptors. Low levels of thrombin activity are neuroprotective while higher levels are deleterious, and we have therefore developed a new method for its direct quantitative measurement in brain slices following stroke. Thrombin activity was measured by a fluorescent substrate on fresh coronal slices taken from the ipsilateral and contralateral hemispheres 24-72 h following permanent right middle cerebral artery occlusion. Prolyl endopeptidase and aminopeptidases were inhibited as a critical step to insure the specificity of the assay for thrombin detection. Infarct volume was assessed using TTC staining. Thrombin activity in the right ischemic hemisphere was significantly higher compared to the contralateral hemisphere (32 ± 6 and 27 ± 10 mU/ml, mean ± SE in the two most affected slices from the ischemic hemisphere vs. 21 ± 6 and 8 ± 2 mU/ml in corresponding contralateral slices; p < 0.05). Thrombin levels in the ischemic and contralateral hemispheres were significantly higher compared to healthy control mice and were above the range known to be protective to brain cells. A significant correlation was found between thrombin activity in the ischemic hemisphere and the infarct volume. Results of studies based on this method may translate into potential thrombin based therapies.

Retinal ganglion cells: Energetics, compartmentation, axonal transport, cytoskeletons and vulnerability

Retinal ganglion cells (RGCs) are specialized projection neurons that relay an immense amount of visual information from the retina to the brain. RGC signal inputs are collected by dendrites and output is distributed from the cell body via very thin (0.5-1 μm) and long (∼50 mm) axons. The RGC cell body is larger than other retinal neurons, but is still only a very small fraction (one ten thousandths) of the length and total surface area of the axon. The total distance traversed by RGCs extends from the retina, starting from synapses with bipolar and amacrine cells, to the brain, to synapses with neurons in the lateral geniculate nucleus. This review will focus on the energy demands of RGCs and the relevant tissues that surround them. RGC survival and function unexceptionally depends upon free energy, predominantly adenosine triphosphate (ATP). RGC energy metabolism is vastly different when compared to that of the photoreceptors. Each subcellular component of the RGC is remarkably different in terms of structure, function and extracellular environment. The energy demands and distribution of each component are also distinct as evidenced by the uneven distribution of mitochondria and ATP within the RGC - signifying the presence of intracellular energy gradients. In this review we will describe RGCs as having four subcellular components, (1) Dendrites, (2) Cell body, (3) Non-myelinated axon, including intraocular and optic nerve head portions, and (4) Myelinated axon, including the intra-orbital and intracranial portions. We will also describe how RGCs integrate information from each subcellular component in order achieve intracellular homeostatic stability as well as respond to perturbations in the extracellular environment. The possible cellular mechanisms such as axonal transport and axonal cytoskeleton proteins that are involved in maintaining RGC energy homeostasis during normal and disease conditions will also be discussed in depth. The emphasis of this review will be on energetic mechanisms within RGC components that have the most relevance to clinical ophthalmology.

Disruptions in the regulation of extracellular glutamate by neurons and glia in the rat striatum two days after diffuse brain injury

Disrupted regulation of extracellular glutamate in the central nervous system contributes to and can exacerbate the acute pathophysiology of traumatic brain injury (TBI). Previously, we reported increased extracellular glutamate in the striatum of anesthetized rats 2 days after diffuse brain injury. To determine the mechanism(s) responsible for increased extracellular glutamate, we used enzyme-based microelectrode arrays (MEAs) coupled with specific pharmacological agents targeted at in vivo neuronal and glial regulation of extracellular glutamate. After TBI, extracellular glutamate was significantly increased in the striatum by (∼90%) averaging 4.1±0.6 μM compared with sham 2.2±0.4 μM. Calcium-dependent neuronal glutamate release, investigated by local application of an N-type calcium channel blocker, was no longer a significant source of extracellular glutamate after TBI, compared with sham. In brain-injured animals, inhibition of glutamate uptake with local application of an excitatory amino acid transporter inhibitor produced significantly greater increase in glutamate spillover (∼ 65%) from the synapses compared with sham. Furthermore, glutamate clearance measured by locally applying glutamate into the extracellular space revealed significant reductions in glutamate clearance parameters in brain-injured animals compared with sham. Taken together, these data indicate that disruptions in calcium-mediated glutamate release and glial regulation of extracellular glutamate contribute to increased extracellular glutamate in the striatum 2 days after diffuse brain injury. Overall, these data suggest that therapeutic strategies used to regulate glutamate release and uptake may improve excitatory circuit function and, possibly, outcomes following TBI.

