On mathematical models of microdialysis: geometry, steady-state models, recovery and probe radius

OFM-recirculation and OFM-suction: advanced in-vivo open flow microperfusion (OFM) methods for direct and absolute quantification of albumin in interstitial fluid

OBJECTIVE

To implement OFM-recirculation and OFM-suction capable of direct and absolute in-vivo quantification of albumin in the ISF of pigs.

APPROACH

OFM-recirculation and OFM-suction were used to collect ISF in-vivo in pigs and lymph was collected from the same pigs after OFM sampling. Blood was collected before and after OFM sampling, plasma was isolated and mean albumin plasma concentrations per pig were used to yield albumin ISF-to-plasma ratios. We characterized the quality of the collected undiluted ISF via (1) stable albumin ISF-to-plasma ratio in OFM-recirculation and in OFM-suction samples, (2) comparison of albumin ISF-to-plasma ratios from OFM-recirculation and OFM-suction and (3) comparison of normalized albumin concentrations in the ISF and lymph.

MAIN RESULTS

Both advanced OFM methods were successfully implemented and albumin was quantified from the collected ISF samples. OFM-recirculation reached stable albumin ISF-to-plasma ratios after 20 recirculation cycles. Absolute ISF albumin concentrations were 11.2 mg ml^-1 (OFM-recirculation) and 14.2 mg ml^-1 (OFM-suction). Albumin ISF-to-plasma ratios were 0.39 ± 0.04 (OFM -recirculation) and 0.47 ± 0.1 (OFM-suction).

SIGNIFICANCE

Knowledge of the ISF protein content is of major importance when assessing PK/PD effects, especially of highly protein bound drugs. Up to now, only blood albumin values have been available to determine the degree of protein binding in several tissues. OFM-recirculation and OFM-suction allow direct, absolute quantification of albumin in ISF for the first time and enable investigation of the degree of protein binding of a drug directly in its target tissue.

Sampling insulin in different tissue compartments using microdialysis: methodological aspects

Sampling the concentration of insulin in human skin using microdialysis is challenging because of low intracutaneous concentrations and low recovery, presumably due to adsorption of insulin to the microdialysis system. In this study, we aimed to (1) measure how the concentration of insulin varies in three different tissue compartments (intracutaneous, subcutaneous and intravenous) and (2) to study how much insulin is adsorbed to the microdialysis catheter membranes and tubing during a typical microdialysis experiment, both in vivo and in vitro. We hypothesized that (1) the concentration of insulin decreases from the intravenous compartment to the intracutaneous and subcutaneous tissue, and that (2) adsorption of insulin to the microdialysis membrane and tubing impairs the recovery of insulin from the tissue. In this experimental study, microdialysis catheters were inserted intracutaneously, subcutaneously and intravenously in 11 healthy subjects. Systemic endogenous hyperinsulinemia was induced by intake of an oral glucose load. Insulin concentration was measured in the dialysate and in the extracted samples from the catheter membrane and tubings. In vitro microdialysis was performed to investigate the temporal resolution of the adsorption. After an oral glucose load insulin concentration increased intravenously, but not in the intracutaneous or subcutaneous compartments, while glucose, lactate and pyruvate concentrations increased in all compartments. The adsorption of insulin to the microdialysis membrane in vivo was highest in the intravenous compartment (p = 0.01), compared to the intracutaneous and subcutaneous compartments. In vitro, the adsorption to the microdialysis membrane was highest one hour after sampling, then the concentration gradually decreased after three and five hours of sampling. The concentration of insulin in peripheral tissues is low, probably due to decreasing tissue vascularity. Adsorption of insulin to the microdialysis membrane is modest but time-dependent. This finding highlights the importance of a stabilization time for the microdialysis system before sampling tissue analytes.

