Volume 52, Number 12, 1998 APPLIED SPECTROSCOPY 15970003-7028 / 98 / 5212-1597$2.00 / 0

q 1998 Society for Applied Spectroscopy

Measurement of Glucose in Water with First-OvertoneNear-Infrared Spectra

KEVIN H. HAZEN,* MARK A. ARNOLD,² and GARY W. SMALLDepartment of Chemistry and Optical Science and Technology Center, University of Iowa, Iowa City, Iowa 52242 (K.H.H., M.A.A.);

and Center for Intelligent Chemical Instrumentation and Department of Chemistry, Ohio University, Athens, Ohio 45701 (G.W.S.)

Partial least-squares (PLS) regression analysis was used to build

calibration models for three unique spectral data sets of glucose in

water. Spectra in the ® rst data set were collected with a 2.0 mmoptical pathlength. For these data, the measured root-mean-square

(rms) noise of 100% lines over the 5975± 5850 cm 2 1 spectral range

was 4.5 micro-absorbance units ( m AU). Spectrometer upgrades per-mitted a 5.2 mm optical pathlength for the second data set, and the

resulting spectra had an rms noise of 5.9 m AU. Further spectrom-

eter adjustments allowed the use of a 10.0 mm optical pathlengthfor the third data set, and the resulting spectral rms noise was 8.4

m AU. In each case, the instrumentation was modi® ed individually

in order to provide high radiant powers at the detector while avoid-ing detector saturation. Poor calibration models for the ® rst data

set indicate that a 2.0 mm optical pathlength is insuf® cient for ad-

equate glucose measurements at clinically relevant concentrations.Calibration and prediction errors for the data collected at 5.2 and

10.0 mm pathlengths ranged from 0.40± 0.50 and 0.35± 0.40 mM,

respectively. Digital Fourier ® ltering signi® cantly improved modelperformance by reducing the required number of latent variables

(factors) in the PLS models and by reducing the wavelength depen-

dency of these models. For the best calibration model, spectra inthe data set corresponding to a 10.0 mm pathlength were Fourier

® ltered with a Gaussian-shaped ® lter de® ned in digital frequency

units ( f ) by a mean position of 0.0206 f and a standard deviationwidth of 0.0031 f. These ® ltered spectra were then submitted to a

one-factor PLS model that is limited to the 5975± 5850 cm2 1 spectral

range. Consideration of different spectral ranges and an analysis ofspectral loading vectors indicate that the 5920 cm 2 1 absorption band

for glucose is critical for useful analytical measurements.

Index Headings: Near-infrared spectroscopy; Spectroscopic glucose

measurements; Partial least-squares regression; Digital Fourier ® l-tering.

INTRODUCTION

In pursuit of the direct noninvasive measurement ofglucose in human tissue, several studies have illustratedthe determination of clinically relevant levels of glucosein biological samples from near-infrared (near-IR) spectracollected over the combination band region (4800±4200cm 2 1).1±11 Unfortunately, the transmission of light at thesewavelengths is poor through human tissue. Scatteringprocesses and strong absorption by water and fatty tis-sue12 severely reduce the optical throughput in this re-gion. When a solid-state near-IR detector is used in con-junction with a blackbody source and Fourier transformspectrometer, the intrinsic detector noise is often the lim-iting noise source of the measurement. In this case, re-duced optical throughput causes a signi® cant increase in

Received 29 May 1998; accepted 24 August 1998.* Present address: Instrumentation Metrics, Inc., 2085 Technology Cir-

cle, Suite 201, Tempe, AZ 85284.² Author to whom correspondence should be sent.

spectral noise and renders this spectral region unaccept-able for noninvasive measurements. For this reason, the® rst-overtone region (6500 ±5500 cm 2 1) and shor terwavelengths have been proposed for noninvasive bloodglucose measurements.12±24 Absorption properties of hu-man tissue are less severe in the ® rst-overtone region;however, scattering effects are more pronounced.

The poor transmission properties of human tissue inthe combination band region motivate an evaluation ofthe ® rst-overtone region for measuring glucose at phys-iological levels in aqueous media. This report details ourability to measure clinically relevant levels of glucosefrom ® rst-overtone near-IR spectra. The effects of opticalpathlength and spectral range are established for a seriesof multivariate calibration models computed through theapplication of partial least-squares (PLS) regression toboth raw and digitally ® ltered spectra. The relationshipbetween spectral quality and model performance is alsoevaluated for spectra collected from three different spec-trometer con® gurations.

