Mean residence time in peripheral tissue: a linear disposition parameter useful for evaluating a drug's tissue distribution

Engineering targeted in vivo drug delivery. I. The physiological and physicochemical principles governing opportunities and limitations

A physiologically based model is presented to aid prediction of the pharmacological benefits to be derived from the administration of a drug as a targeted drug-carrier combination. An improvement in the therapeutic index and an increase in the therapeutic availability are the primary benefits sought. A measure of the former is obtained from the value of the drug targeting index, a newly derived parameter. Both the drug targeting index and the therapeutic availability are directly calculable. The minimum information needed for approximating both parameters is the candidate drug's total-body clearance and some knowledge of the target site's anatomy and blood flow. Drugs with high total-body clearance values that are known to act at target tissues having effective blood flows that are small relative to the blood flow to the normal eliminating organs will benefit most from combination with an efficient, targeted carrier. Direct elimination of the drug at the target site or at the tissue where toxicity originates dramatically improves the drug targeting index value. The fraction of drug actually released from the carrier at both target and nontarget sites can radically affect index values. In some cases a 1% change in the fraction of the dose delivered to the target can result in a 50% change in the drug targeting index value. It is argued that most drugs already developed have a low potential to benefit from combination with a drug carrier. The approach allows one to distinguish clearly those drugs that can benefit from combination with targeted in vivo drug carriers from those drugs that cannot.

Pharmacokinetics of recombinant bifunctional fusion proteins

INTRODUCTION

The development of biotechnology has enabled the creation of various recombinant fusion proteins as a new class of biotherapeutics. The uniqueness of fusion proteins lies in their ability to fuse two or more protein domains, providing vast opportunities to generate novel combinations of functions. Pharmacokinetic (PK) studies, which are critical components in preclinical and clinical drug development, have not been fully explored for fusion proteins. The lack of general PK models and study guidelines has become a bottleneck for translation of fusion proteins from basic research to the clinic.

AREAS COVERED

This article reviews the current status of PK studies for fusion proteins, covering the processes that affect PK. According to their PK properties, a classification of fusion proteins is suggested along with examples from the clinic or under development. Current limitations and future perspectives for PK of fusion proteins are also discussed.

EXPERT OPINION

A PK model for bifunctional fusion proteins is presented to highlight the importance of mechanistic studies for a thorough understanding of the PK properties of fusion proteins. The model suggests investigating the receptor binding and subsequent intracellular disposition of individual domains, which can have dramatic impact on the PK of fusion proteins.

Residual fraction of the area under the curve as a qualitative criterion in pharmacokinetic studies

The aim of the present study was to determine whether the residual area under the curve (AUC(res%); expressed as % of total value of AUC) could be used as a parameter for the qualitative evaluation of pharmacokinetic studies.We propose new criteria for the qualitative evaluation of pharmacokinetic analysis. Two sets of hypothetical data that illustrate the relationship between concentration and time were used for the analysis of drug pharmacokinetics. Non-compartmental analysis was applied for the calculations. The results obtained from the hypothetical data were compared with those obtained from an in vivo study in which 3-week-old broiler chickens were administered 10 mg/kg b.w. enrofloxacin intravenously (iv) or per os (po). In the first set of data (A-D), AUC(res%) values were as follows: A= 16.29% and B = 20.79% for iv administration and C = 29.61% and D = 27.90% for po administration. In the next set of data (E-G), AUC(res%) values after oral administration were 25.30% (E), 23.18% (F), and 20.79% (G). The AUC(res%) values after iv administration of enrofloxacin were similar to po administration; the range of iv and po administration values were 14.35% to 17.50% and 11.14% to 28.33% of the total AUC, respectively. The analysis of the hypothetical data indicates that AUC(res%) is not an optimal method for the evaluation of pharmacokinetic studies.

