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Multivariate methodology for surface enhanced Raman chemical imaging of lymphocytes
Chemometrics and Intelligent Laboratory Systems 81 (2006) 13 – 20 www.elsevier.com/locate/chemolab
Multivariate methodology for surface enhanced Raman chemical imaging of lymphocytes Charlotte Eliasson a,1, Johan Engelbrektsson a, Anders Lore´n a,2, Jonas Abrahamsson b, Katarina Abrahamsson a, Mats Josefson c,* a
Department of Chemistry and Biotechnology/Analytical and Marine Chemistry, Chalmers University of Technology, SE-412 96 Go¨teborg, Sweden b Department of Paediatrics, Sahlgrenska University Hospital, Go¨teborg University, SE-416 85 Go¨teborg, Sweden c Pharmaceutical Analytical R&D, AstraZeneca, SE-431 83 Mo¨lndal, Sweden Received 11 June 2005; accepted 22 June 2005 Available online 19 January 2006
Abstract Surface enhanced Raman spectroscopy (SERS) was used to study the uptake of rhodamine 6G in human lymphocytes. In total four Raman images of lymphocytes were used. The aim was to find a multivariate methodology capable of separating spectra with chemical information from those that mainly contained the surface enhanced background, in order to create chemical images. The standard PCA procedure was compared with PCA of standard normal variate (SNV) corrected spectra, spectra baseline corrected in the wavelet domain, and variable trimming before PCA, to isolate unique spectra. It was not straightforward to perform a standard PCA for overview, since the small background variation in many variables dominated over the Raman band variation that only occur in few variables. It was shown that wavelet filtering could remove background variations and that variable trimming followed by PCA modelling left the unique Raman spectra as outliers, which facilitated interpretation of the Raman score images. D 2005 Elsevier B.V. All rights reserved. Keywords: PCA; SNV-transformation; Wavelets; Variable trimming; SERS; Chemical imaging; Multivariate analysis; Single cells
1. Introduction Chemical imaging is a concept that includes several steps before interpretable images are produced. These steps are: sample preparation, measurements, conversion of acquired data into images, and image analysis. The technique has been applied to studies of surfaces where the aim was to create maps of their chemical composition, such as tablet homogeneity by NIR [1]. Our goal is to measure intracellular levels of drugs, especially the anti-cancer anthracyclines e.g., doxorubicin.
* Corresponding author. Fax: +46 31 776 37 27. E-mail address: [email protected] (M. Josefson). 1 Present address: Department of Pure and Applied Chemistry, University of Strathclyde, 295 Cathedral Street, Glasgow, G4 0PL, Scotland. 2 Present address: Swedish National Testing and Research Institute, Box 857, SE-501 15 Bora˚s, Sweden. 0169-7439/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemolab.2005.06.014
Knowledge of the intracellular location, as well as the concentration of the drug, would improve disease treatment protocols. A suitable technique to study intracellular components in vivo is surface enhanced Raman spectroscopy (SERS). Generally, the Raman response is weak and subjected to a large fluorescence background in living cells. A solution is to simultaneously enhance the signal and quench the fluorescence by the introduction of metal surfaces (in our case, silver and gold colloids) and thereby, enable measurements of organic compounds in the micro- to nanomolar levels. In SERS, the background varies in intensity and shape, both between spectra and in individual spectra as Raman bands and spectral background are enhanced by the same mechanism [2]. Earlier studies have shown that it is possible to acquire SER spectra from within a cell and spectral interpretation was performed manually by Kneipp et al. [3] A first multivariate evaluation of rhodamine 6G in a cell was made
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CA) and either with or without rhodamine 6G (1 mM, Sigma-Aldrich). Immediately before the measurements, the culture media together with the colloids and analyte were removed and the cells were washed repeatedly with phosphate buffered saline (PBS) solution at pH 7.4 with 10 mM HEPES. The cells remained in the PBS-buffer throughout the experiments. Raman measurements (1 s acquisitions) were performed on single cells using an inverted confocal microscope and a Dilor LabRam INV Raman spectrometer. The cells were mapped utilising the xy-stage of the microscope in 1 Am steps covering an area of approximately 20 20 Am2. The laser and objective used was a 632.8 nm He / Ne laser and 100 (NA= 0.75), respectively. Image A differed in that it was mapped with a 784.7 nm diode laser and a 60 (NA= 1.20) objective. Images C and D are listed as having the same characteristics and differ mainly in total intensity and the shape of spectral features.
by [4]. In this paper we generalize the multivariate approach to account for both natural cell components and artificially introduced compounds. Principal components analysis (PCA) can be used to extract overlapping spectral features [5,6]. If an introduced substance dominates spectra from the cell, PCA can also be used to extract overlapping spectral features that have low signal to noise ratio [4]. Total intensity maps can then be used to show the distribution of intracellular components. Many pixels with high intensities in such images may contain only surface enhanced background with little chemical information. The variation in shape and intensity of the background may therefore dominate the spectral variation. Consequently, isolated SER spectra that are chemically informative in an image can be hard to find in a systematic way from PCA score plots, since the chemically informative spectra often are outliers in the PCA model. It is possible to make PCA models and remove the odd spectra in several rounds during modelling. The baseline variation can be reduced with baseline subtraction. However, both stepwise removal of odd spectra and manual verification of the polynomial fit of the baseline to spectra are tedious and time-consuming if many cells are to be analysed. There is also a significant risk that chemical information is distorted or lost at the baseline removal. The aim with this study was to find a multivariate methodology with the capability to separate spectra with chemical information from those that mainly contain variations in the background. The ideal methods should avoid repetitive PCA modelling and keep the baseline variation as unbiased as possible. This was attempted by comparison of standard PCA procedure with PCA of standard normal variate corrected spectra (SNV) [7], PCA of baseline corrected spectra in the wavelet domain [8,9], and variable trimming to isolate the odd spectra as high PCA residuals.
