multivariate calibration models based on the direct analysis of near-infrared single-beam spectra

1330 Volume 51, Number 9, 1997 APPLIED SPECTROSCOPY0003-7028 / 97 / 5109-1330$2.00 / 0q 1997 Society for Applied Spectroscopy

Multivariate Calibration Models Based on the DirectAnalysis of Near-Infrared Single-Beam Spectra

GENG LU, XIANGJI ZHOU, MARK A. ARNOLD,* and GARY W. SMALLDepartment of Chemistry, University of Iowa, Iowa City, Iowa 52242 (G.L., X.Z., M.A.A.); and Center for Intelligent ChemicalInstrumentation, Department of Chemistry, Clippinger Laboratories, Ohio University, Athens, Ohio 45701-2979 (G.W.S.)

Multivar iate calibration models are generated for glucose, gluta-mine, and asparagine on the basis of partial least-squares regressionanalysis of near-infrared single-beam spectra covering the 5000±4000-cm 2 1 (2000± 2500-nm) spectral range. Models are constructedwith both raw and digitally Fourier -® ltered single-beam spectra.Model performance is evaluated and compared with that of anal-ogous models constructed from the corresponding computed absor-bance spectra. Five unique data sets are examined correspondingto the measurement of (A) glucose in phosphate buffer with differ-ent temperatures, (B) glucose with variable albumin protein levels,(C) glucose with variable triacetin levels, (D) glucose and glutaminein a set of binary mixtures, and (E) glutamine and asparagine in aset of binary mixtures. In all cases, models based on single-beamspectra perform as well as those based on computed absorbancespectra.

Index Headings: Near-infrared analysis; Single-beam spectral anal-ysis; Spectroscopic glucose measurements.

INTRODUCTION

The possibility of performing noninvasive blood glu-cose measurements with near-infrared (near-IR) spectros-copy has received considerable attention in recentyears.1± 7 Most reported approaches to date are based onextracting analytical information from transmission mea-surements based on passing a band of near-IR radiationthough some region of the body. This type of measure-ment is complicated by the strongly absorbing and highlyscattering characteristics of the human body.

In attempting to establish the feasibility of noninvasiveglucose measurements, the philosophy of our researchprogram is to increase the complexity of the sample ma-trix systematically while validating our ability to measureclinically relevant levels of glucose accurately at eachstep. These studies have been performed with a conven-tional Fourier transform spectrometer and have consistedof transmission measurements performed with samplesheld in standard liquid cells. Single-beam spectra of theglucose samples are obtained through this procedure.

To construct quantitative calibration models with spec-tra of this type, it is standard practice to convert the spec-tra to absorbance units by ratioing the collected single-beam spectra of the samples to a similarly collected back-ground single-beam spectrum and converting the result-ing transmittance values to absorbance. If the instrumentresponse function of the spectrometer has remained stablebetween the background and sample single-beam mea-surements, the computed absorbance spectrum approxi-mates the spectrum that would be obtained in a true dou-ble-beam spectral measurement.

Received 25 September 1996; accepted 15 March 1997.* Author to whom correspondence should be sent.

The conversion of the single-beam spectra to absor-bance units has two purposes. First, since the Beer-Lam-bert law describes a linear relationship between absor-bance and concentration, it is generally held that the useof spectra in absorbance units will facilitate the devel-opment of linear calibration models for use in predictinganalyte concentrations. Second, if a background spectrumcan be collected that provides a good match to the samplematrix, the resulting ratioed spectrum will be simpli® edand the analyte spectral features will be enhanced. Stateddifferently, the ratioing procedure will remove a principalsource of variation from the spectrum (i.e., the instrumentresponse function) that is unrelated to the spectral re-sponse of the analyte.

In our work, as the matrix complexity has increasedfrom simple aqueous buffer solutions to more demandingmatrices such as undiluted plasma, human serum, andwhole blood, a fundamental limitation of using ratioedspectra has surfaced. This limitation is based on the dif-® culty of identifying a representative background spec-trum for use in computing the ratioed absorbance spec-trum. For example, in the analysis of blood, a glucose-depleted sample of the blood for use in collecting a back-ground spectrum is not typically available. In this situa-tion, we have ratioed single-beam spectra from complexsamples to a reference spectrum obtained from a simpleaqueous buffer solution.6,7 As the sample matrix has be-come more complicated, however, the mismatch betweensample and background spectra has become more severe.Our ® ndings indicate that a severely mismatched back-ground spectrum degrades analytical performance by in-troducing spectral variation that is unrelated to the anal-yte.4

Two additional issues cast further doubt on the wisdomof converting the sample spectra to absorbance units inthe glucose analysis. First, the near-IR spectral responseof the aqueous sample matrix is so temperature-sensitivethat, even under strict experimental control, there willinvariably be some degree of temperature variation be-tween the sample and background spectra. This variationleads to the introduction of baseline shifts and curvaturethat can interfere with the construction of calibrationmodels.5 Second, the near-IR spectra of biological sam-ples consist of a series of broad, heavily overlapped spec-tral bands. The glucose bands represent a tiny componentof the overall absorbance and are heavily overlapped withthe bands of water, proteins, fats, and other matrix con-stituents.7 A spectral response of this type violates theassumptions upon which the Beer-Lambert law is based.Thus, there is no guarantee of a linear relationship be-tween absorbance and concentration. For this reason, cal-

APPLIED SPECTROSCOPY 1331

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ibration models constructed from near-IR spectra tend tobe multivariate in nature, often requiring a large numberof model terms.8

Given these problems, an alternative strategy would beto construct calibration models directly from the single-beam spectra of aqueous samples. The major complica-tions of using single-beam spectra directly are created byan inability to remove transient spectral artifacts causedby uncontrollable instrument and environment variations.Nevertheless, the complications caused by poorlymatched background spectra and the long-range goal ofnoninvasive clinical measurements, which precludes col-lection of a suitable background spectrum, motivate aninvestigation to assess the utility of calibration modelsbased on single-beam spectra.

