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Theoretical and experimental investigation of
near-infrared light propagation in a model of the
adult head
Eiji Okada, Michael Firbank, Martin Schweiger, Simon R. Arridge, Mark Cope, and
David T. Delpy
Near-infrared light propagation in various models of the adult head is analyzed by both time-of-flight
measurements and mathematical prediction. The models consist of three- or four-layered slabs, the
latter incorporating a clear cerebrospinal fluid ~CSF! layer. The most sophisticated model also incor-
porates slots that imitate sulci on the brain surface. For each model, the experimentally measured mean
optical path length as a function of source–detector spacing agrees well with predictions from either a
Monte Carlo model or a finite-element method based on diffusion theory or a hybrid radiosity–diffusion
theory. Light propagation in the adult head is shown to be highly affected by the presence of the clear
CSF layer, and both the optical path length and the spatial sensitivity profile of the models with a CSF
layer are quite different from those without the CSF layer. However, the geometry of the sulci and the
boundary between the gray and the white matter have little effect on the detected light distribution.
© 1997 Optical Society of America
Key words: Near-infrared spectroscopy, optical path length, spatial sensitivity profile, oxygenation
monitoring.
1. Introduction
Since its first proposal
1
the technique of near-
infrared spectroscopy ~NIRS! has been increasingly
applied for the noninvasive measurement of tissue
oxygenation in the brain,
2–6
and several different in-
struments are now available for clinical
monitoring.
7–10
The development of the quantita-
tive measurement of absorption change by a modified
Beer–Lambert law made a significant advance in
NIRS studies.
11
The quantification of NIRS data re-
quires a knowledge of the optical path length in the
tissue, which is considerably farther than the physi-
cal distance between source and detector. Direct
time-of-flight measurement with a picosecond pulsed
laser and streak camera initially enabled the mean
flight time ~^t&!, and hence the mean optical path
length could be derived experimentally for a rat
head,
11
an adult head,
12
and a neonatal head
12,13
;
larger studies have recently been completed in which
phase-resolved techniques were used.
14,15
In the
NIRS calculations, the head is assumed to be a ho-
mogeneous medium, although in reality the source
and detection fibers are attached onto the surface of
the head, requiring the light to pass through the
surface tissue layers such as scalp, skull, and cere-
brospinal fluid ~CSF! both before and after passing
through the brain tissue. The clinically important
factors in NIRS monitoring of cerebral oxygenation
are the contribution of the absorption change in the
brain to the detected signal and the volume of tissue
interrogated, and these are obviously affected by the
inhomogeneity of the head and the measurement ge-
ometry. Because these factors cannot be obtained
experimentally, it is vital to be able to predict accu-
rately the light propagation in an inhomogeneous
structure, such as the head, by mathematical meth-
ods.
Several different mathematical techniques have
When this work was performed, E. Okada, M. Firbank, M.
Schweiger, M. Cope, and D. T. Delpy were with the Department of
Medical Physics and Bioengineering, University College London,
First Floor, Shropshire House, 11-20 Capper Street, London WC1E
6JA, UK. S. R. Arridge was with the Department of Computer
Science, University College London, Gower Street, London WC1
6BT, UK. E. Okada is now with the Department of Electronics
and Electrical Engineering, Keio University, 3-14-1 Hiyoshi,
Kohoku-ku, Yokohama 223, Japan.
Received 8 March 1996; revised manuscript received 12 June
1996.
0003-6935y97y00021-11$10.00y0
© 1997 Optical Society of America
1 January 1997 y Vol. 36, No. 1 y APPLIED OPTICS 21
been used to describe light propagation in scattering
tissue, and some preliminary modeling of simple lay-
ered structures have shown that the light penetra-
tion into deeper regions ~e.g., the brain! is strongly
affected by the optical properties of the surface
layer.
16–24
The presence of a relatively clear layer
~e.g., CSF! that has both low scattering and absorp-
tion coefficients has been shown especially to alter the
light propagation in the head.
21,24
However, in al-
most all these studies, the boundary of each layer has
had a simple geometry such as a flat or curved sur-
face that is significantly different from real head
structures. More sophisticated models are needed
for a rigorous analysis of light propagation in the
adult head. For example, the brain surface is actu-
ally deeply folded with many CSF-filled sulci, and it
is likely that light propagation in the brain is affected
by the sulcus structure.