EXPERIMENTAL

Apparatus and Reagents. Spectra were collectedwith a Nicolet 740 Fourier transform spectrometer (Nic-olet Analytical Instruments, Madison, WI) equipped forthe near-IR region by use of a calcium ¯ uoride beam-splitter and a 2 mm 2 cryogenically cooled indium anti-monide (InSb) detector. Incident light was restricted tothe range of 6579±5540 cm 2 1 (1.52±1.81 m m) by use ofa standard H-band interference ® lter (Barr Associates,Westford, MA). This ® lter transmitted 78% of the inci-dent light at 5920 cm 2 1. Different source powers, aperturesettings, and software gain settings were used for sampleswith different optical pathlengths. For the 2 mm samples,the standard 75 W tungsten±halogen lamp was replacedwith a 150 W lamp. The aperture and gain settings were125 and 1, respectively. These settings are speci® ed inthe arbitrary units selected in the Nicolet SX softwarethat controlled the spectrometer. A setting of 330 corre-sponds to the widest aperture. A 250 W lamp was usedfor the 5.2 and 10 mm samples, with the aperture andgain set at 70 and 4, respectively, for the 5.2 mm samples,and 330 and 4, respectively, for the 10 mm samples.

Samples were contained in a temperature-controlledcell mount (Wilmad, Buena, NJ) equipped with two sap-phire windows (25 mm diameter and 0.9 mm thick). Tem-peratures were maintained at 37.0 ( 6 0.1) 8 C with a VWRModel 1140 refrigerated water bath (VWR Scienti® c,Chicago, IL). Temperatures were monitored by placing acopper-constantan thermocouple (Omega, Inc., Stamford,CT) directly in the sample solution within the sample

1598 Volume 52, Number 12, 1998

TABLE I. Speci ® cations for glucose data sets.

2.0 mmpathlength

5.2 mmpathlength

10.0 mmpathlength

Number of samplesNumber of spectraMean glucose conc. (mM)Standard deviation of glucose

conc. (mM)Glucose conc. range (mM)

6720012.73

7.251.35±24.9

6318513.69

7.632.13±28.6

7321913.15

7.691.19±28.1

FIG. 1. Absorbance spectra for water (broken line) and glucose so-lutions (solid lines) with the indicated concentrations.

holder. An Omega 670 digital meter was used to readsolution temperatures.

All glucose solutions were prepared by dissolvingdried reagent-grade glucose in a pH 7.4 working buffer.This buffer was composed of 0.1 M phosphate and 0.483g/L 5-¯ uorouracil (preservative). Buffer solutions wereprepared with type I reagent-grade water obtained froma three-stage Milli-Q water puri® cation unit (Millipore,Inc., Bedford, MA). Actual glucose concentrations weredetermined by using a YSI 2300 STAT Plus analyzer(Yellow Springs Instruments, Inc., Yellow Springs, OH).

Procedures. Double-sided interferograms consistingof 16 384 points were collected on the basis of 256 coad-ded scans. These interferograms were triangularly apo-dized and Fourier transformed to produce single-beamspectra with a point spacing of 1.9 cm 2 1. This high levelof resolution was used to remain consistent with our ear-lier work in the combination region. Mertz phase correc-tion was applied with a phase array based on 200 pointson each side of the interferogram center burst. The re-sulting single-beam spectra were transferred to a SiliconGraphics Indigo workstation (Silicon Graphics, MountainView, CA) for further processing. The spectral processingsoftware used on the Silicon Graphics system was im-plemented in FORTRAN 77. Subroutines used in imple-menting the digital ® ltering and multiple linear regressioncalculations were taken from the IMSL software package(IMSL, Inc., Houston, TX).

For each pathlength, spectra were collected during asingle data collection session. Spectra were collected ina random order with respect to glucose concentration. Allspectra were collected in triplicate without removing thesample from the spectrometer. Three background spectraof glucose-free buffer were collected after every thirdsample. Table I summarizes the number of samples andthe corresponding number of spectra for each data set.One spectrum in the 2 mm data set and four spectra inthe 5.2 mm data set were inadvertently lost while beingtransferred to the Indigo workstation. Table I also pro-vides the mean, standard deviation, and range of glucoseconcentrations in each of these data sets. For the 2.0 mmdata set, all spectra corresponding to 10 and 9 randomlyselected samples were placed in the monitoring and pre-diction data sets, respectively. For the 5.2 mm data, allspectra for nine randomly selected samples were placedin the monitoring data set and a second group of spectracorresponding to another set of nine samples was placedin the prediction data set. For the 10.0 mm data, the mon-itoring and prediction data sets corresponded to all spec-tra associated with two unique groups of 10 randomlyselected samples.