2.2. Multivariate evaluation Four different cell images were selected to represent different scenarios. These were images with varying signal to noise ratios (S / N) and varying number of spectral features. (Table 1). The images were unfolded and indexed with the spectra row-wise as observations subjected to multivariate analysis calculation. Resulting scores for each principal component were folded back into images again. The indexed images were imported into a multivariate software (Simca-P, version 10.0.4, Umetrics, Umea˚, Sweden). All wave numbers below 300 cm 1 were removed and the remaining data set was centred prior to modelling. Four different strategies were used; standard PCA modelling, SNV transformation, wavelet filtering and variable trimming. Modelling with PCA was performed afterwards, and the models from the different methods were imported through Simca-QP (version 10.0.4.2) into in-house imaging software (Determinator IV, version 0.42) to visualise the scores as images. Interpretation and evaluation of the different approaches were based on the scores, loadings and residuals of the PCA models together with the score images. SNV transformation was applied to entire spectra used for modelling.
2. Experimental 2.1. Analytical procedure Lymphocytes, obtained and treated as described previously [4], were incubated in DMEM 10% calf serum supplemented cultivation media with gold colloids (2600 colloids per cell, 60 nm in diameter, Ted Pella Inc., Redding,
2.2.1. Wavelets Wavelet decomposition of spectra by Discrete Wavelet Transform (DWT) is a tool that can be used both for filtering
Table 1 An overview of the general characteristics of the images used for modelling Image
k/nm
Rhodamine 6G
S / N-ratio
Information rich spectra
Background
A B C D
785 633 633 633
No No Yes Yes
High Average Low Low
Many Many Few Few
Minor Yes Changing slope Changing slope
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and reduction of data. The DWT sorts the variation in a spectrum based on frequency and position. Wavelet coefficients are arranged in scales. Each scale is a position dependent map of the raw spectrum. In DWT the most detail rich scale occupies half of the coefficients. The length of the scales are divided by 2 for each less detailed scale down to a single scalar containing the spectrum average. The wavelet coefficients can be treated in a conceptually similar way as a power spectrum where the modelling of frequencies goes from low to high while the scale length is going from 1 to half of the total number of coefficients. The wavelet coefficients can be linearly combined to reconstruct the original spectrum. Baseline shapes may be removed by omitting coefficients in the low frequency scales. The fast wavelet transformation technique Symmlet 10 was used for all wavelet transformations. All spectra were padded to the nearest power of 2 by a linear slope and all scales down to the average were calculated. 2.2.2. Variable trimming Spectra from the image were unfolded to a table with each spectrum as a row and each column as a wavenumber entry. Each column was trimmed to replace 25% of the data points having the highest intensities by missing values. In this way, the majority of the high intensity Raman peaks was removed. If a single spectrum contained more than 50% missing values, it was removed totally from the model data set. Missing values in remaining spectra were handled according to the ‘‘single component projection’’ method as described in Nelson et al. [10]. Spectra and parts of spectra that described the background and remaining Raman spectra with low intensity peaks were mean centred and subjected to PCA modelling. The PCA model was used for projection of all original non-trimmed spectra in the data set. Raman spectra with a relatively high S / N-ratio yielded high residuals in the PCA prediction, since they were not incorporated in the model. A limit was set for the residual and all spectra over this limit were rated as extreme spectra. The limited set of extreme spectra was then viewed and analysed. Thus, the PCA model was used to describe the general variability within the
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image. The prediction residuals were used to limit the number of spectra that had to be investigated thoroughly.
3. Results and discussion Four different images, image A – D, were selected in order to represent different qualities of data. The cells in all images had been incubated with gold colloids, and the cells in image C and D were also incubated with rhodamine 6G. All images contained a cell on a glass surface surrounded by PBS buffer solution. Due to the nature of the surface enhancement in SERS, the images are made up of spectra with high and low signal intensities. They are also made up of spectra from essentially non-enhanced background from outside the cell as well as surface enhanced background from within the cell. Spectra with Raman features from intracellular components can be found more or less frequent over the image, in addition the baseline shape varies from spectrum to spectrum. All spectra in the images contained background signal, either from within or outside the cell structure. In the cell we had a few spots of high intensity surface enhanced peaks, together with areas of surface enhanced and non-enhanced background. Outside the cell we have essentially only nonenhanced background but with another shape than from within the cell. Both image A and B contained many information rich spectra with a high S / N-ratio (Fig. 1). The images contained spectra with varying quality and a changing background signal (Table 1). In order to maintain cellular proliferation, short acquisition times were used, which for some pixels resulted in low S / N-ratio spectra in the images. 3.1. Principal components analysis The majority of the spectra in the images contained baseline variations overlaid with high frequency noise. Principal components analysis modelled the baseline variation in early components. The Raman spectra carrying chemical information deviated from the background signal,
Fig. 1. The original mapped image of cell A, shown as total spectral intensity (A) and the corresponding microscopy image (B).