A Review on Microdialysis Calibration Methods: the Theory and Current Related Efforts

Microdialysis is a sampling technique first introduced in the late 1950s. Although this technique was originally designed to study endogenous compounds in animal brain, it is later modified to be used in other organs. Additionally, microdialysis is not only able to collect unbound concentration of compounds from tissue sites; this technique can also be used to deliver exogenous compounds to a designated area. Due to its versatility, microdialysis technique is widely employed in a number of areas, including biomedical research. However, for most in vivo studies, the concentration of substance obtained directly from the microdialysis technique does not accurately describe the concentration of the substance on-site. In order to relate the results collected from microdialysis to the actual in vivo condition, a calibration method is required. To date, various microdialysis calibration methods have been reported, with each method being capable to provide valuable insights of the technique itself and its applications. This paper aims to provide a critical review on various calibration methods used in microdialysis applications, inclusive of a detailed description of the microdialysis technique itself to start with. It is expected that this article shall review in detail, the various calibration methods employed, present examples of work related to each calibration method including clinical efforts, plus the advantages and disadvantages of each of the methods.

Decline of lactate in tumor tissue after ketogenic diet: in vivo microdialysis study in patients with head and neck cancer

In head and neck squamous cell carcinoma (HNSCC) aerobic glycolysis is the key feature for energy supply of the tumor. Quantitative microdialysis (μD) offers an online method to measure parameters of the carbohydrate metabolism in vivo. The aim was to standardize a quantitative μD-study in patients with HNSCC and to prove if a ketogenic diet would differently influence the carbohydrate metabolism of the tumor tissue. Commercially available 100 kDa-CMA71-μD- catheters were implanted in tumor-free and in tumor tissue in patients with HNSCC for simultaneous measurements up to 5 days. The metabolic pattern and circadian rhythm of urea, glucose, lactate, and pyruvate was monitored during 24 h of western diet and subsequent up to 4 days of ketogenic diet. After 3 days of ketogenic diet the mean lactate concentration declines to a greater extent in the tumor tissue than in the tumor-free mucosa, whereas the mean glucose and pyruvate concentrations rise. The in vivo glucose metabolism of the tumor tissue is clearly influenced by nutrition. The decline of mean lactate concentration in the tumor tissue after ketogenic diet supports the hypothesis that HNSCC tumor cells might use lactate as fuel for oxidative glucose metabolism.

Validation and use of microdialysis for determination of pharmacokinetic properties of the chemotherapeutic agent mitomycin C - an experimental study

BACKGROUND

Mitomycin C is a chemotherapeutic agent used in the treatment of peritoneal surface malignancies, administered as hyperthermic intraperitoneal chemotherapy after cytoreductive surgery. Pharmacokinetic studies have been based on analyses of blood, urine and abdominal perfusate, but actual tissue concentrations of the drug have never been determined. Microdialysis is an established method for continuous monitoring of low-molecular substances in tissues, and in the present study microdialysis of mitomycin C was studied in vitro and in vivo.

METHODS

Using in vitro microdialysis, relative recovery was determined when varying drug concentration, temperature and perfusion flow rate. In vivo microdialysis was performed in rats to verify long-term stability of relative recovery in four compartments (vein, peritoneum, extraperitoneal space and hind leg muscle). Subsequently, intravenous and intraperitoneal bolus infusion experiments were performed and pharmacokinetic parameters were calculated.

RESULTS

In vitro, compatibility of mitomycin C and microdialysis equipment was demonstrated, and relative recovery was stable over an adequate concentration range, moderately increased by raising medium temperature and increased when flow rate was reduced, all according to theory. In vivo, stable relative recovery was observed over seven hours. Mitomycin C exhibited fast and even distribution in rat tissues, and equal bioavailability was achieved by intravenous and intraperitoneal infusion. The half-life of mitomycin C calculated after intravenous infusion was 40 minutes.

CONCLUSIONS

Mitomycin C concentration can be reliable monitored in vivo using microdialysis, suggesting that this technique can be used in pharmacokinetic studies of this drug during hyperthermic intraperitoneal chemotherapy.

In vivo methods for the assessment of topical drug bioavailability

This paper reviews some current methods for the in vivo assessment of local cutaneous bioavailability in humans after topical drug application. After an introduction discussing the importance of local drug bioavailability assessment and the limitations of model-based predictions, the focus turns to the relevance of experimental studies. The available techniques are then reviewed in detail, with particular emphasis on the tape stripping and microdialysis methodologies. Other less developed techniques, including the skin biopsy, suction blister, follicle removal and confocal Raman spectroscopy techniques are also described.

