Spectral Simulation Methodology for Calibration Transfer ofNear-Infrared Spectra

YUSUF SULUB* and GARY W. SMALL�Department of Chemistry and Optical Science and Technology Center, University of Iowa, Iowa City, Iowa 52242

A spectrum simulation method is described for use in the development

and transfer of multivariate calibration models from near-infrared

spectra. By use of previously measured molar absorptivities and solvent

displacement factors, synthetic calibration spectra are computed using

only background spectra collected with the spectrometer for which a

calibration model is desired. The resulting synthetic calibration set is used

with partial least squares regression to form the calibration model. This

methodology is demonstrated for use in the analysis of physiological levels

of glucose (1–30 mM) in an aqueous matrix containing variable levels of

alanine, ascorbate, lactate, urea, and triacetin. Experimentally measured

data from two different Fourier transform spectrometers with different

noise levels and stabilities are used to evaluate the simulation method.

With the more stable instrument (A), well-performing calibration models

are obtained, producing a standard error of prediction (SEP) of 0.70 mM.

With the less stable instrument (B), the calibration based solely on

synthetic spectra is less successful, producing an SEP value of 1.58 mM.

For cases in which the synthetic spectra do not describe enough spectral

variance, an augmentation protocol is evaluated in which the synthetic

calibration spectra are augmented with the spectra of a small number of

experimentally measured calibration samples. For instruments A and B,

respectively, augmentation with measured spectra of nine samples lowers

the SEP values to 0.64 and 0.85 mM.

Index Headings: Simulation; Near-infrared spectroscopy; Calibration

transfer; Partial least squares; PLS; Glucose.

INTRODUCTION

Near-infrared (NIR) spectroscopy is a widely used analyticalmeasurement tool in pharmaceutical, petroleum, industrial, andagricultural applications.1–4 The technique requires little or nosample preparation and is nondestructive, reagentless, simple,and fast. In addition, NIR spectroscopy exhibits the capabilityto extract quantitative information of several species within asample from a measured spectrum, thereby making thismeasurement approach ideal for multicomponent determina-tions in complex sample matrixes.

The principal drawback to this method is the occurrence ofbroad and highly overlapping spectral bands in the NIR region.In a complex sample, it is very unlikely that selectivequantitative measurements can be made on the basis of asingle wavelength. Consequently, quantitative calibrationsmust be based on information at multiple wavelengths, therebyrequiring the use of multivariate modeling techniques. Therequirement for the use of multivariate calibration methods inNIR spectroscopy adds significant complexity to the designand implementation of a quantitative analysis.

One aspect of this complexity is the potential for degradationof the performance of the calibration model over time due tochanges in the instrumental response or changes in the physical

parameters associated with the data collection (e.g., sampletemperature). A similar deterioration is expected whencalibration models that are generated with one instrument areapplied to spectral data collected with another instrument. Anobvious solution to this problem is recalibrating to incorporatespectral features present in the prediction samples. However,this approach is expensive and time consuming.

Several strategies have been developed in the past to remedyissues associated with variation in the instrumental andenvironmental responses. Collectively termed calibrationtransfer techniques, they include calibration standardization,calibration updating, and preprocessing methods. Standardiza-tion involves transforming data collected with one instrumentto be compatible with data acquired by another. This istypically done by employing a set of representative samples tocollect data with both instruments, followed by the calculationof an instrumental transfer function. Kowalski and co-workers5,6 have described two such procedures, termed directstandardization (DS) and piecewise direct standardization(PDS). These techniques are related and use global and severallocal regression models, respectively, to generate a transfor-mation matrix that relates the two sets of spectra. In this way,spectra collected with a secondary instrument can betransformed to be compatible with a calibration modeldeveloped with data collected with a primary instrument.

Calibration updating techniques involve the incorporation ofnew features that are unique to the prediction data into theoriginal calibration model. Haaland and Melgaard7,8 engi-neered several prediction-augmented classical least-squares(PACLS) methods in which spectral variations that are presentin the prediction samples can be augmented either to classicalleast squares or partial least squares (PLS) calibration modelsduring the validation step. Zhang et al.9 proposed the use of aguided model reoptimization algorithm. This method aims atdiscerning through optimization the best wavelength range andsubset of samples to use in reoptimizing the original calibrationmodel. A small set of updating samples is measured to guidethe optimization.

