OPTICS LETTERS / Vol. 27, No. 4 / February 15, 2002
Diffuse-reflectance spectroscopy from 500 to 1060 nm by
correction for inhomogeneously distributed absorbers
R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg
Photodynamic Therapy and Optical Spectroscopy Program, Department of Radiation Oncology, Daniel den Hoed Cancer Center,
University Hospital Rotterdam, Groene Hilledjik 301, Rotterdam Z-H 3075EA, The Netherlands
Received September 27, 2001
Diffuse-reflectance spectroscopy for measurement of the absorption and scattering coefficients of biological
tissue produces reliable results for wavelengths from 650 to 1050 nm.
homogeneously distributed absorbers. A correction factor is introduced for inhomogeneous distribution of
blood concentrated in discrete cylindrical vessels.This factor extends the applicability of diffusion the-
ory to lower wavelengths. We present measurements of in vivo optical properties in the wavelength range
500–1060 nm. © 2002 Optical Society of America
Implicitly, this approach assumes
Detailed knowledge of the optical properties of tissues
is essential for optimizing optical diagnostic methods
in medicine as well as therapeutic laser applications.
Photon propagation in turbid biological tissues can be
described by use of diffusion theory.
and Kienle and Patterson2adapted the diffusion
approximation with extrapolated boundary conditions
to describe steady-state spatially resolved diffuse-
ported the use of spatially resolved diffuse-reflectance
spectroscopy for the noninvasive determination of the
optical properties of in vivo human tissue and deter-
mined the absolute chromophore concentrations based
on this analysis.3
Rather than calculating optical
properties for each of the wavelengths separately, the
analysis considered the whole data set and calculated
the absorption and reduced scattering spectra over
the entire wavelength range.
analysis we assumed Lorentz–Mie scattering:
Farrell et al.1
Doornbos et al.3
As a constraint, in the
where b is a constant and is related to the size
of the scattering particles.4
range from 650 to 1050 nm, the resulting absorption
spectrum appeared to be equal to the sum of the
specific absorption of four individual absorbers, i.e.,
hemoglobin, oxyhemoglobin, fat, and water.3
approach assumes that all absorbers are distributed
homogeneously. Other researchers have found simi-
Extrapolated to wavelengths below
650 nm, the sum of the absorption of these four basic
components usually overestimates the absorption
calculated from the reflectance at these wavelengths
by an order of magnitude.
of the diffusion approximation is that scattering domi-
ma ,, ?ms?1 2 g??.
the extrapolated optical properties, one is tempted to
attribute this discrepancy to a breakdown of diffusion
theory in the lower-wavelength range.8
values of the optical properties measured in this range
do not justify this conclusion.
A condition for the validity
Investigators evaluating near-infrared (NIR) spec-
When they used the lower wavelengths in the NIR
range, incorrect values of blood oxygenation and vol-
ume resulted.This problem has been attributed to
the fact that blood is not a homogeneously distributed
absorber but a strong absorber concentrated in a small
fraction of the volume, i.e., the blood vessels.
case of a sufficiently large vessel radius and strong
absorption, less light reaches the center of the blood
vessel.Hence, the measured absorption coefficient
will be smaller than expected on the basis of the same
amount of homogeneously distributed blood in the
tissue. Correction factors have been either derived
analytically or based on Monte Carlo simulations by
use of randomly distributed cylindrical vessels with
Another field of study in which a
similar problem was encountered is laser treatment
of port-wine stains. Modeling the color of port-wine
stains (i.e., the wavelength region 450–700 nm)
required a wavelength-dependent correction factor
for the blood volume that accounted for the effect of
the blood’s being concentrated in vessels.12,13
analytical formula for this correction factor was based
summarizes the various correction factors found in
the literature as a function of the vessel’s optical
density ?ma,blRvessel?. All these factors are very close
to one another, except for the one presented by Liu
We hypothesize that incorporation of the
correction for inhomogeneously distributed absorbers
into the spatially resolved diffuse steady-state diffuse-
reflectance model will extend the validity of this
approach to lower wavelengths.
present experimental results that support this con-
cept.Since our calculation of optical properties from
a set of diffuse-reflectance measurements employs a
least-squares minimization routine that frequently
utilizes the correction factor, we chose to use the
correction factor proposed in Eq. (2) of Ref. 13, as it is
the simplest analytical expression available:
In this Letter we
0146-9592/02/040246-03$15.00/0© 2002 Optical Society of America
February 15, 2002 / Vol. 27, No. 4 / OPTICS LETTERS
Verkruysse et al.12) depend only on the product Rvesselma,bl,
and the influence of scattering was considered negli-
gible.Talsma et al.10incorporated scattering by blood
?ms0? 2.54 mm21?. For the equation from Liu et al., we
set the absorption of the surrounding tissue to zero.
