A comparison of PCA and MAF for ToF-SIMS image interpretation

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Research ArticleReceived: 23 December 2008 Revised: 7 May 2009 Accepted: 9 May 2009 Published online in Wiley Interscience:

(www.interscience.wiley.com) DOI 10.1002/sia.3084

A comparison of PCA and MAF for ToF-SIMSimage interpretationAlex Henderson,∗ John S. Fletcher and John C. Vickerman

While time-of-flight secondary ion mass spectrometry (ToF-SIMS) image generation has been useful in the determination ofthe spatial distribution of chemistry in a broad application area, the amount of secondary ion signal available in each pixelremains small, hampering the use of multivariate analysis (MVA) approaches. The pre-treatment of data commonly comprisestwo approaches to increase pixel signal intensity prior to MVA: mass channel summation and pixel summation. Recent advancesin instrumentation have lead to much greater signal per image pixel such that a true spectrum can be discerned at each pointacross the sample. In this study, we determine the outcomes of these two pre-treatments prior to principal components analysis(PCA) and maximum autocorrelation factor (MAF) analysis in comparison with high signal intensity data.

Both PCA and MAF analyses of the high signal intensity data are presented with MAF being identified as the most effectiveapproach. Image data was reduced in intensity to determine the effectiveness of MVA with lower spectral intensity. MAF wasfound to outperform PCA on such data, although both techniques were useful in the identification of the chemistry present.The data were then mass summed, using a number of different approaches, to reduce mass resolution, leading to a detrimentaleffect on PCA analysis, but little discernable change to MAF output. Reducing the spatial resolution by summing spectra fromadjacent pixels, however, lead to a severe blurring of the MAF image structure, with PCA performing well.

Conclusions and recommendation for pre-treatment and MVA technique selection are presented. Copyright c© 2009 JohnWiley & Sons, Ltd.

Keywords: ToF-SIMS; secondary ion mass spectrometry; multivariate analysis; principal components analysis; PCA; maximumautocorrelation factor analysis; MAF; image processing; HeLa cells

Introduction

When generating secondary ion mass spectrometry (SIMS) imageswith time-of-flight secondary ion mass spectrometry (ToF-SIMS)instruments equipped with pulsed primary sources of atomic ionsthere is a limit to the amount of molecular information than can begenerated from each pixel.[1] The static limit imposes a cut-off inthe number of chemically relevant ions that can be extracted fromthe small analysis area typically defining a pixel. Even with clusterion sources, where the static limit is relaxed,[2 – 4] the duty cycle ofthe instrument and/or the low primary ion current may impose apractical limit to the time taken to acquire a significant spectrumat each pixel. In order to maximise the analytical potential of aSIMS image, multivariate analysis (MVA) is often used, both to helpin the identification of the chemistry present and also to increasethe image contrast and thereby identify regions of interest. Withthe new instrumentation recently developed, incorporating bothsmall spot cluster ion sources and quasi-continuous analysis, wecan now generate images with a high secondary ion yield perpixel in a manageable timeframe.[5,6] This allows us to consider theeffectiveness of MVA strategies in the interpretation of ToF-SIMSimages.

It has been shown that MVA methods, particularly principalcomponents analysis (PCA), can provide a useful tool fordiscriminating between ToF-SIMS data either for classification ofproteins based on amino acid fragment variation,[7,8] classificationof tissue spectra from organs in mouse embryos[9] or theidentification of microorganisms.[10,11] In the case of ToF-SIMSimage analysis such analyses can be used to improve imagecontrast, to identify regions of interest and, in each case, to

then output the associated variables (m/z values) for chemicalidentification.[12]

PCA has come to be extensively used in the analysis of collectionsof SIMS spectra and SIMS images.[13 – 15] In PCA, we seek to convertthe many mass channels present in a collection of spectra into asmaller number of independent terms that express the chemicalvariation of the dataset more clearly. This is done through ananalysis of the variance of each mass channel across the dataset,where the combination of mass channels containing the mostvariance is termed the first principal component (PC 1) andsubsequent combinations, with decreasing variance, labelled withincreasing number PC 2, PC 3 etc. up to PC n where n is thelower value of either the number of mass channels (variables)submitted to analysis or the number of spectra (pixels) used. Thisis a correlation in the mass domain.

