Food Chemistry 145 (2014) 625–631

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Food Chemistry journal homepage: www.elsevier.com/locate/foodchem

Analytical Methods

An application of wavelet moments to the similarity analysis of three-dimensional fingerprint spectra obtained by high-performance liquid chromatography coupled with diode array detector Hong Lin Zhai ⇑, Bao Qiong Li, Yue Li Tian, Pei Zhen Li, Xiao Yun Zhang College of Chemistry & Chemical Engineering, Lanzhou University, Lanzhou 730000, PR China

a r t i c l e

i n f o

Article history: Received 21 October 2012 Received in revised form 18 May 2013 Accepted 28 August 2013 Available online 5 September 2013 Keywords: Three-dimensional fingerprint spectra Traditional chinese medicine Similarity analysis Shape feature Wavelet moment

a b s t r a c t More and more the three-dimensional (3D) fingerprint spectra, which can be obtained by high performance liquid chromatography coupled with diode array detector (HPLC-DAD), are applied to the analysis of drugs and foods. A novel approach to the similarity analysis of traditional Chinese medicines (TCMs) was proposed based on the digital image processing using 3D HPLC-DAD fingerprint spectra. As the one of shape features of digital grayscale image, wavelet moments were employed to extract the shape features from the grayscale images of 3D fingerprint spectra of different Coptis chinensis samples, and used to the similarity analysis of these samples. Compared with the results obtained by traditional features including principal components and spectrum data under single-wavelength, our results represented the more reliable assessment. This work indicates that the better features of fingerprint spectra are more important than similarity evaluation methods. Wavelet moments, which possess multi-resolution specialty and the invariance property in image processing, are more effective than traditional spectral features for the description of the systemic characterisation of mixture sample. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Traditional Chinese medicines (TCMs) have been widely used in Asian countries, especially in China for thousands of years. A TCM sample is often a complex mixture containing many chemical components, and the therapeutic effect is based on the synergic effect of its major components (van Beek & Montoro, 2009). However, the compositions of the pharmacologically active components in the same kind of TCMs are different due to their different geographical locations, climate, saving conditions, pretreatments and other factors, which directly influence therapeutic effects. With more and more countries and regions in the world have accepted TCMs, there is an necessary task to develop an accurate method for the quality control and assessments of TCMs. As a strategy for the assessment of TCMs, the fingerprint techniques have been widely applied owing to emphasis on the systemic characterisation of the chemical compositions in TCMs, especially chromatographic fingerprint techniques have been regarded as the first choice by WHO (World Health Organisation) and other organisations (FDA, 2000; WHO, 2002). State Food and Drug Administration of China (SFDA) suggested that all of herbal should be evaluated by their chromatogram

⇑ Corresponding author. Tel.: +86 931 8912596; fax: +86 931 8912582. E-mail address: [email protected] (H.L. Zhai). 0308-8146/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.foodchem.2013.08.112

similarities, which derive from the correlation coefficient and/or cosine value between samples and their standards (China, 2002). High-performance liquid chromatography (HPLC) fingerprint analysis has been drawn much attention owing to its higher resolving power, rapidity, simplification and reproducibility. And the similarity analysis is a conventional method that describes the similarity or difference of the fingerprints quantitatively. Up to now, there are many methods to compute similarities, such as the cosine of angle, Pearson correlation coefficient and Euclidean distance. However, the traditional HPLC fingerprint spectra (obtained at a single-fixed wavelength, and contained only chromatographic information) are not to reveal the systemic characteristic of complex sample completely, and not sensitive enough to distinguish the difference among many TCM samples. At the same time, the selection of single-fixed wavelength has certain subjectivity. It has been found that the similarity results obtained under different wavelengths maybe different (Yan, Xin, Luo, Wang, & Cheng, 2005). In addition, based on the chromatographic spectra directly, the similarity analysis is often affected by many factors such as noise signals, the shifts of peaks and baseline. HPLC coupled with photodiode array detector (DAD) has become the most common instrument in many analytical laboratories. Utilising the specialty of multi-wavelength in DAD, HPLC-DAD fingerprint spectra in the three-dimensional (3D) space of wavelength-retention time- absorption intensity can be readily

