Drug solubility studies by using combined solubilization techniques

This study focuses on the development of mathematical models that explain and predict the combined effects of pH control and complexants (cyclodextrin), pH control and surfactants, as well as pH control and cosolvents on the total solubility of the drug. The total solubility of the drug is expressed as the sum of the concentrations of individual species. In complexant-water and surfactant-water systems free unionized drug [Dᵤ] and free ionized drug [Dᵢ] are present along with either complexed unionized drug [DᵤL] and complexed ionized drug [DᵢL], or micellar unionized drug [DᵤM] and micellar ionized drug [DᵢM], respectively. On the other hand, in cosolvent-water system the only species present are free unionized drug [Dcᵤ] and free ionized drug [Dcᵢ]. The equations developed show that a pH change favoring ionization of the drug not only increases the concentration of the ionized species in water, but also increases the concentration of the ionized species in cyclodextrins, micelles, or cosolvents. In fact, the concentration of the ionized species in the complexant, micelle, or cosolvent can be greater than those of the unionized species. The solubility data of flavopiridol and several other drugs reported in the literature support these conclusions. A mathematical model is also developed to describe the combined effect of cosolvency and complexation on non-polar drug solubilization. The total drug solubility is determined by the summation of three drug species present in the solution: free drug [D], drug-ligand binary complex [DL], and drug-ligand-cosolvent ternary complex [DLC]. The proposed equation describes the dependencies of these three species upon the intrinsic drug solubility, [Dᵤ], the cosolvent solubilizing power, sigma, the binary and ternary intrinsic complexation constants, K(b)ⁱⁿᵗ and K(t)ⁱⁿᵗ, and the cosolvent destabilizing powers for the binary and the ternary complexes, ρ(b) and ρ(t). The equation explains the decline in the solubility of fluasterone (a non-polar drug) produced by low cosolvent concentrations as well as the increase in the solubility produced by high cosolvent concentrations that are observed at all cyclodextrin concentrations