Coupling Drug Dissolution with BCS.

PURPOSE: The purpose of this study is to develop a Temporal Biopharmaceutic Classification System (T-BCS), linking Finite Dissolution Time (F.D.T.) and Mean Dissolution Time (M.D.T.) for Class I/III drugs and Mean Dissolution Time for saturation (M.D.T.s.) for Class II/IV drugs. METHODS: These parameters are estimated graphically or by fitting dissolution models to experimental data and coupled with the dose-to-solubility ratio (q) for each drug normalized in terms of the actual volume of dissolution medium (900 mL). RESULTS: Class I/III drugs consistently exhibited q values less than 1, aligning with expectations based on their solubility, while some Class II/IV drugs presented a deviation from anticipated q values, with observations of q < 1. This irregularity was rendered to the dissolution volume of 250 mL used for biopharmaceutical classification purposes instead of 900 mL applied as well as the dual classification of some sparingly soluble drugs. Biowaivers were also analyzed in terms of M.D.T., F.D.T. estimates and the regulatory dissolution time limits for rapidly and very-rapidly dissolved drugs. CONCLUSIONS: The T-BCS is useful for establishing correlations and assessing the magnitude of M.D.T., F.D.T., or M.D.T.s. for inter- and intra-class comparisons of different drugs and provide relationships between these parameters across all the models that were utilized.

Application of the Finite Absorption Time (F.A.T.) Concept in the Assessment of Bioequivalence.

PURPOSE: Το formulate a methodology for the assessment of bioequivalence using metrics, which are based on the physiologically sound F.A.T. METHODS: The equations of the physiologically based finite time pharmacokinetic models for the one-and two-compartment model with one and two input stages of absorption were solved to derive metrics for the extent and rate of absorption. Simulated data were used to study the proper way for the estimation of metrics. A bioequivalence study was analyzed using these metrics. RESULTS: The rate of drug absorption was found to be equal to the slope of the amount absorbed versus time curve. The amount of drug absorbed at the end of the absorption process, corresponding to the blood concentration at F.A.T. is an indicator of the extent of absorption. The plot of the ratio test/reference of the simulated data for the amount absorbed as a function of time becomes constant beyond the end of drug absorption from the formulation exhibiting the longer absorption. The assessment of the bioequivalence study was based on the slope of the amount absorbed versus time curve for the rate of absorption, while the estimate for the constant ratio test/reference for the amount absorbed was used for the assessment of extent of absorption. CONCLUSIONS: The assessment of rate in bioequivalence studies can be based on the estimation of slope of the percent absorbed versus time curve while the constant ratio test/reference for the amount of drug absorbed is an indicator of the extent of absorption.

IVIVC Revised.

PURPOSE: To revise the IVIVC considering the physiologically sound Finite Absorption Time (F.A.T.) and Finite Dissolution Time (F.D.T.) concepts. METHODS: The estimates τ and τd for F.A.T. and F.D.T., respectively are constrained by the inequality τd ≤ τ; their relative magnitude is dependent on drug's BCS classification. A modified Levy plot, which includes the time estimates for τ and τd was developed. IVIVC were also considered in the light of τ and τd estimates. The modified Levy plot of theophylline, a class I drug, coupled with the rapid (30 min) and very rapid (15 min) dissolution time limits showed that drug dissolution/absorption of Class I drugs takes place in less than an hour. We reanalyzed a carbamazepine (Tegretol) bioequivalence study using PBFTPK models to reveal its complex absorption kinetics with two or three stages. RESULTS: The modified Levy plot unveiled the short time span (~ 2 h) of the in vitro dissolution data in comparison with the duration of in vivo dissolution/absorption processes (~ 17 h). Similar results were observed with the modified IVIVC plots. Analysis of another set of carbamazepine data, using PBFTPK models, confirmed a three stages absorption process. Analysis of steady-state (Tegretol) data from a paediatric study using PBFTPK models, revealed a single input stage of duration 3.3 h. The corresponding modified Levy and IVIVC plots were found to be nonlinear. CONCLUSIONS: The consideration of Levy plots and IVIVC in the light of the F.A.T. and F.D.T. concepts allows a better physiological insight of the in vitro and in vivo drug dissolution/absorption processes.

Revamping Biopharmaceutics-Pharmacokinetics with Scientific and Regulatory Implications for Oral Drug Absorption.