Calibration models were developed with spectra in ab-

sorbance units by use of the same procedures describedin previous work.4,7,9 The spectra in absorbance unitswere computed by dividing each single-beam spectrumby the immediately preceding background spectrum andthen converting the resulting transmittance values to ab-sorbance. When necessary, Fourier ® ltering was imple-mented by subjecting the entire spectrum (full spectralrange) to the digital Fourier ® lter algorithm and then se-lecting the required spectral range for analysis. A randomnumber generator was used to distribute the samples intoseparate calibration, monitoring, and prediction data sets.All spectra for a given sample were moved as a group,and no sample was used in more than one data set. Allspectra corresponding to nine or ten samples were placedin the monitoring and prediction data sets.

RESULTS AND DISCUSSION

Absorption Bands and Spectral Range. The relativeposition and size of the absorption bands for water andglucose are presented in Fig. 1. This water absorbancespectrum corresponds to a spectrum of a 1 mm thicksample of the working buffer referenced to an air back-ground spectrum. Although the presented spectral rangecorresponds to a window between two water absorptionbands centered at 6870 and 5200 cm 2 1, the magnitude ofthe water absorbance is considerably greater than that forglucose. The glucose absorbance spectra were computedby use of a background spectrum of the working bufferand are presented for a series of glucose standards withan optical pathlength of 10 mm. These spectra reveal ab-sorption features centered at 6200, 5920, and 5775 cm 2 1.The relatively strong absorbance from water overshadowsthe broad and poorly distinguished bands centered at6200 and 5775 cm 2 1. These ® ndings corroborate earlierwork to identify glucose in concentrated dry mixtures andfruit juice samples.25,26

An important parameter used in computing a multi-variate calibration model is the spectral range supplied tothe model building method. When latent variable meth-ods such as PLS regression are employed to build cali-bration models, the spectral range dictates which spectralpoints are used in the computation of the latent variables.The spectral range should include information describingthe concentration variation of the analyte and other ma-

APPLIED SPECTROSCOPY 1599

FIG. 2. Representative 100% line for overtone spectra (solid line)computed from two water spectra collected sequentially. A water ab-sorbance spectrum (broken line) is superimposed for comparison. Thepathlength for the 100% line spectra was 10 mm and the pathlength forthe water absorbance spectrum was 1 mm.

TABLE II. Noise and PLS model parameters for the three spectral data sets.

Rangea

2.0 mm pathlength

N/bb Factc SECd SEPe

5.2 mm pathlength

N/bb Factc SECd SEPe

10.0 mm pathlength

N/bb Factc SECd SEPe

6579±55406300±57006300±59755975±58505850±5700

12027.38.652.252.71

2113977

1.491.285.211.815.85

2.601.024.661.685.77

2653.212.271.182.08

21121175

0.920.321.460.553.29

1.560.722.440.552.66

3165.003.490.842.97

121894

11

3.130.132.950.432.88

4.000.443.580.423.71

a Spectra range (cm 2 1).b Average rms noise computed across 100% lines divided by sample thickness ( m AU/mm).c Optimum number of PLS factors.d Standard error of calibration (mM).e Standard error of prediction (mM).

trix constituents while excluding regions dominated bynoise or other artifacts that might become incorporatedinto the model on the basis of chance correlations. Suit-able spectral ranges can be identi® ed by either a statis-tically driven optimization scheme, such as a modi® edgrid search or a genetic algorithm,27±32 or an arbitraryselection on the basis of known absorption properties forthe analyte of interest. The second method was used here,given the simplicity of the sample matrix and the well-de® ned spectral features for glucose.

The following spectral ranges were examined for theglucose models: 6579±5540, 6300±5700, 6300±5975,5975±5850, and 5850±5700 cm 2 1. This ® rst range cor-responds to the 50% transmission frequencies of the in-cident radiation and, therefore, essentially represents thewhole spectral range. The second range includes all threeglucose absorption bands but trims the high noise andlimited glucose information at the higher and lower fre-quency extremes. The last three ranges isolate each of thethree glucose absorption features (see Fig. 1).

