Mathematical Models to Explore Potential Effects of Supersaturation and Precipitation on Oral Bioavailability of Poorly Soluble Drugs.

Poorly soluble drugs are increasingly formulated into supersaturating drug delivery systems which may precipitate during oral delivery. The link between in vitro drug concentration profiles and oral bioavailability is under intense investigation. The objective of the present work was to develop closed-form analytical solutions that relate in vitro concentration profiles to the amount of drug absorbed using several alternate assumptions and only six parameters. Three parameters define the key features of the in vitro drug concentration-time profile. An additional three parameters focus on physiological parameters. Absorption models were developed based on alternate assumptions; the drug concentration in the intestinal fluid: (1) peaks at the same time and concentration as in vitro, (2) peaks at the same time as in vitro, or (3) reaches the same peak concentration as in vitro. The three assumptions provide very different calculated values of bioavailability. Using Case 2 assumptions, bioavailability enhancement was found to be less than proportional to in silico examples of dissolution enhancement. Case 3 assumptions lead to bioavailability enhancements that are more than proportional to dissolution enhancements. Using Case 1 predicts drug absorption amounts that fall in between Case 2 and 3. The equations developed based on the alternate assumptions can be used to quickly evaluate the potential improvement in bioavailability due to intentional alteration of the in vitro drug concentration vs. time curve by reformulation. These equations may be useful in making decisions as to whether reformulation is expected to provide sufficient bioavailability enhancement to justify the effort.