An initial slope method for model structure: independent estimation of the elimination rate constant of a metabolite

A model structure-independent method for calculating the true elimination rate constant of a primary metabolite is presented. It does not require direct metabolite administration and uses data on drug and metabolite blood (plasma) concentrations after a bolus drug input. The method has been tested and compared with the moment method and the area function method using errorless and errant data simulated on the basis of one- and two-compartment models of the metabolite kinetics. In contrast to known methods the proposed method provided exact estimates of the elimination rate constant in the case of errorless data of both one- and two-compartment models. However the estimates are sensitive to random errors in the concentration data.     

An area function method for calculating the apparent elimination rate constant of a metabolite

A simple method for determination of the apparent elimination rate constant of a metabolite (km) has been developed. This procedure requires calculation of area intervals under the plasma concentration-time curves of the parent drug and its derived metabolite. The method has been evaluated and compared with the Chan moment method using both errorless and errant data. The approach is accurate for various ratios of elimination rate constants of drug and metabolite, allows several values of km to be averaged, but works best using data prior to the metabolite tmax.     

The Area Function Method for Assessing the Drug Absorption Rate in Linear Systems with Zero-Order Input

A noncompartmental approach for determination of the apparent zero-order absorption rate constant (k ₀) has been developed. The procedure evolves from the convolution integral and requires individual oral-dose plasma concentration values and calculation of area intervals under the plasma concentration–time curves after intravenous administration. The proposed method was evaluated and compared with the Wagner–Nelson, Loo–Riegelman, deconvolution, nonlinear regression, and moment methods using errorless and errant simulation data for one- or two-compartment models. The area function method is generally equal to the best of these techniques (nonlinear regression) and superior to the weaker methods (moment, deconvolution, Loo–Riegelman), especially for errant two-compartment data. Coupled with a companion procedure for constructing fraction absorbed versus time plots and assessing first-order absorption rate constants, the area function methods offer direct and accurate means of discerning drug absorption kinetics without the need for assignment of a disposition model for drugs with linear elimination kinetics.     

A method for calculating the mean absorption time of drugs undergoing reversible and first-pass metabolism

A method has been derived for calculating the mean absorption time of an oral drug and its interconversion metabolite which is generated from the drug systemically and presystemically. The method evolves from the convolution integral and requires plasma AUC and AUMC values after separate intravenous administration of the drug and its interconversion metabolite and oral administration of the drug. It can also be used to calculate the mean input time of a drug undergoing reversible metabolism and administered by any other extravascular route. Results of a simulation study using both errorless and errant data indicate that, when the absorption rate constant of a drug or its interconversion metabolite is not much larger than the apparent elimination rate constant, the proposed method performs satisfactorily. However, when the absorption rate constant of a drug or its interconversion metabolite is much larger than the apparent elimination rate constant, the proposed method appears to be inaccurate.     

An area function method for calculating the apparent elimination rate constant of a metabolite

A simple method for determination of the apparent elimination rate constant of a metabolite (k_m) has been developed. This procedure requires calculation of area intervals under the plasma concentration-time curves of the parent drug and its derived metabolite. The method has been evaluated and compared with the Chan moment method using both errorless and errant data. The approach is accurate for various ratios of elimination rate constants of drug and metabolite, allows several values of k_m to be averaged, but works best using data prior to the metabolite tax.This work was supported in part by National Institutes of Health grant 24211.     

