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Title
Possible correlation between blood glucose concentration and the reduced scattering
coefficient of tissues in the near infrared.
Permalink
https://escholarship.org/uc/item/39j4m5x9
Journal
Optics letters, 19(24)
ISSN
0146-9592
Authors
Maier, JS
Walker, SA
Fantini, S
et al.
Publication Date
1994-12-01
DOI
10.1364/ol.19.002062
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2062 OPTICS LETTERS / Vol. 19, No. 24 / December 15, 1994
Possible correlation between blood glucose concentration
and 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 index
between the extracellular fluid and the cellular components plays a role in determining the reduced scattering
coefficient (GA') of tissue. Hence a physical correlation may exist between the reduced scattering coefficient and
glucose concentration. We have designed and constructed a frequency-domain near-infrared tissue spectrometer
capable of measuring the reduced scattering coefficient of tissue with enough precision to detect changes in glucose
levels in the physiological and pathological range.
Millions of diabetics around the world measure their
blood glucose concentration several times a day.
Essentially, all the current methods for glucose
determination require patients to obtain blood by
lancing a finger. They then perform a quantitative
analysis of blood sugar by monitoring a chemical re-
action with the blood sample. Reference 1 provides
a brief review of the diverse minimally invasive ap-
proaches to monitoring blood glucose. Other ideas
include sensors implanted subcutaneously,
2
direct
measurement of plasma index of refraction,
3
and
noninvasive chemometric analysis of tissue effective
absorption spectra.
4
In this Letter we investigate modifications of light
transport through tissues as a result of changes in
glucose concentration. We focus our attention on
near-infrared light because tissue absorption in this
spectral region is low, leading to harmless penetra-
tion of light deep into the tissue. Recently we de-
veloped a sensitive frequency-domain near-infrared
tissue spectrometer capable of separately measuring
reduced scattering (p,2) and absorption (Ma) coeffi-
cients in tissues.
5
Using this instrument, we can in-
dependently assess the effect of glucose concentration
on the absorption and scattering properties of tissues.
The method is based on measurement of the prod-
uct of the reduced scattering coefficient and the mean
index of refraction of tissue (n) at a single wavelength
(850 nm). We propose a model that correlates this
product (n/r,
1
) to changes in the refractive indices
of the blood plasma and interstitial fluid [together
known as the extracellular fluid (ECF)].
Light scattering occurs in tissues because of the
mismatch of index of refraction between the ECF
and the membranes of the cells composing the tissue.
The index of refraction of ECF (nECF) varies with
dissolved sugar concentration, whereas the index of
the cellular membranes (neeii) is assumed to remain
relatively constant. In the near infrared the index
of refraction of the ECF is nECF - 1.348-1.352,6'7
whereas the index of refraction of the cellular
membranes and protein aggregates is in the range
ncell - 1.350-1.460.78
Adding glucose to blood will
raise the refractive index of the ECF, which will
cause a change in the scattering characteristic of
the tissue as a whole. Our approach is based on
the principle that physiological changes in the glu-
cose concentration in the ECF can cause measurable
changes in the product of the reduced scattering co-
efficient of the tissue and the mean refractive index
of the tissue (ng.l').
The in vitro experiment is described as follows: we
measured the product nMS' at 850 nm of a Liposyn-
glucose suspension (1.5% lipid solid content) as
a function of glucose concentration, using a pre-
viously described frequency-domain technique.
9
Briefly, this technique involves placing an intensity-
modulated light source deep in the medium to be
studied. The phase and the intensity of the photon-
density wave generated by this source are measured
with high precision at several source-detector sepa-
rations. These measurements are combined with
equations analytically derived from linear transport
theory to yield the ratio of the absorption coefficient
to the mean refractive index (Ma/n) and the product of
the mean refractive index and the reduced scattering
coefficient (nAf') characteristic of the medium.
