BIOPHOTONICS - ArrayFire · in HPLC grade water, Sigma Aldrich, UK). Suspen-sions of the PC-3 cells (150 ml) were cytospun (800 RPM, 5 minutes, low acceleration) onto calcium

FULL ARTICLE

RMieS-EMSC correction for infrared spectraof biological cells: Extension using full Mie theoryand GPU computing

Paul Bassan1, Achim Kohler2, Harald Martens2; 3, Joe Lee4, Edward Jackson1,Nicholas Lockyer1, Paul Dumas5, Michael Brown6, Noel Clarke6; 7; 8, and Peter Gardner*; 1

1 School of Chemical Engineering and Analytical Science, Manchester Interdisciplinary Biocentre, University of Manchester,131 Princess Street, Manchester, M1 7DN, UK

2 Nofima Mat, Centre for Biospectroscopy and Data Modelling, Osloveien 1, 1430 �As, Norway3 CIGENE, Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1430 �As, Norway4 School of Chemical Engineering and Analytical Science, The Mill, The University of Manchester, Oxford Road,

Manchester, M13 9PL, UK5 Synchrotron SOLEIL, L’Orme des Merisiers, BP48 – Saint Aubin, 91192 Gif-sur-Yvette Cedex, France6 Genito Urinary Cancer Research Group, School of Cancer and Enabling Sciences, Paterson Institute for Cancer Research, The Univer-

sity of Manchester, Manchester Academic Health Science Centre, The Christie NHS Foundation Trust, Manchester, UK, M20 4BX, UK7 Department of Urology, The Christie NHS Foundation Trust, Manchester, UK, M20 4BX, UK8 Department of Urology, Salford Royal NHS Foundation Trust, Salford, UK, M6 8HD, UK

Received 26 February 2010, revised 4 April 2010, accepted 5 April 2010Published online 26 April 2010

Key words: FTIR, single cells, cell nucleus, infrared microspectroscopy, anomalous dispersion artefact, signal correction,EMSC, Mie scattering, resonant Mie scattering

# 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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In the field of biomedical infrared spectroscopy it is of-ten desirable to obtain spectra at the cellular level. Sam-ples consisting of isolated single biological cells are par-ticularly unsuited to such analysis since cells are strongscatterers of infrared radiation. Thus measured spectraconsist of an absorption component often highly dis-torted by scattering effects. It is now known that thepredominant contribution to the scattering is ResonantMie Scattering (RMieS) and recently we have shownthat this can be corrected for, using an iterative algo-rithm based on Extended Multiplicative Signal Correc-tion (EMSC) and a Mie approximation formula. Herewe present an iterative algorithm that applies full Miescattering theory. In order to avoid noise accumulationin the iterative algorithm a curve-fitting step is imple-mented on the new reference spectrum. The new algo-rithm increases the computational time when run on anequivalent processor. Therefore parallel processing by aGraphics Processing Unit (GPU) was employed to re-

duce computation time. The optimised RMieS-EMSCalgorithm is applied to an IR spectroscopy data set ofcultured single isolated prostate cancer (PC-3) cells,where it is shown that spectral distortions from RMieSare removed.

Resonant Mie Scattering (RMieS) distortion of infraredspectra from single cells can now be corrected for usingan algorithm incorporating full Mie theory

* Corresponding author: e-mail: [email protected], Tel.: 0161 306 4463, Fax: 0161 306 5201

Early View publication onwww.interscience.wiley.com(issue and page numbers not yet assigned;citable using Digital Object Identifier – DOI)

J. Biophoton. 1–12 (2010) / DOI 10.1002/jbio.201000036

1. Introduction

In the field of biomedical infrared spectroscopythere is a drive towards obtaining spectra at highspatial resolution such that biologically relevant in-formation can be obtained at the single cell level [1–12]. This desire for spatially resolved chemical infor-mation applies equally to cells in tissue or isolatedcells deposited onto an infrared compatible sub-strate. The goal is to compare the biochemistry asso-ciated with one cell with that of neighbouring cellsin the tissue or culture, usually in an attempt to ob-tain specific signatures or markers for disease. Un-fortunately this is rarely possible since a measuredspectrum often contains contributions from absorp-tion, reflection and scattering [13, 14]. Biologicalcells are typically a few micrometres to a few tens ofmicrometres in diameter. This is comparable in sizeto the wavelength of mid-infrared radiation used ina conventional infrared microspectroscopy system.Consequently the cells in the sample scatter the in-frared radiation being used to probe them very effi-ciently. Thus the resulting spectrum contains contri-butions from both effects. Given that cell size andshape (morphology) is variable within any givensample, obtaining subtle differences in biochemistryalone, from a measured spectrum, is very difficult toachieve. It is therefore imperative that methods aredeveloped to separate the scattering contributionsand the pure absorption contribution from the meas-ured spectrum [15–16]. In order to do this one mustfirst understand the predominant cause of the scat-tering phenomenon. In 2005, Mohlenhoff et al. pos-tulated that Mie scattering from the cell nucleus wasthe cause of the strong broad oscillations in the spec-trum baseline [17]. In 2008, Kohler et al. publishedthe first reliable correction for these Mie type scat-tering oscillations in the baseline [18], but the sharpreduction in intensity on the high wavenumber sideof the Amide I band, often mistakenly called the“dispersion artefact” frequently remained uncor-rected [18]. Recently, Bassan et al. demonstratedthat both the broad oscillation in the baseline andthe “dispersion artefact” could be described by thephenomenon of Resonant Mie Scattering (RMieS)[16, 19]. It should be noted that the term “dispersionartefact” is a misnomer since the pronounced dip inintensity is only indirectly related to anomalous dis-persion and it is not an artefact. It is also not solelya reflection component, as is often mistakenly be-lieved, and although there may well be a pure reflec-tion contribution, this is adequately incorporated inthe resonant Mie scattering model (as reflection is aspecial case of scattering which is explained by Mietheory [20]).