Kappa opioid receptor signaling in the basolateral amygdala regulates conditioned fear and anxiety in rats

BACKGROUND

The kappa opioid receptor (KOR) system contributes to the prodepressive and aversive consequences of stress and is implicated in the facilitation of conditioned fear and anxiety in rodents. Here, we sought to identify neural circuits that mediate KOR system effects on fear and anxiety in rats.

METHODS

We assessed whether fear conditioning induces plasticity in KOR or dynorphin (the endogenous KOR ligand) messenger RNA (mRNA) expression in the basolateral (BLA) and central (CeA) nuclei of the amygdala, hippocampus, or striatum. We then assessed whether microinfusions of the KOR antagonist JDTic (0-10 μg/side) into the BLA or CeA affect the expression of conditioned fear or anxiety. Finally, we examined whether fear extinction induces plasticity in KOR mRNA expression that relates to the quality of fear extinction.

RESULTS

Fear conditioning upregulated KOR mRNA in the BLA by 65% and downregulated it in the striatum by 22%, without affecting KOR levels in the CeA or hippocampus, or dynorphin levels in any region. KOR antagonism in either the BLA or CeA decreased conditioned fear in the fear-potentiated startle paradigm, whereas KOR antagonism in the BLA, but not the CeA, produced anxiolytic-like effects in the elevated plus maze. Effective fear extinction was associated with a 67% reduction in KOR mRNA in the BLA.

CONCLUSIONS

These findings suggest that fear conditioning and extinction dynamically regulate KOR expression in the BLA and provide evidence that the BLA and CeA are important neural substrates mediating the anxiolytic-like effects of KOR antagonists in models of fear and anxiety.

Oxytocin-messages via the cerebrospinal fluid: behavioral effects; a review

The cerebrospinal fluid (CSF) usually is considered as a protective 'nutrient and waste control' system for the brain. Recent findings suggest, however, that the composition of CSF is actively controlled and may play an influential role in the changes in brain activity, underlying different behavioral states. In the present review, we present an overview of available data concerning the release of oxytocin into the CSF, the location of the oxytocin-receptive brain areas and the behavioral effects of intracerebroventricular oxytocin. About 80% of the oxytocin-receptive areas are located close to the ventricular or subarachnoid CSF, including the hypothalamic 'Behavior Control Column' (L.W.Swanson, 2003). As a conclusion we suggest that 'CSF-oxytocin' contributes considerably to the non-synaptic communication processes involved in hypothalamic-, brainstem- and olfactory brain areas and behavioral states and that the flowing CSF is used as a 'broadcasting system' to send coordinated messages to a wide variety of nearby and distant brain areas.