In this work, ® ve independent spectral data sets areused to compare the analytical performance of calibrationmodels based on single-beam and ratioed absorbancespectra. Each data set and the corresponding absorbance-based calibration models have been described previous-ly.5,6,8,9 These data sets correspond to the measurement of(A) glucose in phosphate buffer at different temperatures;(B) glucose in a variable protein matrix; (C) glucose ina matrix with different levels of triacetin; (D) binarymixtures of glucose and glutamine in phosphate buffer;and (E) glutamine and asparagine in phosphate buffer.

EXPERIMENTAL

Experimental details have been published elsewherefor each data set, and the relevant features for each aresummarized in Table I.5,6,8,9 Samples were prepared withreagent-grade chemicals obtained from common sup-pliers. For all data sets, the solvent was a 0.1 M phos-phate buffer (pH 7.2± 7.4). Individual samples were pre-pared by mixing appropriate amounts of stock solutionsand diluting with the buffer. In all cases, near-IR spectrawere collected over the spectral range from 5000 to 4000cm2 1 (2000± 2500 nm) with a Nicolet 740 Fourier trans-form spectrometer (Nicolet Analytical Instruments, Mad-ison, WI). This spectral range corresponds to the com-bination spectral region and was isolated by placing amultilayer interference ® lter (Barr Associates, Westford,MA) in front of the sample cell. The sample pathlengthwas 1 mm throughout, and samples were contained in atemperature-controlled sample cell with Infrasil quartzwindows. Double-sided interferograms consisting of16,384 points were collected on the basis of 256 coaddedscans. The interferograms were sampled at every zero-crossing of the HeNe reference laser, producing spectrawith a point spacing of 1.9 cm2 1 and a maximum fre-quency of 15,798.57 cm2 1. Single-beam spectra were ob-tained by Fourier processing the interferograms with tri-angular apodization and Mertz phase correction. Thesecalculations were performed with software resident onthe Nicolet 620 computer controlling the spectrometer. Ingeneral, three replicate spectra were collected for eachsample. The order in which the samples were measuredwas randomized with respect to concentration to ensurethat no correlations were introduced between concentra-tion and time. Periodically throughout the data collection,spectra of the phosphate buffer were acquired for sub-sequent use in computing absorbance values for the sam-

1332 Volume 51, Number 9, 1997

FIG. 1. Near-IR single-beam spectra of buffer (solid line),10 mM glu-cose in buffer (short dashed line), 10 mM glucose and 66.5 g/L BSAin buffer (dotted line), and 10 mM glucose and 10.66 mM triacetin inbuffer (dash-dot line). Spectra for buffer and 10 mM glucose in bufferare essentially identical. The inset ampli® es single-beam spectra to high-light differences. An absorbance spectrum corresponding to 10 mMglucose in phosphate buffer is superimposed on these single-beam spec-tra.

ple spectra. Other relevant information about the ® ve datasets is provided in Table I.

The computed single-beam spectra were transferred toa Silicon Graphics Iris Indigo R4000 computer (SiliconGraphics, Inc., Mountain View, CA) operating under Irix(Version 5.2). The remaining calculations reported herewere performed on the Silicon Graphics computer withoriginal software written in FORTRAN 77. Multiple lin-ear regression and Fourier transform calculations used inthe development of the calibration models were per-formed with subroutines from the IMSL library (IMSL,Inc., Houston, TX).

Calibration models were generated by application ofpartial least-squares (PLS) regression10 to a subset ofspectra termed the calibration set. The spectra corre-sponding to individual samples were assigned randomlyto the calibration set. Across the ® ve data sets, the cali-bration set typically contained 75± 90% of the availablesamples. All replicate spectra of a selected sample werecarried together into the calibration set, with the remain-ing spectra assigned to a prediction set for use in evalu-ating the computed models. The performance of the mod-els was judged on the basis of values for the standarderror of calibration (SEC), standard error of prediction(SEP), and mean percent error of prediction (MPEP).SEC and SEP denote the root-mean-squared error in pre-dicted concentrations for the spectra in the calibrationandprediction sets, respectively. The degrees of freedom usedin the SEC calculation are adjusted for the number ofterms in the calibration model. The value of MPEP iscomputed as

n ÃC 2 Ci i 3 100%O Ci5 1 iMPEP 5 (1)n

where Ci is the actual analyte concentration associatedwith spectrum i, CÃ i is the corresponding concentrationpredicted by the model, and n denotes the number ofspectra in the prediction set.

Fourier ® ltering was evaluated as a preprocessing toolfor use in eliminating unwanted variation from both thesingle-beam and absorbance spectra. This procedure usesthe Fourier transform to model the spectrum as a sum ofsine and cosine waveforms. The ® lter attenuates the am-plitudes of speci® ed sine and cosine frequencies, therebyserving to suppress certain features in the spectrum. Forexample, baseline variation tends to be modeled by low-frequency sines and cosines, while spectral noise is mod-eled primarily by high frequencies. In the work per-formed here, the frequency response of the ® lter wasspeci® ed as a Gaussian function de® ned by a bandpassposition and width. These position and width parameterswere expressed in units of digital frequency ( f) as themean and standard deviation, respectively, of the corre-sponding Gaussian. The digital frequency scale has arange of 0 ± 0.5, where 0.5 designates the maximum sine/cosine frequency of the data. The ® lter is applied by mul-tiplying the frequency response function by the result ofthe Fourier transform. After the application of the ® lter,the inverse Fourier transform returns the ® ltered data tothe original domain (i.e., to the single-beam or absor-bance spectrum). In previous work with computed ab-sorbance spectra, a protocol was developed for couplingFourier ® ltering with PLS regression.11