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background signal and chemically relevant information were mixed in the score plot. 3.3. Wavelet decomposition and filtering combined with principal components analysis
Fig. 2. A score plot for the first two principal components of a PCA model of image C. The background is projected as a linear cluster slightly below the origin.
since they were composed of distinct, narrow bands. In a given model some of these spectra were found as outliers in the model. In order to find the majority of the information carrying spectra, repetitive PCA modelling was necessary to isolate a few outliers in each round. In general, PCA gave an overall better understanding of the chemical variations in the cells compared to evaluation with the software of the Raman instrument. Score plots of the different image models showed that most spectra were confined to a specific area, and a minority of the spectra were outliers (Fig. 2). This was most pronounced for images C and D where the change in the background signal formed a linear sloping cluster in the score plot. Spectra to the far left originated from the background outside the cell, and those to the lower right were background signal from within the cell. This was verified by correlation with the physical locations within the image. The spectra with more specific chemical information were projected as a more scattered cluster starting from the upper right corner for really detailed spectra diagonally down to the cell part of the background cluster.
Wavelet decomposition applied to Raman spectra represents a less biased way than polynomial fitting for removal of both high frequency noise and low frequency background, while retaining the information content present in the spectra. A PCA of image spectra decomposed into wavelet coefficients is identical to that of the raw data if all coefficients are present. However, selected coefficients can be removed to reduce effects that mask the chemical information, such as low-frequency changes in the background or high-frequency noise. Comparison of representative spectra from the PCA score plot with the same spectra in the wavelet domain, allows us to identify and remove the coefficients that correspond to interferences such as background variations or noise. Different orthogonal wavelet families were tested empirically. The Symmlet wavelet was used as it cause little visible artefacts in reconstructed Raman spectra and is one of the least asymmetric
3.2. Standard normal variate normalisation combined with principal components analysis Standard normal variate normalisation prior to PCA modelling was applied to each individual spectrum in the images. It is a method to normalise the total spectral intensities and to correct the offsets. Normalisation by SNV is a common pre-treatment technique and has previously been applied to SER spectra [11,12]. Standard normal variate transformation of entire spectra prior to PCA modelling of our images was not beneficial. The models for all images were poor with low explained variation (R 2 = 0.2 – 0.6) and prediction capabilities ( Q 2 = 0.1 – 0.6). The score plots had the same general pattern as in the PCA models, but the central cluster of background spectra had expanded. Thereby, spectra with
Fig. 3. Loading plot reconstructed from all wavelets coefficients of the first two principal components in a PCA model of image C (A). The low frequency part (30 out of 1024 coefficients) of corresponding wavelet decompositions is shown in (B).
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orthogonal wavelet base functions. The family member 10 was selected since it provides better smoothing than shorter wavelets due to its length. Fig. 3A shows the first two principal components out of four from a PCA model of image C. The loadings shown are reconstructed from all available wavelet coefficients. The large variation in the loadings is the difference in slope and shape of the background. The score plot for this model is shown in Fig. 2, where the dominating effects of the background slope on the second principal component can bee seen as a linear cluster. Removal of this background variation from the model is accomplished by comparison of the loadings as wavelet coefficients, which is seen in Fig. 3B. The number of removed wavelet coefficients was determined by interpreting the loadings and spectra in the wavelet domain. The main variation between component one and two is the baseline shape, while the spectral features are similar. In the wavelet loadings this is expressed as a larger difference between component 1 and 2 at low coefficient numbers. At higher wavelet coefficient numbers the difference between the components is smaller for component 1 and 2. The baseline variation can be reduced by omitting the lower wavelet coefficients since these
Fig. 4. Loadings (A) and score plot (B) of the first and second principal component after low frequency wavelet filtering of spectra in image C. The loadings are shown with a vertical offset for clarity. Rhodamine bands at 610, 770, 1180, 1360 and 1510 cm 1 are marked by stars.
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Fig. 5. The first (p1) and second (p2) loading vector for the PCA model of image A after spectral trimming. The first loading vector mainly comprises of a change of baseline level, whereas the second loading contains lowlevel spectral features. The loading vectors of the third and fourth component (not shown) contained mostly noise.
describe the low frequency variations present in the background. The number of removed coefficients was determined by finding the point where the two magnitude profiles from component 1 and 2 merge. Then a second step was made from a new PCA model where the cut point was further refined to get as clean representation of the spectra in the non-wavelet presentation of the loadings as possible. Removal of the first nine wavelet coefficients and calculation of a new PCA model yielded the loadings and corresponding score plots shown in Fig. 4. After the correction, the background spectra with low chemical information content were all clustered at the origin of the score plot with little effect on the model (Fig. 4B). Most of the peaks in the loadings of the first principal component can be identified as rhodamine 6G, the test substance added to this cell (Fig. 4A, top). Similar results were obtained from image D, which contained background variation of the same type. The model where low frequency wavelet coefficients
Fig. 6. A plot of the normalised spectral residuals (ordinate) for each spectrum (abscissa) in image A. In this case, the selection limit for indication of interesting spectra was set to 50.
