A Simple One-Parameter Percent Dissolved Versus Time Dissolution Equation that Accommodates Sink and Non-sink Conditions via Drug Solubility and Dissolution Volume

Abstract

AbstractIn vitro dissolution generally involves sink conditions, so dissolution equations generally do not need to accommodate non-sink conditions. Greater use of biorelevant media, which are typically less able to provide sink conditions than pharmaceutical surfactants, necessitates equations that accommodate non-sink conditions. One objective was to derive an integrated, one-parameter dissolution equation for percent dissolved versus time that accommodates non-sink effects via drug solubility and dissolution volume parameters, including incomplete solubility. A second objective was to characterize the novel equation by fitting it to biorelevant dissolution profiles of tablets of two poorly water-soluble drugs, as well as by conducting simulations of the effect of dose on dissolution profile. The Polli dissolution equation was derived, $$\% \;dissolved=100\%\left[1-\frac{\left({{M}_{0}-c}_{s}V\right)}{{M}_{0}-{{c}_{s}Ve}^{{-k}_{d}\left(\frac{{{M}_{0}-c}_{s}V}{V}\right)t}}\right]$$ % d i s s o l v e d = 100 % 1 - M 0 - c s V M 0 - c s V e - k d M 0 - c s V V t , where M0 is the drug dose (mg), cs is drug solubility (mg/ml), V is dissolution volume (ml), and kd is dissolution rate coefficient (ml/mg per min). Maximum allowable percent dissolved was determined by drug solubility and not a fitted extent of dissolution parameter. The equation fit tablet profiles in the presence and absence of sink conditions, using a single fitted parameter, kd, and where solubility ranged over a 1000-fold range. kd was generally smaller when cs was larger. FeSSGF provided relatively small kd values, reflecting FeSSGF colloids are large and slowly diffusing. Simulations showed impact of non-sink conditions, as well as plausible kd values for various cs scenarios, in agreement with observed kd values. The equation has advantages over first-order and z-factor dissolution rate equations. An Excel file for regression is provided. Graphical Abstract