Previous papers on the subject of correcting theeffects of Mie scattering in IR spectra of scatteringsamples have utilised the van de Hulst approxima-

tion equation [20], for the calculation of the Miescattering efficiency [18, 19]. This equation is an ap-proximation used instead of full Mie theory [21],which is significantly more complicated and compu-tationally expensive to implement. There are a num-ber of conditions under which the van de Hulstequation should be used: for homogenous non-ab-sorbing spherical particles. Highly scattering samplesmeasured with IR (i.e. single cells and tissues) areinhomogeneous non-spherical absorbing particlesrendering the equation of limited applicability.

Previous work by Bassan et al. [19] used anadapted form of the van de Hulst equation wherethe real refractive, n, used was not a constant, butvariable. This was a “spectrum” obtained from theKramers–Kronig transform of a reference spectrum.A comparison of measured and theoretical datausing PMMA microspheres shows that this adapta-tion of the van de Hulst equation was a reasonablesubstitute for the full Mie theory [16].

In this paper we introduce full Mie theory and amethod of optimising the reference spectrum itera-tively. Full Mie theory is considerably more compu-tationally expensive to implement, and so we haveharnessed the power of graphics processing unit(GPU) computing to reduce this time.

The full Mie theory (RMieS-EMSC) algorithm isapplied to a typical data set consisting of spectrafrom single isolated prostate cancer (PC-3) cellswhich have been a focus of our research recently[6–8, 22, 23].

2. Experimental

2.1 Cell culture

Cells from the PC-3 human prostate adenocarcino-ma cell line were seeded in 25 ml sterile plastic cul-ture flasks (Fisher Scientific, UK). After culturing(37 �C, 5% CO2, in air) in PC-3 media (Ham’s F12,7% FCS and 2 mM L-glutamine, Sigma Aldrich,UK) to approximately 80% confluency, the mediawas removed. The cells were then washed in Dulbec-co’s Phosphate Buffered Saline (DPBS) (10 ml, Sig-ma Aldrich, UK), after which 1 ml trypsin solution(0.5 mg/ml trypsin; 0.2 mg/ml EDTA in PBS, SigmaAldrich, UK) was added and the cells were incu-bated (3 minutes, 37 �C, 5% CO2, in air). The cellswere then re-suspended in the growth media (4 ml)and removed for centrifugation. Once removed, thecell suspension was centrifuged (800 g, 5 minutes)and the supernatant discarded. The cells were thenre-suspended in DPBS (5 ml) and centrifuged as be-fore. Finally, the DPBS was removed and the cellswere suspended – and fixed – in ethanol (4 ml, 70%

P. Bassan et al.: RMieS-EMSC correction for infrared spectra of biological cells2

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# 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.biophotonics-journal.org

in HPLC grade water, Sigma Aldrich, UK). Suspen-sions of the PC-3 cells (150 ml) were cytospun (800RPM, 5 minutes, low acceleration) onto calciumfluoride (CaF2) slides for FTIR analysis.

2.2 Synchrotron infraredmicro-spectroscopy

The synchrotron FTIR micro-spectroscopy data wererecorded at the synchrotron SOLEIL on the SMISbeamline, details of which can be found elsewhere[24]. The spectra were obtained using a Nicolet Nic-Plan microscope equipped with an MCT detector.Spectra were recorded by co-adding 512 interfero-grams at 8 cm�1 resolution. The size of the aperturewas 20 � 20 mm2, which roughly matched the diam-eter of the cells such that each cell was fully illumi-nated.