Preprocessing in conjunction with signal processing tech-niques has also been extensively used to remove sources ofvariance in the data emanating from instrumental and physicalcontributions. Woody and co-workers10 employed orthogonalsignal correction (OSC) in transferring multivariate calibrationmodels across four instruments, and de Noord11 examinedways of using second-derivative calculations in conjunctionwith multiplicative signal correction to remove spectralvariation and thereby make calibrations more robust. Sjoblomet al.12 illustrated the effectiveness of removing instrumentalsignatures with OSC and compared it to other preprocessingtechniques. Our laboratory has done extensive work to assessthe capabilities of digital filtering in tackling the aforemen-tioned problems.13–16

Received 18 September 2006; accepted 18 January 2007.* Present address: Novartis Pharmaceuticals Corp., One Health Plaza,Bldg. 401/B244B, East Hanover, NJ 07936-1080.

406 Volume 61, Number 4, 2007 APPLIED SPECTROSCOPY0003-7028/07/6104-0406$2.00/0

� 2007 Society for Applied Spectroscopy

Although these approaches might address issues associatedwith instrumental drift and temperature fluctuations, all thesetechniques still require a significant amount of calibration data.To overcome this shortcoming, we propose a scheme thatmathematically simulates real or measured spectra usingbackground measurements to generate a synthetic data set.This is based on the analogy that the inherent absorbance of thespecies in a particular sample matrix remains unchanged and isa direct representation of the extended version of the Beer–Lambert law for multi-component systems. Using previouslymeasured absorptivity and solvent displacement values foreach component in the sample matrix, the transmittance andthereby the absorbance of the sample can be obtained.Subsequently, synthetic spectra are generated by integratingthis information with background measurements that encodeinstrumental and environmental responses that vary withrespect to time.

The concept of combining pure-component spectra of theknown components of the sample with separate backgroundmeasurements is consistent with much of the current researchin multivariate calibration. The PACLS methods referencedabove, as well as the technique of hybrid linear analysisdeveloped by Berger et al.,17 employ this idea. The use ofnumerical simulation has also recently been exploited tounderstand and implement multivariate calibrations. Tarumi etal.18 have used a simulation approach to model the impact ofvariation in quantities such as temperature and scattering on invivo NIR spectra of tissue. Maruo et al.19,20 have used anumerical model of light propagation through tissue to simulatein vivo diffuse reflectance spectra and have developed acalibration procedure that employs these simulated spectra.

In this paper, a calibration approach based on simulatedspectra is investigated in the context of determining physio-logical levels of glucose in a six-component aqueous matrixinvestigated with transmission measurements performed withtwo different Fourier transform (FT) NIR spectrometers. Thesimulation method is compared with conventional calibrationsbased on measured calibration data. In addition, to incorporatemore sources of spectral variation into the model, anaugmentation protocol that involves adding several measuredspectra into the simulated calibration data set is alsoinvestigated.

EXPERIMENTAL

Apparatus and Reagents. Data used in this study weretaken from previous work in our laboratory9 and consisted ofNIR spectra collected from 80 samples. Each sample wascomposed of a mixture of glucose, sodium lactate, urea,sodium ascorbate, alanine, and triacetin in phosphate buffer.Details regarding solution preparations were reported previ-ously.9 A randomized experimental design was employed inthe generation of the 80 samples in order to minimizecorrelations between the component concentrations. Pairwisecorrelation coefficients among the concentrations ranged from�0.18 to 0.11. The concentration ranges for glucose, lactate,urea, ascorbate, alanine, and triacetin were 0.68–34.27, 1.18–33.34, 1.20–30.23, 1.18–22.55, 1.75–38.32, and 0.46–27.95mM, respectively.

Separate data sets were collected with two FT spectrometers,a Nicolet Nexus 670 and a Nicolet Magna 540 (ThermoElectron Corp., Madison, WI). Both instruments were equippedwith a tungsten-halogen source, CaF2 beam splitter, and liquid

nitrogen cooled InSb detector. These Nexus and Magnaspectrometers and their corresponding data sets will henceforthbe termed A and B, respectively. The same demountable liquidtransmission cell with a 20 mm diameter circular aperture(Model 118–3, Wilmad-Labglass, Buena, NJ), sapphirewindows (Meller Optics, Providence, RI), and 1.5 mm pathlength was used with both instruments. A refrigerated waterbath that circulated water through an integrated jacket in thesample cell was used to control the temperature of the samplewithin the physiological range of 37 6 0.1 8C. Sampletemperatures were monitored by use of a copper-constantanthermocouple probe (Omega Engineering, Stamford, CT)placed in a port in the cell.