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3.4. Variable trimming combined with principal components analysis
Fig. 7. Original surface enhanced Raman spectra from image A, spectra observation number 63 and 77.
were removed, was comprised of four principal components and had an R 2 of 0.3 and a Q 2 of 0.2. The low Q 2 value indicates that there are a relatively large number of unique spectra not fitting into the PCA model.
The variable trimming method is based on modelling of background and common features in order to find the unique spectra not fitting into the model. This was achieved by trimming, where the highest Raman peaks were removed and the trimming was made along the variable direction. In this way, the shape of the sloping baseline is preserved for the PCA model, while most high intensity peaks are removed. This made it possible to model the general variation between the baseline and low intensity spectra with the explained variation (R 2 = 0.9) and prediction capability ( Q 2 = 0.9) at four components. The model was then used as a description of the spectral variation of the background in the image. Maximum spectral magnitudes and the loadings from the model were then observed to verify that the model contained mostly background and abundant spectral features (Fig. 5). After trimming to remove 25% of the data points at high intensities for each wavenumber, the maximum intensity level of image A
Fig. 8. A comparison of the score images of image A for the 4 different methods. The number of components differs between the methods due to a different number of significant components. Please note that the sign of the PCA scores may be reversed. The grey part in the variable trimmed images represents the removed spectra.
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spectra left in the training set was 60 and the lowest count was 10, compared to the original maximum intensity level of around 5000. Image C had a range between 970 and 1020, and a maximum original intensity around 1500. Image A had an overall higher S / N-ratio than image C. Subsequently, a limited set of spectra at high residual levels, was identified by PCA prediction. Thus, this method made it easier to find the chemically informative spectra. The advantage is that different types of baselines and abundant spectra are found in the PCA model, while Raman spectra with a higher S / N-ratio are indicated by their residual level (Fig. 6). The residual peak maxima contain the spectra with many strong Raman bands. The limits for selection of spectra should be chosen in such a way that the peak maxima remain while the number of selected spectra similar to the baseline is reduced. Thus, the bases of the residual peaks are omitted (Fig. 6). Therefore, the limit of the residuals was set to 50 for image A. The method is relatively robust, and will handle situations where background spectra are trimmed together with the information rich spectra. The occasionally trimmed background spectra will have a low residual in the prediction step, and will not be indicated for further exploration. Examples of selected spectra are shown in Fig. 7. Lymphocytes have a relatively large cell nucleus, and therefore, it is probable to find spectral features related to DNA. This can be seen in Fig. 7 where DNA marker bands can be seen in the spectral regions at 830, 1000, and 1130-1150 cm 1. Several bands over the whole spectral range indicate the presence of nucleotides [13 – 19]. An alternative to variable trimming would be to use the prediction residuals from a robust PCA [20] model. In the present case we wanted to have more control over which spectra that were included in the model. The aim was to have all baseline spectra and all common spectral features included and cut out spectra with high Raman intensities. With the robust PCA we would be less focused on selection of spectral features. For each method, PCA score images were created for the significant PCA components (Fig. 8). These images are the summary of the variations at all wavenumbers used in the PCA. Each image shows a separate variation that is linearly independent of the other score images. The expectation for the PCA of wavelet-filtered spectra was that the model should be cleaner and easier to interpret. This was not proved for image A, since the images are similar to those from standard PCA. For image C that contained much more background variation, the expectation was correct. The poor performance of SNV pre-treatment is clearly illustrated by the A score images. The variable trimmed PCA score images show missing pixels in grey at the positions of the removed high intensity spectra due to more than 50% missing variables after trimming. At the edges of the cell we can observe score values from low intensity spectra. In this case the full information from the image is obtained by examining the PCA model in combination with the addi-
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tional individual spectra that have the highest residuals at prediction using the trimmed PCA model.
4. Concluding remarks In the case where cells have been mapped with SERS, PCA score plots do not reveal the differences between Raman spectra; two observations close to each other may contain very different spectra. The PCA algorithm will model the dominating variation, in this case the background. Normalisation by SNV changed the balance between the background and the Raman spectra with chemical information in such a way that it masked the chemical information. With wavelet filtering the background domination in the PCA models for images C and D was reduced. This is useful in the presence of large background variations, but will not aid interpretation to any larger extent when backgrounds are low. Two observations close to each other in the score plot may still contain very different spectra, which is illustrated with the low Q 2 obtained. Another way to extract the information is to use variable trimming to leave only the background and abundant spectral variations in the PCA model. This type of model will recognise the spectra containing unique chemical information as deviations from the model. Thus, the residuals from the prediction of the original spectra can be used to find the information rich spectra in a straightforward way. This method was found to be relatively robust for variations in the setting of limits for the amount of data that is trimmed. If too much is removed, the residuals will still be low for spectra that are not unique, thus limiting the total number of spectra that have to be viewed manually. Both the background reduction with wavelets and the variable trimming were useful to reduce the initial problems in the PCA. These methods may be used separately but can also be combined.
Acknowledgements The Swedish Research Council, the Kristina Stenborg Foundation, and Queen Silvia Children Hospital Research Foundation funded this work. Dr. Mark Nicolas at AstraZeneca R&D Mo¨lndal, is acknowledged for pointing out the general problem with PCA finding a few unique spectra in an image, and Dr. Olof Svensson also at AstraZeneca R&D Mo¨lndal, for constructive comments on the manuscript.
