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Influence of temperature on water and aqueous glucose absorption spectra in thenear- and mid-infrared regions at physiologically relevant temperatures

Jensen PS Bak J Andersson-Engels Stefan

Published inApplied Spectroscopy

DOI101366000370203321165179

2003

Link to publication

Citation for published version (APA)Jensen PS Bak J amp Andersson-Engels S (2003) Influence of temperature on water and aqueous glucoseabsorption spectra in the near- and mid-infrared regions at physiologically relevant temperatures AppliedSpectroscopy 57(1) 28-36 httpsdoiorg101366000370203321165179

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Download date 04 Apr 2020

28 Volume 57 Number 1 2003 APPLIED SPECTROSCOPY0003-7028 03 5701-0028$200 0q 2003 Society for Applied Spectroscopy

In uence of Temperature on Water and Aqueous GlucoseAbsorption Spectra in the Near- and Mid-Infrared Regionsat Physiologically Relevant Temperatures

PETER SNOER JENSEN JIMMY BAK and STEFAN ANDERSSON-ENGELSRisoslash Nat Lab Denmark (PSJ JB) and University of Lund Sweden (PSJ SA-E)

Near- and mid-infrared absorption spectra of pure water and aque-ous 10 gdL glucose solutions in the wavenumber range 8000ndash950cm21 were measured in the temperature range 30ndash42 8C in steps of2 8C Measurements were carried out with an FT-IR spectrometerand a variable pathlength transmission cell controlled within 0028C Pathlengths of 50 mm and 04 mm were used in the mid- andnear-infrared spectral region respectively Difference spectra wereused to determine the effect of temperature on the water spectraquantitatively These spectra were obtained by subtracting the 378C water spectrum from the spectra measured at other tempera-tures The difference spectra reveal that the effect of temperatureis highest in the vicinity of the strong absorption bands with anumber of isosbestic points with no temperature dependence andrelatively at plateaus in between On the basis of these spectraprospects for and limitations on data analysis for infrared diagnos-tic methods are discussed As an example the absorptive propertiesof glucose were studied in the same temperature range in order todetermine the effect of temperature on the spectral shape of glucoseThe change in water absorption associated with the addition of glu-cose has also been studied An estimate of these effects is given andis related to the expected level of infrared signals from glucose inhumans

Index Headings Water absorption Glucose absorption Tempera-ture dependence Transmission cell FT-IR Principal componentanalysis PCA Infrared Near-infrared

INTRODUCTION

The use of near- and mid-infrared spectroscopy for thecharacterization of compounds in biological systems islimited by the strong absorption of water The penetrationdepth is short where the water absorbs strongly For agiven wavenumber the pathlength optimizes the signal-to-noise ratio (SNR) when the water absorbance is ap-proximately 1ln 1012 The SNR decreases rapidly in re-gions of strong water absorption as the pathlength devi-ates from the optimal Therefore given a necessary depthof penetration water limits the spectral regions that maybe used for precise measurements The absorption of wa-ter also depends strongly on temperature This dependen-cy is most important in spectroscopic examinations ofbiological systems with a high water content under ex-perimental conditions where precise control of the tem-perature is unattainable For instance it is well knownthat the temperature in the extremities can be several de-grees below that of the body core3 Temperature thus in- uences current and future medical applications of near-and mid-infrared spectroscopy Two notable examples arethe work on noninvasive determination of blood glucose

Received 8 August 2002 accepted 24 August 2002 Author to whom correspondence should be sent

concentration to facilitate regulation of insulin in patientssuffering from the increasingly prevalent disease diabetesmellitus4ndash8 and the application of infrared lasers for med-ical treatment and diagnostics9

The water absorption spectrum has been studied in the elds of physical chemistry and biomedical spectroscopyBertie and Lan10 measured the water absorption spectrumin a wide spectral range at 25 6 1 8C and report a com-pilation of the best current values at that temperature inthe range 15 000ndash1 cm21 These authors also state thatthere are no reliable detailed investigations of the vari-ation of water absorption with temperature Libnau etal1112 studied water absorption variation with tempera-ture using an attenuated total re ectance (ATR) cell inthe wavenumber range 4000ndash900 cm21 to determinechanges in the structure of liquid water They presentspectra measured at temperatures of 2 46 and 96 8CVenyaminov and Prendergast1 studied the effect of in-creasing temperature from 25ndash50 8C using a 35 mmtransmission cell in the wavenumber ranges 4000ndash2600and 2350ndash1430 cm21 Rahmelow and Hubner13 studiedthe effect of changing temperature by 1 8C at 25 8C usinga 7 mm transmission cell in the range 3000ndash1000 cm21Kelly and Barlow14 studied the effect in the wavenumberrange 11 800ndash6250 cm21 with temperatures spanning 17ndash45 8C to determine tissue temperature Hazen Arnoldand Small15 examined the problem in the range that con-tains combination bands of glucose ie 4800ndash4200cm21 letting temperature vary within 32ndash41 8C Theseauthors showed that bandpass ltering of data could re-move baseline variations caused by temperature changesin this narrow wavenumber range

The aim of this study was to investigate the tempera-ture dependency of water and glucose solutions in themid- and near-infrared spectral range for future applica-tions in the biomedical eld Our focus is on the practicalconsequences of temperature variations for quantitativemeasurement of trace components in aqueous solutionsThe study is thus limited to spectral ranges outside thefundamental water bands where the penetration depth isnot too limited by the strong absorption from water In-formation about the spectral features in these parts of thewater spectrum is useful when spectral regions are soughtfor quanti cation of small amounts of compounds suchas glucose urea and creatinine in aqueous solutionswhen samples are under limited temperature control asis the case with in vivo and on-line measurements

Absorption spectra of pure water at temperatures in therange 30ndash42 8C in both the mid- and near-infrared regionare presented The spectral data measured in this work

APPLIED SPECTROSCOPY 29

are compared to available spectral data found in the lit-erature measured at slightly lower temperatures Differ-ence spectra were calculated by subtracting the 37 8Cspectrum from those measured at other temperatures Theabsorption spectrum of water at 37 8C and the differencespectra have been tabulated for future use The differencespectra can be used to extract optimal spectral regions fordetection of trace organic components in aqueous solu-tions We used the difference spectra to estimate the in- uence of temperature on the expected glucose signals inhumans Finally it was demonstrated experimentally thatfeatures of the glucose spectrum and the underlying waterabsorption spectrum behave differently in the two spec-tral ranges when the temperature varies

EXPERIMENTAL

Spectra were measured using a Bomem MB155 Fou-rier transform infrared (FT-IR) spectrometer equippedwith a wide-range deuterated triglycine sulfate (DTGS)detector For measurements in the mid-infrared regionthe source was an 800 K SiC Globar For measurementsin the near-infrared region the source was a 150 Wquartzndashhalogen lamp Measurements were performed at8 cm21 resolution using coaddition of 512 double-sided(symmetrical) double-buffered scans (both forward andbackward scan used) each containing 2 3 8192 pointsThe total acquisition time for each spectrum was 320 sAll measurements were carried out with an instrumentgain setting of one Interferograms were transferred to anIntel PII based Linux workstation for data analysis Allanalysis was performed using custom routines written inANSI C Interferograms were apodized using a cosinewindow prior to Fourier transformation and single-beamintensity spectra were calculated using full-phase infor-mation16 without zero- lling as

I ( ) 5 C( )cos F( ) 1 S ( )sin F( )n n n n n (1)

where C( ) is the cosine and S ( ) is the sine transformn nof the interferogram and F( ) is the phase de ned by tannF( ) 5 S ( )C( )n n n

Transmission Cell Samples were placed in a variablepathlength liquid transmission cell (Specac 7000) withplane parallel and uncoated ZnSe windows The trans-mission cell pathlength was calibrated by the fringe meth-od before measurements took place The pathlength couldbe varied between 20 mm and 6 mm with an accuracyof 65 mm This enabled optimization of the SNR for agiven wavenumber region by adjusting the pathlength toachieve a mean absorbance level of approximately 1ln10 A pathlength of 50 mm was used in the mid-infraredregion although a pathlength of 20 mm optimizes theSNR in the range 1500ndash950 cm21 The longer pathlengthwas chosen to reduce interference fringes in the spectradue to multiple re ections within the cell caused by thehigh index of refraction of the ZnSe windows (n 5 24)compared to that of water (n 5 133) and to reduce therelative uncertainty of the pathlength setting This choiceminimized a systematic effect at the cost of increasednoise which was then reduced by coaddition of interfer-ograms A pathlength of 04 mm was used in the near-infrared region providing optimal SNR in the range5000ndash4000 cm21 Temperature was controlled within

6002 8C by a Eurotherm 4208 temperature control unitwhich measured sample temperature through the cell ll-ing port with a PT100 thermo element and heated the cellby a nichrome wire wound around the cell body Thelarge mass (m 5 640 g) of the transmission cell causedit to be very resistant to temperature changes providingexcellent stability during the measurements The stabilitywas obtained at the expense of the time (1 h) requiredfor the cell to stabilize when the temperature was changed2 8C

Reagents Aqueous glucose solutions (1 gdL) wereprepared and the cell was lled the day before measure-ments took place allowing air bubbles caught in the cellto diffuse and equilibrium to be reached between the al-pha and beta forms of glucose when present Reagentgrade a-D-glucose (BDH Laboratory Supplies PooleEngland) was weighed using an analytical balance anddissolved in 05 L distilled and de-ionized Millipore wa-ter (15 MV)

Experimental and Data Analytical Procedure Fourrepeat measurements were taken and subsequently aver-aged at each of the temperatures 30 32 34 36 37 3840 and 42 8C with approximately 1 h between each setThe temperature was changed without adjusting the path-length to avoid baseline variations caused by any uncer-tainty in pathlength setting An air reference spectrumwas measured on an empty 10 mm pathlength cell afterthe last set of measurements on the samples took placeThe long pathlength of the reference cell was chosen toeliminate interference fringes in the reference measure-ment by making the fringe period smaller than the chosenresolution In each wavenumber region the absorbancespectra of pure water and glucose solutions were calcu-lated The spectra representing pure water were baselinecorrected for the wavenumber-dependent difference inFresnel transmission between the two ZnSendashair interfacesin the air- lled reference and the two ZnSendashwater inter-faces in the water- lled sample The baseline correctionwas carried out by calculating the change in Fresneltransmission using the tabulated values of the index ofrefraction of water at 25 8C given by Bertie and Lan10

and a constant index of refraction of 24 for the ZnSewindows This correction term was subsequently addedto all the absorbance spectra The near-infrared absorp-tion spectra were also baseline corrected by subtractionof the mean value of the spectrum in the range 10 000ndash8000 cm21 These spectra were converted to molar ab-sorptivity by dividing by the molarity of water at therelevant temperature and the transmission cell pathlength

The variation of the glucose absorption bands withtemperature was investigated by carrying out the samemeasurements on the 10 gdL glucose solutions and bycomparing the glucose absorbance spectra with those ofpure water

Principal component analysis (PCA) was used to sep-arate the data sets into a noise part and a structure partwith the rst principal components describing the system-atic variation in the spectral data This technique wasused to compare the effects of temperature and the pres-ence of glucose on the water absorption spectra The PCAsoftware was based on ANSI C programs using double-precision versions of subroutines from Numerical Reci-

30 Volume 57 Number 1 2003

FIG 1 Water molar absorptivity at 30 and 42 8C in the mid-infraredregion The transmission cell pathlength is 50 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C

FIG 2 Difference in water molar absorptivity with temperature around37 8C in the mid-infrared region The insertion shows the absorptionspectrum of glucose in the region 1500ndash950 cm21 (y-axis not to scale)

FIG 3 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the mid-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 1 and 2 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half of the level shown in this gure

pes in C17 A detailed description of the PCA method canbe found in the literature1819

RESULTS AND DISCUSSION

Pure Water Mid-infrared Region The absorption ofpure water in units of molar absorptivity measured at 30and 42 8C in the region 5000ndash950 cm21 is shown in Fig1 The strong fundamental OH stretch and bend bands ofwater centered at 3500 and 1600 cm21 are not resolvedIn the same plot our data are compared to the data givenby Bertie and Lan10 measured at 25 8C Their data agreewell with our measured data with the differences beinglargely systematic and following the trend indicated bythe shift from 30ndash42 8C in our data Given the differencein temperature and the fact that our data had been base-line corrected using Bertie and Lanrsquos data for the refrac-tive index of water at 25 8C we did not expect perfectagreement The accuracy of the pathlength setting of thetransmission cell may be estimated from this agreementwith the tabulated data of Bertie and Lan to be well with-in 2 mm Figure 2 shows the spectra obtained by sub-tracting the spectrum measured at 37 8C from the spectrameasured at 30 32 34 36 38 40 and 42 8C in the range3000ndash950 cm21 Data for the range 8000ndash3800 cm21 arepresented in a separate section to follow These differencespectra are given in units of molar absorptivity and areexpected to be more accurate than the absolute spectrapresented in Fig 1 since the correction for difference inFresnel transmission which is common to all the spectracancels in the subtraction The improved accuracy of thedifference spectra can be veri ed by the symmetry of thedifference spectra around the 37 8C reference and by thecoincidence of the isosbestic points in the spectrum