Pharmacokinetic aspects of biotechnology products

In recent years, biotechnologically derived peptide and protein-based drugs have developed into mainstream therapeutic agents. Peptide and protein drugs now constitute a substantial portion of the compounds under preclinical and clinical development in the global pharmaceutical industry. Pharmacokinetic and exposure/response evaluations for peptide and protein therapeutics are frequently complicated by their similarity to endogenous peptides and proteins as well as protein nutrients. The first challenge frequently comes from a lack of sophistication in various analytical techniques for the quantification of peptide and protein drugs in biological matrices. However, advancements in bioassays and immunoassays--along with a newer generation of mass spectrometry-based techniques--can often provide capabilities for both efficient and reliable detection. Selection of the most appropriate route of administration for biotech drugs requires comprehensive knowledge of their absorption characteristics beyond physicochemical properties, including chemical and metabolic stability at the absorption site, immunoreactivity, passage through biomembranes, and active uptake and exsorption processes. Various distribution properties dictate whether peptide and protein therapeutics can reach optimum target site exposure to exert the intended pharmacological response. This poses a potential problem, especially for large protein drugs, with their typically limited distribution space. Binding phenomena and receptor-mediated cellular uptake may further complicate this issue. Elimination processes--a critical determinant for the drug's systemic exposure--may follow a combination of numerous pathways, including renal and hepatic metabolism routes as well as generalized proteolysis and receptor-mediated endocytosis. Pharmacokinetic/pharmacodynamic (PK/PD) correlations for peptide and protein-based drugs are frequently convoluted by their close interaction with endogenous substances and physiologic regulatory feedback mechanisms. Extensive use of pharmacokinetic and exposure/response concepts in all phases of drug development has in the past been identified as a crucial factor for the success of a scientifically driven, evidence-based, and thus accelerated drug development process. Thus, PK/PD concepts are likely to continue and expand their role as a fundamental factor in the successful development of biotechnologically derived drug products in the future.

Pharmacokinetics of 125I-labelled Walterinnesia aegyptia venom and its distribution of the venom and its toxin versus slow absorption and distribution of IGG, F(AB')2 and F(AB) of the antivenin

A three-compartment open pharmacokinetic model best fitted the data obtained following the i.v. injection of the venom, toxin and the immunoglobulin fractions into either rabbits or mice. The venom and toxin, however, possessed pharmacokinetic characteristics that were significantly different from the immunoglobulin fractions. The venom and toxin had very highly significantly greater disposition rate constants to the shallow and deep tissue compartments and overall elimination rate constant from the central compartment than any of the immunoglobulin fractions. This was reflected in other pharmacokinetic parameters, including highly significantly smaller areas under the curve (AUC) and highly significantly greater volumes of the central compartment (Vc), shallow tissue compartment (Vt shallow), deep tissue compartment (Vt deep) and total body clearance (TBC). In rabbits, F(ab')2 possessed the fastest disposition rate constants and the shortest distribution half-lives, while Fab showed the slowest disposition rate constants and the longest distribution half-lives. The same picture occurred in mice except that the values for Fab were between those of F(ab')2 and IgG. The time needed by the venom and toxin to reach maximum tissue concentration (tmax) ranged between 7 and 15 min and 60 and 180 min for the shallow and deep tissue compartments, respectively. The immunoglobulin fractions required 8-26-fold these times to attain tmax; F(ab')2 was the fastest to achieve its maximal concentration. Following i.m. injection, very fast absorption of venom and toxin took place, with the toxin reaching tmax within 5-20 min and 90% of the injected dose absorbed within 60 min. The bioavailability factor (F) was 0.82 and 0.88 for the venom and toxin, respectively. Fab had an F-value of 0.36 and required 4.3 and 47.4-fold the time taken by the venom and toxin to achieve tmax. The calculated values of F for F(ab')2 and IgG were 0.25 and 0.26, respectively. In the physiologically based pharmacokinetics (PBPK), the venom and toxin reached tmax in the different organs studied very rapidly while the immunoglobulin fractions required several-fold this time to attain tmax. F(ab')2 possessed the highest CPmax, the smallest AUC and the shortest t1/2 beta in the different tissues; Fab had values between F(ab)2 and IgG. It is concluded that F(ab')2 possesses pharmacokinetic characteristics that render it most suitable for use in serotherapy of snake and scorpion envenoming. It should be injected i.v. in doses higher than calculated neutralizing doses to compensate for the slow rate of distribution. Because of slow and incomplete absorption, the i.m. injection of the immunoglobulin fractions would be of little value in serotherapy.

