Psoralea, as a Chinese medicinal herb, is distributed throughout the world. Psoralen, a heterocyclic aromatic compound, is one of the main active ingredients of psoralea, and is increasingly being utilized in dermatology for the photochemotherapy of diseases.1-3 The use of psoralen in medicine has been associated with a higher incidence of skin cancer. 4,5 Therefore, it is significant to quantify psoralen (PSO) in biological fluids. Several HPLC methods have been reported for the determination of psoralens [6][7][8][9][10][11][12] in callus cultures, vitro culture, plants, and citrus essential oils. The gas chromatography method has been demonstrated for determination of psoralens in phytomedicines. 13 However, these methods are either troublesome or timeconsuming. It is necessary to explore more simple methods for the determination of PSO in complicated systems.With the increasing popularity of advanced instrumentation that generates multidimensional data array for each sample, trilinear decomposition models have become an area of much current activity in chemometrics research. [14][15][16][17][18] The attractive merit derived from three-way data arrays is attributed to that several components of interest can be quantified even in the presence of unknown interferents, usually called a "secondorder advantage". [19][20][21] Generally, algorithms for the decomposition of three-way data arrays can be divided into two categories. One approach is based on generalized eigenanalysis to resolve the data arrays, which typically works well when the signal-to-noise ratio is high, with the well-known examples of the generalized rank annihilation method (GRAM) 22-24 and the direct trilinear decomposition (DTLD) method. [25][26][27] Unfortunately, GRAM is constrained to use only one standard and one mixture sample at a time. Although the DTLD method allows for a direct solution through multiple samples, it requires the construction of two pseudosamples, which unavoidably causes a loss of information in multiple samples.Furthermore, these approaches may occasionally yield imaginary solutions and exhibit inflated variance. An alternative approach is an iterative one, [28][29][30][31][32][33][34][35][36][37][38][39][40][41] represented by parallel factor analysis (PARAFAC), proposed by Harshman.
38These have successfully solved many practical problems, such as environmental monitoring, 42 This paper describes a newly developed approach, an alternating normalization-weighted error (ANWE) method, and PARAFAC for the trilinear analysis of excitation-emission matrix fluorescence data. The results demonstrated that the determination of PSO can be conveniently achieved in plasma samples using excitation-emission matrix fluorescence coupled to second-order calibration, and that the performance of the ANWE method is similar or better than that of PARAFAC.
NomenclatureThroughout this paper, scalars are represented by lower-case italics: bold lower-case characters mean vectors; bold capitals designate two-way matrices; underlined bold ...