Two procedures were used to identify the optimal po-sition and width of the ® lter bandpass. The procedureused for data sets A ± C matched that described before.11

The samples in the calibration set were subdivided intoa calibration subset and a monitoring set, and a grid-search procedure was used to build calibration modelswith spectra ® ltered with various combinations of ® lterpositions and widths. For each ® lter tested, the model wascomputed with the calibration subset and tested by pre-dicting the concentrations corresponding to the spectra inthe monitoring set. For data sets D and E, an alternativestrategy was implemented in which samples correspond-ing to a speci® ed fraction of the calibration set were ran-domly extracted and used to form the monitoring set.This procedure was repeated six times at each combina-tion of ® lter position and ® lter width, thus forming sixrandom splittings of the data. The decision regarding theeffectiveness of a given set of ® lter parameters was basedon pooling the calibration and prediction results fromeach calibration/monitoring subset. The latter procedurehas proven slightly more robust as the in¯ uence of anypotentially outlying samples in either the calibration ormonitoring sets is diluted. The data sets used in this workwere large and consistent enough, however, to ensure thatboth procedures were able to provide analogous results.

RESULTS AND DISCUSSION

Characteristics of Single-Beam Spectra. Water is thepredominant component in the matrices examined in thiswork. The high concentration and strong absorption fea-tures of water largely dictate the structural features of thecorresponding single-beam spectra. Representative sin-gle-beam spectra are presented in Fig. 1 for comparison.


The plotted spectra correspond to phosphate buffer, phos-phate buffer with 10 mM glucose, phosphate buffer with10 mM glucose and 66.5 g/L albumin protein, and phos-phate buffer with 10 mM glucose and 10.66 mM triace-tin. The raw spectra have different intensity levels be-cause of differences in the instrument response functionof the spectrometer when the data sets were collected. Toenhance comparisons, we normalized each spectrum byscaling the maximum intensity to unity. A computed ab-sorbance spectrum of 10 mM glucose in buffer is alsoincluded.

The basic shape is the same for all of the single-beamspectra. A maximum intensity is observed at 4514 cm2 1

(2215 nm), which corresponds to the minimum water ab-sorbance in this spectral region. The intensity decreasesat both lower and higher wavenumbers corresponding tothe strong water absorption bands centered at 3800 (2632nm) and 5200 cm2 1 (1923 nm), respectively. Even at4514 cm2 1, the in¯ uence of water is signi® cant. The ab-sorbance at 4514 cm2 1 is approximately 1.0 for a 1-mm-thick sample of water, which corresponds to the absorp-tion of 90% of the incident radiation.

No differences can be visualized when comparing sin-gle-beam spectra of phosphate buffer with and withoutglucose (i.e., these spectra overlap in Fig. 1). Absorptionof light by glucose is simply too small to alter the spectralappearance signi® cantly. Some differences can be ob-served, however, in the presence of albumin protein andtriacetin. Slightly lower intensities are evident at the char-acteristic N± H and C± H combination bands of protein at4603 cm2 1(2172 nm) and 4368 cm2 1(2289 nm), respec-tively. A similar decrease in intensity is observed at thecharacteristic C± H combination band of triglycerides(4445 cm2 1, 2250 nm). Similarly, analyte absorption fea-tures are not readily apparent in single-beam spectra fromthe binary mixtures of glucose and glutamine or gluta-mine and asparagine. The effects of unavoidable instru-mental variations, such as minor alignment changes andsource intensity ¯ uctuations, are generally eliminated inabsorbance spectra by using appropriately collected back-ground spectra. With single-beam spectra, however, suchvariations are retained within the data set. Intensity vari-ation can be signi® cant even under ideal conditions ofspectrometer operation. For example, we have measuredthe intensity at 4514 cm2 1 for 18 individual single-beamspectra of phosphate buffer. These spectra were collectedover a 14-day period as part of a routine data collectionsession. The mean intensity was 88.25 Nicolet single-beam units (NSBUs), and the standard deviation was 2.28NSBUs, which corresponds to a 2.6% variation. A vari-ation of this magnitude is larger than the intensitychanges due to absorptions from the highest concentra-tions of either glucose, glutamine, or asparagine.

Glucose Measurements in Buffer. Constant Temper-ature. The feasibility of building functioning PLS cali-bration models with single-beam spectra was initially es-tablished by analyzing spectra of glucose in phosphatebuffer. In this experiment, 191 spectra corresponding to64 samples were extracted from data set A listed in TableI. These spectra were collected at 37 8 C, and the glucoseconcentration ranged from 1 to 20 mM. The spectra weredivided into a calibration set (58 samples and 173 spec-tra) and a prediction set (6 samples and 18 spectra). PLS

calibration models were constructed for glucose by using1 to 20 PLS factors in conjunction with the 4457± 4354-cm2 1 (2244± 2297-nm) spectral range. This spectral rangeisolates the 4400-cm2 1 (2273-nm) glucose absorptionband, which was found to be ideal during the analysis ofcomputed absorbance spectra.5 The best calibration mod-el was based on four PLS factors and exhibited SEC, SEP,and MPEP values of 0.33 mM, 0.43 mM, and 4.84%,respectively. The PLS procedure was not signi® cantly af-fected by variation in single-beam spectral intensities dueto changes in the instrument response function over thecourse of the data collection. No spectral normalizationcalculations were needed.