The noise level of the measurements may be estimatedfrom Fig 3 which shows the difference spectrum of 368C with 37 8C as reference and the subtraction of two 378C spectra These two difference spectra were obtainedfrom one of the four repeat measurements in the 36 8Cset and two of the repeat measurements in the 37 8C setThe spectra shown in Figs 1 and 2 are averages of foursuch repeat measurements and consequently the noiselevel in Figs 1 and 2 is half that shown in Fig 3 We

estimate the uncertainty to be less than 0006 L mole21

cm21 in the spectral region 3000ndash1000 cm21 (013 com-pared to the absolute value at 1200 cm21) It is observedby inspection of Fig 3 that the noise level in most partsof the spectrum is very small compared to the spectralchange caused by a change in temperature of 1 8C In theregion 1200ndash1000 cm21 the noise level and the changewith a temperature difference of 1 8C is comparable The37 8C absorption spectrum and the difference spectra with37 8C as reference are tabulated in Table I The variationsin water absorption with temperature are seen to be largeon the anks of the absorption bands and small in thelocal minima of the water absorption spectra It is clearthat these variations do not depend in a simple way onthe absolute value of the water absorption spectrum Theripple pattern most clearly visible between 2800 and2500 cm21 in the 30 8C difference spectrum is an artifactof the double re ection between the windows

APPLIED SPECTROSCOPY 31

TABLE I Mid-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 60005 L mole21 cm21 in the ranges 1580ndash960 and 2900ndash1700 cm21 and 6001 L mole21 cm21 in the ranges 960ndash950 and 3000ndash2900 cm21 Absolute 37 8C spectra are 6001 L mole21 cm21 in the ranges 1580ndash950 and 3000ndash1850 cm21 6004 L mole21 cm21 in the range1600ndash1580 cm21 and 6025 L mole21 cm21 in the range 1850ndash1700 cm21 Interpolation should be performed separately in the ranges 1600ndash950 and 3000ndash1700 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

960 6026 5562 4548 3306 1123 21698 24765 268841000 5061 20421 0286 0525 0279 21047 21818 225241040 4589 21556 20640 20135 0014 20453 20613 207921080 4368 22172 21057 20170 0110 20352 20580 202941120 4267 21724 20745 20253 20022 20493 20883 209381160 4272 20920 20397 20032 0105 20659 20911 213181200 4314 20181 0381 0544 0430 20622 21169 219221240 4379 0878 1151 0911 0407 20897 21851 227631280 4437 1836 1740 1396 0604 21036 22240 235201320 4485 3110 2763 1959 0819 21270 22939 245341360 4540 4665 3942 2637 1122 21501 23536 256151400 4619 6150 5038 3419 1366 21756 24358 269051440 4757 7493 6072 3972 1529 22160 25179 281751480 4998 8806 7020 4616 1778 22369 25729 290781520 5487 9113 7458 4931 1947 22651 26196 299911540 5969 8695 7340 4795 1830 22572 26097 296521560 6784 6470 5676 3854 1354 22457 25636 285161580 8330 1628 2195 2518 1424 22346 23218 245291600 11484 214393 29225 29421 23575 25385 22047 10081700 9315 11525 11446 6353 1225 26157 210935 2166231710 7432 11180 9599 6097 1966 23481 27995 2129711720 6012 9164 7639 4999 2151 22557 26190 2100081740 4217 5573 4593 3066 1194 21718 23988 263001760 3241 3712 3062 2027 0836 21128 22648 241301800 2369 1654 1405 1004 0437 20607 21362 220271840 2067 0043 0213 0289 0204 20352 20663 208991880 1988 20626 20433 20158 0017 20122 20089 00641920 2076 21872 21254 20635 20151 0072 0418 08961960 2300 23087 22133 21135 20329 0131 0697 13012000 2641 22280 21524 20774 20203 0019 0316 06702040 3010 20419 20017 0196 0179 20473 20927 214292080 3283 3658 3026 2076 0872 21174 22877 246022120 3380 7655 6065 3944 1572 21869 24763 276782160 3254 10315 7973 5061 1995 22297 25856 294512200 2971 10547 8143 5139 1978 22293 25865 294442240 2627 9720 7449 4712 1855 22107 25377 286662280 2297 8677 6664 4233 1662 21847 24764 276442320 2001 7563 5763 3677 1464 21649 24206 267222360 1746 6983 5246 3381 1357 21491 23851 260462400 1541 5893 4501 2878 1157 21284 23286 252202440 1364 5543 4174 2662 1060 21164 22973 247322480 1215 4628 3575 2330 0941 21048 22655 242002520 1087 4103 3047 1948 0789 20853 22188 234372560 0996 3311 2536 1660 0679 20718 21850 228772600 0944 2117 1661 1152 0515 20631 21502 223212640 0948 2223 1590 1044 0441 20469 21198 218192680 1024 1644 1337 0940 0420 20453 21148 217472720 1167 1188 1018 0782 0389 20537 21213 218832760 1405 1903 1463 1022 0473 20542 21357 221102800 1781 2556 2051 1401 0613 20721 21820 228842840 2345 3698 3036 2067 0883 21121 22772 244842880 3178 6363 5120 3369 1405 21728 24368 271222920 4426 11161 8683 5640 2226 22856 27053 2116042960 6242 18889 14913 9305 3656 24510 211303 2189033000 8957 30558 23785 13195 5239 28559 219045 233430

Inspection of the difference spectra reveals that the re-gion 1200ndash1000 cm21 and the region 2800ndash2500 cm21

appear to be better suited to measurement of trace com-ponent signals These two regions show only slightbroad-band variation of the water absorption with tem-perature The rst region changes little with temperature(less than 003 L mole21 cm21 across the 12 8C temper-

ature difference) It is also known to contain glucose sig-nals from the pyranose ring vibrations The insert in Fig2 illustrates the position of the glucose absorption bands(y-axis not to scale)

Near-Infrared Region The absorption of pure waterin units of molar absorptivity measured at 30 and 42 8Cin the spectral range 8000ndash3800 cm21 is shown in Fig

32 Volume 57 Number 1 2003

FIG 4 Water molar absorptivity at 30 and 42 8C in the near-infraredregion The transmission cell pathlength is 04 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C andPalmer and Williams20 measured at 27 8C

FIG 5 Difference in water molar absorptivity with temperature around37 8C in the near-infrared region The insertion shows the second de-rivative absorption spectrum of glucose in the region 4800ndash4200 cm21

(y-axis not to scale)

FIG 6 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the near-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 4 and 5 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half the level shown in this gure

4 In the same plot our data are compared to data mea-sured and tabulated by other groups2010 It should be not-ed that the data of the other groups were obtained atlower temperatures (25 and 27 8C) Good agreement ex-ists in the major part of the spectrum with only minordiscrepancies being observed around the combinationband at 5160 cm21 as previously noted by Bertie andLan10 As in the mid-infrared region our spectra weremeasured at a higher temperature and baseline correctedfor the difference in Fresnel transmission using tabulateddata on the refractive index of water at 25 8C We thusdid not expect perfect agreement

Figure 5 displays the spectra obtained by subtractingthe water spectrum measured at 37 8C from the spectrameasured at temperatures 30 32 34 36 38 40 and 428C These difference spectra are given in units of molarabsorptivity Again these difference spectra were ex-pected to be more accurate than the absolute spectraTheir accuracy can be veri ed from the symmetry of thedifference spectra around the 37 8C reference in Fig 5

The noise level may be estimated from Fig 6 whichshows the difference spectrum of 36 8C with 37 8C asreference and the subtraction of two 37 8C spectra Thesetwo spectra were obtained from one of the four repeatmeasurements at 36 8C and two of the repeat measure-ments at 37 8C The spectra shown in Figs 4 and 5 areaverages of four such repeat measurements and conse-quently the noise level is twice as low The uncertaintyof these difference spectra is less than 7 3 1024 L mole21

cm21 (03 compared to the absolute value at 4500cm21) Again it is observed that the noise level is wellbelow the change in the spectrum induced by a changein temperature of 1 8C In the mid-infrared region wefound a 013 uncertainty relative to the signal strengthwhich is twice as good This nding may indicate thatthe mid-infrared region is better suited to measurementof trace organic components in samples where a smalldepth of penetration gives access to the signal from thetrace component of interest

The 37 8C absorption spectrum and the differencespectra with 37 8C as reference are tabulated in Table II

The variations in the water absorption due to temperatureare observed to be of a broad-band nature The changesare obviously highest in the vicinity of the absorptionbands with a number of isosbestic points with no tem-perature dependence and relatively at plateaus in be-tween The isosbestic points occur close to the points inthe spectrum where the water bands peak or are at a min-imum Spectral regions such as 4500ndash4200 and 6500ndash5500 cm21 show a small and almost at dependency ontemperature This explains the success of the ltering ap-proach used by Hazen Arnold and Small1521 to removebaseline variations caused by changes in temperature

Glucose has spectral features from overtone and com-bination bands in the regions mentioned above If glucoseis present in the solution its signal will be superposedon a nearly at baseline The glucose signals which con-tain narrow bands may easily be separated from thebroad-band variation of water using a high-pass lter

APPLIED SPECTROSCOPY 33

TABLE II Near-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 610 3 1024 L mole21 cm21 in the ranges 5000ndash4000 and 7500ndash5500 cm21 and 615 3 1023 L mole21 cm21 in the ranges 4000ndash3800 and 5500ndash5000 cm 21 Absolute 37 8C spectra are 60001 L mole21 cm21 in the ranges 5000ndash3800 and 7500ndash5500 cm 21 and 60005 Lmole21 cm21 in the range 5500ndash5000 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

3800 1292 26655 24800 22832 20937 1369 3593 59383840 1044 25379 23999 22529 20872 0839 2713 45703880 0931 24492 23303 22089 20699 0731 2281 38223920 0892 23672 22684 21670 20554 0596 1793 30163960 0860 22694 21941 21203 20369 0436 1313 21664000 0790 21825 21302 20799 20251 0277 0855 14244040 0682 21203 20855 20551 20173 0173 0552 09224080 0570 20824 20581 20372 20112 0118 0380 06414120 0478 20568 20396 20256 20077 0075 0259 04344160 0406 20380 20254 20167 20050 0048 0166 02884200 0347 20254 20163 20107 20029 0030 0113 01934280 0257 20171 20103 20072 20020 0017 0074 01304360 0198 20163 20094 20067 20018 0015 0069 01214440 0167 20104 20049 20036 20007 0006 0042 00734520 0155 20008 0025 0009 0008 20011 20009 200104600 0161 0131 0131 0076 0029 20034 20080 201284680 0183 0342 0290 0175 0061 20068 20187 203074760 0226 0655 0529 0325 0110 20121 20347 205744840 0295 1096 0861 0533 0178 20191 20565 209424920 0395 1616 1250 0774 0256 20272 20820 213725000 0549 1979 1527 0955 0320 20320 21013 217105080 0779 1906 1460 0925 0308 20277 20939 216845160 1015 0417 0557 0340 0121 0003 0006 203785200 1051 21791 21111 20623 20180 0411 1228 13425240 0966 23878 22604 21674 20442 0654 2000 29505260 0843 24004 22856 21779 20571 0636 2034 32075280 0645 23212 22297 21453 20466 0525 1607 26635300 0437 22133 21520 20968 20315 0340 1072 17965320 0286 21275 20884 20567 20181 0196 0638 10755360 0142 20473 20288 20190 20059 0063 0228 03915400 0096 20228 20107 20074 20020 0025 0106 01835480 0076 20082 0007 20003 0003 20003 0026 00505560 0074 0002 0073 0037 0018 20016 20016 200225640 0068 0096 0145 0080 0031 20034 20064 201045720 0056 0149 0186 0107 0040 20043 20092 201515800 0046 0184 0213 0124 0045 20048 20107 201745880 0042 0222 0241 0139 0051 20054 20125 202085960 0041 0252 0265 0154 0054 20059 20142 202336040 0042 0276 0281 0166 0059 20062 20152 202496120 0046 0300 0297 0177 0063 20065 20165 202716200 0050 0325 0314 0188 0066 20069 20175 202856280 0057 0358 0335 0199 0069 20073 20191 203176360 0068 0409 0370 0224 0076 20082 20218 203616440 0082 0487 0422 0258 0088 20092 20253 204216520 0103 0584 0491 0302 0102 20107 20304 205066600 0130 0682 0563 0350 0119 20121 20353 205896680 0166 0755 0613 0382 0128 20134 20394 206576760 0207 0716 0582 0364 0123 20127 20378 206356840 0244 0468 0400 0252 0088 20091 20270 204606920 0254 0075 0111 0071 0029 20029 20082 201517000 0249 20608 20400 20251 20078 0083 0259 04247080 0213 21069 20753 20469 20149 0161 0505 08447120 0175 20974 20684 20426 20137 0147 0460 07737160 0127 20714 20492 20306 20099 0103 0335 05627200 0083 20476 20318 20197 20063 0068 0223 03747240 0055 20320 20202 20125 20040 0042 0145 02467320 0032 20160 20085 20053 20017 0015 0060 01057400 0025 20097 20041 20024 20007 0005 0028 00527480 0018 20057 20013 20006 0000 20001 0009 00147500 0016 20050 20010 20003 0000 20003 0005 0008

