Background correction in near-infrared spectra of plant extracts by orthogonal signal correction

Background correction in near-infrared spectra of plant extracts by orthogonal signal correction first-author corresp ‡Corresponding Author ‡Corresponding Author †E-mail:chengyy@zju.edu.cn †E-mail:chengyy@zju.edu.cn chengyy@zju.edu.cn Pharmaceutical Informatics Institute, Zhejiang University, Hangzhou 310027, China Pharmaceutical Informatics Institute, Zhejiang University, Hangzhou 310027, China In near-infrared (NIR) analysis of plant extracts, excessive background often exists in near-infrared spectra. The detection of active constituents is difficult because of excessive background, and correction of this problem remains difficult. In this work, the orthogonal signal correction (OSC) method was used to correct excessive background. The method was also compared with several classical background correction methods, such as offset correction, multiplicative scatter correction (MSC), standard normal variate (SNV) transformation, de-trending (DT), first derivative, second derivative and wavelet methods. A simulated dataset and a real NIR spectral dataset were used to test the efficiency of different background correction methods. The results showed that OSC is the only effective method for correcting excessive background. Background correction Plant extracts Orthogonal signal correction Near-infrared spectroscopy INTRODUCTION 1 When using near-infrared (NIR) spectroscopy to analyze plant extracts, excessive background often exists within the NIR spectra. It is mainly caused by the strong absorbance of the solvent, such as water and ethanol. In addition, the absorbance of the active constituents in plant extracts is often weak and disguised by the excessive background. It is necessary to correct the excessive background, but how to achieve this goal is still troublesome. The classical method to subtract background is to fit the background as a line or a polynomial curve. Offset correction is an old method applied to correct flat background (Candolfi et al., 1999 1999 ). Multiplicative scatter correction (MSC) (Geladi et al., 1985 1985 ) and standard normal variate (SNV) transformation (Barnes et al., 1989 1989 ) are proposed as methods for correcting multiplicative scatter effect in NIR spectra, but they can also be used to correct sloping background. De-trending (DT) (Karstang and Kvalheim, 1991 1991 ) is a method to correct curvilinear background by modelling the background as a function of wavelengths with a second-degree polynomial. But in many cases, the background is not as “ideal” as a line or a polynomial curve, so the above methods are inefficient. Another very common method for background correction is mathematical derivative of the spectrum (Tahboub and Pardue, 1985 1985 ) usually first derivative and second derivative. A flat background can be removed by first derivative, and a sloping background can be removed by second derivative. In fact, derivative can be seen as removing low-frequency components and amplifying high-frequency components of the spectrum. By selecting proper order of derivative, the background can be removed as low-frequency components, but meanwhile the noise is amplified. However, wavelet method is a more efficient method than derivative method. The spectrum can be decomposed into different frequency components by wavelet functions, and the background can be removed by setting the very-low-frequency components to zero values (Alsberg et al., 1997 1997 ), whereas the noise is not amplified and noise can be removed as very high frequency components (Barclay and Bonner, 1997 1997 ). Background correction based on wavelet had been reported. Ma and Zhang ( 2003 2003 ) applied wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry. Tan and Brown ( 2002 2002 ) developed a criterion based on Shannon entropy to judge and remove the low-frequency background reasonably and automatically. Mittermayr et al.