Procedures. Data from spectrometer A were collected overseven days with six individual sessions, while spectra frominstrument B were collected over five days with five sessions.The data collection protocol involved collecting three replicatespectra for each sample without removing the sample cell fromthe spectrometer. The run order of the measurements wasrandomized to minimize correlations between componentconcentrations and time. Buffer spectra (three consecutivereplicates) were collected periodically during each measure-ment day. For data sets A and B, respectively, a total of 42 and45 buffer spectra were acquired across all of the data collectionsessions.

Raw data from both spectrometers were composed ofdouble-sided interferograms consisting of 4096 points basedon 256 coadded scans sampled at every two zero-crossings ofthe reference HeNe laser. Interferograms were then Fourierprocessed with one level of zero-filling, triangular apodization,and Mertz phase correction to yield single-beam spectra with apoint spacing of 1.9 cm�1. All spectra were then subsequentlytransferred to a Silicon Graphics Origin 200 R12000 server(Silicon Graphics, Inc., Mountain View, CA) operating underIrix (Version 6.5, Silicon Graphics, Inc.). A second-orderpolynomial wavenumber interpolation was performed on thissystem with original software written in Fortran 77 to align thesingle-beam spectral points of the two instruments. Furthercalculations were performed using Matlab (Version 6.5, TheMathWorks, Inc., Natick, MA) installed on a Dell Precision450 workstation (Dell Computer Corp., Austin, TX) operatingunder Red Hat Linux WS (Version 3, Red Hat, Inc., Raleigh,NC).

THEORY

Spectrum Simulation Approach. The goal of the researchpresented here was to develop a spectral simulation approach togenerate synthetic spectra for use in building calibrationmodels. The resulting models could be subsequently appliedto predict glucose concentrations in experimentally measuredspectra. The calculation of synthetic spectra is based on thepremise that a single-beam spectrum output from the FTspectrometer is a culmination of the absorbance of the analyte,convolved with the responses of the instrument and back-ground matrix. This can be represented by

IðmÞ ¼ I0ðmÞTðmÞ ð1Þ

where I(m) corresponds to the single-beam response, I0(m) isthe source spectrum or instrumental profile, and T(m) representsthe overall transmittance of the sample. All of these parametersare functions of wavenumber, m. Assuming that intermolecular

APPLIED SPECTROSCOPY 407

interactions have a negligible effect on the absorption and therefractive index of the sample is constant with respect to m, thetransmittance for a particular sample can be represented inaccordance with the Beer–Lambert law by

TðmÞ ¼ 10�½ReðmÞbc� ð2Þ

where the e are the absorptivity values for each constituentwithin the sample, b is the optical path length, and c representsthe concentration of each component in the sample. Thesummation is a representation of the overall absorbance fromall the constituents in each sample. The absorbance for asample can be represented by

As ¼ e1ðmÞbc1 þ e2ðmÞbc2 þ � � � þ enðmÞbcn ð3Þ

where As is the absorbance for sample s, and ei and ci

correspond to the absorptivity and concentration of each of nconstituents, respectively.

The buffer spectra that were collected periodically were usedto obtain an estimate of I0(m). Assuming that water is thedominant component in the buffer and that the phosphate saltswithin the buffer have a negligible effect on the concentrationof water enables the combination of Eqs. 1 and 2 for a single-component system to give

I0ðmÞ ¼ IbðmÞ3 10½ebðmÞcb� ð4Þ

where Ib(m) and eb(m) correspond to the single-beam spectralintensity and absorptivity of the buffer (water).

The transmittances of the calibration samples were obtainedby implementing Eqs. 2 and 3 using the experimentallymeasured absorptivities of the six constituent species and waterat 37 8C.21 In conjunction with these parameters, an opticalpath length of 1.5 mm and concentration values correspondingto the prepared amounts were input into the simulationalgorithm. The concentration of water, cwater, was based onits density measurements at 37 8C with its magnitudeattenuated with respect to the overall dissolution of the sixcomponents and their respective solvent displacement fac-tors.21 The resulting water concentration is given by

cwater ¼ cpure water �X6

i¼1

dici ð5Þ

where cpure water is the concentration of pure water at 37 8C, di

is the solvent displacement factor for component i, and ci

denotes the corresponding reference concentration.Using the computed source spectra in Eq. 4, the component

concentration matrix, and the absorptivities for the sevencomponents including water as inputs into Eqs. 3, 2, and 1,respectively, synthetic single-beam spectra were generated forthe samples in both the calibration and prediction sets for eachinstrument. In an effort to mimic the variation that existed inreal measurements, reported means and standard deviations ofthe absorptivity measurements for each component21 were usedto compute three replicate spectra for each sample (i.e., themean absorptivity was used to generate one spectrum, whilethe mean 6 the standard deviation was used in the generationof the other two replicates). Buffer spectra in the calibrationand prediction data sets were used to provide multipleestimates of I0(m), and these source spectra were assignedrandomly in the generation of the simulated data.

