Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. I. Derivations and theoretical analysis

The approach presented enables a model independent representation of the pharmacokinetics of drugs with a liner disposition and some drugs with a nonlinear disposition. The approach is based on a decomposition of the drug disposition into an elimination function q(c) and a distribution function h(t). The q function represents the net effect of all disposition processes which work toward a reduction in the systemic drug level. The h function represents the net effect of all disposition processes which slow down the rate of decline of the systemic drug level by returning drug from the peripheral environment to the systemic circulation. Several theorems relating q and h to the drug disposition are presented which uniquely define these functions mathematically. The disposition decomposition is of particular significance in three main areas of pharmacokinetics: (1) evaluation of drug absorption, (2) drug level predictions including steady state predictions, (3) and elucidation of drug disposition kinetics. The practical significance of the decomposition method in these three areas is discussed, and various procedures for the application of the method are proposed. The decomposition method represents a model independent alternative to pharmacokinetic models such as linear compartmental models, the recirculation model, and some physiologic models. This also includes nonlinear forms of such models, as long as the nonlinearity is due to a central nonlinear elimination. The greatest promise and significance of the disposition decomposition approach appears to be its application to nonlinear pharmacokinetics. In contrast to linear pharmacokinetics the kinetic analysis in such cases has been limited to model dependent methods employing specific pharmacokinetic models, due to the lack of model independent alternatives. The novel development presented offers such alternatives. For some applications these alternatives appear more rational in the sense that the analysis becomes more general and objective and may be based on fewer assumptions.     

Theorems and implications of a model independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. I. Derivations and theoretical analysis

The approach presented enables a model independent representation of the pharmacokinetics of drugs with a linear disposition and some drugs with a nonlinear disposition. The approach is based on a decomposition of the drug disposition into an elimination function q(c) and a distribution function h(t). The qfunction represents the net effect of all disposition processes which work toward a reduction in the systemic drug level. The hfunction represents the net effect of all disposition processes which slow down the rate of decline of the systemic drug level by returning drug from the peripheral environment to the systemic circulation. Several theorems relating qand hto the drug disposition are presented which uniquely define these functions mathematically. The disposition decomposition is of particular significance in three main areas of pharmacokinetics: (1) evaluation of drug absorption, (2) drug level predictions including steady state predictions, and (3)elucidation of drug disposition kinetics. The practical significance of the decomposition method in these three areas is discussed, and various procedures for the application of the method are proposed. The decomposition method represents a model independent alternative to pharmacokinetic models such as linear compartmental models, the recirculation model, and some physiologic models. This also includes nonlinear forms of such models, as long as the nonlinearity is due to a central nonlinear elimination. The greatest promise and significance of the disposition decomposition approach appears to be its application to nonlinear pharmacokinetics. In contrast to linear pharmacokinetics the kinetic analysis in such cases has been limited to model dependent methods employing specific pharmacokinetic models, due to the lack of model independent alternatives. The novel development presented offers such alternatives. For some applications these alternatives appear more rational in the sense that the analysis becomes more general and objective and may be based on fewer assumptions.     

Predicting Drug Disposition via Application of a Biopharmaceutics Drug Disposition Classification System

Abstract: A Biopharmaceutics Drug Disposition Classification System (BDDCS) was proposed to serve as a basis for predicting the importance of transporters in determining drug bioavailability and disposition. BDDCS may be useful in predicting: routes of drug elimination; efflux and absorptive transporters effects on oral absorption; when transporter‐enzyme interplay will yield clinically significant effects (e.g. low drug bioavailability and drug‐drug interactions); and transporter effects on post‐absorptive systemic drug levels following oral and i.v. dosing. For highly soluble, highly permeable Class 1 compounds, metabolism is the major route of elimination and transporter effects on drug bioavailability and hepatic disposition are negligible. In contrast for the poorly permeable Class 3 and 4 compounds, metabolism only plays a minor role in drug elimination. Uptake transporters are major determinants of drug bioavailability for these poorly permeable drugs and both uptake and efflux transporters could be important for drug elimination. Highly permeable, poorly soluble, extensively metabolized Class 2 compounds present the most complicated relationship in defining the impact of transporters due to a marked transporter‐enzyme interplay. Uptake transporters are unimportant for Class 2 drug bioavailability, (ensure space after,) but can play a major role in hepatic and renal elimination. Efflux transporters have major effects on drug bioavailability, absorption, metabolism and elimination of Class 2 drugs. It is difficult to accurately characterize drugs in terms of the high permeability criteria, i.e. ≥90% absorbed. We suggest that extensive metabolism may substitute for the high permeability characteristic, and that BDDCS using elimination criteria may provide predictability in characterizing drug disposition profiles for all classes of compounds.     