In an ideal chemical system, the number of meaningfulcomponents is governed by the number of spectra from differentchemicals present in the sample, with the remaining componentsforming a model of the noise present in the data. However, suchan ideal system neglects non-linear contributions such as matrixeffects or non-linear instrumental parameters such as detectorsaturation. For model systems, the number of chemicals present

∗ Correspondence to: Alex Henderson, Surface Analysis Research Centre,Manchester Interdisciplinary Biocentre, School of Chemical Engineering and An-alytical Science, The University of Manchester, 131 Princess Street, Manchester,M1 7DN, UK. E-mail: [email protected]

Surface Analysis Research Centre, Manchester Interdisciplinary Biocentre,School of Chemical Engineering and Analytical Science, The University ofManchester, 131 Princess Street, Manchester, M1 7DN, UK

Surf. Interface Anal. 2009, 41, 666–674 Copyright c© 2009 John Wiley & Sons, Ltd.

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A comparison of PCA and MAF for ToF-SIMS

in a sample is known a priori. However, for analysis of real worldsamples, such as those encountered in the analysis of biologicalsystems, the number of separate chemicals is unknown and theconcentration of some is likely to be so low that their spectra appearas noise. One of the decisions that an analyst must make thereforeis to determine the point at which the principal components nolonger explain meaningful chemistry and begin to model noise inthe system.

Maximum autocorrelation factor (MAF) analysis has beensuggested to be useful in the analysis of SIMS images; however, todate, there has been little evidence of MAF in the literature.[16,17]

MAF analysis can be considered to be an extension of PCAapplicable to images.[18] MAF also not only attempts to identify thevariance in mass channels corresponding to spectral contributionsbut also considers the relationship between pixels in the image.During an MAF analysis, a correlation is calculated between theimage and the same image offset by one pixel, typically diagonally.MAF is therefore specific to image analysis and identifies acorrelation in the spatial domain as well as the mass domain.

Experimental

The ToF-SIMS data were acquired using an Ionoptika J105 3DChemical Imager. This instrument has been described in detailelsewhere.[5] Briefly, it is a ToF-SIMS instrument that allows theprimary ion beam(s) to be operated in a d.c. mode by sampling theresulting secondary ion beam using a linear buncher. The massspectrometry is thus decoupled from the sputtering event andthe duty cycle of the instrument is greatly improved comparedto conventional instruments that utilise pulsed ion beams. Theinstrument is fitted with 40 keV C60

+ and Aun+ ion sources,

incorporates sophisticated sample handling and also has thecapability to perform MS/MS analysis.

The high duty cycle of the instrument, coupled to the propertiesof C60 that allow collection of molecular information from thesample at primary ion doses far in excess of the traditionalSIMS static limit, enables the generation of data that is idealfor the testing of multivariate methods for data interpretation andvisualisation. The data set we have used is from a sample of HeLacells that were entirely consumed during the SIMS analysis, thusthe signal in each pixel is much higher than would be observedin a routine static SIMS image. The cells were cultured on poly-L-lysine coated silicon shards for 24 h at 37 ◦C with 5% CO2. Thecells were freeze dried and washed briefly in 0.15 M ammoniumformate solution prior to ToF-SIMS analysis. Typical cell diameteris 20 µm. The image was acquired using 40 keV C60

+ primaryions scanned over 128 × 128 pixels and the field of view of theimage is 88 × 108 µm2 corresponding to a pixel dimension of∼0.7 × 0.8 µm2. The total ion dose used was 3 × 1014 ions cm−2.The total sum of intensity across the 128 × 128 pixel image was1.6 × 108 counts corresponding to approximately 104 counts perpixel.