Understanding wiring and volume transmission

The proposal on the existence of two main modes of intercellular communication in the central nervous system (CNS) was introduced in 1986 and called wiring transmission (WT) and volume transmission (VT). The major criterion for this classification was the different characteristics of the communication channel with physical boundaries well delimited in the case of WT (axons and their synapses; gap junctions) but not in the case of VT (the extracellular fluid filled tortuous channels of the extracellular space and the cerebrospinal fluid filled ventricular space and sub-arachnoidal space). The basic dichotomic classification of intercellular communication in the brain is still considered valid, but recent evidence on the existence of unsuspected specialized structures for intercellular communication, such as microvesicles (exosomes and shedding vesicles) and tunnelling nanotubes, calls for a refinement of the original classification model. The proposed updating is based on criteria which are deduced not only from these new findings but also from concepts offered by informatics to classify the communication networks in the CNS. These criteria allowed the identification also of new sub-classes of WT and VT, namely the "tunnelling nanotube type of WT" and the "Roamer type of VT." In this novel type of VT microvesicles are safe vesicular carriers for targeted intercellular communication of proteins, mtDNA and RNA in the CNS flowing in the extracellular fluid along energy gradients to reach target cells. In the tunnelling nanotubes proteins, mtDNA and RNA can migrate as well as entire organelles such as mitochondria. Although the existence and the role of these new types of intercellular communication in the CNS are still a matter of investigation and remain to be fully demonstrated, the potential importance of these novel types of WT and VT for brain function in health and disease is discussed.

Microinjection of codeine into the region of the caudal ventral respiratory column suppresses cough in anesthetized cats

We investigated the influence of microinjection of codeine into the caudal ventral respiratory column (cVRC) on the cough reflex. Experiments were performed on 36 anesthetized spontaneously breathing cats. Electromyograms (EMGs) were recorded bilaterally from inspiratory parasternal and expiratory transversus abdominis (ABD) muscles and unilaterally from laryngeal posterior cricoarytenoid and thyroarytenoid muscles. Repetitive coughing was elicited by mechanical stimulation of the intrathoracic airways. The unilateral microinjection of codeine (3.3 mM, 20-32 nl) in the cVRC reduced cough number by 29% (P < 0.01) and expiratory cough amplitudes of esophageal pressure by 33% (P < 0.05) as well as both ipsilateral and contralateral ABD EMGs by 35% and 48% (P < 0.01 and P < 0.01, respectively). No cough depression was observed after microinjections of vehicle. There was no significant effect of microinjection of codeine in the cVRC (3.3 mM, 30-40 nl) on ABD activity induced by a microinjection of D,L-homocysteic acid (30 mM, 27-40 nl) in the same location. However, a cumulative dose of codeine (0.1 mg/kg, 330 nmol/kg) applied into the brain stem circulation through the vertebral artery reduced the ABD motor response to cVRC D,L-homocysteic acid microinjection (30 mM, 28-32 nl) by 47% (P < 0.01). These results suggest that 1) codeine can act within the cVRC to suppress cough and 2) expiratory premotoneurons within the cVRC are relatively insensitive to this opioid.

Targeted drug delivery for treatment and imaging of glioblastoma multiforme

Glioblastoma multiforme is a grade IV astrocytic tumor with a very high mortality rate. Although current treatment often includes surgical resection, this rarely removes all primary tumor cells, so is usually followed by radiation and/or chemotherapy. Remaining migratory tumor cells invade surrounding healthy tissue and contribute to secondary and tertiary tumor recurrence; therefore, despite significant research into glioma removal and treatment, prognosis remains poor. A variety of treatment modalities have been investigated to deliver drug to these cells, including systemic, diffusive and convection-enhanced delivery (CED). As systemic delivery is limited by molecules larger than approximately 500 Da being unable to cross the blood-brain barrier (BBB), therapeutic concentrations are difficult to attain; thus, localized delivery options relying on diffusion and CED have been used to circumvent the BBB. Although CED enables delivery to a greater volume of tissue than diffusive delivery alone, limitations still exist, requiring that these delivery strategies be improved. This review enumerates the strengths and weaknesses of these currently used strategies and details how predictive mathematical modeling can be used to aid investigators in optimizing these delivery modalities for clinical application.