In this study, in a variety of models of the adult
head, the effect of both the presence of the surface
tissues ~including a clear CSF layer! around the brain
and the brain anatomy itself have been investigated
by the use of solid slab phantoms that consist of lay-
ers with different optical properties. The simplest
adult head model is a three-layered slab without a
clear layer, whereas the most sophisticated model
has four layers, including a clear layer together with
slots that imitate the sulci. Time point-spread func-
tions for several different detection positions on the
outer surface are measured with a picosecond laser
and a streak camera, and the effect of the layered
structures is evaluated in terms of the mean optical
path length. The experimental data are compared
with the results of both Monte Carlo ~MC! and finite-
element calculations, which are also used to predict
the mean optical path length in each layer. Because
the path of individual photons can be traced in the
MC calculation, the spatial sensitivity profile in each
model has also been predicted, and the effects of the
surface layers on the volume of tissue interrogated in
the adult brain by NIRS instruments are discussed.
2. Optical Path in Near-Infrared Spectroscopy
The NIRS technique relies on the application of a
modified Beer–Lambert law
11
to convert measured
variations in attenuation ~DOD, where OD is the op-
tical density! into quantitative changes in the absorp-
tion coefficient ~Dm
a
! in the tissue. In the modified
Beer–Lambert law, the mean optical path length ^L&
replaces the physical distance between the source
and the detector:
DOD < Dm
a
^L& 5 Dm
a
c^t&.(1)
The mean optical path length is significantly greater
than the distance between the source and the detec-
tor because of the large amount of scattering in the
tissue. Thus a priori knowledge of the mean optical
path length is needed to quantify the change in ab-
sorption by the use of the modified Beer–Lambert
law. The mean optical path length can be derived
from the mean time of flight ^t& and the speed of light
c in the tissue. The mean time of flight can be ob-
tained from the temporal point-spread function
~TPSF!, which is the temporal intensity distribution
of a picosecond pulsed light that is broadened because
of the different scattering paths in the medium.
Although biological tissue has an inhomogeneous
structure, the tissue is assumed to be homogeneous
in the modified Beer–Lambert law. If it can be as-
sumed that the inhomogeneous tissue consists of sev-
eral homogeneous media, a partial mean optical path
length can be defined.
19
The partial mean optical
path length ^L
i
& is the mean optical path length that
the detected light travels within a particular medium
i, and the variation in attenuation of the detected
light across the tissue can be approximated by the
sum of the product of the partial mean optical path
lengths and the corresponding absorption coefficient
changes in each layer ~Dm
ai
!:
DOD <
(
Dm
ai
^L
i
&.(2)
The mean optical path length ^L&, which is the sum
of the partial mean optical path length • ^L
i
&, can be
calculated from the experimental TPSF measured
with a picosecond pulsed laser system. However,
the TPSF contains no direct information about the
time that the light has spent in each medium, and
hence the partial mean optical path length cannot be
obtained experimentally.
If the change in the absorption coefficient in each
medium is the same, then the partial mean optical
path length indicates the contribution that each me-
dium makes to the change in the output signal. It
should, however, be noted that, in general, the
changes in absorption in each medium are not the
same because of differences in hemoglobin content.
For instance, the normal CSF layer contains no he-
moglobin, and hence it does not contribute to the
change in the output signal. Although the partial
mean optical path length indicates the signal contri-
bution of each medium, it does not show the spatial
distribution of the volume contributing to the output
signal. The volume of tissue interrogated with
NIRS instruments can, however, be calculated as the
spatial sensitivity profile,
22
which is deduced from
the accumulated optical path histories of the photons
reaching the detector.
25,26
3. Methods
A. Adult Head Models
The adult head models used in this study are inho-
mogeneous slabs that consist of three or four different
homogeneous media. The geometries of the models
and the optical properties for each layer of the model
are shown in Fig. 1 and Table 1, respectively. The
simplest three-layered model @Fig. 1~a!# consists of a
12-mm-thick surface layer that imitates the scalp
and skull, a 4-mm-thick gray-matter layer, and a
white-matter layer. The optical properties for these
layers have been chosen from the reported data on
the optical properties of tissue.
27–29
The first four-
22 APPLIED OPTICS y Vol. 36, No. 1 y 1 January 1997
layered model @Fig. 1~b!# has a 2-mm-thick clear layer
that imitates the CSF between the 10-mm-thick sur-
face layer and the gray-matter layer. The simplest
model of the brain structure @Fig. 1~c!# has an uneven
boundary between the gray matter and the white
matter. The gray-matter layer has thick areas, 14
mm in thickness and 9 mm in width, placed every 15
mm. In the most sophisticated brain model @Fig.