( 2001 2001 ) removed the highly varying background successfully by wavelet vanishing moments. But when excessive background existed, the frequency contributions of analytical signal and background can hardly be discriminated, and then background cannot be separated from spectrum by derivative or wavelet method. Some methods based on multivariate calibration had been proposed for background correction. Schechter ( 1995 1995 ) proposed a method for correcting nonlinear fluctuating background by using two reference spectra with known concentrations. But it can only be used in monovariate analytical systems. Sun ( 1997 1997 ) proposed a PCA (Principal Component Analysis)-like method to remove the excessive background from a set of NIR spectra of human blood by assuming some of the principal components represented the background variations. A specially designed experiment was used to identify principal components whether they represented the excessive background or not, although the principal components representing background often contain the information of interest components and could not be removed. In practice, the complexity and the need of some prior knowledge restrict the application of these methods. Unfortunately, it seems that none of the classical methods are suitable for correcting excessive background. A new popular method called orthogonal signal correction (OSC) showing potential for correcting excessive background was introduced by Wold et al.( 1998 1998 ) for removing synthetical noise including background, scatter effect, etc. It works by removing the parts linearly unrelated (orthogonal) to the response of the calibration model. As a preprocessing method, OSC is widely and successfully applied to spectral analysis of NIR (Sjoblom et al., 1998 1998 ), NMR (Brindle et al., 2003 2003 ), and DRIFTS (Peussa et al., 2000 2000 ). In this paper, OSC and other common background correction methods were used to correct the excessive background. A simulated dataset and a real NIR spectral dataset were analyzed by different background correction methods, whose results showed that the OSC method is the only effective method for correcting excessive background. THEORY 1 The basic idea of OSC is very simple and can be understood easily. When pretreating the NIR spectra in multivariate analysis, we simply want to remove from the spectral matrix ( X ) only the part that is unrelated to the response matrix ( Y ), namely the part that is orthogonal (or as close as possible orthogonal) to the response matrix ( Y ). To achieve such orthogonality, the matrix X can be decomposed into score matrix T , which is required to be orthogonal to Y , and loading matrix P . To obtain the OSC score matrix T , different algorithms have been developed. (Wold et al., 1998 1998 , Sjoblom et al., 1998 1998 , Fearn, 2000 2000 ), direct orthogonalization (DO) (Andersson, 1999 1999 ), direct OSC (DOSC) (Westerhuis et al., 2001 2001 ), orthogonal projection to latent structures (OPLS) (Trygg and Wold, 2002 2002 ). A previous study of ours showed that the results obtained by different OSC algorithms were similar, and that the best were those of Sjoblom et al.( 1998 1998 ). So the Sjoblom’s OSC algorithm is used, which is described in the following text. For distinguishing ability, the final score vector, loading vector and weight vector of OSC are represented by t ⊥ , p ⊥ and w ⊥ . Before the calculations, X and Y are centered and scaled as usual. In the first step, the first principal component of X is calculated as the initial score vector, t . This ensures that t is an optimal linear summary of X . Then orthogonalize t to Y t new =(1− Y ( Y T t ) −1 Y T ) t Next, calculate a new weight vector w by $${\mathbf{w}}{\text{ = }}{{{\mathbf{X}}^{\text{T}} {\mathbf{t}}_{{\text{new}}} } \mathord{\left/{\vphantom {{{\mathbf{X}}^{\text{T}} {\mathbf{t}}_{{\text{new}}} } {({\mathbf{t}}_{{\text{new}}}^{\text{T}} {\mathbf{t}}_{{\text{new}}} )}}} \right.\kern-\nulldelimiterspace} {({\mathbf{t}}_{{\text{new}}}^{\text{T}} {\mathbf{t}}_{{\text{new}}} )}}$$ And scale w to unit length $${\mathbf{w}}{\text{ = }}{\mathbf{w}}/\left\| {\mathbf{w}} \right\|$$ Now calculate the new score vector t t = X w Repeat Eqs.