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.     

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

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

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

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

Diffusion of water in cat ventricular myocardium

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

Diffusion in the slice microenvironment and implications for physiological studies

The brain cell microenvironment includes the extracellular space surrounding the cell together with the cellular elements that define the space. The dense packing of cells in the mammalian nervous system ensures that the extracellular space is narrow but highly complex in geometry. Recent studies with ion-selective micropipettes have revealed that the cerebellar slice can support changes in [K+]o that resemble those seen in the intact preparation. In the slice, [K+]o responses of individual cells can even be resolved. Studies with iontophoretic techniques and quantitative analysis in the slice have shown that the extracellular space has diffusion properties, characterized by a volume fraction and a tortuosity, that are very similar to those seen in the intact animal. These data confirm that the microenvironment in the slice is comparable to that in the intact animal. The diffusion parameters can be used to make predictions about the time necessary for substances to diffuse into slices under various conditions. Such estimates, together with other studies, indicate that it is probably inadvisable to use slices with thicknesses in excess of 300--400 micrometers, and that the bathing conditions can be critical in maintaining slice viability.     

Extrasynaptic transmission and the diffusion parameters of the extracellular space

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

Diffusion properties of the brain in health and disease

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

Extracellular space diffusion and extrasynaptic transmission

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

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

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

Determination of Brain Interstitial Concentrations by Microdialysis

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

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

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

Characterization of three-dimensional tissue cultures using electrical impedance spectroscopy

Electrical impedance spectroscopy was used to characterize the cell environment of multilayered cell cultures (MCCs), a culture system in which cells are grown on a permeable support membrane to form a thick disc of cells with tumor-like properties. Cultures were grown using SiHa tumor cells as well as V79 wild-type cells and V79/DOX cells cultivated to exhibit multidrug resistance. Electrical impedance measurements were made on MCCs over a frequency range of 0. 1 kHz to 1 MHz. Data analysis using a simple electrical model for the cell environment yielded estimates for parameters related to the intra- and extracellular resistance and net membrane capacitance, which were then related to MCC thickness. The extracellular fraction and tortuosity of the MCCs were determined in separate experiments where the rate of diffusion and the equilibrium level of C14-inulin, which does not penetrate the cell membrane, was measured within MCCs. Impedance measurements predicted the barrier to diffusion posed by the extracellular space of MCCs to be roughly two times greater than that inferred from the C14-inulin experiments. However, the relative ranking of the three cell types used to grow MCCs was similar for the two methods. Results indicate that impedance spectroscopy is well suited for use in characterizing the MCC cell environment, offering a fast, nondestructive method for monitoring cell culture growth and integrity.     

Three-dimensional modeling of the brain's ECS by minimum configurational energy packing of fluid vesicles

The extracellular space of the brain is the heterogeneous porous medium formed by the spaces between the brain cells. Diffusion in this interstitial space is the mechanism by which glucose and oxygen are delivered to the brain cells from the vascular system. It is also a medium for the transport of certain informational substances between the cells (called volume transmission), and for drug delivery. This work involves three-dimensional modeling of the extracellular space as void space in close-packed arrays of fluid membrane vesicles. These packings are generated by minimizing the configurational energy using a Monte Carlo procedure. Both regular and random packs of vesicles are considered. A random walk algorithm is then used to compute the geometric tortuosities, and the results are compared with published experimental data. For the random packings, it is found that although the absolute values for the tortuosities differ, the dependence of the tortuosity on pore volume fraction is very similar to that observed in experiment. The tortuosities we measure are larger than those computed in previous studies of packings of convex polytopes, and modeling improvements, which require higher resolution studies and an improved modeling of brain cell shapes and mechanical properties, could help resolve remaining discrepancies between model simulations and experiment. It is also shown that the specular reflection scheme is the appropriate technique for implementing zero-flux boundary conditions in random walk simulations commonly encountered in diffusion problems.     

Issues involved in the transmission of chemical signals through the brain extracellular space

