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Quantification of ternary mixtures of heavy metal cations from metallochromic absorbance spectra using neural network inversion

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Quantification of ternary mixtures of heavy metal cations from metallochromic absorbance spectra using neural network inversion
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  Quantification of Ternary Mixtures of Heavy MetalCations from Metallochromic Absorbance SpectraUsing Neural Network Inversion Dan Mikami, † Toshifumi Ohki, ‡ Ken Yamaji, † Saeko Ishihara, ‡ Daniel Citterio, § Masafumi Hagiwara, † and Koji Suzuki* ,‡,§,# Departments of Information and Computer Science and Applied Chemistry, Keio University, 3-14-1 Hiyoshi,Kohoku-ku, Yokohama 223-8522, Japan, Kanagawa Academy of Science and Technology (KAST), KSP West 614,3-2-1 Sakado, Takatsu-ku, Kawasaki 213-0012, Japan, and Core Research for Evolutional Science and Technology (CREST), JST Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan  Anewmethodbasedonartificialneuralnetworks(ANN)fortheprocessingofspectrophotometricdataisproposedand illustrated on the example of the simultaneousquantificationofternarymixturesofzinc,cadmium,andmercury cations in aqueous solutions. Three types of commerciallyavailablemetallochromic indicators wereused as a simple model setup to create spectral dataanalogous to those normally received from an opticalsensorarray. Inconventional ANN trainingmethodsforchemical sensors based on spectrophotometric data, acalibration is established bymathematicallycorrelatingthe measured optical signal as network input with theconcentrationofthecalibrationsampleasnetworkoutput.In several situations, however, especiallywhen dealingwithmixedsamplesolutions,therelationshipbetweenameasuredabsorptionspectrumandthecorrespondingionconcentrations is ambiguous, resultingin an “ill-posedproblem”.Ontheotherhand,ifthetrainingdirectionisreversedbycorrelatingknownsampleconcentrationswithmeasuredoptical signals, therelationshipbecomesrea-sonablefortheANNtoobtainitsstructure.Theproposedmodel illustrated in this paper is based on a morereasonable direct mapping and estimation by artificialneural network inversion (ANNI). In the trainingstep,samplemixtures of known concentrations areopticallymeasuredtoconstructnetworkscorrelatingtheinputdata(ion concentrations) and the output data (absorptionspectra). In theestimation step, theion concentrationsofunknownsamplesareestimatedusingtheconstructedANN.Themeasuredspectraoftheunknownsamplesarefed to theoutputlayer, and theappropriateinputcon-centrationsaredeterminedbyANNI. WhentrainingtheANNsystemwith143ternarymixturesofZn 2 + ,Cd 2 + ,andHg 2 + in aconcentration rangefrom1 to100  µ M, root-mean-square errors of prediction (RMSEP) of 0.45(Zn 2 + ),0.96(Cd 2 + ),and0.32  µ M(Hg 2 + )wereobservedfor the estimation of concentrations in 30 test sam-ples, usingthe ANNI procedure. This newly proposedmodel,whichinvolvestheconstructionofanANNbasedondirectmappingandestimationbyANNI,opensuponewaytoovercomethelimitationsofnonselectivesensors,allowingtheuseofmoreeasilyaccessiblesemiselectivereceptorstorealizesmartchemical sensingsystems. In recent years, processing of analytical data by computermethods has become routine. Due to the immense progress inanalytical instrumentation, enormous amounts of data can nowbe acquired within a short time. This situation required thedevelopment of special mathematical and statistical methods inorder toextract thedesiredquantitativechemical informationfromthe overall data, giving rise to the field of chemometrics. Thetechnique of data mining, which searches for relationships andcorrelationswithin largeamountsof raw data,hasbecomehighlyimportant. In this context methods such as principal componentanalysis(PCA),cluster analysis,discriminant analysis,partial least-squares analysis (PLS), and artificial neural networks (ANN) arewidely used among others for complicated information process-ing. 1 Chemometrical methods have been widely applied for theanalysisof samplemixtures 2 - 11 and in combination with chemical * Corresponding author. E-mail: suzuki@applc.keio.ac.jp. Fax:  + 81-45-564-5095. Tel.:  + 81-45-566-1568. † Department of Information and Computer Science, Keio University. ‡ Department of Applied Chemistry, Keio University. § Kanagawa Academy of Science and Technology. # Core Research for Evolutional Science and Technology.