This is illustrated by the insert in Fig 5 which showsthe second derivative absorption spectrum of aqueousglucose in the combination band 5000ndash4000 cm21 They-axis of this insert is not to scale Figure 5 shows that

quantitative in vivo spectroscopy will be very dif cult inthe vicinity of the stronger absorption bands Realistictemperature variations close to 37 8C have an enormousimpact on the appearance of the water spectrum leaving

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

APPLIED SPECTROSCOPY 29

are compared to available spectral data found in the lit-erature measured at slightly lower temperatures Differ-ence spectra were calculated by subtracting the 37 8Cspectrum from those measured at other temperatures Theabsorption spectrum of water at 37 8C and the differencespectra have been tabulated for future use The differencespectra can be used to extract optimal spectral regions fordetection of trace organic components in aqueous solu-tions We used the difference spectra to estimate the in- uence of temperature on the expected glucose signals inhumans Finally it was demonstrated experimentally thatfeatures of the glucose spectrum and the underlying waterabsorption spectrum behave differently in the two spec-tral ranges when the temperature varies

EXPERIMENTAL

Spectra were measured using a Bomem MB155 Fou-rier transform infrared (FT-IR) spectrometer equippedwith a wide-range deuterated triglycine sulfate (DTGS)detector For measurements in the mid-infrared regionthe source was an 800 K SiC Globar For measurementsin the near-infrared region the source was a 150 Wquartzndashhalogen lamp Measurements were performed at8 cm21 resolution using coaddition of 512 double-sided(symmetrical) double-buffered scans (both forward andbackward scan used) each containing 2 3 8192 pointsThe total acquisition time for each spectrum was 320 sAll measurements were carried out with an instrumentgain setting of one Interferograms were transferred to anIntel PII based Linux workstation for data analysis Allanalysis was performed using custom routines written inANSI C Interferograms were apodized using a cosinewindow prior to Fourier transformation and single-beamintensity spectra were calculated using full-phase infor-mation16 without zero- lling as

I ( ) 5 C( )cos F( ) 1 S ( )sin F( )n n n n n (1)

where C( ) is the cosine and S ( ) is the sine transformn nof the interferogram and F( ) is the phase de ned by tannF( ) 5 S ( )C( )n n n

Transmission Cell Samples were placed in a variablepathlength liquid transmission cell (Specac 7000) withplane parallel and uncoated ZnSe windows The trans-mission cell pathlength was calibrated by the fringe meth-od before measurements took place The pathlength couldbe varied between 20 mm and 6 mm with an accuracyof 65 mm This enabled optimization of the SNR for agiven wavenumber region by adjusting the pathlength toachieve a mean absorbance level of approximately 1ln10 A pathlength of 50 mm was used in the mid-infraredregion although a pathlength of 20 mm optimizes theSNR in the range 1500ndash950 cm21 The longer pathlengthwas chosen to reduce interference fringes in the spectradue to multiple re ections within the cell caused by thehigh index of refraction of the ZnSe windows (n 5 24)compared to that of water (n 5 133) and to reduce therelative uncertainty of the pathlength setting This choiceminimized a systematic effect at the cost of increasednoise which was then reduced by coaddition of interfer-ograms A pathlength of 04 mm was used in the near-infrared region providing optimal SNR in the range5000ndash4000 cm21 Temperature was controlled within

6002 8C by a Eurotherm 4208 temperature control unitwhich measured sample temperature through the cell ll-ing port with a PT100 thermo element and heated the cellby a nichrome wire wound around the cell body Thelarge mass (m 5 640 g) of the transmission cell causedit to be very resistant to temperature changes providingexcellent stability during the measurements The stabilitywas obtained at the expense of the time (1 h) requiredfor the cell to stabilize when the temperature was changed2 8C

Reagents Aqueous glucose solutions (1 gdL) wereprepared and the cell was lled the day before measure-ments took place allowing air bubbles caught in the cellto diffuse and equilibrium to be reached between the al-pha and beta forms of glucose when present Reagentgrade a-D-glucose (BDH Laboratory Supplies PooleEngland) was weighed using an analytical balance anddissolved in 05 L distilled and de-ionized Millipore wa-ter (15 MV)

Experimental and Data Analytical Procedure Fourrepeat measurements were taken and subsequently aver-aged at each of the temperatures 30 32 34 36 37 3840 and 42 8C with approximately 1 h between each setThe temperature was changed without adjusting the path-length to avoid baseline variations caused by any uncer-tainty in pathlength setting An air reference spectrumwas measured on an empty 10 mm pathlength cell afterthe last set of measurements on the samples took placeThe long pathlength of the reference cell was chosen toeliminate interference fringes in the reference measure-ment by making the fringe period smaller than the chosenresolution In each wavenumber region the absorbancespectra of pure water and glucose solutions were calcu-lated The spectra representing pure water were baselinecorrected for the wavenumber-dependent difference inFresnel transmission between the two ZnSendashair interfacesin the air- lled reference and the two ZnSendashwater inter-faces in the water- lled sample The baseline correctionwas carried out by calculating the change in Fresneltransmission using the tabulated values of the index ofrefraction of water at 25 8C given by Bertie and Lan10

and a constant index of refraction of 24 for the ZnSewindows This correction term was subsequently addedto all the absorbance spectra The near-infrared absorp-tion spectra were also baseline corrected by subtractionof the mean value of the spectrum in the range 10 000ndash8000 cm21 These spectra were converted to molar ab-sorptivity by dividing by the molarity of water at therelevant temperature and the transmission cell pathlength

The variation of the glucose absorption bands withtemperature was investigated by carrying out the samemeasurements on the 10 gdL glucose solutions and bycomparing the glucose absorbance spectra with those ofpure water

Principal component analysis (PCA) was used to sep-arate the data sets into a noise part and a structure partwith the rst principal components describing the system-atic variation in the spectral data This technique wasused to compare the effects of temperature and the pres-ence of glucose on the water absorption spectra The PCAsoftware was based on ANSI C programs using double-precision versions of subroutines from Numerical Reci-

30 Volume 57 Number 1 2003

FIG 1 Water molar absorptivity at 30 and 42 8C in the mid-infraredregion The transmission cell pathlength is 50 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C

FIG 2 Difference in water molar absorptivity with temperature around37 8C in the mid-infrared region The insertion shows the absorptionspectrum of glucose in the region 1500ndash950 cm21 (y-axis not to scale)

FIG 3 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the mid-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 1 and 2 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half of the level shown in this gure

pes in C17 A detailed description of the PCA method canbe found in the literature1819

RESULTS AND DISCUSSION

Pure Water Mid-infrared Region The absorption ofpure water in units of molar absorptivity measured at 30and 42 8C in the region 5000ndash950 cm21 is shown in Fig1 The strong fundamental OH stretch and bend bands ofwater centered at 3500 and 1600 cm21 are not resolvedIn the same plot our data are compared to the data givenby Bertie and Lan10 measured at 25 8C Their data agreewell with our measured data with the differences beinglargely systematic and following the trend indicated bythe shift from 30ndash42 8C in our data Given the differencein temperature and the fact that our data had been base-line corrected using Bertie and Lanrsquos data for the refrac-tive index of water at 25 8C we did not expect perfectagreement The accuracy of the pathlength setting of thetransmission cell may be estimated from this agreementwith the tabulated data of Bertie and Lan to be well with-in 2 mm Figure 2 shows the spectra obtained by sub-tracting the spectrum measured at 37 8C from the spectrameasured at 30 32 34 36 38 40 and 42 8C in the range3000ndash950 cm21 Data for the range 8000ndash3800 cm21 arepresented in a separate section to follow These differencespectra are given in units of molar absorptivity and areexpected to be more accurate than the absolute spectrapresented in Fig 1 since the correction for difference inFresnel transmission which is common to all the spectracancels in the subtraction The improved accuracy of thedifference spectra can be veri ed by the symmetry of thedifference spectra around the 37 8C reference and by thecoincidence of the isosbestic points in the spectrum

The noise level of the measurements may be estimatedfrom Fig 3 which shows the difference spectrum of 368C with 37 8C as reference and the subtraction of two 378C spectra These two difference spectra were obtainedfrom one of the four repeat measurements in the 36 8Cset and two of the repeat measurements in the 37 8C setThe spectra shown in Figs 1 and 2 are averages of foursuch repeat measurements and consequently the noiselevel in Figs 1 and 2 is half that shown in Fig 3 We

estimate the uncertainty to be less than 0006 L mole21

cm21 in the spectral region 3000ndash1000 cm21 (013 com-pared to the absolute value at 1200 cm21) It is observedby inspection of Fig 3 that the noise level in most partsof the spectrum is very small compared to the spectralchange caused by a change in temperature of 1 8C In theregion 1200ndash1000 cm21 the noise level and the changewith a temperature difference of 1 8C is comparable The37 8C absorption spectrum and the difference spectra with37 8C as reference are tabulated in Table I The variationsin water absorption with temperature are seen to be largeon the anks of the absorption bands and small in thelocal minima of the water absorption spectra It is clearthat these variations do not depend in a simple way onthe absolute value of the water absorption spectrum Theripple pattern most clearly visible between 2800 and2500 cm21 in the 30 8C difference spectrum is an artifactof the double re ection between the windows

APPLIED SPECTROSCOPY 31

TABLE I Mid-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 60005 L mole21 cm21 in the ranges 1580ndash960 and 2900ndash1700 cm21 and 6001 L mole21 cm21 in the ranges 960ndash950 and 3000ndash2900 cm21 Absolute 37 8C spectra are 6001 L mole21 cm21 in the ranges 1580ndash950 and 3000ndash1850 cm21 6004 L mole21 cm21 in the range1600ndash1580 cm21 and 6025 L mole21 cm21 in the range 1850ndash1700 cm21 Interpolation should be performed separately in the ranges 1600ndash950 and 3000ndash1700 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

960 6026 5562 4548 3306 1123 21698 24765 268841000 5061 20421 0286 0525 0279 21047 21818 225241040 4589 21556 20640 20135 0014 20453 20613 207921080 4368 22172 21057 20170 0110 20352 20580 202941120 4267 21724 20745 20253 20022 20493 20883 209381160 4272 20920 20397 20032 0105 20659 20911 213181200 4314 20181 0381 0544 0430 20622 21169 219221240 4379 0878 1151 0911 0407 20897 21851 227631280 4437 1836 1740 1396 0604 21036 22240 235201320 4485 3110 2763 1959 0819 21270 22939 245341360 4540 4665 3942 2637 1122 21501 23536 256151400 4619 6150 5038 3419 1366 21756 24358 269051440 4757 7493 6072 3972 1529 22160 25179 281751480 4998 8806 7020 4616 1778 22369 25729 290781520 5487 9113 7458 4931 1947 22651 26196 299911540 5969 8695 7340 4795 1830 22572 26097 296521560 6784 6470 5676 3854 1354 22457 25636 285161580 8330 1628 2195 2518 1424 22346 23218 245291600 11484 214393 29225 29421 23575 25385 22047 10081700 9315 11525 11446 6353 1225 26157 210935 2166231710 7432 11180 9599 6097 1966 23481 27995 2129711720 6012 9164 7639 4999 2151 22557 26190 2100081740 4217 5573 4593 3066 1194 21718 23988 263001760 3241 3712 3062 2027 0836 21128 22648 241301800 2369 1654 1405 1004 0437 20607 21362 220271840 2067 0043 0213 0289 0204 20352 20663 208991880 1988 20626 20433 20158 0017 20122 20089 00641920 2076 21872 21254 20635 20151 0072 0418 08961960 2300 23087 22133 21135 20329 0131 0697 13012000 2641 22280 21524 20774 20203 0019 0316 06702040 3010 20419 20017 0196 0179 20473 20927 214292080 3283 3658 3026 2076 0872 21174 22877 246022120 3380 7655 6065 3944 1572 21869 24763 276782160 3254 10315 7973 5061 1995 22297 25856 294512200 2971 10547 8143 5139 1978 22293 25865 294442240 2627 9720 7449 4712 1855 22107 25377 286662280 2297 8677 6664 4233 1662 21847 24764 276442320 2001 7563 5763 3677 1464 21649 24206 267222360 1746 6983 5246 3381 1357 21491 23851 260462400 1541 5893 4501 2878 1157 21284 23286 252202440 1364 5543 4174 2662 1060 21164 22973 247322480 1215 4628 3575 2330 0941 21048 22655 242002520 1087 4103 3047 1948 0789 20853 22188 234372560 0996 3311 2536 1660 0679 20718 21850 228772600 0944 2117 1661 1152 0515 20631 21502 223212640 0948 2223 1590 1044 0441 20469 21198 218192680 1024 1644 1337 0940 0420 20453 21148 217472720 1167 1188 1018 0782 0389 20537 21213 218832760 1405 1903 1463 1022 0473 20542 21357 221102800 1781 2556 2051 1401 0613 20721 21820 228842840 2345 3698 3036 2067 0883 21121 22772 244842880 3178 6363 5120 3369 1405 21728 24368 271222920 4426 11161 8683 5640 2226 22856 27053 2116042960 6242 18889 14913 9305 3656 24510 211303 2189033000 8957 30558 23785 13195 5239 28559 219045 233430

