A simple model for complex dissolution kinetics: a case study of norfloxacin

A new semi-empirical model, particularly useful for studying complex dissolution kinetics, is presented here. It uses only two 'fit parameters', each possessing physically relevant units (in the time domain). The model is based on the idea that dispersion (variation) in the activation energy barrier may arise in certain cases, as a result of (quantized) molecular kinetic energies affecting the speed of the rate-determining step (r.d.s.) of the dissolution event. For such 'dispersive dissolutions', the r.d.s. is assumed to involve 2D denucleation. The author's dispersive kinetic model is shown to be applicable to the dissolution of various formulations of norfloxacin which produce very asymmetric, sigmoidal concentration versus time (C-t) profiles. It is derived by assuming an activation energy distribution having the functional form of the Maxwell-Boltzmann (M-B) distribution, coupled with a first-order rate expression. However, this model can also be reduced to give the same functional form as the classical Noyes-Whitney equation, in order to accurately fit/describe dissolution profiles which appear logarithmic (such profiles are due to dissolution phenomena that are not dispersive; i.e. for cases where the activation energy is essentially single-valued). Thus, the kinetic model presented in this work may potentially find broad applicability to the modeling of various dissolution trends observed in the literature.