Pharmacokinetic estimations from microdialysis data

Summary Microdialysis has recently been adapted for sampling the extracellular fluid of various organs in order to measure drug concentrations, and the first clinical application has been published. My aim here is to provide simple rules about how to analyse pharmacokinetic data from such studies. The plotting of data on a time scale and the estimation of C (0) and slopes is not a trivial problem when multicompartmental models are assumed or sampling intervals are unequal. I have developed formulae and algorithms to solve the problem. A simple rule of thumb is given, suggesting when these formulae need to be applied. It is shown that the calculations of half-life and slopes is similar to standard methods for equal sample intervals and that calculation of AUC and clearance may be even more accurate for microdialysis data than for ordinary blood sampling, because of the time-integral character of the dialysis method. I have dealt with both zero-order and first-order kinetics.     

RIA-linked microdialysis sampling in the awake rat: Application to free-drug pharmacokinetics of hydrocortisone

The purpose of this research was to combine microdialysis sampling techniques with a highly sensitive radioimmunoassay (RIA) to study the in vivo kinetic response of pharmacologically important substances. This technique allowed for a dense sampling regimen from an awake, free-roaming experimental animal with no loss of blood and with rapid analysis of the dialysate. An important methodological criterion for accurate quantitation of a test drug in the extracellular space was knowledge of the relative recovery of the sampling system at the time of experimentation. Accordingly, the factors which influenced the recovery of drug during dense in vivo microdialysis sampling were examined and an analytical technique was developed to measure the instantaneous recovery of drug from the extracellular space. This information was applied to in vivo (iv) sampling experiments on anaesthetized and awake, free-roaming rats following bolus and multiple long-term iv administrations of the highly protein bound steroid (i.e. greater than 90%), hydrocortisone-21-phosphate. These studies indicated that unbound hydrocortisone levels as determined by the RIA-linked microdialysis (RIALM) technique fluctuated rapidly between each 2-min sampling interval, but nevertheless decreased to predose endogenous concentrations in a first-order fashion (t1/2 = 17-29 min). The rapid fluctuations of unbound hydrocortisone may reflect real pharmacokinetic or pharmacodynamic phenomena, attributed, perhaps, to reequilibration of the unbound drug pool with proteins and tissues in the blood.     

On the recording of sample times and parameter estimation from repeated measures pharmacokinetic data

A pharmacokinetic screen has been advocated for the characterization of the population pharmacokinetics of drugs during Phase 3 clinical trials. A common perception encountered in the collection of such data is that the accuracy of sampling times relative to dose is inadequate. A prospective simulation study was carried out to evaluate the effect of error in the recording of sampling times on the accuracy and precision of population parameter estimates from repeated measures pharmacokinetic data. A two-compartment model with intravenous bolus input(s) (single and multiple doses) was assumed. Random and systematic error in sampling times ranging from 5–50% using profile (block) randomized design were introduced. Sampling times were simulated in EXCEL while concentration data simulation and analysis were done in NONMEM. The effect of error in sampling times was studied at levels of variability ranging from 15–45% for a drug assumed to be dosed at its elimination half-life. One hundred replicate data sets of 100 subjects each were simulated for each case. although estimates of clearance (CitCL) and variability in clearance were robust for most of the sampling time errors, there was an increase in bias and imprecision in overall parameter estimation as intersubject variability was increased. If there is interest in parameters other thanCL, then the design of prospective population studies should include procedures for minimizing the error in the recording of sample times relative to dosing history. The views expressed in this article are personal opinions of the authors and not those of the US Food and Drug Administration.     

Lesion of medial prefrontal cortex reduces morphine-induced extracellular dopamine level in the ventral tegmental area: a microdialysis study in rats

Drug addiction is a chronic disorder characterized by compulsive drug-seeking behavior despite severe negative consequences. Most abused drugs increase dopamine release in the ventral tegmental area (VTA) and in the nucleus accumbens (NA). The medial prefrontal cortex (mPFC), a part of the mesocorticolimbic dopaminergic system, receives dopaminergic projections from VTA; and in turn, sends glutamatergic projections to both VTA and NA. The present study was designed to further investigate the involvement of the mPFC in the release of dopamine in the VTA by using in vivo microdialysis and high performance liquid chromatography with electrochemical detection (HPLC-ECD). Electrical lesion of the mPFC decreased the level of dopamine in the VTA to approximately 26.8% of basal level. Acute morphine (40 mg/kg i.p.) treatment increased the level of dopamine in the VTA, while the lesion of mPFC immediately before morphine administration attenuated the effects of acute morphine on the level of dopamine. These results suggest that the mPFC modulates dopamine release into the VTA.     