Different correction factors for inhomogeneously
The first two (Svaasend et al.13and
Ω1 2 exp?22ma,bl?l?Rvessel?
where ma,bl?l? is the absorption coefficient of whole
blood and Rvesselis the vessel radius.
absorption coefficient of the tissue that we use in our
analysis consists of two parts, the inhomogeneously
and the homogeneously distributed contributions:
ma0?l? ? Cdiff?l?n?SmaHbO2?l? 1 ?1 2 S?maHb?l??
where ma0?l? is the effective absorption coefficient;
maHbO2?l? is the absorption coefficient of fully oxy-
coefficient of fully deoxygenated whole blood; n is the
blood volume fraction; S is the oxygen saturation of
the blood; Cdiff?l? is the correction factor for exposure
of blood vessels to diffuse light; and ciand mai?l? are
the volume fraction and the absorption coefficient of
the homogeneous distributed absorber, respectively.
Note that by using this approach we obtain an esti-
mate of the volume fractions of the homogeneously
distributed absorbers, the blood volume fraction and
oxygenation, and the vascular radius, R.
additional fitting constraint we force all absorbing
chromophore volume fractions to add up to 100%.
This constraint increased the stability of the fit.
ure 2 shows the results of two in vivo measurements.
The ma0residue is defined as the relative difference
between the measurement and the model.
parison, we calculated mawithout the correction factor,
based on reflectance measurements from 650 to 1050,
and extrapolated to shorter wavelengths.3
residue stays within 65% down to 500 nm, whereas
for the classical approach the residues exceed 100%
below 600 nm (not shown).
500 nm, the signal-to-noise ratio decreases because
For wavelengths below
of low light-source output and low grating efficiency.
Table 1 summarizes the data from several tissue
types, obtained with this approach.
of the fitted values were derived by calculation of
the covariance matrix and are an indication of how
precisely these parameters are defined by the given
data set.Not shown are the covariances.
they were roughly equal to the variances.
and NIR wavelength range, the resulting absorption
spectra are in good agreement with those found by
The measurement from the wrist was
deliberately taken from the visible veins in the skin.
In the red
measured absorption spectra (filled squares) according to
the homogeneous model (dashed curves) and the inhomo-
geneous model [Eq. (3); solid curves].
ma0?ma,model2 ma,meas?ma,model? is also shown.
duced scattering spectra (filled circles) can be seen above
the absorption spectra and are the results of fitting ms0?l0?
and b of Eq. (1) to the reflectance spectra.
Results of fitting the absorbing components on the
The relative residue
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OPTICS LETTERS / Vol. 27, No. 4 / February 15, 2002
Table 1. Contributions of the Absorbing Constituents and the Tissue Oxygenation Levels of
Several Tissue Typesa
aThe variances of vessel radius Rvesselare relatively small.
scattering curve [ln?ms0? versus ln?l?] and the scattering coefficient (ms0at l0? 1000 nm) were derived according to Eq. (1).
scattering and absorption spectra can accurately be described with the parameters shown here.
variance of the parameter value, calculated from the covariance matrix.
The columns showing the scattering-fit parameter, i.e., the slope of the
Values in parentheses indicate the
The vascular diameter found there seems to underes-
timate the actual diameter.
correlation between the blood volume fraction and the
vessel radius was found [Spearman’s rank correlation
coefficient, 0.854 ?0.521 2 0.961? p ? 0.007].
Based on the preliminary data presented here,
we conclude that our analysis is feasible down to
500 nm and proves to be beneficial for expanding the
wavelength range for application of diffuse-reflectance
spectroscopy. We believe that the range can even be
extended to lower wavelengths when the lamp’s out-
put power and the grating efficiency are adapted for
absorption coefficient can easily be implemented in
time- and frequency-domain techniques.
the utilization of this concept may have several
advantages.It may provide accurate tissue optical
properties for wavelengths below 650 nm and conse-
quently may permit the quantitative determination
of tissue absorbers such as cytochrome and bilirubin
or drugs that show absorption outside the NIR range.
Moreover, the technique may permit monitoring of
dynamic processes that involve changes in vessel
diameter resulting, for instance, from blood pressure
changes, erythema, or more-long-term changes such as
those that occur as a result of treatment of port-wine
stains.The accuracy of the parameter Rvessel from
our measurements depends strongly on its relation
to the actual size of the vessels.
the correction factor by Svaasand et al.13takes into
consideration vessels with a circular cross section of a
single diameter only.In tissue there will be variable
sizes and shapes, which will be different at different
depths in the tissue. Based on the optical properties
of in vivo tissue that we determined, and accounting
for the fact that the wavelength range below 600 nm
A strong and significant
The concept of an effective
The derivation of
has the largest effect on the value of Rvessel, we expect
Rvesselto refer to blood vessels in the top 1 mm of the
This work was supported by European Community
grantsBMH4 CT96-2260 and QLRT-1999-30690,
OPTIMAMM. R. Van Veen’s e-mail address is veen@
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