Extension of Trilinear Decomposition Method with an Application to the Flow Probe Sensor

Booksh, Karl S.; Lin, Zhihao; Wang, Ziyi.; Kowalski, Bruce R.

doi:10.1021/ac00087a022

Cited by 145 publications

(51 citation statements)

References 7 publications

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“…where NAS i is the net analyte signal for component i (that is, the signal unique to that component), and S is the total signal for the sample collected [27,28]. In geometrical terms, the NAS is the sine of the angle between the signal for component i projected onto the subspace defined by all other components in the sample [29].…”

Section: Theorymentioning

confidence: 99%

Evaluation of the multivariate selectivity of multi‐way liquid chromatography methods

Cantwell

Porter

Rutan

2007

Journal of Chemometrics

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Multivariate figures of merit are used to characterize the sensitivity, selectivity, and precision of multi-dimensional liquid chromatography (LC) methods. Specifically in this work, we used a multivariate selectivity parameter to characterize the performance of orthogonal LC and twodimensional liquid chromatography (2D-LC) methods with and without diode array detection (DAD), and to aid in the optimization of these new separation approaches. We found that the average selectivity of 47 drug compounds was increased by as much as 58% upon the addition of a second, orthogonal separation. We also found that the selectivity for some individual drug compounds improved by more than a factor of two when DAD detection was used compared to single wavelength detection. In the comprehensive 2D-LC simulations, using a multi-channel detector increased the average selectivity of 500 components by 7.3% for a 21 s cycle time. The multivariate selectivity parameter was shown to be useful for determining the information gained when additional dimensions of data are collected on multi-dimensional instrumentation.

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Section: Theorymentioning

confidence: 99%

Evaluation of the multivariate selectivity of multi‐way liquid chromatography methods

Cantwell

Porter

Rutan

2007

Journal of Chemometrics

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“…It is to resolve the data arrays by utilizing an eigenanalysis-based procedure, which typically works well when the signal-to-noise ratio is high. The generalized rank annihilation method (GRAM) [15][16][17] and the direct trilinear decomposition (DTLD) method [18][19][20] are wellknown examples. Unfortunately, GRAM is constrained to use only one standard and one mixture sample at a time.…”

Section: 14mentioning

confidence: 99%

Determination of Daunomycin in Human Plasma and Urine by Using an Interference-free Analysis of Excitation-Emission Matrix Fluorescence Data with Second-Order Calibration

et al. 2006

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IntroductionDaunorubicin (DNR), discovered in the early 1960s, is an anthracycline antibiotic with antiblastic and anticancer activity, which is linked by the formation of intercalative complexes with DNA and the inhibition of both DNA and RNA synthesis. Although it still remains an important component for many current chemotherapy protocols of acute and myelogenous leukemia, cardiotoxicity is a serious problem, especially in the case of overdoses.1 It is thus important for determining DNR in human plasma and urine. Various instrumental methods, such as polarography, 2 high-performance liquid chromatography, 3-5 the enzymatic immunological method, 6 voltammetry, 7 capillary electrophoresis, 8,9 and electrospray ionization mass spectrometry 10 have been reported for DNR determination in biological fluids and in dosage forms. However, these methods are either troublesome or time-consuming.With the development of modern analytical instrumentation that generate a multidimensional data array for each sample, multiway data arrays have been prominently useful for the quantitative analysis of complex multicomponent samples. Particularly, three-way data arrays following the trilinear model, such as excitation-emission fluorescence matrices, have been gaining widespread analytical acceptance. 11Although, interestingly, there are many models for three-way data arrays, only the PARAFAC model ensures uniqueness in a straightforward way. 12In addition, the decomposition of a three-way data array built with response matrices measured for many samples is often unique, allowing relative concentrations and spectral profiles of individual sample components to be extracted directly. That is, the analysis of several components of interest can be quantified even in the presence of unknown interferents, commonly called the "second-order advantage". 13,14The different multiway methods used to resolve multicomponent mixtures belong to three main groups. The first group is direct solution. It is to resolve the data arrays by utilizing an eigenanalysis-based procedure, which typically works well when the signal-to-noise ratio is high. The generalized rank annihilation method (GRAM) 15-17 and the direct trilinear decomposition (DTLD) method 18-20 are wellknown examples. Unfortunately, GRAM is constrained to use only one standard and one mixture sample at a time. Although the DTLD method takes into account a direct solution through multiple samples, it is required to construct two pseudosamples, which unavoidably results in the loss of information in multiple samples. In addition, these methods may occasionally produce imaginary solutions and exhibit inflated variance. The second main group includes least-squares methods. Bilinear least squares (BLLS) is a recently introduced technique, based on a direct least-squares procedure. 21,22 The third main group is an iterative one. 12,23-40 Iterative algorithms have been widely employed. The PARAFAC algorithm proposed by Harshman 34 is a representative method of the third group. These have succ...