The determination of mean residence time using statistical moments:It is correct

The present communication seeks to end a controversy created by a recent publication regarding the applicability of statistical moment principles for determination of mean residence time of drug in the body ¯t_b.It is shown that the equation ¯t_b=AUMC/AUC iscorrect when applied to pharmacokinetic systems in which the total drug elimination rate is directly proportional to the drug concentration in the systemic circulation, i.e., firstorder central elimination. More general equations for ¯t_b in terms of elimination rate, amount eliminated, and amount in the body are presented along with demonstrations of their utility.     

在体微透析结合HPLC测定小鼠纹状体细胞外尿嘧啶含量

目的利用在体微透析结合高效液相色谱法建立检测小鼠纹状体细胞外尿嘧啶含量的方法。方法色谱柱为反向VertiSep GES-C18(150 mm×4.6 mm,5μm),流动相为乙腈-0.02 mol/L磷酸二氢钠(2:98),调pH值为3～4,流速为0.8 mL/min,检测波长为260 nm。柱温:0～5℃。结果尿嘧啶的保留时间约为4.5 min,且在0.05～1.0μg/mL范围内线性关系良好(R2=0.998 4)。结论该方法准确、灵敏、方便,重复性好,可用于脑微透析样品中尿嘧啶的含量测定。     

Calculations and Application of Mean Residence Times for Drugs Which Demonstrate One-Compartment Distribution and Michaelis-Menten Elimination

Pharmaceutical Research -     

Tissue targeted metabonomics: metabolic profiling by microdialysis sampling and microcoil NMR

The concentration of low molecular weight compounds in tissues can yield valuable information about the metabolic state of an organism. Studies of changes in the metabolic state or metabonomics can reflect disease pathways, drug action, or toxicity. This research aims to develop a new approach, tissue targeted metabonomics. Microdialysis sampling and microcoil NMR analysis are employed to compare basal and ischemic metabolic states of various tissues (blood, brain, and heart) of Sprague–Dawley rats. Microdialysis sampling is localized, making the metabolic profile tissue specific. Coupling to NMR analysis is highly advantageous, because a complete metabolic profile is obtained in a single spectrum. However, small sample volumes and low analyte concentrations make analysis of microdialysis samples challenging. Microcoil NMR uses low sample volumes and has improved mass sensitivity, relative to standard 5 mm probes. The coupling of these techniques is a potentially powerful tool for metabonomics analysis.     

Comparison of in vitro BBMEC permeability and in vivo CNS uptake by microdialysis sampling

The studies presented in this report were designed to assess the correlation of the bovine brain microvessel endothelial cell (BBMEC) apparent permeability coefficient (P_app) and in vivo BBB penetration using microdialysis sampling. A mathematical model was developed to describe the relationship of brain extracellular fluid (ECF) concentration to free drug in plasma. The compounds studied have a broad range of physico-chemical characteristics and have widely varying in vitro and in vivo permeability across the blood–brain barrier (BBB). BBMEC permeability coefficients vary in magnitude from a low of 0.9×10⁻⁵ cm/s to a high value of 7.5×10⁻⁵ cm/s. Corresponding in vivo measurements of BBB permeability are represented by clearance (CL_in) into the brain ECF and range from a low of 0.023 μl/min/g to a high of 12.9 μl/min/g. While it is apparent that in vitro data from the BBMEC model can be predictive of the in vivo permeability of a compound across the BBB, there are numerous factors both prior to and following entry into the brain which impact the ultimate uptake of a compound. Even in the presence of high BBB permeability, factors such as high plasma protein binding, active efflux across the BBB, and metabolism within the CNS can greatly limit the ultimate concentrations achieved. In addition, concentrations in the intracellular space may not be the same as concentrations in the extracellular space. While these data show that the BBMEC permeability is predictive of the in vivo BBB permeability, the complexity of the living system makes prediction of brain concentrations difficult, based solely on the in vitro measurement.     

Accuracy of noncompartmental pharmacokinetic parameters estimated from bolus injection and steady-state infusion data

A Monte Carlo simulation study was carried out to examine the accuracy of parameters derived from curve moments. Impulse response (IR) and washout (WO) concentration-time curves, based on a triexponential model, were analyzed by numerical integration and regression analysis. Both designs were tested according to their robustness to measurement error and model misspecification. Performance of the methods was judged using the median error (ME) and the median absolute error (MAE) of 1000 simulations. The WO design provided better estimates of mean disposition residence time and worse estimates of the normalized variance of disposition residence times (CV _d ² ) than its rival. At 20% measurement noise, theMAE ofCV _d ² was less than 13%. The WO design was much more robust to model misspecification. Numerical integration performed as good as, or better than, regression analysis. Both methods are very sensitive to tail-area error, meaning that special attention needs to be paid to this aspect of experimental design. This study demonstrates that it is possible to obtain good estimates of higher moment parameters in a well-designed experiment.     