Impact of low percentage of data below the quantification limit on parameter estimates of pharmacokinetic models

The objectives of the simulation study were to evaluate the impact of BQL data on pharmacokinetic (PK) parameter estimates when the incidence of BQL data is low (e.g. ≤10%), and to compare the performance of commonly used modeling methods for handling BQL data such as data exclusion (M1) and likelihood-based method (M3). Simulations were performed by adapting the method of a recent publication by Ahn et al. (J Phamacokinet Pharmacodyn 35(4):401–421, 2008). The BQL data in the terminal elimination phase were created at frequencies of 1, 2.5, 5, 7.5, and 10% based on a one- and a two-compartment model. The impact of BQL data on model parameter estimates was evaluated based on bias and imprecision. The simulations demonstrated that for the one-compartment model, the impact of ignoring the low percentages of BQL data (≤10%) in the elimination phase was minimal. For the two-compartment model, when the BQL incidence was less than 5%, omission of the BQL data generally did not inflate the bias in the fixed-effect parameters, whereas more pronounced bias in the estimates of inter-individual variability (IIV) was observed. The BQL data in the elimination phase had the greatest impact on the volume of distribution estimate of the peripheral compartment of the two-compartment model. The M3 method generally provided better parameter estimates for both PK models than the M1 method. However, the advantages of the M3 over the M1 method varied depending on different BQL censoring levels, PK models and parameters. As the BQL percentages decreased, the relative gain of the M3 method based on more complex likelihood approaches diminished when compared to the M1 method. Therefore, it is important to balance the trade-off between model complexity and relative gain in model improvement when the incidence of BQL data is low. Understanding the model structure and the distribution of BQL data (percentage and location of BQL data) allows selection of an appropriate and effective modeling approach for handling low percentages of BQL data.     

Rapid methods for bioavailability determination utilizing urinary excretion data.

Two equations were developed which enable urinary excretion data to be utilized for estimating drug bioavailability within 12 hr-starting between one and two half-lives of the drug, depending upon the relative rates of absorption, distribution, and elimination. Both equations were examined using simulated data for both the one- and two-compartment open models. One equation was tested using literature data with excellent results.     

An incremental method for the study of the absorption of drugs whose kinetics are described by a two-compartment model: estimation of the microscopic rate constants

A method is proposed for estimating the overall absorption kinetics of drugs (expressed as percent of total amount absorbed versus time) from plasma data. It is applicable to the study of drugs whose kinetics can be described by linear one- or two-compartment models. Use is made of an iterative process based on the differential equations of the model and on linear interpolation of plasma data. The method does not require that the overall absorption kinetics should be apparent first-order and/or that the model parameters should be estimated from a previous experiment. It was tested for the influence of data scatter: added noise (CV = 10%) resulted in a variability of percent absorbed versus time of the same order of magnitude. During the calculations, the microscopic rate constants are estimated and optimalized. Data scatter resulted in wide variations in the estimates of the two-compartment model parameters. However, when a sufficiently large number of plasma concentration-time curves were studied, an average model could be determined with a reasonable precision. Model kinetics calculated from the related parameter estimates were in agreement with the theory. The method permits the exploitation of the various plasma concentration-time curves which are available after the development of an orally administered drug.     

Consequence of equal absorption, distribution and/or elimination rate constants.

When fitting experimental data to an open one- or two-compartment model, with first order kinetics, it may happen that no optimized value is obtained for model parameters. Several authors pointed out that this case is especially encountered when absorption and elimination coefficients approach each other in a one-compartment model or when absorption and exponential elimination or distribution rate constants are equal in a two-compartment model. We analyze these situations of equal coefficients here. Firstly, dealing with a one-compartment model, we get the concentration in the central compartment after a single oral dose and after successive various doses at various times (first order kinetics). Secondly, dealing with a two-compartment model, also for single or successive various doses, the concentration is expressed when absorption and exponential elimination or distribution rate constants are equal. In all cases, the areas under concentration curves and the mean residence time of the drug are calculated even when cancellation of one exponential term occurs. Furthermore, the concentration at steady-state is taken into account.     