3. RMieS-EMSC

3.1. Mie theory

In 1908 Gustav Mie wrote his theory for the scatter-ing of light by homogenous spherical absorbing par-ticles [21]. Until the advent of high speed computing,calculations were considered impractical due to theheavy computation required, particularly when arange of wavelength or sphere diameter is involved.For the purposes of correcting IR spectra fromhighly scattering samples a number of assumptionsand simplifications need to be made, the most impor-tant of which is that the non-spherical particles canbe approximated as several spheres of differentradii. Mie theory requires knowledge of the scatter-ing particle radius, r, and the complex refractive in-dex ratio, h, of scattering particle to air. The realand imaginary parts of the refractive index of air canbe assumed to be the same as vacuum, nair ¼ 1,kair ¼ 0. This simplifies the complex refractive indexratio to the index of the scattering particle andhence this convention will be used throughout thispaper.

Mie theory describes the total loss of light causedby a scattering particle due to both the absorptioncharacteristics of the particle and scattering; the sumof the absorption and scattering efficiencies(Qabs þ Qsca) is termed the extinction efficiency, Qext.Of interest to us are Qsca values of the particle overa range of wavelengths, the full mathematical defini-tion of which is given in the Appendix.

3.2. Implementation of full Mie theoryin the RMieS-EMSC algorithm

Bassan et al. [19] published the first algorithm to cor-rect for resonant Mie scattering of highly scatteringsamples which was based upon a non-resonant Miescattering algorithm by Kohler et al. [18]. Both ofthese algorithms build upon the extended multiplica-tive signal correction (EMSC) by Martens et al. [25].Here we show an optimisation of the RMieS-EMSCwhich uses full Mie theory instead of the van deHulst approximation for the computation of scatter-ing efficiencies. The RMieS-EMSC model is

~ZZRaw ¼ cþmv~~~þ h~ZZRef þXN

i¼1

gi~ppi þ ~EE ð1Þ

where ZRaw ¼ the raw spectrum to be corrected,c ¼ constant offset baseline, m ¼ gradient of slopingbaseline, ZRef ¼ reference spectrum, h ¼ magnitudeof ZRef, N ¼ number of principal components used,g ¼ weight applied to loadings, p, of the Mie scatter-ing matrix and E ¼ un-modelled residual variance.Symbols with arrows above denote vectors, i.e. a col-umn or row of numbers.

The algorithm assumes that the measured spec-trum is a linear combination of a constant and slop-ing baseline, a reference spectrum, a scattering curveand a spectrum of features that could not be mod-elled. The sigma term in the equation is where thevariation due to RMieS is accounted for in the formof weights applied to loadings from the principalcomponent analysis (PCA) decomposition of a ma-trix containing many scattering curves of differentparticle radius and refractive index.

In this paper we change the algorithm such thatthe matrix of RMieS curves is calculated using fullMie theory instead of the van de Hulst approxima-tion. The use of full Mie theory requires certain ma-nipulations to deal with the use of a complex refrac-tive instead of just the real part of the refractive aspreviously implemented. The complex refractive in-dex, h, is defined as

h ¼ n� ik ð2Þ

where n ¼ real part of the refractive index,k ¼ imaginary part of the refractive index andi ¼ the imaginary unit,

ffiffiffiffiffiffiffi�1p

.To calculate the Qsca curves, both real and im-

aginary refractive indices are needed, the startingpoint of which is the reference spectrum. The refer-ence spectrum is taken and normalised such that theAmide I band peak is at an absorbance of 1. At thisstage it is useful to introduce two terms which con-struct the real refractive index, a and b which are

J. Biophoton. (2010) 3

FULLFULLARTICLEARTICLE

# 2010 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheimwww.biophotonics-journal.org

the average refractive index and “resonance param-eter” respectively, such that:

n ¼ aþ bnKK ð3Þwhere nKK is the Kramers–Kronig transform of thereference spectrum minus an average refractive in-dex such that it is centred around zero allowing usto add our own desired average refractive index.

To create a database of Qsca curves coveringmany possibilities, 10 equidistant values of particleradius, r, are used between 2 and 8 mm. A range ofcomplex refractive indices also needs to be covered,and so 10 equidistant coefficients are multipliedwith the Amide I normalised reference spectrumranging from 0 to 0.4. The value of 0 represents anon-absorbing particle, and the upper limit of 0.4 issomewhat arbitrary but an educated guess suggeststhat the value of the Amide I peak in the k spec-trum is not likely to exceed a value of 0.4. For eachof these 10, k, possibilities, a Kramers–Kronig, nKK

has to be calculated and then an average real re-fractive index, a, has to be added. The range of va-lues that a can take is limited by the nKK spectrum,e.g., if the lowest value in the nKK spectrum is �0.1,then the lowest value a can take is 1.1 ensuring thatthe real refractive index never goes below 1. Theupper limit for a has been chosen to be 1.5 which isan appropriate upper limit for biological cells. Using10 equidistant values of r, a and b between the sta-ted ranges gives 1000 permutations and hence 1000Qsca curves which cover many possible particle radiiand complex refractive indices within a realisticrange.

