toward an intelligent ion mobility spectrometer (ims) - B & S Analytik ...

TOWARD AN INTELLIGENT ION MOBILITY SPECTROMETER (IMS)Timothy R. McJunkin, Jill R. Scott, and Carla J. MillerIdaho National Engineering and Environmental Laboratory, Idaho Falls, ID 83415ABSTRACTThe ultimate goal is to design and builda very smart ion mobility spectrometer (IMS)that can operate autonomously. Toaccomplish this, software capable ofinterpreting spectra so that it can be used incontrol loops for data interpretation as well asadjusting instrument parameters is beingdeveloped. Fuzzy logic and fuzzy numbers areused in this IMS spectra classification scheme.Fuzzy logic provides a straight forwardmethod for developing a classification/detection system, whenever rules forclassifying the spectra can be describedlinguistically. Instead of using “max” and“min” values, the product of the truth valuesis used to determine class membership. Usingthe product allows rule-bases that utilize theAND function to allow each condition todiscount truth value in determiningmembership, while rule-bases with an ORfunction are allowed to accumulatemembership. Fuzzy numbers allowencapsulation of the uncertainties due to ionmobility peak widths as well as measuredinstrumental parameters, such as pressureand temperature. Associating a peak with avalue of uncertainty, in addition to makingadjustments to the mobility calculation basedon variations in measured parameters,enables unexpected shifts to be more reliablydetected and accounted for; thereby, reducingthe opportunity for "false negative" results.The measure of uncertainty is anticipated toserve the additional purpose of diagnosing theoperational conditions of the IMS instrument.INTRODUCTIONAn intelligent ion mobility spectrometer(IMS) must have robust automated spectralinterpretation capabilities. IMS spectra areoften complex because of gas-phase ionmoleculeinteractions; therefore, spectralinterpretation methods used for massspectrometry, such as library searches, havebeen considered inappropriate [1]. Mostmethods for classifying IMS spectra have useda variety of neural networks [1-7]. Statisticalmethods have also been used to categorizeIMS spectra [8-10]. Alternatively, onecommercial instrument (Ion Track Itemiser®,Wilmington, MA) employs a non-adaptive formof fuzzy numbers for peak detection.It is not unexpected that neuralnetworks have been exploited to interpret IMSspectra, because their use for spectraclassification in general has exploded since the1980s [11]. Uses of neural networks rangefrom drug discovery [12], agriculture [13],solar system [14], and medical [15]applications as well as ion mobility. Some ofthe advantages of neural networks are theflexibility they offer due to the variety oflearning rules, topologies, and datapresentation formats [1, 2]. Although theiruse has proliferated widely, neural networkscan be costly in time (large number of datasets must be acquired), use of computationalresources (networks must be trained on theselarge data sets), and verification (potentiallytesting of more sets of data especially in thecase of outlying data). The potential for aneural network to “generalize” deteriorates ifthe network is “overtrained”. It has evenbeen noted that neural networks that were"undertrained" (i.e. performing poorly on thetraining data set itself) out perform fullytrainednetworks for making predictions [16].Conventional methods for checking trainingare inadequate and provide little or noinformation about the quality of the training.To address this problem, Nazarov et al. [17]developed a graphical assessment method,based on the Fermi-Dirac distribution, to helpprevent neural net over-training.In this paper, the conceptual design ofour fuzzy-logic inference engine for IMSReceived for review July 2, 2003, Accepted July 28, 2003