For comparison, PLS models were constructed afterconverting these single-beam spectra to absorbance unitsby use of a representative buffer spectrum as the back-ground. Essentially equivalent model performance wasfound with SEC, SEP, and MPEP values of 0.29 mM,0.34 mM, and 4.1% for a four-factor PLS model. SECand SEP values for both spectral types track each otherwhen plotted as a function of the number of PLS factors.These results demonstrate that the PLS algorithm is ableto extract suf® ciently selective glucose information fromthe single-beam spectra to allow valid calibration modelsto be computed.

Variable Temperature. Temperature strongly in¯ uenc-es single-beam spectra because of the temperature sen-sitivity of the underlying water absorption bands. As not-ed before,5 the 5200- and 3800-cm2 1 water absorptionbands shift toward higher frequencies with increasing so-lution temperature. The corresponding changes in the sin-gle-beam intensity are large on the scale of the glucoseabsorbances.5 Systematic variations in solution tempera-ture were used to examine the effects of large spectralvariations on the accuracy of PLS calibration modelsbased on single-beam spectra. Our experimental protocolwas analogous to that reported for absorbance spectra,5

where calibration models were generated from spectracollected at a single temperature (37 8 C), while predic-tions were made from spectra collected at different so-lution temperatures (32± 41 8 C). The calibration data setfor this experiment consisted of 173 single-beam spectrafrom 58 glucose solutions maintained at 37 8 C. For theprediction data set, 178 single-beam spectra were col-lected from six different glucose solutions maintained at10 different temperatures ranging from 32 to 41 8 C at 18 C increments. PLS calibration models were constructedwith four unique spectral regions, and the number of fac-tors was varied from 1 to 20 for each region. These spec-tral ranges, which correspond to those used in the anal-ysis of absorbance spectra, are listed in Table II alongwith results from models based on single-beam and ab-sorbance spectra. Again, the optimal number of PLS fac-tors corresponds to the minimum SEP which, in this case,included prediction errors across all temperatures. Theeffect of temperature is demonstrated by comparing val-ues in Table II for the 4457± 4354-cm2 1 spectral rangewith those discussed above for measurements at 37 8 C.More factors are required to reach a minimum predictionerror, and the resulting SEP is higher for the multipletemperature experiment (10 factors with SEP 5 0.66 mMcompared with four factors with SEP 5 0.34 mM).

Figure 2 summarizes the prediction data as a function


TABLE II. Glucose calibration models with variable sample tem-perature.

Spec-tra

typea

Spectra range(cm-1)

Meanposition

(f)b

Standarddevia-

tion (f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4850± 4220 N/F0.0200

N/F0.0264

N/F0.0015

N/F0.0049

12896

0.080.110.090.12

0.450.110.190.15

4.481.042.001.60

SSAA

4811± 4457 N/F0.0185

N/F0.0200

N/F0.0015

N/F0.0022

9494

0.430.140.490.18

1.860.143.070.19

21.691.56

37.092.01

SSAA

4457± 4354 N/F0.0200

N/F0.0286

N/F0.0020

N/F0.0051

104

101

0.220.130.210.18

0.660.170.730.17

6.811.507.551.88

SSAA

4354± 4227 N/F0.0185

N/F0.0254

N/F0.0015

N/F0.0034

67

1210

0.610.110.540.16

5.080.153.680.17

58.851.35

43.311.75

a S: single beam; A: absorbance.b N/F: no ® ltering.

FIG. 2. Effect of sample temperature on glucose prediction error. (A) SEP values for models computed from the 4457± 4354-cm2 1 spectral rangeand based on single-beam spectra without Fourier ® ltering (open bars), absorbance spectra without Fourier ® ltering (upward slash), and single-beamspectra with Fourier ® ltering (cross hatch). (B) For the model computed from the 4457± 4354-cm2 1 range and based on un® ltered single-beamspectra, concentration correlation plots are provided for sample temperatures of 32 (circle), 33 (square), 34 (diamond), 35 (dotted circle), 36 (dottedsquare), 37 (dotted diamond), 38 (solid circle), 39 (solid square), 40 (solid diamond), and 41 (solid up triangle) 8 C. Additional model parametersare provided in Table II.

of temperature for models based on the 4457± 4354-cm2 1

spectral range. The distribution of the SEP values as afunction of sample temperature is plotted in Fig. 2A forthe optimal models based on un® ltered single-beam spec-tra (open bars), un® ltered absorbance spectra (slashedbars), and Fourier-® ltered single-beam spectra (cross-hatched bars). A temperature-sensitive bias is clearly ev-ident in the model constructed with the un® ltered single-beam spectra. The SEP values decrease as the sampletemperature approaches 37 8 C due to the presence of only37 8 C data in the calibration set. For this model, Fig. 2Bshows a correlation plot of predicted vs. actual glucoseconcentrations, with the temperatures denoted by differ-

ent symbols. Least-squares lines are also plotted on thebasis of the predicted vs. actual data at each temperature.These lines clearly indicate the offsets in the predictedvalues according to the deviation of the temperature from37 8 C. This systematic variation is consistent with theobserved temperature-induced spectral shifts of the waterabsorption bands.

Similar results were obtained with the models basedon the computed absorbance spectra. Again, the calibra-tion model was generated from spectra collected at 378 C, while prediction spectra were collected over the 32±41 8 C temperature range. In this experiment, however,absorbance spectra were computed by use of a back-ground spectrum collected at 37 8 C for all spectra re-gardless of temperature. Pertinent values for this calibra-tion model are provided in Table II for the four spectralranges. The distribution of the SEP values in Fig. 2A isanalogous to that obtained from models based on the sin-gle-beam spectra.