The test image

Inspection of the data using conventional methods, i.e. viewingthe localisation of signal associated with each peak in the massspectrum, shows a number of distinct regions of chemical interestin the image. First, there is the signal arising from the substrateon which the cells were grown, dominated by silicon containingspecies. Secondly, there is organic signal arising from the cells. Of

(a) (b)

(c) (d)

Figure 1. ToF-SIMS images of HeLa cells (scaled then smoothed). (a) Totalion image and single ion images showing easily distinguished chemicalvariation across the sample; (b) m/z 136.1 [max 686 counts (55 afterscaling)]; (c) m/z 184.1 [max 699 counts (20 after scaling)]; and (d) m/z111.9 [max 2067 counts (899 after scaling)]. These ions are assigned toadenine, phosphatidylcholine and silicon, respectively.

this organic signal, some peaks are associated with the entire cell,some with the periphery of the cell and some with the centre ofthe cell. There is also an area that appears to be debris on thesample. If these features are obvious by simple inspection of thedata, they should appear within the first few principal componentsor factors. We have thus decided that the success criteria for ourMVA of the data should clearly capture these features. Some of thepeaks in the mass spectrum that localise to these different regionscan be assigned to known and expected biological species alongwith signals characteristic of the silicon substrate. Fig. 1 shows thetotal ion image along with some of the identified species, m/z 184is a common fragment associated with biological samples as itarises from the phosphatidylcholine head group of phospholipidsassociated with biological membranes, m/z 136 is assigned to the[M+H]+ ion of adenine and the species at m/z 112, localised tothe substrate, is the signal from the Si4+ ion. Of particular interestis the ability of the MVA to identify differences in chemistry withinthe individual cells. Such discrimination would be expected to bemore difficult than the discrimination of cells from the substrateas the species arising from the cells will be predominantly organicwith numerous isobaric interferences. Thus, as an extension ofour success criteria, the optimisation of our MVA approach willbe assessed by the appearance and position/rank of the principalcomponent or factor that illustrates the differences between theouter cellular region (illustrated by the m/z 184 peak) and the innercellular region (i.e. co-localised with the m/z 136 peak).

Since the cells were entirely consumed during the acquisition,there will be some blurring of the signal from inner and outercellular regions due to their relative positions within the threedimensional cell. However, in this work, we are comparing betweenmultivariate approaches rather than seeking to define the exactintra-cellular location of any given species.

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A. Henderson, J. S. Fletcher and J. C. Vickerman

Mathematical treatment

Computer equipment and software

Processing was undertaken using a PC equipped with twodual core Intel Xeon processors and 8 GB RAM running theMicrosoft Windows XP64 operating system. Data was convertedfrom the instrument manufacturer’s file format using in-houseroutines executed in 64-bit MATLAB (The MathWorks, Inc., Natick,Massachusetts). The PCA calculations were performed using theprincomp routine from the MATLAB Statistical Toolbox. The MAFcalculations were performed using the multivariate image analysisadd-on for PLS Toolbox (Eigenvector Research, Inc., Wenatchee,Washington). All other MATLAB routines were written in-house.While MATLAB is a closed software package, the operationsdescribed in this work are non-specific and should be compatiblewith open source mathematical packages.[19]

MVA analyses

In order to improve calculation speed and to prevent divide-by-zero errors, variables (masses) that exhibited no variance (perhapsbecause the particular mass channel contained no data) wereremoved prior to analysis. In order to allow for comparisonbetween the original spectra and the loadings plots, variables ofzero value were inserted into the loadings matrix at the appropriatepositions. No peak selection was performed. All mass channelsbetween 50 and 400 u were used in the analyses.

Prior to PCA analysis the data was Poisson scaled as detailedbelow. Since MAF requires a correlation between the image andoffset versions of the same image, any scaling performed by wayof pre-treatment will be cancelled out during the analysis and sodata scaling is redundant. However, in sections of this article, wemodify the intensity of the spectral signal and so, in certain cases,Poisson scaling was performed so as not to disrupt the characterof the noise in the data. This is outlined below.

While mean centering is not strictly necessary for MVA of SIMSdata,[20,21] the algorithms employed here were preconfigured toperform mean centering.