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“…The Kowalski group has proposed the trilinear decomposition (TLD) method. 14,15 In this work we focused our attention on the ability of GRAM for analyzing the second-order data.…”

Section: Introductionmentioning

confidence: 99%

“…The Kowalski group has proposed the trilinear decomposition (TLD) method. 14,15 In this work we focused our attention on the ability of GRAM for analyzing the second-order data.Fluorescence spectroscopy is a versatile tool mainly used because of its selectivity and sensitivity. Fluorescence spectra can be recorded in difference modes such as emission, excitation, synchronous and excitation-emission matrix (EEM).…”

mentioning

confidence: 99%

Simultaneous Spectrofluorometric Determination of Piroxicam and Pyridoxine Using Generalized Rank Annihilation Method

2006

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One of the most serious problems that can occur in classical quantitative analysis is the presence of one or more spectral interferent-chemical species which affect the instrument response and which are unaccounted for in the calibration process. Advances in chemometric methods allow quantitative analysis in the presence of unidentified interferents if a threeway experimental data matrix is available for each sample. This property is the so-called "second-order advantage" 1 and it is based on the earlier work done in the psychometrics field. 2,3 The use of this advantage in analytical chemistry was proposed by Ho et al. 4 (rank annihilation factor analysis, RAFA), for the multicomponent analysis of fluorescent mixtures using excitation-emission matrix (EEM). Later, Lorber 5 and Sanchez and Kowalski 6 proposed new and simple solutions for the method of Ho et al. and now it is called the generalized rank annihilation method (GRAM).At present, analytical chemistry laboratories have instrumentation that easily generates multidimensional data structures of experimental data for each sample. Fluorescence is a particularly interesting technique because it allows, in a very straightforward manner, the acquisition of this type of information, of which the most typical example is the excitation-emission matrix (EEM). Several algorithms that use second-order data are described in the literature. [7][8][9] Of these, the generalized rank annihilation method (GRAM) 6,11,12 has interesting properties since it only requires two data matrices for quantification: one from the calibration sample and the other from the unknown sample. Recently, it has been proved that GRAM predicts results that are similar to those from the parallel factor analysis (PARAFAC) when only two samples are used, 9 so both methods can be useful as calibration methods for second-order data. But, unlike PARAFAC, GRAM is a non-iterative method which tries to implement the second-order advantage. Second-order calibration using GRAM has several distinct advantages. 13The most pronounced advantage is that it makes possible the quantification of the analyte(s) of interest in samples containing interferents. Those interferents can be completely unknown, that is, it is not necessary that they have been incorporated in the standards used for calibration. Another advantage is that it is possible to recover the individual instrument responses of the analyte(s) of interest, e.g., the excitation and emission spectra can be obtained for the individual analyte(s). This makes it possible to perform qualitative analysis and to check the identity of the analytes. The Kowalski group has proposed the trilinear decomposition (TLD) method. 14,15 In this work we focused our attention on the ability of GRAM for analyzing the second-order data.Fluorescence spectroscopy is a versatile tool mainly used because of its selectivity and sensitivity. Fluorescence spectra can be recorded in difference modes such as emission, excitation, synchronous and excitation-emission matrix (EEM). T...

show abstract

Extension of Trilinear Decomposition Method with an Application to the Flow Probe Sensor

Cited by 145 publications

References 7 publications

Evaluation of the multivariate selectivity of multi‐way liquid chromatography methods

Evaluation of the multivariate selectivity of multi‐way liquid chromatography methods

Determination of Daunomycin in Human Plasma and Urine by Using an Interference-free Analysis of Excitation-Emission Matrix Fluorescence Data with Second-Order Calibration

Simultaneous Spectrofluorometric Determination of Piroxicam and Pyridoxine Using Generalized Rank Annihilation Method

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