RESULTS AND DISCUSSION

Characterization of Measured Data. Figure 1A depicts thepure-component absorbance spectra of glucose, lactate, urea,ascorbate, alanine, and triacetin. A spectrum of phosphate bufferwas used as the background in the absorbance calculation.Negative absorbance values are observed in the spectra due todifferences in water concentration between the samples andbuffer solution. Baseline variations in the spectra can beattributed to a slight temperature mismatch between the sampleand buffer spectra. There are three distinct bands exhibited byglucose, one at 4700 cm�1 corresponding to an O–Hcombination band, and two others at 4400 and 4300 cm�1

corresponding to C–H combination bands. These spectral tracesclearly show the extensive degree of overlap between glucoseand the other five components within the samples. Successfulquantitation of glucose within this sample matrix represents asignificant challenge.

The quality of the measured spectra can be characterized byevaluating the noise or variance between replicate measure-ments of the same sample. This is accomplished by taking theratios of replicate single-beam spectra and converting theresulting transmittance spectra to absorbance units (AU). In the

FIG. 1. (A) Pure-component absorbance spectra of the six components (50mM in phosphate buffer) obtained by taking the ratio of single-beam spectra ofeach constituent to a spectrum of the buffer. The trace of glucose (—) clearlyshows the two C–H combination bands located at 4300 and 4400 cm�1 and theO–H combination band located at 4700 cm�1. The other five constituent speciesare lactate (���), urea (������), ascorbate (—), alanine (� � �), and triacetin(�����). (B) Spectra in AU computed from ratios of single-beam spectra ofphosphate buffer collected with spectrometers A (solid line) and B (dashedline). Forty-two and 45 spectra are plotted for instruments A and B,respectively. The mean buffer spectrum from each instrument was used asthe reference spectrum in the absorbance calculation for spectra from thecorresponding instrument.

408 Volume 61, Number 4, 2007

absence of spectral variance, the resulting noise trace is a flatline at 0.0 AU. Systematic variation will cause the trace to shiftabove or below 0.0 AU, either with or without an inducedslope or curvature. Random noise will be superimposed on thetrace in a manner that is symmetric about the zero line.

Figure 1B depicts such traces computed from the 42 and 45replicate spectra of phosphate buffer collected with instrumentsA (solid line) and B (dashed line), respectively. The mean bufferspectrum from each instrument was used as the reference in theabsorbance calculation. Inspection of the figure reveals bothsystematic shift and curvature in the traces on the order of60.02 AU. Random noise cannot be seen because it is on amuch smaller scale than the systematic variation. Simple shiftsarise from intensity variation in the two single-beam spectrawhose ratios are taken. Curvature is caused by spectral shifts inthe two spectra. Here, despite the attempt to control the sampletemperatures to 60.1 8C, the extreme temperature sensitivity ofthe water spectrum causes variation in the data that is confirmedby the curved traces in the figure. Comparing the scales betweenpanels A and B of Fig. 1 also confirms that the systematicvariation illustrated in panel B is significant when compared tothe signal strengths of the bands of the chemical constituents.

Given that systematic variation can be accounted for by thecalibration model, calculations were also performed to assess therandom noise levels in the spectra of the mixture samples.Within the three replicate spectra of each sample, ratios weretaken among all combinations. A second-order polynomialfunction computed through a least-squares fit was used to modeland subtract the baseline shift and curvature induced by intensitydrift and temperature variation among the replicate spectra. Thiscalculation was performed over the 4500–4300 cm�1 spectralwindow which contains the glucose C–H combination band at4400 cm�1 that is known to be an important spectral feature forquantitative analysis.22 Root-mean-square (RMS) deviationsfrom the fitted quadratic function were computed for all threepossible ratios for each sample.

To assess the overall values for each instrument, theminimum, mean, and maximum values were inspected. Theminimum RMS noise estimates for instruments A and B were2.70 and 5.16 lAU, respectively. The corresponding meanvalues were 6.97 and 23.2 lAU, while the maximum valuescomputed were 47.6 and 52.8 lAU, respectively. The highernoise estimates for the data collected with spectrometer B couldbe attributed at least partially to greater temperature variationsince there were problems encountered with the interfacebetween the thermocouple and the sample cell during the datacollection.9 The more complex curvature exhibited by thedashed lines in Fig. 1B cannot be completely fit by a second-order polynomial and thus some of the temperature variation isincluded in the RMS noise estimate. From these noiseestimates, we can deduce that data collected with instrumentA has superior spectral quality to the measured spectra fromspectrometer B.