PURPOSE: The Wagner-Nelson and Loo-Riegelman methods developed in the 1960s and used since for the construction of percent of drug absorbed as a function of time as well as in in vitro in vivo correlations are re-considered in the light of the physiologically sound Finite Absorption Time (F.A.T.) concept developed recently. METHODS: The classical equations for the percentage of drug absorption as a function of time were modified by taking into account the termination of drug absorption at F.A.T., replacing the parameters associated with the assumption of infinite drug absorption. RESULTS: Mathematical analysis using the relevant Physiologically Based Pharmacokinetic Finite Time (PBFTK) models assuming one- or two-compartment drug disposition, revealed that the modified %absorbed versus time curves are of bilinear type with an ascending limb intersecting the horizontal line at F.A.T. A computer-based methodology is described for the estimation of F.A.T. from experimental data. More than one linear ascending limb is found when more than one absorption phase is operating. Experimental data were analyzed and the estimates for F.A.T were found to be similar to those derived from nonlinear regression analysis using PBFTPK models. CONCLUSION: These results place an end to the routinely reported exponential %absorbed versus time curves prevailing in biopharmaceutics-pharmacokinetics since their inception in the'60 s. These findings point to the use of the F.A.T. concept in drug absorption research and regulatory guidelines such as deconvolution techniques for the assessment of drug input rate, stochastic mean absorption time calculations, population analyses, in vitro in vivo correlations and bioequivalence guidelines.

Physiologically based Pharmacokinetic Models under the Prism of the Finite Absorption Time Concept.

To date, mechanistic modeling of oral drug absorption has been achieved via the use of physiologically based pharmacokinetic (PBPK) modeling, and more specifically, physiologically based biopharmaceutics model (PBBM). The concept of finite absorption time (FAT) has been developed recently and the application of the relevant physiologically based finite time pharmacokinetic (PBFTPK) models to experimental data provides explicit evidence that drug absorption terminates at a specific time point. In this manuscript, we explored how PBBM and PBFTPK models compare when applied to the same dataset. A set of six compounds with clinical data from immediate-release formulation were selected. Both models resulted in absorption time estimates within the small intestinal transit time, with PBFTPK models generally providing shorter time estimates. A clear relationship between the absorption rate and the product of permeability and luminal concentration was observed, in concurrence with the fundamental assumptions of PBFTPK models. We propose that future research on the synergy between the two modeling approaches can lead to both improvements in the initial parameterization of PBPK/PBBM models but to also expand mechanistic oral absorption concepts to more traditional pharmacometrics applications.

The Finite Absorption Time (FAT) concept en route to PBPK modeling and pharmacometrics.

The concept of Finite Absorption Time (FAT) for oral drug administration is set to affect pharmacokinetic analyses, Physiologically-based Pharmacokinetics simulations, and Pharmacometrics.

Re-writing Oral Pharmacokinetics Using Physiologically Based Finite Time Pharmacokinetic (PBFTPK) Models.

PURPOSE: To develop physiologically based finite time pharmacokinetic (PBFTPK) models for the analysis of oral pharmacokinetic data. METHODS: The models are based on the passive drug diffusion mechanism under the sink conditions principle. Up to three drug successive input functions of constant rate operating for a total time τ are considered. Differential equations were written for all these models assuming linear one- or two-compartment-model disposition. The differential equations were solved and functions describing the concentration of drug as a function of time for the central and the peripheral compartment were derived. The equations were used to generate simulated data and they were also fitted to a variety of experimental literature oral pharmacokinetic data. RESULTS: The simulated curves resemble real life data. The end of the absorption processes τ is either equal to tmax or longer than tmax at the descending portion of the concentration time curve. Literature oral pharmacokinetic data of paracetamol, ibuprofen, almotriptan, cyclosporine (a total of four sets of data), and niraparib were analyzed using the PBFTPK models. Estimates for τ corresponding to a single or two or three different in magnitude input rates were derived along with the other model parameters for all data analyzed. CONCLUSIONS: The PBFTPK models are a powerful tool for the analysis of oral pharmacokinetic data since they rely on the physiologically sound concept of finite absorption time.

Revising Pharmacokinetics of Oral Drug Absorption: II Bioavailability-Bioequivalence Considerations.