The magnitude of the temperature-induced errors de-pends on the spectral range. The 4850± 4220-cm2 1 (2062±2370-nm) range is least sensitive to temperature, closelyfollowed by the 4457± 4354-cm2 1 range. Neither the4811± 4457-cm2 1 (2079± 2244-nm) nor the 4354± 4227-cm2 1 (2297± 2366-nm) range performed well individually,producing values of MPEP greater than 20 and 40%, re-spectively. Poor performance is explained by the fact thatthe corresponding glucose absorption bands are locatedin spectral regions most affected by variations in the wa-ter bands (see Fig. 1).

Our previous work with absorbance spectra demon-strated the effectiveness of using Fourier ® ltering to elim-inate the temperature-induced calibration errors describedabove. As discussed previously, these ® lters can remove


FIG. 3. Raw (A) and Fourier-® ltered (B) single-beam spectra for glucose concentrations of 3.09 mM (solid line), 5.80 mM (long dash line), 9.01mM (short dash line), 12.08 mM (dotted line), 15.03 mM (dash-dot line), and 17.98 mM (dash-dot-dot line). All spectra were collected at 37 8 Cand Fourier ® lters used values of 0.02 and 0.002 f for the position and width, respectively.

low-frequency baseline variations and high-frequencyspectral noise. This past success motivated our attemptto apply Fourier ® ltering to single-beam spectra. The ef-fectiveness of Fourier ® ltering in isolating glucose-de-pendent information from single-beam spectra is dem-onstrated in Figs. 3 and 4. Figure 3 shows raw and ® l-tered single-beam spectra collected at 37 8 C. The ® lterposition and width used were 0.02 and 0.002 f, respec-tively. No glucose information is apparent in the rawspectra presented in Fig. 3A. However, a clear relation-ship between spectral intensity and glucose concentrationcan be easily identi® ed after Fourier ® ltering (see Fig.3B). The action of the ® lter can be understood by aninspection of Fig. 4. Figures 4A and 4B plot groups ofamplitude spectra over the range of 0.01± 0.03 f. The am-plitude spectra represent the combined magnitudes of thesine and cosine components obtained by applying theFourier transform to the selected single-beam spectra. InFigs. 4A and 4B, the optimized Gaussian ® lter frequencyresponse function used in the generation of Fig. 3B isplotted as a dashed line superimposed on the amplitudespectra. The area of each amplitude spectrum underneaththe Gaussian is passed by the ® lter to an extent that isweighted by the Gaussian shape, while the area outsidethe Gaussian (i.e., approximately 0± 0.01 and 0.03± 0.5 f)is completely suppressed.

Figure 4A plots two groups of seven amplitude spectracorresponding to 17.98 (solid line) and 5.80 (dotted line)mM glucose collected at 32, 33, 35, 36, 37, 39, and 418 C. All spectra were acquired during the same data col-lection session, thus ensuring that the overall single-beamspectral intensities were consistent. This ® gure illustratesthat the ® lter bandpass identi® es a region of the ampli-tude spectrum in which the variation due to a change inglucose concentration exceeds that due to changes in tem-perature. Outside the ® lter bandpass, little variation isnoted due to the change in glucose concentration (i.e., thesolid and dotted lines are virtually superimposed).

Figure 4B provides further illustration that the ® lterisolates information related to a change in glucose con-

centration. Amplitude spectra are plotted correspondingto 19.19 (solid line), 15.03 (dotted line), 11.39 (dash-dotline), and 3.09 (dashed line) mM glucose collected at 378 C. All spectra were acquired during the same data col-lection session, again ensuring that the single-beam spec-tral intensities were consistent. An inspection of Fig. 4Bcon® rms that the region of the amplitude spectra isolatedby the ® lter is optimal in terms of extracting informationthat relates to variation in glucose concentration. Theplots in Figs. 3 and 4 demonstrate that even though thedominant sources of variation in the single-beam spectraare related to the spectrometer characteristics and the ab-sorbance of the sample matrix, analyte-dependent infor-mation can be isolated directly without the use of a back-ground spectral measurement.

Results of PLS calibration models based on Fourier® ltered spectra are summarized in Table II for the samefour spectral ranges examined before. Inspection of cal-ibration and prediction errors reveals signi® cant improve-ment for all spectral ranges relative to models based onun® ltered single-beam spectra. Models based on ® lteredspectra produce lower errors with fewer factors. The needfor fewer factors suggests the presence of less spectralvariation in the ® ltered spectra, which is consistent withthe removal of temperature-dependent spectral variationsand with the data in Fig. 4A. The true effectiveness ofthe Fourier ® ltering step is illustrated in Fig. 2A, whereprediction errors are plotted as a function of sample tem-perature. No temperature-dependent bias is apparent inresults based on Fourier-® ltered single-beam spectra. Theoptimal ® lter parameters are also provided in Table II foreach of the spectral ranges. The parameters for the ® lterposition and width are similar regardless of spectralrange. These values are also similar to those obtainedwith absorbance spectra.

Glucose Measurements with Variable Protein. Proteinis a major component of most biological ¯ uids and canrepresent a signi® cant interference for glucose measure-ments because of strong near-IR absorption features andhigh concentrations. PLS regression can selectively discrim-


FIG. 4. Amplitude spectra are plotted over the digital frequency range of 0.01± 0.03 f. The dashed line superimposed on the amplitude spectra isa Gaussian ® lter frequency response function characterized by position and width parameters of 0.02 and 0.002 f, respectively. (A) Two groups ofseven amplitude spectra are plotted corresponding to 17.98 (solid line) and 5.80 (dotted line) mM. The spectra in each group were collected at 32,33, 35, 36, 37, 39, and 41 8 C. (B) Amplitude spectra are plotted corresponding to 19.19 (solid line), 15.03 (dotted line), 11.39 (dash-dot line), and3.09 (dashed line) mM. All spectra were collected at 37 8 C.

TABLE III. Glucose calibration models with variable protein.

