IVIVC Revised

Abstract

Purpose

To revise the IVIVC considering the physiologically sound Finite Absorption Time (F.A.T.) and Finite Dissolution Time (F.D.T.) concepts.

Methods

The estimates τ and τ_d for F.A.T. and F.D.T., respectively are constrained by the inequality τ_d ≤ τ; their relative magnitude is dependent on drug’s BCS classification. A modified Levy plot, which includes the time estimates for τ and τ_d was developed. IVIVC were also considered in the light of τ and τ_d estimates. The modified Levy plot of theophylline, a class I drug, coupled with the rapid (30 min) and very rapid (15 min) dissolution time limits showed that drug dissolution/absorption of Class I drugs takes place in less than an hour. We reanalyzed a carbamazepine (Tegretol) bioequivalence study using PBFTPK models to reveal its complex absorption kinetics with two or three stages.

Results

The modified Levy plot unveiled the short time span (~ 2 h) of the in vitro dissolution data in comparison with the duration of in vivo dissolution/absorption processes (~ 17 h). Similar results were observed with the modified IVIVC plots. Analysis of another set of carbamazepine data, using PBFTPK models, confirmed a three stages absorption process. Analysis of steady-state (Tegretol) data from a paediatric study using PBFTPK models, revealed a single input stage of duration 3.3 h. The corresponding modified Levy and IVIVC plots were found to be nonlinear.

Conclusions

The consideration of Levy plots and IVIVC in the light of the F.A.T. and F.D.T. concepts allows a better physiological insight of the in vitro and in vivo drug dissolution/absorption processes.

Appendix

We list below the analytical expressions for 4 cases of drug concentration in the blood as a function of time after oral administration for the one-compartment model with zero-order, finite time absorption kinetics in one or more stages.

• 1 Single input stage of duration τ.

For $0<t\le \tau$,

$$C\left(t\right)=\frac{FD}{{\tau V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}t}\right)$$

(1)

$$C\left(\tau \right)=\frac{FD}{{\tau V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}\tau }\right)$$

(2)

For $\tau <t$,

$$C\left(t\right)=C\left(\tau \right){e}^{-{k}_{el}\left(t-\tau \right)}$$

(3)

• 2 Two consecutive input stages of duration τ₁ and τ₂.

For $0<t\le {\tau }_{1}$,

$$C\left(t\right)=\frac{{F}_{1}D}{{{\tau }_{1}V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}t}\right)$$

(4)

$$C\left({\tau }_{1}\right)=\frac{{F}_{1}D}{{{\tau }_{1}V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}{\tau }_{1}}\right)$$

(5)

For ${\tau }_{1}<t\le {{\tau }_{1}+\tau }_{2}$,

$$C\left(t\right)=C\left({\tau }_{1}\right){e}^{-{k}_{el}\left(t-{\tau }_{1}\right)}+\frac{{F}_{2}D}{{\tau }_{2}{V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}\left(t-{\tau }_{1}\right)}\right)$$

(6)

For ${\tau }_{1}+{\tau }_{2}<t$,

$$C\left(t\right)=C\left({\tau }_{1}+{\tau }_{2}\right){e}^{-{k}_{el}\left(t-{\tau }_{1}-{\tau }_{2}\right)}$$

(7)

• 3 n consecutive input stages each of duration τ_i.

For $0<t\le {\tau }_{1}$,

$$C\left(t\right)=\frac{{F}_{1}D}{{{\tau }_{1}V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}t}\right)$$

(8)

For $\sum_{j=1}^{i-1}{\tau }_{j}<t\le \sum_{j=1}^{i}{\tau }_{j}$,

$$C\left(t\right)=C\left(\sum\nolimits_{j=1}^{i-1}{\tau }_{j}\right){e}^{-{k}_{el}\left(t-\sum\nolimits_{j=1}^{i-1}{\tau }_{j}\right)}+\frac{{F}_{i}D}{{\tau }_{i}{V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}\left(t-\sum\nolimits_{j=1}^{i-1}{\tau }_{j}\right)}\right)$$

(9)

For $\sum_{j=1}^{n}{\tau }_{j}<t$,

$$C\left(t\right)=C\left(\sum\nolimits_{j=1}^{n}{\tau }_{j}\right){e}^{-{k}_{el}\left(t-\sum\nolimits_{j=1}^{n}{\tau }_{j}\right)}$$

(10)

• 4 One input stage of duration τ coupled with n identical doses administered at equal Δt intervals.

For $i\Delta t<t\le \tau +i\Delta t$, where i is an integer with $0\le i<n$

$$C\left(t\right)=C\left(i\Delta t\right){e}^{-{k}_{el}\left(t-i\Delta t\right)}+\frac{FD}{\tau {V}_{d}{k}_{el}}\left(1-{e}^{{-k}_{el}\left(t-i\Delta t\right)}\right)$$

(11)

where $C\left(0\right)=0$

For $\tau +i\Delta t<t\le \left(i+1\right)\Delta t$ or $\tau +n\Delta t<t$,

$$C\left(t\right)=C\left(\tau +i\Delta t\right){e}^{-{k}_{el}\left(t-\left(\tau +i\Delta t\right)\right)}$$

(12)

The latter set of equations was used to generate Fig. 10 and analyze the data shown in Fig. 11.