( 1 1 )~( 4 4 ) until t becomes stable. The final t is now a good describer of the part of X that is orthogonal to Y . The next step is to build a PLS (partial least square) model with X calibrated against t . Proper PLS-components are selected to ensure that t is described well by the model. Calculate the prediction vector b ˆ of the PLS model as the weight vector w ⊥ of OSC, $${\mathbf{w}}_ \bot {\text{ = }}{\mathbf{\hat b}}{\text{ = }}{\mathbf{W}}({\mathbf{P}}^{\text{T}} {\mathbf{W}})^{ - 1} {\mathbf{q}}$$ where W is the weight matrix of the PLS model above, P is the loading matrix, q is the regression coefficient vector for the inner relation between t and the score matrix T . Then the score vector t ⊥ of OSC is calculated by $$t_ \bot = Xw_ \bot$$ And the loading vector p ⊥ of OSC is calculated by $${\mathbf{p}}_ \bot {\text{ = }}{\mathbf{X}}^{\text{T}} {\mathbf{t}}_ \bot /({\mathbf{t}}_{_ \bot }^{\text{T}} {\mathbf{t}}_ \bot )$$ The corrected spectra can be obtained by subtracting the orthogonal part from X , $${\mathbf{X}}_{{\text{OSC}}} {\text{ = }}{\mathbf{X}} - {\mathbf{t}}_ \bot {\mathbf{p}}_{_ \bot }^{\text{T}}$$ Several OSC-components can be removed by repeating the steps above. To correct the new spectra, a score matrix is first calculated. $${\mathbf{T}}_{{\text{new}}} {\text{ = }}{\mathbf{X}}_{{\text{new}}} {\mathbf{W}}_ \bot$$ And then the OSC-component is removed using loading matrix P ⊥ $${\mathbf{X}}_{{\text{OSC}}} {\text{ = }}{\mathbf{X}}_{{\text{new}}} - {\mathbf{T}}_{{\text{new}}} {\mathbf{P}}_{_ \bot }^{\text{T}}$$ EXPERIMENTAL DETAILS 1 Simulated dataset 2 The simulated data mimicked common NIR spectral data with excessive background. A simulated spectrum was obtained by adding a background (a broader Gaussian peak), an analytical signal (a narrower Gaussian peak), and normal distributed noise. The Gaussian peaks were generated by $$x_i {\text{ = }}A\exp [ - \frac{1}{2}(x_i - x_0 )^2 /\sigma ^2 ]$$ where A is the height at the centre, x 0 is the position of the centre and σ is the standard deviation of the Gaussian peak, and $$\sqrt {\text{2}} \sigma$$ is the peak width (Brereton, 2003 2003 ). A simulated dataset with 40 samples and 400 variables were used in this paper. The parameters x 0 , σ of background and analytical signal are shown in Table 1 1 . The peak heights A are proportional to concentrations for analytical signal, whereas the peak heights for background are random. The simulated spectra are shown in Fig. 1 1 . a: The simulated analytical signal, b: The simulated background Parameters Background Analytical signal x 0 180 250 σ 100 10 Real dataset 2 NIR spectral data on process analysis of purification of natural herb (Yang et al., 2003 2003 ) was used to test background correction methods. The eluting process of a natural herb, Coptis chinensis , was monitored by NIR spectroscopy simultaneously. The spectra were measured in the range 11 000 to 4 000 cm −1 with a resolution of 8 cm −1 (1816 points). Forty samples were obtained in eluting process (Fig. 2 2 ). The contents of an active constituent in Coptis chinensis , berberine were determined by HPLC. Computation 2 All computation was performed in Matlab Version 6.5. All wavelet transforms were achieved using the Mathworks wavelet toolbox for Matlab. RESULTS AND DISCUSSION 1 For evaluating the performances of the different background correction methods, calibration models were established by partial least square (PLS) regression in the corrected spectra. The datasets were divided into two sets, one for building PLS model (calibration set) and the other for validating the model (validation set). The optimal number of PLS components was determined by Leave-one-out Cross-Validation. The room mean square errors of correction (RMSEC, calibration set) and prediction (RMSEP, validation set) and the multiple correlation coefficient r 2 of two sets were calculated. Analysis of simulated dataset 2 The simulated data mimicked typical NIR spectral data with excessive background. The peak heights and widths of the background are obviously larger than those of the analytical signals (Fig. 1 1 ). Forty samples were randomly divided into two datasets, 20 in calibration set and the others in validation set. OSC and some classical background correction methods were selected for correction of excessive background. After being corrected by different background correction method, a PLS model of analytical signals was built. The results are shown in Table 2 2 . L.V. is the latent variables of PLS models 2 Correction methods 3 Calibration set 2 Validation set L.V. * * RMSEC r 2 RMSEP r 2 None 7 2.006 0.97430 3.536 0.88620 Offset correction 6 2.277 0.96690 4.447 0.81190 MSC 1 12.070 0.07027 10.200 0.03805 SNV 1 11.980 0.08472 10.330 0.05060 DT 4 2.331 0.96530 3.984 0.85500 First derivative 3 1.428 0.98700 3.172 0.91200 Second derivative 2 1.888 0.97720 10.080 0.11930 Wavelet 4 1.843 0.97830 2.947 0.91970 OSC 2 2.011 0.97420 2.533 0.94640 Without background correction, the RMSEP was 3.536 and the r 2 of the validation set was only 0.8862. The results