Spec-tra

typea

Spectral range(cm-1)

Meanposition

(f)b

Standarddevia-

tion (f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4850± 4220 N/F0.0140

N/F0.0225

N/F0.0010

N/F0.0055

10676

0.310.360.300.35

0.490.190.240.16

2.842.924.313.28

SSAA

4811± 4457 N/F0.0170

N/F0.0190

N/F0.0020

N/F0.0025

678

10

0.520.350.410.35

0.420.190.440.17

6.412.427.002.84

SSAA

4457± 4354 N/F0.0140

N/F0.0185

N/F0.0010

N/F0.0015

6745

0.500.350.540.36

0.520.170.340.17

10.902.355.042.54

SSAA

4354± 4227 N/F0.0170

N/F0.0175

N/F0.0010

N/F0.0010

7799

0.590.350.420.37

0.510.190.510.21

9.262.576.663.43


inate glucose and protein from absorbance spectra comput-ed with a protein-free background spectrum.6 The ability tomeasure glucose selectively from single-beam spectra isdemonstrated below. Our protein data set (listed as data setB in Table I) contains spectra collected from solutions con-sisting of bovine serum albumin (BSA) and glucose dis-solved in a 0.1 M/pH 7.2 phosphate buffer. A total of 100

standard solutions were prepared with 10 levels of BSAvarying from 47.5 to 90.25 g/L and 10 levels of glucoseranging from 1 to 20 mM. An additional 10 glucose solu-tions were prepared without protein. As was done withmodels based on absorbance spectra,6 all spectra associatedwith 0.0, 52.5, and 85.5 g/L BSA were set aside and werenot part of either the calibration, monitoring, or predictiondata sets. As such, 233 spectra from 80 standard solutionswere divided into the different data sets. Speci® cally, 186spectra from 64 standards were used in the calibration setwith the remaining 47 spectra from 16 samples in the pre-diction set. For the Fourier ® lter optimization process, thecalibration set was reduced further by placing 46 spectrafrom 16 samples into the monitoring set. All these data setswere the same as those described before for models basedon absorbance spectra.6

Results are summarized in Table III for all models gen-erated from single-beam spectra of protein-containing so-lutions. For models computed without Fourier ® ltering, theindicated number of factors corresponds to the optimal val-ues as judged by the minimum SEP. For models that em-ployed Fourier ® ltering, ® ve factors were used to determinethe optimal values for the ® lter position and width param-eters, after which the number of factors giving the lowestSEP was established. The tested spectral ranges match thosedescribed above for the measurement of glucose in buffer.These ranges are similar to those reported for the corre-sponding models based on absorbance spectra,6 but they do


FIG. 5. Concentration correlation plots for glucose predictions with protein levels of 0.0 g/L (solid square), 47.5 g/L (circle), 52.25 g/L (soliddiamond), 57.0 g/L (square), 61.75 g/L (diamond), 66.5 g/L (dotted circle), 76.0 g/L (dotted square), 80.75 g/L (dotted diamond), 85.5 g/L (solidup angle), and 90.25 g/L (solid circle). The inset shows SEP values as a function of protein level. All results correspond to the 4457± 4354-cm2 1

spectral range with Fourier-® ltered single-beam spectra (see Table II for further details).

not match exactly. For comparison purposes, new modelswere computed by using these same spectral ranges withboth raw and Fourier-® ltered absorbance spectra, and theresults are included in the table. Models based on un® lteredsingle-beam spectra compare favorably with those gener-ated with un® ltered absorbance spectra. In both cases, thelowest prediction errors are obtained with the widest spec-tral range, which incorporates all three glucose absorptionbands and both protein absorption bands. More factors arerequired for the single-beam model to achieve equivalentprediction performance. Fewer factors are needed and in-ferior performance is indicated for both spectral types withthe narrower spectral ranges. Similar model performanceand optimal ® lter parameters are also obtained with Fourier-® ltered single-beam and absorbance spectra. Prediction er-rors are approximately 0.2 mM regardless of spectral typeor spectral range. This insensitivity to spectral range forFourier-® ltered spectra is consistent with our earlier ® nd-ings. In addition, optimal values for the ® lter parametersare essentially the same for both spectral types over allspectral ranges tested. The optimal ® lter position and widthvalues are on the order of 0.02 and 0.002 f, respectively.

As noted before,6 the prediction errors in Table III maybe overly optimistic, because all the protein levels in theprediction data set are represented exactly in the calibra-

tion set. A more rigorous evaluation was performed byjudging the ability of these models to predict glucoselevels from spectra where the BSA levels were 0.0, 52.25,and 85.5 g/L. The resulting predictions are presented asconcentration correlation plots in Fig. 5. Glucose predic-tions are coded according to protein level. No differencein prediction error is evident when comparing values for52.25 and 85.5 g/L BSA to any other protein level. Theinset shows SEP values for glucose prediction at the var-ious BSA levels tested. Again, no signi® cant differencesare apparent with any of the BSA levels used. Predictionerrors are signi® cantly larger, however, when the BSAlevel is 0.0. Predictions in this latter case require an ex-trapolation outside the boundaries of the calibration mod-el, which result in the offset shown in Fig. 5.

Glucose Measurements with Variable Triacetin. Tri-glycerides are a class of biological compounds that presenta major challenge for the near-IR measurement of glucosebecause of their relatively high concentrations in biologicalmatrices and the existence of a strong near-IR absorptionband at 4450 cm2 1. This absorption band signi® cantly over-laps with the key glucose absorption band centered at 4400cm2 1. Triacetin has been used as a model triglyceride todemonstrate the accuracy of PLS models for glucose withabsorbance spectra.6 This same set of spectra is evaluated


TABLE IV. Glucose calibration models with variable triacetin .

