Re-writing oral pharmacokinetics using physiologically based finite time pharmacokinetic (PBFTPK) models

Pavlos Chryssafidis, Athanasios A. Tsekouras, Panos Macheras

Faculty of Pharmacy, Laboratory of Biopharmaceutics Pharmacokinetics, National and Kapodistrian University of Athens, Athens, Greece

Objectives: The development of the Finite Absorption Time (FAT) concept for oral drug absorption was accomplished recently(1-4). These studies demonstrate that oral drug absorption takes place in a certain period of time in accordance with the biopharmaceutical properties of the drug as well as the physiological gastric, intestinal, and colon transit times reported in the literature(5). However, many physiologically based pharmacokinetic (PBPK) modeling simulation studies, e.g. (6,7), have shown that drug absorption involves complex processes because of the potential dissolution/precipitation/re-dissolution and/or regional drug permeability in the jejunum, ileum, colon of the gastrointestinal tract. These observations call for a computational methodology for the analysis of pharmacokinetic data, which relies on the FAT concept and simultaneously captures the complexity of the drug absorption processes. To this end, this work (8) focuses on the development of physiologically based finite time pharmacokinetic (PBFTPK) models for the analysis of oral pharmacokinetic data.

Methods: Development of PBFTPK models. The core idea for the development relies on the fact that the blood flow in the portal vein has a velocity of 20–40 cm/s(8,9); therefore, sink conditions prevail for the drug transfer from the gastrointestinal lumen to the bloodstream leading to constant drug input rate(s). Up to three successive input functions of constant rate operating for a total time τ were considered. Differential equations were written for the nine models developed assuming linear one- or two-compartment model disposition. The differential equations were solved analytically and functions describing the concentration of the drug as a function of time for the central and the peripheral compartment were derived(8).

Simulation studies. The models' equations were used to simulate concentration and time data assigning one, two, or three-drug input rates operating for different time periods assuming one or two-compartment model kinetics. Simulations were also performed to calculate the derivative dC/dt and plot it as a function of time.

Models fittings. We fitted the models' equations to literature oral PK data of paracetamol (10), ibuprofen(10), almotriptan(11), cyclosporine (12), and niraparib (13). The PBFTPK software used in all model fittings relies on user-defined functions in the Igor programming environment. Due to the complex form of the model equations and the convoluted shape of the resulting x² hypersurface in parameter space with numerous local minima, the determination of initial trial parameter values was crucial and required their manual adjustments. For comparative purposes, we also fitted the conventional one- and two-compartment models with first-order absorption to the experimental data.

Results: 

Simulation studies. The simulated concentration-time curves resemble real-life data reported in the literature. The end of the absorption process τ is either equal to t_max or longer than t_max at the descending portion of the concentration-time curve. In all generated plots the (C(τ), τ) pair is a discontinuity datum point. When t_max= τ, there is a more patent change of the concentration-time curve in the neighborhood of the discontinuity-time point, On the contrary, when t_max < τ, the discontinuity datum point lies in the descending part of the concentration-time curve, and therefore this change is less abrupt. The change of the derivative dC/dt for two examples with t_max= τ and t_max < τ was studied. In the former case, the derivative changes from positive to negative values at t_max= τ; in the latter case, the sign of the derivative is maintained negative close to τ and throughout the descending portion of the curve. These plots demonstrate that under experimental conditions the estimation of τ will be easier when t_max= τ.

Models fittings. In all cases examined, the best ft results using the PBFTPK models were found to be superior to the corresponding results derived from the fitting of the conventional one- and two-compartment models with first-order absorption to the same data. The best fit results [model (one or two), input duration(s), τ(±SD), R²) using the PBFTPK models for each one of the examples studied are as follows a. paracetamol(10) [one, τ=0.51(±0.03)h, R²=0.986] b. ibuprofen (10) [one, τ₁= 0.90(±0.06)h, τ₂=1.4(±0.2)h, R²=0.997] c. almotriptan(11) [one, τ₁=1.11(±0.25)h, τ₂=1.78(±0.3) h, R²=0.994] d. cyclosporine test formulation-fasted (12) [two, τ= 1.57(±0.13)h, R²=0.979] e. cyclosporine test formulation-fed (12) [two, τ= 1.73(±0.13)h, R²=0.978] f. cyclosporine reference formulation-fasted(12) [two, τ= 2.68(±0.10)h, R²=0.992] g. cyclosporine reference formulation-fed (12) [two, τ₁= 0.70(±0.11)h, τ₂= 1.17(±0.11)h, τ₃= 2.79(±0.16)h, R²=0.995] h. niraparib (13) [two, τ₁= 1.36(±0.30)h, τ₂= 2.06(±0.3)h, R²=0.999]. Reliable estimates of the concentration parameter(s) expressed as the ratio of fraction (F) of dose (D) divided by the volume of distribution (V_d), the elimination rate constant for the one-compartment model drugs, or the disposition parameters α and β for the two-compartment model drugs were also derived.

