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.

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.

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.

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.

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.

Interpreting airborne pandemics spreading using fractal kinetics' principles.

Introduction  The reaction between susceptible and infected subjects has been studied under the well-mixed hypothesis for almost a century. Here, we present a consistent analysis for a not well-mixed system using fractal kinetics' principles.  Methods  We analyzed COVID-19 data to get insights on the disease spreading in absence/presence of preventive measures. We derived a three-parameter model and show that the "fractal" exponent h of time larger than unity can capture the impact of preventive measures affecting population mobility.  Results  The h=1 case, which is a power of time model, accurately describes the situation without such measures in line with a herd immunity policy. The pandemic spread in four model countries (France, Greece, Italy and Spain) for the first 10 months has gone through four stages: stages 1 and 3 with limited to no measures, stages 2 and 4 with varying lockdown conditions. For each stage and country two or three model parameters have been determined using appropriate fitting procedures. The fractal kinetics model was found to be more akin to real life.  Conclusion  Model predictions and their implications lead to the conclusion that the fractal kinetics model can be used as a prototype for the analysis of all contagious airborne pandemics.

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.

A fractal kinetics SI model can explain the dynamics of COVID-19 epidemics.

The COVID-19 pandemic has already had a shocking impact on the lives of everybody on the planet. Here, we present a modification of the classical SI model, the Fractal Kinetics SI model which is in excellent agreement with the disease outbreak data available from the World Health Organization. The fractal kinetic approach that we propose here originates from chemical kinetics and has successfully been used in the past to describe reaction dynamics when imperfect mixing and segregation of the reactants is important and affects the dynamics of the reaction. The model introduces a novel epidemiological parameter, the "fractal" exponent h which is introduced in order to account for the self-organization of the societies against the pandemic through social distancing, lockdowns and flight restrictions.

The Biopharmaceutics Classification System (BCS) and the Biopharmaceutics Drug Disposition Classification System (BDDCS): Beyond guidelines.

The recent impact of the Biopharmaceutics Classification System (BCS) and the Biopharmaceutics Drug Disposition Classification System (BDDCS) on relevant scientific advancements is discussed. The major advances associated with the BCS concern the extensive work on dissolution of poorly absorbed BCS class II drugs in nutritional liquids (e.g. milk, peanut oil) and biorelevant media for the accurate prediction of the rate and the extent of oral absorption. The use of physiologically based pharmacokinetic (PBPK) modeling as predictive tool for bioavailability is also presented. Since recent dissolution studies demonstrate that the two mechanisms (diffusion- and reaction-limited dissolution) take place simultaneously, the neglected reaction-limited dissolution models are discussed, regarding the biopharmaceutical classification of drugs. Solubility- and dissolution-enhancing formulation strategies based on the supersaturation principle to enhance the extent of drug absorption, along with the applications of the BDDCS to the understanding of disposition phenomena are reviewed. Finally, recent classification systems relevant either to the BCS or the BDDCS are presented. These include: i) a model independent approach based on %metabolism and the fulfilment (or not) of the current regulatory dissolution criteria, ii) the so called ΑΒΓ system, a continuous version of the BCS, and iii) the so-called Extended Clearance Classification System (ECCS). ECCS uses clearance concepts (physicochemical properties and membrane permeability) to classify compounds and differentiates from BDDCS by bypassing the measure of solubility (based on the assumption that since it inter-correlates with lipophilicity, it is not directly relevant to clearance mechanisms or elimination).

On the unphysical hypotheses in pharmacokinetics and oral drug absorption: Time to utilize instantaneous rate coefficients instead of rate constants.

This work aims to explore the unphysical assumptions associated with i) the homogeneity of the well mixed compartments of pharmacokinetics and ii) the diffusion limited model of drug dissolution. To this end, we i) tested the homogeneity hypothesis using Monte Carlo simulations for a reaction and a diffusional process that take place in Euclidean and fractal media, ii) re-considered the flip-flop kinetics assuming that the absorption rate for a one-compartment model is governed by an instantaneous rate coefficient instead of a rate constant, and, iii) re-considered the extent of drug absorption as a function of dose using an in vivo reaction limited model of drug dissolution with integer and non-integer stoichiometry values. We found that drug diffusional processes and reactions are slowed down in heterogeneous media and the environmental heterogeneity leads to increased fluctuations of the measurable quantities. Highly variable experimental literature data with measurements in intrathecal space and gastrointestinal fluids were explained accordingly. Next, by applying power law and Weibull input functions to a one-compartment model of disposition we show that the shape of concentration-time curves is highly dependent on the time exponent of the input functions. Realistic examples based on PK data of three compounds known to exhibit flip-flop kinetics are analyzed. The need to use time dependent coefficients instead of rate constants in PBPK modeling and virtual bioequivalence is underlined. Finally, the shape of the fraction absorbed as a function of dose plots, using an in vivo reaction limited model of drug dissolution were found to be dependent on the stoichiometry value and the solubility of drug. Ascending and descending limbs were observed for the higher stoichiometries (2.0 and 1.5) with the low solubility drug. In contrast, for the more soluble drug, a continuous increase of fraction absorbed as a function of dose is observed when the higher stoichiometries are used (2.0 and 1.5). For both drugs, the fraction absorbed for the lower values of stoichiometry (0.7 and 1.0) exhibit a non-dependency on dose profile. Our results give an insight into the complex picture of in vivo drug dissolution since diffusion-limited and reaction-limited processes seem to operate under in vivo conditions concurrently.