Spectral quality ultimately limits the analytical utilityof absorption spectroscopy since the spectral signal-to-noise ratio (SNR) dictates the limit of detection. Spectralquality can be conveniently presented as the root-mean-square (rms) noise on 100% lines. In this work rms noiselevels were measured for 20 different buffer spectra col-lected with each spectrometer con® guration. The 100%lines were generated by dividing the second and third

replicate spectra for each sample and converting to ab-sorbance units. Ideally, replicate spectra are identical,which would create 100% lines that are horizontal and¯ at at zero absorbance.

A typical 100% line is presented in Fig. 2 along withan absorbance spectrum of water. For near-IR spectrathrough aqueous samples, the SNR is not constant acrossthe spectrum, but depends on the frequency of the radi-ation. This frequency dependency is illustrated in Fig. 2,where considerably greater noise is evident at both thehigh and low frequency extremes (i.e., greater than 6375cm 2 1 and less than 5700 cm 2 1). The absorption charac-teristics of water are responsible for the frequency de-pendency. A water absorbance spectrum is superimposedon the 100% line in Fig. 2 to show how the spectral noisecorrelates with water absorption. Under our spectrometerconditions, the spectral measurements are detector-noiselimited, which means the noise is constant across thespectrum. The SNR of the measurement, however, de-pends on the optical throughput.33 Higher radiant powersat the detector produce larger signals, thereby providinggreater SNRs and superior spectral quality. Conversely,limited optical throughput results in low radiant powers,poor SNRs, and higher spectral noise. Of course, the op-tical throughput is lower at radiant frequencies stronglyabsorbed by water and, as a result, the SNR is poor atthese frequencies. Finally, computed rms noise on 100%lines depends on the speci® c spectral region selected.

Actual 100% lines are not typically horizontal but ap-pear slightly curved. This curvature is caused by slightdifferences in the spectral collection conditions betweenreplicates. This difference is frequency dependent andtypically corresponds to slight differences in sample tem-perature. In addition, 100% lines can be offset from zerobecause of frequency-independent differences in data col-lection parameters. A difference in instrument alignmentbetween replicates is a possible example.

Root-mean-square noise levels can be computed abouta quadratic least-squares regression curve for a de® nedregion of the 100% line. The second-order ® t accountsfor the curvature within this spectral region, thereby pro-viding a better estimate of spectral noise. Table II listsnormalized noise values computed by dividing the meanrms noise computed across the 20 buffer samples by thesample thickness ( m AU/mm). These noise values are nor-malized in this manner simply to facilitate direct com-parison between instrument con® gurations. For each dataset, the spectral noise is lowest for the 5975±5850 cm 2 1

1600 Volume 52, Number 12, 1998

FIG. 3. Plot of standard errors of calibration and prediction vs. the number of PLS factors (A) and spectral loading plots for the ® rst (B), second(C ), third (D ), and fourth (E ) PLS factors for the 5975±5850 cm 2 1 PLS model.

spectral range, which corresponds to the region withgreatest optical throughput (lowest water absorbance, seeFig. 2). Noise levels are larger for all other spectral rang-es as the optical throughput drops because of water ab-sorption of light. It is dif® cult to compare noise levelsacross data sets. Such a comparison is complicated be-cause different spectrometer con® gurations were used foreach data set in order to minimize noise in the 5975±5850 cm 2 1 region. In addition, transmission spectra ofwater are not linearly related to optical pathlength, whichresults in nonlinear dependencies in spectral quality. Ex-perimentally, the lowest overall normalized noise corre-sponds to the 10 mm pathlength data with the 5975±5850cm 2 1 spectral range. For all other spectral ranges, thelowest normalized noises correspond to the 5.2 mm dataset.

Partial Least-Squares Calibration Models. A seriesof PLS calibration models were computed for each dataset by stepping the number of PLS factors from 1 to 30for each of the ® ve spectral ranges. The optimal numberof PLS factors was determined as that which produced aminimum standard error of prediction (SEP). Perfor-mance parameters for the best calibration models are tab-ulated in Table II.