(1) Duda, R. O.; Hart, P. E.; Stork, D. G.  Pattern Classification  , 2nd ed.; JohnWiley & Sons: New York, 2001.(2) Vitouchova´,M.;Janca´r,L.;Sommer,L. FreseniusJ. Anal. Chem. 1992 , 343  ,274 - 279.(3) Vitouchova´,M.;Janca´r,L.;Sommer,L. FreseniusJ. Anal. Chem. 1992 , 343  ,274 - 279.(4) Ni, Y.  Anal. Chim. Acta   1993 ,  284  , 199 - 205.(5) JiJi, R. D.; Cooper, G. A.; Booksh, K. S.  Anal. Chim. Acta   1999 ,  397  , 61 - 72.(6) Kompany-Zareh, M.; Massoumi, A.  Fresenius J. Anal. Chem.  1999 ,  363  ,219 - 223.(7) Kompany-Zareh,M.;Massoumi,A.;Pezeshk-Zadeh,Sh.  Talanta   1999 , 48  ,283 - 292.(8) Esteves da Silva, J. C. G.; Oliveira, C. J. S.  Talanta   1999 ,  49  , 889 - 897.(9) Thomas, E. V.  Anal. Chem.  2000 ,  72  , 2821 - 2827.(10) Moberg,L.;Karlberg,B.;Blomqvist,S.;Larsson,U. Anal. Chim. Acta   2000 , 411  , 137 - 143.(11) Espinosa-Mansilla, A.; Valenzuela, M. I. A.; Mun˜oz de la Pen˜a, A.; Salinas,F.; Can˜ada F. C.  Anal. Chim. Acta   2001 ,  427  , 129 - 136. Anal. Chem.  2004,  76,  5726 - 5733 5726  Analytical Chemistry, Vol. 76, No. 19, October 1, 2004   10.1021/ac040024e CCC: $27.50 © 2004 American Chemical SocietyPublished on Web 08/21/2004  sensors. 12 - 20 Among those, ANNs are of special interest becauseof their ability for analytical learning inspired by the humanbrain. 21 - 31 ANNscan beapplied in situationswhereother methodsoften fail because a profound knowledge of the theoreticalresponse mechanism in terms of a mathematical function is notrequired. This is especially useful when simultaneously dealingwith a large number of chemical equilibria of different stoichi-ometries as they are often found in mixed samples. Therefore,most applications of ANNs concerning chemical sensing arefocused on multianalyte detection. With the development of electronic nosesfor gaseoussamplemixturesand morerecently,electronic tongues for liquid samples, a paradigm shift in thefield of chemical sensing can beobserved, wherefocusismovedfrom highly selective recognition elements to semiselectivereceptors. 32 - 35 With these developments, ANNs have gained inimportance again.Concerning chemical sensors, a molecular receptor or iono-phore can be regarded as “hardware” and the dataprocessing of the raw signal as “software”. Whereas past studies have mainlyaimed at the improvement of the hardware (e.g., selectivity,sensitivity) and the software (data processing) independently,collaborations between chemists and computer engineers havebecome more common. 36,37 Harmonizing the performance of the hardware with the software, instead of independent develop-ment of both, may enable the establishment of smart chemicalsensing systems in the future. In this paper, we demonstratean application of an artificial neural network system, whichwasspecifically developed for theanalysisof spectrophotometricaldata and which is new in terms of its application to chemicalsensing.The goal of this work is to establish a novel software modelfor spectra analysis and to validate its efficiency. Since thequantification of heavy metal cations in aqueous systems is animportant task in analytical chemistry and thenumber of suitablehighly selective sensors is still limited, 38,39 we selected a simplemultianalyte sensing array using commercially available semi-selectivemetal ion indicatorsasamodel application.Thebindingof the metal ion to the indicator is monitored by measuringabsorption spectraof aqueoussolutionscontaining oneof severaldyes and a mixture of cations.The estimation of the ion concentration based on measuredoptical spectra can sometimes be regarded as an “inverseproblem”. In this example, the cause, meaning the concen-tration of the different ions, is estimated based on the measuredresult, represented by the spectra. In many cases, it is difficultto achieve the inverse mapping which transforms the resultinto the cause since one specific result can be due to differentpossible causes. Conventional methods for multivariate dataanalysis (e.g., back-propagation neural networks and partialleast-squares regression) by themselves do not have the abilityto describe such relationships reliably. Therefore, we proposeand apply a new method consisting of a training step basedon direct mapping and an estimation step based on artificialneural network inversion (ANNI). 