A three-compartment open pharmacokinetic model can explain variable toxicities of cobra venoms and their alpha toxins

The pharmacokinetic profiles of labelled Naja melanoleuca, Naja nivea, Naja nigricollis and Naja haje venoms and their alpha neurotoxins were determined following rapid i.v. injection into rabbits. The data obtained fitted a triexponential equation characteristic of a three-compartment open pharmacokinetic model comprising a central compartment 'blood', a rapidly equilibrating 'shallow' tissue compartment and a slowly equilibrating 'deep' tissue compartment. The distribution half-lives for the shallow compartment ranged from 3.2 to 5 min, reflecting the rapid uptake of venoms and toxins compared with 22-47 min for the deep tissue compartment denoting much slower uptake. The overall elimination half-lives, t1/2 beta, ranged from 15 to 29 hr, indicating a slow body elimination. Peak tissue concentration was reached within 15-20 min in the shallow tissue compartment. The corresponding values for the deep tissue compartment were 120 min for N. melanoleuca and N. nigricollis venoms and their toxins and 240 min for N. nivea and N. haje venoms and their toxins. Steady-state distribution between the shallow tissue compartment and the blood gave values of 0.50 and 0.92 (N. melanoleuca), 1.64 and 1.05 (N. nivea), 0.78 and 0.92 (N. nigricollis) and 1.70 and 1.03 (N. haje) for the venoms and their toxins, respectively. The corresponding values for the deep tissue compartment gave ratios of 3.31 and 3.44 (N. melanoleuca), 2.99 and 1.68 (N. nivea), 3.74 and 3.79 (N. nigricollis) and 1.39 and 2.46 (N. haje) for the venoms and their toxins, respectively. Ratios lower than unity indicate lower venom and toxin concentrations in the tissues than in the blood, while larger ratios denote higher tissue concentrations. The values thus reflect a higher affinity of the venoms and their toxins for the central than the shallow tissue compartment and for the deep tissue than the central compartment. The sites of action of the venoms seem to be located in the deep tissue compartment since most of the pharmacological, biochemical and electrocardiographic effects of the venoms started 30-60 min after i.v. injection. The mean residence time in the body, MRTb, ranged from 20.8 to 51.8 hr, which correlated well with the long duration of the pharmacological and biochemical effects induced by the venoms. The tissue distribution of the venoms and toxins was similar, with the highest uptake being in the kidneys, followed by the stomach, lungs, liver, spleen, intestine, heart and diaphragm. Very high radioactivity was found in the stomach contents, which reached values higher than the kidneys. Some of the biochemical markers were significantly changed by one or more venoms but the grouped parameters did not reflect significant changes in cardiac, renal, hepatic or electrolyte profiles as a function of time. It is concluded that antivenom, even if injected several hours after a cobra bite, is still capable of neutralizing the slowly eliminating venom. To speed up neutralization of the venom effects, doses of antivenom higher than the calculated in vitro neutralizing dose ought to be injected to compensate for the slow rate of transfer of antivenom to the tissues.

Androctonus crassicauda (Olivier), a dangerous and unduly neglected scorpion--I. Pharmacological and clinical studies

Androctonus crassicauda venom has an i.v. LD50 in mice of 0.32 +/- 0.02 mg/kg, which makes the scorpion among the most toxic species in the world. Fifty-one non-fatal and one fatal cases of scorpion sting were presented. Pain and tenderness were very common following the sting. Generalized erythema occurred in 20-25% of all infants and children below the age of 5 years. Severe CNS manifestations including seizures, unconsciousness and marked irritability occurred mainly in infants and young children, while hypertension occurred in the majority of victims below the age of 11 years. Two pregnant victims were treated with antivenom with no bad consequences on mothers or foetuses. The fatal case described was inadequately treated with antivenom and presented a rare situation of intracranial coagulation in the basal cisterns or low in the cranial subarachnoid space. The victim developed moderate hydrocephalus of the communicating type with clear ventricular CSF and strongly xanthocromic fluid from lumbar puncture. The effects of A. crassicauda venom on isolated hearts, atria and anaesthetized rat blood pressure appeared to be mediated largely through stimulation of the autonomic nervous system with predominance of sympathetic stimulation and release of tissue catecholamines. Electrocardiograms recorded simultaneously with blood pressure changes showed evidence of ectopic foci during the hypertensive phase and ischaemia, inferior wall infarction and different degrees of heart block during the late hypotensive phase. Androctonus crassicauda venom was unique in following a three-compartment open model comprising a central compartment 'blood', a rapidly equilibrating 'shallow' tissue compartment and a slowly equilibrating 'deep' tissue compartment. The overall elimination half-life, t1/2 beta, was 24 hr, indicating that the venom has the slowest elimination among all known scorpion venoms. The long stay of the venom in the body might explain the increased risk of toxicity and the good potential for treatment with serotherapy even hours after the sting.

