Stability parameter estimation at ambient temperature from studies at elevated temperatures

The determination of specific kinetic constants k(i) in pH-profile studies is often undertaken at ambient temperature. However, when dealing with a drug substance that is stable at ambient temperature, the pH-profile study is conducted at a chosen elevated temperature and the kinetic parameters are given at this particular elevated temperature. But in stability studies we generally need kinetic constants at ambient or storage temperature for practical reasons (information and storage conditions of formulation). To assess this ambient kinetic information from studies at elevated temperatures, cumulative sequential steps are usually employed with very few statistical concerns on the final estimates. The statistical problems on these final estimates in cumulative procedures are highlighted in many papers. Because these stability parameters are useful for drug formulation and storage conditions, good practical decisions have to be made on the basis of statistically unbiased identified parameters. We propose in this paper a nonlinear model that allows the direct determination of specific activation energies E(ai) that are linked to the specific kinetic constants k(i). Hence, a mathematical relationship between drug concentration C, pH, temperature T, and time t is obtained. Kinetic data from acetylsalicylic acid (ASA) hydrolysis (first-order kinetics) are used to validate the model. The results show that it is possible to obtain directly, by an extrapolation procedure, the kinetic parameters (specific kinetic constants k(i), specific activation energies E(ai), and dissociation constant pK(a)) at low temperature from data gathered at elevated temperatures using more meaningful statistics.