As the Appendix shows, the calculation of Qsca

requires the computation of spherical Bessel andHankel functions which are considered computation-ally intensive and slow. Therefore, an algorithmbased on a stepwise adaptation of Bessel and Han-kel functions to spectra of highly scattering samplesby changing scattering particle radius, r, and thecomplex refractive index ratio, h, of scattering parti-cle to air is not suitable in practice. The computationinvolved would be too time-consuming for practicalpurposes. In order to circumvent tedious calculationsfor the adaptation of each spectrum we approximatethe database of 1000 Mie curves Qsca by a subspacemodel using a few principal components accordingto Kohler et al. [18] and build this subspace model inthe EMSC model of Eq. (1). Since only principalcomponents are used in the model of Eq. (1), the es-timation of parameters by linear regression modelused for the estimation is stable. The subspace mod-elling according to Kohler et al. [18] has been em-ployed by us for the correction of RMieS scatteringusing the approximate formula by van de Hulst [20],but shows its full power here, where calculation ofRMieS scatter curves using the full Mie theory iscomputationally very intensive.

In order to decrease computation time for build-ing the database, a method is discussed to optimisethe calculation of these spherical functions to savetime using graphics processing unit (GPU) comput-ing in the next section.

3.3 Graphics processing unit (GPU)computing

Modern GPUs contain many processing cores eachof which can be used in a similar manner to con-ventional central processing units (CPUs). The com-puter system used here is an Intel 2.4 GHz QuadCore Xeon with 12 GB of RAM and an NVIDIATesla 1060c GPU. This GPU has 240 processingcores which operate at 1.3 GHz each and hence isideally suited to parallel processing, such as the cal-culation of Bessel functions which can be done in-dependently from one another. To calculate a 1000curve Qsca database using Matlab 2009a (Math-works, Natick, MA, USA) on our computer takes89.91 seconds for a spectrum of 1601 intensity val-ues. The only way this calculation can be speededup on the CPU is by having a higher frequencyCPU, i.e., greater than 2.4 GHz. The computationtime of the Qsca database using the van de Hulstapproximation for the same example is 0.324 sec-onds. However due to heat production issues, CPUspeeds are not being increased above typically3.33 GHz, and instead multiple cores (such as Quadcore processors) are being produced which does notnecessarily help certain computation. In the case ofthe spherical Bessel and Hankel functions withinMatlab 2009a, these functions are not able to accessmultiple cores meaning that multiple core machinesproduce no further speed gains.

A toolbox “The Jacket Toolbox” (Accelereyes,Atlanta, GA, USA) available for Matlab containsa programme that acts as an intermediate layer be-tween Matlab and the GPU. Of particular interesthere are the spherical Bessel and Hankel functions.The equivalent computation of the Qsca databasementioned above can be completed in 35.94 sec-onds, a speed gain of 2.48. Although this speedgain may seem trivial for a single spectrum, whenusing the RMieS-EMSC algorithm for correctingIR images with many pixels, this speed gain willsave many hours. The current version of the JacketToolbox (v1.2.2) is going to be improved in thenear future such that the speed gains of thesefunctions will increase by at least an order of mag-nitude which is very significant. In the future moresections of the algorithm will be transferred to theGPU to take advantage of its computational poten-tial.


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3.4. Reference spectrum optimisation

The weakest part of the RMieS-EMSC is the use ofa reference spectrum to provide stability during thelinear regression stage to estimate the scatter contri-butions. The important point is that the perfect refer-ence spectrum to use for a correction is the answerthat is being calculated, i.e., the pure absorbancespectrum of the sample. Since this is never available,a reference spectrum that will be close to the answerbeing sought is required. The result of using a refer-ence spectrum that is “approximately” correct is thatthe corrected spectrum contains elements of thereference spectrum that may not be present in thetrue absorption spectrum of the sample [19]. A solu-tion to this problem is to iteratively improve the re-ference spectrum by using the corrected spectrum ofone iteration as the new reference spectrum for an-other; the rationale being that eventually the cor-rected spectrum would converge on the pure absorb-ance spectrum of the sample [19].

The RMieS-EMSC was previously demonstratedon a simulated data set constructed by adding manyGaussian curves together which were subsequentlydistorted by adding theoretical RMieS curves [19].These spectra were noise free and showed proof ofprinciple, but there are several potential issues thatcan arise when attempting to iteratively correct areal measured spectrum.

The algorithm requires the real refractive indexto be calculated by applying the Kramers–Kronigtransform to the newly corrected spectrum. Meas-ured data often contain noise, and for spectraacquired using a Synchrotron source, the noise is of-ten increased at the low-wavenumber end of thespectrum due to the diffraction limit and/or substratetransmittance. The Kramers–Kronig transform of apoor S/N spectrum will yield an n spectrum of everpoorer S/N, (in a similar way that first derivativespectra are more noisy that the original spectrum). Ifa noisy n spectrum is inserted into the Mie formulae,the resultant Mie scattering curves would exhibitsimilar noise properties which is highly undesirable.In this situation, corrected spectra can often comeout of the algorithm with features of the scatteringremaining, and/or absorbance values below zero incertain regions of the spectrum.