1~d!#, slots 10 mm deep and 1 mm wide that imitate
the sulci filled with the clear CSF are added to the
simple brain model. The thickness of each layer and
the geometry of the sulci and gray matter were cho-
sen from a magnetic resonance image of an adult
head.
B. Experimental Setup
The actual design of the adult head phantoms is
shown in Fig. 2. The phantom was made of epoxy
resin containing TiO
2
to alter its scattering coefficient
and IR absorbing dyes to alter its absorption coeffi-
cient.
30
The phantom for each model consisted of
two parts. The surface layer of 10 mm and 12 mm in
thickness ~which imitated the scalp and skull! formed
the front and the rear walls, respectively, of a box
filled with glycerol, which imitated the CSF. The
second part, a block, 13 cm wide 3 6 cm high 3 8cm
thick, which consisted of the gray-matter and the
white-matter layers, could be positioned inside the
box at a suitable distance away from the inner face of
the front or rear wall. Three different inner blocks
were made with gray- and white-matter geometries,
as shown in Fig. 1. The three-layered model @Fig.
1~a!# was realized when the inner slab was positioned
directly against the inner face of the 12-mm surface
layer. The inner slab was located 2 mm away from
the inner face of the 10-mm surface layer for all the
other models. A picosecond pulsed laser and streak
camera were used to measure the TPSF of the phan-
toms.
11
The laser system consisted of an Ar-ion la-
ser pumping a Ti:sapphire laser and streak camera.
Laser pulses of approximately 2-ps half-maximum
width at the 800-nm wavelength were emitted at 82
MHz. Most of the laser light was delivered to the
surface of the phantom while a part of the laser beam
was sampled and directly relayed to the streak cam-
era as a time-reference pulse. In the case of the
simplest brain model @Fig. 1~c!#, the irradiated spot
was just over the center of the thick gray matter, and
in the sophisticated brain model @Fig. 1~d!#, it was in
the same position, which now coincided with the cen-
ter of a slot. The light emerging from the phantom
was collected in a fiber bundle and was conveyed to
the streak camera. The spacing between the irradi-
ated spot and the fiber bundle was altered horizon-
tally for all the models and also vertically in the case
of the models of Figs. 1~c! and 1~d!~i.e., along the
thick area of the gray matter or the slot!. The
TPSF’s at each source–detector spacing were mea-
sured and stored on a computer. The mean time of
flight was calculated from the TPSF, following soft-
Fig. 1. Schematic designs of the adult head models.
Fig. 2. Construction details for the adult head phantoms.
Table 1. Optical Properties of the Adult Head Models
Tissue Type
Transport Scattering
Coefficient m
s
9
~mm
21
!
Absorption
Coefficient
m
a
~mm
21
!
Scalp and skull 2.0 0.04
CSF 0.01 0.001
Gray matter 2.5 0.025
White matter 6.0 0.005
1 January 1997 y Vol. 36, No. 1 y APPLIED OPTICS 23
ware corrections for nonlinearity, shading sensitivity,
etc., of the streak camera.
C. Monte Carlo Simulation
The MC algorithm used in this study has already
been described
19
and is based on the variance-
reduction technique.
31–33
Isotropic scattering was
assumed, and if a photon crossed the boundary be-
tween different media, the distance to the next scat-
tering event was corrected by the use of the transport
scattering coefficient in the subsequent medium m
sj
9:
l
j
5 ~l
i
2 Dl!m
si
9ym
sj
9,(3)
where l
j
is the path length to the next scattering from
the boundary of the media and Dl is the path length
to the boundary of the media from the previous scat-
tering point. In order to avoid dividing by zero in
this correction process, a transport scattering coeffi-
cient of 0.01 was used for the clear CSF layer. Re-
flection and refraction of light caused by refractive-
index mismatching between the air and the tissue
were taken into account.
When the photon was scattered out of the head
model, the survival weight of the photon was calcu-
lated from the absorption coefficients m
ai
and the ac-
cumulated partial optical path length in each
medium L
i
. The survival weight and partial path
length of the photon were recorded for each detection
position up to a distance of 65 mm from the source.
For cases in which the photon reached detection po-
sitions of 15, 30, or 40 mm, the history of the photon
path weighted by the survival weight was accumu-
lated to obtain the spatial sensitivity profiles.
