Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers
Diffuse-reflectance spectroscopy for measurement of the absorption and scattering coefficients of biological tissue produces reliable results for wavelengths from 650 to 1050 nm. Implicitly, this approach assumes 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 theory to lower wavelengths. We present measurements of in vivo optical properties in the wavelength range 500-1060 nm.
246 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-ref lectance spectroscopy for measurement of the absorption and scattering coefficients of biological
tissue produces reliable results for wavelengths from 650 to 1050 nm. Implicitly, this approach assumes
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
OCIS codes: 160.4760, 170.3660.
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. Farrell
and Kienle and Patterson
adapted the diffusion
approximation with extrapolated boundary conditions
to describe steady-state spatially resolved diffuse-
ref lectance measurements.
Doornbos et al.
ported the use of spatially resolved diffuse-ref lectance
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.
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. As a constraint, in the
analysis we assumed Lorentz–Mie scattering:
where b is a constant and is related to the size
of the scattering particles.
In the wavelength
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.
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 ref lectance at these wavelengths
by an order of magnitude. A condition for the validity
of the diffusion approximation is that scattering domi-
nate absorption: m
共1 2 g兲兴. Looking at
the extrapolated optical properties, one is tempted to
attribute this discrepancy to a breakdown of diffusion
theory in the lower-wavelength range.
values of the optical properties measured in this range
do not justify this conclusion.
Investigators evaluating near-infrared (NIR) spec-
troscopy for noninvasive measurement of blood
oxygenation encountered a comparable problem.
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. In the
case of a suff iciently 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.
analytical formula for this correction factor was based
on straightforward geometrical optics. Figure 1
summarizes the various correction factors found in
the literature as a function of the vessel’s optical
兲. 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-
ref lectance model will extend the validity of this
approach to lower wavelengths. In this Letter we
present experimental results that support this con-
cept. Since our calculation of optical properties from
a set of diffuse-ref lectance 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:
0146-9592/02/040246-03$15.00/0 © 2002 Optical Society of America
February 15, 2002 / Vol. 27, No. 4 / OPTICS LETTERS 247
Fig. 1. Different correction factors for inhomogeneously
distributed absorbers. The first two (Svaasend et al.
Verkruysse et al.
) depend only on the product R
and the inf luence of scattering was considered negli-
gible. Talsma et al.
incorporated scattering by blood
苷 2.54 mm
兲. For the equation from Liu et al., we
set the absorption of the surrounding tissue to zero.
1 2 exp关22m
共l兲 is the absorption coefficient of whole
blood and R
is the vessel radius. The effective
absorption coeff icient of the tissue that we use in our
analysis consists of two parts, the inhomogeneously
and the homogeneously distributed contributions:
共l兲 苷 C
共l兲 1 共1 2 S兲m
共l兲 , (3)
共l兲 is the effective absorption coeff icient;
共l兲 is the absorption coefficient of fully oxy-
genated whole blood; m
共l兲 is the absorption
coefficient of fully deoxygenated whole blood; n is the
blood volume fraction; S is the oxygen saturation of
the blood; C
共l兲 is the correction factor for exposure
of blood vessels to diffuse light; and c
the volume fraction and the absorption coeff icient 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.Asan
additional fitting constraint we force all absorbing
chromophore volume fractions to add up to 100%.
This constraint increased the stability of the fit. Fig-
ure 2 shows the results of two in vivo measurements.
residue is defined as the relative difference
between the measurement and the model. For com-
parison, we calculated m
without the correction factor,
based on ref lectance measurements from 650 to 1050,
and extrapolated to shorter wavelengths.
residue stays within 65% down to 500 nm, whereas
for the classical approach the residues exceed 100%
below 600 nm (not shown). For wavelengths below
500 nm, the signal-to-noise ratio decreases because
of low light-source output and low grating eff iciency.
