Possible correlation between blood glucose concentrationand the reduced scattering
coefficient of tissues in the near infrared
John S. Maier, Scott A. Walker, Sergio Fantini, Maria Angela Franceschini, and Enrico Gratton
Laboratory for Fluorescence Dynamics, Department of Physics, University of Illinois at Urbana- Champaign,1110 West Green Street, Urbana, Illinois 61801-3080
Received September 29, 1994
Tissue glucose levels affect the refractive index of the extracellular fluid. The difference in refractive indexbetween the extracellular fluid and the cellular components plays a role in determining the reduced scatteringcoefficient (GA') of tissue. Hence a physical correlation may exist between the reduced scattering coefficient andglucose concentration. We have designed and constructed a frequency-domain near-infrared tissue spectrometercapable of measuring the reduced scattering coefficient of tissue with enough precision to detect changes in glucoselevels in the physiological and pathological range.
Millions of diabetics around the world measure theirblood glucose concentration several times a day.Essentially, all the current methods for glucosedetermination require patients to obtain blood bylancing a finger. They then perform a quantitativeanalysis of blood sugar by monitoring a chemical re-action with the blood sample. Reference 1 providesa brief review of the diverse minimally invasive ap-proaches to monitoring blood glucose. Other ideasinclude sensors implanted subcutaneously,2 directmeasurement of plasma index of refraction,3 andnoninvasive chemometric analysis of tissue effectiveabsorption spectra.4
In this Letter we investigate modifications of lighttransport through tissues as a result of changes inglucose concentration. We focus our attention onnear-infrared light because tissue absorption in thisspectral region is low, leading to harmless penetra-tion of light deep into the tissue. Recently we de-veloped a sensitive frequency-domain near-infraredtissue spectrometer capable of separately measuringreduced scattering (p,2) and absorption (Ma) coeffi-cients in tissues.5 Using this instrument, we can in-dependently assess the effect of glucose concentrationon the absorption and scattering properties of tissues.The method is based on measurement of the prod-uct of the reduced scattering coefficient and the meanindex of refraction of tissue (n) at a single wavelength(850 nm). We propose a model that correlates thisproduct (n/r,1) to changes in the refractive indicesof the blood plasma and interstitial fluid [togetherknown as the extracellular fluid (ECF)].
Light scattering occurs in tissues because of themismatch of index of refraction between the ECFand the membranes of the cells composing the tissue.The index of refraction of ECF (nECF) varies withdissolved sugar concentration, whereas the index ofthe cellular membranes (neeii) is assumed to remainrelatively constant. In the near infrared the indexof refraction of the ECF is nECF - 1.348-1.352,6'7whereas the index of refraction of the cellular
membranes and protein aggregates is in the rangencell - 1.350-1.460.78 Adding glucose to blood willraise the refractive index of the ECF, which willcause a change in the scattering characteristic ofthe tissue as a whole. Our approach is based onthe principle that physiological changes in the glu-cose concentration in the ECF can cause measurablechanges in the product of the reduced scattering co-efficient of the tissue and the mean refractive indexof the tissue (ng.l').
The in vitro experiment is described as follows: wemeasured the product nMS' at 850 nm of a Liposyn-glucose suspension (1.5% lipid solid content) asa function of glucose concentration, using a pre-viously described frequency-domain technique.9Briefly, this technique involves placing an intensity-modulated light source deep in the medium to bestudied. The phase and the intensity of the photon-density wave generated by this source are measuredwith high precision at several source-detector sepa-rations. These measurements are combined withequations analytically derived from linear transporttheory to yield the ratio of the absorption coefficientto the mean refractive index (Ma/n) and the product ofthe mean refractive index and the reduced scatteringcoefficient (nAf') characteristic of the medium. 10
The light source was a light-emitting diode witha peak wavelength of 850 nm. Its intensity wasmodulated at a frequency of 120 MHz. Over thecourse of the experiment we incrementally added tothe Liposyn suspension a previously prepared so-lution with a glucose concentration of 140 g/L andthe same Liposyn concentration as the suspension.The results are shown in Fig. 1, in which the ex-perimental data are plotted against glucose concen-tration (lower axis) and the refractive index of thewater-glucose mixture (upper axis).
