Comparison of the z-factor and Polli dissolution rate coefficient for monodisperse powders

The Polli dissolution equation and the classical z-factor model both characterize the rate of drug dissolution via a rate coefficient (k_d or z, respectively) and nominally possess the same units (e.g., mL/mg per min). The objective was to assess the numerical similarity of the dissolution rate coefficient k_d in the Polli model to the z-factor in the z-factor model across a wide range of dissolution conditions. Firstly, simulated dissolution profiles of monodisperse particles were generated using the z-factor model under a range of drug solubility, drug or micelle diffusivity, and initial drug particle radius conditions. Each simulated profile from the z-factor model was fitted with the Polli equation, yielding fitted k_d. Secondly, fits for each k_d and z were obtained from previously reported dissolution profiles of different polydisperse drug powders into various media. From the simulation study, the fitted k_d values were generally similar to z-factor values, in parameterizing powder dissolution profiles across a wide range of dissolution conditions. k_d tended to be slightly larger than z, particularly for profiles with over 80% dissolved for the fixed diffusion layer thickness model. From fits to previously reported dissolution profiles, fitted k_d and z values were very similar. Findings show that the one-parameter Polli equation provides an effective, simplified alternative to the z-factor model without a substantial change in parameter value in representing monodisperse or polydisperse particle dissolution across a wide range of dissolution conditions.