Pharmacokinetic models for the saturable absorption of cefuroxime axetil and saturable elimination of cefuroxime.

Since oligopeptidic drugs such as beta-lactam antibiotics share the same carriers in humans and animals, the absorption and elimination kinetics of cefuroxime (C) were investigated in rats. Plasma C concentrations were measured by liquid chromatography. Pharmacokinetics and bioavailability of C in the rat were examined after intravenous (i.v.) administration at three doses (1.78, 8.9 and 17.8mg) of cefuroxime sodium and oral administration at two doses (2.02 and 8.9mg) of cefuroxime axetil (CA). Preliminary fits using data from intravenous administration of C showed that the drug disposition kinetics were clearly nonlinear, with an increase in plasma clearance as the intravenous dose increased. After oral administration of CA, normalized C(max) was higher for smaller dose than for the largest dose. The population pharmacokinetic parameters were obtained by means of nonlinear mixed effect modelling approach according to a nonlinear elimination and nonlinear absorption two-compartment model. The nonlinear elimination could be attributed to a saturable renal tubular reabsorption of the antibiotic and nonlinear intestinal absorption of CA mediated by carrier system. The oral bioavailability of C, calculated by numeric integration of an amount of CA drug absorbed was 22 and 17% for 2.02 and 8.9mg of prodrug administered orally.     

Drug absorption evaluation in the presence of changes in clearance: an algorithm and computer program for deconvolution with exact clearance correction

Most commonly drug absorption is evaluated with a reference dosing given on separate occasions. The assumption that no change in drug disposition is taking place between the drug administrations is often violated resulting in errors in the calculations. A novel deconvolution method is presented which exactly compensates for a change in drug clearance. The method is based on a model independent disposition decomposition-recomposition technique. The distribution function is obtained from an i.v. administration by disposition decomposition. This distribution function is assembled together with the elimination kinetics containing the perturbed clearance to construct the perturbed disposition function in the subsequent disposition recomposition operation. The perturbed absorption response is finally deconvolved using the corresponding perturbed disposition function. It is shown that the perturbed clearance can be obtained from the log-linear terminal disposition phase once the distribution function has been obtained from an i.v. administration. The proposed method is implemented in an algorithm and computer program DCONB and demonstrated using human cimetidine drug level data from an i.v. and oral administration. The usage of DCONB is identical to DECONV previously published. It requires only regular sums of exponentials to be fitted to drug level data. Such fittings are routinely done in pharmacokinetics thereby enabling DCONB to be implemented very simply.     

Michaelis-Menten metabolite formation kinetics: equations relating area under the curve and metabolite recovery to the administered dose

A computational approach which concomitantly determines the capacity-limited rate constants of parent drug elimination and metabolite formation is presented. The approach applies both the presently derived total excretory recovery versus dose relationships of the metabolite and the AUC versus dose relationships of the parent drug to identify the parameters. Three parent drug elimination conditions were assessed: pooled first-order, pooled Michaelis-Menten, and parallel first-order and pooled Michaelis-Menten kinetics. Model and parameter identification criteria are discussed. Literature data for theophylline and two of its metabolites in rats were examined to reveal pooled Michaelis-Menten elimination kinetics of theophylline and capacity-limited formation of the metabolites. The proposed technique is useful for quantitating commonly obtained nonlinear drug disposition data such as AUC and amount of metabolites excreted.     