Effects of Variation in Drug Elimination on Five Methods for Assessing Zero-Order Drug Absorption Rates

The area function method for assessing zero-order (k _o) drug absorption rates was compared to four other methods under conditions where variation occurs in the plasma concentration data and in the elimination rate constant (k _el or k ₁₀) for one- or two-compartment models. For deviant k _el values of a one-compartment model, the most accurate recovery of k _o occurred with the area function method and nonlinear least-squares regression, followed by the Wagner–Nelson and moment analysis methods. With deviant k ₁₀ values for a two-compartment model, the order of superiority of the methods was: area function nonlinear regression > Loo-Riegelman > moment analysis. Moment analysis should generally be reserved for use as an estimation rather than calculation technique. The area function procedure offers particular advantages in ease of data analysis and accuracy of recovered parameters.     

An APL computer program for estimating rate constants of drug absorption

The algorithm of this program for estimating rate constants of drug absorption is mainly based on the Loo-Riegelman method. In order to improve the flexibility of the program, several options for the users were included: one-, two- as well as three-compartment open models with first-order elimination; two optional methods to calculate the area under the curve, i.e. the simple trapezoidal method and the Lagrange method combined with log-trapezoidal approximation and others. In addition to the estimation of the rate constant of drug absorption, this program can be applied for the design of optimal sampling schemes. For this purpose an extra subroutine for simulating plasma drug concentration-time courses is also included.     

Population pharmacokinetics of total and unbound plasma cisplatin in adult patients

AIMS: To investigate the pharmacokinetics of unbound (ultrafilterable) and total plasma platinum using a population approach and to identify patient characteristics that may influence the disposition of the drug. METHODS: Pharmacokinetic and demographic data were collected from adult patients treated with 30-min daily infusions of cisplatin for various malignancies. Unbound and total platinum concentration-time data were analysed using a nonlinear mixed effects model. RESULTS: Data from 43 patients were available for analysis. A linear two-compartment model best described total and unbound platinum plasma concentration-time data. The mean population estimates for total and unbound drug were, respectively, 0.68 and 35.5 l h(-1) for clearance and 21.1 and 23.4 l for central distribution volume (V(1)). Unbound clearance (CL) was dependent on body surface area (BSA) and creatinine clearance, and V(1) was dependent on BSA. The elimination rate constant for plasma-bound platinum (modelled as metabolite formation) was 0.014 h(-1). The pharmacokinetic parameter, f(m)/V(m), a measure of the clearance of unbound platinum due to irreversible plasma binding, was related to serum protein concentration and to the inverse of dose per m(2). The covariate modelling of CL, V(1) and f(m)/V(m) improved the intersubject variabilities associated with these parameters. The final pharmacokinetic models were validated using 200 bootstrap samples from the original datasets. CONCLUSIONS: The results support the conventional dose adjustment of cisplatin based on BSA. They also support the need for a dose reduction in case of renal insufficiency.     

Disposition of pentopril, a new orally active angiotensin-converting enzyme inhibitor, and its active metabolite in rats

The disposition characteristics of pentopril (the ethyl ester) and its active carboxylic acid metabolite (CGS 13934) were determined in conscious rats after separate intravenous administrations of both compounds. The relationship between plasma concentration and pharmacological effect was also evaluated. The extent of apparent bioavailability of the active metabolite was determined after oral administration of pentopril. Pharmacokinetic parameters were calculated from the plasma concentration-time data for both the parent drug and its active metabolite after their separate intravenous administrations using a one-compartment model for the drug and a two-compartment model for the metabolite. The elimination half-life for the drug was approximately 1 min. The elimination half-life for the metabolite was 13 min (SD, +/- 3.5, n = 4) after its direct intravenous administration, but increased to an apparent half-life of 20 min (SD +/- 5, n = 5) when formed in vivo as a metabolite. Comparison of the formation rate of the metabolite and the elimination rate of the parent drug indicated that the parent drug was rapidly and completely hydrolyzed to the acid metabolite as soon as it reached the systemic circulation. No parent drug was detected in plasma after its oral administration. The apparent bioavailability of the acid metabolite was 66% after oral drug administration. A close relation between inhibition of pressor response to angiotensin I (AI) and plasma concentration of the active metabolite was observed when plotted against time after drug or metabolite administration. A Michaelis-Menten function correlated (multiple r2:0.995) well between effect and plasma metabolite concentration with mean concentration for 50% of maximum inhibition, IC50, of 3.6 X 10(-7) M (0.11 microgram/mL).     