Inspection of the difference spectra reveals that the re-gion 1200ndash1000 cm21 and the region 2800ndash2500 cm21

appear to be better suited to measurement of trace com-ponent signals These two regions show only slightbroad-band variation of the water absorption with tem-perature The rst region changes little with temperature(less than 003 L mole21 cm21 across the 12 8C temper-

ature difference) It is also known to contain glucose sig-nals from the pyranose ring vibrations The insert in Fig2 illustrates the position of the glucose absorption bands(y-axis not to scale)

Near-Infrared Region The absorption of pure waterin units of molar absorptivity measured at 30 and 42 8Cin the spectral range 8000ndash3800 cm21 is shown in Fig

32 Volume 57 Number 1 2003

FIG 4 Water molar absorptivity at 30 and 42 8C in the near-infraredregion The transmission cell pathlength is 04 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C andPalmer and Williams20 measured at 27 8C

FIG 5 Difference in water molar absorptivity with temperature around37 8C in the near-infrared region The insertion shows the second de-rivative absorption spectrum of glucose in the region 4800ndash4200 cm21

(y-axis not to scale)

FIG 6 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the near-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 4 and 5 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half the level shown in this gure

4 In the same plot our data are compared to data mea-sured and tabulated by other groups2010 It should be not-ed that the data of the other groups were obtained atlower temperatures (25 and 27 8C) Good agreement ex-ists in the major part of the spectrum with only minordiscrepancies being observed around the combinationband at 5160 cm21 as previously noted by Bertie andLan10 As in the mid-infrared region our spectra weremeasured at a higher temperature and baseline correctedfor the difference in Fresnel transmission using tabulateddata on the refractive index of water at 25 8C We thusdid not expect perfect agreement

Figure 5 displays the spectra obtained by subtractingthe water spectrum measured at 37 8C from the spectrameasured at temperatures 30 32 34 36 38 40 and 428C These difference spectra are given in units of molarabsorptivity Again these difference spectra were ex-pected to be more accurate than the absolute spectraTheir accuracy can be veri ed from the symmetry of thedifference spectra around the 37 8C reference in Fig 5

The noise level may be estimated from Fig 6 whichshows the difference spectrum of 36 8C with 37 8C asreference and the subtraction of two 37 8C spectra Thesetwo spectra were obtained from one of the four repeatmeasurements at 36 8C and two of the repeat measure-ments at 37 8C The spectra shown in Figs 4 and 5 areaverages of four such repeat measurements and conse-quently the noise level is twice as low The uncertaintyof these difference spectra is less than 7 3 1024 L mole21

cm21 (03 compared to the absolute value at 4500cm21) Again it is observed that the noise level is wellbelow the change in the spectrum induced by a changein temperature of 1 8C In the mid-infrared region wefound a 013 uncertainty relative to the signal strengthwhich is twice as good This nding may indicate thatthe mid-infrared region is better suited to measurementof trace organic components in samples where a smalldepth of penetration gives access to the signal from thetrace component of interest

The 37 8C absorption spectrum and the differencespectra with 37 8C as reference are tabulated in Table II

The variations in the water absorption due to temperatureare observed to be of a broad-band nature The changesare obviously highest in the vicinity of the absorptionbands with a number of isosbestic points with no tem-perature dependence and relatively at plateaus in be-tween The isosbestic points occur close to the points inthe spectrum where the water bands peak or are at a min-imum Spectral regions such as 4500ndash4200 and 6500ndash5500 cm21 show a small and almost at dependency ontemperature This explains the success of the ltering ap-proach used by Hazen Arnold and Small1521 to removebaseline variations caused by changes in temperature

Glucose has spectral features from overtone and com-bination bands in the regions mentioned above If glucoseis present in the solution its signal will be superposedon a nearly at baseline The glucose signals which con-tain narrow bands may easily be separated from thebroad-band variation of water using a high-pass lter

APPLIED SPECTROSCOPY 33

TABLE II Near-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 610 3 1024 L mole21 cm21 in the ranges 5000ndash4000 and 7500ndash5500 cm21 and 615 3 1023 L mole21 cm21 in the ranges 4000ndash3800 and 5500ndash5000 cm 21 Absolute 37 8C spectra are 60001 L mole21 cm21 in the ranges 5000ndash3800 and 7500ndash5500 cm 21 and 60005 Lmole21 cm21 in the range 5500ndash5000 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

3800 1292 26655 24800 22832 20937 1369 3593 59383840 1044 25379 23999 22529 20872 0839 2713 45703880 0931 24492 23303 22089 20699 0731 2281 38223920 0892 23672 22684 21670 20554 0596 1793 30163960 0860 22694 21941 21203 20369 0436 1313 21664000 0790 21825 21302 20799 20251 0277 0855 14244040 0682 21203 20855 20551 20173 0173 0552 09224080 0570 20824 20581 20372 20112 0118 0380 06414120 0478 20568 20396 20256 20077 0075 0259 04344160 0406 20380 20254 20167 20050 0048 0166 02884200 0347 20254 20163 20107 20029 0030 0113 01934280 0257 20171 20103 20072 20020 0017 0074 01304360 0198 20163 20094 20067 20018 0015 0069 01214440 0167 20104 20049 20036 20007 0006 0042 00734520 0155 20008 0025 0009 0008 20011 20009 200104600 0161 0131 0131 0076 0029 20034 20080 201284680 0183 0342 0290 0175 0061 20068 20187 203074760 0226 0655 0529 0325 0110 20121 20347 205744840 0295 1096 0861 0533 0178 20191 20565 209424920 0395 1616 1250 0774 0256 20272 20820 213725000 0549 1979 1527 0955 0320 20320 21013 217105080 0779 1906 1460 0925 0308 20277 20939 216845160 1015 0417 0557 0340 0121 0003 0006 203785200 1051 21791 21111 20623 20180 0411 1228 13425240 0966 23878 22604 21674 20442 0654 2000 29505260 0843 24004 22856 21779 20571 0636 2034 32075280 0645 23212 22297 21453 20466 0525 1607 26635300 0437 22133 21520 20968 20315 0340 1072 17965320 0286 21275 20884 20567 20181 0196 0638 10755360 0142 20473 20288 20190 20059 0063 0228 03915400 0096 20228 20107 20074 20020 0025 0106 01835480 0076 20082 0007 20003 0003 20003 0026 00505560 0074 0002 0073 0037 0018 20016 20016 200225640 0068 0096 0145 0080 0031 20034 20064 201045720 0056 0149 0186 0107 0040 20043 20092 201515800 0046 0184 0213 0124 0045 20048 20107 201745880 0042 0222 0241 0139 0051 20054 20125 202085960 0041 0252 0265 0154 0054 20059 20142 202336040 0042 0276 0281 0166 0059 20062 20152 202496120 0046 0300 0297 0177 0063 20065 20165 202716200 0050 0325 0314 0188 0066 20069 20175 202856280 0057 0358 0335 0199 0069 20073 20191 203176360 0068 0409 0370 0224 0076 20082 20218 203616440 0082 0487 0422 0258 0088 20092 20253 204216520 0103 0584 0491 0302 0102 20107 20304 205066600 0130 0682 0563 0350 0119 20121 20353 205896680 0166 0755 0613 0382 0128 20134 20394 206576760 0207 0716 0582 0364 0123 20127 20378 206356840 0244 0468 0400 0252 0088 20091 20270 204606920 0254 0075 0111 0071 0029 20029 20082 201517000 0249 20608 20400 20251 20078 0083 0259 04247080 0213 21069 20753 20469 20149 0161 0505 08447120 0175 20974 20684 20426 20137 0147 0460 07737160 0127 20714 20492 20306 20099 0103 0335 05627200 0083 20476 20318 20197 20063 0068 0223 03747240 0055 20320 20202 20125 20040 0042 0145 02467320 0032 20160 20085 20053 20017 0015 0060 01057400 0025 20097 20041 20024 20007 0005 0028 00527480 0018 20057 20013 20006 0000 20001 0009 00147500 0016 20050 20010 20003 0000 20003 0005 0008

This is illustrated by the insert in Fig 5 which showsthe second derivative absorption spectrum of aqueousglucose in the combination band 5000ndash4000 cm21 They-axis of this insert is not to scale Figure 5 shows that

quantitative in vivo spectroscopy will be very dif cult inthe vicinity of the stronger absorption bands Realistictemperature variations close to 37 8C have an enormousimpact on the appearance of the water spectrum leaving

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

30 Volume 57 Number 1 2003

FIG 1 Water molar absorptivity at 30 and 42 8C in the mid-infraredregion The transmission cell pathlength is 50 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C

FIG 2 Difference in water molar absorptivity with temperature around37 8C in the mid-infrared region The insertion shows the absorptionspectrum of glucose in the region 1500ndash950 cm21 (y-axis not to scale)

FIG 3 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the mid-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 1 and 2 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half of the level shown in this gure

pes in C17 A detailed description of the PCA method canbe found in the literature1819

RESULTS AND DISCUSSION

Pure Water Mid-infrared Region The absorption ofpure water in units of molar absorptivity measured at 30and 42 8C in the region 5000ndash950 cm21 is shown in Fig1 The strong fundamental OH stretch and bend bands ofwater centered at 3500 and 1600 cm21 are not resolvedIn the same plot our data are compared to the data givenby Bertie and Lan10 measured at 25 8C Their data agreewell with our measured data with the differences beinglargely systematic and following the trend indicated bythe shift from 30ndash42 8C in our data Given the differencein temperature and the fact that our data had been base-line corrected using Bertie and Lanrsquos data for the refrac-tive index of water at 25 8C we did not expect perfectagreement The accuracy of the pathlength setting of thetransmission cell may be estimated from this agreementwith the tabulated data of Bertie and Lan to be well with-in 2 mm Figure 2 shows the spectra obtained by sub-tracting the spectrum measured at 37 8C from the spectrameasured at 30 32 34 36 38 40 and 42 8C in the range3000ndash950 cm21 Data for the range 8000ndash3800 cm21 arepresented in a separate section to follow These differencespectra are given in units of molar absorptivity and areexpected to be more accurate than the absolute spectrapresented in Fig 1 since the correction for difference inFresnel transmission which is common to all the spectracancels in the subtraction The improved accuracy of thedifference spectra can be veri ed by the symmetry of thedifference spectra around the 37 8C reference and by thecoincidence of the isosbestic points in the spectrum

The noise level of the measurements may be estimatedfrom Fig 3 which shows the difference spectrum of 368C with 37 8C as reference and the subtraction of two 378C spectra These two difference spectra were obtainedfrom one of the four repeat measurements in the 36 8Cset and two of the repeat measurements in the 37 8C setThe spectra shown in Figs 1 and 2 are averages of foursuch repeat measurements and consequently the noiselevel in Figs 1 and 2 is half that shown in Fig 3 We

estimate the uncertainty to be less than 0006 L mole21

cm21 in the spectral region 3000ndash1000 cm21 (013 com-pared to the absolute value at 1200 cm21) It is observedby inspection of Fig 3 that the noise level in most partsof the spectrum is very small compared to the spectralchange caused by a change in temperature of 1 8C In theregion 1200ndash1000 cm21 the noise level and the changewith a temperature difference of 1 8C is comparable The37 8C absorption spectrum and the difference spectra with37 8C as reference are tabulated in Table I The variationsin water absorption with temperature are seen to be largeon the anks of the absorption bands and small in thelocal minima of the water absorption spectra It is clearthat these variations do not depend in a simple way onthe absolute value of the water absorption spectrum Theripple pattern most clearly visible between 2800 and2500 cm21 in the 30 8C difference spectrum is an artifactof the double re ection between the windows