Within each data set, the best analytical performancecomes from models restricted to the 5975±5850 cm 2 1

spectral range. This range encompasses the 5920 cm 2 1

glucose band and possesses the lowest spectral noise.Similar performance is noted for the 6300±5700 cm 2 1

spectral range, which incorporates both the 5920 and5775 cm 2 1 glucose bands. In fact, the lowest predictionerrors for the 2.0 mm data set come from this wider spec-tral range. It must be noted, however, that the 6300±5700cm 2 1 model requires nearly double the number of latentvariables to achieve this performance. In fact, all modelscomputed over the 6300±5700 cm 2 1 spectral range re-

quire more latent variables relative to the corresponding5975±5850 cm 2 1 models. More complex models are nec-essary to accommodate greater spectral variation andhigher spectral noise in this wider range.

Poor models result from the remaining three spectralregions where noise levels are too high to allow glucoseinformation to be extracted reliably. Although the widestspectral range (6579±5540 cm 2 1 incorporates all threeglucose absorption bands, the large noise levels at boththe high and low frequency extremes greatly degrade theability to retrieve this glucose information. Similarly, therelatively high noise levels of the other restricted spectralregions (6300±5975 and 5850±5700 cm 2 1) coupled withthe poor quality of the corresponding glucose absorptionbands severely limits calibration performance.

Comparison across data sets reveals that models cor-responding to the 5.2 and 10.0 mm data sets signi® cantlyoutperform models from the 2.0 mm data set. In fact,prediction errors are unacceptably high for all calibrationmodels generated with the data collected with a 2.0 mmpathlength. Even though the overall spectral noise is be-low 5 m AU across the 5975±5850 cm 2 1 spectral region,prediction errors are greater than 1.6 mM when the sam-ple thickness is only 2.0 mm. In this case, even with alow noise level, there is simply not suf® cient glucoseabsorbance to allow a viable calibration model to be con-structed. Longer pathlengths and lower noise result insuperior model predictions for the 5.2 and 10.0 mm datasets.

The best calibration model uses only four factors toprovide a measurement error of 0.4 mM. This model cor-responds to the 5975±5850 cm 2 1 spectral range with a10.0 mm optical pathlength. A plot of measurement erroras a function of model size (for the ® rst 10 factors) isprovided in Fig. 3 along with a series of plots showingthe spectral loadings for each factor of the optimum four-

APPLIED SPECTROSCOPY 1601

factor model. The large errors noted in Fig. 3A for the® rst model factor indicate that this factor incorporateslittle glucose-speci® c information. Inspection of the spec-tral loading plot for this ® rst factor (Fig. 3B) con® rmsthe lack of glucose information in the factor. Lower mea-surement errors are obtained with the second, third, andfourth factors, which suggest the presence of glucose-speci® c information in these factors. Indeed, spectralloading plots for these latent variables (Figs. 3C, 3D, and3E) reveal signi® cant contributions of the spectral infor-mation corresponding to the glucose band centered at5920 cm 2 1. In fact, the magnitude of the glucose bandappears largest for the fourth factor, and this factor pro-vides the greatest drop in measurement error. This strongcorrelation between the model performance and the ap-pearance of glucose spectral features within individualmodel factors is direct evidence that the PLS algorithmis modeling glucose.

Similar glucose absorption features are evident inspectral loading plots for the other spectral ranges. Gen-erally, glucose features are most evident in loadings as-sociated with large decreases in measurement error. Theability to distinguish analyte spectral features in theseloading plots diminishes as the spectral noise increasesand other nonanalyte-dependent spectral variations dom-inate the spectra.

Fourier Filtering. Digital Fourier ® ltering is an ef-fective preprocessing tool for enhancing spectral signal-to-noise by reducing both high- and low-frequency noisewithin near-IR spectra.4,7±10 This preprocessing method isparticularly effective at reducing the impact of baselinevariations, such as those induced by temperature differ-ences between the sample and background spectra. 7 Forthis reason, we have evaluated Fourier ® ltering as ameans to enhance the PLS calibration models for glucosecomputed from overtone spectra.

As in previous work, a Gaussian-shaped frequency re-sponse function was used to ® lter the Fourier transformedspectra.4,7±10 The position and width of this ® lter corre-spond to the mean and standard deviation of the Gaussianfunction positioned along a digital frequency ( f ) axis thatlinearly spans values from 0 to 0.5 f . As detailed before,a grid search method was used here to identify the opti-mum combination of mean position and standard devia-tion width.4,7±9 In this work, spectra collected with a givenoptical pathlength were separated into three data sets. Forcomparison purposes, the calibration and prediction datasets were identical to those used above for processing rawspectra. The remaining spectra were placed into a mon-itoring data set that was used to establish the optimumcombination of position and width for the ® lter frequencyresponse function.