10
The light source was a light-emitting diode with
a peak wavelength of 850 nm. Its intensity was
modulated at a frequency of 120 MHz. Over the
course of the experiment we incrementally added to
the Liposyn suspension a previously prepared so-
lution with a glucose concentration of 140 g/L and
the 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 the
water-glucose mixture (upper axis).
To compare the above experimental results with
an appropriate model, we consider the reduced scat-
tering coefficient Mua' = ,Ut(l - g), where Mus is the
microscopically derived scattering coefficient and g
0146-9592/94/242062-03$6.00/0 © 1994 Optical Society of America
December 15, 1994 / Vol. 19, No. 24 / OPTICS LETTERS 2063
no
E
2:
0 2 4 6 8 10 12 14
Glucose Conc. (g/dL)
Fig. 1. Product of the refractive index n and the reduced
scattering 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 solution
suspending the lipid droplets. This solution consists of
water with a varying concentration of dissolved glucose
to change the refractive index. The open squares indi-
cate measured values, whereas the curve is a theoretical
prediction based on the Rayleigh-Gans scattering model
of Eq. (1) with ni = 1.465 and K = 1.30 x 1O3 cm-
1
. The
experimental errors in the data points are of the order of
the 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 n
1
suspended 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 the
reduced 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 scattering
coefficient has the following dependence on the in-
dices of refraction
11
"
2
:
As - n=)
(1)
where K is a proportionality factor related to particle
size, wavelength, and particle density and includes g.
The curve in Fig. 1 corresponds to a plot of this model
for nos' (we assume that n no), where n, and no
are obtained from the CRC Handbook of Chemistry
and Physics and are based on the type of fat in the
suspension (soybean oil) and on the known glucose
concentration, respectively.
7
We set n, = 1.465 and
no = 1.325 + 1.515 x 10-6 X [C], where [C] is the con-
centration of glucose in milligrams per deciliter. For
the curve in Fig. 1, K is equal to 1.30 x 103 cm-1.
We stress that K is the only adjustable parameter
in our application of Eq. (1). For a lipid emulsion
similar to the one that we employed and in the ab-
sence of glucose, an experimentally derived formula
verified by Mie theory calculations'
2
leads to a similar
value for K of 1.25 x 103 cm-
1
.
For the noninvasive in vivo measurement we
used a previously described frequency-domain tissue
spectrometer. Four light sources (light-emitting
diodes with a peak wavelength of 850 nm) are placed
at the skin surface to obtain measurements at sev-
eral source-detector separations. We measured the
response of a nondiabetic male subject to a glucose
load of 1.75 g/kg body weight,
as in a standard glu-
cose tolerance test,'
3
by continuously monitoring the
product nAi' measured on muscle tissue of the sub-
ject's thigh. Instrument acquisition time was 30 s
per data point. Informed consent of the subject and
institutional review board approval were obtained
before the experiment.
Simultaneously, we measured the subject's blood
glucose, using a home blood glucose monitor (One
Touch, Johnson & Johnson) periodically throughout
the experiment. The results of the optical measure-
ment and of the home blood glucose monitor test
are shown in Fig. 2. As the subject's blood glucose
rose, the reduced scattering coefficient decreased.
Figure 3 shows the correlation plot obtained from the
data of Fig. 2. A complete explanation of the results
in the physiological system requires a sophisticated
physical model. However, the simple Rayleigh-
Gans model, which explains the in vitro experiment,
can be used as a first step in the explanation of the
in vivo results. To this end we assume a suspend-
ing medium with refractive index nECF that is close
to the refractive index of the suspended scatterers,
ncell. The
index of refraction of the fluid changes
only slightly [less than 0.05% (Ref. 3)] as a result of
physiological changes in glucose concentration. If
we let nECF(0) be the index of refraction of the ECF
at a baseline physiological glucose concentration, we
can write nECF = nECF(O) + an, with 8n << fECF(O).