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Multivariate methodology for surface enhanced Raman chemical imaging of lymphocytes Charlotte Eliasson a,1, Johan Engelbrektsson a, Anders Lore´n a,2, Jonas Abrahamsson b, Katarina Abrahamsson a, Mats Josefson c,* a
Department of Chemistry and Biotechnology/Analytical and Marine Chemistry, Chalmers University of Technology, SE-412 96 Go¨teborg, Sweden b Department of Paediatrics, Sahlgrenska University Hospital, Go¨teborg University, SE-416 85 Go¨teborg, Sweden c Pharmaceutical Analytical R&D, AstraZeneca, SE-431 83 Mo¨lndal, Sweden Received 11 June 2005; accepted 22 June 2005 Available online 19 January 2006
Abstract Surface enhanced Raman spectroscopy (SERS) was used to study the uptake of rhodamine 6G in human lymphocytes. In total four Raman images of lymphocytes were used. The aim was to find a multivariate methodology capable of separating spectra with chemical information from those that mainly contained the surface enhanced background, in order to create chemical images. The standard PCA procedure was compared with PCA of standard normal variate (SNV) corrected spectra, spectra baseline corrected in the wavelet domain, and variable trimming before PCA, to isolate unique spectra. It was not straightforward to perform a standard PCA for overview, since the small background variation in many variables dominated over the Raman band variation that only occur in few variables. It was shown that wavelet filtering could remove background variations and that variable trimming followed by PCA modelling left the unique Raman spectra as outliers, which facilitated interpretation of the Raman score images. D 2005 Elsevier B.V. All rights reserved. Keywords: PCA; SNV-transformation; Wavelets; Variable trimming; SERS; Chemical imaging; Multivariate analysis; Single cells
1. Introduction Chemical imaging is a concept that includes several steps before interpretable images are produced. These steps are: sample preparation, measurements, conversion of acquired data into images, and image analysis. The technique has been applied to studies of surfaces where the aim was to create maps of their chemical composition, such as tablet homogeneity by NIR [1]. Our goal is to measure intracellular levels of drugs, especially the anti-cancer anthracyclines e.g., doxorubicin.
* Corresponding author. Fax: +46 31 776 37 27. E-mail address: [email protected] (M. Josefson). 1 Present address: Department of Pure and Applied Chemistry, University of Strathclyde, 295 Cathedral Street, Glasgow, G4 0PL, Scotland. 2 Present address: Swedish National Testing and Research Institute, Box 857, SE-501 15 Bora˚s, Sweden. 0169-7439/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemolab.2005.06.014
Knowledge of the intracellular location, as well as the concentration of the drug, would improve disease treatment protocols. A suitable technique to study intracellular components in vivo is surface enhanced Raman spectroscopy (SERS). Generally, the Raman response is weak and subjected to a large fluorescence background in living cells. A solution is to simultaneously enhance the signal and quench the fluorescence by the introduction of metal surfaces (in our case, silver and gold colloids) and thereby, enable measurements of organic compounds in the micro- to nanomolar levels. In SERS, the background varies in intensity and shape, both between spectra and in individual spectra as Raman bands and spectral background are enhanced by the same mechanism [2]. Earlier studies have shown that it is possible to acquire SER spectra from within a cell and spectral interpretation was performed manually by Kneipp et al. [3] A first multivariate evaluation of rhodamine 6G in a cell was made
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CA) and either with or without rhodamine 6G (1 mM, Sigma-Aldrich). Immediately before the measurements, the culture media together with the colloids and analyte were removed and the cells were washed repeatedly with phosphate buffered saline (PBS) solution at pH 7.4 with 10 mM HEPES. The cells remained in the PBS-buffer throughout the experiments. Raman measurements (1 s acquisitions) were performed on single cells using an inverted confocal microscope and a Dilor LabRam INV Raman spectrometer. The cells were mapped utilising the xy-stage of the microscope in 1 Am steps covering an area of approximately 20 20 Am2. The laser and objective used was a 632.8 nm He / Ne laser and 100 (NA= 0.75), respectively. Image A differed in that it was mapped with a 784.7 nm diode laser and a 60 (NA= 1.20) objective. Images C and D are listed as having the same characteristics and differ mainly in total intensity and the shape of spectral features.
by [4]. In this paper we generalize the multivariate approach to account for both natural cell components and artificially introduced compounds. Principal components analysis (PCA) can be used to extract overlapping spectral features [5,6]. If an introduced substance dominates spectra from the cell, PCA can also be used to extract overlapping spectral features that have low signal to noise ratio [4]. Total intensity maps can then be used to show the distribution of intracellular components. Many pixels with high intensities in such images may contain only surface enhanced background with little chemical information. The variation in shape and intensity of the background may therefore dominate the spectral variation. Consequently, isolated SER spectra that are chemically informative in an image can be hard to find in a systematic way from PCA score plots, since the chemically informative spectra often are outliers in the PCA model. It is possible to make PCA models and remove the odd spectra in several rounds during modelling. The baseline variation can be reduced with baseline subtraction. However, both stepwise removal of odd spectra and manual verification of the polynomial fit of the baseline to spectra are tedious and time-consuming if many cells are to be analysed. There is also a significant risk that chemical information is distorted or lost at the baseline removal. The aim with this study was to find a multivariate methodology with the capability to separate spectra with chemical information from those that mainly contain variations in the background. The ideal methods should avoid repetitive PCA modelling and keep the baseline variation as unbiased as possible. This was attempted by comparison of standard PCA procedure with PCA of standard normal variate corrected spectra (SNV) [7], PCA of baseline corrected spectra in the wavelet domain [8,9], and variable trimming to isolate the odd spectra as high PCA residuals.