showed that the prediction of PLS model should be improved. But after correcting by offset correction, MSC, SNV, DT and second derivative, poor results were obtained. It was clear that these methods were unsuitable for the correction of excessive background. The results of the correction by first derivative method and wavelet method were better than the original PLS, but still not acceptable. Use of OSC for correction yielded perfect result. The prediction error and complexity of models were decreased distinctly. Compared to original PLS, RMSEP decreased from 3.536 to 2.533, r 2 increased from 0.8862 to 0.9464, and latent variables of PLS models decreased from 7 to 2. The results of simulated dataset showed that OSC was the only effective method for excessive background correction. Analysis of the real dataset 2 In order to test the efficiency of OSC in practice, the method was tested by real NIR spectral data on Coptis chinensis extracts. Half of the samples were used in the calibration set and the other half in the validation set. Fig. 2 2 shows that the absorbance peaks of the O-H bond at 6944 cm −1 and 5155 cm −1 are very large, these peaks are mainly attributed to water and alcohol. But the absorbance of berberine was so weak that no absorbance peaks can be found in the spectra. Building a PLS model of berberine would be a challenging work. After correction by different background correction method, a PLS model of berberine was built. The results are shown in Table 3 3 showing that without data correction, poor result was obtained. Slightly better or worse results were obtained by the classical data correction methods such as offset correction, MSC, SNV, DT, wavelet, first and second derivative. It seems that these methods are poorly suited for correction of excessive background variations. The best results were obtained by OSC, as shown in the simulated datasets. L.V. is the latent variables of PLS models 2 Correction methods 3 Calibration set 2 Validation set L.V. * * RMSEC r 2 RMSEP r 2 None 2 5.6830 0.6021 5.356 0.4787 Offset correction 4 2.1610 0.9424 4.954 0.6984 MSC 2 4.9940 0.6927 4.994 0.5282 SNV 2 4.9810 0.6942 4.999 0.5289 DT 2 5.6990 0.5998 5.378 0.4528 First derivative 2 2.3600 0.9314 4.447 0.7383 Second derivative 2 4.4660 0.7543 4.967 0.5255 Wavelet 7 0.5967 0.9956 3.612 0.8160 OSC 3 0.8184 0.9852 2.144 0.9487 CONCLUSSION 1 This paper discussed the pretreatment of NIR spectra of plant extracts with emphasis on the problem of excessive background. As mentioned before, many classical background correction methods have been developed. But the classical methods of offset correction, MSC, SNV, DT, first and second derivative, and wavelet, seem unable to correct the excessive background. Thus a novel popular method, OSC, was used to correct the excessive background in this paper. A simulated datasets and a real NIR dataset were used for testing the efficiency of different background correction methods. The result of both simulated dataset and real dataset showed that the OSC is the only effective method for correction of excessive background. References BK Alsberg , AM Woodward , DB Kell . An introduction to wavelet transforms for chemometricians: A time-frequency approach . Chemometrics and Intelligent Laboratory Systems , 1997 . 37 215 - 239 . . An introduction to wavelet transforms for chemometricians: A time-frequency approach CA Andersson . Direct orthogonalization . Chemometrics and Intelligent Laboratory Systems , 1999 . 47 51 - 63 . . Direct orthogonalization VJ Barclay , RF Bonner . Application of wavelet transforms to experimental spectra: Smoothing, denosing, and data set compression . Analytical Chemistry , 1997 . 69 78 - 90 . . Application of wavelet transforms to experimental spectra: Smoothing, denosing, and data set compression RJ Barnes , MS Dhanoa , SJ Lister . Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra . Applied Spectroscopy , 1989 . 43 772 - 777 . . Standard normal variate transformation and de-trending of near-infrared diffuse reflectance spectra RG Brereton . Chemometrics: Data Analysis for the Laboratory and Chemical Plant , 2003 . : Chichester, England John & Wiley , 123 . Chemometrics: Data Analysis for the Laboratory and Chemical Plant JT Brindle , JK Nicholson , PM Schofield , DJ Grainger , E Holmes . Application of chemometrics to H-1 NMR spectroscopic data to investigate a relationship between human serum metabolic profiles and hypertension . Analyst , 2003 . 