APPLIED SPECTROSCOPY 31

TABLE I Mid-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 60005 L mole21 cm21 in the ranges 1580ndash960 and 2900ndash1700 cm21 and 6001 L mole21 cm21 in the ranges 960ndash950 and 3000ndash2900 cm21 Absolute 37 8C spectra are 6001 L mole21 cm21 in the ranges 1580ndash950 and 3000ndash1850 cm21 6004 L mole21 cm21 in the range1600ndash1580 cm21 and 6025 L mole21 cm21 in the range 1850ndash1700 cm21 Interpolation should be performed separately in the ranges 1600ndash950 and 3000ndash1700 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

960 6026 5562 4548 3306 1123 21698 24765 268841000 5061 20421 0286 0525 0279 21047 21818 225241040 4589 21556 20640 20135 0014 20453 20613 207921080 4368 22172 21057 20170 0110 20352 20580 202941120 4267 21724 20745 20253 20022 20493 20883 209381160 4272 20920 20397 20032 0105 20659 20911 213181200 4314 20181 0381 0544 0430 20622 21169 219221240 4379 0878 1151 0911 0407 20897 21851 227631280 4437 1836 1740 1396 0604 21036 22240 235201320 4485 3110 2763 1959 0819 21270 22939 245341360 4540 4665 3942 2637 1122 21501 23536 256151400 4619 6150 5038 3419 1366 21756 24358 269051440 4757 7493 6072 3972 1529 22160 25179 281751480 4998 8806 7020 4616 1778 22369 25729 290781520 5487 9113 7458 4931 1947 22651 26196 299911540 5969 8695 7340 4795 1830 22572 26097 296521560 6784 6470 5676 3854 1354 22457 25636 285161580 8330 1628 2195 2518 1424 22346 23218 245291600 11484 214393 29225 29421 23575 25385 22047 10081700 9315 11525 11446 6353 1225 26157 210935 2166231710 7432 11180 9599 6097 1966 23481 27995 2129711720 6012 9164 7639 4999 2151 22557 26190 2100081740 4217 5573 4593 3066 1194 21718 23988 263001760 3241 3712 3062 2027 0836 21128 22648 241301800 2369 1654 1405 1004 0437 20607 21362 220271840 2067 0043 0213 0289 0204 20352 20663 208991880 1988 20626 20433 20158 0017 20122 20089 00641920 2076 21872 21254 20635 20151 0072 0418 08961960 2300 23087 22133 21135 20329 0131 0697 13012000 2641 22280 21524 20774 20203 0019 0316 06702040 3010 20419 20017 0196 0179 20473 20927 214292080 3283 3658 3026 2076 0872 21174 22877 246022120 3380 7655 6065 3944 1572 21869 24763 276782160 3254 10315 7973 5061 1995 22297 25856 294512200 2971 10547 8143 5139 1978 22293 25865 294442240 2627 9720 7449 4712 1855 22107 25377 286662280 2297 8677 6664 4233 1662 21847 24764 276442320 2001 7563 5763 3677 1464 21649 24206 267222360 1746 6983 5246 3381 1357 21491 23851 260462400 1541 5893 4501 2878 1157 21284 23286 252202440 1364 5543 4174 2662 1060 21164 22973 247322480 1215 4628 3575 2330 0941 21048 22655 242002520 1087 4103 3047 1948 0789 20853 22188 234372560 0996 3311 2536 1660 0679 20718 21850 228772600 0944 2117 1661 1152 0515 20631 21502 223212640 0948 2223 1590 1044 0441 20469 21198 218192680 1024 1644 1337 0940 0420 20453 21148 217472720 1167 1188 1018 0782 0389 20537 21213 218832760 1405 1903 1463 1022 0473 20542 21357 221102800 1781 2556 2051 1401 0613 20721 21820 228842840 2345 3698 3036 2067 0883 21121 22772 244842880 3178 6363 5120 3369 1405 21728 24368 271222920 4426 11161 8683 5640 2226 22856 27053 2116042960 6242 18889 14913 9305 3656 24510 211303 2189033000 8957 30558 23785 13195 5239 28559 219045 233430

Inspection of the difference spectra reveals that the re-gion 1200ndash1000 cm21 and the region 2800ndash2500 cm21

appear to be better suited to measurement of trace com-ponent signals These two regions show only slightbroad-band variation of the water absorption with tem-perature The rst region changes little with temperature(less than 003 L mole21 cm21 across the 12 8C temper-

ature difference) It is also known to contain glucose sig-nals from the pyranose ring vibrations The insert in Fig2 illustrates the position of the glucose absorption bands(y-axis not to scale)

Near-Infrared Region The absorption of pure waterin units of molar absorptivity measured at 30 and 42 8Cin the spectral range 8000ndash3800 cm21 is shown in Fig

32 Volume 57 Number 1 2003

FIG 4 Water molar absorptivity at 30 and 42 8C in the near-infraredregion The transmission cell pathlength is 04 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C andPalmer and Williams20 measured at 27 8C

FIG 5 Difference in water molar absorptivity with temperature around37 8C in the near-infrared region The insertion shows the second de-rivative absorption spectrum of glucose in the region 4800ndash4200 cm21

(y-axis not to scale)

FIG 6 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the near-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 4 and 5 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half the level shown in this gure

4 In the same plot our data are compared to data mea-sured and tabulated by other groups2010 It should be not-ed that the data of the other groups were obtained atlower temperatures (25 and 27 8C) Good agreement ex-ists in the major part of the spectrum with only minordiscrepancies being observed around the combinationband at 5160 cm21 as previously noted by Bertie andLan10 As in the mid-infrared region our spectra weremeasured at a higher temperature and baseline correctedfor the difference in Fresnel transmission using tabulateddata on the refractive index of water at 25 8C We thusdid not expect perfect agreement

Figure 5 displays the spectra obtained by subtractingthe water spectrum measured at 37 8C from the spectrameasured at temperatures 30 32 34 36 38 40 and 428C These difference spectra are given in units of molarabsorptivity Again these difference spectra were ex-pected to be more accurate than the absolute spectraTheir accuracy can be veri ed from the symmetry of thedifference spectra around the 37 8C reference in Fig 5

The noise level may be estimated from Fig 6 whichshows the difference spectrum of 36 8C with 37 8C asreference and the subtraction of two 37 8C spectra Thesetwo spectra were obtained from one of the four repeatmeasurements at 36 8C and two of the repeat measure-ments at 37 8C The spectra shown in Figs 4 and 5 areaverages of four such repeat measurements and conse-quently the noise level is twice as low The uncertaintyof these difference spectra is less than 7 3 1024 L mole21

cm21 (03 compared to the absolute value at 4500cm21) Again it is observed that the noise level is wellbelow the change in the spectrum induced by a changein temperature of 1 8C In the mid-infrared region wefound a 013 uncertainty relative to the signal strengthwhich is twice as good This nding may indicate thatthe mid-infrared region is better suited to measurementof trace organic components in samples where a smalldepth of penetration gives access to the signal from thetrace component of interest

The 37 8C absorption spectrum and the differencespectra with 37 8C as reference are tabulated in Table II

The variations in the water absorption due to temperatureare observed to be of a broad-band nature The changesare obviously highest in the vicinity of the absorptionbands with a number of isosbestic points with no tem-perature dependence and relatively at plateaus in be-tween The isosbestic points occur close to the points inthe spectrum where the water bands peak or are at a min-imum Spectral regions such as 4500ndash4200 and 6500ndash5500 cm21 show a small and almost at dependency ontemperature This explains the success of the ltering ap-proach used by Hazen Arnold and Small1521 to removebaseline variations caused by changes in temperature

Glucose has spectral features from overtone and com-bination bands in the regions mentioned above If glucoseis present in the solution its signal will be superposedon a nearly at baseline The glucose signals which con-tain narrow bands may easily be separated from thebroad-band variation of water using a high-pass lter

APPLIED SPECTROSCOPY 33

TABLE II Near-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 610 3 1024 L mole21 cm21 in the ranges 5000ndash4000 and 7500ndash5500 cm21 and 615 3 1023 L mole21 cm21 in the ranges 4000ndash3800 and 5500ndash5000 cm 21 Absolute 37 8C spectra are 60001 L mole21 cm21 in the ranges 5000ndash3800 and 7500ndash5500 cm 21 and 60005 Lmole21 cm21 in the range 5500ndash5000 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

3800 1292 26655 24800 22832 20937 1369 3593 59383840 1044 25379 23999 22529 20872 0839 2713 45703880 0931 24492 23303 22089 20699 0731 2281 38223920 0892 23672 22684 21670 20554 0596 1793 30163960 0860 22694 21941 21203 20369 0436 1313 21664000 0790 21825 21302 20799 20251 0277 0855 14244040 0682 21203 20855 20551 20173 0173 0552 09224080 0570 20824 20581 20372 20112 0118 0380 06414120 0478 20568 20396 20256 20077 0075 0259 04344160 0406 20380 20254 20167 20050 0048 0166 02884200 0347 20254 20163 20107 20029 0030 0113 01934280 0257 20171 20103 20072 20020 0017 0074 01304360 0198 20163 20094 20067 20018 0015 0069 01214440 0167 20104 20049 20036 20007 0006 0042 00734520 0155 20008 0025 0009 0008 20011 20009 200104600 0161 0131 0131 0076 0029 20034 20080 201284680 0183 0342 0290 0175 0061 20068 20187 203074760 0226 0655 0529 0325 0110 20121 20347 205744840 0295 1096 0861 0533 0178 20191 20565 209424920 0395 1616 1250 0774 0256 20272 20820 213725000 0549 1979 1527 0955 0320 20320 21013 217105080 0779 1906 1460 0925 0308 20277 20939 216845160 1015 0417 0557 0340 0121 0003 0006 203785200 1051 21791 21111 20623 20180 0411 1228 13425240 0966 23878 22604 21674 20442 0654 2000 29505260 0843 24004 22856 21779 20571 0636 2034 32075280 0645 23212 22297 21453 20466 0525 1607 26635300 0437 22133 21520 20968 20315 0340 1072 17965320 0286 21275 20884 20567 20181 0196 0638 10755360 0142 20473 20288 20190 20059 0063 0228 03915400 0096 20228 20107 20074 20020 0025 0106 01835480 0076 20082 0007 20003 0003 20003 0026 00505560 0074 0002 0073 0037 0018 20016 20016 200225640 0068 0096 0145 0080 0031 20034 20064 201045720 0056 0149 0186 0107 0040 20043 20092 201515800 0046 0184 0213 0124 0045 20048 20107 201745880 0042 0222 0241 0139 0051 20054 20125 202085960 0041 0252 0265 0154 0054 20059 20142 202336040 0042 0276 0281 0166 0059 20062 20152 202496120 0046 0300 0297 0177 0063 20065 20165 202716200 0050 0325 0314 0188 0066 20069 20175 202856280 0057 0358 0335 0199 0069 20073 20191 203176360 0068 0409 0370 0224 0076 20082 20218 203616440 0082 0487 0422 0258 0088 20092 20253 204216520 0103 0584 0491 0302 0102 20107 20304 205066600 0130 0682 0563 0350 0119 20121 20353 205896680 0166 0755 0613 0382 0128 20134 20394 206576760 0207 0716 0582 0364 0123 20127 20378 206356840 0244 0468 0400 0252 0088 20091 20270 204606920 0254 0075 0111 0071 0029 20029 20082 201517000 0249 20608 20400 20251 20078 0083 0259 04247080 0213 21069 20753 20469 20149 0161 0505 08447120 0175 20974 20684 20426 20137 0147 0460 07737160 0127 20714 20492 20306 20099 0103 0335 05627200 0083 20476 20318 20197 20063 0068 0223 03747240 0055 20320 20202 20125 20040 0042 0145 02467320 0032 20160 20085 20053 20017 0015 0060 01057400 0025 20097 20041 20024 20007 0005 0028 00527480 0018 20057 20013 20006 0000 20001 0009 00147500 0016 20050 20010 20003 0000 20003 0005 0008

This is illustrated by the insert in Fig 5 which showsthe second derivative absorption spectrum of aqueousglucose in the combination band 5000ndash4000 cm21 They-axis of this insert is not to scale Figure 5 shows that

quantitative in vivo spectroscopy will be very dif cult inthe vicinity of the stronger absorption bands Realistictemperature variations close to 37 8C have an enormousimpact on the appearance of the water spectrum leaving

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

APPLIED SPECTROSCOPY 31

TABLE I Mid-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 60005 L mole21 cm21 in the ranges 1580ndash960 and 2900ndash1700 cm21 and 6001 L mole21 cm21 in the ranges 960ndash950 and 3000ndash2900 cm21 Absolute 37 8C spectra are 6001 L mole21 cm21 in the ranges 1580ndash950 and 3000ndash1850 cm21 6004 L mole21 cm21 in the range1600ndash1580 cm21 and 6025 L mole21 cm21 in the range 1850ndash1700 cm21 Interpolation should be performed separately in the ranges 1600ndash950 and 3000ndash1700 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

