Selecting the particle size distribution for drugs with low water solubility mathematical model

Purpose: To introduce guidelines in selecting the particle size distribution (n0, cm^-1) that will guarantee optimal oral absorption for drugs with low solubility. Methods: Unlike other multi-compartmental models the gastrointestinal tract is modeled as a continuous tube with spatially varying properties. The transport through the intestinal lumen is described using the dispersion model. The model accounts for the dissolution of poly-dispersed powders. Results: The model was used to examine the sensitivity of the absorption on permeability (P) and water solubility (Cs) following administration in different log-normal powders. The absorption exhibits inverse sigmoidal dependence on the mean particle size (rm, m) regardless of the administrated dose or drug properties. Thus, there is an optimal rm that maximizes the benefit-cost ratio of the formulation; finer particles do not improve the absorption while coarser particles decrease it. Using the model we find that the optimal rm depends mainly on the drug Cs and on the geometrical standard deviation (gSTD). Conclusions: The results of this work provide the formulator with guidelines to select both rm and gSTD that guarantee optimal absorption.