Projecte final de Màster Oficial realitzat en col.laboració amb Universitat de Barcelona. Departament d’Electrònica.English: In this work, a Multivariate Curve Resolution (MCR) with Alternating Least Squares (ALS) method is described and used to identify the concentrations of a two-component (ethanol and acetone) mixture analysed with an Ion Mobility Spectrometer. Results allow us to distinguish qualitatively both components at lower concentrations, whereas fail to detect ethanol at higher concentrations. The impossibility of detecting etanol at higher concentrations is caused by higher acetone’s proton affinity

Oller Moreno, Sergio

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MULTIVARIATE CURVE RESOLUTIONAPPLIED TO ION MOBILITY SPECTRASergio OllerPhD Director: Antonio PardoDepartament d’electro`nica, Universitat de Barcelona. 08034 Barcelona, Spain.AbstractIn this work, a Multivariate Curve Resolution (MCR) with Alternating Least Squares (ALS) method isdescribed and used to identify the concentrations of a two-component (ethanol and acetone) mixture analysedwith an Ion Mobility Spectrometer. Results allow us to distinguish qualitatively both components at lowerconcentrations, whereas fail to detect ethanol at higher concentrations. The impossibility of detecting ethanolat higher concentrations is caused by higher acetone’s proton affinity.1 IntroductionIon Mobility Spectrometry is an instrumentalanalytical technique to analyse volatile substancesbased on the drift velocities of gas ions in weakelectric fields. Firstly implemented during 1970’s(Revercomb & Mason, 1975) under the name of“Plasma chromatography”, IMS offered a low-cost,portable, sensitive and fast way of detecting trace or-ganic compounds. Since then, it has been deployed tohelp in the detection of drug trafficking and chemicalwarfare agents, among other fields.Its fundamental principle it’s simple: A bundle ofions (called swarm) taken from the mixture to be anal-ysed is introduced into a tube under an electric field.The ion swarm attains a drift velocity vd proportionalto the applied electric field E as equation 1 states.vd = KE (1)The proportionality coefficientK characteristic of eachpure substance is called ‘mobility coefficient’.The electric current at the end of the tube, whichis caused by the ions colliding with a detector, is mon-itored obtaining a measure of the charged ions thatcross the tube through time. This I(t) plot is calledthe ‘mobility spectrum’ and it presents a peaked shape.The mobility spectrum of different concentrations ofethanol and acetone conforms the dataset used at thepresent work.Multivariate Curve Resolution (MCR) is a set oftechniques which intend to extract information (con-centrations and spectra) of a mixture’s pure compo-nents. Instead of using the most common approachin chemical analysis, which is separating the mixturein its pure chemical components, MCR allows to ex-tract the information directly from the mixture, in thiscase from the mobility spectrum. Avoiding the needof mixture separation has many significant advantagesin the analysis time, cost and portability widening theapplications of IMS.The rest of the paper is structured as follows:Section 2 presents the IMS device, linking thephysical limitations of the measures with the math-ematical properties and limitations of the data mea-sured, described on section 3.Section 4 deals with the explanation of the algo-rithms and the data processing used to extract theconcentrations and spectra from the dataset.Finally, results and a discussion are provided onsection 5.2 Ion Mobility Spectrometer(Eiceman & Karpas, 2005)The Ion Mobility Spectrometer is an analytical de-vice used to identify ionized molecules in gas phase. Itis based on the drift velocities of gas ions acceleratedby an electric field inside a tube of known length. An‘IMS measure’ consists of the distribution of the timesneeded by the ions to travel through the tube: a ‘mo-bility spectrum’.The IMS consists of two main regions: the ion-ization region and the drift region. These regions areseparated by a shutter which marks the time when theionized particles start to drift through the electric field.Particles travel through the electric field and neutral-ize colliding with a detector causing a current flow.The current flow is amplified (and usually convertedto voltage) obtaining the mobility spectrum. Figure 1summarizes this.Figure 1: IMS working principle. Based on picturefound at (Westhoff et al., 2009)2.1 Ionization regionThe ionization of the sample is usually performedat ambient pressure with the levels of moisture andoxygen found in ambient air. Several sources can beused to ionize the samples such as radioactive sources,corona discharges or photo-ionization; although themost common source is the radioactive because of itsreliability, stability and absence of mobile parts andpower supply which diminishes the maintenance