An algorithm and computer program for calculating the mean transit time and distribution rate parameters of generated metabolites undergoing linear tissue distribution and linear or non-linear central elimination

A method is described for calculating the mean transit time and distribution rate parameters of a generated primary metabolite undergoing linear distribution and linear or non-linear central elimination, and of catenary metabolites with any precursor order. It is also applicable to a drug and its interconversion metabolite and does not require separate administration of the metabolite. The method allows steady-state volume of distribution and distribution clearance of a metabolite to be calculated, provided that the central volume of distribution of the metabolite is known. An algorithm and computer program to implement the proposed method are presented. The calculations require the plasma concentration versus time curves of the metabolite and its precursor. The method is applied to both published and simulated data.

A technique for calculating the mean time for equilibration of drug distribution using minimal structural assumptions

Disposition decomposition analysis is used as a framework to derive a parameter for the description of drug distribution kinetics. This parameter, denoted td, is a measure of the mean time for equilibration of distribution in the absence of metabolic drug elimination. The derivation requires only the assumption that distribution is linear, and is generally valid as long as any nonlinearity is due to central nonlinear elimination. The mean time for equilibration of distribution, td, is evaluated in terms of the moments of the distribution function, h(t), derived by disposition decomposition analysis. Estimates of td for several drugs are presented.

Dermal and underlying tissue pharmacokinetics of salicylic acid after topical application

The time course of salicylic acid at a dermal application site and in local underlying tissues below the site in rats was examined using a physiologically based pharmacokinetic model assuming first-order diffusional mass transfer between the dermis and underlying tissues. The concentrations of salicylic acid in tissues below the applied site were measured and compared with plasma concentrations and concentrations in similar tissues on the contralateral side. The direct penetration of salicylic acid was dominant only to a depth of 3-4 mm below the applied site for the first approximately 2 hr after application. The time course of salicylic acid in individual rats was modeled using known tissue blood flows and tissue-tissue clearances by (i) numerical integration and nonlinear regression of a series of differential equations representing events in individual tissues, and (ii) numerical integration and nonlinear regression of a single differential equation representation of the concentration-time course in an individual tissue with a polynomial representation of salicylate concentrations in other input tissues and an exponential representation of the input from the solution. Tissue-tissue clearances were deduced by both nonlinear regression and mass balance analysis (only for underlying dermis) using area-under-the-curves from salicylic acid tissue penetration data in anesthetized rats. The relative importance of direct penetration and blood supply in determining the concentrations of salicylic acid in deeper tissues was assessed by simulations in which either no direct penetration occurred or there was zero input from blood. Simulations confirm that direct penetration is only evident in the superficial tissues for approximately 2 hr. An attempt was also made to examine the dermal pharmacokinetics of salicylic acid using statistical moments.

Mean residence time in multicompartmental models with time delays

Calculation of the mean residence time (MRT) of a drug in a stationary compartmental model is classically carried out from several expressions. Nevertheless, one or more time delays between compartments modify the mean residence times. It is the aim of this paper to propose a general method for MRT calculations, in any n-compartmental models which may include time delays. As examples, catenary and mammillary models are considered.

Optimum numerical integration methods for estimation of area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC)

Eleven numerical methods for estimation of AUC (including 4 new methods) and 22 methods for AUMC (including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the linear trapezoidal rule for AUMC. Others, notably Lagrange and cubic spline methods, were unacceptable because the variance of their estimates was large. These methods should be abandoned. A simple and easily programmed new method, parabolas-through-the-origin then log-trapezoidal rule, performed especially well.

A method for calculating the mean residence times of catenary metabolites

A method for calculating the mean residence times of metabolites in the body, systemic circulation, and peripheral tissue is described. The calculations require the AUC, AUMC, and derivatives of the plasma concentration versus time curves of the metabolite and its precursor. The method is applicable to metabolites with any precursor order and does not require separate administration of the metabolite. The approach is applied to published data for the primary and secondary metabolites of ketamine.