"

Figure 1 (a) Measured spectrum of Matrigel film. (b) Sec-ond derivative spectrum of the Matrigel film. (c) Resultingfitted spectrum. (d) The difference between the measuredand fitted spectra.




To reduce the issue of noise and remaining scat-tering effects within a corrected spectrum a fittingstep was introduced. The newly corrected spectrumis taken and interpolated such that the data spacingcorrespond to 0.5 cm�1, after which a Savitzky-Golaysecond derivative with 9 smoothing is implemented(to locate peak positions to an accuracy of�0.25 cm�1). The region between 1800 and2500 cm�1 contains no biochemical information butstill contains remnants of the scattering effects, andhence is replaced with zeros. Using a peak minimafinding algorithm, the second derivative spectrumyields the wavenumber position of peaks includingsecondary structure peak information of, e.g., theAmide I band. Using these peak positions, a data-base is constructed comprising of Gaussian curves ofvarious widths centred at each peak position. A non-negative linear regression – as peaks can only be po-sitive in an absorbance spectrum – is then per-formed on the corrected spectrum using the Gaus-sian curves as descriptive vectors. Figure 1 shows theresults of this fitting process applied to a measuredspectrum of a thin layer of Matrigel.

Figure 1 shows the quality of the fitting proce-dure, where Figure 1(d) shows the difference be-tween the measured and fitted spectrum. The differ-ence between the spectra is 3 orders of magnitudelower than the measured spectrum and hence it canbe considered a good representation. This fittedspectrum now contains zero noise and since eachGaussian curve was centred on a peak position fromthe second derivative spectrum, it contains no nega-tive values or any scatter contributions.

3.5 Optimisation of the RMieS-EMSCalgorithm

In this paper the RMieS-EMSC algorithm has beenoptimised to incorporate full Mie theory which iscomputed using GPU computing. The iterative im-provement of the reference spectrum has been opti-mised by modelling the corrected spectrum using aGaussian database to reduce noise. The remainderof the algorithm has not been stated because it canbe found in our previous publication [19], however aconcise summary is presented in flow chart formbelow. Figure 2 shows a schematic of the RMieS-EMSC algorithm with the new optimisations pre-sented in this paper highlighted. The callout andreturn from the calculation of the Qsca database tothe GPU represents the calculation of the sphericalBessel and Hankel functions on the GPU so thatthey can be parallel processed for speed optimisa-tion.

4. Results

4.1 Correction of single prostate cancer(PC-3) cells

Figure 3 shows 280 raw FTIR spectra of single iso-lated PC-3 cells on CaF2. Despite all the spectra be-longing to cells from a single cell line, they are ob-

Figure 2 (online color at:www.biophotonics-journal.org)Schematic of the optimizedRMieS-EMSC algorithm withmodifications highlighted.


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viously not all the same, showing significant varia-tion over the whole wavenumber range. The spectraare clearly distorted by resonant Mie scatteringwhich results in broad oscillating baselines, and thedecrease in intensity around 1700 cm�1. The bio-chemistry of these cells is not expected to be identi-cal, due to natural variation and different stages ofthe cell cycle but the spectra were expected to bevery similar in appearance.

As we have previously shown [16, 19], the differ-ences observed in Figure 3 can be fully explainedand are caused by resonant Mie scattering. The mor-phological characteristics of each cell, namely thesize and shape of the cell, the size of the nucleus andother organelles varies significantly amongst the 280cells measured. RMieS is dependent on the scatter-ing particle radius and refractive index properties[16, 19] so it is not surprising that the spectra lookvery different. These scattering effects distort thepure absorbance spectrum of each cell which is ofinterest to us and yields the spectrum of limited use,and the biochemical information cannot be trusted.

Using the RMieS-EMSC algorithm, the presenceof the scattering effects can be significantly reducedyielding corrected spectra which more closely resem-ble the pure absorbance spectrum of each cell [19].Figure 4 shows the 280 spectra shown in Figure 3,corrected using the RMieS-EMSC algorithm incor-porating the full Mie theory. Five iterations of thealgorithm were used after which there was no signifi-

cant change in the resulting spectra. It is immedi-ately obvious that the removal of scattering contri-butions produces a much more internally consistentlooking set of spectra.

Although some variation in the spectra is stillpresent, this is to be expected since there will be nat-ural variation within a cell line.

An important feature of biological spectra is theband shape and peak maximum position of the AmideI band. This is important since under non-scatteringconditions the position and shape of the Amide I bandcan be indicative of protein secondary structure. Fig-ure 5 shows an expanded plot of the Amide I band ofthe raw spectra in Figure 3, the mean peak position is1650.5 cm�1 (central dashed trace). The lowest andhighest peak position of the Amide I bands is 1624.4and 1656.9 cm�1, a range of 32.5 cm�1.