By replacement of the Rayleigh-Gans parameters K,
no, and n, with the corresponding tissue parameters
KT, nECF, and ncell, respectively, Eq. (1) becomes
Is' = KT[ncell -nECF(O) - An]
(2)
where 8n is neglected in the denominator because it
is much less than nECF(O) and we assume n -nECF(O)-
4,
18.05
8.00
E
-9 7.95
> 7.90
c
7.85
7.80
0
150 Cal
140 E
130 C:
0
120 ()
110
0(
80
100 '3
90 CD
0
80 o
0 20 40 60 80 100 120 140
Time (minutes)
Fig. 2. Glucose tolerance test performed on a human
subject. 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 as
determined by a home blood glucose monitor. A dashed
curve joins the circles to aid the eye. The solid curve
is the continuous measurement of n/ip' on the thigh of
the subject made with our portable frequency-domain
near-infrared spectrometer. The data acquired every
30 s were averaged in sets of five to produce the plot.
2064
OPTICS
LETTERS
/ Vol.
19, No.
24 / December
15,
1994
8.05
8.00
tI
,E
0Z
7.95-
7.90 i
7.85J
7.80-
7.75
80 90
100 110 120
130 140 150
Blood Glucose Conc. (mg/dL)
Fig. 3. Correlation
plot of the data shown
in Fig. 2.
The open squares
indicate the correlation
between the
blood glucose as measured with
the home blood glucose
monitor with the measured
product ng
8
' averaged
over
a time of 2.5 min centered on the time the
finger was
lanced for the measurement.
The errors in
nut' shown
here are the standard
deviations of the five
measure-
ments
averaged to generate a single scattering point.
The errors in blood glucose
concentration are estimated
to be ±2.5 mg/dL.
The curve is the
theoretical result
according 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
1.350
and 1.360. It is not possible
to calculate KT a pri-
ori because
of the random inhomogeneous
nature of
tissues. We chose
to make KT
equal to the mea-
sured value of nga' at [C]
= 82 mg/dL multiplied
by {nEcF(0)/[n.c11
- nEcF(0)]2}.
In
this fashion
we ob-
tained
KT = 7.28 x 103 cm-'.
The curve in Fig.
3 is
the plot of Eq.
(2) with these parameters. We
found
a higher sensitivity of nAt' to changes in
glucose con-
centration for the in
vivo measurement than
that for
the in vitro
measurement.
Our claims for the correlation
between blood glu-
cose concentration and reduced scattering
coefficient
are based on a simple physical
model for light trans-
port in tissues. This model
accounts for the changes
of the
reduced scattering coefficient of tissues owing
to changes in the refractive index of ECF.
The nov-
elty of our method lies in exploiting the
better match
of 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 tissue
scattering. Clearly our approach assumes
a value
for the baseline and, in this sense, can
provide only
a 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 precision
of the measurement
of the reduced scattering coeffi-
cient
and the separation of scattering changes from
absorption
changes, as obtained with our frequency-
domain spectrometer. However, we observe
that the
physical
model that we propose is only
a possible
explanation
of the glucose-induced scattering effect.
Other physiological
effects related to glucose concen-
tration could
account for the observed variations of
the reduced scattering coefficient
with time.
Because glucose
has low absorption
at 850 nm
relative to other
tissue constituents
the absorption
coefficient is negligibly
affected by glucose concen-
tration. This was borne
out in both the in vitro
and the in vivo
experiments that we conducted. Be-
cause
the reduced scattering coefficient is more
af-
fected
by changes of glucose
concentration, the
fact
that
scattering dominates the transport properties
of 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
absorbed
near-infrared
light employed in this technique is
ac-
tually in the spectral region
of choice.
During
the course
of our study
we learned
that
other researchers
are developing a similar ap-
proach
to noninvasive glucose
monitoring."
4
Our
research is
supported by National
Institutes of
Health grants RR03155 and
CA57032 and by the
University of
Illinois at Urbana-Champaign.
We
thank Albert
Cerussi for help in performing the
in vitro experiment.
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