Comparison of different mathematical models for the tensile strength-relative density profiles of binary tablets

During the last decade the evolution of the pharmaceutical dosage form design has been important. In controlled release matrix tablets, the tensile strength is an essential parameter to consider, because a minimal mechanical strength is needed for tablet production, handling and avoidance of any dose dumping during its use. Recent developments in percolation theory led to the theoretical proposal of lattice strength that was applied to the tensile strength of tablets. This mechanical property was described as a power law of the relative density involving a critical value that corresponds to the percolation threshold. The objective of the present work is to estimate these mechanical thresholds in KCl-Ethocel100 tablets that were manufactured from different sieve fractions (100-150, 150-200, 250-300 microm). Three power law models are compared regarding the best fit of the tensile strength-relative density profiles. The main criteria for this choice are the Akaike's Information Criterion (AIC), the analysis of the residuals in conjunction with the soundest physical meaning of the models. Accordingly, a power law model was chosen that assumes an initial strength parameter. No correlation could be established between the different mixture ratios or sieve fractions with the critical relative densities. The study showed that an equation based on percolation theory can adequately model tablet strength-density profiles from matrix tablets.