Toward an Intelligent Ion Mobility Spectrometer (IMS) - 31OR B) = 0.6 + 0.7 - (0.6)(0.7) = 0.88 > 0.7= maximum (0.6,0.7). For the AND caseusing the same memberships m(A AND B) =(0.6)(0.7) = 0.42 < 0.6 = minimum(0.6,0.7). The result of using this method isillustrated again in the discussion section ofthis paper with IMS classification rules.Fuzzy Numbers: Given a value of a realnumber that is measured with someinstrument, there is some uncertainty due tothe accuracy and precision of the instrument.Fuzzy numbers provide a method forexpressing this uncertainty [22]. Take thefuzzy number “five.” “Five” will have amembership value of 1 at 5.0 on the realnumber line. Depending on the uncertainty ofthe value, “five” could have zero membershipat the values of 4.5 and 5.5. The shape of thefuzzy number could be chosen as a triangle,piecewise linearly interpolating between thedefined points above. This is essentially themethod Ion Track Itemiser® uses in allowingfor mobilities around the expected mobility ofan ion but discounting, with a Gaussianshape, increasing distance from the centervalue.Combining: This paper combines thetwo fuzzy methods above. Linguistic rulescan be formed based on the combination ofIMS peaks required for positive detection of asubstance. The ratio of a peak’s amplitude tothe amplitude in the rule-base required for anion to completely satisfy a requirement formsthe fuzzy membership function. The classmembership of a combination of peaks iscomputed based on products. The finaldecision to set an alarm is based on athreshold greater than 0 and less than orequal to 1 depending on the desiredsensitivity. The shape and width of the fuzzynumber is determined by the peak width ofthe ion and other possible factorscontributing to the uncertainty of IMSmeasurement. This gives a novel adaptivetwist to the use of fuzzy numbers in IMS.RESULTS & DISCUSSIONFigure 1: Cumulative plasmagram of sample with three differentexplosive standards obtained with a Barringer IONSCAN®instrument. Peaks are detected with local maxima and inflectionpoints. Peak width is determined at the point of maximum slope oneither side of the peak that has the greatest distance to the peakcenter. Calibration peak is indicated with a vertical line. Refer toTable 1 for details on peaks referred to by letters A-Q.The first step toward automated datainterpretation is locating the peaks within anIMS spectrum. Figure 1 shows a compositespectrum formed by the summation of the 15spectra taken of a mixed explosive sample(25 ng/mL each TNT, RDX, and PETN). Todetermine the peak width, the location of themaximum slope on each side of the peak isused. The widestdistance from eachmaximum slope to thecenter of the peak isused to define the halfwidthof the peak.Deconvolution based onpredicted peak shape isnot currently utilized;however, this techniquemay be employed in thefuture to "disentangle"peaks [23, 24].IMS spectra haveintrinsically wide peaksgiven the randomdistribution of thecollisions of the samesubstance with theambient gas and/orreactant in the drifttube. Temperature,pressure, humidity,electric field, andcleanliness of theapparatus influence thetiming and shape ofthese peaks. Therefore,the standard expression(Eq. 1) for reduced ionCopyright © 2003 by International Society for Ion Mobility Spectrometry

32 - Toward an Intelligent Ion Mobility Spectrometer (IMS)Table 1: Details on detected peaks from Figure 1.Label Peak (mS) Width(mS) Ko AmpA 6.70 0.150 2.41 19.6B 7.45 0.125 2.16 297.3C 8.17 0.100 1.97 33.2D 8.52 0.150 1.89 40.6E 9.40 0.150 1.72 67.6F Cal 9.77 0.150 1.65 81.5G 10.50 0.125 1.54 10.3H TNT 11.15 0.125 1.45 126.5I RDX-C 11.65 0.125 1.38 129.9J RDX-NO 12.30 0.125 1.31 56.6K 12.87 0.125 1.25 32.3L RDX-F 13.40 0.150 1.20 139.7M PETN-NO 14.62 0.225 1.10 19.2N PETN-F 15.60 0.125 1.03 13.9O 16.10 0.050 1.00 8.2P 16.40 0.150 0.98 9.2Q RDX-D 17.02 0.175 0.95 79.9mobility compensates for several factors toallow comparisons among spectra [25].Ko = (L/t)(1/E)(P/760)(273/T)(Eq. 1)Equation 1 makes adjustments basedon measured temperature (T), pressure (P),and electric field (E), distance from gatingshutter to the collection sensor (L), and themeasured time from the gate opening todetection (t). For this equation, pressure isgiven in units of Torr and temperature inKelvin. In some cases there may be otherfactors, such as humidity, which are notcompensated for in equation 1. Applicationof the fuzzy inference engine described belowcan compensate for