Sophisticated Models

The MAD analysis is mathematically simple, which is part of its appeal. However, more sophisticated models involve differential equations that do not necessarily have analytical solutions and, therefore, need to be solved numeri- cally. The mathematical model to be presented as follows has the ability to simu- late the kinetics of a polydisperse crystalline powder. This has wide applicability In Vitro Release and Biopharmaceutics Classification 9 because of the prevalence of immediate-release dosage forms containing drug as a crystalline powder. One of the assumptions of the model is that the crystalline drug particles are completely wetted and dispersed initially. The model does not describe the kinetics of wetting. However, by comparing theoretical simulations of the dissol- ution rate with actual dissolution from the dosage form, one can gain insight into the extent that wetting is slowing the rate of dissolution. Validating and refining the model requires powder dissolution data that is independent of the effects of dispersion and wetting since this is an assumption of the model. This may require developing an experimental technique that uses a surfactant at a concentration that will not enhance solubility but will improve wetting. The technique may also require a brief period of vigorous mixing to achieve dispersion and wetting. High-quality data is required to validate dissol- ution theory as well as gain insight into some of the more elusive aspects such as how to handle hydrodynamics. One of the goals of this chapter is to convince the reader that dissolution can be explained and predicted based on theory and that this is worthwhile in terms of shortening the time it takes to develop drug products. Perhaps the most dramatic way would be to show that, based on the solubility and permeability of a drug candidate, inherent absorption would never be good enough to allow the drug to become a product. Knowing this, project teams could decide whether to drop drug candidates and pursue others, or to commit resources in an attempt to over- come the solubility issue and accept the higher development cost and risk of failure in doing so. For the formulator, however, not knowing the effect of particle size on dissolution rate and absorption or whether poor disintegration or wetting is affecting the dissolution rate can lead to costly delays in development that could require the need to repeat toxicological and clinical studies. Although the Biopharmaceutics Classification System (BCS) (13), discussed later, and MAD analysis are useful and attractive because of their simplicity, both are limited in terms of guidance that might be extracted from solubility, per- meability, dissolution, and other pharmacokinetic data. Neither can describe the kinetics of absorption leading to insight into the effects of drug particle size and hydrodynamic conditions that would lead to a mechanistically based in vitro/in vivo correlation. They would also not allow one to make a rational estimation as to when dissolution samples should be taken and whether the dissolution test would be discriminating to significant differences in dosage forms. To do this, a more sophisticated model is needed such as the one described subsequently. The dissolution rate of crystalline drug is proportional to its solubility, surface area, and diffusion coefficient. It is also dependent on the hydrodynamic conditions, but in a less well understood way. These relationships can be summar- ized in a Noyes–Whitney (14) type equation.