Poisson scaling

Prior to PCA analysis, scaling of the data was performed followingthe procedure outlined in the draft International Standard18 115[22] based on work by Keenen and Kotula,[20] itself developedfrom the work of Cochran and Horne.[23] Briefly, data from ToF-SIMS instruments are collected in a pulse counted manner, whichis subject to an uncertainty explained by Poisson statistics. Thisuncertainty is equal to the mean of the signal intensity. Multivariatealgorithms such as PCA and MAF are designed to account forthe variance in the data. Since the data here will have variancerelated to the signal intensity (are heteroscedastic), the algorithmswill perform sub-optimally. The approach of Keenan and Kotula,commonly called Poisson scaling, attempts to account for thisby performing a scaling such that the estimated variance dueto counting statistics is equal on all variables (intensity values atdifferent masses) so MVA can better account for other sourcesof variance, for example, those due to sample chemistry. Thealgorithm used by Keenen and Kotula assumes that row andcolumn sums are preserved. This entails a scaling of eachspectrum (row) independently, in addition to the scaling ofintensity (column) to compensate for Poisson statistical variance(see Appendix A).

Channel summation (mass binning)

The use of channel summation, or mass binning, plays an importantrole in MVA. In the treatment of a collection of time-of-flightspectra, one use of such summation is to ‘digitally align’ spectrathat may have been mass calibrated differently, perhaps due tosample topography or charging effects. Where two (or more)spectra are calibrated differently, the precise mass correspondingto the nth time channel in one spectrum will not be the same asthat for the nth time channel in the second spectrum. Therefore,when the data are expressed as a matrix comprised of rows ofspectra, any given column will contain intensities from differentmass values. For a SIMS image, where the spectrum at each pixelhas been acquired using the same instrumental parameters, thedata is likely to be consistently mass calibrated. Here, however,bin-summation is performed for two reasons: first, in order toreduce the number of variables submitted to the multivariatealgorithms. A typical SIMS spectrum contains anywhere between105 and 106 mass channels. Typical MVA algorithms require thismass domain to be reduced to a few thousands (or fewer) selectedor summed channels as a practical limit for processing on personalcomputers. Secondly, many ToF-SIMS images are very sparse. Thatis to say, they contain a proportionately large number of zerovalues. For example, a typical ToF-SIMS image may contain atotal of 1 × 108 counts distributed over 65 536 pixels. This givesan average of ∼1500 counts distributed over the 1 × 105 masschannels making up the pixel’s spectrum. A second reason forbin-summation is therefore to circumvent the sparse nature of thedata from inhibiting a meaningful analysis. We examined four massbinning strategies to determine their influence on the outcomeof PCA and MAF analyses: 1, 0.5 and 0.1 u all centred on nominalmass and 0.5 u with the bin edge aligned to nominal mass. Moredetails on the exact alignment are given in Appendix B.

Pixel summation

Composite datasets were produced to investigate the impactof the pixel dimension with respect to sample feature sizeon the image contrast produced in the scores output. Imageswere re-sampled by summing the spectra in adjacent pixels inboth the x- and y-directions. This produces a dataset containingone quarter of the original pixels. By summing together thespectra from neighbouring pixels, we increase the signal-to-noisecharacteristics of the data. In order that the re-sampled imagerepresented the original data more closely, the data was reduced inintensity prior to pixel summation. Here, we first Poisson scaled thespectra to spread noise due to Poisson statistics evenly throughoutthe data. Then we divided the value of the intensity for each masschannel in each pixel by 4, rounding down to the next lowestinteger value to better match the quantised characteristics ofpulse counted data. This has the effect of removing any intensityfalling below 1 count in the reduced spectrum.

Resultant image scaling for display

The colour scale used to display images should ideally capturethe major variation in the intensity of signal at each pixel. Pixelswith very high values (and in the case of scores plots, verylow values) can mask changes in intensity elsewhere in theimage. These pixels can be considered as outliers with respectto the rest of the data in the image. To avoid this, we havescaled the scores (and secondary ion) data prior to an imagebeing reproduced here. The statistical spread of the scores values

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(a) (b)

(c) (d)

Figure 2. Total secondary ion image from 0.1 u mass binned data showingthe difference in information content between scaled and unscaled data.(a) Unscaled (max: 39979 counts); (b) scaled only (max: 24069 counts);(c) smoothed only; and (d) scaled then smoothed.

was considered and the upper quartile (qU), lower quartile (qL)and interquartile range (iqr = qU − qL) of the scores data foreach principal component/factor were calculated. Upper andlower limits were determined at Limitupper = qU + (1.5 · iqr) andLimitlower = qL − (1.5 · iqr), respectively. For each image, any valuegreater than Limitupper was set to that value and likewise any valuelower than Limitlower was set to that lower limit. This scales theimage contrast to cover the majority of the variance in the dataand prevents outliers obscuring information.