40,41 During the training step,the ion concentrations are correlated with the absorbancespectra, linking the cause and the result in a proper direction.For the estimation of unknown samples, the measured spectraare fed to the output layer of the constructed network. Then, theinput (ion concentrations) is determined using ANNI. Instead of inverse mapping using conventional methods resulting in unrea-sonable estimations, this combination of direct mapping andnetwork inversion enablesthemorereliablequantification of ionsin mixed solutions. To the best of our knowledge, the techniqueof network inversion has not been applied to the analysis of spectral databefore. In amodel experiment we demonstrate thesimultaneous quantification of Zn 2 + , Cd 2 + , and Hg 2 + in mixedaqueous solutions using three metallochromic indicators, meth-ylthymol blue, murexide, and 4,7-dihydroxy-1,10-phenanthroline,as the single “sensor elements” combined into a sensor array.Thissimplemodel study showsthat nonselectivemultiplesensingelements or sensors together with the newly proposed softwareprocedure allow the realization of multiple and selective analytedeterminations. THEORETICAL CONSIDERATIONS SpectralAnalysis. Theabsorption spectraof metallochromicindicators vary with the concentration of metal ions in a mixed (12) Abdollahi, H.  Anal. Chim. Acta   2001 ,  442  , 327 - 336.(13) Saurina, J.; Herna´ndez-Cassou, S.  Anal. Chim. Acta   2001 ,  438  , 335 - 352.(14) Beebe, K. R.; Kowalski, B. R.  Anal. 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Analyst   2000 , 125  , 2049 - 2053.(33) Lavigne,J.L.;Savoy,S.;Clevenger,M.B.;Ritchie,J.E.;McDoniel,B.;Yoo,S.-J.; Anslyn, E. V.; McDevitt, J. T.; Shear, J. B.; Neikirk, D.  J. Am. Chem.Soc.  1998 ,  120  , 6429 - 6430.(34) Albert, K. J.; Lewis, N. S.; Schauer, C. L.; Sotzing, G. A.; Stitzel, S. E.; Vaid,T. P.; Walt, D. R . Chem. Rev.  2000 ,  100  , 2595 - 2626.(35) Raimundo, I. A.; Narayanaswamy, R.  Anal. Chim. Acta   2003 ,  90  , 189 - 197.(36) Lavigne, J. J.; Anslyn, E. V.  Angew. Chem., Int. Ed.  2001 ,  40  , 3118 - 3130.(37) Lavine, B. K.; Workman, J., Jr.  Anal. Chem.  2002 ,  74  , 2763 - 2769.(38) Goodey, A.; Lavigne, J. J.; Savoy, S. M.; Rodriguez, M. D.; Curey, T.; Tsao,A.; Simmons, G.; Wright, J.; Yoo, W. J.; Sohn, Y.; Anslyn, E. V.; Shear, J. B.;Neikirk, D. P.; McDevitt, J. T.  J. Am. Chem. Soc.  2001 ,  123  , 2259 - 2570.(39) Bu¨hlmann, P.; Pretsch, E.; Bakker, E.  Chem. Rev.  1998 ,  98  , 1593 - 1687.(40) Linden, A.; Kindermann, J.  Proc. Int. Joint Conf. Neural Networks(IJCNN)  ,Washington, DC, 1989; Vol. 2, pp 425 - 430.(41) Jensen, C. A.; Russell, D. R.; Marks, R. J.; El-Sharkawi, M. A.; Jung, J.-B.;Miyamoto,R.T.;Anderson,G.M.;Eggen,C.J. Proc. IEEE   1999 , 87  ,1536 - 1549. Analytical Chemistry, Vol. 76, No. 19, October 1, 2004   5727  sample. In other words, the concentration of the ion is thecause leading to the result of changing absorption spectra.Therefore, to estimate the concentration of an unknown samplemixturefrom itsabsorption spectrum meanstoestimatethecausefrom the result, posing a typical inverse problem. The difficultywith the inverse problem encountered here is the fact that theinverse mapping is not generally available due to the possiblenonexistence of an appropriate answer or due to the lack of uniqueness in the reverse relationship as a result of usingnonselective and nonlinearly responding sensors in mixedsamplesolutions. Thissituation, which leadsto unreliableestima-tions,istermedan“ill-posedproblem”.Figure1showsaschematicrepresentation of the