Design of experiments, a powerful tool for method development in forensic toxicology: Application to the optimization of urinary morphine 3-glucuronide acid hydrolysis

The application of the design of experiments to optimize method development in the field of forensic toxicology using the urinary morphine 3-glucuronide acid hydrolysis as an example is described. Morphine and its trideuterated analogue (used as an internal standard) were extracted from urine samples by liquid-liquid extraction (ToxiTubes® A) and derivatized by silylation. Chromatographic analysis was done by gas chromatography-mass spectrometry in the selected ion monitoring mode. Using the peak area ratio (morphine-to-internal standard) as the response, we investigated the independent variables that could influence the acid hydrolysis, including temperature (range 70-130 °C), acid volume (range 500-1,000 μL) and time (range 15-90 min). A 2³ full factorial design for the screening and a response surface methodology, including a central composite design for optimization, were applied. The factors which influenced the response to a greater extent were temperature and its interaction both with time and acid volume. By application of a multiple regression analysis to the experimental data, a second-order polynomial equation was obtained. The optimal predicted conditions for morphine 3-glucuronide acid hydrolysis were 115 °C, 38 min and 500 μL for temperature, time and acid volume, respectively. Using design of experiments, instead of the one factor at a time approach, we achieved the optimum combination of all factor values, and this allowed the best results to be obtained, simultaneously optimizing resources. In addition, time and money can be saved, since other approaches are in general more time-consuming and laborious, and do not take into account the interactions between factors.