operating conditions thatare not or cannot be explicitly measured.In Figure 1, the detected peaks areshown with a vertical line indicatingamplitude and a horizontal line indicatingwidth. Letters A-Q label each peak (see Table1 for details on each peak). The calibrantpeak (Cal) was located based on theBarringer IONSCAN® expected location oftheir standard calibrant. The conversionfactor (Cf) is found by the product of the timeof the calibrant peak (tcal) and mobility ofthe calibrant ion (Kocal),Cf = (Kocal)( tcal)(Eq. 2)Solving equation 2 for Ko, thetransform from time to mobility is:Ko = Cf / t(Eq. 3)Using the calculated conversion factor,we then translate the peaks with their widthsinto a mobility spectrum according toequation 3. By using the actual location ofthe calibrant peak to determine the time tomobility conversion factor, the softwarecompensates for unmeasured operatingvariables that are not contained in equation1.Figure 2 shows the mobility spectrum ofthe peaks from the plasmagram in Figure 1.The plateaus of the peak representations(Fig. 2) are the translation of the end pointsof the widths of the peaks shown at the peakamplitude (Fig. 1). The base width of thepeak is twice the peak width converted tomobility. The choice of twice the width for thebase is arbitrary and could be modified asCopyright © 2003 by International Society for Ion Mobility Spectrometry

Toward an Intelligent Ion Mobility Spectrometer (IMS) - 33heuristic evidence indicates. Otherfactors influencing uncertainty couldalso be factored into the evaluations byaltering the shape of therepresentations. Note that peaks of thesame width in time are not necessarilythe same width in the mobilityspectrum. This is a direct result of theconversion (Eq. 3) using the reciprocalof time, giving the "faster" ions moreuncertainty in terms of mobility value.The trapezoid shapes in themobility representation form the basisfor determining membership values(i.e. fuzzification) for fuzzy-logic rulebase. The mechanism used for findinga membership value for a particular ionof interest is demonstrated in Figure 3.A molecule of known mobility iscompared to a peak by placing avertical line at the expected mobilityKo. The length of the line segment isthe full confidence threshold (Afko) atwhich there is no ambiguity that the ionis present with enough abundance tomake a positive assignment. Theamplitude (AKo) is defined as wherethe vertical line intersects the trapezoid. Theratio of the amplitude to the full confidencethreshold is the membership value. We willuse the notation "m(Ko,S)" for themembership value of the given spectrum (S)for the mobility (Ko) for a specific ion.Therefore the membership is defined as:m(Ko,S) = AKo/AfKo(Eq. 4)Membership value can be thought of asa truth or confidence value, where completeconfidence value is one and no confidencevalue is zero. If the line segment is fullycontained in a trapezoid the membership isfull, m(Ko,S) = 1, while a line segmentcompletely outside of the trapezoid has zeromembership, m(Ko,S) = 0. To limit themembership to the range 0 to 1, equation 4is modified to:m(Ko,S) = min (AKo/AfKo, 1)(Eq. 5)In the simplest case of a compound (M)that can be classified with just one peak, theFigure 2: Translation of peak locations and widths tomobility based on location of calibrant. Shape of thepeak representation is based on the peak width andamplitude and represents the uncertainty of themobility of the ion the peak represents.total membership is strictly the membershipvalue for that single peak:m(M,S) = m(Ko,S)(Eq. 6)In Figure 3, the intersection of the linesegment occurs on the slope of the trapezoid.The intersection amplitude A(Ko) is about 60and the required amplitude for full confidenceis set at 140, making the membership value60/140 or 0.43. Ko was far enough from thepeak representation that there is lowconfidence that this peak is associated withan ion with mobility Ko. Had the peak beencentered on the given Ko the ratio wouldhave been over 0.9 with relatively highconfidence that the substance M is present.Fuzzy logic allows the formation ofmore complex rules that requirecombinations of peaks. The membershipvalues associated with the rules are carriedthrough the logical expressions allowingflexibility and interpolation, which Bayesianor Boolean based systems cannot. Thisboundary flexibility is necessary to moreaccurately reflect how a human analyst wouldinterpret spectra [20]. We use the product tocombine membership values for the ANDoperation and the products logicalcounterpart for the OR operation. A ruleCopyright © 2003 by International Society for Ion Mobility Spectrometry