Extracellular space volume measured by two-color pulsed dye infusion with microfiberoptic fluorescence photodetection

The extracellular space (ECS) is the aqueous matrix surrounding cells in solid tissues. The only method to measure ECS volume fraction (alpha) in vivo has been tetramethylammonium iontophoresis, a technically challenging method developed more than 25 years ago. We report a simple, quantitative method to measure alpha by microfiberoptic fluorescence detection of a self-quenched green dye, calcein, and a reference red dye, sulforhodamine 101, after pulsed iontophoretic infusion. The idea is that the maximum increase in calcein fluorescence after iontophoresis is proportional to the aqueous volume into which the dye is deposited. We validated the method theoretically, and experimentally, using cell-embedded gels with specified alpha and ECS viscosity. Measurements in living mice gave alpha of 0.20 +/- 0.01 in brain, 0.13 +/- 0.02 in kidney and 0.074 +/- 0.01 in skeletal muscle. The technical simplicity of the "pulsed-infusion microfiberoptic photodetection" method developed here should allow elucidation of the relatively understudied biological roles of the ECS.

Potassium dynamics in the epileptic cortex: new insights on an old topic

The role of changes in the extracellular potassium concentration [K(+)](o) in epilepsy has remained unclear. Historically, it was hypothesized that [K(+)]( o) is the causal factor for epileptic seizures. This so-called potassium accumulation hypothesis led to substantial debate but subsequently failed to find wide acceptance. However, recent studies on the pathophysiology of tissue from epileptic human patients and animal epilepsy models revealed aberrations in [K(+)](o) regulation. Computational models of cortical circuits that include ion concentration dynamics have catalyzed a renewed interest in the role of [K(+)](o) in epilepsy. The authors here connect classical and more recent insights on [K(+)]( o) dynamics in the cortex with the goal of providing starting points for a next generation of [K(+)](o) research. Such research may ultimately lead to an entirely new class of antiepileptic drugs that act on the [K(+)](o) regulation system.

Temporal and spatial control of neural effects following intracerebral microinfusion

Spatial and temporal control of neural drug delivery is critical for many therapeutic applications and analyses of brain patterns and behavior. Specifically, for localized injections that serve to deliver drug or inactivate an isolated tissue region in order to observe changes in neural activity at that site, excess distribution into surrounding regions may confound analysis or adversely affect healthy tissue. Here, we develop a mass transport model that simulates a short period of initial infusion of inactivating drug, followed by a successive convective wash with artificial cerebrospinal fluid (aCSF), while tracking the regions of tissue that are above a certain threshold concentration of inactivating agent. We analyze the effect of parameters such as effective diffusion coefficient, extracellular volume fraction, and injectate concentration upon spatiotemporal distribution profiles. Further, we observe the effects of following the initial injection with a wash-out period with aCSF upon the breadth of the volume affected by the injectate. These simulations indicate that, by injecting small volumes of drug at low concentrations and following them with an aCSF flush, a well-delineated region of tissue can be altered for a controlled duration.

Determination of zeta-potential in rat organotypic hippocampal cultures

zeta-potentials of entities such as cells and synaptosomes have been determined, but zeta of brain tissue has never been measured. Electroosmotic flow, and the resulting transport of neuroactive substances, would result from naturally occurring and experimentally or clinically induced electric fields if zeta is significant. We have developed a simple method for determining zeta in tissue. An electric field applied across a rat organotypic hippocampal slice culture (OHSC) drives fluorescent molecules through the tissue by both electroosmotic flow and electrophoresis. Fluorescence microscopy is used to determine each molecule's velocity. Independently, capillary electrophoresis is used to measure the molecules' electrophoretic mobilities. The experiment yields zeta-potential and average tissue tortuosity. The zeta-potential of OHSCs is -22 +/- 2 mV, and the average tortuosity is 1.83 +/- 0.06. In a refined experiment, zeta-potential is measured in various subregions. The zeta-potentials of the CA1 stratum pyramidale, CA3 stratum pyramidal, and dentate gyrus are -25.1 +/- 1.6 mV, -20.3 +/- 1.7 mV, and -25.4 +/- 1.0 mV, respectively. Simple dimensional arguments show that electroosmotic flow is potentially as important as diffusion in molecular transport.