Quantitative determination of unbound cefoperazone in rat bile using microdialysis and liquid chromatography

Cefoperazone is a third generation cephalosporin antibiotic with a broad spectrum against gram-positive and gram-negative bacteria. It is clinically effective in the treatment of the biliary tract infections. In the present study, we utilized microdialysis sampling technique with shunt linear probe for continuous monitoring levels of cefoperazone from rat biliary ducts. The effects of berberine (a potential P-glycoprotein enhancer) pretreatment were also evaluated. Analysis of cefoperazone in the dialysates was achieved using a reversed phase RP-18 column (250 mm x 4.6 mm i.d.; particle size 5 microm) maintained at ambient temperature. The mobile phase comprised 100 mM monosodium phosphate (pH 5.5)-methanol (70:30, v/v), and the flow rate of the mobile phase was 1 ml/min. The UV detector wavelength was set at 254 nm. The area under the concentration-time curve and elimination half-life of cefoperazone were about 242.3+/-13.4 min mg/ml and 64.1+/-28.2 min, respectively. No significant effect was showed on the pharmacokinetics of cefoperazone with berberine pretreatment. This study represents a successful application of biliary microdialysis sampling technique, which is feasible for pharmacokinetic and biliary drug excretion studies.     

Experimental design and efficient parameter estimation in population pharmacokinetics

A computer simulation technique used to evaluate the influence of several aspects of sampling designs on the efficiency of population pharmacokinetic parameter estimation is described. Although the simulations are restricted to the one-compartment one-exponential model, they provide the basis for a discussion of the structural aspects involved in designing a population study. These aspects include number of subjects required, number of samples per subject, and timing of these samples. Parameter estimates obtained from different sampling schedules based on two- and three-point designs are evaluated in terms of accuracy and precision. These simulated data sets include noise terms for both inter- and intraindividual variability. The results show that the population fixed-effect parameters (mean clearance and mean volume of distribution) for this simple pharmacokinetic model are efficiently estimated for most of the sampling schedules when two or three points are used, but the random-effect parameters (describing inter- and intraindividual variability) are inaccurate and imprecise for most of the sampling schedules when only two points are used. This drawback was remedied by increasing the number of data points per individual to three.Supported by the Scottish Home and Health Department (Biomedical Research Committee).     

Unifying the mathematical modeling of in vivo and in vitro microdialysis

A unifying approach is presented for developing mathematical models of microdialysis that are applicable to both in vitro and in vivo situations. Previous models for cylindrical probes have been limited by accommodating analyte diffusion through the surrounding medium in the radial direction only, i.e., perpendicular to the probe axis, or by incomplete incorporation of diffusion in the axial direction. Both radial and axial diffusion are included in the present work by employing two-dimensional finite element analysis. As in previous models, the nondimensional clearance modulus (Θ) represents the degree to which analyte clearance from the external medium influences diffusion through the medium for systems exhibiting analyte concentration linearity. Incorporating axial diffusion introduces a second dimensionless group, which is the length-to-radius aspect ratio of the membrane. These two parameter groups uniquely determine the external medium permeability, which is time dependent under transient conditions. At steady-state, the dependence of this permeability on the two groups can be approximated by an algebraic formula for much of the parameter ranges. Explicit steady-state expressions derived for the membrane and fluid permeabilities provide good approximations under transient conditions (quasi-steady-state assumption). The predictive ability of the unifying approach is illustrated for microdialysis of sucrose in vivo (brain) and inert media in vitro, under both well-stirred and quiescent conditions.     

In vivo and in vitro microdialysis sampling of free fatty acids

Microdialysis is a technique that allows continuous sampling of compounds from the interstitial fluid of different tissues with minimal influence on surrounding tissues and/or whole body function. In the present study, the feasibility of using microdialysis as a technique to sample free fatty acids (FFA) was investigated both in vitro and in vivo, by use of a high molecular weight (MW) cut-off membrane (3 MDa) and a push–pull system to avoid loss of perfusion fluid through the dialysis membrane. The relative recovery was examined in vitro for three different concentrations of radiolabelled oleic acid-BSA solutions (oleic acid:BSA molar ratio 1:1) and for various temperatures and flow rates. The recovery of oleic acid was found to be dependent on the concentration of analyte in the medium surrounding the membrane (17.3%, 29.0% and 30.6% for 50, 100 and 200 μM oleic acid-BSA solutions, respectively). Addition of 0.25% BSA to the perfusion fluid resulted, however, in a concentration-independent recovery of 31.4%, 28.1% and 28.1% for the 50, 100 and 200 μM solutions, respectively.