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available. Owing to including the chromatographic information under various wavelengths and the UV spectra at different retention times, the 3D fingerprint spectra can reveal the quality characteristic of TCMs completely (Zhai, Hu, Huang, & Chen, 2010). Therefore, the similarity analysis based on the 3D fingerprint spectra of TCMs should be more objective, and the results obtained have higher accuracy. Although principal component analysis (PCA) and partial least squares (PLS) analysis were introduced into the extraction of the most influential components in matrix measured for the similarity analysis (Ni, Liu, & Kokot, 2011; Yan et al., 2005), the most of researchers only used DAD to select a suitable single-fixed wavelength. The similarity of the 3D fingerprint spectra is the matching result of fingerprint spectra in the 3D space, which means the comparison of entire spectra. Direct comparison of 3D fingerprint spectra is a hard task. In PCA or PLS analysis, regarding the different wavelengths or retention times as original variants only emphasise the chromatographic or UV spectral information. When the 3D HPLC-DAD fingerprint spectrum of a TCM sample was transformed into grayscale image, this image represented spectrum completely. Thus the similarity analysis of 3D fingerprint spectra is turned into the matching analysis of these images. Image processing techniques have been applied to many fields, such as passport recognition and face verification (Kim & Kim, 2008), aircraft recognition in infrared image (Zhang, Liu, Wang, & Guan, 2009), biological shape characterisation of automatic image recognition and diagnosis of protozoan parasites (Castañón, Fraga, Fernandez, Gruber, & da F Costa, 2007), grayscale medical image annotation (Setia, Teynor, Halawani, & Burkhardt, 2008). The quantitative analyses and hierarchical clustering of the different TCM samples were carried out based on the density analysis of digital grayscale images for the 3D spectra of HPLC-DAD (Zhai et al., 2010). In this work, the 3D fingerprint spectrum obtained from HPLC-DAD was translated into digital grayscale image, and the wavelet moments as the shape features of this digital image were calculated and employed to the similarity analysis. 2. Materials and methodology 2.1. Samples and data Coptis chinensis is a kind of traditional Chinese medicine materials. Ten samples derived from different procedures, batches and pretreatments in two manufactories were collected. The column of Kromasil ODS (4.6 mm  150 mm, 5 lm) and the guard column of Kromasil ODS (4.6 mm  10 mm, 5 lm) were used. The mobile phases were composed of NaH2PO4 (0.2 mol/L): SDS (7.00 mmol/ L): acetonitrile (35:35:30, V:V:V). The flow rate was 1.0 mL/min, and the column compartment was kept at the temperature of 30 °C. The injection volume was 10 lL. The 3D fingerprint spectra of the samples were measured and generated by HPLC (Waters 2965, USA) coupled with DAD (Waters 2996, USA), which included noise signals and the drifts peaks under the same chromatographic conditions. The absorption intensities in the 3D spectrum were recorded as an n-by-m data matrix, in which the n rows correspond to the retention times from 0 min to 12.5 min (total 744 points), the m columns to the wavelengths from 210 nm to 496 nm (total 242 points). As an example, the 3D fingerprint spectrum of one sample is depicted in Fig. 1a.

turns into a grayscale image. The inverted grayscale image of Fig. 1a is shown as Fig. 1b. Compared Fig. 1a with Fig. 1b, we can find that the different peaks in the 3D fingerprint spectrum of HPLC-DAD correspond to the different densities of regions in the grayscale image completely. 2.2.2. The calculation of wavelet moments The calculation of wavelet moments has been well described in many monographs and articles (Murtagh & Starck, 2008; Reginska & Wakulicz, 2009; Shen & Ip, 1999; Zhang et al., 2009). Here a brief description is given as follows: Let f(x,y) represents the density distribution function of a image in Cartesian coordinates, and the geometric moments of (p + q) order are defined as:

