Moore–Penrose generalized inverse mixture design applied in low‐density dispersive liquid–liquid microextraction

• Published in: Journal of chemometrics Vol. 34; no. 12
• Main Authors: Bazzana, Matheus Julien Ferreira, Saczk, Adelir Aparecida, Faria, Letícia Rodrigues, Campos, João Pedro, Alves, Nadja Gomes, Borges, Cleber Nogueira
• Format: Journal Article
• Language: English
• Published: Chichester Wiley Subscription Services, Inc 01.12.2020
• Subjects: Animal tissues; blood serum; Density; Design; Design modifications; Dispersion; Fatty acids; Generalized inverse; linoleic acid; Mass transfer; Metabolism; Microorganisms; miniaturized technique; mixture design; Parameter estimation; Polynomials; ruminants
• ISSN: 0886-9383; 1099-128X
• DOI: 10.1002/cem.3275

The modification in the nutritional composition of the ruminant diet causes significant alterations in the fatty acids (FAs) structure supplemented because of the action of rumen microorganisms. The modification in the FAs structure alters the role that these play in the ruminant metabolism. The Folch method is the most often used to determine fatty acids in these animals' tissues and presents certain disadvantages such as the great volume of solvent and low mass transfer from the analyte to the extracting phase. Thus, we tested the low‐density dispersive liquid–liquid microextraction (LD‐DLLME) as an alternative method to determine these substances. In this paper, a simples‐augmented mixture design was used. The Scheffé's polynomial was applied in that design, and Moore–Penrose generalized matrix inverse was used because of the possibility of concurrently determining value estimates of coefficients of the parameters that represent cubic terms. The application of the modeling allowed the chemical interpretation of the LD‐DLLME best extraction condition for linoleic acid in ruminant serum samples. In this paper, we propose the application of Moore–Penrose generalized inverse to determine Scheffé full cubic model and concurrently determine the three coefficients dij. This procedure allows the chemical interpretation of Scheffé's mixture model, making it possible to optimize the LD‐DLLME extraction technique to determine linoleic acid in ruminant serum samples.