Theorems and implications of a model-independent elimination/distribution function decomposition of linear and some nonlinear drug dispositions. IV. Exact relationship between the terminal log-linear slope parameter beta and drug clearance

An exact formula relating the terminal log-linear beta parameter and the drug clearance is derived. The expression is valid for drugs with a linear, polyexponential disposition kinetics. The formula is useful for calculating the clearance when the clearance has changed between drug administrations and requires only drug level data from the terminal, log-linear elimination phase in addition to data from a single separate i.v. administration in the same subject. Data from an i.v. administration are necessary in order to apply the disposition decomposition technique to isolate and uniquely define the distribution kinetics in terms of the distribution function h(t). The different clearances can then be calculated from the beta values of the log-linear terminal drug level data and the parameters of h(t). The theoretical basis of the method and its assumptions and limitations are discussed and various pertinent theorems are presented. A computer program enabling an easy implementation of the proposed method is also presented. The mathematical and computational procedures of the method are demonstrated using kinetic data from i.v. and oral administrations of cimetidine, diazepam, and pentobarbital in human subjects. The classical V.beta method of approximating the clearance as the product of volume of distribution and beta is considered for comparison. For the three drugs considered the V.beta method which assumes a single exponential disposition kinetics leads to excessive errors when applied in absolute clearance comparisons. However, when applied in relative comparisons in the form of the "beta correction" the errors cancel out to some extent depending on the magnitude of the distribution kinetic effect. Whenever possible it is advisable to apply the proposed method to avoid such errors.     

Stepwise determination of multicompartment disposition and absorption parameters from extravascular concentration-time data. Application to mesoridazine, flurbiprofen, flunarizine, labetalol, and diazepam

When disposition is monoexponential, extravascular concentration-time (C, t) data yield both disposition and absorption parameters, the latter via the Wagner-Nelson method or deconvolution which are equivalent. Classically, when disposition is multiexponential, disposition parameters are obtained from intravenous administration and absorption data are obtained from extravascular C, t data via the Loo-Riegelman or Exact Loo-Riegelman methods or via deconvolution. Thus, in multiexponential disposition one assumes no intrasubject variation in disposition, a hypothesis that has not been proven for most drugs. Based on the classical two- and three-compartment open models with central compartment elimination, and using postabsorptive extravascular C, t data only, we have developed four equations to estimate k10 when disposition is biexponential and two other equations to estimate k10 when disposition is triexponential. The other disposition rate constants are readily obtained without intravenous data. We have analyzed extravascular data of flurbiprofen (12 sets), mesoridazine (20 sets), flunarizine (5 sets), labetalol (9 sets), and diazepam (4 sets). In the case of diazepam intravenous C, t data were also available for analysis. After disposition parameters had been estimated from the extravascular data the Exact Loo-Riegelman method with the Proost modification was applied to the absorptive extravascular data to obtain AT/VP as a function of time. These latter data for each subject and each drug studied were found to be fitted by a function indicating either simple first-order absorption, two consecutive first-order processes, or zero-order absorption. After absorption and disposition parameters had been estimated, for each set of extravascular data analyzed, a reconstruction trend line through the original C, t data was made. The new methods allow testing of the hypothesis of constancy of disposition with any given drug. There is also a need for new methods of analysis since the majority of drugs have no marketed intravenous formulation, hence the classical methods cannot be applied.     

Contribution of multidrug resistance-associated protein 2 to secretory intestinal transport of organic anions

Various mechanisms can influence the intestinal absorption and oral bioavailability of drugs. The barrier effects of efflux transporters may be one of the critical factors limiting the bioavailability of certain drugs. It has been reported that multidrug resistance-associated protein 2 (Mrp2) is expressed in the mucosal membrane of the epithelium of the small intestine and secretes various drugs into the jejunum lumen. However, it is possible that total intestinal secretion of Mrp2 substrates is accounted for the contribution of Mrp2 and other transporter(s) to the intestinal secretion of Mrp2 substrates. In this study, we found that phenolsulfonphthalein and pravastatin, both Mrp2 substrates, are transported by different transport systems in the intestine. These results suggest that contribution of transporters to the drug transport may be a critical factor affecting drug disposition and drug-drug interaction. In addition to evaluating the substrate specificity of a transporter, it is important to be aware of the contribution of a transporter to drug disposition.     