Insulin and contraction increase nutritive blood flow in rat muscle in vivo determined by microdialysis of L-[14C]glucose

In the present study, a mathematical model using the microdialysis outflow: inflow (O/I) ratio of the novel analogue L-[14C]glucose has been developed which allows the calculation of the nutritive (and non-nutritive) flow in muscle as a proportion of total blood flow. Anaesthetized rats had microdialysis probes carrying L-[14C]glucose inserted through a calf muscle group (tibialis/plantaris/gastrocnemius). The nutritive fraction of total blood flow was determined under basal conditions and in response to contraction (electrical field stimulation), insulin (hyperinsulinaemic euglycaemic clamp with 10 mU min(-1) kg(-1) insulin) or saline control from limb blood flow and the microdialysis O/I ratio of L-[14C]glucose. Both contraction and insulin infusion decreased the O/I ratio of L-[14C]glucose and increased total limb blood flow. Calculations based on mathematical models using L-[14C]glucose O/I and limb blood flow revealed that during basal conditions, the nutritive fraction of total flow was 0.38 +/- 0.06, indicating that basal flow was predominantly non-nutritive. Contraction and insulin increased the nutritive fraction to 0.82 +/- 0.24 (P < 0.05) and 0.52 +/- 0.12 (P < 0.05). Thus the increase in limb blood flow from insulin was fully accommodated by nutritive flow, while contraction increased nutritive flow at the expense of non-nutritive flow. This novel method using microdialysis and the O/I ratio of L-[14C]glucose allows the determination of the nutritive fraction of total flow in muscle as well as the proportion of total flow that may be redistributed in response to contraction and insulin.

CEREBRAL UPTAKE OF DRUGS IN HUMANS

1. Drugs that target the central nervous system (CNS) are under-represented in the pharmacopoeia because of the difficulties of overcoming passive and active defences of the blood-brain barrier (BBB). Methods have been developed in drug discovery to make decisions about whether a compound crosses the BBB. Less is known about how the rate and extent of CNS penetration of a drug affects its clinical behaviour, largely because of past difficulties in measuring the cerebral uptake of drugs in humans. Three methods for doing so are reviewed. 2. Microdialysis is sometimes used as a clinical tool for monitoring the brain in neurointensive care and opportunistic pharmacological studies are possible. The method is relatively cheap and simple, measures free drug concentrations and is better suited to characterizing slowly changing brain drug concentrations. 3. Measuring cerebral drug uptake using positron emission tomography imaging requires the use of short-lived isotopes (labelled drug or labelled receptor ligand). Data with high spatial and temporal resolution can be collected, but the method requires expensive infrastructure. 4. Jugular bulb catheters collect pure brain venous blood and are sometimes placed for neuromonitoring. Cerebral drug uptake is inferred from the arterial to cerebral venous concentration difference. The method is relatively cheap and simple and allows global brain concentrations to be estimated. It is better suited to characterizing rapidly changing brain concentrations and effects. 5. The cerebral kinetics of a cerebro-active drug can make substantial contributions to its clinical behaviour. For example, loperamide is a peripherally acting opioid that has little CNS effect due to the active efflux transport of loperamide from the brain back into the blood by transporters including P-glycoprotein. The opioids alfentanil and fentanyl differ in their duration of action largely because of differences in their cerebral distribution volume rather than differences in systemic kinetics. The onset of anaesthesia of the intravenous anaesthetic propofol is governed almost completely by the kinetics of the first-pass passage of the drug through the brain and is more affected by changes in cerebral blood flow than hepatic clearance. 6. Continuing to exploit and develop these methods may provide new avenues to enhance the safety and efficacy of cerebro-active drugs in clinical practice.