To compare the above experimental results withan appropriate model, we consider the reduced scat-tering coefficient Mua' = ,Ut(l - g), where Mus is themicroscopically derived scattering coefficient and g
Fig. 1. Product of the refractive index n and the reducedscattering coefficient ,-/'t of the Liposyn-glucose suspen-sion as a function of the glucose concentration (lower axis)and the index of refraction (upper axis) of the solutionsuspending the lipid droplets. This solution consists ofwater with a varying concentration of dissolved glucoseto change the refractive index. The open squares indi-cate measured values, whereas the curve is a theoreticalprediction based on the Rayleigh-Gans scattering modelof Eq. (1) with ni = 1.465 and K = 1.30 x 1O3 cm-1. Theexperimental errors in the data points are of the order ofthe dimensions of the open squares.
is the average of the cosine of the scattering angle.Microscopically, Mie theory rigorously treats scatter-ing by spherical scatterers of index of refraction n1suspended in a medium of index of refraction no.We employ the Rayleigh-Gans theory as an approxi-mation to Mie theory to find the dependence of thereduced scattering coefficient on the indices of refrac-tion n, and no. With this theory, which is appropri-ate when In,/no - 11 << 1,11 the reduced scatteringcoefficient has the following dependence on the in-dices of refraction 11" 2 :
As - n=) (1)
where K is a proportionality factor related to particlesize, wavelength, and particle density and includes g.The curve in Fig. 1 corresponds to a plot of this modelfor nos' (we assume that n no), where n, and noare obtained from the CRC Handbook of Chemistryand Physics and are based on the type of fat in thesuspension (soybean oil) and on the known glucoseconcentration, respectively.7 We set n, = 1.465 andno = 1.325 + 1.515 x 10-6 X [C], where [C] is the con-centration of glucose in milligrams per deciliter. Forthe curve in Fig. 1, K is equal to 1.30 x 103 cm-1.We stress that K is the only adjustable parameterin our application of Eq. (1). For a lipid emulsionsimilar to the one that we employed and in the ab-sence of glucose, an experimentally derived formulaverified by Mie theory calculations'2 leads to a similarvalue for K of 1.25 x 103 cm- 1 .
For the noninvasive in vivo measurement weused a previously described frequency-domain tissuespectrometer. Four light sources (light-emittingdiodes with a peak wavelength of 850 nm) are placedat the skin surface to obtain measurements at sev-eral source-detector separations. We measured the
response of a nondiabetic male subject to a glucoseload of 1.75 g/kg body weight, as in a standard glu-cose tolerance test,'3 by continuously monitoring theproduct nAi' measured on muscle tissue of the sub-ject's thigh. Instrument acquisition time was 30 sper data point. Informed consent of the subject andinstitutional review board approval were obtainedbefore the experiment.
Simultaneously, we measured the subject's bloodglucose, using a home blood glucose monitor (OneTouch, Johnson & Johnson) periodically throughoutthe experiment. The results of the optical measure-ment and of the home blood glucose monitor testare shown in Fig. 2. As the subject's blood glucoserose, the reduced scattering coefficient decreased.Figure 3 shows the correlation plot obtained from thedata of Fig. 2. A complete explanation of the resultsin the physiological system requires a sophisticatedphysical model. However, the simple Rayleigh-Gans model, which explains the in vitro experiment,can be used as a first step in the explanation of thein vivo results. To this end we assume a suspend-ing medium with refractive index nECF that is closeto the refractive index of the suspended scatterers,ncell. The index of refraction of the fluid changesonly slightly [less than 0.05% (Ref. 3)] as a result ofphysiological changes in glucose concentration. Ifwe let nECF(0) be the index of refraction of the ECFat a baseline physiological glucose concentration, wecan write nECF = nECF(O) + an, with 8n << fECF(O).By replacement of the Rayleigh-Gans parameters K,no, and n, with the corresponding tissue parametersKT, nECF, and ncell, respectively, Eq. (1) becomes
Is' = KT[ncell -nECF(O) - An] (2)
where 8n is neglected in the denominator because itis much less than nECF(O) and we assume n -nECF(O)-
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Fig. 2. Glucose tolerance test performed on a humansubject. At time t = 45 min the subject ingested a glu-cose load of 160 g of table sugar (1.75 g/kg body weight).The open circles indicate blood glucose concentration asdetermined by a home blood glucose monitor. A dashedcurve joins the circles to aid the eye. The solid curveis the continuous measurement of n/ip' on the thigh ofthe subject made with our portable frequency-domainnear-infrared spectrometer. The data acquired every30 s were averaged in sets of five to produce the plot.