cost.For any source used, the total charge used to ion-ize the samples is fixed. This means that the num-ber of particles that can be ionized at one experimentis finite. This restriction implies that there are non-linearities in the spectra: Superposition of two spectrawith different concentrations (i.e. one sample exclu-sively with ethanol and one sample exclusively withacetone) will not lead to the spectrum of the com-bined sample (i.e. a sample of a mixture of ethanoland acetone).Moreover, the proton affinity of a substance (whichis the affinity of a substance to be ionized by a proton)will cause some components to be ionized easier thanothers. The components of the mixture with lowerproton affinity may not be ionized, and therefore notdetected at the end of the tube. These neutral parti-cles may get stranded in the tube interfering with themoving ions, that’s why they must be removed.For each source, there are different reactant ionsthat lead to peaks at the mobility spectrum. Thesepeaks are higher if there is no sample introduced. Thereactant ion peaks (RIP), showed in figure 2 are re-duced as the charge of these reactant ions is used toionize the samples.2.2 Drift regionIons travel from the shutter to the detector underthe electric field. In order to avoid interference be-tween the travelling ions and neutral particles strandedon the tube, a drift gas is expelled from the detector-100 0 100 200 300 400 500 600 700 0  5  10  15  20  25  30Intensity (Arbitrary Units)Drift time (ms)IMS spectra showing the RIP shapeFigure 2: Spectrum sample taken without any concen-tration of ethanol nor acetone. The RIP is shown.in the opposite direction of the ions. The drift gasis chosen to be inert with the ions, guaranteeing thatno chemical reaction will be produced in the drift re-gion that would alter the travelling times. Close to theshutter a gas outlet is placed to eject the gas.3 DatasetOur dataset consists of 25 spectra with differentconcentrations of ethanol and acetone. The list of con-centrations used is available as an appendix (see table1). The ion mobility spectrometer used to take thespectra is the GDA2 from Airsense Analytics.Each spectrum consists of 895 points, so all thespectra combined form a 25× 895 matrix named D.4 Multivariate Curve Resolu-tion (Ferre´, 1997)MCR techniques are based on the assumption thatthe matrix D, which contains in each row a spectrumwith a particular concentration of ethanol and ace-tone, can be factorized in the product of two matrices:C, which accounts for the concentrations of the puresubstances and ST , which accounts for the spectrumof each pure substance. This factorization is shownon equation 2. The E term accounts for experimentalerrors.D = CST + E (2)Given D as an m × n matrix, with m the num-ber of spectra, and n the number of points for eachspectrum, the decomposition of C and S has a widerange of mathematical solutions. The number of puresubstances, which determines the dimensions of C andS, is not fixed and has to be determined. If C is anm × k matrix and ST is an k × n, then k has to beunderstood as the number of pure substances in themixture.Once the number of components is fixed, an ini-tial estimation of the concentrations must be given toALS to begin the iterations. The initial estimation iscrucial to correctly identifying the spectra of the dif-ferent substances, and the physical constraints to thesolution (such as non-negativity or unimodality), willbe imposed between ALS iterations.The Matlab MCR-ALS Toolbox fromJaumot et al. (2005) has been used with thePLS Toolbox from EigenvectorResearch (2011)to implement the data processing.4.1 PreprocessingThe first step in the analysis consists on a prepro-cessing to clean the data. This preprocessing includesfour different phases.• Replicated spectra are removed.• Baseline removal• Noise filtering• Peak alignmentThe IMS device gives many replicas from eachspectrum. These replicas are redundant and they mustbe removed from the dataset.As with many other spectrometers, there exists abaseline which, in our case, is corrected by fitting andsubtracting a fourth order polynomial to the first 200points and the latest 450 points of each spectra.To reduce the noise, a Savitzky-Golay filter ofgrade 2 and a window of 9 points is applied to thespectra. The Savitzky-Golay filter fits to each point apolynomial of degree 2 in our case, using the 9th pointscloser to the current point. The evaluation of the fittedpolynomial at the treated point gives the output valueof the filter. One of the main advantages of this filterin front of others is that it preserves the position andwidth of the relative maximum and minimum pointsof the spectra.Finally, all the spectra are aligned. To do so, allthe local maximum of all the spectra are detected. Weconsider that the two peaks should be aligned if thedistance between them is smaller than 0.1ms.4.2 Number of componentsWe