960 6026 5562 4548 3306 1123 21698 24765 268841000 5061 20421 0286 0525 0279 21047 21818 225241040 4589 21556 20640 20135 0014 20453 20613 207921080 4368 22172 21057 20170 0110 20352 20580 202941120 4267 21724 20745 20253 20022 20493 20883 209381160 4272 20920 20397 20032 0105 20659 20911 213181200 4314 20181 0381 0544 0430 20622 21169 219221240 4379 0878 1151 0911 0407 20897 21851 227631280 4437 1836 1740 1396 0604 21036 22240 235201320 4485 3110 2763 1959 0819 21270 22939 245341360 4540 4665 3942 2637 1122 21501 23536 256151400 4619 6150 5038 3419 1366 21756 24358 269051440 4757 7493 6072 3972 1529 22160 25179 281751480 4998 8806 7020 4616 1778 22369 25729 290781520 5487 9113 7458 4931 1947 22651 26196 299911540 5969 8695 7340 4795 1830 22572 26097 296521560 6784 6470 5676 3854 1354 22457 25636 285161580 8330 1628 2195 2518 1424 22346 23218 245291600 11484 214393 29225 29421 23575 25385 22047 10081700 9315 11525 11446 6353 1225 26157 210935 2166231710 7432 11180 9599 6097 1966 23481 27995 2129711720 6012 9164 7639 4999 2151 22557 26190 2100081740 4217 5573 4593 3066 1194 21718 23988 263001760 3241 3712 3062 2027 0836 21128 22648 241301800 2369 1654 1405 1004 0437 20607 21362 220271840 2067 0043 0213 0289 0204 20352 20663 208991880 1988 20626 20433 20158 0017 20122 20089 00641920 2076 21872 21254 20635 20151 0072 0418 08961960 2300 23087 22133 21135 20329 0131 0697 13012000 2641 22280 21524 20774 20203 0019 0316 06702040 3010 20419 20017 0196 0179 20473 20927 214292080 3283 3658 3026 2076 0872 21174 22877 246022120 3380 7655 6065 3944 1572 21869 24763 276782160 3254 10315 7973 5061 1995 22297 25856 294512200 2971 10547 8143 5139 1978 22293 25865 294442240 2627 9720 7449 4712 1855 22107 25377 286662280 2297 8677 6664 4233 1662 21847 24764 276442320 2001 7563 5763 3677 1464 21649 24206 267222360 1746 6983 5246 3381 1357 21491 23851 260462400 1541 5893 4501 2878 1157 21284 23286 252202440 1364 5543 4174 2662 1060 21164 22973 247322480 1215 4628 3575 2330 0941 21048 22655 242002520 1087 4103 3047 1948 0789 20853 22188 234372560 0996 3311 2536 1660 0679 20718 21850 228772600 0944 2117 1661 1152 0515 20631 21502 223212640 0948 2223 1590 1044 0441 20469 21198 218192680 1024 1644 1337 0940 0420 20453 21148 217472720 1167 1188 1018 0782 0389 20537 21213 218832760 1405 1903 1463 1022 0473 20542 21357 221102800 1781 2556 2051 1401 0613 20721 21820 228842840 2345 3698 3036 2067 0883 21121 22772 244842880 3178 6363 5120 3369 1405 21728 24368 271222920 4426 11161 8683 5640 2226 22856 27053 2116042960 6242 18889 14913 9305 3656 24510 211303 2189033000 8957 30558 23785 13195 5239 28559 219045 233430

Inspection of the difference spectra reveals that the re-gion 1200ndash1000 cm21 and the region 2800ndash2500 cm21

appear to be better suited to measurement of trace com-ponent signals These two regions show only slightbroad-band variation of the water absorption with tem-perature The rst region changes little with temperature(less than 003 L mole21 cm21 across the 12 8C temper-

ature difference) It is also known to contain glucose sig-nals from the pyranose ring vibrations The insert in Fig2 illustrates the position of the glucose absorption bands(y-axis not to scale)

Near-Infrared Region The absorption of pure waterin units of molar absorptivity measured at 30 and 42 8Cin the spectral range 8000ndash3800 cm21 is shown in Fig

32 Volume 57 Number 1 2003

FIG 4 Water molar absorptivity at 30 and 42 8C in the near-infraredregion The transmission cell pathlength is 04 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C andPalmer and Williams20 measured at 27 8C

FIG 5 Difference in water molar absorptivity with temperature around37 8C in the near-infrared region The insertion shows the second de-rivative absorption spectrum of glucose in the region 4800ndash4200 cm21

(y-axis not to scale)

FIG 6 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the near-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 4 and 5 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half the level shown in this gure

4 In the same plot our data are compared to data mea-sured and tabulated by other groups2010 It should be not-ed that the data of the other groups were obtained atlower temperatures (25 and 27 8C) Good agreement ex-ists in the major part of the spectrum with only minordiscrepancies being observed around the combinationband at 5160 cm21 as previously noted by Bertie andLan10 As in the mid-infrared region our spectra weremeasured at a higher temperature and baseline correctedfor the difference in Fresnel transmission using tabulateddata on the refractive index of water at 25 8C We thusdid not expect perfect agreement

Figure 5 displays the spectra obtained by subtractingthe water spectrum measured at 37 8C from the spectrameasured at temperatures 30 32 34 36 38 40 and 428C These difference spectra are given in units of molarabsorptivity Again these difference spectra were ex-pected to be more accurate than the absolute spectraTheir accuracy can be veri ed from the symmetry of thedifference spectra around the 37 8C reference in Fig 5

The noise level may be estimated from Fig 6 whichshows the difference spectrum of 36 8C with 37 8C asreference and the subtraction of two 37 8C spectra Thesetwo spectra were obtained from one of the four repeatmeasurements at 36 8C and two of the repeat measure-ments at 37 8C The spectra shown in Figs 4 and 5 areaverages of four such repeat measurements and conse-quently the noise level is twice as low The uncertaintyof these difference spectra is less than 7 3 1024 L mole21

cm21 (03 compared to the absolute value at 4500cm21) Again it is observed that the noise level is wellbelow the change in the spectrum induced by a changein temperature of 1 8C In the mid-infrared region wefound a 013 uncertainty relative to the signal strengthwhich is twice as good This nding may indicate thatthe mid-infrared region is better suited to measurementof trace organic components in samples where a smalldepth of penetration gives access to the signal from thetrace component of interest

The 37 8C absorption spectrum and the differencespectra with 37 8C as reference are tabulated in Table II

The variations in the water absorption due to temperatureare observed to be of a broad-band nature The changesare obviously highest in the vicinity of the absorptionbands with a number of isosbestic points with no tem-perature dependence and relatively at plateaus in be-tween The isosbestic points occur close to the points inthe spectrum where the water bands peak or are at a min-imum Spectral regions such as 4500ndash4200 and 6500ndash5500 cm21 show a small and almost at dependency ontemperature This explains the success of the ltering ap-proach used by Hazen Arnold and Small1521 to removebaseline variations caused by changes in temperature

Glucose has spectral features from overtone and com-bination bands in the regions mentioned above If glucoseis present in the solution its signal will be superposedon a nearly at baseline The glucose signals which con-tain narrow bands may easily be separated from thebroad-band variation of water using a high-pass lter

APPLIED SPECTROSCOPY 33

TABLE II Near-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 610 3 1024 L mole21 cm21 in the ranges 5000ndash4000 and 7500ndash5500 cm21 and 615 3 1023 L mole21 cm21 in the ranges 4000ndash3800 and 5500ndash5000 cm 21 Absolute 37 8C spectra are 60001 L mole21 cm21 in the ranges 5000ndash3800 and 7500ndash5500 cm 21 and 60005 Lmole21 cm21 in the range 5500ndash5000 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

3800 1292 26655 24800 22832 20937 1369 3593 59383840 1044 25379 23999 22529 20872 0839 2713 45703880 0931 24492 23303 22089 20699 0731 2281 38223920 0892 23672 22684 21670 20554 0596 1793 30163960 0860 22694 21941 21203 20369 0436 1313 21664000 0790 21825 21302 20799 20251 0277 0855 14244040 0682 21203 20855 20551 20173 0173 0552 09224080 0570 20824 20581 20372 20112 0118 0380 06414120 0478 20568 20396 20256 20077 0075 0259 04344160 0406 20380 20254 20167 20050 0048 0166 02884200 0347 20254 20163 20107 20029 0030 0113 01934280 0257 20171 20103 20072 20020 0017 0074 01304360 0198 20163 20094 20067 20018 0015 0069 01214440 0167 20104 20049 20036 20007 0006 0042 00734520 0155 20008 0025 0009 0008 20011 20009 200104600 0161 0131 0131 0076 0029 20034 20080 201284680 0183 0342 0290 0175 0061 20068 20187 203074760 0226 0655 0529 0325 0110 20121 20347 205744840 0295 1096 0861 0533 0178 20191 20565 209424920 0395 1616 1250 0774 0256 20272 20820 213725000 0549 1979 1527 0955 0320 20320 21013 217105080 0779 1906 1460 0925 0308 20277 20939 216845160 1015 0417 0557 0340 0121 0003 0006 203785200 1051 21791 21111 20623 20180 0411 1228 13425240 0966 23878 22604 21674 20442 0654 2000 29505260 0843 24004 22856 21779 20571 0636 2034 32075280 0645 23212 22297 21453 20466 0525 1607 26635300 0437 22133 21520 20968 20315 0340 1072 17965320 0286 21275 20884 20567 20181 0196 0638 10755360 0142 20473 20288 20190 20059 0063 0228 03915400 0096 20228 20107 20074 20020 0025 0106 01835480 0076 20082 0007 20003 0003 20003 0026 00505560 0074 0002 0073 0037 0018 20016 20016 200225640 0068 0096 0145 0080 0031 20034 20064 201045720 0056 0149 0186 0107 0040 20043 20092 201515800 0046 0184 0213 0124 0045 20048 20107 201745880 0042 0222 0241 0139 0051 20054 20125 202085960 0041 0252 0265 0154 0054 20059 20142 202336040 0042 0276 0281 0166 0059 20062 20152 202496120 0046 0300 0297 0177 0063 20065 20165 202716200 0050 0325 0314 0188 0066 20069 20175 202856280 0057 0358 0335 0199 0069 20073 20191 203176360 0068 0409 0370 0224 0076 20082 20218 203616440 0082 0487 0422 0258 0088 20092 20253 204216520 0103 0584 0491 0302 0102 20107 20304 205066600 0130 0682 0563 0350 0119 20121 20353 205896680 0166 0755 0613 0382 0128 20134 20394 206576760 0207 0716 0582 0364 0123 20127 20378 206356840 0244 0468 0400 0252 0088 20091 20270 204606920 0254 0075 0111 0071 0029 20029 20082 201517000 0249 20608 20400 20251 20078 0083 0259 04247080 0213 21069 20753 20469 20149 0161 0505 08447120 0175 20974 20684 20426 20137 0147 0460 07737160 0127 20714 20492 20306 20099 0103 0335 05627200 0083 20476 20318 20197 20063 0068 0223 03747240 0055 20320 20202 20125 20040 0042 0145 02467320 0032 20160 20085 20053 20017 0015 0060 01057400 0025 20097 20041 20024 20007 0005 0028 00527480 0018 20057 20013 20006 0000 20001 0009 00147500 0016 20050 20010 20003 0000 20003 0005 0008

This is illustrated by the insert in Fig 5 which showsthe second derivative absorption spectrum of aqueousglucose in the combination band 5000ndash4000 cm21 They-axis of this insert is not to scale Figure 5 shows that

quantitative in vivo spectroscopy will be very dif cult inthe vicinity of the stronger absorption bands Realistictemperature variations close to 37 8C have an enormousimpact on the appearance of the water spectrum leaving

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

32 Volume 57 Number 1 2003

FIG 4 Water molar absorptivity at 30 and 42 8C in the near-infraredregion The transmission cell pathlength is 04 mm Measurements com-pared with data taken from Bertie and Lan10 measured at 25 8C andPalmer and Williams20 measured at 27 8C

FIG 5 Difference in water molar absorptivity with temperature around37 8C in the near-infrared region The insertion shows the second de-rivative absorption spectrum of glucose in the region 4800ndash4200 cm21

(y-axis not to scale)

FIG 6 Difference in water molar absorptivity of 1 8C compared tothat of water at 37 8C in the near-infrared region Also shown is thedifference between two repeat measurements of the same sample toillustrate the noise level of the measurement Figures 4 and 5 containdata that are an average of four such repeat measurements Accordinglythe noise level of those averaged data is half the level shown in this gure

