Supplementary Material
Determination of Aqueous Antibiotic Solutions Using SERS Nanogratings
Koh Yiin Hong1, Carlos Diego Lima de Albuquerque1,2, Ronei J. Poppi2, Alexandre G. Brolo1,3* (1) Department of Chemistry, University of Victoria, Victoria, BC V8P 5C2, Canada (2) Institute of Chemistry, University of Campinas (Unicamp), CP 6154, 13084-971 Campinas, São Paulo, Brazil. (3) Center for Advanced Materials and Related Technologies (CAMTEC), University of Victoria, Victoria, BC, V8W 2Y2, Canada * Email:
[email protected], Telephone: 1 (250) 721-7167, Fax: 1 (250) 721-7147
Theory and application
Multivariate Curve Resolution (MCR) [1] is a class of algorithms useful to solve mixed signals where the traditional univariate methods are not able to carry out. Among of MCR methods, the Non-Negative Matrix Factorization (NMF) showed to be useful for imaging processing [2], when it was compared with other traditional decomposition methods, such as Principal Components Analysis (PCA) and Vector quantization (VQ). The NMF can be applied in environmental data processing, where it is not required prior knowledge about the analyte. NMF method has also been used in separation of overlapping chromatograms [3], deconvolution of fluorescence spectra [4] and to solve complex gene expression data [5]. Albuquerque and Poppi [6] applied the NMF with alternating least square algorithm (NMF-ALS) for in situ detection of an important environmental contaminant (Malathion) in fruits peels without pre-treatment of sample. The authors related that the proposed method was useful to recover the pesticide spectrum even in the presence of several regions of overlapping with the fruit spectra. Additionally, the recovered spectrum was easily assigned to the signature of the analyte in solution. Moreover, this method showed be very sensitive, where the limit of detection for Malathion was estimated to 0.1 ppm. Although several works in the literature show useful advantages of NMF and NMF-ALS algorithm most of them tackle signal resolution problems [2-4,6] and semi-quantitative [5] approaches. Recently, Albuquerque and Poppi [7] presented the first quantitative approach of NMFALS with multi-correlation constraint (MCC) method to achieve the multi-product calibration of melamine simultaneously in two different milks (UHT and infant formula). This NMF-ALS with MCC was able to determine the melamine in the presence of interferences, even in the presence of matrix effect due the different lacteal matrices with several chemical compositions. The limit of detection achieved was around 0.3 mg L-1 which is lower than the maximum residue limit established. Those applications prove the ability of NMF method to solve complex analytical problems and therefore we used it in this present work. The goal of NMF resolution method is to obtain the scores and loadings that contain the information about the analyte without the interferences from the data original matrix of mixtures. Figure S1 shows a typical scheme of the NMF-ALS decomposition to
generate a so-called pseudo-calibration curve (scores values versus known concentration) through processing of the chemical images used in this work.
Figure S1. Typical scheme showing the NMF-ALS method to processing and to achieve calibration curves from hyperspectral images.
The hyperspectral cubes (X × Y × λ) representing each map of concentrations of the analyte are unfolded generating an augmented matrix ( D ). The D matrix is called augmented because it contains the spectra of all pixels. Therefore, pixels and SERS intensities are in the row-wise and column-wise directions, respectively. D can be decomposed in tree other matrices: C (scores), ST (loadings), and E (error matrix). The C and ST stores the information about the concentration in the pixels and the unmixing calculated spectra of analyte. Therefore, the C and ST can be used to calibrate (dash line) or to evaluate the distribution of the analyte onto the surface (distribution maps), and to certify the analyte identity by comparing with the pure spectrum of the analyte in solution. The E matrix stores the residuals non-modeled (uncorrelation information: noise, baseline effect) by NMF-ALS algorithm. The average scores ( S ) in each image can be directly related with the concentration of analyte, since the method relates the average scores versus nominal concentrations, instead the usual signal instrumental versus nominal concentrations.
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