Pharmacokinetics of pyridostigmine in dogs

The pharmacokinetics of the cholinesterase inhibitor pyridostigmine has been studied in six male Beagle dogs after iv infusion and after oral doses as an immediate-release syrup and as an extended-release tablet, all at a level of approximately 0.6 mg/kg. Pyridostigmine was characterized as a drug of relatively long terminal half-life (8.3 h +/- 2.1 SD), low systemic clearance (13 mL/min/kg +/- 1 SD) and high volumes of distribution (Vd lambda z, 8.7 L/kg +/- 1.9 SD and Vdss, 3.9 L/kg +/- 0.9 SD). The ratio of mean residence times in tissues and plasma was greater than 4, indicating a high affinity of peripheral tissues for the drug. This ratio was about twofold higher in three of the dogs than in the others. Pyridostigmine was slowly and incompletely bioavailable in these dogs; the systemic availability was 44.4% +/- 4.3 SD from the syrup and 33.6% +/- 9.5 SD from the tablet. Pyridostigmine disposition in these dogs was largely determined by distribution processes.

Regional pharmacokinetics. III. Modelling methods

Regional pharmacokinetics is the study of drug concentrations in specific regions of the body due to drug uptake and elution. Mathematical methods of interpreting regional pharmacokinetic data can vary greatly in their complexity depending on their intended use (i.e. to describe or predict), but must reinforce rather than replace experimental pharmacokinetics. 'Black box' analysis provides and empirical method for the study of complex pharmacokinetic systems using either statistical moment or linear systems analysis. However, these methods are only applicable to linear and time-invariant systems, and ignore the large body of information concerning the physiological and physiochemical basis of regional pharmacokinetics. Clearance concepts are suitable for describing linear drug uptake processes, but mass balance principles have wider applications in describing the rate and extent of both drug uptake and elution. Compartmental models of a region can vary from single compartment descriptions based on the concept of venous equilibrium to complex multi-compartmental models of the intravascular, interstitial, and intracellular spaces, in which drug transport between compartments is a function of drug binding and ionization. Ultimately, as more regional pharmacokinetic information is obtained, more complex three dimensional models may be necessary such as those used to describe the uptake of oxygen from capillaries.

Simultaneous pharmacokinetic modeling of a drug and two metabolites: application to albendazole in sheep

Albendazole pharmacokinetic parameters were determined in lambs after iv, oral, and intraruminal single administrations. The parent drug and two metabolites, albendazole sulfoxide and albendazole sulfone, were simultaneously determined in whole blood, plasma, and urine using an HPLC method. The parent drug was only recovered in plasma when injected intravenously. For other routes, only the two metabolites were detectable; they were present in red blood cells and plasma at equal concentrations. The pharmacokinetic parameters were determined by using compartmental models which simultaneously described the two oxidative steps and the urinary excretion of the sulfoxide derivative. Dose-dependent pharmacokinetics was studied in the dose range 0.95-3.8 mg/kg. The results showed that clearance remained constant within the tested dose range since the area under the curve normalized to the dose was similar in the cases of sulfoxide and sulfone metabolites, whatever the route of administration. The drug appeared to be extensively metabolized in the body regardless of the route of administration. Sulfoxidation probably took place in liver, but other tissues seemed to be responsible for the formation of the sulfoxide which has been described as the major anthelmintic derivative of albendazole.

Drug redistribution and mean transit time concepts for nonlinear pharmacokinetic systems

Equations for the mean number of cycles through the peripheral system (R) and the mean transit time through the central compartment (MTTc) are derived for intravenous drugs with linear distribution and linear or nonlinear central elimination. This R is a function of distribution clearance (CLD), dose, and area under the plasma concentration-time curve (AUC). The MTTc is a function of the central volume of distribution, CLD, dose, and AUC. The application of the proposed calculations of R and MTTc was illustrated by computer simulations.

Compartmental mean residence time in a mammillary model with an effect compartment after intravenous or oral administration

A general estimation of mean residence time (MRT) in an effect compartment E, associated with a linear mammillary n-compartment model is presented: elimination takes place from the central and the effect compartments. Even though no sample is available from E, the MRT of the drug in this compartment can be estimated after intravenous or oral administration. Furthermore, the effect of MRT is independent of the route of administration. Also, with no new calculation, the method provides the area under the amount-time curve in compartment E.