The capability of the method to measure FFA together with glycerol was investigated in vivo in visceral adipose tissue of rats, before and after lipolytic treatment with the β₃-adrenergic agent, BRL37344. BRL37344 caused an increase in both dialysate FFA and glycerol, although the increase was markedly higher for glycerol, amounting to 24.5% and 329.2% increase from baseline, respectively. Subsequent in vitro test of probe performance revealed a decrease in the dialysing properties with regard to FFA, but not glycerol. This suggests that clogging of the membrane pores after 110 min prevented the measurement of the full FFA response in vivo.     

微透析-高效液相色谱法测定米诺环素大鼠血液和脑内的药动学

目的:研究米诺环素在大鼠血液和脑内的药动学。方法:采用微透析结合高效液相色谱技术,测定米诺环素大鼠血浆蛋白结合率;大鼠尾静脉注射米诺环素,测定给药后10h内不同时间点大鼠血液、海马CA1区中游离药物的浓度。结果:米诺环素大鼠血浆蛋白结合率为82.08%,给药后迅速进入脑组织,在给药后3.83h左右浓度达到峰值,其后缓慢下降,脑组织的游离药物-时间曲线下面积(AUC0-10h)可达血液的62.42%。结论:微透析结合高效液相色谱技术可以测定米诺环素的大鼠血浆蛋白结合率,并实现大鼠血液和脑组织中游离米诺环素浓度的动态监测。结果表明米诺环素易于透过血脑屏障,且能长时间维持较高浓度,从而发挥其神经保护作用。     

Analytical Expressions for Combining Population Pharmacokinetic Parameters from Different Studies

We provide a set of formulas that allow the combination of separately performed analyses of population pharmacokinetic (PK) studies, without any further computational effort. More specifically, given the point estimates and uncertainties of two population PK analyses, the formulas provide the point estimates and uncertainties of the combined analysis, including the mean population values, the between-subject variability, and the residual variability. To derive the formulas we considered distributional assumptions applicable for the conjugate priors of the Bayesian problem of “unknown mean and variance.” In order to demonstrate the approach, the formulas were applied to an example involving the results of fitting two real experimental datasets. The formulas presented offer an easy-to-use method of combining different analyses particularly applicable to a combination of literature information.     

Method of moment estimation in the COGARCH(1,1) model

Summary We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are strongly mixing with exponential rate, we show that the resulting estimators are consistent and asymptotically normal. We investigate the empirical quality of our estimators in a simulation study based on the variance gamma driven COGARCH(1,1) model. The estimated volatility with corresponding residual analysis is also presented. Finally, we fit the model to high‐frequency data.     

The direct comparison of health and ulcerated stomach tissue: a multiple probe microdialysis sampling approach

The ability to directly compare gastric ulcerated and healthy tissue would aid in the understanding of the physiological differences between these tissue types. Presently, these comparisons can only be drawn by the use of separate animal groups, which results in increased study variability. The focus of this research was to develop a four-probe microdialysis sampling approach to directly compare ulcerated and healthy tissue in the same animal. After controlled chemical ulcer induction, probes were implanted in the ulcerated and healthy stomach submucosa, stomach lumen and in the blood. To assess the significance of this multiple probe approach, drug concentrations in each probe location were monitored after selected compounds were dosed to the ligated stomach by oral gavage. Analysis of the dialysate samples was performed by HPLC-UV and concentration-time curves and pharmacokinetics analyses were used to determine differences between these tissue types.     

Mean Residence Time of Oral Drugs Undergoing First-Pass and Linear Reversible Metabolism

Equations for the mean residence times in the body (MRT) and AUMC/AUC of a drug and its metabolite have been derived for an oral drug undergoing first-pass and linear reversible metabolism. The mean residence times of the drug or interconversion metabolite in the body after oral drug are described by equations which include the mean absorption time (MAT), the mean residence times of the drug or metabolite in the body after intravenous administration of the drug, the fractions of the dose entering the systemic circulation as the parent drug and metabolite, and the systemically available fractions of the drug (F _p ^p) or metabolite (F _m ^p). Similarly, the AUMC/AUC of the drug and metabolite after oral drug can be related to the MAT, ratios of the fraction of the dose entering the systemic circulation to the systemically available fraction, the first-time fractional conversion of each compound, and AUMC/AUC ratios after separate intravenous administration of each compound. The F _p ^p and F _m ^p values, in turn, are related to the first-pass availabilities of both drug and metabolite and the first-time fractional conversion fractions. The application of these equations to a dual reversible two-compartment model is illustrated by computer simulations.