# Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers

**Abstract**

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

et al.

1

and Kienle and Patterson

2

adapted the diffusion

approximation with extrapolated boundary conditions

to describe steady-state spatially resolved diffuse-

ref lectance measurements.

1,2

Doornbos et al.

3

re-

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.

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. As a constraint, in the

analysis we assumed Lorentz–Mie scattering:

m

s

0

苷 m

s

0

共l

0

兲共l兾l

0

兲

2b

, (1)

where b is a constant and is related to the size

of the scattering particles.

4

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.

3

This

approach assumes that all absorbers are distributed

homogeneously. Other researchers have found simi-

lar results.

5–7

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

a

,, 关m

s

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.

8

However, the

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

various radii.

9–11

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

The

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

density 共m

a,bl

R

vessel

兲. All these factors are very close

to one another, except for the one presented by Liu

et al.

11

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.

13

and

Verkruysse et al.

12

) depend only on the product R

vessel

m

a,bl

,

and the inf luence of scattering was considered negli-

gible. Talsma et al.

10

incorporated scattering by blood

共m

s

0

苷 2.54 mm

21

兲. For the equation from Liu et al., we

set the absorption of the surrounding tissue to zero.

C

diff

共l兲 苷

Ω

1 2 exp关22m

a,bl

共l兲R

vessel

兴

2R

vessel

m

a,bl

共l兲

æ

,

(2)

where m

a,bl

共l兲 is the absorption coefficient of whole

blood and R

vessel

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:

m

a

0

共l兲 苷 C

diff

共l兲n关Sm

aHbO

2

共l兲 1 共1 2 S兲m

aHb

共l兲兴

1

X

i

c

i

m

ai

共l兲 , (3)

where m

a

0

共l兲 is the effective absorption coeff icient;

m

aHbO

2

共l兲 is the absorption coefficient of fully oxy-

genated whole blood; m

aHb

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

diff

共l兲 is the correction factor for exposure

of blood vessels to diffuse light; and c

i

and m

ai

共l兲 are

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.

The m

a

0

residue is defined as the relative difference

between the measurement and the model. For com-

parison, we calculated m

a

without the correction factor,

based on ref lectance measurements from 650 to 1050,

and extrapolated to shorter wavelengths.

3

The m

a

0

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

others.

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

m

a

0

共m

a, model

2m

a, meas

兾m

a, model

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

s

0

共l

0

兲

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

a

Blood Vessel m

s

0

at

Blood Oxygenation Water Fat Radius 1000 nm

Position (%) (%) (%) (%) 共mm兲共m

21

兲 Slope

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

a

The variances of vessel radius R

vessel

are relatively small. The columns showing the scattering-fit parameter, i.e., the slope of the

scattering curve [ln

共m

s

0

兲 versus ln共l兲] and the scattering coefficient (m

s

0

at l

0

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

coefficient,

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

vessel

from

our measurements depends strongly on its relation

to the actual size of the vessels. The derivation of

the correction factor by Svaasand et al.

13

takes 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

has the largest effect on the value of R

vessel

, we expect

R

vessel

to refer to blood vessels in the top 1 mm of the

skin.

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@

kfih.azr.nl.

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- CitationsCitations91
- ReferencesReferences18

- "The optical parameters a [198][199][200][201][202][203][204][205][206][207][208][209][210][211][212][213][214] , the frequencydomain technique [85, 113, 202] and the time-domain technique [85, 121, 119, 198, 201,[206][207][208][209] 212] of transmission spectroscopy are most frequently used. The reflectance spectroscopy is also often used for in vivo measurements of the breast optical parameters, both in the frequency-domain [25, 179, 199, 200, 205, 209] and in the time-domain [25, 201, 214] and continuous-wave [179, 199, 200, 203, 204, 211] techniques. The near IR spectroscopy makes use of the same principles and the same methods of data recording, as the modern optical imaging methods, based on the detection of diffusely scattered light, and in this sense is their direct predecessor. "

- "These gradients depend on the metabolic demands of the tissue in relationship to the mi crocirculatory blood flow level. [17] In the brain, metabolism low ers tissue oxygen concentration, causing large oxygen diffusion gradients. H ow ever, blood flow is large to compensate for this, resulting in intravascular longitudinal oxygen gradients that are relatively small. "

- "For techniques such as diffuse reflection spectroscopy, the same effect occurs on a larger scale because blood is not distributed homogeneously in tissue, but concentrated in vessels . Van Veen et al. [55] propose a correction factor introduced by Svaasand [56] that, interestingly, takes exactly the same form as Eq. 3 (but now with the vessel diameter as the length parameter instead of the diameter of the RBC), although it is derived in a completely different manner. "

[Show abstract] [Hide abstract]**ABSTRACT:**Optical property measurements on blood are influenced by a large variety of factors of both physical and methodological origin. The aim of this review is to list these factors of influence and to provide the reader with optical property spectra (250-2,500 nm) for whole blood that can be used in the practice of biomedical optics (tabulated in the appendix). Hereto, we perform a critical examination and selection of the available optical property spectra of blood in literature, from which we compile average spectra for the absorption coefficient (μ a), scattering coefficient (μ s) and scattering anisotropy (g). From this, we calculate the reduced scattering coefficient (μ s') and the effective attenuation coefficient (μ eff). In the compilation of μ a and μ s, we incorporate the influences of absorption flattening and dependent scattering (i.e. spatial correlations between positions of red blood cells), respectively. For the influence of dependent scattering on μ s, we present a novel, theoretically derived formula that can be used for practical rescaling of μ s to other haematocrits. Since the measurement of the scattering properties of blood has been proven to be challenging, we apply an alternative, theoretical approach to calculate spectra for μ s and g. Hereto, we combine Kramers-Kronig analysis with analytical scattering theory, extended with Percus-Yevick structure factors that take into account the effect of dependent scattering in whole blood. We argue that our calculated spectra may provide a better estimation for μ s and g (and hence μ s' and μ eff) than the compiled spectra from literature for wavelengths between 300 and 600 nm.

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