4 In the same plot our data are compared to data mea-sured and tabulated by other groups2010 It should be not-ed that the data of the other groups were obtained atlower temperatures (25 and 27 8C) Good agreement ex-ists in the major part of the spectrum with only minordiscrepancies being observed around the combinationband at 5160 cm21 as previously noted by Bertie andLan10 As in the mid-infrared region our spectra weremeasured at a higher temperature and baseline correctedfor the difference in Fresnel transmission using tabulateddata on the refractive index of water at 25 8C We thusdid not expect perfect agreement

Figure 5 displays the spectra obtained by subtractingthe water spectrum measured at 37 8C from the spectrameasured at temperatures 30 32 34 36 38 40 and 428C These difference spectra are given in units of molarabsorptivity Again these difference spectra were ex-pected to be more accurate than the absolute spectraTheir accuracy can be veri ed from the symmetry of thedifference spectra around the 37 8C reference in Fig 5

The noise level may be estimated from Fig 6 whichshows the difference spectrum of 36 8C with 37 8C asreference and the subtraction of two 37 8C spectra Thesetwo spectra were obtained from one of the four repeatmeasurements at 36 8C and two of the repeat measure-ments at 37 8C The spectra shown in Figs 4 and 5 areaverages of four such repeat measurements and conse-quently the noise level is twice as low The uncertaintyof these difference spectra is less than 7 3 1024 L mole21

cm21 (03 compared to the absolute value at 4500cm21) Again it is observed that the noise level is wellbelow the change in the spectrum induced by a changein temperature of 1 8C In the mid-infrared region wefound a 013 uncertainty relative to the signal strengthwhich is twice as good This nding may indicate thatthe mid-infrared region is better suited to measurementof trace organic components in samples where a smalldepth of penetration gives access to the signal from thetrace component of interest

The 37 8C absorption spectrum and the differencespectra with 37 8C as reference are tabulated in Table II

The variations in the water absorption due to temperatureare observed to be of a broad-band nature The changesare obviously highest in the vicinity of the absorptionbands with a number of isosbestic points with no tem-perature dependence and relatively at plateaus in be-tween The isosbestic points occur close to the points inthe spectrum where the water bands peak or are at a min-imum Spectral regions such as 4500ndash4200 and 6500ndash5500 cm21 show a small and almost at dependency ontemperature This explains the success of the ltering ap-proach used by Hazen Arnold and Small1521 to removebaseline variations caused by changes in temperature

Glucose has spectral features from overtone and com-bination bands in the regions mentioned above If glucoseis present in the solution its signal will be superposedon a nearly at baseline The glucose signals which con-tain narrow bands may easily be separated from thebroad-band variation of water using a high-pass lter

APPLIED SPECTROSCOPY 33

TABLE II Near-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 610 3 1024 L mole21 cm21 in the ranges 5000ndash4000 and 7500ndash5500 cm21 and 615 3 1023 L mole21 cm21 in the ranges 4000ndash3800 and 5500ndash5000 cm 21 Absolute 37 8C spectra are 60001 L mole21 cm21 in the ranges 5000ndash3800 and 7500ndash5500 cm 21 and 60005 Lmole21 cm21 in the range 5500ndash5000 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

3800 1292 26655 24800 22832 20937 1369 3593 59383840 1044 25379 23999 22529 20872 0839 2713 45703880 0931 24492 23303 22089 20699 0731 2281 38223920 0892 23672 22684 21670 20554 0596 1793 30163960 0860 22694 21941 21203 20369 0436 1313 21664000 0790 21825 21302 20799 20251 0277 0855 14244040 0682 21203 20855 20551 20173 0173 0552 09224080 0570 20824 20581 20372 20112 0118 0380 06414120 0478 20568 20396 20256 20077 0075 0259 04344160 0406 20380 20254 20167 20050 0048 0166 02884200 0347 20254 20163 20107 20029 0030 0113 01934280 0257 20171 20103 20072 20020 0017 0074 01304360 0198 20163 20094 20067 20018 0015 0069 01214440 0167 20104 20049 20036 20007 0006 0042 00734520 0155 20008 0025 0009 0008 20011 20009 200104600 0161 0131 0131 0076 0029 20034 20080 201284680 0183 0342 0290 0175 0061 20068 20187 203074760 0226 0655 0529 0325 0110 20121 20347 205744840 0295 1096 0861 0533 0178 20191 20565 209424920 0395 1616 1250 0774 0256 20272 20820 213725000 0549 1979 1527 0955 0320 20320 21013 217105080 0779 1906 1460 0925 0308 20277 20939 216845160 1015 0417 0557 0340 0121 0003 0006 203785200 1051 21791 21111 20623 20180 0411 1228 13425240 0966 23878 22604 21674 20442 0654 2000 29505260 0843 24004 22856 21779 20571 0636 2034 32075280 0645 23212 22297 21453 20466 0525 1607 26635300 0437 22133 21520 20968 20315 0340 1072 17965320 0286 21275 20884 20567 20181 0196 0638 10755360 0142 20473 20288 20190 20059 0063 0228 03915400 0096 20228 20107 20074 20020 0025 0106 01835480 0076 20082 0007 20003 0003 20003 0026 00505560 0074 0002 0073 0037 0018 20016 20016 200225640 0068 0096 0145 0080 0031 20034 20064 201045720 0056 0149 0186 0107 0040 20043 20092 201515800 0046 0184 0213 0124 0045 20048 20107 201745880 0042 0222 0241 0139 0051 20054 20125 202085960 0041 0252 0265 0154 0054 20059 20142 202336040 0042 0276 0281 0166 0059 20062 20152 202496120 0046 0300 0297 0177 0063 20065 20165 202716200 0050 0325 0314 0188 0066 20069 20175 202856280 0057 0358 0335 0199 0069 20073 20191 203176360 0068 0409 0370 0224 0076 20082 20218 203616440 0082 0487 0422 0258 0088 20092 20253 204216520 0103 0584 0491 0302 0102 20107 20304 205066600 0130 0682 0563 0350 0119 20121 20353 205896680 0166 0755 0613 0382 0128 20134 20394 206576760 0207 0716 0582 0364 0123 20127 20378 206356840 0244 0468 0400 0252 0088 20091 20270 204606920 0254 0075 0111 0071 0029 20029 20082 201517000 0249 20608 20400 20251 20078 0083 0259 04247080 0213 21069 20753 20469 20149 0161 0505 08447120 0175 20974 20684 20426 20137 0147 0460 07737160 0127 20714 20492 20306 20099 0103 0335 05627200 0083 20476 20318 20197 20063 0068 0223 03747240 0055 20320 20202 20125 20040 0042 0145 02467320 0032 20160 20085 20053 20017 0015 0060 01057400 0025 20097 20041 20024 20007 0005 0028 00527480 0018 20057 20013 20006 0000 20001 0009 00147500 0016 20050 20010 20003 0000 20003 0005 0008

This is illustrated by the insert in Fig 5 which showsthe second derivative absorption spectrum of aqueousglucose in the combination band 5000ndash4000 cm21 They-axis of this insert is not to scale Figure 5 shows that

quantitative in vivo spectroscopy will be very dif cult inthe vicinity of the stronger absorption bands Realistictemperature variations close to 37 8C have an enormousimpact on the appearance of the water spectrum leaving

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

APPLIED SPECTROSCOPY 33

TABLE II Near-infrared molar absorptivity of pure water at 37 8C and pure water difference spectra of 30ndash42 8C with 37 8C pure wateras reference The original spectra may be recovered by four-point polynomial interpolation with the following uncertainties Differencespectra are 610 3 1024 L mole21 cm21 in the ranges 5000ndash4000 and 7500ndash5500 cm21 and 615 3 1023 L mole21 cm21 in the ranges 4000ndash3800 and 5500ndash5000 cm 21 Absolute 37 8C spectra are 60001 L mole21 cm21 in the ranges 5000ndash3800 and 7500ndash5500 cm 21 and 60005 Lmole21 cm21 in the range 5500ndash5000 cm21

ncm21

37 8CL

mole cm

D30 8C001 L

mole cm

D32 8C001 L

mole cm

D34 8C001 L

mole cm

D36 8C001 L

mole cm

D38 8C001 L

mole cm

D40 8C001 L

mole cm

D42 8C001 L

mole cm

3800 1292 26655 24800 22832 20937 1369 3593 59383840 1044 25379 23999 22529 20872 0839 2713 45703880 0931 24492 23303 22089 20699 0731 2281 38223920 0892 23672 22684 21670 20554 0596 1793 30163960 0860 22694 21941 21203 20369 0436 1313 21664000 0790 21825 21302 20799 20251 0277 0855 14244040 0682 21203 20855 20551 20173 0173 0552 09224080 0570 20824 20581 20372 20112 0118 0380 06414120 0478 20568 20396 20256 20077 0075 0259 04344160 0406 20380 20254 20167 20050 0048 0166 02884200 0347 20254 20163 20107 20029 0030 0113 01934280 0257 20171 20103 20072 20020 0017 0074 01304360 0198 20163 20094 20067 20018 0015 0069 01214440 0167 20104 20049 20036 20007 0006 0042 00734520 0155 20008 0025 0009 0008 20011 20009 200104600 0161 0131 0131 0076 0029 20034 20080 201284680 0183 0342 0290 0175 0061 20068 20187 203074760 0226 0655 0529 0325 0110 20121 20347 205744840 0295 1096 0861 0533 0178 20191 20565 209424920 0395 1616 1250 0774 0256 20272 20820 213725000 0549 1979 1527 0955 0320 20320 21013 217105080 0779 1906 1460 0925 0308 20277 20939 216845160 1015 0417 0557 0340 0121 0003 0006 203785200 1051 21791 21111 20623 20180 0411 1228 13425240 0966 23878 22604 21674 20442 0654 2000 29505260 0843 24004 22856 21779 20571 0636 2034 32075280 0645 23212 22297 21453 20466 0525 1607 26635300 0437 22133 21520 20968 20315 0340 1072 17965320 0286 21275 20884 20567 20181 0196 0638 10755360 0142 20473 20288 20190 20059 0063 0228 03915400 0096 20228 20107 20074 20020 0025 0106 01835480 0076 20082 0007 20003 0003 20003 0026 00505560 0074 0002 0073 0037 0018 20016 20016 200225640 0068 0096 0145 0080 0031 20034 20064 201045720 0056 0149 0186 0107 0040 20043 20092 201515800 0046 0184 0213 0124 0045 20048 20107 201745880 0042 0222 0241 0139 0051 20054 20125 202085960 0041 0252 0265 0154 0054 20059 20142 202336040 0042 0276 0281 0166 0059 20062 20152 202496120 0046 0300 0297 0177 0063 20065 20165 202716200 0050 0325 0314 0188 0066 20069 20175 202856280 0057 0358 0335 0199 0069 20073 20191 203176360 0068 0409 0370 0224 0076 20082 20218 203616440 0082 0487 0422 0258 0088 20092 20253 204216520 0103 0584 0491 0302 0102 20107 20304 205066600 0130 0682 0563 0350 0119 20121 20353 205896680 0166 0755 0613 0382 0128 20134 20394 206576760 0207 0716 0582 0364 0123 20127 20378 206356840 0244 0468 0400 0252 0088 20091 20270 204606920 0254 0075 0111 0071 0029 20029 20082 201517000 0249 20608 20400 20251 20078 0083 0259 04247080 0213 21069 20753 20469 20149 0161 0505 08447120 0175 20974 20684 20426 20137 0147 0460 07737160 0127 20714 20492 20306 20099 0103 0335 05627200 0083 20476 20318 20197 20063 0068 0223 03747240 0055 20320 20202 20125 20040 0042 0145 02467320 0032 20160 20085 20053 20017 0015 0060 01057400 0025 20097 20041 20024 20007 0005 0028 00527480 0018 20057 20013 20006 0000 20001 0009 00147500 0016 20050 20010 20003 0000 20003 0005 0008

This is illustrated by the insert in Fig 5 which showsthe second derivative absorption spectrum of aqueousglucose in the combination band 5000ndash4000 cm21 They-axis of this insert is not to scale Figure 5 shows that

quantitative in vivo spectroscopy will be very dif cult inthe vicinity of the stronger absorption bands Realistictemperature variations close to 37 8C have an enormousimpact on the appearance of the water spectrum leaving

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

34 Volume 57 Number 1 2003

FIG 7 Mid-infrared absorption spectrum of aqueous glucose at 1 gdL concentration 50 mm pathlength at temperatures 42 37 and 30 8C

FIG 8 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of 1 gdL glucose solution

only a few spectral windows open for quantitative anal-ysis The compounds of biomedical interest must havespectral features in these windows in order to be mea-sured quantitatively as well as qualitatively