P-glycoprotein: a defense mechanism limiting oral bioavailability and CNS accumulation of drugs

Transport by ATP-dependent efflux pumps such as P-glycoprotein is an increasingly recognized determinant of drug disposition. P-glycoprotein does not only contribute to multidrug resistance (MDR) in tumor cells, it is also expressed in normal tissues with excretory function such as liver, kidney and intestine. Apical expression of P-glycoprotein in such tissues results in reduced drug absorption from the gastrointestinal tract and enhanced drug elimination into bile and urine. Moreover, expression of P-glycoprotein in the endothelial cells of the blood-brain barrier prevents entry of certain drugs into the central nervous system. Human P-glycoprotein has been shown to transport a wide range of structurally unrelated drugs such as digoxin, quinidine, cyclosporine and HIV-1 protease inhibitors. Drug administration to P-glycoprotein knock-out and control mice provided data on the importance of P-glycoprotein for absorption after oral administration and penetration through the blood-brain barrier. Moreover, P-glycoprotein knock-out mice were used to identify inhibition of P-glycoprotein-mediated transport as a mechanism for drug interactions such as the digoxin-quinidine interaction. Studies in humans indicate a particular importance of intestinal P-glycoprotein for bioavailability of the immunosuppressant cyclosporine. Moreover, induction of intestinal P-glycoprotein by rifampin has now been identified as the major underlying mechanism of reduced digoxin plasma concentrations during concomitant rifampin therapy. In summary, P-glycoprotein functions as a defense mechanism, which determines bioavailability and CNS concentrations of drugs. Modification of P-glycoprotein function is an important underlying mechanism of drug interactions in humans. However, disposition of a drug and its metabolites frequently is not only determined by P-glycoprotein, but also by drug-metabolizing enzymes and possibly by drug transporters other than P-glycoprotein [e.g. members of the MRP family (MRP = multidrug resistance-associated proteins)].     

Limitations of the MANOVA of statistical moments in bioequivalence trials of drugs with slow elimination rate: a study with spironolactone

The capacity of the statistical moments for detecting bioavailability changes in bioequivalence studies of drugs with high disposition mean residence time (MRT) is analysed. Two bioavailability trials were carried out with spironolactone in which extent and rate of absorption were modified in a controlled way. The statistical analysis employed was a two-way MANOVA of statistical moments of the urinary excretion profiles of canrenone. The results indicate a loss in the sensitivity of MRT for detecting changes in absorption rate as drug elimination rate decreases.     

肝脏“代谢-转运互作”及其对药物药代动力学、疗效和毒性影响的研究进展

肝脏是药物代谢和排泄的主要器官。肝脏药物代谢酶和膜转运体对肝细胞内药物处置及其临床疗效和毒性产生重要影响。近年来,国内外学者发现被称为"代谢-转运互作"的动力学现象,其对药物药代动力学(生物利用度)、药物相互作用具有显著影响。药物代谢酶与转运体间的功能相互作用是目前药物代谢和药代动力学研究的热点之一。本文对肝脏代谢-转运互作进行了探究,并系统阐述了这种互作对药物(特别是Ⅱ相药物代谢)的药物相互作用、药代动力学、临床疗效和毒性反应的影响。今后应进一步阐明肝脏代谢-转运互作机制,有助于研究体内药物处置及药物相互作用,为临床合理用药提供新思路和新技术。     

Stepwise determination of multicompartment disposition and absorption parameters from extravascular concentration-time data. Application to mesoridazine,flurbiprofen, flunarizine,labetalol, and diazepam