Quantitative analysis of these data sets involved partitioningthe spectral data into calibration and prediction sets. Spectracollected on the last two days in each data set were designatedinto the prediction set while the data collected during thepreceding days were assigned to the calibration set. Imple-menting this scheme, 52 and 60 samples were assigned to thecalibration sets and the remaining 28 and 20 samples wereplaced in the prediction sets for data sets A and B, respectively.Replicate spectra were carried together into the respective

subsets. Calibration models were developed by use of PLSregression23 applied directly to the single-beam data. Prepro-cessing involved normalizing and mean centering the single-beam data before application of PLS. To determine the bestspectral region for modeling, a wavenumber search approachwas employed. This involved probing the 4833–4099 cm�1

region by extracting range sizes between 600 and 400 cm�1 insteps of 25 cm�1 and shifting the starting wavenumber positionin steps of 50 cm�1. Normalized, mean-centered single-beamspectral data from the calibration subset spanning allcombinations of the wavenumber search space were input intothe PLS algorithm employing 1 to 18 latent variables. Thesemodels were then validated via a full leave-one-out cross-validation. The performance of the generated calibrationmodels was evaluated on the basis of the cross-validationstandard error of prediction (CV-SEP), computed as

CV-SEP ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

i¼1

ðyi � yiÞ2

n

vuuutð6Þ

where yi is the reference concentration, yi is the predictedconcentration, and n is the number of spectra in the calibrationset. Values of CV-SEP were computed over all combinationsof wavenumber subsets and PLS latent variables. Sorting theCV-SEP values enabled the selection of the best wavenumberrange. The number of latent variables was subsequentlyoptimized by employing the F-test statistic at the 95%confidence level. The smallest number of latent variables wassought that produced a value of CV-SEP that was statisticallyindistinguishable from the minimum CV-SEP.

Table I lists the standard errors of calibration (SEC) andprediction (SEP) corresponding to the optimal models. Thesestatistics were computed in a manner analogous to Eq. 6. Thecalculation of SEP used the external prediction set. Incomputing the SEC value, the degrees of freedom wereadjusted to account for the number of latent variables used.This is an approximation that is widely used, although itsaccuracy in assessing the rank of the model has beenquestioned because all spectral resolution elements contributeto each latent variable.24

As anticipated from the noise calculations, the predictionresults for spectrometer A (SEC¼ 0.33 mM, SEP¼ 0.44 mM)were better than those from instrument B (SEC¼0.63 mM, SEP¼ 0.76 mM). Figure 2A displays the concentration correlationplot for spectrometer A for both calibration and predictionsamples. Figure 2B is a similar correlation plot for experimentB. These relationships clearly show the success in extractingquantitative glucose information from the measured spectra.

Comparison of Measured and Simulated Data. Todetermine whether the simulation approach achieved a similarlevel of spectral variability, the mean-centered experimentallymeasured single-beam spectra obtained from both instrumentswere compared with their simulated counterparts. The spectraare plotted in Figs. 3A and 3B for spectrometer A and Figs. 4Aand 4B for spectrometer B. In both cases, the mean simulatedsingle-beam spectrum was used to generate the mean-centereddata in both the measured and simulated domains. From aninspection of the plots, the simulated and experimentallymeasured spectra are visually similar.

Principal component analysis (PCA) was also applied tocompare the similarity between the measured and simulated

APPLIED SPECTROSCOPY 409

data sets. Figure 5 depicts score plots constructed from the firstand second principal components. Data input into the PCAcalculation were the mean-centered measured single-beamspectra across the 4833–4099 cm�1 range. The measured andsimulated spectra were then projected onto the computedprincipal components to obtain the scores. Panels A and B inFig. 5 correspond to the data for instruments A and B,respectively. Two principal components explain more than99% of the total variance in the data in each case. Examiningthese plots reveals a high degree of overlap between the

measured and corresponding simulated data. Similar overlapbetween the measured and simulated data was observed whenother combinations of the scores along the 12 computedprincipal components were plotted. These results provide a firstlevel of validation regarding the viability of the spectrumsimulation approach.