2.2. Multivariate evaluation Four different cell images were selected to represent different scenarios. These were images with varying signal to noise ratios (S / N) and varying number of spectral features. (Table 1). The images were unfolded and indexed with the spectra row-wise as observations subjected to multivariate analysis calculation. Resulting scores for each principal component were folded back into images again. The indexed images were imported into a multivariate software (Simca-P, version 10.0.4, Umetrics, Umea˚, Sweden). All wave numbers below 300 cm 1 were removed and the remaining data set was centred prior to modelling. Four different strategies were used; standard PCA modelling, SNV transformation, wavelet filtering and variable trimming. Modelling with PCA was performed afterwards, and the models from the different methods were imported through Simca-QP (version 10.0.4.2) into in-house imaging software (Determinator IV, version 0.42) to visualise the scores as images. Interpretation and evaluation of the different approaches were based on the scores, loadings and residuals of the PCA models together with the score images. SNV transformation was applied to entire spectra used for modelling.
2. Experimental 2.1. Analytical procedure Lymphocytes, obtained and treated as described previously [4], were incubated in DMEM 10% calf serum supplemented cultivation media with gold colloids (2600 colloids per cell, 60 nm in diameter, Ted Pella Inc., Redding,
2.2.1. Wavelets Wavelet decomposition of spectra by Discrete Wavelet Transform (DWT) is a tool that can be used both for filtering
Table 1 An overview of the general characteristics of the images used for modelling Image
k/nm
Rhodamine 6G
S / N-ratio
Information rich spectra
Background
A B C D
785 633 633 633
No No Yes Yes
High Average Low Low
Many Many Few Few
Minor Yes Changing slope Changing slope
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and reduction of data. The DWT sorts the variation in a spectrum based on frequency and position. Wavelet coefficients are arranged in scales. Each scale is a position dependent map of the raw spectrum. In DWT the most detail rich scale occupies half of the coefficients. The length of the scales are divided by 2 for each less detailed scale down to a single scalar containing the spectrum average. The wavelet coefficients can be treated in a conceptually similar way as a power spectrum where the modelling of frequencies goes from low to high while the scale length is going from 1 to half of the total number of coefficients. The wavelet coefficients can be linearly combined to reconstruct the original spectrum. Baseline shapes may be removed by omitting coefficients in the low frequency scales. The fast wavelet transformation technique Symmlet 10 was used for all wavelet transformations. All spectra were padded to the nearest power of 2 by a linear slope and all scales down to the average were calculated. 2.2.2. Variable trimming Spectra from the image were unfolded to a table with each spectrum as a row and each column as a wavenumber entry. Each column was trimmed to replace 25% of the data points having the highest intensities by missing values. In this way, the majority of the high intensity Raman peaks was removed. If a single spectrum contained more than 50% missing values, it was removed totally from the model data set. Missing values in remaining spectra were handled according to the ‘‘single component projection’’ method as described in Nelson et al. [10]. Spectra and parts of spectra that described the background and remaining Raman spectra with low intensity peaks were mean centred and subjected to PCA modelling. The PCA model was used for projection of all original non-trimmed spectra in the data set. Raman spectra with a relatively high S / N-ratio yielded high residuals in the PCA prediction, since they were not incorporated in the model. A limit was set for the residual and all spectra over this limit were rated as extreme spectra. The limited set of extreme spectra was then viewed and analysed. Thus, the PCA model was used to describe the general variability within the
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image. The prediction residuals were used to limit the number of spectra that had to be investigated thoroughly.
3. Results and discussion Four different images, image A – D, were selected in order to represent different qualities of data. The cells in all images had been incubated with gold colloids, and the cells in image C and D were also incubated with rhodamine 6G. All images contained a cell on a glass surface surrounded by PBS buffer solution. Due to the nature of the surface enhancement in SERS, the images are made up of spectra with high and low signal intensities. They are also made up of spectra from essentially non-enhanced background from outside the cell as well as surface enhanced background from within the cell. Spectra with Raman features from intracellular components can be found more or less frequent over the image, in addition the baseline shape varies from spectrum to spectrum. All spectra in the images contained background signal, either from within or outside the cell structure. In the cell we had a few spots of high intensity surface enhanced peaks, together with areas of surface enhanced and non-enhanced background. Outside the cell we have essentially only nonenhanced background but with another shape than from within the cell. Both image A and B contained many information rich spectra with a high S / N-ratio (Fig. 1). The images contained spectra with varying quality and a changing background signal (Table 1). In order to maintain cellular proliferation, short acquisition times were used, which for some pixels resulted in low S / N-ratio spectra in the images. 3.1. Principal components analysis The majority of the spectra in the images contained baseline variations overlaid with high frequency noise. Principal components analysis modelled the baseline variation in early components. The Raman spectra carrying chemical information deviated from the background signal,
Fig. 1. The original mapped image of cell A, shown as total spectral intensity (A) and the corresponding microscopy image (B).