PURPOSE: To explore the application of the parameters of the physiologically based finite time pharmacokinetic (PBFTPK) models subdivided in first-order (PBFTPK)1 and zero-order (PBFTPK)0 models to bioavailability and bioequivalence. To develop a methodology for the estimation of absolute bioavailability, F, from oral data exclusively. METHODS: Simulated concentration time data were generated from the Bateman equation and compared with data generated from the (PBFTPK)1 and (PBFTPK)0 models. The blood concentration Cb(τ) at the end of the absorption process τ, was compared to Cmax; the utility of [Formula: see text] and [Formula: see text] in bioequivalence assessment was also explored. Equations for the calculation of F from oral data were derived for the (PBFTPK)1 and (PBFTPK)0 models. An estimate for F was also derived from an areas proportionality using oral data exclusively. RESULTS: The simulated data of the (PBFTPK)0 models exhibit rich dynamics encountered in complex drug absorption phenomena. Both (PBFTPK)1 and (PBFTPK)0 models result either in Cmax = Cb(τ) or Cmax > Cb(τ) for rapidly- and not rapidly-absorbed drugs, respectively; in the latter case, Cb(τ) and τ are meaningful parameters for drug's rate of exposure. For both (PBFTPK)1 and (PBFTPK)0 models, [Formula: see text] or portions of it cannot be used as early exposure rate indicators. [Formula: see text] is a useful parameter for the assessment of extent of absorption for very rapidly absorbed drugs. An estimate for F for theophylline formulations was found close to unity. CONCLUSION: The (PBFTPK)1 and (PBFTPK)0 models are more akin to in vivo conditions. Estimates for F can be derived from oral data exclusively.

Revising Pharmacokinetics of Oral Drug Absorption: I Models Based on Biopharmaceutical/Physiological and Finite Absorption Time Concepts.

ABSRACT: PURPOSE: To demonstrate that oral drug absorption is terminated in finite time. To develop models based on biopharmaceutical/physiological and finite absorption time concepts. METHODS: The models are based on i) the passive drug diffusion mechanism under the sink conditions principle ii) the rate limiting role of the drug's properties solubility and permeability and iii) the relevant restrictions associated with the gastrointestinal transit times of drug in the stomach, the small intestines and the colon. Two input functions of constant rate are considered for the absorption of drug from i) the stomach/small intestines with an upper limit of 5 h and ii) the colon with an upper limit of 30 h. Branched differential equations were written for the time course of drug in the body. RESULTS: Simulations were performed using different scenarios, assuming a variety of drug properties and limited or non-existent absorption from the colon. Literature oral data of cephradine, ibuprofen, flurbiprofen and itraconazole were analyzed. For all drugs examined, nice fittings of the branched differential equations to the experimental data were observed. CONCLUSIONS: For all drugs the absorption process was terminated in the small intestine. The meaning of partial AUCs, Cmax, tmax are questioned. Applications of these models to IVIVC are anticipated.

Fractional calculus in pharmacokinetics.

We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics". The presence of fractional kinetics has important clinical implications such as the lack of a half-life, observed, for example with the drug amiodarone and the associated irregular accumulation patterns following constant and multiple-dose administration. Building models that accurately reflect this behaviour is essential for the design of less toxic and more effective drug administration protocols and devices. This article introduces the readers to the theory of fractional pharmacokinetics and the research challenges that arise. After a short introduction to the concepts of fractional calculus, and the main applications that have appeared in literature up to date, we address two important aspects. First, numerical methods that allow us to simulate fractional order systems accurately and second, optimal control methodologies that can be used to design dosing regimens to individuals and populations.

Pharmacokinetic analysis of inhaled salmeterol in asthma patients: Evidence from two dry powder inhalers.

Salmeterol (SAL) is a long-acting ß2-adrenergic agonist, which is widely used in the therapy of asthma. The aim of this study was to investigate the pharmacokinetics (PK) of inhaled salmeterol in asthma patients using two different dry powder inhalers. This analysis was based on data from 45 subjects who participated in a two-sequence, four-period crossover bioequivalence (BE) study after single administration of the test (T) and reference (R) products. In order to mimic more closely the real treatment conditions, activated charcoal was not co-administered. Plasma concentration-time (C-t) data were initially analysed using classic non-compartmental PK approaches, while the main objective of the study was to apply population PK modeling. The relative fraction of the dose absorbed via the lungs (RL ) was set as a parameter in the structural model. The plasma C-t profiles of salmeterol showed a biphasic time course indicating a parallel pulmonary and gastrointestinal (GI) absorption. A two-compartment disposition model with first order absorption from the GI and very rapid absorption from lungs (like an i.v. bolus) was found to describe successfully the C-t profiles of salmeterol. The estimated RL value was 13% suggesting a high gut deposition of inhaled salmeterol. Women were found to exert less capability to eliminate salmeterol than men, while body weight (in allometric form) was found to be an important covariate on the peripheral volume of distribution.

An insight into the properties of a two-stage design in bioequivalence studies.