Optimum ® lter parameters were established by as-sessing all combinations of 80 possible mean positionsand 50 possible standard deviation widths. Tested meanvalues ranged from 0 to 0.048 f with 0.0006 f step sizesand tested standard deviations ranged from 0 to 0.025 fwith 0.0005 f step sizes. For each combination of meanand standard deviation, PLS models were generated withthe correspondingly Fourier ® ltered spectra in the cali-bration data set. For each combination of mean and stan-dard deviation, PLS models were constructed with 1 to20 factors. Once computed, each model was used to pre-

dict the glucose concentrations corresponding to the spec-tra in the monitoring set. Model performance was as-sessed by computing an objective function de® ned as thereciprocal of the sum of mean squared errors of the cal-ibration and monitoring data (1/[MSEC 1 MSEM],where MSEC and MSEM correspond to the mean-squared errors computed with the calibration and moni-toring spectra, respectively). Three-dimensional surfaceplots of the objective function vs. the ® lter position andwidth were constructed to identify the optimum ® lter pa-rameters (lowest combination of calibration and monitor-ing errors). PLS calibration models with 1 to 30 factorswere then generated with spectra treated by the optimizedFourier ® lter, and the ideal number of model factors cor-responded to that which gave the lowest SEP. This opti-mization procedure was repeated for each spectral rangeand optical pathlength.

Several trends became apparent while generating the400 surface plots described above. Typical surface plotsare presented in Fig. 4 that correspond to the 10 mm dataset over the 5975±5850 cm 2 1 spectral range. For thesedata, the use of a single PLS factor during ® lter optimi-zation provides a well-de® ned peak (see Fig. 4A). For agiven standard deviation, the response value increasesand then decreases as the mean position of the frequencyresponse function is scanned across this peak. With threePLS factors, a ridge begins to form where the peak meanposition increases as the standard deviation increases (seeFig. 4B). In fact, the peak mean value for a given stan-dard deviation is roughly twice that of the standard de-viation. Because 95% of the area of the Gaussian fre-quency response function lies within two standard devi-ations of the mean, such a ridge structure indicates thatvery low digital frequencies (i.e., baseline deviations) arebeing rejected for all ® lters de® ned by values riding alongthe top of this ridge. By the time ® ve PLS factors areinvolved, many combinations of mean and standard de-viation provide roughly equivalent calibration and mon-itoring errors (see Fig. 4C). Recalling that four PLS fac-tors are optimal when processing these raw, un® lteredspectra, the surface plot in Fig. 4C indicates that modelperformance is relatively insensitive to Fourier ® ltering,because this number of PLS factors can essentially modelany un® ltered spectral features (i.e., baseline variations).The use of more than ® ve factors results in large, noisy,poorly de® ned surface plots characteristic of over-mod-eling.

Surface plots for other spectral ranges are similar tothose described above. Generally, a sharp peak is foundwith few factors, a ridge forms with an intermediate num-ber of factors, and a noisy plateau forms when the num-ber of factors used in the optimization matches the op-timum number found with raw un® ltered spectra. In gen-eral, more factors are needed to achieve optimal perfor-mance as the spectral range is widened and more noiseis incorporated into these models. For the 5975±5850,6579±5540, and 6300±5700 cm 2 1 spectral ranges, 5, 13,and 19 factors are required to produce the noisy plateaustructures typi® ed in Fig. 4C.

Optimum values for the mean position and standarddeviation width are similar for all ® ve spectral ranges.These values are summarized in Table III for the 10.0mm pathlength data. In addition, these values are similar

1602 Volume 52, Number 12, 1998

FIG. 4. Surface plots for optimizing Fourier ® lter parameters for the 5975±5850 cm 2 1 spectral region when using one (A), three (B), and ® ve(C ) PLS factors.

TABLE III. Optimum Gaussian ® lter parameters for the 10.0 mmdata set.