22
The
photon paths were projected onto an x–z plane to
record the two-dimensional spatial sensitivity pro-
files. After 10,000,000 input photons were traced,
the mean optical path length, partial mean optical
path length, the intensity of the detected light nor-
malized by source intensity, and the spatial sensitiv-
ity profiles were calculated.
D. Finite-Element Method
The time-independent diffusion equation,
34
which is a
well-known approximation of the radiative transfer
equation,
35
has been used to describe light propaga-
tion in tissue:
2¹ z k~r!¹F~r! 1 m
a
~r!F~r! 5 q
0
~r!,(4)
where k~r! is the diffusion coefficient, k~r!5$3@m
a
~r!
1m
s
9~r!#%
21
, F~r! is the photon density, and q
0
~r! is
the isotropic source distribution. In this study, a
finite-element method
36,37
~FEM! was used to solve
the diffusion equation, and the outgoing fluence ~exi-
tance!G~r!was calculated by
G~r! 5 2k~r!eˆ z ¹F~r!,(5)
where eˆ is the vector normal to the detection area.
In order to obtain the partial mean optical path
length from the exitance, it is assumed that the op-
tical path length in each layer does not vary with a
small absorption change. The difference in exitance
DG caused by a 1% absorption change in a particular
layer i was predicted, and the partial mean optical
pathlength ^L
i
& in layer i was calculated by
^L
i
& 5 DGyDm
ai
.(6)
Although the FEM can be applied to three-
dimensional models, in this study a two-dimensional
rectangular model was used to keep the memory size
required for matrix manipulation within a reason-
able limit. For the three-layered model, the rectan-
gular domain was divided into approximately 21,000
triangular subspaces and Robin boundary conditions
were used.
37
An isotropic point source located at a
distance 1ym
s
9 below the surface layer at the irradi-
ated position was used to approximate a collimated
incident laser beam.
37
Because the diffusion equation no longer holds in a
medium that has a low scattering coefficient, the
FEM could not be directly applied to the models of
Figs. 1~b!–1~d! with a clear CSF layer, so a hybrid
radiosity–diffusion theory model
24
was used instead.
The concept of the hybrid radiosity–diffusion model is
to predict light propagation in the scattering regions
by the diffusion theory and in the clear CSF layer by
a radiosity method and to combine the two results in
an iterative scheme until a minimum change in exi-
tance is achieved. It is assumed that the light in the
scattering tissue, such as scalp, skull, and brain,
obeys the diffusion equation ~4!, and the light propa-
gating without diffusion in the CSF complies with the
radiosity equation.
24
The FEM was applied to the
two rectangular domains, one being the surface layer
and the other the gray- and the white-matter layers.
The surface and the inner domains were divided into
approximately 7000 and 13,000 triangles, respec-
tively. The photon density at the inner boundary of
the surface domain arising from the incident beam on
its outer surface was first calculated by the FEM, and
from this resulting photon density the outgoing radi-
ance I~ p, s! at any point p traveling in direction s on
the surface was obtained. With this outgoing radi-
ance, the radiosity theory was used to calculate the
resulting irradiance G
R
~q! on an area dA at position q
on the outer surface of the inner domain across the
clear CSF layer:
G
R
~q! 5
**
A
I~p, s!cos~u
1
!cos~u
2
!
uru
2
exp~2urum
a
!dA,(7)
where u
1
, u
2
are the angles between s and normal
components of the surface of the two layers, m
a
is the
absorption coefficient of the CSF layer, s points from
p to q. The photon density in the inner domain
caused by the irradiance on its surface was then cal-
culated by the FEM, and the resulting outgoing ra-
diance from the inner domain was similarly obtained.
The resulting radiance was then again used as an
input to the radiosity equation, which calculated the
fluence back onto the inner face of the surface do-
main, and the photon density in the surface layer was
recalculated. This process was iterated until the
24 APPLIED OPTICS y Vol. 36, No. 1 y 1 January 1997
change in the total exitance became negligible ~,1%
change!.
The simple and the sophisticated brain models
@Figs. 1~c! and 1~d!, respectively# have different cross
sections in the x–z and the y–z planes, but the cross
section in the x–z plane was used for the two-
dimensional approximation for both these models.
The partial mean optical path lengths in the models
with the clear CSF layers were calculated in the same
way as for the three-layered model.