34 - Toward an Intelligent Ion Mobility Spectrometer (IMS)Figure 3: Figure 3. Illustration of the translation calculation of theconfidence factor for rule only requiring an individual peak. The ratio of theintersection amplitude of the Ko line with the fuzzy mobility representationto the full confidence amplitude gives the confidence (i.e. fuzzymembership) factor. Note if the line is fully enclosed in the trapezoid shapethe confidence is 1.0 (or full confidence).requiring the presence of several peaks isdemonstrated in Figure 4. This examplerequires the presence of four peaks (Pa ANDPb AND Pc AND Pd); therefore, the totalmembership is:m(P,S) = m(Pa,S) m(Pb,S) m(Pc,S)m(Pd,S)(Eq. 7)where Px (x = a, b, c, or d) is thereduced mobility for each required peak. Theillustration shows all four peaks are presentwith Pb and Pd above the required threshold(segment is inside the trapezoid) and Pa andPc with ratios of 0.8 and 0.9, respectively.The total membership, using equation 7,gives (0.8)(1.0)(0.9)(1.0) = 0.72. Theproduct operator allows both terms that areless than 1.0 to discount the final result,while use of the minimum would have given amembership of 0.8.The equivalent of the product operatorfor the OR function allows membership to beadditive. An example of a case when an ORrule would be appropriate is where acompound forms dual (or multiple) adducts inthe ionization process. In the case of twopossible adducts, one or both of the adductsmay form. If both adducts are formed, theymay form with very different amplitudes. Inthe case where both adducts are present, butslightly below the truth threshold for thepresence of either adduct by itself, the ORfunction allows the overall confidence to beincreased. The OR function essentiallyreinforces the overall confidence, which moreaccurately reflects the decision makingprocess of a human analyst.Figure 5 shows a case where a rulecombines both AND and OR functions in therule Ra AND { Rb OR Rc } with totalmembership:m(R,S) = m(Ra,S){ m(Rb,S) + m(Rc,S)- m(Rb,S) m(Rc,S)}(Eq. 8)The OR term has an additioncomponent. The subtraction of the productCopyright © 2003 by International Society for Ion Mobility Spectrometry

Toward an Intelligent Ion Mobility Spectrometer (IMS) - 35Figure 4: Example of a rule that requires the combination of four peaks. A membershipvalue for each required mobility is determined and then combined using the product term.The resulting confidence level discounts truth value for any peak whose confidence is notfull (a zero confidence of any of the terms obviously causes an overall zero confidence).Figure 5: Example of a rule requiring one ion, Ra, and either Rb or Rc. Use of theproduct equivalent for the OR allows for the confidence of Rb and Rc to be additive andaccumulate truth value.term imposes a maximum of 1.0 as a resulton the OR operator. In Figure 5, all threerequired peaks are present with truth valuesfor each peak as follows: m(Ra,S) = 0.9,Copyright © 2003 by International Society for Ion Mobility Spectrometry

36 - Toward an Intelligent Ion Mobility Spectrometer (IMS)m(Rb,S) = 0.6, and m(Rc,S) = 0.5. The RbOR Rc term is found, using the bracketedform of equation 8, to be 0.6 + 0.5 -(0.6)(0.5) = 0.8. The resulting membershipvalue is greater than the condition withmaximum membership value of 0.6, showingthe additive property of the OR operator. Themembership of the entire rule is found bymultiplying the membership of Ra with theresult of the OR term, (0.9)(0.8) = 0.72. Thefact that both conditions in the OR term arepresent is allowed to make up for the lowerconfidence in Rb and Rc. This reflects higherconfidence because both peaks are present