The estimates for the absorption rate constant in pharmacokinetics and pharmacometrics are wrong: A new era based on the finite absorption time concept rises
Nikos Alimpertis, Athanasios A. Tsekouras, and Panos Macheras
ATHENA Research Center and National and Kapodistrian University of Athens
Introduction: Common practice in pharmacokinetic analyses and data evaluation as well as in simulations is based on the assumption that absorption of drugs administered orally or otherwise lasts forever. This practice, which goes counter to plain facts, e.g. digestion terminates within hours, has been pointed out in several recent publications [1-4]. The Finite Absorption Time (F.A.T.) concept  in conjunction with zero-order kinetics was proven to be meaningful and then incorporated in various data analyses. It was shown that Physiologically Based Finite Time Pharmacokinetic (PBFTPK) models  with one or more absorption stages for one- or two-compartment drugs provided adequate and meaningful data fits. Furthermore, the F.A.T. concept was shown to affect bioavailability and bioequivalence assessment [7, 8], because, once absorption ceases, there is no more information to be gained from prolonged sampling. Very recently, we were able to show conclusively that the traditional analysis of percent of drug absorbed is in full agreement with the more or less abrupt termination of drug absorption.
Objectives: To show the potential impact the concept of Finite Absorption Time can have across many fields pertaining to drugs and their formulations, from inception to in vitro and in vivo studies, to clinical trials and approval, to development of generics, to in vitro - in vivo correlations and PBPK studies.
Methods: We developed custom written software modules describing various scenarios of one- and two-compartment disposition models with as many as five successive zero-order absorption stages and incorporated them in adaptable non-linear regression analysis commercial software (Igor by Wavemetrics). We have analyzed a large number of experimental pharmacokinetic data. Most drugs were administered orally, with immediate or modified release, but the set also included pulmonary, intramuscular, intranasal and transdermal drugs. In the majority of cases, data were retrieved from journal publications, which necessitated manual digitization.
The primary goal of the fits was the determination of the model that described the data best, at an adequate level of parameter uncertainty and parameter cross correlation, F.A.T. being the most interesting quantity found. In all cases we also attempted fits with classical models with first-order, infinite duration for absorption stage. Subsequently, the parameters determined with the FBFTPK models allowed further calculation of partial or total areas under the curve (AUC) for performing comparisons among formulations. Furthermore, relying on the elimination rate constant parameters that resulted from the fits, the percent of drug absorbed could be established as a function of post-dose time. This processing allowed an independent determination of the F.A.T.
Results: In the vast majority of data sets analyzed the FBFTPK models performed better than the corresponding classical models, tracking the data more closely and providing meaningful estimates both for input rate constants and the F.A.T. (τ) of the absorption stage or stages. Oftentimes, τ was found to be extremely short and usually of the order of post-dose time required to reach maximum drug concentration in the blood stream, tmax. In cases of multiple successive absorption stages, τ could be greater than tmax. Drugs with complex absorption kinetics (e.g., oxybutynin, mavoglurant) could be described successfully by these models . Hence, the PBFTPK models are meaningful alternatives of the stochastic approaches based on inverse Gaussian functions used for the analysis of complex absorption data. Besides orally administered drugs, we treated data for drugs delivered pulmonary (e.g., salmeterol, fluticasone, budesonide, formoterol), intramuscularly (e.g., naloxone), intranasally (e.g., naloxone, amiloride), transdermally (e.g., oxybutynin) [3,7]. Comparisons of partial AUCs up to the time of absorption termination rather than to infinite time showed that the bioequivalence of formulations can be assessed based solely on sampling limited up to time τ (e.g., salmeterol, fluticasone, budesonide, formoterol, digoxin, axitinib) [7,8,9]. Consequently, bioequivalence trials do not need to be extended beyond τ, thus saving in time, resources, cost and increasing volunteer availability. Similarly, the percent of drug absorbed (e.g., paracetamol, ibuprofen, niraparib, cyclosporine) showed a distinct change in slope at τ indicating that correlations between in vitro and in vivo studies should be extended only for the time that is realistic to expect drug dissolution and absorption. From comparisons between PBPK simulations and corresponding PBFTPK fits for immediate release formulations (e.g., etoricoxib, gaboxadol, dipyridamole, pioglitazone, Merck compound C, losartan) a clear relationship between the absorption rate and the product of permeability and luminal concentration was observed . This work  opens an new avenue of research towards the study of the relationships/correlations between the chemical structure (molecular descriptors) or biopharmaceutical properties, e.g., solubility or permeability and pharmacokinetic observations, e.g., (AUC)0-τ, estimate for τ.
Conclusion: A software for the pharmacokinetic analysis of concentration-time data based on PBFTPK models, being build up right now, is a useful and powerful tool for the pharmaceutical scientist. Thus, a new library of PBFTPK models will be at the disposal of pharmacometricians for population analyses. Furthermore, the results of the present study have important implications in the regulatory setting. The parameters Cmax and (AUC)0-∞ and their use in the FDA and EMA bioequivalence guidelines have to be reconsidered; similarly, the prolonged sampling designs recommended in these guidelines should be also reconsidered.
Overall, the concept of F.A.T. is set to sweep many aspects of how formulations are developed, studied, how they function, how they are tested and how different formulations are compared.
 Macheras P (2019) Pharm Res. 36:94. https://doi.org/10.1007/s11095-019-2633-4
 Tsekouras AA, Macheras P (2022) Eur J Pharm Sci 176:106265 https://doi.org/10.1016/j.ejps.2022.106265
 Macheras P, Tsekouras AA (2023) J Pharmacokin Pharmacodyn, 50:5-10 https://doi.org/10.1007/s10928-022-09832-w
 Macheras P, Tsekouras AA (2023) Revising Oral Pharmacokinetics, Bioavailability and Bioequivalence Based on the Finite Absorption Time Concept, Springer, Cham
 Macheras P, Chryssafidis P (2020) Pharm Res 37:187. https://doi.org/10.1007/s11095-020-02894-w
 Chryssafidis P, Tsekouras AA, Macheras P (2022) Pharm Res 39:691. https://doi.org/10.1007/s11095-022-03230-0
 Chryssafidis P, Tsekouras AA, Macheras P (2021) Pharm Res 38:1345-1356 https://doi.org/1007/s11095-021-03078-w
 Tsekouras AA, Macheras P (2021) Pharm Res 38, 1635-1638. https://doi.org/10.1007/s11095-021-03121-w. Erratum in: Pharm Res. 2021;38:2185
 Alimpertis N, Tsekouras AA, Macheras P (2022) Revising the assessment of bioequivalence in the light of finite absorption time concept: The axitinib case. Poster presented at the 30th PAGE meeting, Ljubljana, Slovenia, 28 June-1 July 2022
 Wu D, Tsekouras AA, Macheras P and Kesisoglou F (2023) Pharm Res 40:419-429 https://doi.org/10.1007/s11095-022-03357-0