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background signal and chemically relevant information were mixed in the score plot. 3.3. Wavelet decomposition and filtering combined with principal components analysis
Fig. 2. A score plot for the first two principal components of a PCA model of image C. The background is projected as a linear cluster slightly below the origin.
since they were composed of distinct, narrow bands. In a given model some of these spectra were found as outliers in the model. In order to find the majority of the information carrying spectra, repetitive PCA modelling was necessary to isolate a few outliers in each round. In general, PCA gave an overall better understanding of the chemical variations in the cells compared to evaluation with the software of the Raman instrument. Score plots of the different image models showed that most spectra were confined to a specific area, and a minority of the spectra were outliers (Fig. 2). This was most pronounced for images C and D where the change in the background signal formed a linear sloping cluster in the score plot. Spectra to the far left originated from the background outside the cell, and those to the lower right were background signal from within the cell. This was verified by correlation with the physical locations within the image. The spectra with more specific chemical information were projected as a more scattered cluster starting from the upper right corner for really detailed spectra diagonally down to the cell part of the background cluster.
Wavelet decomposition applied to Raman spectra represents a less biased way than polynomial fitting for removal of both high frequency noise and low frequency background, while retaining the information content present in the spectra. A PCA of image spectra decomposed into wavelet coefficients is identical to that of the raw data if all coefficients are present. However, selected coefficients can be removed to reduce effects that mask the chemical information, such as low-frequency changes in the background or high-frequency noise. Comparison of representative spectra from the PCA score plot with the same spectra in the wavelet domain, allows us to identify and remove the coefficients that correspond to interferences such as background variations or noise. Different orthogonal wavelet families were tested empirically. The Symmlet wavelet was used as it cause little visible artefacts in reconstructed Raman spectra and is one of the least asymmetric
3.2. Standard normal variate normalisation combined with principal components analysis Standard normal variate normalisation prior to PCA modelling was applied to each individual spectrum in the images. It is a method to normalise the total spectral intensities and to correct the offsets. Normalisation by SNV is a common pre-treatment technique and has previously been applied to SER spectra [11,12]. Standard normal variate transformation of entire spectra prior to PCA modelling of our images was not beneficial. The models for all images were poor with low explained variation (R 2 = 0.2 – 0.6) and prediction capabilities ( Q 2 = 0.1 – 0.6). The score plots had the same general pattern as in the PCA models, but the central cluster of background spectra had expanded. Thereby, spectra with
Fig. 3. Loading plot reconstructed from all wavelets coefficients of the first two principal components in a PCA model of image C (A). The low frequency part (30 out of 1024 coefficients) of corresponding wavelet decompositions is shown in (B).
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orthogonal wavelet base functions. The family member 10 was selected since it provides better smoothing than shorter wavelets due to its length. Fig. 3A shows the first two principal components out of four from a PCA model of image C. The loadings shown are reconstructed from all available wavelet coefficients. The large variation in the loadings is the difference in slope and shape of the background. The score plot for this model is shown in Fig. 2, where the dominating effects of the background slope on the second principal component can bee seen as a linear cluster. Removal of this background variation from the model is accomplished by comparison of the loadings as wavelet coefficients, which is seen in Fig. 3B. The number of removed wavelet coefficients was determined by interpreting the loadings and spectra in the wavelet domain. The main variation between component one and two is the baseline shape, while the spectral features are similar. In the wavelet loadings this is expressed as a larger difference between component 1 and 2 at low coefficient numbers. At higher wavelet coefficient numbers the difference between the components is smaller for component 1 and 2. The baseline variation can be reduced by omitting the lower wavelet coefficients since these
Fig. 4. Loadings (A) and score plot (B) of the first and second principal component after low frequency wavelet filtering of spectra in image C. The loadings are shown with a vertical offset for clarity. Rhodamine bands at 610, 770, 1180, 1360 and 1510 cm 1 are marked by stars.
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Fig. 5. The first (p1) and second (p2) loading vector for the PCA model of image A after spectral trimming. The first loading vector mainly comprises of a change of baseline level, whereas the second loading contains lowlevel spectral features. The loading vectors of the third and fourth component (not shown) contained mostly noise.
describe the low frequency variations present in the background. The number of removed coefficients was determined by finding the point where the two magnitude profiles from component 1 and 2 merge. Then a second step was made from a new PCA model where the cut point was further refined to get as clean representation of the spectra in the non-wavelet presentation of the loadings as possible. Removal of the first nine wavelet coefficients and calculation of a new PCA model yielded the loadings and corresponding score plots shown in Fig. 4. After the correction, the background spectra with low chemical information content were all clustered at the origin of the score plot with little effect on the model (Fig. 4B). Most of the peaks in the loadings of the first principal component can be identified as rhodamine 6G, the test substance added to this cell (Fig. 4A, top). Similar results were obtained from image D, which contained background variation of the same type. The model where low frequency wavelet coefficients
Fig. 6. A plot of the normalised spectral residuals (ordinate) for each spectrum (abscissa) in image A. In this case, the selection limit for indication of interesting spectra was set to 50.