tosome extent.Finally, a threshold (h) is set based onthe desired sensitivity within the range 0 to1, so that the final decision for substance Min spectrum S is given as:If (m(M,S) h), then set ALARM(M)(Eq.9)This provides a crisp result, which isrequired to determine whether to indicatepositive detection of a substance.SUMMARYThe process of detecting substancesbegins with calculating an expected time for acalibrant peak based on the measuredtemperature, pressure, and the electric fieldstrength. The plasmagram is searched for thepeak nearest the expected time for thecalibrant. Assuming that the calibrant peak isfound within some error bound, a conversionfactor is calculated to translate time-of-flightto reduced mobility. This conversion factoraccounts for other non-explicit factors in theinstrument operation. If the calibrant peak isnot found with the calculated boundaries,then the instrument is not operating withinspecifications or there is an error in samplepreparation and/or injection. All peaks andpeak widths are then identified. The peakwidth is found using the steepest slope onboth sides of the peak, using the side thathas the greatest distance from the peakcenter to define the half width. All peak widthend points are converted to reducedmobilities by the conversion factor anddisplayed as trapezoids with a base of twicethe width. From a database of substances,sets of indicator peaks with defined fullconfidence thresholds are compared to themobility peak trapezoids. A membershipvalue for each indicator peak is found basedon the ratio of the intersection with thetrapezoids and the full confidence threshold.The individual memberships are thencombined using fuzzy logic operations.Finally, a threshold based on requiredsensitivity is applied to determine if asubstance is detected.ACKNOWLEDGEMENTSThe authors would like to thank MichaelC. Evans for the data used in the analysesand Dr. Charles R. Tolle for his helpfulconversations. The authors also gratefullyacknowledge support from the United StatesDepartment of Energy, under contract DE-AC07-99ID13727 BBWI.REFERENCES[1] Bell, S.E., et al., Connectionist HyperprismNeural-Network for the Analysis of IonMobility Spectra - an Empirical-Evaluation.Journal of Chemical Information andComputer Sciences, 1993. 33(4): p. 609-615.[2] Bell, S., et al., Classification of ion mobilityspectra by functional groups using neuralnetworks. Analytica Chimica Acta, 1999.394(2-3): p. 121-133.[3] Bell, S., et al., Neural network recognition ofchemical class information in mobility spectraobtained at high temperatures. AnalyticalChemistry, 2000. 72(6):p. 1192-1198.[4] Boger, Z. and Z. Karpas, Application ofNeural Networks for Interpretation of IonMobility and X-Ray-Fluorescence Spectra.Analytica Chimica Acta, 1994. 292(3): p.243-251.[5] Boger, Z. and Z. Karpas, Use of NeuralNetworks for Quantitative Measurements inIon Mobility Spectrometry (Ims). Journal ofChemical Information and ComputerSciences, 1994. 34(3): p. 576-580.[6] Eiceman, G.A., E.G. Nazarov, and J.E.Rodriguez, Chemical class information in ionmobility spectra at low and elevatedtemperatures. Analytica Chimica Acta, 2001.433(1): p. 53-70.[7] Simpson, M., et al., Use of Pattern-Recognition for Signatures Generated byLaser- Desorption Ion Mobility Spectrometryof Polymeric Materials. Analyst, 1993.118(10): p. 1293-1298.[8] Snyder, A.P., et al., Multivariate Statistical-Analysis Characterization of Application-Based Ion Mobility Spectra. Analytica ChimicaActa, 1995. 316(1): p. 1-14.[9] Horrak, U., J. Salm, and H. Tammet,Statistical characterization of air ion mobilityspectra at Tahkuse Observatory:Classification of air ions. Journal ofGeophysical Research-Atmospheres, 2000.105(D7): p. 9291-9302.[10] Clark, J.M., K.A. Daum, and J.H. Kalivas,Demonstrated potential of ion mobilityspectrometry for detection of adulteratedperfumes and plant speciation. AnalyticalLetters, 2003. 36(1): p. 215-244.[11] Zupan, J. and J. Gasteiger, Neural networks:A new method for solving chemical problemsCopyright © 2003 by International Society for Ion Mobility Spectrometry

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