Spectral range(cm 2 1)

Mean position( f)

Standard deviationwidth ( f)

6579±55406300±57006300±59755975±58505850±5700

0.02040.02580.01980.02060.0186

0.00350.00550.00250.00310.0020

to those found optimal for reducing noise and baselinevariations in near-IR spectra collected over the combi-nation band region (4800±4200 cm 2 1).1,4±10 As noted be-fore, this type of Fourier ® ltering is relatively insensitiveto the shape of these near-IR absorption bands for speci® cchemical species.4

PLS calibration models from Fourier ® ltered spectrawere computed for each optical pathlength and each spec-tral range. In all cases, the optimum Fourier ® lter param-eters were used, and the number of model factors wasstepped from 1 to 30. Results from PLS models providingthe lowest SEP for each optical pathlength are tabulatedin Table IV.

The effectiveness of Fourier ® ltering as a preprocess-ing step is demonstrated by comparing performance fromPLS models built with ® ltered and un® ltered spectra.Comparison of results in Tables II and Table IV revealsthat calibration and prediction errors are generally lowerand/or fewer factors are typically required for models

from ® ltered spectra. Furthermore, calibration and pre-diction errors are consistent for all spectral ranges forboth the 5.2 and 10.0 mm pathlength data sets. Consis-tency across spectral ranges is not observed with the un-® ltered data. The Fourier ® ltering step reduces spectralnoise across the entire spectrum, thereby rendering theanalysis less sensitive to spectral range. In general, mea-surement errors are approximately 1±2 mM for the 2 mmpathlength data, 0.4±0.5 mM for the 5.2 mm pathlengthdata, and 0.35±0.40 mM for the 10.0 mm pathlength data.

The effectiveness of Fourier ® ltering is further evidentby comparing spectra before and after being passedthrough this digital ® lter. The spectra presented in Fig.5A correspond to a representative series of raw absor-bance spectra in the 10 mm data set. Although the glu-cose features can be distinguished in some of these spec-tra, baseline curvature and offsets make visual quanti® -cation dif® cult. The spectra in Fig. 5B are obtained afterpassing the raw absorbance spectra through a Fourier ® l-ter. For this ® lter, the mean position and standard devia-tion width are 0.0206 and 0.0031 f , respectively, whichmatch the optimal values found for the 5975±5850 cm 2 1

spectral region. The impact of Fourier ® ltering is striking,with a clearly distinguishable feature corresponding tothe 5920 cm 2 1 glucose absorption band. As Fourier ® l-tered spectra resemble derivative spectra, the zero cross-ings at 5885 and 5940 cm 2 1 represent in¯ ection pointsalong the glucose absorption band, and the minima at5865 and 5965 cm 2 1 correspond to the base of this glu-

APPLIED SPECTROSCOPY 1603

TABLE IV. PLS model parameters for Fourier ® ltered spectra.

Rangea

2.0 mm pathlength

Factb SECc SEPd

5.2 mm pathlength

Factb SECc SEPd

10.0 mm pathlength

Factb SECc SEPd

6579±55406300±57006300±59755975±58505850±5700

232118117

1.231.471.372.062.37

1.030.811.551.691.96

11111465

0.530.400.550.550.77

0.410.410.440.520.56

149

101

10

0.380.350.350.460.40

0.390.340.380.400.40

a Spectral range (cm 2 1).b Optimum number of PLS factors.c Standard error of calibration (mM).d Standard error of prediction (mM).

FIG. 6. Concentration correlation plot for the 5975±5850 cm 2 1 modelwith one PLS factor and a Fourier ® lter with a frequency responsefunction speci® ed by a mean position of 0.0206 f and standard devia-tion width of 0.0031 f . Symbols indicate calibration (V), monitoring(n), and prediction (c) spectra.

FIG. 5. Raw (A) and Fourier ® ltered (B) overtone spectra for a seriesof samples with the indicated glucose concentrations. The Fourier ® lterused a mean position of 0.0206 f and standard deviation width of0.0031 f for the Gaussian frequency response function.

cose band. These points are roughly identi® able in theun® ltered spectra shown in Fig. 5A.

In general, Fourier ® ltering improves model perfor-mance by enhancing the SNR values for these spectra.The improved performance is most striking for the 10.0mm data set over the 5975±5850 cm 2 1 spectral range. Inthis case, a single PLS factor is suf® cient to measureclinically relevant levels of glucose. The concentrationcorrelation plot for this model is presented in Fig. 6. Cal-ibration, monitoring, and prediction data closely followthe ideal unity line. As expected for an SEP of 0.40, thescatter in this plot indicates a prediction capability of 61 mM.