may know the number of pure chemical sub-stances in the original mixture (i.e. in our experiment,we know we only have ethanol and acetone). This maygive us a hint on the number of components, althoughwe must take into account the different RIPs we mayhave. To estimate the number of components k witha more rigorous method, a singular value decomposi-tion of the data matrix is performed and the numberof components is estimated by counting the most sig-nificant singular values.4.3 Initial estimationThere are different ways to obtain an initial esti-mation of the concentration and the spectra matrices.Given that the different spectra we use come from dif-ferent experiments (i.e. not a temporal evolution), wemay discard popular methods such as Evolving FactorAnalysis (Keller & Massart, 1992) that are suitable forstudying chemical mechanisms where mixture compo-nents form and disappear linking temporally differentspectra. As this is not our case, we have opted bya more suitable method to obtain initial estimations:SIMPLISMA.4.3.1 SIMPLISMASIMPLISMA (Windig & Guilment, 1991), whichstands for “SIMPLe to use Interactive Self-modellingMixture Analysis” allows to perform an initial esti-mation of the concentrations and spectra with littleintervention from the user. It is based on the coeffi-cient of variation of the spectra points which is definedin 3, where µ stands for the mean and σ stands for thestandard deviation of the spectra points.cv =σµ(3)The largest this coefficient is, the more informationthat drift time instant is supposed to add. As thiscoefficient is not well defined for µ ∼ 0, an offset α isadded to µ to compensate. Therefore, the purity of avariable is defined as stated in equation 4.pj =σjµj + α(4)For each drift time of the D matrix, the purityof the spectra is computed, defining a purity vectorof components pj , j = 1...n. The indexes of the klargest components of the purity vector are stored inan array sl, l = 1...k. A matrix A is defined, and itselements ai,l are defined as ai,l = di,sl . In plain words,A contains a selection of the columns of the matrixD, this is the spectra of the drift times with largestpurity.The initial estimation of the spectra ST0 is given asthe solution of the overdetermined system presentedon equation 5. This solution can be obtained usingleast squares.AST0 = D (5)Finally an estimation of the concentrations can be ob-tained with C0 = DST0+.4.4 Alternate least squaresThe equation 2 can be solved using the equations6 and 7 iteratively.S = C+D (6)C = DS+ (7)In these equations, the symbol + stands for the pseu-doinverse matrix.The Moore-Penrose pseudoinverseThe Moore-Penrose pseudoinverse matrix is a gen-eralization of matrix inversion which tries to repro-duce many of the properties of a matrix inverse. Itis generalized to non square matrices, and for squareand invertible matrices both the inverse and the pseu-doinverse are the same. A simple implementation ofthe Moore-Penrose pseudoinverse matrix consists onobtaining the singular value decomposition of the ma-trix (let A be the matrix, its singular value decom-position would be A = USV T ) and then comput-ing A+ = V S+UT to obtain the pseudoinverse of A.Here, S+ denotes the pseudoinverse of a diagonal ma-trix, which is computed by taking the reciprocal of thenon-zero elements in the diagonal and transposing thematrix.Between each iteration, several physical con-straints are applied to the concentrations and spectramatrices.4.4.1 ConstraintsNon-negativityThe non negativity constraint adds physical mean-ing to concentrations and spectra. It can be applied byforcing to zero negative contributions or using a softerapproach using non negative least squares algorithm(Lawson & Hanson, 1995).UnimodalityAs it has been shown that the ethanol, acetone andreactant ion peaks do not overlap, we may impose theunimodality constraint on the spectra by not allowingspectra overlaps with more than a fixed tolerance.Spectra normalizationThere is a scaling degree of freedom in the factor-ization D = CST , any valid solution will be valid ifC is multiplied by a scalar and ST is multiplied byits reciprocal. By imposing the spectra normalizationcondition, we constrain the scale ambiguity.5 Results and DiscussionFigures 3a and 3b show the recovered concentra-tions compared to the experimental concentrations.It can be seen how for lower experimental concen-trations, the resolved concentrations are close to theexpected result, even though the resolved concentra-tions never reach zero when the experimental does.This may be explained by the fact that, as it is shownon figure 4, there is some overlapping in the spectra. 0 100 200 300 400 500 600 700 800 900 1000 0  5  10  15  20  25Concentration (ppb)ExperimentRecovered and original ethanol concentrationsExperimentalResolved(a) Ethanol 0 200 400 600 800 1000 1200 0  5  10  15  20  25Concentration (ppb)ExperimentRecovered and original acetone concentrationsExperimentalResolved(b) AcetoneFigure 3: Original concentrations and recovered con-centrations in different experiments. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 7  8  9  10  11  12  13  14Resolved Spectra (AU)Drift time (ms)IMS spectra showing the resolved peaksAcetoneRIPEthanolFigure 4: Resolved spectra for the three pure compo-nents: RIP, ethanol and acetone.This overlapping increases the range of possible solu-tions, making it more difficult to distinguish betweenthe components.As concentrations increase, ethanol detection be-comes more and more difficult and the only detectedcomponent (apart from RIP) is the acetone. Thisseems to be caused by the higher proton affinityof the acetone (823kJ/mol) with respect to ethanol(788kJ/mol) (Jolly, 1991). In other words, as ace-tone has more proton affinity, it takes all the availablecharge letting the ethanol unionized and therefore un-detected.An alternative view of the resolved concentrationsis shown on figure 5. In those plots we can see the re-covered concentrations of ethanol and acetone in termsof the respective experimental concentrations. Ideallythese plots should overlap with the identity function(i.e. the resolved concentrations are the experimentalones). For the acetone (5b), the tendency to identitycan be seen, especially in lower ethanol concentrations;however, for the ethanol (5a), the identity is clearlylost as the acetone concentration is different than zero.It is clear that as the concentration of the other com-ponent increases, the resolution degrades. In ethanolthe effect is much more severe due to the smaller pro-ton affinity. 0 200 400 600 800 1000 0  200  400  600  800  1000Resolved ConcentrationsExperimental ConcentrationsEthanol regressionAcetone: 0 ppbAcetone: 270.5 ppbAcetone: 541 ppbAcetone: 811.5 ppbAcetone: 1082 ppb(a) Ethanol 0 200 400 600 800 1000 1200 0  200  400  600  800  1000  1200Resolved ConcentrationsExperimental ConcentrationsAcetone regressionEthanol: 0 ppbEthanol: 240 ppbEthanol: 480 ppbEthanol: 719.9 ppbEthanol: 959.9 ppb(b) AcetoneFigure 5: Recovered vs. Experimental concentrations.6 Conclusions and Further workIn this work, the suitability of MCR-ALS methodfor separating two pure components of a mixture ofethanol and acetone analysed by an IMS has beentested.Initial estimations for concentrations and spectrahave been taken using the SIMPLISMA algorithm,and they have been refined and constrained with al-ternating least squares.Results show that for lower concentrations, the re-covered concentrations follow qualitatively the exper-imental concentrations, whereas for higher concentra-tions the IMS saturates, and only acetone, which hasa higher proton affinity, is recognized.Future work may be oriented to testing with dif-ferent mixtures, using different components. It alsowould be interesting to try other non-linear factoriza-tion methods, to see if non-linearities affect stronglythe results.AcknowledgementsI would like to thank Antonio Pardo, Ana VeronicaGuaman and Vı´ctor Pomareda for their support, an-swers and patience through the whole project. Thanksalso to Daniel Calvo for the IMS measurements.I would also like to thank my friends, colleaguesand family whose moral support has been invaluable.ReferencesEiceman, G. & Karpas, Z. 2005 Ion mobility spec-trometry. CRC Press.EigenvectorResearch 2011 Matlab pls toolbox.Ferre´, R. 1997 Ana`lisi de mescles mitjanc¸ant res-olucio´ multivariant de corbes . Arxius de les Seccionsde Cie`ncies v. 1. Institut d’Estudis Catalans.Jaumot, J., Gargallo, R., de Juan, A. &Tauler, R. 2005 A graphical user-friendly inter-face for mcr-als: a new tool for multivariate curveresolution in matlab. Chemometrics and IntelligentLaboratory Systems 76 (1), 101 – 110.Jolly, W. 1991 Modern inorganic chemistry.McGraw-Hill.Keller, H. & Massart, D. 1992 Evolving factoranalysis. Chemometrics and intelligent laboratorysystems 12 (3), 209–224.Lawson, C. & Hanson, R. 1995 Solving least squaresproblems . SIAM.Revercomb, H. & Mason, E. 1975 Theory ofplasma chromatography/gaseous electrophoresis. re-view. Analytical Chemistry 47 (7), 970–983.Westhoff, M., Litterst, P., Freitag, L.,Urfer, W., Bader, S. & Baumbach, J. 2009 Ionmobility spectrometry for the detection of volatileorganic compounds in exhaled breath of patientswith lung cancer: results of a pilot study. Thorax64 (9), 744.Windig, W. & Guilment, J. 1991 Interactiveself-modeling mixture analysis. Analytical chemistry63 (14), 1425–1432.AppendixExp. # Etanol (ppb) Acetona (ppb)1 0 02 240 03 0 270.54 480 05 240 270.56 0 5417 719.9 08 480 270.59 240 54110 0 811.511 959.9 012 719.9 270.513 480 54114 240 811.515 0 108216 959.9 270.517 719.9 54118 480 811.519 240 108220 959.9 54121 719.9 811.522 480 108223 959.9 811.524 719.9 108225 959.9 1082Table 1: Experimental concentrations of the differentexperiments

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