4. Results
Experimental results for the mean time of flight are
compared with the predictions of the MC method
~MCM! and the FEM in Fig. 3. The corresponding
mean optical path length calculated from the mean
time and the speed of light in the epoxy resin is also
shown in each figure. On a SunSparc 20 worksta-
tion, the calculation for each model took ;200-h CPU
time for the MCM, 3-min CPU time for the FEM
based on the diffusion theory, and 15-min CPU time
for the FEM based on the hybrid radiosity–diffusion
theory. The experimental results and predictions
~MCM and FEM! for the mean time of flight as a
function of spacing are in good agreement for all mod-
els. However, statistical noise in the MC results is
notable at detection positions of greater than 30 mm.
The mean time for all the models at detection posi-
tions up to 20 mm are almost the same. For the
models of Figs. 1~b!–1~d!, which have the clear CSF
layer, once the detection position is greater than 20
mm the mean time increases only slowly with spacing
between source and detector whereas for the three-
layered model @Fig. 1~a!# without the clear layer, it
continues to increase rapidly. The differences in
mean time between all the models with a clear CSF
layer are not significant over the whole range of de-
tection positions. In both the simple brain model
@Fig. 1~c!# and the sophisticated brain model @Fig.
1~d!#, the direction of the detection position ~horizon-
tal or vertical! produced no statistically significant
differences in mean time, so data in regard to the
vertical detection positions are not shown.
The partial mean optical path length in each layer
in the models is shown in Fig. 4. The partial optical
path length cannot be obtained from the experimen-
tal TPSF, so only the results predicted by the MCM
and the FEM are compared. The predictions of both
methods show the same tendency. In the three-
layered model the partial mean optical path length of
both the gray- and the white-matter layers is small at
detection positions up to 30 mm. This means that
Fig. 3. Mean time of flight and corresponding mean optical path length as functions of the detection position predicted by the MCM and
the FEM compared with experimental results ~61SD!.
1 January 1997 y Vol. 36, No. 1 y APPLIED OPTICS 25
the light is largely confined to the surface layer.
Once the detection position is greater than 30 mm,
the partial mean optical path lengths of both the
gray- and the white-matter layers ~and beyond 50
mm especially the white-matter layer! steeply in-
crease. From the FEM results, the partial mean
optical path length of the white-matter layer exceeds
that of the surface layer at detection positions of
greater than 60 mm. In the models of Figs. 1~b!–1~d!
with the clear CSF layer, the relationships between
detection position and partial mean optical path
lengths are similar, but are completely different from
those in the three-layered model of Fig. 1~a!. The
partial mean optical path lengths of the deeper layers
are small at detection positions up to 15 mm. Once
the detection position exceeds 15 mm, the partial
mean optical path lengths of both the CSF and the
gray-matter layer start to increase. The partial
mean optical path lengths of both the surface and the
gray-matter layers remain almost constant at detec-
tion positions of greater than 30 mm, whereas that of
CSF layer continues to gradually increases. The
partial mean optical path length of the white-matter
layer is still small, even when the detection position
exceeds 60 mm.
The intensity of detected light predicted by both
the MCM and the FEM is shown in Fig. 5. The
results are normalized by the source intensity, and in
the case of the simple and the sophisticated brain
models @Figs. 1~c! and 1~d!, respectively# only the re-
sults of horizontal detection are shown. The MCM
and FEM predictions agree well for all the models.
Up to 20 mm, the intensity for all the models is the
same as a function of the detection position. Beyond
20 mm, the rate of decline in the intensity with the
detection position for all the models with a clear CSF
layer diminishes whereas that for the three-layered
model continues at approximately the same rate.
The MC-calculated spatial sensitivity profiles for
the three- and the four-layered models @Figs. 1~a! and
1~b!, respectively# at a detection position of 15 mm are
shown in Figs. 6~a! and 6~b!, respectively. The con-
tours are drawn for every 12.5% fall from the maxi-
mum sensitivity point, and the extreme contour
indicates a relative sensitivity of 0.3%. In both Figs.
6~a! and 6~b! the spatial sensitivity profiles are con-
Fig. 4. Partial mean optical path length as a function of detection position predicted by the MCM ~symbols! and the FEM ~curves!.