PURPOSE: Unveil the properties of a two-stage design (TSD) for bioequivalence (BE) studies. METHODS: A TSD with an upper sample size limit (UL) is described and analyzed under different conditions using Monte Carlo simulations. TSD was split into three branches: A, B1, and B2. The first stage included branches A and B1, while stage two referred to branch B2. Sample size re-estimation at B2 relies on the observed GMR and variability of stage 1. The properties studied were % BE acceptance, % uses and % efficiency of each branch, as well as the reason of BE failure. RESULTS: No inflation of type I error was observed. Each TSD branch exhibits different performance. Stage two exhibits the greatest % BE acceptances when highly variable drugs are assessed with a low starting number of subjects (N1) or when formulations differ significantly. Branch A is more frequently used when variability is low, drug products are similar, and a large N1 is included. BE assessment at branch A is very efficient. CONCLUSIONS: The overall acceptance profile of TSD resembles the typical pattern observed in single-stage studies, but it is actually different. Inclusion of a UL is necessary to avoid inflation of type I error.

Re-examining Naloxone Pharmacokinetics After Intranasal and Intramuscular Administration Using the Finite Absorption Time Concept.

BACKGROUND AND OBJECTIVES: Naloxone for opioid overdose treatment can be administered by intravenous injection, intramuscular injection, or intranasal administration. Published data indicate differences in naloxone pharmacokinetics depending on the route of administration. The aim of this study was to analyze pharmacokinetic data in the same way that we recently successfully applied the concept of the finite absorption time in orally administered drug formulations. METHODS: Using the model equations already derived, we performed least squares analysis on 24 sets of naloxone concentration in the blood as a function of time. RESULTS: We found that intramuscular and intranasal administration can be described more accurately when considering zero-order absorption kinetics for finite time compared with classical first order absorption kinetics for infinite time. CONCLUSIONS: One-compartment models work well for most cases. Two-compartment models provide better details, but have higher parameter uncertainties. The absorption duration can be determined directly from the model parameters and thus allow an easy comparison between the ways of administration. Furthermore, the precise site of injection for intramuscular delivery appears to make a difference in terms of the duration of the drug absorption.

Bioequivalence of highly variable drugs: a comparison of the newly proposed regulatory approaches by FDA and EMA.

PURPOSE: To explore the comparative performance of the recently proposed bioequivalence (BE) approaches, FDA(s) and EMA(s), by the FDA working group on highly variable drugs and the EMA, respectively; to compare the impact of the GMR-constraint on the two approaches; and to provide representative plots of % BE acceptance as a function of geometric mean ratio, sample size and variability. METHODS: Simulated BE studies and extreme GMR versus CV plots were used. Three sequence, three period crossover studies with two treatments were simulated using four levels of within-subject variability. RESULTS: The FDA(s) and EMA(s) approaches were identical when variability was <30%. In all other cases, the FDA(s) method was more permissive than EMA(s). The major discrepancy was observed for variability values >50%. The GMR-constraint was necessary for FDA(s), especially for drugs with high variabilities. For EMA(s), the GMR-constraint only became effective when sample size was large and variability was close to 50%. CONCLUSIONS: A significant discrepancy in the performances of FDA(s) and EMA(s) was observed for high variability values. The GMR-constraint was essential for FDA(s), but it was of minor importance in case of the EMA(s).

Elucidating the role of dose in the biopharmaceutics classification of drugs: the concepts of critical dose, effective in vivo solubility, and dose-dependent BCS.

PURPOSE: To develop a dose dependent version of BCS and identify a critical dose after which the amount absorbed is independent from the dose. METHODS: We utilized a mathematical model of drug absorption in order to produce simulations of the fraction of dose absorbed (F) and the amount absorbed as function of the dose for the various classes of BCS and the marginal cases in between classes. RESULTS: Simulations based on the mathematical model of F versus dose produced patterns of a constant F throughout a wide range of doses for drugs of Classes I, II and III, justifying biowaiver claim. For Classes I and III the pattern of a constant F stops at a critical dose Dose(cr) after which the amount of drug absorbed, is independent from the dose. For doses higher than Dose(cr), Class I drugs become Class II and Class III drugs become Class IV. Dose(cr) was used to define an in vivo effective solubility as S(eff) = Dose(cr)/250 ml. Literature data were used to support our simulation results. CONCLUSIONS: A new biopharmaceutic classification of drugs is proposed, based on F, separating drugs into three regions, taking into account the dose, and Dose(cr), while the regions for claiming biowaiver are clearly defined.