Following scaling, images were smoothed for display purposesusing a one-point cosine taper smoothing routine.[24] Examplesof the scaling and smoothing procedures are shown in Fig. 2.The scaled and smoothed image (Fig. 2(d)) indicates subcellularfeatures most clearly. Scores images are shown with positive scoresin green and negative scores in red. Note that these scaling andsmoothing treatments are for display purposes only and have nobearing on the MVA techniques used.

Results and Discussion

Comparison criteria

As discussed above, we define an improvement in an analysiswhen the inner and outer compartments of the cellular structureare well defined. This cell marker, shown in Fig. 3(b and c), shouldappear as a low principal component or autocorrelation factorindicating a high degree of anticorrelation between these twostates. Good contrast is determined visually where well-definedseparation of species is apparent.

Comparison between PCA and MAF

Data binned to 0.1 u was analysed by both PCA and MAF. Poissonscaling improved the PCA analysis in comparison to unscaled

(a) (b) (c)

Figure 3. Scaled, smoothed images of HeLa cells showing (a) the total ionimage; (b) PC 6; and (c) MAF 4. MAF captures the distinction betweeninner and outer cellular regions more clearly than PCA. Comparison withthe total ion image shows the additional information available followingmultivariate analysis.

data. The cell marker component appeared spread between PCs 8and 9, but appeared at PC 6 following Poisson scaling. Followingthis result, all further PCA analyses were performed on Poissonscaled data. The scores images for PCA of Poisson scaled data andthose produced by the MAF analysis are shown in Fig. 4(a and b),respectively. MAF analysis indicated the cell marker factor at MAF4, improving further on the PCA result.

The contrast in MAF 4 is also more distinct than in the PCA resultas can be seen in Fig. 3. Comparison of the loadings produced by PC6 and MAF 4, shown in Fig. 5, indicate a high level of similarity in thespectral features identified with positive and negative loading.[25]

The PCA scores, in general, exhibit more noise making the MAFeasier to interpret.

The five most intense positively loaded spectral features (greenin Fig. 4) for both PCA and MAF were selected for use in a fingerprintlibrary search.[26] In both cases, three of these five featuresgenerated hits for phosphatidylcholine containing molecules. Asimilar search for the five most intense negatively loaded spectralfeatures (red in Fig. 4) generated hits at the 3 from 5 level fordeoxyadenosine, deoxyguanosine and spectra from proteins suchas fibronectin, thus reinforcing the manually identified chemistry.

Intensity reduction

Many SIMS images exhibit low secondary ion signal per pixel. Here,we address this by determining how the result from an average of104 secondary ions per pixel is modified by a reduction in intensity.The data, binned to 0.1 u, was reduced in intensity by dividing byfactors of 4 and 10. When dividing by a scalar value, we must becareful to preserve the characteristics of the noise. Poisson noiseis a function of peak intensity and so dividing by a constant willbe inconsistent peak to peak. Here, we select to Poisson scalethe data prior to the division. Each resultant intensity value isthen rounded down to the nearest lower integer to simulate thequantised characteristics of data with low signal intensity. Thismeans that reduced signal falling below 1 count was removedentirely. The average secondary ion yield per pixel is shown inTable 1.

Table 1. Average secondary ion intensity per image pixel for imageswhere the spectral intensity has been reduced following Poisson scaling

Originaldata

Poissonscaled

intensity

Poissonscaled

intensity/4

Poissonscaled

intensity/10

Average SI per pixel 9990 2050 350 100


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1 2 3

4 5 6

7 8 9

1 2 3

4 5 6

7 8 9

Figure 4. Scores images from Poisson scaling then PCA (left ≡ a) and MAF (right ≡ b) of the 0.1 u data in the original intensity and 128 × 128spatial resolution. Principal component numbers and autocorrelation factors are given in each image. The intra-cellular marker appears in the fourthautocorrelation factor compared to the sixth principal component indicating that MAF captures the intra-cellular character more readily.

