Software using Physiologically Based Finite Time Pharmacokinetic (PBFTPK) Models
Nikos Alimpertis, Athanasios A. Tsekouras, and Panos Macheras
ATHENA Research Center and National and Kapodistrian University of Athens
Introduction: The collapse of the physicomathematical fallacy of infinite time of oral drug absorption (1-4), was followed by the development of the finite absorption time (F.A.T.) concept (5). In this context, Physiologically Based Finite Time Pharmacokinetic (PBFTPK) models were developed (6), which rely on the principles: i) finite absorption time, τ for drug absorption processes and ii) zero-order drug input (single or multiple) because of the passive drug absorption under sink conditions and the high blood flow rate 20-40 cm/s in the vena cava (7). The PBFTPK models were applied successfully to a large number of experimental data and were superior to the classical models based on the first-order absorption notion (3-6, 8). Meaningful parameters for drug’s input rate(s) and duration of absorption stage(s) were estimated using nonlinear regression analysis.
Objectives: To develop software based on PBFTPK models for pharmaceutical scientists and pharmacometricians.
Methods: The software that we developed is composed of three main parts. The first part of the software is used for fitting of the PBFTPK models to experimental pharmacokinetic data (4, 6). The quality of the fit is established by comparing the sum of squares of deviations χ2, between calculated values from the models and experimental points. Parameter uncertainties are calculated directly from parameter variances. Parameter correlations are derived from parameter covariances and corresponding variances. The second part relies on the construction of percent absorbed versus time plots used in deconvolution programs. We modified the fundamental Wagner-Nelson and Loo-Riegelman equations in terms of the F.A.T concept. Routines allow the coupling of percent absorbed, time data with percent drug dissolved of in vitro experiments for the development of in vitro in vivo correlations. The last part of the software contains algorithms of a revised bioequivalence assessment approach using as a key parameter the cumulative AUC ratio of the test over the reference formulation as a function of time (9).
Results: We analyzed, using the software based on PBFTPK models, a plethora of pharmacokinetic data and estimated the drug input rate(s) and the duration of each one of the absorption stages. The reliability and superiority of PBFTPK models over the classical first-order one- and two-compartment models was justified by the statistical metrics. The analysis of pharmacokinetic data using the modified Wagner-Nelson and Loo-Riegelman equations revealed percent absorbed versus time plots of bi-linear type. This finding places an end to the exponential curves routinely generated from the classical Wagner-Nelson and Loo-Riegelman equations as well as the deconvolution techniques. The intersection of the linear limbs of the bi-linear plots corresponds to the termination or the completion of drug absorption processes. The plots of the cumulative AUC ratio of the test over the reference formulation versus time exhibit a nonlinear increase as a function of time; they end up to a horizontal linear segment parallel to the time axis. This horizontal line corresponds to the magnitude of the relative bioavailability of the ratio test/reference formulations.
Conclusion: This software has enhanced analytical power, compared to the classical software, since the physiological notion of F.A.T. is incorporated into all algorithms. Besides, pharmacometricians can use the PBFTPK models library for population analyses.
References
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