An incremental method for the study of the absorption of drugs whose kinetics are described by a two-compartment model: Estimation of the microscopic rate constants

A method is proposed for estimating the overall absorption kinetics of drugs (expressed as percent of total amount absorbed versus time) from plasma data. It is applicable to the study of drugs whose kinetics can be described by linear one- or two- compartment models. Use is made of an iterative process based on the differential equations of the model and on linear interpolation of plasma data. The method does not require that the overall absorption kinetics should be apparent first-order and/or that the model parameters should be estimated from a previous experiment. It was tested for the influence of data scatter: added noise (CV= 10%) resulted in a variability of percent absorbed versus time of the same order of magnitude. During the calculations, the microscopic rate constants are estimated and optimalized. Data scatter resulted in wide variations in the estimates of the two-compartment model parameters. However, when a sufficiently large number of plasma concentration-time curves were studied, an average model could be determined with a reasonable precision. Model kinetics calculated from the related parameter estimates were in agreement with the theory. The method permits the exploitation of the various plasma concentration-time curves which are available after the development of an orally administered drug.     

Population pharmacokinetic of losartan and its active metabolite E-3174 in five different ethnic populations of China

The aim of this study was to develop a combined population pharmacokinetic (PPK) model for losartan and its active metabolite E-3174 in five Chinese ethnicities for individualized drug therapy in clinical practice. HPLC method was used to determine the blood levels of losartan and E-3174 simultaneously. One-, two- and three-compartment models were fitted to plasma concentration time data of 50 Chinese healthy subjects (including Han, Mongolian, Korean, Hui and Uigur) using nonlinear mixed-effect modeling (NONMEM). From the basic model of losartan, the effects of demography and biochemical covariates were investigated, which were added one by one by the forward inclusion and backward elimination. The final models of losartan and E-3174 were connected by first order or transit compartment model. Pharmacokinetic parameters of losartan and its active metabolite E-3174 were assessed simultaneously in one integrated model with the plausible covariates on the key pharmacokineticparameters of E-3174. Nonparametric bootstrap was used for the model stability validation. The data of losartan were best described using a two-compartment model with linear elimination. The time to reach C_max of losartan and E-3174 were obtained to be 0.9 and 3.8 h, respectively. Two transit compartments were chosen with adequate fit of the delayed T_max of E-3174. The population estimates for transformation of losartan to E-3174 was about 73.9%. Ethnicity factor showed significant influence on the non-metabolizing E-3174 clearance CL₁₀, the peripheral compartment clearance CL₂ and the central compartment volume V₁of losartan and also has a significant effect on the transit rate (Kt). A total of 925 out of 1000 iterations succeeded in minimization.The PPK models were steady and reliable. Ethnicity factor showed significant influence on both losartan clearance and the transition from losartan to E-3174, no covariate influencing the PK parameters of E-3174 was identified.     

Development of a microcomputer program for statistical evaluation of potential pharmacokinetic drug interactions

A simple and self-explanatory program in BASIC for the statistical evaluation of potential pharmacokinetic drug interactions is described. This program, using the data (times and drug concentrations) obtained from two different populations, and with the help of graphic computing techniques, allows the determination and statistical comparison of pharmacokinetic parameters (disposition constants, transfer rate constants, area under the concentration—time curves, etc.) for one- and two-compartment open models after intravenous or extravasal administration. The program is organized in subroutines so that it can be easily modified or extended to other pharmacokinetic models by the user.     