Effects of first-pass metabolism on metabolite mean residence time determination after oral administration of parent drug

Metabolite kinetics after oral drug administration can be determined, without separate metabolite administration, using the concepts of mean residence time (MRT). The MRT of parent drug and metabolite after oral administration of the parent drug, MRTp,p(oral) and MRTm,p(oral), can be calculated directly from the drug and metabolite profiles. The difference between MRTm,p(oral) and MRTp,p(oral), termed Delta MRT, yields an estimate of MRT of metabolite when the metabolite is given as an iv bolus, MRTm,m(iv). The calculation is simple for drugs that are known to undergo, negligible first-pass metabolism. Correction can also be made when extent of first-pass metabolism is known. Ambiguity is encountered, however, when the degree of first-pass metabolism is unknown. When the delta MRT is negative, then first-pass metabolism must be considered. A positive value of delta MRT, on the other hand, is not a definitive indication of the absence of first-pass metabolism. It may occur in the presence or absence of first-pass metabolism. Ignoring the possibility of first-pass metabolism when a positive value of delta MRT occurs may lead to an incorrect estimate of MRTm,m(iv). The estimation error is relatively small, however, when MRTm,m(iv) much greater than MRTp,p(iv), even when first-pass metabolism is extensive. This situation may apply to the administration of a prodrug.

Mean time parameters in pharmacokinetics. Definition, computation and clinical implications (Part II)

Part I of this article, which appeared in the previous issue of the Journal, covered the following topics: fundamental definitions, general mean time parameter relationships and mean time parameters of classical compartmental systems. It also offered a number of examples to clarify and illustrate the various concepts.

Intra and interindividual variability in the kinetics of a poorly and highly metabolising solvent

Human subjects were experimentally exposed three times simultaneously to tetrachloroethene (PER) and trichloroethene (TRI) under conditions of rest and exercise. In each subject the individual kinetics for both PER and TRI were determined three times by means of frequent sampling of alveolar air up to 70-500 and 20-310 hours respectively. For PER the following parameters were found: the weighted pulmonary clearance (Clpul) = 0.27-0.64 l/min, terminal half time (t1/2(z] = 54-250 hours, mean residence time (MRT) = 35-155 hours, and volume of distribution (Vdss) = 1100-3570 1. For TRI the apparent hepatic clearance (CLhep) = 0.5-1.7 l/min, weighted Clpul = 0.41-1.48 l/min, t1/2(z) = 13-55 hours, MRT = 2.3-22 hours, and the Vdss = 420-3100 1. The intra and intersubject variation in the kinetics were reflected in the predictions of the individual time course of the solvent in the blood at repeated exposure up to five weeks (eight hours a day, five days a week). For PER the intrasubject variation in the predicted concentrations on the Monday mornings was within 5-15% whereas the intersubject variation was about twofold. For TRI the intrasubject variation in the predicted morning concentrations was substantial (two to threefold), whereas the intersubject variation was about 10-fold. The intrasubject variation was probably caused mainly by the level of exercise during exposure. The Clhep was not greatly influenced by the level of exercise, whereas exercise during exposure increased the MRT. Exercise during exposure probably speeds up the process of distribution and, therefore, there is a lower concentration in the blood relative to the increased respiratory intake. As a consequence, despite the increased Clpul and the rather unchanged Clhep, pulmonary and metabolic excretion will be delayed and the MRT increased. The MRT is more suited to predict the individual cumulation of both PER and TRI than the terminal t1/2(z).

Center of gravity of drug level curves: a model-independent parameter useful in bioavailability studies