Random-walk model of diffusion in three dimensions in brain extracellular space: comparison with microfiberoptic photobleaching measurements

Diffusion through the extracellular space (ECS) in brain is important in drug delivery, intercellular communication, and extracellular ionic buffering. The ECS comprises approximately 20% of brain parenchymal volume and contains cell-cell gaps approximately 50 nm. We developed a random-walk model to simulate macromolecule diffusion in brain ECS in three dimensions using realistic ECS dimensions. Model inputs included ECS volume fraction (alpha), cell size, cell-cell gap geometry, intercellular lake (expanded regions of brain ECS) dimensions, and molecular size of the diffusing solute. Model output was relative solute diffusion in water versus brain ECS (D(o)/D). Experimental D(o)/D for comparison with model predictions was measured using a microfiberoptic fluorescence photobleaching method involving stereotaxic insertion of a micron-size optical fiber into mouse brain. D(o)/D for the small solute calcein in different regions of brain was in the range 3.0-4.1, and increased with brain cell swelling after water intoxication. D(o)/D also increased with increasing size of the diffusing solute, particularly in deep brain nuclei. Simulations of measured D(o)/D using realistic alpha, cell size and cell-cell gap required the presence of intercellular lakes at multicell contact points, and the contact length of cell-cell gaps to be least 50-fold smaller than cell size. The model accurately predicted D(o)/D for different solute sizes. Also, the modeling showed unanticipated effects on D(o)/D of changing ECS and cell dimensions that implicated solute trapping by lakes. Our model establishes the geometric constraints to account quantitatively for the relatively modest slowing of solute and macromolecule diffusion in brain ECS.

Stochastic binding of Ca2+ ions in the dyadic cleft; continuous versus random walk description of diffusion

Ca(2+) signaling in the dyadic cleft in ventricular myocytes is fundamentally discrete and stochastic. We study the stochastic binding of single Ca(2+) ions to receptors in the cleft using two different models of diffusion: a stochastic and discrete Random Walk (RW) model, and a deterministic continuous model. We investigate whether the latter model, together with a stochastic receptor model, can reproduce binding events registered in fully stochastic RW simulations. By evaluating the continuous model goodness-of-fit for a large range of parameters, we present evidence that it can. Further, we show that the large fluctuations in binding rate observed at the level of single time-steps are integrated and smoothed at the larger timescale of binding events, which explains the continuous model goodness-of-fit. With these results we demonstrate that the stochasticity and discreteness of the Ca(2+) signaling in the dyadic cleft, determined by single binding events, can be described using a deterministic model of Ca(2+) diffusion together with a stochastic model of the binding events, for a specific range of physiological relevant parameters. Time-consuming RW simulations can thus be avoided. We also present a new analytical model of bimolecular binding probabilities, which we use in the RW simulations and the statistical analysis.

Are quantum dots ready for in vivo imaging in human subjects?

Nanotechnology has the potential to profoundly transform the nature of cancer diagnosis and cancer patient management in the future. Over the past decade, quantum dots (QDs) have become one of the fastest growing areas of research in nanotechnology. QDs are fluorescent semiconductor nanoparticles suitable for multiplexed in vitro and in vivo imaging. Numerous studies on QDs have resulted in major advancements in QD surface modification, coating, biocompatibility, sensitivity, multiplexing, targeting specificity, as well as important findings regarding toxicity and applicability. For in vitro applications, QDs can be used in place of traditional organic fluorescent dyes in virtually any system, outperforming organic dyes in the majority of cases. In vivo targeted tumor imaging with biocompatible QDs has recently become possible in mouse models. With new advances in QD technology such as bioluminescence resonance energy transfer, synthesis of smaller size non-Cd based QDs, improved surface coating and conjugation, and multifunctional probes for multimodality imaging, it is likely that human applications of QDs will soon be possible in a clinical setting.

Cellular pathways of energy metabolism in the brain: Is glucose used by neurons or astrocytes?