inverse relationship between the result(absorbance) and the cause (concentration). The first arrow,mapping a point from A into B, denotes an example of directmapping, which does not suffer from problems as mentionedabove. The second arrow, mapping a point from B into A, is anexample of inverse mapping, which estimates a correct answer.Such a situation is encountered when a sensor selectivelyresponds to a specific ion and its concentration lies within thedynamic response range. The third arrow represents anexample of inverse mapping not leading to a correct answerdue to the nonexistence of an appropriate solution. The fourtharrow, which does not lead to a single answer, shows a lackof uniqueness. This case is commonly observed when a sensordoes not respond to a specific analyte with high selectivitybut to several analytes simultaneously. A unique correctanswer by inverse mapping is only obtained in the situationdescribed by arrow 2, which applies when using highly selec-tive sensors. In this situation only, an inverse mapping trans-forms a measured absorbance value into a concentration value.For the simultaneous determination of several ions in mixedsolutions with poorly selective sensors, this situation is rarelyencountered.A semiselectivesensor may similarly respond toconcentrationchangesof several cationswhen exposed tomixed solutions,andit becomes impossible to distinguish between the single analytecontribution totheoverall signal change.Thisleadstoan ill-posedsituation due to alack of uniqueness as described above (Figure1,arrow (4)).Conventional calibration methodsbased on inversemapping may fail in such cases. On theother hand, it isassumedthat direct mapping results in more reasonable results. AnalysisProcedure.  The newly proposed method requiresseparateacquisition of thespectral datafor every sensor in mixedsolutions. Figure 2 shows a schematic outline of the completeprocess, which can be divided into two steps, the training stepand theestimation step.In thetraining step(Figure2A),separateneural networks are created for each sensor in the array andtrained tolearn thecorrelation between theion concentration andtheresulting spectra(direct mapping) using theback-propagationlearning algorithm.However,sincethetarget isthequantificationof an unknown ion concentration using ameasured spectrum,theresulting networks have to be inversed in the estimation stepfollowing thetraining session.In theestimation step(Figure2B),the measured spectra of test samples are fed to the output layerof the constructed network, and network inversion is applied tosearch for the appropriate input (ion concentrations). Thisprocedure is repeated for all three networks, resulting in threecandidate concentration ranges. Then all the predictions arecombined and theoverlapping datapointsareaveraged to outputthe final result. In the following, the training step and theestimation step will be discussed in more detail.The ANN applied in this model is a commonly used three-layer feed-forward neural network shown in Figure 3. Thishierarchical ANN consists of one input layer (IL) with  I   inputneurons, one hidden layer (HL) with  J   neurons, and one outputlayer (OL) with  K   neurons. The input neurons and the hiddenneurons, as well as the hidden and the output neurons, areconnected by connection weightsof   V   ji   and  W  kj   respectively. Thelearning algorithm used in the training step is back-propagation.This method has been proven useful for learning complicatedrelationships between input and output. However, as mentionedabove, BP-ANNs are not successful in some cases of inverseproblems.Toovercomethisproblem,thedirection of training forthenetwork isinversed compared to conventional applicationsof BP-ANNs,wherethespectral changesarefed intotheinput layerand the ion concentrations are received from the output layer.The advantage of the opposite training direction is that there isonly onecorrect output (spectrum) for every concentration input.In addition, we used a modified definition of the error to copewith a wide range of concentrations. Normally, the error  E   