Two classes of substances exist within the extracellular space: energetic and informational. Examples of the former are glucose, dissolved oxygen and CO2 while the latter include excitatory amino acids, cathecholamines and opiates. The simple ions Na+ and Cl- are generally associated with energetic processes while extracellular K+ and Ca2+ tend to be informational in function. Local release of an informational substance brings about a concentration gradient that causes the substance to be dispersed in the extracellular space by diffusion. This process is modified relative to a free aqueous medium by the constraints of volume fraction, tortuosity and uptake. Volume fraction is defined simply as the fraction of a brain region that is extracellular. If a given quantity of substance is released into a region with a reduced volume fraction then the substance will reach a higher concentration than it would in a free medium. Tortuosity is related to the increase in the path length of the random walk of a diffusing particle due to the necessity to navigate around cellular obstructions. Tortuosity manifests itself as a decrease in the diffusion coefficient. Uptake represents the movement of a substance from the extracellular space to the intracellular. Since initially a concentration gradient exists in this direction and all membranes have some permeability some concentration-dependent uptake always occurs. In addition there exist specific carrier-mediated uptake processes for some substances such as amino acids or catecholamines. In some regions the dispersal process can be dominated by uptake rather than diffusion. While volume fraction, tortuosity and uptake have all been demonstrated by a technique based on the use of radiolabels and other methods, these classical techniques have limited spatial and temporal resolution. The advent of methods based on micro-injection of substances by iontophoresis or pressure and subsequent detection with ion-selective microelectrodes (ISMs) or voltammetric microsensors (VMs) has opened a new window onto the dynamic local behavior of the extracellular space. In the last decade our laboratory and others have studied the migration of the test substances tetramethylammonium, tetraethylammonium, AsF6- and alpha naphthalene sulfonate, the endogenous ions K+ and Ca2+, the epileptogenic agent penicillin and the neurotransmitter dopamine. These studies have been carried out on the cerebellum and some other regions in a variety of species that include rat, turtle, skate and an intervertebrate, the cuttlefish.(ABSTRACT TRUNCATED AT 400 WORDS)     

Conductance of porous media depends on external electric fields

In obstacle-filled media, such as extracellular or intracellular lumen of brain tissue, effective ion-diffusion permeability is a key determinant of electrogenic reactions. Although this diffusion permeability is thought to depend entirely on structural features of the medium, such as porosity and tortuosity, brain tissue shows prominent nonohmic properties, the origins of which remain poorly understood. Here, we explore Monte Carlo simulations of ion diffusion in a space filled with overlapping spheres to predict that diffusion permeability of such media decreases with stronger external electric fields. This dependence increases with lower medium porosity while decreasing with radial (two-dimensional or three-dimensional) compared with homogenous (one-dimensional) fields. We test our predictions empirically in an electrolyte chamber filled with microscopic glass spheres and find good correspondence with our predictions. A theoretical insight relates this phenomenon to a disproportionately increased dwell time of diffusing ions at potential barriers (or traps) representing geometric obstacles when the field strength increases. The dependence of medium ion-diffusion permeability on electric field could be important for understanding conductivity properties of porous materials, in particular for the accurate interpretation of electric activity recordings in brain tissue.     

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.     

Anomalous Extracellular Diffusion in Rat Cerebellum

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

Brain interstitial fluid drainage and extracellular space affected by inhalational isoflurane: in comparison with intravenous sedative dexmedetomidine and pentobarbital sodium

Brain interstitial fluid drainage and extracellular space are closely related to waste clearance from the brain. Different anesthetics may cause different changes of brain interstitial fluid drainage and extracellular space but these still remain unknown. Herein,effects of the inhalational isoflurane, intravenous sedative dexmedetomidine and pentobarbital sodium on deep brain matters' interstitial fluid drainage and extracellular space and underlying mechanisms were investigated. When compared to intravenous anesthetic dexmedetomidine or pentobarbital sodium, inhalational isoflurane induced a restricted diffusion of extracellular space, a decreased extracellular space volume fraction, and an increased norepinephrine level in the caudate nucleus or thalamus with the slowdown of brain interstitial fluid drainage. A local administration of norepinephrine receptor antagonists, propranolol,atipamezole and prazosin into extracellular space increased diffusion of extracellular space and interstitial fluid drainage whilst norepinephrine decreased diffusion of extracellular space and interstitial fluid drainage. These findings suggested that restricted diffusion in brain extracellular space can cause slowdown of interstitial fluid drainage, which may contribute to the neurotoxicity following the waste accumulation in extracellular space under inhaled anesthesia per se.     

Quantitative dual-probe microdialysis: mathematical model and analysis

Steady-state microdialysis is a widely used technique to monitor the concentration changes and distributions of substances in tissues. To obtain more information about brain tissue properties from microdialysis, a dual-probe approach was applied to infuse and sample the radiotracer, [3H]mannitol, simultaneously both in agar gel and in the rat striatum. Because the molecules released by one probe and collected by the other must diffuse through the interstitial space, the concentration profile exhibits dynamic behavior that permits the assessment of the diffusion characteristics in the brain extracellular space and the clearance characteristics. In this paper a mathematical model for dual-probe microdialysis was developed to study brain interstitial diffusion and clearance processes. Theoretical expressions for the spatial distribution of the infused tracer in the brain extracellular space and the temporal concentration at the probe outlet were derived. A fitting program was developed using the simplex algorithm, which finds local minima of the standard deviations between experiments and theory by adjusting the relevant parameters. The theoretical curves accurately fitted the experimental data and generated realistic diffusion parameters, implying that the mathematical model is capable of predicting the interstitial diffusion behavior of [3H]mannitol and that it will be a valuable quantitative tool in dual-probe microdialysis.