This range of peak positions is far greater thanwould be expected, for a sample of cells from thesame cell line as is the case here. The true Amide Ipeak position has been distorted due to resonantMie scattering and if taken at face value, incorrectconclusions regarding protein secondary structuremay be drawn inappropriately. To produce reliablepeak positions the effects of resonant Mie scatteringhave to be removed, Figure 6 shows an expandedplot of the Amide I band for the corrected spectrafrom Figure 4.

The Amide I peak positions of the corrected spec-tra are significantly different from the raw spectra, with

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Figure 3 (online color at: www.biophotonics-journal.org)Raw transmission FTIR microscopy spectra of 280 isolatedsingle PC-3 cells.

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Figure 4 (online color at: www.biophotonics-journal.org)RMieS-EMSC corrected spectra of the data set shown inFigure 3.




the mean peak position now at 1655.2 cm�1. The mini-mum and maximum peak positions are now 1650.1and 1659.7 cm�1 respectively, a range of 9.6 cm�1.

4.2 Comparison with “Rubber Band”and previous Mie scattering correction

Despite the well known problem of scattering arte-facts in spectra of biological cells, in the absence of ascattering correction algorithm a simple “baselinecorrection” has often been employed using the so-called “rubber band” method [26, 27].

Figure 7(a) shows one of the raw spectra fromthe data set in Figure 3 and is very typical of a singlecell spectrum exhibiting the classic sloping baselinebetween the C–H stretching region and the Amide Iband. The blue dots indicate a typical baseline cor-rection using the rubber band method. The resultingcorrected spectrum is shown in Figure 7(b). As canbe seen the spectrum looks very good and is similarto the RMieS-EMSC corrected spectra in Figure 7(cand d). What is important however, is that the posi-tion of the Amide I band is not corrected properlyby the rubber band method and is still significantlylow-wavenumber shifted due to the RMieS. Therubber band method corrected peak position is at1650 cm�1, compared with 1654 cm�1 using theRMieS-EMSC algorithms. Although one could arguethat we do not know what the “correct” position ofthis band should be, extensive testing of the RMieSalgorithm on simulated data strongly indicates thatthe RMieS-EMSC correction results in an Amide Iband position within 1 cm�1 of the correct value[19]. Figure 7(c) is the spectrum corrected with theRMieS-EMSC algorithm using the van de Hulst ap-proximation. Figure 7(d) shows the same spectrumcorrected using the algorithm presented in thispaper, incorporating the full Mie scattering theory.A comparison of the two spectra shows that they areessentially identical with the Amide I band positionat 1654 cm�1 in both cases and the same intensitydistribution in the diagnostically important regionfrom 1500–1000 cm�1. Thus, it is clear that as a spec-tral correction method the previous RMieS-EMSCalgorithm is as good as the new algorithm using thefull Mie theory, and importantly it is significantlyquicker. This begs the question, why develop thenew algorithm? The answer to this is two-fold.Firstly, the fact that the algorithms based on the ap-proximation and the full Mie theory agree almostexactly demonstrate the validity of using the van deHulst approximation. Secondly, although the van deHulst approximation works, it transpires that thescattering parameters, e.g., radii of scatterers andrefractive index combinations that lead to the cor-

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Figure 5 (online color at: www.biophotonics-journal.org)Amide I bands of the raw spectra from Figure 3. Dashedtraces from left to right show, maximum, mean and mini-mum peak positions respectively.

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Figure 6 (online color at: www.biophotonics-journal.org)Amide I peak positions of the corrected spectra from Fig-ure 4. Dashed traces from left to right show: maximum,mean and minimum peak positions.


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rected spectra are slightly different in each case.Pijanka et al. [28] have shown that this scattering in-formation can also be of diagnostic value. It is im-portant therefore to obtain the best possible esti-mate of the scattering parameters if these are to besubsequently used [28]. This will be the subject of afuture paper.

5. Conclusion and discussion

In this paper we have introduced full Mie theory andthe manipulations required to deal with the complexrefractive index in the calculation of Qsca. These func-tions are slow to compute due to spherical Bessel andHankel functions, however we have shown that usingthe Accelereyes Jacket toolbox for GPU computingwithin Matlab can speed calculations up significantly.This speed gain will improve in the near future as theJacket toolbox is optimised further.

The use of the reference spectrum in the RMieS-EMSC which is the weak point of the algorithm hasbeen optimised such that before the newly correctedspectrum is used as the new reference, it is modelledand fitted using Gaussians placed at specific posi-tions located from the second derivative spectrum.This produces a noise free spectrum with no nega-tive values or any scattering remnants that were pre-viously a potential problem.

