Power Law IVIVC: an Application of Fractional Kinetics for Drug Release and Absorption

Most correlations between in vitro and in vivo data (IVIVC) rely on linear relationships. However, non-linear IVIVC can be also observed, justified and validated. The purpose of the present work was the development of a methodology for power law IVIVC, which mirror power law kinetics under in vitro and in vivo conditions. Fractional calculus was used to justify power law kinetics for zero-order processes in disordered media. Power law kinetics was observed in a large number of in vitro data sets. When "zero-order" release and absorption is considered in terms of fractional calculus the following power law IVIVC between the fraction released F(r) and the fraction absorbed F(a), is obtained: F(a)=microF(r)(lambda)-beta, where mu is a constant related to the rate constants and the orders of the release/absorption kinetics, lambda is the ratio of the orders of the kinetics under in vitro and in vivo conditions and beta accounts for a time shift between the in vitro and in vivo processes; We used literature data to develop power law IVIVC and derive estimates for mu, lambda and beta; the simulated pharmacokinetic profiles using the in vitro release data and the IVIVC developed compared well with the actual in vivo data.