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 overcome 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, permeability, 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 summarized in a Noyes -Whitney (14) type equation:
k=-™(Ct-)< (14)
where Xs is the mass of solid drug remaining at any time t, D is the drug diffusion coefficient, S is the drug surface area, h is the hydrodynamic diffusion layer thickness, Cs is the drug solubility, Xd is the mass of dissolved drug at any time t, and V is the volume of fluid in which the drug is dissolving.
In trying to solve the earlier equation, it should be noted that the drug surface area would not remain constant as drug dissolves after being released from typical dosage forms. The amount of dissolved drug would also not be constant. As a result, the rate of dissolution is continually changing. Dissolution testing is typically done under sink conditions; therefore, the Xd/V term is small compared to Cs so that former can be ignored. However, in trying to establish a mechanistically based in vitro/in vivo correlation, the assumption that sink conditions would exist in the GI tract is an especially bad one for poorly soluble drugs. Also, as will be shown, testing dissolution under sink conditions is not necessary and can make instrumental analysis of dissolution more difficult. What is required is a numerical solution of the Noyes- Whitney equation to make the application of the theory as general as possible by eliminating the need to make frequently bad assumptions in order to solve the equation analytically.