Evaluation of Prediction Performance. Using the simu-lated calibration spectra representing data derived from eachinstrument, PLS calibration models were generated for glucoseand subsequently applied to both the experimentally measuredprediction set and the corresponding prediction set of simulatedspectra. The type of wavenumber search, number of PLSfactors tested, and preprocessing steps performed were similarto those applied to the measured calibration data and discussedpreviously. Model sizes (number of latent variables) wereoptimized using the same approach employing the F-testdescribed previously. Table I lists the SEC and SEP valuesobtained with the simulated data sets, as well as the SEP values(denoted SEP-x) achieved when the calibration modelsconstructed from the simulated calibration data were appliedto the prediction sets of experimentally measured spectra.

When applied to simulated data alone, the calibration modelsproduced excellent values of SEC and SEP for bothinstruments. When the models computed with the simulatedcalibration spectra were applied to the measured predictiondata, the results were quite different for the two instruments.Simulation results for data obtained using spectrometer A werequite good with an SEP-x value of 0.70 mM. The resultsachieved with instrument B were not as successful, however,

TABLE I. Summary of calibration and prediction results.

SpectrometerWavenumber

(cm�1) LVaSECb

(mM)SEP

(mM)SEP-xc

(mM)

Measured data A 4733–4133 12 0.33 0.40d

B 4533–4183 12 0.63 0.76d

Simulated data A 4783–4183 11 0.28 0.34e 0.70B 4733–4158 15 0.23 0.35e 1.58

a Number of latent variables in PLS model.b Result based on predicting glucose in measured and simulated calibration

samples.c Result based on using simulated calibration models to predict glucose in

measured prediction samples.d Result based on predicting glucose in measured prediction samples.e Result based on predicting glucose in simulated prediction samples.

FIG. 2. Concentration correlation plots of predicted versus reference glucoseconcentrations in the experimentally measured calibration (*) and prediction(n) samples, respectively, obtained with spectrometers (A) A and (B) B. Forinstrument A, values of r2 for the calibration and prediction data are 0.9991 and0.9984, respectively. The corresponding values for instrument B are 0.9962 and0.9950. The wavenumber range and number of PLS factors associated witheach model are listed in Table I.

FIG. 3. Mean-centered single-beam spectra of the entire 80 sample data set(first replicate in each sample shown) corresponding to measured data from (A)spectrometer A and (B) its simulated counterpart.

410 Volume 61, Number 4, 2007

producing an SEP-x value of 1.58 mM. These results track thequality of the data from the two instruments as describedpreviously during the discussion of the noise calculations.However, in both cases, the prediction performance obtainedwith the simulated data is inferior to that achieved with modelscomputed from the full set of experimentally measuredcalibration spectra. This suggests that the simulated data donot completely represent the spectral variation encounteredwith the prediction samples. Of particular note is thetemperature variation encountered during the data collectionwith instrument B. This variation was not captured with thesimulated spectra.

Figure 6A displays a concentration correlation plot for theprediction samples measured with spectrometer A, using bothmeasured and simulated calibration models. This plot visuallycompares the modeling capabilities between the measured andsimulated data sets. Figure 6B shows a similar correlation plotfor data corresponding to instrument B. In this case, the plotconfirms that the measured calibration model significantlyoutperforms the simulation approach.

Augmentation Protocol. The results presented abovedemonstrate with some success the possibility of replacingconventional calibration measurements with simulated spectra.The success of this methodology depends on the extent towhich the buffer or background data used as the basis for thesimulation incorporates non-chemical variability that existswithin the prediction data. With a stable spectrometer andexperimental setup (e.g., good temperature stability), a small

number of background spectra may be able to capture thisvariation successfully. This was the case with the data frominstrument A. The simulation approach becomes moreproblematic when the instrument or experimental setup is lessstable. This was the case with the data from instrument B.

For the case of less stable data, the only way to overcomethis negative effect is to include more background or bufferspectra to better characterize the instrumental and environ-mental parameters. In the current experiment, this wasproblematic because a total of only 42 or 45 buffer spectrawere collected with instruments A and B, respectively, acrossall the data collection sessions.

In such cases, another potential approach is to augment thesimulated calibration spectra with the experimentally measuredspectra of a small number of calibration samples. With thisstrategy, the simulation approach is used to reduce the numberof required calibration samples rather than to eliminate themaltogether.

To test this strategy, measured sample spectra werecombined with the simulated data sets in an effort toincorporate more instrumental and environmental information.The new data sets were then used to re-compute the PLScalibration models.