Evaluating tissue perfusion using labelled water indicator microdialysis in a rat model of haemorrhagic shock

The indicator microdialysis technique with (3)H(2)O was evaluated as a method for assessing local blood flow in skeletal muscle and liver in a rat model of haemorrhagic shock. Microdialysis probes were inserted into the hind limb muscle and liver of 12 rats and perfused with a solution containing (3)H(2)O. Haemorrhagic shock was induced in eight rats by repeated blood withdrawals; four rats were used as a control group. The outflow to inflow (O/I) ratio of water activity, lactate and pyruvate contents in the dialysate were repeatedly measured. The ratio of lactate to pyruvate (L/P) was calculated. There was no correlation between blood loss and O/I ratio (r = 0.323 for liver, r = 0.300 for muscle), between the mean arterial pressure and O/I ratio (r = 0.460 for liver, r = -0.301 for muscle) or between the concentration of lactate and O/I ratio (r = -0.237 for liver, r = 0.454 for muscle). A significant correlation was found between blood loss and lactate concentration in muscle (r = 0.619, p < 0.0001). We suppose that microdialysis with (3)H(2)O cannot be used as a sensitive method to estimate regional blood flow changes during haemorrhagic shock in rats. Measuring lactate, pyruvate and L/P ratio in the microdialysate seems to be a superior method to assess tissue hypoperfusion caused by haemorrhagic shock in rats.

Glucose Recovery with Bare and Hydrogel-Coated Microdialysis Probes: Experiment and Simulation of Temporal Effects

In vitro microdialysis glucose sampling was used to test the transient and steady-state suitability of antifouling hydrogel coatings, composed of 2-hydroxyethyl methacrylate, vinylpyrrolidinone, and poly(ethylene glycol). The in vitro glucose diffusion coefficients of bare microdialysis membranes and hydrogel coatings were determined experimentally to be 1.1 x 10-6 and 3.2 x 10-6 cm2/s, respectively. These values were used to numerically simulate the effect of the hydrogel on glucose transport across the microdialysis membrane using a convection-diffusion transport model. The times for dialysate at the exit of the bare and hydrogel-coated microdialysis probes to reach 95% of steady state were calculated to be 20 and 66 s, respectively. However, the experimental data showed that 95% of steady-state glucose recoveries were reached after 4-5 min. Numerical simulations incorporating the Taylor dispersion in the outlet tubing showed the time difference was caused almost completely by convective transport in the outlet tubing with negligible contribution from analyte profile broadening. These data indicated that the hydrogel coatings imposed 44% reduction in glucose permeability and consequently 26% reduction in the percent recovery. The effect of hydrogel coatings on the time to reach the steady-state recovery was insignificant compared with the time required for convection of glucose in the outlet tubing.

Local controlled drug delivery to the brain: mathematical modeling of the underlying mass transport mechanisms

The mass transport mechanisms involved in the controlled delivery of drugs to living brain tissue are complex and yet not fully understood. Often the drug is embedded within a polymeric or lipidic matrix, which is directly administered into the brain tissue, that is, intracranially. Different types of systems, including microparticles and disc- or rod-shaped implants are used to control the release rate and, thus, to optimize the drug concentrations at the site of action in the brain over prolonged periods of time. Most of these dosage forms are biodegradable to avoid the need for the removal of empty remnants after drug exhaustion. Various physical and chemical processes are involved in the control of drug release from these systems, including water penetration, drug dissolution, degradation of the matrix and drug diffusion. Once the drug has been released from the delivery system, it has to be transported through the living brain tissue to the target site(s). Again, a variety of phenomena, including diffusion, drug metabolism and degradation, passive or active uptake into CNS tissue and convection can be of importance for the fate of the drug. An overview is given of the current knowledge of the nature of barriers to free access of drug to tumour sites within the brain and the state of the art of: (i) mathematical modeling approaches describing the physical transport processes and chemical reactions which can occur in different types of intracranially administered drug delivery systems, and of (ii) theories quantifying the mass transport phenomena occurring after drug release in the living tissue. Both, simplified as well as complex mathematical models are presented and their major advantages and shortcomings discussed. Interestingly, there is a significant lack of mechanistically realistic, comprehensive theories describing both parts in detail, namely, drug transport in the dosage form and in the living brain tissue. High quality experimental data on drug concentrations in the brain tissue are difficult to obtain, hence this is itself an issue in testing mathematical approaches. As a future perspective, the potential benefits and limitations of these mathematical theories aiming to facilitate the design of advanced intracranial drug delivery systems and to improve the efficiency of the respective pharmacotherapies are discussed.