The center of gravity (CG) of a drug level curve [c(t)] has the time coordinate AUMC/AUC and the concentration coordinate AUCC/2AUC, where AUC, AUMC, and AUCC are the integrals from time t = zero to t = infinity of c(t), tc(t), and c(t).c(t), respectively. An algorithm and computer program for determining CG when c(t) is given by a sum of exponentials is presented and its use is demonstrated with oral cimetidine data. Simulations indicate that the CG appears more suitable for comparison of absorption rates than mean absorption time (MAT) parameters. The limitation of the MAT parameter is due to the fact that this parameter is scale independent in that it only considers the shape and not the magnitude of the drug level or absorption rate curve. The MAT is therefore independent of the extent (F) of absorption. This limitation is not shared by the CG. When dealing with first-order absorption, the absorption rate of drug from product A will consistently (all t greater than 0) be larger than the absorption rate from product B (tested in the same subject) if MATA greater than MATB and AUCA/AUCB greater than MATA/MATB (assuming a time-invariant linear disposition). The above inequality relationships strongly contrast the common thinking about the "nonproblematic" use of MAT in absorption rate comparisons. Since both CG and MAT suffer some fundamental limitations, it is recommended that whenever problems arise, one should compare absorption rates by nonparametric system analysis methods (e.g., deconvolution) if possible.

Mean residence time for drugs subject to enterohepatic cycling

A physiologically realistic model of enterohepatic cycling (EHC) which includes separate liver and gallbladder compartments, discontinuous gallbladder emptying and first-order absorption from both an oral formulation and secreted bile (kapo and kab, respectively) has been developed. The effect of EHC on area under the first-moment curve (AUMC) of drug concentration in plasma and on parameters derived from the AUMC was investigated. Unlike AUC, AUMC is dependent on the time and time-course of gallbladder emptying, increasing as the interval between gallbladder emptying increases. Consequently, mean residence time (MRT) is also a time-dependent parameter. Analytical solutions for MRTiv and MRTpo were derived. Mean absorption time (MAT = MRTpo - MRTiv) is also time-dependent, contrary to findings previously published for a model of EHC with a continuous time lag. MAT is also dependent on kapo, kba and the hepatic extraction ratio. The difference between MRTpos for two formulations with unequal kapo values may deviate from the difference in the inverse of their absorption rate constants. Implications for design and interpretation of pharmacokinetic studies include (i) MAT values may be dominated by the time-course of recycling rather than the time-course of the initial absorption, depending on the extent of EHC and (ii) the unpredictable nature of the time of gallbladder emptying will contribute to intrasubject variability in derived parameters during crossover studies. Knowledge of the extent of EHC is invaluable in deciding whether modification of the in vitro release characteristics of an oral formulation will have any effect on the overall time-course of absorption in vivo. Techniques to monitor or control gallbladder emptying may be helpful for reducing variability in pharmacokinetic studies for compounds which are extensively cycled in bile.

General treatment of mean residence time, clearance, and volume parameters in linear mammillary models with elimination from any compartment

A general treatment for mean residence time, clearance, and volume parameters in linear mammillary models which includes the possibility of first-order elimination from compartments other than the central compartment is presented. The interrelationship between noncompartmentally derived parameters and compartmentally derived pharmacokinetic microconstants is described. The concept of exit site dependent and exit site independent parameters is introduced in the development of these treatments. Explications of mean residence time in terms of elimination rate, amount eliminated, and amount in the body are presented together with demonstrations of their utility.

Linear and nonlinear system approaches in pharmacokinetics: how much do they have to offer? I. General considerations

System approaches in pharmacokinetics are defined as generalizing and simplifying modeling approaches that mathematically model a general property of the pharmacokinetic system without modeling specifically the individual kinetic processes responsible for the general property considered. The rationale for the use of system approaches is discussed and the kinetic basis of some of the approaches is presented. An overview of the approaches is presented together with a comparison to classical approaches involving specific pharmacokinetic models. Examples are given from different application areas involving problems in linear and nonlinear pharmacokinetics and in pharmacodynamics. The advantages, disadvantages, and limitations of the system approaches are discussed. In several application areas the system approach offers some rational methods and procedures with distinct advantages over more traditional approaches.

System approaches in pharmacokinetics: II. Applications

Pharmacokinetic system approaches mathematically describe a general property of a pharmacokinetic system without modeling in specific terms the kinetic processes responsible for the general property. Certain applications of the system approach including methods for evaluating drug delivery, drug distribution, drug secretion, and biotransformation in linear and nonlinear pharmacokinetics are presented and discussed. Linear system formulae for various mean time disposition parameters and a disposition decomposition-recomposition system approach for predicting drug levels when the drug clearance changes are presented and discussed. System approaches offer certain advantages over traditional approaches for many practical applications.