We have subsequently shown that the optimisedRMieS-EMSC algorithm incorporating the full Mietheory can be used to correct a typical data setrecorded from 280 single prostate cancer cells. The

correction converts unusable raw data into a seriesof spectra that reflect the natural variations within atypical cell line population. Comparison with base-line correction methods that are freely availablewithin standard commercial FTIR software showthat if biochemical information relating to proteins isrequired some form of RMieS correction should beused. Importantly we demonstrate that the previousRMieS-EMSC correction using the van de Hulst ap-proximation corrects the spectra as well as theRMieS-EMSC based on the full Mie theory but thelatter (although not show here) will give better moreaccurate scattering parameters.

APPENDIX

Mie theory

The Mie scattering efficiency, Qsca, is defined as:

Qsca ¼2x2

X1n¼1

ð2nþ 1Þ janj2 þ jbnj2n o

ðA1Þ

an ¼w0nðyÞ wnðxÞ � hwnðyÞ w0nðxÞw0nðyÞ znðxÞ � hwnðyÞ z0nðxÞ

ðA2Þ

bn ¼hw0nðyÞ wnðxÞ � wnðyÞ w0nðxÞhw0nðyÞ znðxÞ � wnðyÞ z0nðxÞ

ðA3Þ

wnðzÞ ¼ffiffiffiffiffiffipz

2

rJnþ1=2ðzÞ ðA4Þ

Figure 7 (online color at:www.biophotonics-journal.org) (a)Spectrum of a single PC-3 cellexhibiting RMieS. Blue markersand connecting dashed lines showthe points used for performing arubber band correction (b) Spec-trum corrected using rubber bandcorrection. (c) Spectrum correctedusing the van de Hulst basedRMieS-EMSC algorithm (5 itera-tions). (d) Spectrum correctedusing the full Mie theory basedRMieS-EMSC algorithm (5 itera-tions).




znðzÞ ¼ffiffiffiffiffiffipz

2

rHð2Þnþ1=2ðzÞ ðA5Þ

x ¼ 2pr~vv ðA6Þy ¼ 2pr~vvh ðA7Þh ¼ h1=h2 ðA8ÞWhere, h1 ¼ complex refractive index of scatteringparticle, h2 ¼ complex refractive index of surround-ing medium, r ¼ particle radius; J and H(2) denotethe 1st kind Bessel and 2nd kind Hankel functionsrespectively. z ¼ x or y.

Acknowledgements We would like to thank (i) theEPSRC/RSC analytical fund for studentships for PB andEJ; (ii) James Malcolm from Accelereyes for his help withthe Bessel and Hankel functions in the Accelereyes Jackettoolbox for Matlab; (iii) all the staff on the SMIS beam-line for their assistance during our visit and (iv) the Agri-cultural Food Research Foundation.

Paul Bassan received hisB.Sc. in Physics at the Uni-versity of Warwick U.K. in2006 and his an M.Sc. inMedical Physics at the Uni-versity of Manchester U.K.in 2007. In October 2007 hejoined the Gardner group at

the University of Manchester and is currently research-ing the fundamental principles of mid-IR light scatter-ing (namely Mie scattering) in single cell and tissuesamples as used in FTIR spectroscopy. In the future heplans to apply the RMieS-EMSC to FTIR imaging datawith the use of parallel computing using graphics pro-cessing unit (GPU) computing.

Achim Kohler received hismaster degree in physics atthe University of Freiburg inGermany in 1997 and ob-tained his Ph.D. in the fieldof Quantum Chaos in theo-retical physics in 1999. Aftera short period as a program-mer in software industry de-veloping graphical informa-tion systems, he started as aresearch scientist at NofimaMat. At Nofima Mat his re-search focuses on biospec-

troscopy and data modelling for biospectroscopy andbiology in general. He is the leader of the research pro-gram on data modelling and the founder of the virtualCentre for Biospectroscopy and Data modelling atCampus �As.

Harald Martens has a back-ground in biochemical engi-neering and has worked inthe field of chemometricssince the early 70-ies, focus-ing on the conversion ofhigh-dimensional biologicaland chemical measurementsinto meaningful chemical in-formation. He took part indeveloping the PLS regres-sion method in the early 80-ies and the Multiplicative

Signal Correctrion (MSC). He defended his dr.techn.thesis at the Norwegian University of Science and Tech-nology, Trondheim, Norway in 1985. In the 90-ies heworked on model-based compression of video signals.He is currently Professor II, CIGENE/Inst.Math.Sci. &Technol., Norwegian U. of Life Sciences, �As and Seniorresearch scientist, Norwegian Food Research Institute,�As, Norway, and Adjunct professor, University of Co-penhagen, Faculty of Life Sciences, Denmark.