Aqueous Solutions of Glucose As mentioned in theintroduction glucose measurement is important for thecontrol and regulation of blood glucose concentrationThe direct effect of temperature on the glucose spectrumand the indirect effect of change in the underlying waterspectrum were estimated for temperatures varying around37 8C A solution of 1 gdL which is a factor of tenhigher than the concentrations found in blood and bodyliquids was used to obtain a level of absorption wellabove the noise level The various effects of temperaturecould then be extracted and estimated The estimated ef-fects were then scaled down by a factor of 10 to representthe glucose concentration of 100 mgdL expected in body uids

Mid-infrared Region The relatively weak glucosespectral features from the vibrations in the pyranose ringfall in the spectral range 1500ndash980 cm21 This is shownin Fig 7 which shows the absorbance spectrum of 1 gdL aqueous glucose at 30 37 and 42 8C with the waterabsorption spectrum measured at the same pathlength andtemperature subtracted It is well known and can also beseen in Fig 2 that this spectral range is found betweenthe fundamental band 2 (1643 cm21) and the librationnband L (800ndash500 cm21) of water Figures 1 and 2 alsonclearly show that due to its high molarity and number ofbroad absorption bands water absorbs everywhere in thespectrum The absorbance of water at a pathlength of 50mm can vary from 0 to 6004 (relative to 37 8C) in the1500ndash980 cm21 spectral range within the temperaturerange studied here These absorbance values are foundby multiplying the data in Fig 2 by the pathlength andmolarity of water The glucose spectrum between 1100and 1000 cm21 has the highest absorbance values (0003ndash0009 scaled to 100 mgdL see Fig 7)

The insert in Fig 2 shows that in this spectral regionthe in uence of temperature on the water spectrum is ata minimum (60002 au as temperature is varied from30 to 42 8C) making it ideal for determining glucoseconcentration However the part of the glucose spectrum

in the region 1200ndash1500 cm21 has only weak features(absorbance values less than 0002) Calculations basedon the data displayed in Fig 2 show that the change inabsorbance of water in this region is between 001 and004 Consequently it seems likely that it will be dif cultto use this part of the glucose spectrum for quantitativeanalysis even if the data is pretreated using methods likeFourier ltering or construction of second derivatives fol-lowed by multivariate calibration techniques

The size of the potential matrix effects between thesolvent (H 2O) and solute (glucose) and the effect of mu-tarotation of glucose were also examined Figure 7 showsthat the glucose spectra representing three different tem-peratures vary slightly in regard to the position of theglucose peaks There is a small shift in peak height (3)of the 1080 cm21 band relative to the total band heightFigure 8 shows the rst loading vectors from a separatePCA analysis of the pure water data and of the aqueousglucose data An empty cell was used for reference mea-surements in both cases These loading vectors whichdescribe the change in water features due to the temper-ature change may be compared and useful informationextracted If matrix effects were present a signi cant dif-ference between these loading vectors would be expectedAs can be seen from Fig 8 this effect is not observedThe two loading vectors are almost identical in shapeOnly small glucose features are observed in the water 1glucose loading vector

The absence of the matrix effect may be explained bythe fact that the glucose spectral features originate fromvibrations between atoms inside the pyranose ring Theinteractions between the functional groups of glucose andthe hydroxy groups in water do not in uence these vi-brations The fact that the absorption features from glu-cose are observed in the rst loading vector which mod-els the temperature variation indicates that the glucosesignal depends on temperature Mutarotation in water be-tween the two glucose anomeres designated a and b is awell-known phenomenon We believe the loading plot re-veals some of the effects of this The PCA analysis sug-gests that the glucose peak at 1080 cm21 known to bespeci c for the b form of glucose 22 is changed by 00031

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

APPLIED SPECTROSCOPY 35

FIG 9 Subtraction of the absorbance spectrum of pure water from theabsorbance spectrum of the 1 gdL glucose aqueous solution at 37 8Cand a pathlength of 04 mm The difference between two pure waterabsorbance spectra at 38 and 37 8C at the same pathlength is shown forcomparison Glucose speci c bands are seen at 4000ndash4500 cm21

FIG 10 First loading vector describing the change in absorbance ofpure water with temperature and rst loading vector describing the cor-responding change in absorbance of a 1 gdL aqueous glucose solution

au (3) This nding con rms the estimate made fromFig 7 The relative concentration of the two anomeres atdifferent temperatures has been calculated from values ofthe equilibrium constant for the reaction given by Ken-drew23 We calculate a 14 change in concentration asthe temperature is varied from 30 to 42 8C which isslightly lower than the 3 change in the signal foundexperimentally These estimates show that the changes insignal due to mutarotation in the 12 8C interval are smallcompared to the changes in the underlying water bands

We nd that changes in the spectral features of waterare the major contributors to temperature-dependent var-iation in the spectrum between 1500ndash980 cm21 Theshape of the glucose spectrum is more or less unchangedin the investigated range of temperatures and the directeffect of temperature on the glucose spectrum is negli-gible compared to the in uence of water For sampleswhere a small depth of penetration is suf cient the re-gion between 1100 and 1000 cm21 is well suited forquantitative analysis In this range the glucose signalsare at a maximum and temperature-dependent changes inthe water spectrum are at a minimum This region alsoshows promise for measurement of phosphates and sul-fates in aqueous solutions under less controlled thermalconditions

Near-Infrared Region Figure 9 shows the subtractionof the pure water spectrum measured at 04 mm path-length and 37 8C temperature from the 1 gdL aqueousglucose spectrum measured at the same pathlength andtemperature Also shown is the difference spectrum of a38 8C pure water spectrum with 37 8C water as referenceThe addition of 1 gdL glucose can be seen to have anin uence on the underlying water spectrum that is equiv-alent to a change of 1 8C in temperature The glucose-speci c signals in the spectral region 4500ndash4200 cm21

are a factor of 10 smaller than this matrix effect Scalingthis result to a typical glucose concentration of 100 mgdL reveals that the effect of this concentration is com-parable to a temperature change of 01 8C Moreover theeffect of the glucose signal itself is seen to be a factor of10 smaller than that of the underlying water spectrum

This result indicates that baseline variations are intro-duced in the near-infrared spectrum when the glucoseconcentration changes even when temperature is understrict control No such matrix effects are observed in themid-infrared region This matrix effect suggests that thequanti cation of glucose from the near-infrared combi-nation band requires a baseline correction even in situa-tions where temperature is well controlled

The effect of glucose on the temperature dependencyof the underlying water absorption spectrum is furtherillustrated in Fig 10 which shows the rst loading vectorresulting from a PCA analysis of pure water in the tem-perature range 36 to 42 8C and the rst loading vectorresulting from a separate PCA analysis of the 1 gdLaqueous glucose in the same temperature range Thesetwo loading vectors differ in shape in particular aroundthe absorption bands of water showing that water ab-sorption varies differently with temperature as glucose isadded The change in the water absorption with the ad-dition of glucose is not merely an offset depending onthe glucose concentration Once again this effect is smallin the 4500ndash4200 cm21 region containing combinationbands of glucose The glucose-speci c signals in this re-gion do not show up in the 1 gdL glucose loading vectorindicating that these signals do not change with temper-ature

A summary of the above results is given in Table IIIwhich compares the spectral regions 1200ndash1000 and5000ndash4000 cm21 The effect of temperature and the un-certainty of the measurements are nearly equal in the twospectral regions In contrast the absorbance of pure wateris almost three times higher and the glucose signal is seento be two orders of magnitude higher in the mid-infraredregion In the near-infrared region matrix effects fromthe interaction between water and glucose are strongerthan the glucose signal itself by an order of magnitudeThe mutarotation of glucose is found to have little in u-ence on the spectra with a change of 03 when tem-perature changes by 1 8C in the mid-infrared region Nosuch change is observed in the near-infrared region Theabove results indicate that the mid-infrared spectral re-gion is better suited to quanti cation of glucose under

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)

36 Volume 57 Number 1 2003

TABLE III Comparison between the spectral regions 1200ndash1000 and 5000ndash4000 cm21 The data shown are the absorbance of pure water(column 1) the change in absorbance with a temperature change of 1 8C (column 2) the uncertainty of the measurement (column 3) theabsorbance of aqueous glucose with pure water as reference (column 4) the change in glucose absorbance with a temperature change of 18C (column 5) and the change in underlying water absorbance with addition of glucose (column 6) All values are in absorbance units Thepathlengths for the mid- and near-infrared data were 50 mm and 04 mm respectively

Spectral region

Pure water

Absorb DT 5 1 8C Uncertainty

100 mgdL aqueous glucose

Absorb DT 5 1 8C Matrix effect

1200ndash1000 cm21

5000ndash4000 cm2112044

6 3 1024

8 3 102416 3 1023

15 3 10239 3 1023

7 3 10253 3 1025

NONO

5 3 1024

circumstances where a short pathlength is possible Ashort pathlength is certainly possible in making labora-tory measurements When it comes to noninvasive di-agnostics however it may be dif cult to nd a suitablemeasurement site at which mid-infrared spectroscopymay be employed

CONCLUSION

An accurate determination of the in uence of variationin physiologically relevant temperatures on the spectrumof pure water was carried out in the mid- and near-infra-red regions Water absorption spectra were comparedwith existing reference spectra and changes in tempera-ture with 37 8C water as reference were tabulated Thetemperature was controlled within 002 8C comparedwith typical accuracies of 01 8C in other studies Thelimitations that changes in the pure water absorptionspectrum impose on the quanti cation of trace compo-nents in aqueous solutions when temperature variationsexist was discussed The in uence of temperature on a 1gdL aqueous glucose solution was studied In the mid-infrared region the variation of the spectrum was domi-nated by the change of the water spectrum alone and theaddition of glucose did not signi cantly change the un-derlying water spectrum The glucose spectrum itself wasfound to change only weakly This change was explainedby a change in the equilibrium between the a and b formof glucose with temperature In the near-infrared regionthe addition of 1 gdL glucose to pure water caused theunderlying water spectrum to change This change pre-vented successful subtraction of a pure water referencein order to isolate glucose signals and suggests that base-line correction by Fourier high-pass ltering may be nec-essary even when temperature is under control

ACKNOWLEDGMENTS

The authors are grateful to the DANAK accredited temperature cal-ibration facility at Risoslash National Laboratory for help with the thermo-station of the transmission cell This work has been carried out under

grant no RK93097500006003500920 from the Danish ResearchAcademy and has received nancial support from the Danish Center forBiomedical Optics and New Laser Systems

1 S Venyaminov and F G Prendergast Anal Biochem 248 234(1997)

2 H L Mark and P R Grif ths Appl Spectrosc 56 633 (2002)3 Y Houdas and E F J Ring Human Body Temperature Its Mea-

surements and Regulation (Plenum Press New York 1982)4 T M Blank T L Ruchti S F Malin and S L Monfre LEOS

Newsletter 13 9 (1999)5 H M Heise and R Marbach Cell Mol Biol 44 899 (1999)6 J J Burmeister and M A Arnold Clin Chem 45 1621 (1999)7 M R Robinson Robust accurate non-invasive analyte monitor Pat-

ent 5830132 US Patent (1998)8 K J Ward D M Haaland M R Robinson and R P Eaton Appl

Spectrosc 46 959 (1992)9 A Welch and M van Gemert Optical-Thermal Response of Laser-

Irradiated Tissue (Plenum Press New York 1995)10 J E Bertie and Z Lan Appl Spectrosc 50 1047 (1996)11 F O Libnau J Toft A A Christy and O M Kvalheim J Am

Chem Soc 116 8311 (1994)12 F O Libnau O M Kvalheim A A Christy and J Toft Vib

Spectrosc 7 243 (1994)13 K Rahmelow and W Hubner Appl Spectrosc 51 160 (1997)14 J J Kelly K A Kelly and C H Barlow Proc SPIE-Int Soc

Opt Eng 2389 818 (1995)15 K H Hazen M A Arnold and G W Small Appl Spectrosc 48

477 (1994)16 J E Bertie in Analytical Applications of FT-IR to Molecular and

Biological Systems J R Durig Ed (D Reidel Publishing Com-pany Dordrecht Holland 1980) vol 57 of NATO Advanced StudyInstitutes Series CmdashMathematical and Physical Sciences

17 W H Press S A Teukolsky W T Vetterling and B P FlanneryNumerical Recipes in C The Art of Scienti c Computing (Cam-bridge University Press Cambridge 1995) 2nd ed

18 H Martens and T Naeligs Multivariate Calibration (John Wiley andSons New York 1989)

19 S Wold K Esbensen and P Geladi Chemom Intell Lab Syst2 37 (1987)

20 K F Palmer and J Williams J Opt Soc Am 64 1107 (1974)21 K H Hazen M A Arnold and G W Small Appl Spectrosc 52

1597 (1998)22 F O Libnau A A Christy and O M Kvalheim Vib Spectrosc

7 139 (1994)23 J C Kendrew and E A Molwyn-Hughes Proc R Soc London

Ser A 176 352 (1940)