(a) (b)

Figure 5. Loadings plots from (a) PC 6 and (b) MAF 4 showing the similarity in mass peaks identified and the difference in noise level.

It is important to note that this scaling followed by integerrounding is not the same as reducing the primary ion beamcurrent or other instrumental parameters to reduce the measuredintensity by the same scalar. The noise structure is very different.It is included here to illustrate different computational effects thatcould occur during data processing.

The reduction in available intensity information has a markedeffect on the PCA analysis. Reducing by a factor 4 moved the cellmarker component from PC 6 to a combination of PCs 11 and 12.Further reduction lead to the marker component falling outsidethe first 20 principal components; unlikely to be noticed in a typicalanalysis. Gross changes in chemistry, for example, the separationbetween organic and inorganic species remained visible in PCs1–5. The MAF analysis fared much better in that the reductionin intensity by a factor of 4 had little effect on the result; the cellmarker information still appearing in MAF 4. Reduction by a factorof 10 moved the cell marker to MAF 6, still readily observed by theanalyst.

The change in the amount of variance explained by eachprincipal component and autocorrelation factor, for each of theintensity reduced datasets, is shown in Fig. 6(a and b), respectively.For PCA, the amount of variance explained by the first PC variesin line with the amount of data remaining in the dataset. Theremaining PCs are not affected by the data reduction. For MAF,

there is almost no change in the amount of variance explainedby a given PC for reductions in the data up to a factor of 10.This indicates that even with poor signal intensity there is enoughinformation in the fragmentation pattern to indicate chemistry.

Mass binning

In order to determine the degree to which mass resolution isinvolved in the MVA of images, the data was mass binned togenerate new spectra with bin widths of 1, 0.5 and 0.1 u, centredon the nominal mass, and 0.5 u with the bin edge on the nominalmass (centre-split). This is detailed in Appendix B. Both PCA andMAF were performed on these mass resolution reduced data sets;the data being Poisson scaled prior to PCA analysis.

The result from MAF analysis is only slightly influenced by thereduction in mass bin size. For data centred on the nominal mass,the cell marker moved from MAF 3 to MAF 4 as the bin widthwas reduced from 1 to 0.1 u. The 0.5 u centred and 0.5 u centre-split showed an inversion between MAF 3 and MAF 4 indicatingthat the centre-split data will separate any inorganic contributiondifferently.

For PCA the treatment introduced larger variation. The lack ofspatial correlation requires the PCA algorithm to be more relianton mass resolution. Here the 0.5 u centred data separates the


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(a) (b)

Figure 6. Percentage of variance explained by each principal component (a) and autocorrelation factor (b). Reducing the intensity up to a factor of 10shows little effect on either PCA or MAF, other than in the first component/factor.

Table 2. Average secondary ion intensity, approximate dimensionand percentage of cell sampled per image pixel where both thespectral intensity and spatial resolution have been reduced

Poissonscaled

intensity

Poisson scaledintensity/4,

pixel numberreduced by 4

Poisson scaledintensity/16,pixel numberreduced by 16

Average SI perpixel

2080 1370 780

Pixeldimension

∼0.7 × 0.8 µm2 ∼1.4 × 1.7 µm2 ∼2.8 × 3.4 µm2

Percentage ofcell takenup by pixel

∼0.2% ∼0.8% ∼3.0%

lipid signal into two components, while the 0.5 centre-split dataseparates the organic from inorganic signals into two componentsbefore identifying the cellular material. The 0.1 u data separates the(in)organic signal into four components before, again, identifyingthe cellular material in PC 6. The indication here is that there isa difference between the two 0.5 u binned datasets in that theinorganic component is enhanced in the centre-split data. The 0.1u data combines these differences.

Spatial reduction

When confronted by low signal intensity in a SIMS image, manyanalysts would consider combining pixels to produce a lowercontrast image with more secondary ion signal per pixel, prior toMVA. Here we consider the outcome of such a procedure.