In vivo microdialysis for PK and PD studies of anticancer drugs

In vivo microdialysis technique has become one of the major tools to sample endogenous and exogenous substances in extracellular spaces. As a well-validated sampling technique, microdialysis has been frequently employed for quantifying drug disposition at the desired target in both preclinical and clinical settings. This review addresses general methodological considerations critical to performing microdialysis in tumors, highlights selected preclinical and clinical studies that characterized drug disposition in tumors by the use of microdialysis, and illustrates the potential application of microdialysis in the assessment of tumor response to cancer treatment.

Microdialysis—theoretical background and recent implementation in applied life-sciences

In the past decade microdialysis has become a method of choice in the study of unbound tissue concentrations of both endogenous and exogenous substances. Microdialysis has been shown to offer information about substances directly at the site of action while being well tolerable and safe. The large variety of its field of application has been demonstrated. However, a few challenges have to be met to make this method generally applicable in routine applications. This review will provide an overview over theoretical aspects that have to be considered during the implementation of microdialysis. Moreover, a comparison between microdialysis and other tissue sampling techniques will demonstrate advantages and limitations of the methods mentioned. Subsequently, it will present a critical synopsis of a variety of scientific/biomedical applications of this method with emphasis on the most recent literature, focussing on target tissues while giving examples of substances examined. It is concluded that microdialysis will be of great value in future investigations of pharmacokinetics, pharmacodynamics and in monitoring of disease status and progression.

Measuring drug concentrations using pulsatile microdialysis: theory and method development in vitro

A novel method of rapidly sampling drug concentrations, based on pulsatile microdialysis (PMD), was developed. In PMD, a dialysate fluid is pumped into a microdialysis probe, allowed to occupy the probe while at rest for some time, and then flushed at a high rate. A model that is based on a Fick's Laws was solved and tested, using methazolamide (MTZ) as the test drug in a variety of experimental setups, including time-dependent donor concentrations. Calibration plots of the donor versus sample concentrations were linear. There was excellent agreement between the calculated and experimental values of the fraction recovered obtained from the calibration plots. In a system for which the donor concentration declined in a first order manner, the data obtained using PMD and direct sampling of the donor were in nearly exact agreement with the theoretical value of k=0.09 min(-1). PMD was also able to collect data points quickly enough to characterize the rapid binding kinetics of MTZ by activated charcoal. It was concluded that PMD is an accurate method of sampling drug concentrations, and can obtain samples over shorter time intervals and more frequently than previously available methods.

Axially symmetric semi-infinite domain models of microdialysis and their application to the determination of nutritive flow in rat muscle

Theoretical models for the description of microdialysis outflow:inflow (O/I) ratio for 3H2O and [14C]ethanol were developed, taking into account the nutritive fraction of total blood flow in muscle. The models yielded an approximately exponential decay expression for the O/I ratio, dependent on the physical dimensions of a linear probe (length and radius), the flow rate through the probe, muscle blood flow (including the nutritive fraction) and the diffusion coefficients for the tracer in the probe and muscle. The models compared favourably with experimental data from the constant-flow perfused rat hindlimb. Estimates of the nutritive fraction of total blood flow from experimental data were determined by minimizing the error between model and experimental data. The nutritive fraction was found to be 0.22 +/- 0.04 under basal perfusion conditions. When 70 nM noradrenaline (norepinephrine) was included in the perfusion medium, the nutritive fraction was 0.91 +/- 0.06 (P < 0.05). The inclusion of 300 nM serotonin, decreased the nutritive fraction to 0.05 +/- 0.01 (P < 0.05). This model can be applied to the determination of nutritive fraction of skeletal muscle blood flow in physiologically relevant microvascular conditions such as during exercise and in disease states.

Development of a dog microdialysis model for determining synovial fluid pharmacokinetics of anti-arthritis compounds exemplified by methotrexate

PURPOSE

The purpose of this study was to develop and validate an animal model of drug disposition in synovial fluid (SF) by comparing microdialysis with arthrocentesis using the anti-arthritic drug methotrexate (MTX).