Fig. 3. Correlation plot of the data shown in Fig. 2.The open squares indicate the correlation between theblood glucose as measured with the home blood glucosemonitor with the measured product ng8 ' averaged overa time of 2.5 min centered on the time the finger waslanced for the measurement. The errors in nut' shownhere are the standard deviations of the five measure-ments averaged to generate a single scattering point.The errors in blood glucose concentration are estimatedto be ±2.5 mg/dL. The curve is the theoretical resultaccording to the Rayleigh-Gans model.
Using the CRC table for the dependence of the in-dex of refraction of water solution on glucose concen-tration, we obtain An = 1.515 X 10-1 X [AC], where[AC] is the change in glucose concentration in mil-ligrams per deciliter from the physiological baseline.'For nECF(O) and ncell we chose typical values of 1.350and 1.360. It is not possible to calculate KT a pri-ori because of the random inhomogeneous nature oftissues. We chose to make KT equal to the mea-sured value of nga' at [C] = 82 mg/dL multipliedby {nEcF(0)/[n.c11 - nEcF(0)]2}. In this fashion we ob-tained KT = 7.28 x 103 cm-'. The curve in Fig. 3 isthe plot of Eq. (2) with these parameters. We founda higher sensitivity of nAt' to changes in glucose con-centration for the in vivo measurement than that forthe in vitro measurement.
Our claims for the correlation between blood glu-cose concentration and reduced scattering coefficientare based on a simple physical model for light trans-port in tissues. This model accounts for the changesof the reduced scattering coefficient of tissues owingto changes in the refractive index of ECF. The nov-elty of our method lies in exploiting the better matchof index of refraction between ECF and cellular mate-rials caused by an increase in glucose concentration.An increase of glucose concentration in the physio-logical range decreases the total amount of tissuescattering. Clearly our approach assumes a valuefor the baseline and, in this sense, can provide onlya relative measurement that permits monitoring glu-cose levels over an extended period of time. Key fac-tors for the success of this approach are the precisionof the measurement of the reduced scattering coeffi-cient and the separation of scattering changes fromabsorption changes, as obtained with our frequency-domain spectrometer. However, we observe that thephysical model that we propose is only a possibleexplanation of the glucose-induced scattering effect.
Other physiological effects related to glucose concen-tration could account for the observed variations ofthe reduced scattering coefficient with time.
Because glucose has low absorption at 850 nmrelative to other tissue constituents the absorptioncoefficient is negligibly affected by glucose concen-tration. This was borne out in both the in vitroand the in vivo experiments that we conducted. Be-cause the reduced scattering coefficient is more af-fected by changes of glucose concentration, the factthat scattering dominates the transport propertiesof near-infrared light in tissues is actually advanta-geous in refractive-index-based glucose monitoring.Provided that one can separate absorption and scat-tering effects, the highly scattered slightly absorbednear-infrared light employed in this technique is ac-tually in the spectral region of choice.
During the course of our study we learned thatother researchers are developing a similar ap-proach to noninvasive glucose monitoring."4 Ourresearch is supported by National Institutes ofHealth grants RR03155 and CA57032 and by theUniversity of Illinois at Urbana-Champaign. Wethank Albert Cerussi for help in performing thein vitro experiment.
References
1. B. H. Ginsberg, Clin. Chem. 38, 1596 (1992).2. G. S. Wilson, Y. Zhang, G. Reach, D. Moatti-Sirat,
V. Poitout, D. R. Th6venot, F. Lemonnier, and J. Klein,Clin. Chem. 38, 1613 (1992).
3. Y. Liu, P. Hering, and M. 0. Scully, Appl. Phys. B 54,18 (1992).
4. M. R. Robinson, R. P. Eaton, D. M. Haaland,G. W. Koepp, E. V. Thomas, B. R. Stallard, andP. L. Robinson, Clin. Chem. 38, 1618 (1992).
5. S. Fantini, M. A. Franceschini, J. S. Maier, S. A.Walker, B. Barbieri, and E. Gratton, "Frequency-domain multichannel optical detector for noninvasivetissue spectroscopy and Oximetry," Opt. Eng. (to bepublished).