isdefined as shown in eq 1, whereas we used the definition givenin eq 2,with  K   being the number of output neurons of the BP-ANN,  y  k  the estimated output, and  y   ˆ k   the target output of the  k  th outputnode. The output of the network is calculated as follows:where “net” is the net input value and  o   the output value. Thetransfer functionsused in thehidden and theoutput neuronsareboth sigmoidal functions defined in eq 7. Based on the back-propagationalgorithm,theconnectionweightsbetweenthehiddenand theoutput layer  W  kj   areoptimized by thefollowing calculation E   ) 12 ∑ k  ) 1 K  ( y  k  - y   ˆ k  ) 2 (1) E   ) 12 ∑ k  ) 1 K  ( y  k  - y   ˆ k  y  k  ) 2 (2) y   ˆ k  ) f   (net k  ) (3)net k  ) ∑  j  ) 1 J  o   j  W  kj   (4) o   j   ) f   (net  j  ) (5)net  j   ) ∑ i  ) 1 I  x  i  W   ji   (6) f   ( x  )  )  11 + e - x   (7) W  kj   ) W  kj   - η ∂ E  ∂ W  kj  (8) 5728  Analytical Chemistry, Vol. 76, No. 19, October 1, 2004   whereIn asimilar manner, the weights between the input neurons andthe hidden neurons  V   ji   are determined as follows:In the estimation step, the technique of network inversion isapplied to test sample data, not previously used for networktraining. Again, this procedure is performed separately for thespectral data of every single sensor. The inversion is done bycomputing iteratively an input vector which minimizes the sumof square errors to approximate a given output target. Thisnetwork inversion is a numerical searching process based on agradient descent algorithm. The algorithm is well-known as aclassical minimization/ maximization method for searching aninput value resulting in a minimized/ maximized error function.In somecasesof an ill-posed problem,thisminimizing of thesumof squareerrorsisapowerful solution toestimatean approximateanswer. In this process, the neural network system constructedduring the training step is now used to search for possible, atfirst unknown, input data(concentrations), leading to the experi-mentally measured output (absorbance). At first, arandom inputvalue  x  i  0 ( i   )  1, 2, ...,  i  , ...,  I  ) is created, which is then iterated asmathematically described by eqs 12 - 14,with  η  being the learning coefficient. ProvidedFollowing these calculations, the appropriate input values aresearched and determined. EXPERIMENTAL SECTION Reagents.  Commercially available reagents of the highestgrade were used for the preparations of the aqueous testelectrolytes and pH buffer solutions. The distilled and deionizedwater used had aresistivity of greater than 1.5 × 10 7 Ω cm at 25 ° C.Themetallochromicindicatorsmethylthymol blue(MTB) andmurexideammonium salt (MAS) werebought from Tokyo KaseiKogyo Co. (Tokyo, Japan) and used as received. 4,7-Dihydroxy-1,10-phenanthroline (DHP) was obtained from Aldrich ChemicalCo. (Milwaukee, WI). To increase the solubility in water, thephenanthroline indicator was transformed into the disodium saltby treating 1 equiv of indicator with 2 equiv of 1 M NaOH inmethanolicsolution.After evaporation of thesolvents,theresidualdye was dried under high vacuum and used without furtherpurification. Instruments.  All absorbance spectra were recorded on aSPECTRAmax PLUS384 microplate reader (Molecular DevicesCorporation, Sunnyvale, CA) using Costar UV-plate 96-well flatbottom microplates (Corning Inc., Corning, NY). Preparation ofSampleSolutions for ANN TrainingandTesting. A total of 144 ternary mixtures of Zn 2 + , Cd 2 + , and Hg 2 + (all acetatesalts) in magnesium acetatebuffered (pH  ) 5.70,  I   ) 0.0075 M) solutions were prepared as stock samples. Stocksolutionsfor themetal indicatorswereprepared separately in thesame buffer solution. The samples for the actual measurementwerepreparedby mixing1:1of ionstock andindicator stock insidethewellsof amicroplate. Beforespectraacquisition, thesampleswere allowed to equilibrate for 20 min. The final concentrationsfor the indicator dyes were 1.80 × 10 - 4 M for MTB, 1.51 × 10 - 4 M for MAS, and 3.78 × 10 - 5 M for DHP. The investigated metalion concentrations were 1, 2.6, 6.4, 16.0, 40.0, and 100  µ M forZn 2 + and