Table 1 summarizes the data from several tissue
types, obtained with this approach. The variances
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. In general,
they were roughly equal to the variances. In the red
and NIR wavelength range, the resulting absorption
spectra are in good agreement with those found by
5 – 7
The measurement from the wrist was
deliberately taken from the visible veins in the skin.
Fig. 2. Results of fitting the absorbing components on the
measured absorption spectra (filled squares) according to
the homogeneous model (dashed curves) and the inhomo-
geneous model [Eq. (3); solid curves]. The relative residue
兲 is also shown. The re-
duced scattering spectra (filled circles) can be seen above
the absorption spectra and are the results of fitting m
and b of Eq. (1) to the ref lectance spectra.
248 OPTICS LETTERS / Vol. 27, No. 4 / February 15, 2002
Table 1. Contributions of the Absorbing Constituents and the Tissue Oxygenation Levels of
Several Tissue Types
Blood Vessel m
Blood Oxygenation Water Fat Radius 1000 nm
Position (%) (%) (%) (%) 共mm兲共m
Forearm 2.0 (0.2) 63.1 (4.7) 59.7 (9.6) 33.3 (29.7) 36.5 (0.5) 963.5 21.06
Forearm 2.9 (0.2) 64.8 (3.7) 58.7 (9.2) 33.5 (30.7) 61.8 (0.6) 766.8 21.20
Forehead 1.6 (0.2) 75.1 (6.2) 60.4 (12.2) 38.1 (32.4) 20.2 (0.5) 931.8 21.30
Biceps 1.0 (0.6) 87.4 (18.2) 58.1 (8.6) 40.9 (29.1) 23.4 (1.3) 925.5 20.72
Forearm 1.0 (0.5) 70.1 (8.0) 55.9 (7.9) 43.2 (23.4) 13.2 (0.8) 871.3 20.92
Biceps 0.6 (0.3) 64.2 (11.0) 57.3 (7.2) 42.1 (18.6) 12.0 (0.9) 918.3 21.27
Wrist 11.5 (1.9) 71.8 (3.6) 88.6 (25.4) 0.0 (96.6) 101.1 (0.8) 220.4 20.18
Biceps 0.9 (0.6) 73.3 (12.6) 56.1 (8.6) 43.0 (27.4) 22.3 (1.9) 1073.0 20.85
Biceps 1.4 (0.1) 86.0 (4.6) 35.8 (6.5) 62.9 (22.6) 30.1 (0.5) 692.8 21.18
Chest (male) 2.0 (0.2) 92.1 (3.8) 60.4 (8.9) 37.6 (25.4) 71.5 (1.6) 433.6 22.84
Breast (female) 1.2 (0.1) 87.4 (3.5) 51.2 (5.2) 47.6 (14.3) 30.7 (0.7) 344.8 21.90
The variances of vessel radius R
are relatively small. The columns showing the scattering-fit parameter, i.e., the slope of the
scattering curve [ln
兲 versus ln共l兲] and the scattering coefficient (m
苷 1000 nm) were derived according to Eq. (1). Tissue
scattering and absorption spectra can accurately be described with the parameters shown here. Values in parentheses indicate the
variance of the parameter value, calculated from the covariance matrix.
The vascular diameter found there seems to underes-
timate the actual diameter. A strong and significant
correlation between the blood volume fraction and the
vessel radius was found [Spearman’s rank correlation
0.854 共0.521 2 0.961兲 p 苷 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-ref lectance
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
lower-wavelength regions. The concept of an effective
absorption coefficient can easily be implemented in
time- and frequency-domain techniques. We believe
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 R
our measurements depends strongly on its relation
to the actual size of the vessels. The derivation of
the correction factor by Svaasand et al.
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
has the largest effect on the value of R
, we expect
to refer to blood vessels in the top 1 mm of the
This work was supported by European Community
grants BMH4 CT96-2260 and QLRT-1999-30690,
OPTIMAMM. R. Van Veen’s e-mail address is veen@
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