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3.4. Variable trimming combined with principal components analysis
Fig. 7. Original surface enhanced Raman spectra from image A, spectra observation number 63 and 77.
were removed, was comprised of four principal components and had an R 2 of 0.3 and a Q 2 of 0.2. The low Q 2 value indicates that there are a relatively large number of unique spectra not fitting into the PCA model.
The variable trimming method is based on modelling of background and common features in order to find the unique spectra not fitting into the model. This was achieved by trimming, where the highest Raman peaks were removed and the trimming was made along the variable direction. In this way, the shape of the sloping baseline is preserved for the PCA model, while most high intensity peaks are removed. This made it possible to model the general variation between the baseline and low intensity spectra with the explained variation (R 2 = 0.9) and prediction capability ( Q 2 = 0.9) at four components. The model was then used as a description of the spectral variation of the background in the image. Maximum spectral magnitudes and the loadings from the model were then observed to verify that the model contained mostly background and abundant spectral features (Fig. 5). After trimming to remove 25% of the data points at high intensities for each wavenumber, the maximum intensity level of image A
Fig. 8. A comparison of the score images of image A for the 4 different methods. The number of components differs between the methods due to a different number of significant components. Please note that the sign of the PCA scores may be reversed. The grey part in the variable trimmed images represents the removed spectra.
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spectra left in the training set was 60 and the lowest count was 10, compared to the original maximum intensity level of around 5000. Image C had a range between 970 and 1020, and a maximum original intensity around 1500. Image A had an overall higher S / N-ratio than image C. Subsequently, a limited set of spectra at high residual levels, was identified by PCA prediction. Thus, this method made it easier to find the chemically informative spectra. The advantage is that different types of baselines and abundant spectra are found in the PCA model, while Raman spectra with a higher S / N-ratio are indicated by their residual level (Fig. 6). The residual peak maxima contain the spectra with many strong Raman bands. The limits for selection of spectra should be chosen in such a way that the peak maxima remain while the number of selected spectra similar to the baseline is reduced. Thus, the bases of the residual peaks are omitted (Fig. 6). Therefore, the limit of the residuals was set to 50 for image A. The method is relatively robust, and will handle situations where background spectra are trimmed together with the information rich spectra. The occasionally trimmed background spectra will have a low residual in the prediction step, and will not be indicated for further exploration. Examples of selected spectra are shown in Fig. 7. Lymphocytes have a relatively large cell nucleus, and therefore, it is probable to find spectral features related to DNA. This can be seen in Fig. 7 where DNA marker bands can be seen in the spectral regions at 830, 1000, and 1130-1150 cm 1. Several bands over the whole spectral range indicate the presence of nucleotides [13 – 19]. An alternative to variable trimming would be to use the prediction residuals from a robust PCA [20] model. In the present case we wanted to have more control over which spectra that were included in the model. The aim was to have all baseline spectra and all common spectral features included and cut out spectra with high Raman intensities. With the robust PCA we would be less focused on selection of spectral features. For each method, PCA score images were created for the significant PCA components (Fig. 8). These images are the summary of the variations at all wavenumbers used in the PCA. Each image shows a separate variation that is linearly independent of the other score images. The expectation for the PCA of wavelet-filtered spectra was that the model should be cleaner and easier to interpret. This was not proved for image A, since the images are similar to those from standard PCA. For image C that contained much more background variation, the expectation was correct. The poor performance of SNV pre-treatment is clearly illustrated by the A score images. The variable trimmed PCA score images show missing pixels in grey at the positions of the removed high intensity spectra due to more than 50% missing variables after trimming. At the edges of the cell we can observe score values from low intensity spectra. In this case the full information from the image is obtained by examining the PCA model in combination with the addi-
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tional individual spectra that have the highest residuals at prediction using the trimmed PCA model.
4. Concluding remarks In the case where cells have been mapped with SERS, PCA score plots do not reveal the differences between Raman spectra; two observations close to each other may contain very different spectra. The PCA algorithm will model the dominating variation, in this case the background. Normalisation by SNV changed the balance between the background and the Raman spectra with chemical information in such a way that it masked the chemical information. With wavelet filtering the background domination in the PCA models for images C and D was reduced. This is useful in the presence of large background variations, but will not aid interpretation to any larger extent when backgrounds are low. Two observations close to each other in the score plot may still contain very different spectra, which is illustrated with the low Q 2 obtained. Another way to extract the information is to use variable trimming to leave only the background and abundant spectral variations in the PCA model. This type of model will recognise the spectra containing unique chemical information as deviations from the model. Thus, the residuals from the prediction of the original spectra can be used to find the information rich spectra in a straightforward way. This method was found to be relatively robust for variations in the setting of limits for the amount of data that is trimmed. If too much is removed, the residuals will still be low for spectra that are not unique, thus limiting the total number of spectra that have to be viewed manually. Both the background reduction with wavelets and the variable trimming were useful to reduce the initial problems in the PCA. These methods may be used separately but can also be combined.
Acknowledgements The Swedish Research Council, the Kristina Stenborg Foundation, and Queen Silvia Children Hospital Research Foundation funded this work. Dr. Mark Nicolas at AstraZeneca R&D Mo¨lndal, is acknowledged for pointing out the general problem with PCA finding a few unique spectra in an image, and Dr. Olof Svensson also at AstraZeneca R&D Mo¨lndal, for constructive comments on the manuscript.
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