Reducing the intensity of a dataset by a factor of 4 and thenreducing the spatial resolution by a factor of 2 (four times fewerpixels) will produce a similar dataset to the original in terms ofions per pixel. Since the reduction in spectral intensity includesa rounding down of any fractional counts there will also be aremoval of noise with the removal of reduced spectral intensity<1 count. The average ion count per pixel is given in Table 2.

Note that there is no loss of spectral mass resolution as it is onlythe intensity and spatial distribution of the data that are beingmodified. Therefore it is expected that the PCA analysis, whichrelies solely on mass resolution, will outperform MAF analysiswhere spatial resolution is important. This assumption is partiallyborne out in the analysis. The PCA outcome shown in Fig. 7(a)contains the cellular information, but this is now spread out over

at least three principal components – PCs 3, 4 and 7. Visual contrastis enhanced since we now have a single pixel representing thechemistry of four original pixels.

The MAF analysis produces loadings (Fig. 8) that appear to bemeaningful in that they have the form of a SIMS spectrum ratherthan uniformly distributed noise, but the spatial distribution of thescores as shown in Fig. 7(b) is difficult to align with the original datain Fig. 4(b). Being presented with the scores images in Fig. 7(b),without prior knowledge such as the MAF results from data thathad not been pixel reduced (Fig. 4(b)) would make it difficult foran analyst to draw any conclusions from the analysis.

A further reduction in spatial resolution and intensity wasperformed by Poisson scaling, dividing the intensity by 16,rounding down as before, and reducing the data to a 32 × 32pixel image – a 16-fold decrease in spatial resolution. Here PCAstill gave some contrast relating to the inorganic components nowsplit across PC 2 and PC 3 and the cell structure across PCs 4–6.The MAF algorithm was unable to generate a result, reporting asingular matrix error.

Although the secondary ion signal per pixel is somewhatreduced, the act of summing the spectra from adjacent pixelshas markedly changed the PCA and MAF analyses even thoughthe mass resolution remains constant. One explanation as to whythe MAF has performed so poorly here is that the percentage ofcellular material that is represented by a pixel becomes a largerproportion of the cell. This, coupled with the difference in shapebetween a square pixel and a rounded cell, leads to a combinationof the chemistry in adjacent pixels. Since MAF takes the chemistryin adjacent pixels into account, their similarity will lead to anincreased autocorrelation and result in a blurring of the scoresimage.

Conclusion and Recommendations

We have seen that when there is sufficient spectral intensity ateach image pixel, MVA can greatly assist the SIMS analyst with datainterpretation. However, when there is a limited spectral intensity,the steps taken by the analyst in pre-processing the data beforeMVA may have a significant impact on the information returned.MAF analysis outperforms PCA where the spatial distribution ofchemistry is large with respect to the pixel dimension.

In order to increase spectral intensity, summing mass channelstogether is preferred to summing pixels, particularly if MAF analysisis planned. The inorganic contribution to a peak will clearly fall into


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1 2 3

4 5 6

7 8 9

Figure 7. Scores images produced from 0.1 u data, divided by 4 (following Poisson scaling) and spatially reduced to 64 × 64 pixels. PCA (left ≡ a) andMAF (right ≡ b). Principal components and autocorrelation factor numbers are given in each image. The cell marker is visible in PCs 3, 4 and 7, but onlypartially visible in MAF 4.

12

3

6

98

4 5

7

Figure 8. Loadings on MAF where both the spectral intensity and the number of pixels have been reduced by a factor 4 (following Poisson scaling)showing that some of the loadings may still identify chemistry even though the spatial location may be difficult to discern. Autocorrelation factornumbers are indicated.

the same bin as the organic contribution when the data is binnedto 1 u, and yet the first principal component or autocorrelationfactor separates the inorganic substrate from the organic cellularmaterial well. Therefore, it is the fragmentation pattern that is thedominant factor in MVA rather than mass resolution. If a separationbetween inorganic and organic components is expected, thenmass binning using a centre-split approach with the bin edgealigned with nominal mass may be beneficial.