To implement the augmentation experiment, the Kennard–

FIG. 4. Mean-centered single-beam spectra of the entire 80 sample data set(first replicate in each sample shown) corresponding to measured data from (A)spectrometer B and (B) its simulated counterpart.

FIG. 5. Principal component (PC) score plot comparing the distributionbetween the measured and simulated mean-centered single-beam data. (A) Plotof scores along PC 2 versus PC 1 for measured (þ) and simulated (*) data setscorresponding to data acquired with spectrometer A. (B) Plot of scores alongPC 2 versus PC 1 for measured (þ) and simulated (*) data acquired withspectrometer B. For both data sets, the PCs were computed from the mean-centered measured spectra, and the measured and simulated spectra were thenprojected onto these PCs to obtain the corresponding scores.

APPLIED SPECTROSCOPY 411

Stone subset selection algorithm25 was applied to theconcentration space spanned by the calibration samples. Thiscalculation was performed separately for the calibration setscollected with each instrument. Fifteen samples were selectedto serve as candidates for augmentation. After these sampleswere removed, a second group of 10 samples was selected foruse in monitoring the augmentation. The augmentation wasthen performed in five steps, with the spectra corresponding tothree of the 15 samples being added at each step. Samples wereadded in the order selected by the Kennard–Stone method. Thethree replicate spectra associated with each sample wereincluded in the augmentation. Thus, augmenting 3, 6, 9, 12,and 15 samples resulted in adding 9, 18, 27, 36, and 45measured spectra to the simulated spectra in the calibration set.

At each step, a new PLS model was formed by use of thecurrent calibration set. The same optimization proceduredescribed previously was used to identify the wavenumberrange and number of PLS latent variables. The resulting modelwas then applied to predict the glucose concentrationscorresponding to the 10 samples (30 spectra) in the monitoringset. The value of SEP for the monitoring set will be termed thestandard error of monitoring (SEM).

The value of SEM was used to decide when to terminate theaugmentation. The procedure was halted if the value of SEM

dropped below 0.5 mM or if the change between successiveSEM values after each augmentation step was less than 0.02mM. Table II lists the values of SEC, SEP for the simulatedspectra in the prediction set, SEM, and SEP-x.

The results in Table II show that for instrument A, the SEP-xvalue dropped from 0.70 mM to 0.68 mM after theaugmentation of the simulated spectra with the experimentalspectra of three calibration samples. The SEP-x dropped furtherto 0.60 mM after six measured samples were included into thesynthetic calibration algorithm, although it rose to 0.64 mMwhen the termination criterion (change in SEM , 0.02 mM)was reached at nine augmented samples.

With spectrometer B, the value of SEP-x increased slightlyfrom 1.58 to 1.60 mM after the augmentation of the spectra ofthree measured samples. After the addition of the spectracorresponding to six and nine measured samples, the SEP-xdecreased to 0.93 and 0.85 mM, respectively. The terminationcriterion was reached at nine samples.

Each sample addition incorporates more information fromthe measured data into the simulated data and the lessdissimilar these data sets (measured versus simulated) become.Comparing the SEP-x values after augmentation with thosecomputed from the measured calibration set (Table I) showsthe level of success that is achieved by this simulatedcalibration-augmentation protocol. This clearly indicates thatthe inclusion of spectral components or shapes from themeasured calibration data into the simulated data set ultimatelygenerates a more robust synthetic calibration model withsuperior quantitative predictive performance. Greater improve-ment is observed in the case of spectrometer B because of thelarger variability in the measured data collected with thisinstrument.

Absorbance Data Analysis. In addition to working withsingle-beam data, the performance of this methodology withconventional absorbance measurements was investigated.Measured, simulated, and phosphate buffer spectral datacorresponding to instruments A and B were utilized in thisstudy. The number of buffer spectra collected each day, foreach instrument, varied from 3 to 9. These spectra werecollected before, during, and after each of the data collectionsessions and therefore each one of them could be employed tocompute the absorbance measurements.

To investigate which buffer spectral manipulation bestrepresented the true background, several strategies were

FIG. 6. Concentration correlation plots of predicted versus reference glucoseconcentrations corresponding to prediction samples measured with (A)spectrometer A and (B) spectrometer B. The calibration model in each casewas generated from measured calibration data (n) or simulated data (&). Forinstruments A and B, respectively, the r2 values corresponding to models basedon simulated data are 0.9974 and 0.9890. The corresponding values for modelsbased on measured data are 0.9984 and 0.9950. Details for each model andprediction errors are listed in Table I.

TABLE II. Augmentation results.