Joe Lee received his B.Sc. inchemistry at the Universityof Leeds in 1951 and hisPh.D. in physical chemistryat the same university in1955. In 1956 he was ap-pointed as an ICI ResearchFellow in the Inorganic andPhysical Chemistry Depart-ment of the University of Li-verpool. In 1959, he moved

to the then Manchester College of Science and Technol-ogy as Lecturer in Chemistry. Before retiring in 1997 asa Senior Lecturer at the University of Manchester Insti-tute of Science and Technology (UMIST), he had lec-tured in all the standard aspects of physical chemistryand in the proper application of mathematics and statis-tics to chemistry. His research interests included high re-solution NMR, UV/visible emission spectroscopy offlow discharge systems and theoretical aspects of tem-perature-programmed gas chromatography. Since retire-ment, as a Visiting Research Fellow in UMIST and laterin the University of Manchester, he has been involvedwith theoretical aspects of infrared spectroscopy of thin-films and more recently of cancer cells, particularly inthe understanding of scattering distortions.

Edward Jackson obtained aB.Sc. in Zoology from LeedsUniversity in 2005 and amaster of Science in Analy-tical Biosciences and DrugDesign from the Universityof Salford in 2007. Cur-rently, Edward is studying


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BIOPHOTONICS


for a Ph.D. in analytical science at the University ofManchester, based at the Manchester InterdisciplinaryBiocentre. Edward’s research uses a combination oftime-of-flight secondary ion mass spectrometry (ToF-SIMS) and synchrotron source based infrared micro-spectroscopy to study cancer at a cellular level.

Nicholas Lockyer received aPh.D. in 1996 from theUMIST on laser ionisationmass spectrometry of bio-molecules. After a period ofpost-doctoral work develop-ing imaging time-of-flightsecondary ion mass spectro-metry (ToF-SIMS) instru-mentation he was awarded a2 year Special Research Fel-

lowship from the Leverhulme Trust. In 2002 he was ap-pointed Lecturer in the Department of Chemistry atUMIST. In 2004 he joined the School of Chemical En-gineering and Analytical Science at the University ofManchester where he currently holds a Senior Lecture-ship. His research interests include the development ofimaging mass spectrometry, particularly applications inbiology and medicine and associated fundamental as-pects of the technique.

Paul Dumas is Research Di-rector at the CNRS, andbeamline manager of the In-frared Station at the FrenchNational Synchrotron facil-ity, SOLEIL. He promotedthis analytical technique inFrance, at LURE, where hewas responsible for the de-sign and construction of aninfrared microscope beam-line at LURE, the FrenchNational synchrotron center,

until its closure in December 2003. His research pro-gram, apart for surface science, includes studies of indi-vidual cells in biology, geological inclusions, astrophy-sics, soft matter and archeology.

Mick Brown obtained aPh.D. in molecular virologyin 1995 from the Institutefor Animal Health, Comp-ton/University of Reading,UK. He then spent fiveyears within the Departmentof Molecular Biology at thePaterson Institute for Can-cer Research, Manchester,UK using avipox viral vec-

tors as potential immunotherapeutic agents againstcervical cancer. He then moved to the ICRF ClinicalCentre, St James Hospital in Leeds, UK where he con-tinued his interests in cancer immunotherapy utilisingembryonic stem cells and avipox viral vectors. Since2002 he has been an associate scientist within NoelClarke’s Genito Urinary Cancer Research Groupwhere he leads the laboratory research team investigat-ing urological malignancies with a particular interest inthe mechanism of metastasis and the development ofnovel diagnostic/prognostic biomarkers.

Noel Clarke is Professor ofUrological Oncology atManchester University. Hequalified in London in 1981,completing his Fellowship ofthe Royal College of Sur-geons in 1985 and his re-search thesis in prostate can-

cer biology and metastasis in 1990. He was appointedas Consultant Urological Surgeon to the Christie andSalford Royal Hospitals in Manchester in 1993 and hasspecialized in the management of Urological Cancerand complex pelvic and retroperitoneal tumours. He iscurrently the Director of the Manchester UniversityGU Cancer Research Group and the pan-ManchesterMCRC biobank. His research encompasses basicscience, translational cancer studies and Phase 2/3 trialsin Urological Cancer.

Peter Gardner obtained aPh.D. in surface vibrationalspectroscopy in 1988 fromthe University of East An-glia. After four years at theFritz Haber Institute (MPG)in Berlin he joined theChemistry Department atthe University of Cambridgein 1992 studying catalyticsystems and then in

1994 moved to the Chemistry Department at UMIST.In 2004, he joined the School of Chemical Engineeringand Analytical Science and is part of the centre for in-strumentation and analytical science (CIAS). He has akeen interest in understanding the underlying basis ofspectral discrimination in biological systems. His grouphave also been influential in solving the long standingproblem of spectral distortions in infrared spectra ofsingle eukaryotic cells and in 2009 were the first to at-tribute the problem to the phenomenon of resonantMie scattering (RMieS).




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BIOPHOTONICS - ArrayFire · in HPLC grade water, Sigma Aldrich, UK). Suspen-sions of the PC-3 cells (150 ml) were cytospun (800 RPM, 5 minutes, low acceleration) onto calcium