METHODS

Microdialysis probes were calibrated in vitro with the no net flux method using dog synovial fluid. The probes were implanted surgically into the stifle joint space of four dogs and were dialyzed overnight using a portable microinfusion pump. The membrane integrity of the probes was monitored by retrodialysis using an internal standard. After an intravenous bolus of 2.5 mg/kg of MTX, unbound concentrations in synovial fluid, as well as total plasma concentrations, were measured by liquid chromatography tandam mass spectrometer (LC/MS/MS) in samples collected from 0 to 48 h postdose.

RESULTS

The probe membrane remained intact at least 48 h after implantation. The mean probe recovery and unbound fraction of MTX in SF were 46.8% and 44.8%, respectively. The unbound fraction of MTX was 44% in synovial fluid. MTX penetrated into the joint space rapidly, with maximal concentrations of 6.6 microM reached at approximately 1 h postdose. The unbound MTX area under the curve in SF was approximately 40% of the total area under the curve in plasma. These data agree well with the previous data obtained for MTX using arthrocentesis.

CONCLUSION

In contrast with arthrocentesis, microdialysis enables the collection of multiple serial SF samples from individual animals with minimal trauma and potential blood contamination. This animal model should prove valuable for studying the disposition of new antiarthritis compounds or biomarkers in SF.

Assessment of cutaneous drug delivery using microdialysis

During the last decade microdialysis has been successfully applied to assess cutaneous drug delivery of numerous substances, indicating the large potential for bioequivalence/bioavailability evaluation of topical formulations. The technique has been shown to be minimally invasive and supply pharmacokinetic information directly in the target organ for cutaneous drug delivery with high temporal resolution without further intervention with the tissue after implantation. However, there are a few challenges that need to be addressed before microdialysis can be regarded as a generally applicable routine technique for cutaneous drug delivery assessments. Firstly, the technique is currently not suitable for sampling of highly lipophilic compounds and, secondly, more studies are desirable for elucidation of the variables associated with the technique to increase reproducibility. The present literature indicates that the condition of the skin at the individual assessment sites is the main variable, but also variables associated with relative recovery, differentiation between the pharmacokinetic parameters (i.e., lag time, distribution, absorption and elimination rate) can influences the reproducibility of the technique. Furthermore, it has been indicated that cutaneous microdialysis in rats may be useful for prediction of dermal pharmacokinetic properties of novel drugs/topical formulations in man.

A review of membrane sampling from biological tissues with applications in pharmacokinetics, metabolism and pharmacodynamics

This review provides an overview of membrane sampling techniques, microdialysis and ultrafiltration, and cites illustrations of their applications in pharmacokinetics, metabolism and/or pharmacodynamics. The review organizes applications by target tissue and general type of information gleaned. It focuses on recently published microdialysis studies (1999 to this writing) and offers the first review of ultrafiltration sampling studies. The advantages and limitations of using microdialysis and ultrafiltration sampling as tools for obtaining pharmacokinetic and metabolism data are discussed. Numerous examples are described including studies in which several types of data are collected simultaneously. Reports that study local metabolism of drug delivered through the probe are also presented.

Theory relating in vitro and in vivo microdialysis with one or two probes

In this paper, we further develop the general theory of microdialysis by extending the linear model of Bungay et al. to provide a theoretical basis for in vitro and in vivo microdialysis. Specifically, we considered the effect of active clearance processes on in vivo microdialysis, and thereby elaborated the theory of Benveniste et al. to endogenous compounds. We examined the use of steady state tissue diffusion resistance with negligible clearance processes to interpret microdialysis data. The influence of the tissue properties on the in vitro and in vivo recoveries in dual-probe microdialysis was analyzed and we simulated the effect of the operating parameters on dual probe microdialysis performance. We estimated that the minimum clearance rate constant detectable by microdialysis in a quasi-steady state is about 5.5 x 10(-5) s(-1). This minimum rate constant establishes a criterion, below which inhibition of the active clearance processes does not show detectable influences on the microdialysis extraction efficiency.

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.

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.