When disposition is monoexponential, extravascular concentrationtime (C, t) data yield both disposition and absorption parameters, the latter via the Wagner-Nelson method or deconvolution which are equivalent. Classically, when disposition is multiexponential, disposition parameters are obtained from intravenous administration and absorption data are obtained from extravascular C, tdata via the Loo-Riegelman or Exact Loo-Riegelman methods or via deconvolution. Thus, in multiexponential disposition one assumes no intrasubject variation in disposition, a hypothesis that has not been proven for most drugs. Based on the classical two and threecompartment open models with central compartment elimination, and using postabsorptive extravascular C, tdata only, we have developed four equations to estimate k₁₀ when disposition is biexponential and two other equations to estimate k₁₀ when disposition is triexponential. The other disposition rate constants are readily obtained without intravenous data. We have analyzed extravascular data of flurbiprofen (12 sets), mesoridazine (20 sets), flunarizine (5 sets), labetalol (9 sets), and diazepam (4 sets). In the case of diazepam intravenous C, tdata were also available for analysis. After disposition parameters had been estimated from the extravascular data the Exact Loo-Riegelman method with the Proost modification was applied to the absorptive extravascular data to obtain A_T/V_p as a function of time. These latter data for each subject and each drug studied were found to befitted by a function indicating either simple firstorder absorption, two consecutive firstorder processes, or zero order absorption. After absorption and disposition parameters had been estimated, for each set of extravascular data analyzed, a reconstruction trend line through the original C, tdata was made. The new methods allow testing of the hypothesis of constancy of disposition with any given drug. There is also a need for new methods of analysis since the majority of drugs have no marketed intravenous formulation, hence the classical methods cannot be applied.     

Active secretion and enterocytic drug metabolism barriers to drug absorption

Intestinal phase I metabolism and active extrusion of absorbed drug have only recently been recognized as major determinants of oral drug bioavailability. Both CYP3A4, the major phase I drug metabolizing enzyme in humans, and the multidrug efflux pump, P-glycoprotein (P-gp), are present at high levels in the villus enterocytes of the small intestine, the primary site of absorption for orally administered drugs. Moreover, these proteins are induced by many of the same compounds and demonstrate a broad overlap in substrate and inhibitor specificities, suggesting that they act as a concerted barrier to drug absorption. Clinical studies have demonstrated that inhibition of CYP3A4-mediated intestinal metabolism can significantly improve the oral bioavailability of a wide range of drugs. Intestinal P-gp is a major route of elimination for both orally and intravenously administered anticancer drugs in animal models, and experiments with the Caco-2 cell line have provided strong evidence that inhibition of intestinal P-gp is another means by which oral drug bioavailability could be enhanced.     

Application of Mean Residence-Time Concepts to Pharmacokinetic Systems with Noninstantaneous Input and Nonlinear Elimination

Equations describing the mean residence time (MRT) of drugs in the body are derived for drugs that are administered by first-and zero-order rates into systems with Michaelis–Menten elimination. With computer simulations, the validity of these equations, the differences between them, and the conventional approach using the AUMC/AUC or the summation of mean times are demonstrated by examining calculations of the percentage of the administered dose eliminated at the MRT and AUMC/AUC. The effects of the absorption rate on the AUC and on the approximate and true MRT values in a nonlinear pharmacokinetic system are also illustrated with computer simulations. It was previously found that the true MRT_iv = V _ss · AUC_iv/dose for an iv bolus. The total MRT (sum of input and disposition) of a drug after noninstantaneous administration was found to be a function of the MRT_iv, two values of AUC (iv and non-iv), and exactly how the drug is administered expressed as the mean absorption time (MAT). In addition, a theoretical basis is proposed for calculation of the bioavailability of drugs in both linear and nonlinear pharmacokinetic systems.     

