Pavlos Chrysafidis1,2,Panos Macheras1,2
1Department of Pharmacy, National and Kapodistrian University of Athens, 2PharmaInformatics Unit, ATHENA Research Center, Athens, Greece,
Objectives: To analyze literature data of oral drug absorption using the biopharmaceutical-physiologically based finite absorption time pharmacokinetic (PBFTPK) models [1].
Methods: The following set of differential equations were used for the analysis of data assuming a single oral drug administration and one-compartment model disposition. The first set of equations depict the evolution of phenomena in the gastrointestinal tract for the fully absorbed Class I drugs, i.e. absorption in the stomach and small intestine is terminated at time τi; beyond τi. only elimination operates:
Vd*dCb/dt = kI –kel*Cb*Vd = D/τi –kel*Cb*Vd for 0<t<τi (1.1)
dCb/dt = – kel*Cb for t>=τi (1.2)
The second set of equations depicts the evolution of pharmacokinetic phenomena in the gastrointestinal tract for Class II, III, IV drugs. In this case, absorption may continue beyond time τi until time τc with a much smaller rate in the colon because of the reduction of the surface area of the gastrointestinal membrane; finally, beyond time τc only elimination operates:
Vd*dCb/dt = kj –kel*Cb*Vd = Fi*D/τi for 0<t<=τi (2.1)
Vd*dCb/dt = kj,c – kel*Cb*Vd = [(1-Fi)/τc–τi]*λ – kel*Cb*Vd for τi<t<=τc (2.2)
dCb/dt = – kel*Cb for t>τc (2.3)
The following validations are considered:
Cb is the drug concentration in blood at time t, Fi is the fraction of dose D absorbed up to time τi, Vd is the volume of distribution, kI is the zero-order absorption rate constant for Class I drugs, whereas kj is the zero-order absorption rate constant for Class II,III, IV drugs (j=II or III, or IV) in the stomach and small intestine; kj,c is the zero-order absorption rate constant for the absorption phase taking place in the colon for Class II, III, IV drugs and λ is a coe?cient (0<λ<1) associated with the reduction of the penetration rate due to small surface area (SA)C value, kel is the elimination first-order rate constant for all drug classes; τi represents the time of the absorption in the stomach and small intestine and τc the instance of time where absorption in colon ceases. For a drug following two-compartment model disposition, similar equations were written. For example, Eq 1.1 becomes:
V*dCb/dt = k1 – (k12+k10)*Cb + k12 for 0<t<=τi (3.1)
while Eqs 1.2 and 2.3 are written
dCb/dt = –(k12+k10) + k21*C2 for t>τc (3.2)
where k12, k10, k21 are the microconstants of the two-compartment model and C2 the drug concentration in the peripheral compartment.
All equations were integrated using Mathematica; SciPy’s v.1.4.1 method of curve fitting was used for their fitting to the experimental data. The algorithm used for the minimization process is Levenberg-Marquardt, appropriate for nonlinear least-squares problems. All plots were depicted with SciPy’s matplotlib.
Results: Literature data of cephradine [2], ibuprofen[2] and itraconazole [3] were analyzed. All (Cb, t) data belonging to the declining limbs of cephradine and ibuprofen profiles were analyzed using Eq. 1.2. The semi-logarithmic plot revealed very nice fittings, i.e. R2 values 0.9831 and 0.9892 were found for cephradine and ibuprofen, respectively. Based on the estimates of their respective elimination rate constants (0.87/h, 0.89/h ), Eqs (1.1, 1.2) were fitted to the entire set of data. The R2 values of the fittings were 0.9723 and 0.997 for cephradine and ibuprofen, respectively. Itraconazole, being considered a two-compartment model Class II drug, was evaluated using the equations (3.1)-(3.2). From the general equation that describes a two-compartment model disposition, i.e.
Cb = A*exp(-at) +B*exp(-bt) (3.3)
estimates for the constants a, A,b, B were computed with a least-squares approach using all itraconazole data of the declining limb. A nice fitting was obtained, R2=0.9768. Subsequently, estimates for the microconstants k12, k10, k21 derived algebraically, followed by curve-fitting of equations (3.1) and (3.2) to the experimental data of itraconazole. For the entire set of data, the algorithm converged with an R2 metric 0.9746 which is very promising for the proposed absorption finite time concept.
Conclusions: For the first time, oral data were analyzed on the basis of the finite absorption time concept [1]. For the three examples examined all data demonstrated that the absorption phase was completed at τi. This opens new avenues for research in the areas of bioavailability, bioequivalence, IVIVC, interspecies scaling, and pharmacometrics.
References:
[1] Pavlos Chryssafidis, Panos Macheras. Revising Pharmacokinetics of Oral Drug Absorption. Models Based on Biopharmaceutical Physiological and Finite Absorption Time Concepts: I Theory and Simulations. Submitted to this PAGE meeting for oral presentation.
[2] Mei-Ling Chen. An alternative Approach for Assessment of Rate of Absorption in Bioequivalence studies. Pharmaceutical Research, Vol. 9, No. 11, 1992.
[3] Thomas C. Hardin, John R. Graybill, Richard Fetchick, R. Woestenborghs, Michael G. Rinaldi, John G. Kuhn. Pharmacokinetics of Itraconazole following Oral Administration to Normal Volunteers. ANTIMICROBIAL AGENTS AND CHEMOTHERAPY, Sept. 1988, p. 1310-1313
Reference: PAGE () Abstr 9539 [www.page-meeting.org/?abstract=9539]
Poster: Oral: Methodology - New Tools