Data analysis of kinetic modelling used in drug stability studies: isothermal versus nonisothermal assays

Kinetic modelling was applied to predict the stability of cholecystokinin fragment CCK-4 in aqueous solution, which was analyzed by isothermal and nonisothermal methods using a validated stability indicating HPLC method.

The isothermal studies were performed in the temperature range 40 to 80 degrees C at pH 12 and ionic strength 0.01 M as constants, whereas nonisothermal stability studies were performed using a linear increasing temperature program, heating rate 0.25 degrees C/h and a temperature interval 40-82 degrees C. The isothermal studies require two-step linear regression to estimate the parameters, resulting in a well-defined confidence interval. Nonisothermal kinetic studies require nonlinear or linear regression by previous transformation of data to estimate the parameters. In this case, the two most popular approaches, derivative and integral, were used and compared.

Under isothermal conditions, an apparent first-order degradation process was observed at all temperatures. The linear Arrhenius plot suggested that the CCK-4 degradation mechanism was the same within the studied temperature range, with quite large uncertainties due to the small number of degrees of freedom based only on the scatter in the plot, and giving an estimated shelf life at 25 degrees C of 35.2 days. The derivative approach yields high variability in the Arrhenius parameters, since they are dependent on the number of polynomial terms chosen, so several statistical criteria were applied to select the best model. The integral approach allows activation parameters to be calculated directly from experimental data, and provides results in good agreement with those of the traditional method, but have the advantage that the uncertainty in the final result directly reflects the goodness of fit of the experimental data to the chosen kinetic model. The application of the bootstrap technique to estimating confidence limits for the Arrhenius parameters and shelf life is also illustrated, and shows there is no difference between the asymptotic and bootstrap confidence intervals.

Nonisothermal studies give us fast and valuable information about drug stability, although their potential for predicting isothermal behaviour is conditioned by the data analysis method applied.