System approaches in pharmacokinetics: I. Basic concepts

System approaches mathematically describe a general property of a pharmacokinetic system without modeling in specific terms the kinetic processes responsible for the general property considered. Definitions, basic concepts, kinetic basis, and rationale for system approaches as well as advantages and disadvantages of system approaches are presented and discussed. It appears that the system approaches may offer certain advantages over more traditional methods for many practical applications.

Mean residence time in peripheral tissue

The published methods for determining the mean residence time for drugs in peripheral tissue are reviewed in terms of assumptions involved, advantages and disadvantages. A method for determining mean transit time in peripheral tissue is proposed; this may be a more useful indicator of the tissue retention properties for drug compounds.

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. III. Peripheral bioavailability and distribution time concepts applied to the evaluation of distribution kinetics

Disposition decomposition analysis (DDA) is applied to evaluate the rate and extent of drug delivery from the sampling compartment to the peripheral system, i.e., peripheral bioavailability. Four parameters are introduced which are useful in quantifying peripheral bioavailability. The compounded peripheral bioavailability, F comp, is the ratio between the total compounded amount of drug transferred to the peripheral system and the injected dose, D. The AUC peripheral bioavailability, FAUC, is the ratio between the area under the amount vs. time curves for the peripheral system and the sampling compartment. The distribution time td, is the time following an i.v. bolus at which the net transfer of drug to the peripheral system reverses in direction. The maximum peripheral bioavailability, Fmax, is the maximum fraction of an i.v. bolus dose that is present in the peripheral system at any one time. Equations are derived which permit estimation of those parameters from drug concentrations in the sampling compartment. Simple algorithms and a computer program are provided for estimating Fcomp, FAUC, td, Fmax, and other parameters relevant to DDA for drugs that exhibit a linear polyexponential bolus response. Estimates of Ecomp, FAUC, td, and Fmax are presented for several drugs.

Interpretation and estimates of mean residence time with statistical moment theory

The definitions of mean residence time of drug molecules in the body (MRT) from the literature are reviewed. A formal definition of MRT, based on excretion of drug molecules and amount of drug, a parameter which is independent of constancy of both clearance and volume of distribution, is introduced and compared to other existing definitions of MRTs, that is, MRT for the two-compartment model, MRT for the stochastic model, and MRT based on amount in the body. The inherent assumptions of the methods for determining the various MRTs are discussed. Published information on coefficients and constants (Collier) which describe a biexponential drug decay in the systemic circulation were utilized to illustrate the similarities and differences in MRTs. MRTs were calculated from theoretical relationships as well as estimated from simulated data based on equivalent conditions. The MRTs based on area under the moment curve/area under the curve (AUMC/AUC) for the two-compartment model and AUC/C(0) for the stochastic model assume a constancy in clearance and in volume of distribution, respectively.

Single pass mean residence time in peripheral tissues: a distribution parameter intrinsic to the tissue affinity of a drug

The single pass mean residence time in peripheral tissues, tp1, is a characteristic constant of linear pharmacokinetic systems and nonlinear systems with linear distribution kinetics. It is descriptive of distribution kinetics in such systems and is not dependent on elimination kinetics as are other related parameters, e.g., mean residence time in peripheral tissues, tp. Equations are derived which permit estimation of tp1 from experimental data for systems in which no peripheral elimination occurs. The type of data required are systemic drug levels resulting from iv administration. The probability density function for single pass residence time in peripheral tissues is derived. It is shown that tp1 is related to the amount of drug in the peripheral tissues at steady state according to (Ap)ss = CLdCsstp1, where CLd is the distribution clearance, and Css is the steady-state systemic drug level. Values of tp1 are presented for several drugs.

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 tb. It is shown that the equation tb = AUMC/AUC is correct 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., first-order central elimination. More general equations for tb in terms of elimination rate, amount eliminated, and amount in the body are presented along with demonstrations of their utility.

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. II. Clearance concepts applied to the evaluation of distribution kinetics

The disposition decomposition approach is employed to derive clearance parameters descriptive of drug distribution kinetics. The name distribution clearance, CLd, is given to a characteristic constant of linear and some nonlinear pharmacokinetic systems. CLd is the clearance associated with the steady-state rate of drug transfer from the peripheral tissues to the systemic circulation. Also introduced is the elimination clearance, CLe, which is associated with the total drug transfer rate from the systemic circulation in linear systems. Estimates of CLd and CLe are presented for several drugs.