Within the world of chemometrics, design of experiment (DoE) is a multivariate technique whose application should be desirable in any research study. It aims at rationally planning the experiments to gain the maximum information of a chemical system with the minimum experimental effort 1,2. Despite being introduced almost a century ago (1935), it is still not widely employed by chemists and its usefulness continues to be underestimated. The application of one or more suitable experimental designs allows to perform a reasonable number of experiments to optimize even very complex analytical problems, avoiding the costly and tedious OVAT strategy. Indeed, through the application of response surface methodology, simple mathematical models can be built, relating the independent variables to the considered response(s), thus estimating effects and interactions. Depending on the research stage, as well as available time and costs, a “fit-for-purpose” experimental design can be chosen among screening designs (full factorial, Plackett-Burman) and response surface designs (central composite, Box-Behnken…). Herein, several applications of DoE in both sample preparation and instrumental analysis are presented, also highlighting the importance of combining DoE with other simple chemometric tools, such as principal component analysis. Generally, when several variables hypothetically influence more responses, a first screening followed by a response surface design is necessary. This approach was applied to maximize the QuEChERS-LC-MS/MS method accuracy in the determination of phytoestrogens in soy-based food. A Plackett-Burman design was used to explore the significance of 7 variables, 3 of which were then studied by a Box-Behnken design. Satisfactory mathematical models were obtained for the 10 responses involved, and a pareto-front strategy was employed to find the compromise for the optimal conditions. The power of DoE is particularly evident when dealing with chromatographic separations. A central composite design allowed to understand the effect of flow, temperature and gradient velocity on peak resolution of 21 bioactive compounds, analysed by non-aqueous reverse phase chromatography. In less than one day of analysis (just seventeen runs) the data were collected and the best conditions to separate coeluted peaks were defined. The extraction of 16 polycyclic aromatic hydrocarbons (PAHs) from complex matrices was optimized in three different applications, by employing suitable experimental designs and by combining DoE with PCA. Two studies regarded the magnetic molecular imprinted polymer dispersive extraction from seawater and plant extracts, respectively. In the first, 9 variables were studied by a screening design of 12 experiments and the correlation among responses was investigated by PCA. Two models (instead of 16) were built and revealed that only one variable significantly affected the recovery, with a consequent rapid optimization. In the second study, the D-optimal design was employed, defining the most informative experiments to explore the effect of 4 variables on the PAHs recovery (with 18 experiments). Finally, a recent work regarded the optimization of a SPME method for the PAHs analysis in plant material, for which two sequential central composite designs were employed, since the first gave indications on a better region of the experimental domain to explore. In both cases, the models were built after an exploratory data analysis by PCA and the optimal conditions were rapidly identified. All these case studies demonstrate that DoE represents the winning strategy to face complex chemical problems and solve them in a costly- and timely-effective manner.
The power of DoE: how to solve complex analytical problems by multivariate optimization strategies
Barbara Benedetti
2023-01-01
Abstract
Within the world of chemometrics, design of experiment (DoE) is a multivariate technique whose application should be desirable in any research study. It aims at rationally planning the experiments to gain the maximum information of a chemical system with the minimum experimental effort 1,2. Despite being introduced almost a century ago (1935), it is still not widely employed by chemists and its usefulness continues to be underestimated. The application of one or more suitable experimental designs allows to perform a reasonable number of experiments to optimize even very complex analytical problems, avoiding the costly and tedious OVAT strategy. Indeed, through the application of response surface methodology, simple mathematical models can be built, relating the independent variables to the considered response(s), thus estimating effects and interactions. Depending on the research stage, as well as available time and costs, a “fit-for-purpose” experimental design can be chosen among screening designs (full factorial, Plackett-Burman) and response surface designs (central composite, Box-Behnken…). Herein, several applications of DoE in both sample preparation and instrumental analysis are presented, also highlighting the importance of combining DoE with other simple chemometric tools, such as principal component analysis. Generally, when several variables hypothetically influence more responses, a first screening followed by a response surface design is necessary. This approach was applied to maximize the QuEChERS-LC-MS/MS method accuracy in the determination of phytoestrogens in soy-based food. A Plackett-Burman design was used to explore the significance of 7 variables, 3 of which were then studied by a Box-Behnken design. Satisfactory mathematical models were obtained for the 10 responses involved, and a pareto-front strategy was employed to find the compromise for the optimal conditions. The power of DoE is particularly evident when dealing with chromatographic separations. A central composite design allowed to understand the effect of flow, temperature and gradient velocity on peak resolution of 21 bioactive compounds, analysed by non-aqueous reverse phase chromatography. In less than one day of analysis (just seventeen runs) the data were collected and the best conditions to separate coeluted peaks were defined. The extraction of 16 polycyclic aromatic hydrocarbons (PAHs) from complex matrices was optimized in three different applications, by employing suitable experimental designs and by combining DoE with PCA. Two studies regarded the magnetic molecular imprinted polymer dispersive extraction from seawater and plant extracts, respectively. In the first, 9 variables were studied by a screening design of 12 experiments and the correlation among responses was investigated by PCA. Two models (instead of 16) were built and revealed that only one variable significantly affected the recovery, with a consequent rapid optimization. In the second study, the D-optimal design was employed, defining the most informative experiments to explore the effect of 4 variables on the PAHs recovery (with 18 experiments). Finally, a recent work regarded the optimization of a SPME method for the PAHs analysis in plant material, for which two sequential central composite designs were employed, since the first gave indications on a better region of the experimental domain to explore. In both cases, the models were built after an exploratory data analysis by PCA and the optimal conditions were rapidly identified. All these case studies demonstrate that DoE represents the winning strategy to face complex chemical problems and solve them in a costly- and timely-effective manner.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