Cd 2 + and 1, 2.6, 6.4, and 16.0  µ M for Hg 2 + . All possibleternary mixtureswereprepared and analyzed.In total,144spectrafrom 300 to 700 nm were measured for each of the metal ionindicators. Theevaluation of theANN wasperformed based on across-validation using theleave-one-out method. In thiscase, 143samples out of the total of 144 were used for the training of theANN.Here,theremaining onesampleistreated asthetest sampleand used to evaluate the reliability of the constructed network.Thespectraof thetest samplewerefed to theoutput layer of thenetwork, and the input data (ion concentrations) estimated byANNI. This procedure was repeated for 30 different test solu-tions to evaluate the versatility of the network. The test sam-ples were selected in the following manner. From the total of  ∂ E  ∂ W  kj  )  1 y   ˆ k  ( y  k  - y   ˆ k  y   ˆ k  ) y  k  (1 - y  k  ) o   j   (9) V   ji   ) V   ji   - η ∂ E  ∂ V   ji  (10) ∂ E  ∂ V   ji  ) ∑ k  ) 1 K  1 y   ˆ k  ( y  k  - y   ˆ k  y   ˆ k  ) y  k  (1 - y  k  ) w  kj  o   j  (1 - o   j  ) x   j   (11) y   ˆ  ) g  ( x  n t  ) (12) E   ≡ 12 ∑ k  ) 1 K  ( y  k  - y   ˆ k  y  k  ) 2 (13) x  i t  + 1 ) x  i t  - η ∂ E  ∂ x  i  (14) ∂ E  ∂ x  i  ) ∑ k  ) 1 K  ∂ E  k  ∂ x  i  (15) ∂ E  k  ∂ x  i  ) y   ˆ k  y  k  2 ( y  k  - y   ˆ k  y  k  ) y  k  (1 - y  k  ) ∑  j  ) 1 J  W  kj  o   j  (1 - o   j  ) V   ji   (16) Figure 1.  Schematic representation of an inverse relationshipbetween a cause (concentration of the analyte) and the correspondingresult (measured absorbance for an indicator): (1) direct mappingwith unique correlation; (2) inverse mapping leading to the correctanswer; (3) inverse mapping with nonexisting answer; (4) inversemapping with lack of uniqueness. Analytical Chemistry, Vol. 76, No. 19, October 1, 2004   5729  144samples,theupper and lower limiting concentrationsfor eachion were excluded to keep the test samples within the rangedefined by thetraining samples.Out of theremaining 32samples,30sampleswith estimableresulting concentrationswereused fortesting. Training of ANN and Network Inversion.  Out of thecompletespectral data,threewavelengthswereselectedfrom eachset of spectra for the final network construction: 312, 340, and360 nm for DHP, 448, 548, and 608 nm for MTB, and 480, 536,and 552 nm for MAS. These wavelengths are in the vicinity of the wavelengths of maximum absorbance of each spectrum andreflect theincreaseand decreasein absorption aswell astheshiftin the peak. Preliminary tests have shown that the use of threecarefully selected wavelengths was sufficient, with no significantimprovements observed by using the complete spectra. Theconcentration values were normalized by  c  norm  )  100  ×    c   inorder to fit all values in the interval 0 - 1. The three normalizedcation concentrations were used as input and the absorbance atthe three selected wavelengths as output data for the training of the BP-ANN. The following network architecture was selected:3input neurons,3output neurons,10hidden neurons,and 200000trainingepochs.Duringthenetwork inversion,5000iterationswitha learning coefficient  η  of 0.01 were performed to calculatecandidate concentration ranges for each analyte in the mixture.Then thepredictionsfrom threesensorswerecombined,and theoverlapping datapointswereaveraged to givethefinal concentra-tion estimation. To avoid the result to fall in a local minimum,20000different datapointswererandomly picked asthefirst inputvalue  x  i  0 . All data were processed on Free BSD based personalcomputers using C language. Figure 2.  Schematic outline of the data processing system: (A) Training step: construction and training of separate BP-ANNs for each of thesensors in the array. The ion concentrations of the training samples are correlated with their spectra. (B) Estimation step: estimation ofconcentrations for the test sample by network inversion. The spectral data of the test sample are fed to the output layer (OL) of the network tosearch for the corresponding input. 5730  Analytical Chemistry, Vol. 76, No. 19, October 1, 2004 
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