Effect of maturation on drug disposition in pediatric patients

Maturational changes in the physiologic processes that govern drug disposition in pediatric patients are described, and evaluation of data from pediatric drug studies is discussed. Gastrointestinal absorption depends on gastric pH, gastric emptying time, intestinal transit time, and gastrointestinal enzymatic activity; the overall effect of age-related alterations in these variables is poorly understood. Maturational changes in the skin affect percutaneous absorption. Distribution of drugs is affected by alterations in vascular perfusion, body composition, tissue binding, and plasma protein binding. For most water-soluble drugs, volume of distribution is increased in neonates. Age-related changes in biotransformation are complex because the rate of development of phase 1 and phase 2 metabolic pathways varies and metabolic pathways may be induced by in utero exposure to inducing agents. For most drugs, biotransformation is decreased in the neonate, increases from one to five years of age, and decreases after puberty to adult values. The kidneys of neonates are inefficient at drug elimination, leading initially to prolonged elimination half-lives of many drugs. Clearance of some drugs may be greater in infants than in older children and adults because of disproportionate development of renal filtration and secretion in relation to reabsorption. Few data on maturational changes in physiologic processes that affect drug disposition are available for any one drug in a specific pediatric population. In the development of research protocols, careful attention should be paid to the design limitations of published studies.     

Bioavailability of drugs with long elimination half-lives

Methods for estimating the bioavailability of drugs with long elimination half-lives are examined. Provided both absorption and disposition are linear a simple linear regression method is developed which can be used to calculate bioavailability in situations where only an incomplete estimate of the area under the curve (AUC) is available. The regression method and the traditional method of comparing the AUC following an oral dose to the AUC following an i.v. dose were applied to simulated data. It was found that the AUC ratio method works well as long as absorption is complete within the time over which the AUC is computed. The regression method is less precise than the AUC ratio method but is more accurate for drugs with long absorption half-lives. When applied to published data on a beta blocker the two methods produced comparable results. The bioavailability of amiodarone in three human subjects was calculated to be 0.20, 0.44 and 0.98 using the regression method with similar results from the ratio method. It is not possible to estimate the clearance of amiodarone from single dose data.     

Clinical pharmacokinetics in veterinary medicine.

Veterinary and human pharmacology differ principally in the range of species in which drugs are used and studied. In animals, as in humans, an understanding of the dose-effect relationship can be obtained by linking pharmacokinetic behaviour with pharmacodynamic information. Studies of different classes of drugs support the assumption that the range of therapeutic plasma concentrations in animals is generally the same as in humans. The requirement for species differences in dosage or administration rate (dose/dosage interval) may be attributed to variations in pharmacokinetic behaviour or pharmacodynamic activity, or both. When administering a drug orally, the bioavailability from a dosage form can vary widely. This is particularly the case between ruminant animals (cattle, sheep and goats), horses and carnivorous species (dogs and cats). Species variations in bioavailability can be avoided by parenteral administration. Formulation of parenteral preparations and location of intramuscular injection site can, at least in horses and cattle, influence bioavailability. Comparative pharmacokinetic studies help to explain differences in absorption and disposition processes that may underlie species variations in response to fixed dosages of a drug. Certain marker substances are useful in quantifying the activity of metabolic pathways or efficiency of excretion processes. Prediction of preslaughter withdrawal times in food-producing animals represents an application of pharmacokinetics in the field of drug residues. The drug residue profile can be obtained by combining fixed dose pharmacokinetic studies with measurement of drug concentrations in selected tissues and organs of the body. This approach offers an economical advantage in that fewer animals are required for residue studies. In domestic animals, as in humans, the disposition of most drugs can be interpreted in terms of a 2- (generally) or 3-compartment open model. Species variations in pharmacokinetic behaviour of a drug are usually attributed to differences in the rate of elimination rather than distribution and metabolism of the drug, although the principal metabolic pathway may differ. With certain notable exceptions, the herbivorous species (horses and ruminant animals) metabolise lipid-soluble drugs more rapidly than carnivorous species (dogs and cats). Humans metabolise drugs slowly in comparison with animals. Half-life values reflect this; insufficient data are available to base interspecies comparison on mean residence time. Intrinsic hepatic clearance of phenazone (antipyrine) [microsomal oxidation] in humans is approximately one-seventh of that in domestic animals.(ABSTRACT TRUNCATED AT 400 WORDS)