Spec-tral

typea

Spectra range(cm-1)

Meanposition

(f)b

Standarddevia-

tion (f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4850± 4220 N/F0.0315

N/F0.0215

N/F0.0055

N/F0.003

6559

0.550.410.680.42

0.540.510.560.50

4.996.015.495.77

SSAA

4811± 4457 N/F0.0265

N/F0.0200

N/F0.003N/F

0.0015

97

1210

0.550.440.460.43

0.880.550.980.50

9.466.68

11.716.25

SSAA

4457± 4354 N/F0.0205

N/F0.0195

N/F0.0005

N/F0.0015

7757

0.470.420.530.45

0.580.510.680.50

6.445.876.835.26

SSAA

4354± 4227 N/F0.026N/F

0.016

N/F0.0005

N/F0.0050

105

129

0.570.480.460.46

0.880.550.700.61

10.627.319.036.83


TABLE V. Glucose calibration models in glucose/glutamine bi-nary mixtures.

Spec-tra

typea

Spectra range(cm-1)

Meanposition

(f)b

Standarddevia-

tion (f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4800± 4250 N/F0.025N/F

0.025

N/F0.004N/F

0.004

10675

0.650.690.570.64

0.500.470.430.36

3.193.212.481.89

SSAA

4800± 4470 N/F0.02N/F0.02

N/F0.003N/F

0.003

7666

1.010.760.880.66

0.910.470.480.42

5.003.282.913.50

SSAA

4470± 4250 N/F0.025N/F

0.023

N/F0.004N/F

0.003

7866

0.740.700.640.65

0.500.480.410.38

3.463.022.212.14

SSAA

4350± 4250 N/F0.030N/F

0.025

N/F0.004N/F

0.004

8756

0.770.710.910.72

0.960.520.550.62

7.023.184.023.71


TABLE VI. Glutamine calibration models in glucose/glutaminebinary mixtures.

Spec-tra

typea

Spectra range(cm-1)

Meanposition

(f)b

Standarddevia-

tion (f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4800± 4250 N/F0.045N/F

0.024

N/F0.0013

N/F0.005

13687

0.430.680.700.87

0.830.970.860.88

6.807.567.607.95

SSAA

4700± 4450 N/F0.045N/F

0.018

N/F0.0013

N/F0.004

9564

0.550.700.780.93

0.911.031.010.90

7.777.698.716.73

SSAA

4650± 4320 N/Fb

0.045N/F

0.019

N/Fb

0.0013N/F

0.004

10685

0.590.690.610.87

0.870.970.960.86

6.957.039.908.86

SSAA

4450± 4320 N/F0.005N/F

0.019

N/F0.0013

N/F0.005

8677

0.680.740.740.86

1.101.031.061.18

8.737.23

13.3813.12


here to assess models based on single-beam spectra. Ourtriacetin data set is composed of 253 single-beam spectragenerated from 86 standard solutions. Within this data set,triacetin values range from 7.17 to 17.02 mM and glucoselevels range from 1 to 20 mM. The calibration set contained208 spectra from 71 solutions, and the prediction set con-tained 45 spectra from 15 solutions. For ® lter optimization,the calibration set was reduced to 157 spectra (53 solutions)after 51 spectra (18 solutions) were transfered to the mon-itoring set. Six PLS factors were used to identify the bestFourier ® lter parameters. Comparisons between modelsbased on single-beam and absorbance spectra reveal essen-tially the same results as noted above for measurements ofglucose in buffer with variable temperature and glucose inbuffer with variable levels of BSA. Optimization results andmodel performance are summarized in Table IV for thisvariable triacetin data set. Again, prediction errors are es-sentially the same for all spectral ranges regardless of thespectral type. With this data set, slightly fewer PLS factorswere needed for the single-beam models. Fourier ® lteringof either single-beam or absorbance spectra results in mod-els with lower prediction errors and less sensitivity to spec-tral range. Prediction errors for all spectral ranges are eitherequivalent or slightly lower for models based on ® lteredsingle-beam spectra compared with ® ltered absorbancespectra. Errors in glucose prediction are essentially constantacross all levels of triacetin, which indicates no predictionbias caused by variations in the levels of this triglyceride.

Measurement of Glucose and Glutamine in BinaryMixtures. As a ® rst step toward developing near-IRspectroscopic methods for monitoring bioreactors non-invasively, we have established the ability to measureboth glucose and glutamine in a set of binary mixtures.Accurate measurements were demonstrated for each an-alyte from individual PLS models generated from bothraw and Fourier-® ltered absorbance spectra.8 The corre-sponding models based on single-beam spectra are eval-uated here. The glucose/glutamine data set is composedof 209 spectra collected from 70 standard solutions. Glu-cose and glutamine concentrations were selected random-ly for each solution, and, as noted before, no correlationexists between these concentrations across the entire data

set.8 Glucose and glutamine values ranged from 1.10 to58.91 and 1.41 to 30.65 mM, respectively. Distributionof the spectra into calibration, prediction, and monitoringsets is described elsewhere.8 Results are summarized inTables V and VI for glucose and glutamine models basedon raw and Fourier-® ltered spectra. The spectral rangesused for these models incorporate different combinationsof absorbance bands for glucose and glutamine, respec-tively. Comparison of values in Table V for glucose mod-els based on un® ltered spectra reveals a trend where ab-sorbance spectra typically outperform single-beam spec-tra. This trend is not as clear when comparing SEP valuesfor glutamine models based on un® ltered spectra (TableVI). Glutamine models based on single-beam spectra ac-tually possess lower prediction errors for several of thetested spectral ranges. For models based on ® ltered spec-tra, however, prediction errors are slightly higher for bothglucose and glutamine when models are constructed fromsingle-beam spectra as opposed to absorbance spectra.