The analysis of data underlines the fact that the duration, τ, of the absorption process is a fundamental biopharmaceutical parameter of the drug when administered as an immediate-release formulation. The type of immediate-release formulation can also have an impact on the τ estimate (see cyclosporine results). In all examples analyzed the estimate for τ was found to be equal to t_max. However, τ values higher than t_max were found by analyzing axitinib data of a bioequivalence study using the PBFTPK models (14). Since τ is conceptually associated with the fundamental biopharmaceutical properties of solubility and permeability (2), drugs/immediate release formulations can be classified into i) rapidly absorbing τ < 1.5h like paracetamol; ii) medium absorbing 1.5 ≤ τ < 5h like ibuprofen, almotriptan, cyclosporine (test administered under fed conditions) and niraparib; iii) slow absorbing 5 ≤ τ < 30h not observed in the present study. For the first two categories, drug absorption takes place only in the small intestine, while for the third category, colon absorption is also operating.

Conclusions: The duration, τ, of the absorption process is a fundamental biopharmaceutical parameter of the drug when administered as an immediate-release formulation. 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.

References:

• [1]Macheras P. On an unphysical hypothesis of Bateman equation and its implications for pharmacokinetics.Pharm Res. 2019;36:94. https://doi.org/10.1007/s11095-019-2633-4
• [2]Macheras P, Chryssafidis P. Revising Pharmacokinetics of Oral Drug Absorption: I Models Based on Biopharmaceutical/Physiological and Finite Absorption Time Concepts. Pharm Res. 2020;37:187. https://doi.org/10.1007/s11095-020-02894-w. Erratum: Pharm Res. 2020;37:206. https://doi.org/10.1007/s11095-020-02935-4.
• [3]Chryssafidis P, Tsekouras AA, Macheras P. Revising Pharmacokinetics of Oral Drug Absorption: II Bioavailability-Bioequivalence Considerations, Pharm Res. 2021;38:1345-1356. https://doi.org/10.1007/s11095-021-03078-w.
• [4]Tsekouras AA, Macheras P.Re-examining digoxin bioavailability after half a century: Time for changes in the bioavailability concepts. Pharm Res. 2021;38:1635-1638. https://doi.org/10.1007/s11095-021-03121-w.
• [5]Abuhelwa A, Foster DJR, Upton RN. A Quantitative Review and Meta-models of the Variability and Factors Affecting Oral Drug Absorption-Part II: Gastrointestinal Transit Time. AAPS J 2016;18:1322–1333.https://doi.org/10.1208/s12248-016-9953-7.
• [6]Sjögren E, Westergren J, Grant I, Hanisch G, Lindfors L, Lennernäs H, Abrahamsson B, Tannergren C, In silico predictions of gastrointestinal drug absorption in pharmaceutical product development: application of the mechanistic absorption model GI-Sim, Eur J Pharm Sci 2013;49:679-698. https://doi.org/10.1016/j.ejps.2013.05.019.
• [7]Sager JE, Yu J, Ragueneau-Majlessi I, Isoherranen N. Physiologically Based Pharmacokinetic (PBPK) Modeling and Simulation Approaches: A Systematic Review of Published Models, Applications, and Model Verification.Drug Metab Dispos. 2015;43:1823-37. https://doi.org/10.1124/dmd.115.065920.
• [8]Chryssafidis P, Tsekouras AA, Macheras P. Re-writing oral pharmacokinetics using physiologically based finite time pharmacokinetic (PBFTPK) models. Pharm Res. 2022;39. https://doi.org/10.1007/s11095-022-03230-0.
• [9]Iranpour P, Lall C, Houshyar R, Helmy M, Yang A, Choi JI, Ward G, Goodwin SC. Altered Doppler flow patterns in cirrhosis patients: an overview. Ultrasonography. 2016;35:3–12. https://doi.org/10.14366/usg.15020.
• [10]Atkinson HC, Stanescu I, Frampton C, Salem II, Beasleyr CPH, Robson R. Pharmacokinetics and Bioavailability of a Fixed-Dose Combination of Ibuprofen and Paracetamol after Intravenous and Oral Administration. Clin Drug Investig. 2015;35:625–32. https://doi.org/10.1007/s40261-015-0320-8.
• [11]Jansat JM, Costa J, Salva P, Fernandez FJ, Martinez-Tobed A. Absolute bioavailability, pharmacokinetics, and urinary excretion of the novel antimigraine agent almotriptan in healthy male volunteers. J Pharmacokin Pharmacodyn. 2002;42:1303–10. https://doi.org/10.1177/0091270002239359.
• [12]Mueller EA, Kovarik JM, van Bree JB, Grevel J, Lucker PW, Kutz K. Influence of a fat-rich meal on the pharmacokinetics of a new oral formulation of cyclosporine in a crossover comparison with the market formulation. Pharm Res. 1994;11:151–5. https://doi.org/10.1023/a:1018922517162.
• [13]Van Andel L, Rosing H, Zhang Z, Hughes L, Kansra V, Sanghvi M, Tibben MM, Gebretensae A, Schellens JHM, Beijnen JH. Determination of the absolute oral bioavailability of niraparib by simultaneous administration of a 14C-microtracer and therapeutic dose in cancer patients. Cancer Chemother Pharmacol. 2018;81:39–46. https://doi.org/10.1007/s00280-017-3455-x.
• [14]Alimpertis N, Tsekouras AA, Macheras P. Revising the assessment of bioequivalence in the light of finite absorption time concept: The axitinib case. Poster submitted to This PAGE meeting, Ljubljana, Slovenia, 28 June-1 July, 2022.

Reference: PAGE 30 (2022) Abstr 10089 [www.page-meeting.org/?abstract=10089]

Poster: Methodology - New Modelling Approaches