A population growth model of dissolution

To develop a new approach for describing drug dissolution which does not require the presuppositions of time continuity and Fick's law of diffusion and which can be applied to both homogeneous and heterogeneous media.

The mass dissolved is considered to be a function of a discrete time index specifying successive "generations" (n). The recurrence equation: phi n + 1 = phi n + r(1 - phi n)(1 - phi n X0/theta) was derived for the fractions of dose dissolved phi n and phi n+1, between generations n and n + 1, where r is a dimensionless proportionality constant, X0 is the dose and theta is the amount of drug corresponding to the drug's solubility in the dissolution medium.

The equation has two steady state solutions, phi ss = 1 when (X0/theta) < or = 1 and phi ss = theta/X0 when (X0/theta) > 1 and the usual behavior encountered in dissolution studies, i.e, a monotonic exponential increase of phi n reaching asymptotically the steady state when either r < theta/X0 < 1 or r < 1 < theta/X0. Good fits were obtained when the model equation was applied to danazol data after appropriate transformation of the time scale to "generations". The dissolution process is controlled by the two dimensionless parameters theta/X0 and r, which were found to be analogous to the fundamental parameters dose and dissolution number, respectively. The model was also used for the prediction of fraction of dose absorbed for highly permeable drugs.

The model does not rely on diffusion principles and therefore it can be applied under both homogeneous and non-homogeneous conditions. This feature will facilitate the correlation of in vitro dissolution data obtained under homogeneous conditions and in vivo observations adhering to the heterogeneous milieu of the GI tract.