128 32 - 36 . . Application of chemometrics to H-1 NMR spectroscopic data to investigate a relationship between human serum metabolic profiles and hypertension A Candolfi , RD Maesschalck , D Jouan-Rimbaud , PA Hailey , DL Massart . The influence of data pre-processing in the pattern recognition of excipients near-infrared spectra . Journal of Pharmaceutical and Biomedical Analysis , 1999 . 21 115 - 132 . . The influence of data pre-processing in the pattern recognition of excipients near-infrared spectra T Fearn . On orthogonal signal correction . Chemometrics and Intelligent Laboratory Systems , 2000 . 50 47 - 52 . . On orthogonal signal correction P Geladi , D MacDougall , H Martens . Linearization and scatter-correction for near-infrared reflectance spectra of meat . Applied Spectroscopy , 1985 . 39 491 - 500 . . Linearization and scatter-correction for near-infrared reflectance spectra of meat TV Karstang , K Kvalheim . Multivariate prediction and background correction using local modelling and derivative spectroscopy . Analytical Chemistry , 1991 . 63 767 - 772 . . Multivariate prediction and background correction using local modelling and derivative spectroscopy XG Ma , ZX Zhang . Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry . Analytica Chimica Acta , 2003 . 485 233 - 239 . . Application of wavelet transform to background correction in inductively coupled plasma atomic emission spectrometry CR Mittermayr , HW Tan , SD Brown . Robust calibration with respect to background variation . Applied Spectroscopy , 2001 . 55 827 - 833 . . Robust calibration with respect to background variation M Peussa , S Harkonen , J Puputti , L Niinisto . Application of PLS multivariate calibration for the determination of the hydroxyl group content in calcined silica by DRIFTS . Journal of Chemometrics , 2000 . 14 501 - 512 . . Application of PLS multivariate calibration for the determination of the hydroxyl group content in calcined silica by DRIFTS I Schechter . Correction for nonlinear fluctuating background in monovariable analytical systems . Analytical Chemistry , 1995 . 67 2580 - 2585 . . Correction for nonlinear fluctuating background in monovariable analytical systems J Sjoblom , O Svensson , M Josefson , H Kullberg , S Wold . An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra . Chemometrics and Intelligent Laboratory Systems , 1998 . 44 229 - 244 . . An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra JG Sun . Statistical analysis of NIR data: Data pretreatment . Journal of Chemometrics , 1997 . 11 525 - 532 . . Statistical analysis of NIR data: Data pretreatment YR Tahboub , HL Pardue . Evaluation of multiwavelength first- and second-derivative spectra for the quantitation of mixtures of polynuclear aromatic hydrocarbons . Analytical Chemistry , 1985 . 57 38 - 41 . . Evaluation of multiwavelength first- and second-derivative spectra for the quantitation of mixtures of polynuclear aromatic hydrocarbons HW Tan , SD Brown . Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration . Journal of Chemometrics , 2002 . 16 228 - 240 . . Wavelet analysis applied to removing non-constant, varying spectroscopic background in multivariate calibration J Trygg , S Wold . Orthogonal projections to latent structures (O-PLS) . Journal of Chemometrics , 2002 . 16 119 - 128 . . Orthogonal projections to latent structures (O-PLS) JA Westerhuis , S de Jong , AK Smilde . Direct orthogonal signal correction . Chemometrics and Intelligent Laboratory Systems , 2001 . 56 13 - 25 . . Direct orthogonal signal correction S Wold , H Antti , F Lindgren , J Ohman . Orthogonal signal correction of near-infrared spectra . Chemometrics and Intelligent Laboratory Systems , 1998 . 44 175 - 185 . . Orthogonal signal correction of near-infrared spectra NL Yang , YY Cheng , HB Qu . A new method for process analysis of purification of natural herb using NIRS . Acta Chimica Sinica , 2003 . 61 742 - 747 . . A new method for process analysis of purification of natural herb using NIRS 10.1631/jzus.2005.B0838 Project supported by the Zhejiang Province Key Technologies R & D Program (No. 021103549) and the National Key Technologies R & D Program (No. 2001BA701A45), China 2005-01-17 2005-04-30 2005-07-29 2022-01-05 Copyright © 2005, Journal of Zhejiang University Science 2005 Journal of Zhejiang University-SCIENCE B (Biomedicine and Biotechnology) 08 6B