As displayed by the solid line in Fig. 7, the ® rst, andonly, spectral loading vector for the model represented inFig. 6 resembles the spectral features of Fourier ® ltered

glucose spectra. Fourier ® ltered spectra are also plottedin Fig. 7 over the 5975±5850 cm 2 1 spectral range. Themean and standard deviation for this ® lter are the optimalvalues for the model (i.e., 0.026 and 0.0031 f , respec-tively). Filtered spectra are presented for a series of sam-ples with glucose concentrations ranging from 4.43 to28.1 mM. Clearly, this spectral loading vector is essen-tially identical to the ® ltered glucose absorption featurein this spectral range.

CONCLUSION

PLS analysis of raw overtone spectra indicates thatthe 5920 cm 2 1 glucose band is critical for useful calibra-tion models. Glucose bands centered at 6200 and 5775cm 2 1 do not provide suf® cient information owing to highspectral noise in these regions. As expected for infor-mation derived from absorbance spectra, longer opticalpathlengths and lower spectral noise yield superior pre-diction errors for spectral regions that encompass the5920 cm 2 1 glucose band.

Direct comparison between the different data sets iscomplicated by the fact that both pathlength and spectralnoise vary between these data sets. Ideally, one would

1604 Volume 52, Number 12, 1998

FIG. 7. Spectral loading vector (solid line) for the calibration modelde® ned in Fig. 6 superimposed on Fourier ® ltered glucose absorbancespectra over the 5975±5850 cm 2 1 spectral range. Glucose concentrationsfrom bottom to top at 5920 cm 2 1 are 4.43, 8.19, 12.1, 16.0, 20.4, 24.2,and 28.1 mM.

like to keep the normalized noise ( m AU/mm) constantacross the data sets in order to assess pathlength effects.Nevertheless, useful information can be extracted fromthese data in terms of the pathlength. For example, wecan say that a 2 mm optical pathlength is insuf® cient forsound glucose measurements when the spectral noise is2.25 m AU/mm or greater. Even with digital ® ltering toenhance signal-to-noise, prediction errors range from 1to 2 mM for the 2 mm pathlength data. Acceptable cal-ibration models can be achieved by increasing the opticalpathlength to 5.2 mm with a concomitant decrease inspectral noise (1.18 m AU/mm). Measurement errors dropto ; 0.4±0.5 mM. By increasing the optical pathlength to10.0 mm and lowering the spectral noise to 0.84 m AU/mm, the best analytical performance is achieved with thefewest model factors. In this case, prediction errors are0.35±0.4 mM.

These ® ndings demonstrate the critical relationshipbetween optical pathlength, spectral noise, and measure-ment error. This relationship has important implicationsfor the potential of measuring blood glucose noninva-sively from overtone spectra. Successful noninvasiveblood glucose measurements require long optical path-lengths through the medium of interest combined withlow spectral noise. It would not be possible to measuremillimolar levels of glucose with overtone spectra whenthe optical pathlength is less than 2 mm unless the spec-tral noise is signi® cantly less than 2.25 m AU/mm. Anapproach based on diffuse re¯ ectance measurementswould be challenging given the limited effective opticalpathlengths that are possible owing to small penetrationdepths of radiation at these wavelengths into skin tissue.34

Clearly, pathlength and spectral noise must be consideredwhen designing a noninvasive blood glucose system, andthese parameters must be reported when describing suchinstrumentation.

It is also important to stress that the ® ndings reportedhere were obtained under the simplest possible matrixconditions with glucose dissolved in temperature-con-trolled, nonscattering aqueous solutions. For this reason,the prediction errors reported here are certainly overly

optimistic as an indicator of analytical performance fornoninvasive blood glucose measurements. Although ouranalysis of the spectral loading vectors clearly indicatethe existence of glucose-speci® c information in the PLScalibration models, the existence of information relatedto the displacement of water by glucose cannot be ig-nored. The extent to which water displacement informa-tion is incorporated into these models will over estimateprediction abilities because such information will not beavailable from spectra collected in more complex, multi-component systems such as spectra collected noninva-sively from human subjects. Finally, the complexities as-sociated with scattering, temperature, pressure, and chem-ical interferences will further degrade performance whenthe system is extended to noninvasive human measure-ments.

ACKNOWLEDGMENTS

We wish to acknowledge Ms. Mary Pollard for her contributions inthe early phases of this project. The ® nancial support from the NationalInstitute of Diabetes and Digestive and Kidney Diseases (DK-45126) isgreatly appreciated.

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