Most techniques presently available to measure cerebral activity in humans and animals, i.e. positron emission tomography (PET), autoradiography, and functional magnetic resonance imaging, do not record the activity of neurons directly. Furthermore, they do not allow the investigator to discriminate which cell type is using glucose, the predominant fuel provided to the brain by the blood. Here, we review the experimental approaches aimed at determining the percentage of glucose that is taken up by neurons and by astrocytes. This review is integrated in an overview of the current concepts on compartmentation and substrate trafficking between astrocytes and neurons. In the brain in vivo, about half of the glucose leaving the capillaries crosses the extracellular space and directly enters neurons. The other half is taken up by astrocytes. Calculations suggest that neurons consume more energy than do astrocytes, implying that astrocytes transfer an intermediate substrate to neurons. Experimental approaches in vitro on the honeybee drone retina and on the isolated vagus nerve also point to a continuous transfer of intermediate metabolites from glial cells to neurons in these tissues. Solid direct evidence of such transfer in the mammalian brain in vivo is still lacking. PET using [(18)F]fluorodeoxyglucose reflects in part glucose uptake by astrocytes but does not indicate to which step the glucose taken up is metabolized within this cell type. Finally, the sequence of metabolic changes occurring during a transient increase of electrical activity in specific regions of the brain remains to be clarified.

Microstructural changes in ischemic cortical gray matter predicted by a model of diffusion-weighted MRI

PURPOSE

To understand the diffusion attenuated MR signal from normal and ischemic brain tissue in order to extract structural and physiological information using mathematical modeling, taking into account the transverse relaxation rates in gray matter.

MATERIALS AND METHODS

We fit our diffusion model to the diffusion-weighted MR signal obtained from cortical gray matter in healthy subjects. Our model includes variable volume fractions, intracellular restriction effects, and exchange between compartments in addition to individual diffusion coefficients and transverse relaxation rates for each compartment. A global optimum was found from a wide range of parameter permutations using cluster computing. We also present simulations of cell swelling and changes of exchange rate and intracellular diffusion as possible cellular mechanisms in ischemia.

RESULTS

Our model estimates an extracellular volume fraction of 0.19 in accordance with the accepted value from histology. The absolute apparent diffusion coefficient obtained from the model was similar to that of experiments. The model and the experimental results indicate significant differences in diffusion and transverse relaxation between the tissue compartments and slow water exchange. Our model reproduces the signal changes observed in ischemia via physiologically credible mechanisms.

CONCLUSION

Our modeling suggests that transverse relaxation has a profound influence on the diffusion attenuated MR signal. Our simulations indicate cell swelling as the primary cause of the diffusion changes seen in the acute phase of brain ischemia.

Mechanisms to explain the reverse perivascular transport of solutes out of the brain

Experimental studies and observations in the human brain indicate that interstitial fluid and solutes, such as amyloid-beta (Abeta), are eliminated from grey matter of the brain along pericapillary and periarterial pathways. It is unclear, however, what constitutes the motive force for such transport within blood vessel walls, which is in the opposite direction to blood flow. In this paper the potential for global pressure differences to achieve such transport are considered. A mathematical model is constructed in order to test the hypothesis that perivascular drainage of interstitial fluid and solutes out of brain tissue is driven by pulsations of the blood vessel walls. Here it is assumed that drainage occurs through a thin layer between astrocytes and endothelial cells or between smooth muscle cells. The model suggests that, during each pulse cycle, there are periods when fluid and solutes are driven along perivascular spaces in the reverse direction to the flow of blood. It is shown that successful drainage may depend upon some attachment of solutes to the lining of the perivascular space, in order to produce a valve-like effect, although an alternative without this requirement is also postulated. Reduction in pulse amplitude, as in ageing cerebral vessels, would prolong the attachment time, encourage precipitation of Abeta peptides in vessel walls, and impair elimination of Abeta from the brain. These factors may play a role in the pathogenesis of cerebral amyloid angiopathy and in the accumulation of Abeta in the brain in Alzheimer's disease.