Mpq ¼

Z Z

f ðx; yÞxp yq dxdy ðp; q ¼ 0; 1; 2 . . .Þ

ð1Þ

In polar coordinates, there are x = rcos(h) and y = rsin(h). Substitute them into Eq. (1), and the general expression of moments can be obtained as follows:

F p;q ¼

Z Z

f ðr; hÞg p ðrÞejqh rdrdh ðjrj 6 1; 0 6 h 6 2pÞ

ð2Þ

When the expression of gp(r) adopts function wm,n(r), the Eq. (2) gives wavelet moments. A set of wavelet basis functions can be generated by translation and scaling the mother wavelet, written as:

  1 rb wa;b ðrÞ ¼ pffiffiffi w a a

ð3Þ

where, a is the scaling factor, b is the shift factor, and w(r) is mother wavelet function. For the digital image, parameters a and b in Eq. (3) can only take discrete values. Suppose a = 2m (m = 0, 1, 2,. . .) and b = n2m (n = 0, 1, 2,. . ., 2m+1), the wavelet function is changed into: m

wm;n ðrÞ ¼ 2 2 wð2m r  nÞ ðm ¼ 0; 1; 2; . . . ; n ¼ 0; 1; 2; . . . ; 2mþ1 Þ

ð4Þ

In this work, cubic B-spline function was adopted as mother wavelet function. Here it is presented (Shen & Ip, 1999):

4anþ1 ð2r  1Þ2 wðrÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rw cosð2pf0 ð2r  1ÞÞ exp  2 2rw ðn þ 1Þ 2pðn þ 1Þ

! ð5Þ

in which, n = 3, a = 0.697066, f0 = 0.409177, and r2w = 0.561145. From Eqs. (2) and (4), the expression of wavelet moments is obtained:

Z Z

f ðr; hÞwmn ðrÞejqh rdrdh Z  Z Z ¼ wmn ðrÞr f ðr; hÞejqh dh dr ¼ Sq ðrÞwmn ðrÞrdr

W mnq ¼

ð6Þ

R where, Sq ðrÞ ¼ f ðr; hÞejqh dh Generally, the wavelet moment invariants (Fmnq) are denoted from Eq. (6):

F mnq ¼ jjW mnq jj ¼ jj

Z

Sq ðrÞwmn ðrÞrdrjj

ðm ¼ 0; 1; 2; 3; . . . ; n ¼ 0; 1; . . . ; 2mþ1 ;

ð7Þ and q ¼ 0; 1; 2; 3; . . .Þ

2.2. Analytical method of similarity 2.2.1. The digital image of 3D spectrum The data in two-dimensional table (intensity matrix, 744*242) was transformed to grayscale values, and then the 3D spectrum

2.2.3. Similarity measurement The cosine of angle method is often used to describe the similarity and dissimilarity among the fingerprint spectra quantitatively. Supposed that there are two fingerprint spectra, and their feature

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Fig. 1. The fingerprint spectrum of one sample (a) the three-dimensional spectrum obtained with HPLC-DAD (b) the inverted digital grayscale image of the 3D HPLC-DAD spectrum.

vectors are denoted as X and Y, respectively. The cosine of the angle:

Pm i¼1 xi yi R ¼ cosðhÞ ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Pm 2 Pm 2 i¼1 ðxi Þ i¼1 ðyi Þ

ð8Þ

where, m is the number of features, and xi(yi) is the ith feature in X(Y). According to Eq. (8), the similarity values can be calculated among these samples, and then the distances of similarity values can be used to construct a diagram (clustering tree). The cophenet-

ic correlation coefficient (C) proposed by Sokal and Rohlf (Sokal & Rohlf, 1962) for the hierarchical cluster tree is defined as the linear correlation coefficient between the cophenetic distances of similarity values obtained from the tree. It can be described as follows:

P

 zÞ  dÞðZ ij   P 2  2 i