TABLE VII. Asparagine calibration models in asparagine/gluta-mine binary mixtures.

Spec-tra

typea

Spectra range(cm-1)

Meanposition

(f)b

Standarddevia-tion(f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4800± 4250 N/F0.025N/F0.02

N/F0.004N/F

0.005

129

1210

0.110.150.110.14

0.140.140.200.18

2.112.363.482.50

SSAA

4700± 4450 N/F0.02N/F

0.018

N/F0.001N/F

0.002

9574

0.930.171.110.19

1.230.191.320.22

18.823.29

20.003.42

SSAA

4650± 4320 N/F0.02N/F0.02

N/F0.001N/F

0.002

97

108

0.180.170.140.18

0.180.180.220.24

2.802.942.903.92

SSAA

4450± 4320 N/F0.02N/F

0.018

N/F0.001N/F

0.001

8679

0.290.210.330.22

0.400.220.390.27

6.263.694.933.84


TABLE VIII. Glutamine calibration models in asparagine/gluta-mine binary mixtures.

Spec-tra

typea

Spectra range(cm-1)

Meanposition

(f)b

Standarddevia-

tion (f)b

PLSfac-tors

SEC(mM)

SEP(mM)

MPEP(%)

SSAA

4800± 4250 N/F0.035N/F0.02

N/F0.008N/F

0.003

11998

0.090.110.120.13

0.080.090.100.10

1.712.392.192.25

SSAA

4700± 4450 N/F0.02N/F0.02

N/F0.003N/F

0.002

9798

0.890.150.700.16

1.140.121.270.12

22.893.22

31.582.49

SSAA

4650± 4320 N/F0.03N/F0.02

N/F0.005N/F

0.003

10988

0.110.120.150.13

0.090.090.120.10

1.791.812.422.00

SSAA

4450± 4320 N/F0.02N/F

0.018

N/F0.001N/F

0.002

7766

0.180.130.210.15

0.220.100.220.12

4.462.274.832.51


This trend is evident from the tabulated SEP values.Mean differences in SEP values from ® ltered spectra (sin-gle-beam minus absorbance) across all tested spectralranges were 0.13 and 0.12 mM for glucose and glutaminemodels, respectively. Again, ® ltered spectra (single-beamand absorbance) yield superior model performance withless sensitivity to spectral range.

Measurement of Glutamine and Asparagine in Bi-nary Mixtures. The last sample matrix tested correspondsto our recent effort to evaluate the selectivity of near-IRspectroscopy by attempting to differentiate glutamine andasparagine in aqueous solutions. These amino acids differby only one methylene unit, which results in only minorspectral differences in the combination region. An analysisof PLS models based on absorbance spectra has been pub-lished for this data set.9 This analysis demonstrates suf® -cient selectivity to resolve these structurally similar com-pounds. The glutamine/asparagine data set is composed of197 spectra collected from 66 unique standard solutions.Glutamine and asparagine concentrations were preparedrandomly in each solution. A regression analysis shows nocorrelation between the concentrations of these speciesthroughout the data set.9 Spectra associated with 16 standardsolutions (48 spectra) were selected randomly for the pre-diction set. The remaining 149 spectra from 50 solutionswere used in the calibration set. Description and perfor-mance of the best calibration models for asparagine andglutamine are listed in Tables VII and VIII, respectively.Prediction errors are essentially identical for models basedon single-beam and absorbance spectra. SEP values areconsistently lower when single-beam spectra are used, butthese differences are small. In addition, no signi® cant dif-ferences in prediction errors are indicated from models with® ltered vs. un® ltered spectra.

CONCLUSION

The results presented in this paper demonstrate that validcalibration models can be generated from single-beam

near-IR spectra. Even though the analyte signals employedin this work represented only a small fraction of the vari-ation present in the single-beam spectra, the digital ® lteringand multivariate calibration methods employed were stillable to extract the analyte-dependent information and use itto build successful calibration models. These models wereobserved to predict analyte concentrations accurately undera variety of matrix conditions. This ® nding encourages fur-ther development of near IR spectroscopic methods for non-invasive in vivo monitoring where relevant reference spectraare not possible due to mismatches between the sample andreference matrices.

ACKNOWLEDGMENT

The ® nancial support from the National Institutes of Health (Grantnumber DK 45126) is acknowledged.

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Spectrosc. 47, 875 (1993).4. R. E. Shaffer, G. W. Small, and M. A. Arnold, Anal. Chem. 68,

2663 (1996).5. K. H. Hazen, M. A. Arnold, and G. W. Small, Appl. Spectrosc. 48,

477 (1994).6. S. Pan, H. Chung, M. A. Arnold, and G. W. Small, Anal. Chem.

68, 1124 (1996).7. L. A. Marquardt, M. A. Arnold, and G. W. Small, Anal. Chem. 65,

3271 (1993).8. H. Chung, M. A. Arnold, M. Rhiel, and D. W. Murhammer, Appl.

Biochem. Biotech. 50, 109 (1995).9. X. Zhou, H. Chung, M. A. Arnold, M. Rhiel, and D. W. Murham-

mer, in Biosensor and Chemical Sensor Technology: Process Mon-itoring and Control, K. R. Rogers, A. Mulchandani, and W. Zhou,Eds. (ACS Symposium Series 613 (ACS, Washington, D.C., 1995),Chap. 12, pp. 116± 132.

10. H. Martens and T. Nñ s, Multivariate Calibration (Wiley, NewYork, 1989), Chap. 3.

11. G. W. Small, M. A. Arnold, and L. A. Marquardt, Anal. Chem. 65,3279 (1993).

multivariate calibration models based on the direct analysis of near-infrared single-beam spectra

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