I-30 Pavlos Chrysafidis

A paradigm shift in oral drug absorption: The rise of 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: To explore the application of the parameters of the physiologically based finite time pharmacokinetic (PBFTPK) models (1) subdivided in first-order (PBFTPK)1 (2-5) and zero-order (PBFTPK)0 (2) models to bioavailability and bioequivalence. To develop methodologies for the estimation of absolute bioavailability F from oral data exclusively.

Methods: 

For (PBFTPK)1 models, Eqs.1 and 2 based on the one compartment model (2-4) were used in the simulations

  Cb(t)=[FDkα/Vd(kα-kel)](e-kαt-e-kelt )                      t≤τ                                    (1)

    Cb(t)=Cb(τ)e-kel(t-τ)                                             t>τ                                    (2)

where Cb(t) is the drug concentration in the body (compartment) at time t, D is the dose, Vd is the volume of distribution, τ is the duration of absorption, ka, kel are the absorption and elimination rate constants, respectively.

For (PBFTPK)0 models, Eq. 3 based on the one-compartment model (1) was used in the simulations.

    Cb(t)= (FD/τVdkel)(1-e-kelt)                     t≤ τ                                   (3)

 while for t>τ, Eq. 2 applies. Equations with multiple successive constant input rates were also written and used in the simulations. The following equation was derived for the (PBFTPK)0 model,

[AUC0-oo ] hy.i.v= (FD/kelτVdkel)(ekelτ-1)=[AUC0-oo] (1/kelτ)(ekelτ-1) (4)

Re-arranging, we get

F=  [AUC0-oo]/[AUC0-oo ] hy.i.v  = kelτ/(ekelτ-1)                                                                    (5)

where [AUC0-oo] hy.i.v is the area under the curve, calculated from the oral data, corresponding to a hypothetical intravenous bolus administration of the same dose, and [AUC0-oo] is the area under the curve for the orally administered dose from time zero to infinity.

In a similar manner, the following equations were derived for the (PBFTPK)1 model,

 F=(1- kel/kα )[(1- ekατ )/(1- e-(kα-kel )τ)]        (6) 

 [AUC0-oo]=FD/Vdkel(1- e-kατ)                      (7)

Eq. 8 applies to both one-compartment models with zero- or first-order absorption of time duration, τ and first-order elimination.

   F=[AUC0-oo] oral Dose / [AUC0-oo] hy.i.v FDose            (8)

Solving in terms of F,      

F2 =  [AUC0-oo] oral  / [AUC0-oo] hy.i.v                                                                          (9)

The positive root of Eq. 9 provides an estimate for F.

Literature concentration-time data for theophylline (6), flurbiprofen (7), and cephradine (8) were fit with Eqs.1 and 2 or 3 and 2. Standard least squares method was used to adjust model parameters, for the (PBFTPK)0 and (PBFTPK)1 models.

Results: The simulated data of the (PBFTPK)0 models with more than one constant input rate exhibit rich dynamics, which are usually encountered in drug absorption phenomena. For both (PBFTPK)1 and (PBFTPK)0 models the drug concentration at the end of the absorption process, Cb(τ) was found to be equal to Cmax for rapidly absorbed or smaller to Cmax for not rapidly absorbed drugs; in the latter case, Cb(τ) and τ are meaningful parameters for the drug’s rate of exposure. For both (PBFTPK)1 and (PBFTPK)0 models, [AUC0-τ] or portions of it cannot be used as early exposure rate indicators. Τhe area under the curve for the orally administered dose from time τ to infinity, [AUCτ-οο] is a useful parameter for the assessment of the extent of absorption for very rapidly absorbed drugs, e.g., inhalation products.

Excellent fits of all equations were observed for all data sets (6-8) analyzed. The parameter estimates were further used to derive estimates for F using Eqs.5 and 6. The F values found for the theophylline formulations (6) were equal to 1.04 and 0.97 for the (PBFTPK)1 and (PBFTPK)0 models, respectively. These estimates are in full agreement with the reported value for F, 0.96 ± 0.03 for immediate release theophylline tablets (12). F computed for flurbiprofen (100 mg capsules) (7) using Eq.5 was found equal to 0.97 compared to the mean 0.96 found in the literature (13). F was also computed from Eq. 5 for cephradine (500mg capsules) (8) and found equal to 0.80 relative to a mean value of 0.90 found in the literature (8).

Conclusions: The realization that gastrointestinal absorption takes place in finite time and the development of (PBFTPK)0 and (PBFTPK)1 models open a new era in the scientific and regulatory aspects of biopharmaceutical sciences. Estimates for F of theophylline, flurbiprofen and cephradine were derived from oral data exclusively. Several areas of research such as in vitro in vivo correlations, oral interspecies, or pediatric pharmacokinetic scaling studies will be affected. 

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Reference: PAGE 29 (2021) Abstr 9710 [www.page-meeting.org/?abstract=9710]

Poster: Drug/Disease Modelling - Absorption & PBPK