Spectrometer

No. ofaugmented

samplesWavenumber

(cm�1) LVaSECb

(mM)SEPc

(mM)SEMd

(mM)SEP-xe

(mM)

A 3 4733–4283 11 0.39 0.44 0.91 0.686 4733–4283 11 0.45 0.40 0.85 0.609 4733–4283 11 0.33 0.25 0.85 0.64

B 3 4733–4133 13 0.54 0.49 1.49 1.606 4733–4133 13 0.57 0.49 1.35 0.939 4733–4133 12 0.57 0.49 1.36 0.85

a Number of latent variables in PLS model.b Result based on predicting glucose in simulated calibration samples.c Result based on predicting glucose in simulated prediction samples.d Result based on using simulated-augmented calibration models to predict

glucose in the measured monitoring samples.e Result based on using simulated-augmented calibration models to predict

glucose in measured prediction samples.

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investigated. These included using the mean, first, middle, andlast buffer spectrum for each day. Each of these fourconfigurations was evaluated on the basis of calibration andprediction performance with the measured data. On the basis ofSEP values, the best results were obtained when the ratio wastaken of the single-beam spectra to the first buffer spectrumcollected each day.

This approach was subsequently used to compute spectra inAU from the synthetic single-beam calibration spectra. Theresulting spectra were used in the construction of PLScalibration models as described previously. The same wave-number optimization and selection of latent variables wereperformed as before. The corresponding performance statisticsfor these models are listed in Table III. These results are similarto the performance of the calibration models computed withsimulated single-beam spectra. Slightly improved prediction isobserved with the data from instrument B, while slightly worseresults are obtained with instrument A.

CONCLUSION

The results presented in this study clearly demonstrate thecapability of simulating NIR spectral data from backgroundmeasurements for the generation of synthetic multivariatecalibration models that can be used to predict analyteconcentrations in measured prediction samples. This candrastically reduce the time, effort, and expense of generatingan entire sample set and its corresponding spectral data. Theperformance of the calibration models computed with mea-sured and simulated spectra was indicative of the inherentstability of each corresponding instrument as described by theRMS noise estimates. Although the prediction results based onsolely synthetic spectra were not as good as the correspondingresults obtained with a full set of measured calibration data, itshould be emphasized that only buffer spectra were utilized inthe formulation of the simulated calibration models. Nocalibration samples were required.

Efforts were made to accommodate more non-chemicalspectral responses by augmenting a few measured samplesselected from the calibration concentration space to thesynthetic data sets. Optimized calibration models generatedfrom these augmented simulated data sets improved theprediction results for the measured data from both spectrom-eters A and B. Interestingly, the latter data set showed a largerreduction in the error values. This was a consequence ofincorporating more effects associated with temperature varia-tion into the synthetic data generation, since the data set from

spectrometer B exhibited higher noise values caused bytemperature fluctuations.9

It is hypothesized that better simulation results withoutaugmentation could be obtained if more buffer or backgroundspectra were collected each day. This would allow bettercharacterization of changes in both the instrumental profile andeffects such as variation in sample temperature. This is thesubject of ongoing work in our laboratory.

The proposed synthetic calibration algorithm can also beused to correct the degrading effects of long-term spectrometerdrift by incorporating spectral variations present in theprediction samples into the generation of the calibrationspectra. This can be implemented by employing buffer spectracollected in the same time span as the prediction samples intothe simulation and thereby accommodating instrumental andtemperature information inherent to a particular measurementsession. Further testing of the synthetic methodology underthese conditions is also the subject of ongoing work.

The principal limitation of this methodology is that all thechemical components in the system need to be characterized ifaccurate synthetic spectra are to be obtained. This can only befeasible with a well-characterized sample. Fortunately, thereare many applications in which the sample matrix is fixed andknown. The proposed methodology should be very useful insuch cases. Industrial process control and process monitoringapplications represent one such area of potential use for thismethodology.

ACKNOWLEDGMENT

This research was supported by the National Institutes of Health under grantDK60657.

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TABLE III. Performance of calibration models with simulated absor-bance spectra.

SpectrometerWavenumber

(cm�1) LVaSECb

(mM)SEPc

(mM)SEP-xd

(mM)

A 4883–4308 13 0.40 0.52 0.86B 4733–4283 12 0.53 0.62 1.17

a Number of latent variables in PLS model.b Result based on predicting glucose in simulated absorbance calibration

samples.c Result based on predicting glucose in simulated absorbance prediction

samples.dResult based on using simulated absorbance calibration models to predict

glucose in measured prediction samples.

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