Some pitfalls in selecting descriptive pharmacokinetic models

Some pitfalls in selecting pharmacokinetic models are enumerated. To calculate the pharmacokinetic parameters of a drug that exhibits a biphasic convex plasma concentration-time curve, a two-compartment model does not automatically have to be applied. When only the parent drug in plasma is considered, a two-compartment model seems to be most appropriate. However, when the kinetic behavior of the metabolite has to be taken into account, and when a metabolic equilibrium underlies the metabolic elimination, the two-compartment model may not be appropriate. Also, when calculating the kinetic parameters of a drug with a concave biphasic plasma concentration-time curve, a capacity-limited metabolic conversion is not the automatic explanation for this observation. Limitations in renal excretion and bioavailability may be the reasons for this behavior. Convex and concave biphasic plasma concentration-time curves are illustrated, using sulfonamides as test compounds.     

Interpretation of absorption rate data for inhaled fluticasone propionate obtained in compartmental pharmacokinetic modeling

OBJECTIVE: Reports characterizing the pharmacokinetics of inhaled fluticasone propionate (FP) using compartmental approaches have suggested that the absorption of FP into the systemic circulation is rapid with a half-life of approximately 10 min. We believe that this is a classical case of misassignment of the pharmacokinetic parameter estimates, a problem often encountered while modeling pharmacokinetic data. The objective of this study was to illustrate and analyze this problem using actual blood level data of FP obtained in 14 healthy subjects. MATERIALS AND METHODS: Serum concentration-time data of FP were obtained from a double-blind, randomized study involving single and multiple twice-daily inhalations of 500 microg via a dry powder device, Diskus. The profiles were fitted using one- and two-compartment pharmacokinetic models with first order absorption. Various permutations of the resulting exponential rate constants were analyzed to determine the combination that was most consistent with the underlying physical process. RESULTS: The two-compartment body model with first order absorption gave excellent fits for the observed FP concentrations after both single and multiple dosing. Even though peak levels were reached relatively early (30 - 90 min) after inhalation, the combination that most appropriately described the underlying process was alpha > Ka > beta, i.e. slow absorption, rapid distribution and slower elimination kinetics. The absorption, distribution and elimination half-lives resulted to be 3.8 h, 9.9 min and 13.6 h, respectively, consistent with the high lipophilicity and sustained dissolution characteristics observed in vitro. CONCLUSIONS: Analysis of FP pharmacokinetics after inhalation represents a classical case of potential misassignment of the exponential rate constants, which if ignored, could lead to erroneous interpretations regarding the underlying process. The study also elucidates the pitfall of using t(max) to calculate absorption rate.     

Pharmacokinetic prodrug modeling: in vitro and in vivo kinetics and mechanisms of ancitabine bioconversion to cytarabine

Conversion rates of the prodrug ancitabine to the antileukemic cytarabine have been measured in vivo (rabbits) and in vitro (in the presence of rabbit blood and human red blood cells, blood, and plasma) using HPLC analyses for the prodrug, drug, and its inactive metabolite, 1-beta-D-arabinosyluracil. These observed pH-dependent in vitro rate constants were consistent with those for chemical hydrolysis determined from controls using Tris buffers. Hydrolysis of ancitabine to cytarabine is chemically, not enzymatically, mediated. The blood concentration-time course for administered compound was described by a two-compartment open model following a rapid intravenous injection of prodrug, drug, or metabolite in each of three rabbits. The in vivo conversion rate constant (kc) following a rapid intravenous prodrug injection was estimated by simultaneous nonlinear regression of ancitabine and cytarabine blood concentration-time courses using equations for two-compartment prodrug and drug with all possible models describing potential conversion sites. The best fit was obtained for the case allowing simultaneous conversion of the prodrug in both central and peripheral compartments to the drug in the central compartment with a common value for kc. The resulting kc value (0.09 h-1, three rabbits) is similar to that for chemical hydrolysis (0.07 h-1) at 38.8 degrees C. Reasons why this agreement is regarded as fortuitous are discussed.