Our recommendations therefore are as follows:

1. Use MAF rather than PCA for images with low spectral intensity.

2. Sum mass channels together to improve MVA.3. To separate inorganic material from organic, mass binning

using a centre-split approach, with the bin edge aligned withnominal mass, may be beneficial.

4. Summing pixels together prior to MAF analysis may give amisleading result.

5. Image scaling and smoothing can assist in visually identifyingregions of interest.

6. Poisson scaling prior to PCA can improve the outcome.


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Figure 9. Location and width of mass bins. (a) 1 u centred; (b) 0.5 u centred; (c) 0.5 u centre-split; (d) 0.1 u centred.

Acknowledgements

We thank Dean Jackson and Sadia Rabbani of the Universityof Manchester for providing and culturing the HeLa cells foranalysis. This research was supported by a grant from theUK Engineering and Physical Sciences Research Council (Grantnumber EP/C008251/1).

Appendix A

Data structure

In this text, an image is defined as a 3D data ‘cube’ with each x –yplane describing the spatial distribution of a particular mass. This2D matrix can be ‘unfolded’ to produce a 2D array of spectra whereeach row represents a spectrum from a particular pixel. The rowsare aligned such that each column represents the intensity valuesfor any given mass. In order to convert between an image and thematrix of the spectra contained within it, we can use the followingMATLAB code:

[xpixels, ypixels, massvalues] = size(image);spectra = reshape(image, xpixels × ypixels, massvalues);

In order to reconstruct an image from scores values obtainedthrough PCA or MAF analysis, we can use the following MATLABcode:

scoresimage = reshape(scores, xpixels, ypixels, massvalues);

Poisson scaling

Consider a spectral data matrix X = m × n with m spectral rowsand n mass values. The matrix can be Poisson scaled to producethe output variable scaler using the following MATLAB code:

a = sqrt(mean(X , 2));b = sqrt(mean(X));scaler = a∗b;scaledX = X/scaler;

where a is the square root of the average pixel; b is the square rootof the average spectrum; scaler is the outer product of a and b and

has the same dimensions as X ; and scaledX is the Poisson scaledversion of X where each value is divided by the equivalent valuein scaler.

Appendix B

Here we define the four mass bin strategies used to align the dataprior to analysis.

1 u centred

The channels in each spectrum were summed together such thatall channels falling within ±0.5 u of a nominal mass were assignedto that nominal mass. m1.0 = ∑

(mi ± 0.5 u) where mi is initiallyset to the first integer mass value and subsequent masses areincremented by 1.0 u. Example output: mass bin centres 75, 76, 77u etc. See Fig. 9(a).

0.5 u centred

The channels in each spectrum were summed together such thatall channels falling within±0.5 u of a nominal mass or half-nominalmass were assigned to that mass value. This produces narrowermass bins than the 1 u centred data, with additional mass bins‘between’ the peaks. m0.5c = ∑

(mi ± 0.25 u) where mi is initiallyset to the first integer mass value and subsequent masses areincremented by 0.5 u. Example output: mass bin centres 75.0, 75.5,76.0 u etc. See Fig. 9(b).

0.5 u centre-split

The channels in each spectrum were summed together such thatall channels falling within ±0.25 u of a nominal mass +0.25 u, wereassigned to that mass value. This produces new mass bins wherethe bin edge lies on a nominal mass. The advantage of such aprocedure is that spectral features that are mass deficient (typicallyinorganic species) will fall into a separate mass bin to those that aremass sufficient (typically organic species). m0.5s = ∑

(mi ± 0.25 u)where mi is initially set to 0.25 u above the first integer massvalue and subsequent masses are incremented by 0.5 u. Exampleoutput: mass bin centres 75.25, 75.75, 76.25 u etc. See Fig. 9(c).


67

4


0.1 u centred

The channels in each spectrum were summed together such thatall channels falling within ±0.05 u of a nominal mass +0.1 u, wereassigned to that mass value. m0.1 = ∑

(mi ± 0.05 u) where mi

is initially set to the first integer mass value (nominal mass) andsubsequent masses are incremented by 0.1 u. Example output:mass bin centres 75.0, 75.1, 75.2 u etc. See Fig. 9(d).

References

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A comparison of PCA and MAF for ToF-SIMS image interpretation

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