26 APPLIED OPTICS y Vol. 36, No. 1 y 1 January 1997
fined to the surface layer, so the results for Fig. 6~b!
will also apply to the simple and the sophisticated
brain models of Figs. 1~c! and 1~d!, respectively,
whose differences in the geometry occur only under
the CSF layer. Figures 7~a!–7~d! show the spatial
sensitivity profiles for all the models at a detection
position of 30 mm. In the case of the simple and the
sophisticated brain models, the results of horizontal
detection are also shown. At this detection position
the number of detected photons is not sufficient to
provide good statistics; however, the general ten-
dency for the localization of the sensitive area can be
recognized. In the three-layered model of Fig. 7~a!
the spatial sensitivity profile is still largely confined
to the surface layer, and little light penetrates into
the gray matter. The spatial sensitivity profile of
the four-layered model of Fig. 7~b! spreads farther
toward the clear CSF and the gray-matter layers;
Fig. 5. Normalized intensity of detected light for each model as a
function of the detection position predicted by the MCM and the
FEM.
Fig. 6. Spatial sensitivity pro-
files with a detection fiber 15 mm
distant from the light source
along the horizontal ~x! axis.
Fig. 7. Spatial sensitivity pro-
files with a detection fiber 30 mm
distant from the light source
along the horizontal ~x! axis.
1 January 1997 y Vol. 36, No. 1 y APPLIED OPTICS 27
however, very little light reaches the white-matter
layer. Although light reaches the gray-matter layer,
there are no significant differences between the spa-
tial sensitivity profiles of all three models with a clear
CSF layer @Figs. 7~b!–7~d!#. The spatial sensitivity
profiles at a detection position of 40 mm are shown in
Figs. 8~a! and 8~d!. Contours have not been drawn
on these profiles because of poor statistics. In the
three-layered model of Fig. 8~a! the spatial sensitivity
profile is still confined mainly to the surface layer.
In the other models @Figs. 8~b!–8~d!# the spatial sen-
sitivity profile has shifted toward the deeper layers,
and an apparent light path can be seen around the
clear CSF layer. However, the detected light still
does not tend to penetrate into the white-matter
layer. A slight difference in the spatial sensitivity
profiles can be observed between the four-layered
model of Fig. 8~b!, the simple brain model of Fig. 8~c!,
and the most sophisticated brain model of Fig. 8~d!.
Finally, Fig. 9 shows the vertical spatial sensitivity
profiles of all the models at a detection position of 30
mm. The spatial sensitivity profiles for all the mod-
els with a clear CSF layer spread around the CSF
layer. The profiles of the four-layered model of Fig.
9~b! and the simple brain model of Fig. 9~c! are almost
identical. In the most sophisticated brain model of
Fig. 9~d!, the source and the detector were positioned
above a sulcus, and it can be seen that light pene-
trates more deeply in the area along the sulcus.
However, the spatial sensitivity profile around the
sulcus is still confined to the gray-matter layer with
little penetration into the white matter.
5. Discussion
In the adult head, experiment has shown that the
mean optical path length divided by the spacing be-
tween source and detector, the differential path-
length factor, is approximately constant for detection
positions greater than 25 mm
12
at a value of ;6, but
increases at closer detection positions. Because the
mean optical path lengths for all the phantoms with
a clear CSF layer also show this tendency, the results
from these models are thought to reasonably mimic
the actual light propagation in the adult head.
In the MCM, the full three-dimensional geometry
is faithfully replicated, and therefore the errors in
prediction are caused mainly by inadequate photon
statistics. The MC results show that although the
clear CSF layer increases the intensity of the de-
tected light and hence improves the statistics, signif-
icant error is still notable once the detection position
is beyond 30 mm. On the other hand, both the nor-
mal and the hybrid FEM predictions show reasonable
agreement with the experimental results in spite of
being only two-dimensional approximations. This
indicates that these techniques can probably be used
with some confidence to calculate mean optical path
lengths in complex heterogeneous media. This is
important because, in the practical use of NIRS on
the human adult, the fiber spacing is often from 30 to
60 mm, and the statistical error of MC predictions for
reasonable computation times is large, beyond a de-
tection position of 30 mm.
The mean optical path lengths for the models with
Fig. 8. Spatial sensitivity pro-
files with a detection fiber 40 mm
distant from the light source
along the horizontal ~x! axis.
28 APPLIED OPTICS y Vol. 36, No. 1 y 1 January 1997
a clear CSF layer increase slowly beyond a detection
position of 25 mm whereas those of the three-layered
model continue to increase steeply. It is obvious
that the clear CSF layer considerably affects the
mean optical path length at these large spacing.
The features of light propagation in the adult head
can thus be placed in these categories according to
the detection position: ~1! at small detection posi-
tions ~#15 mm! the mean optical path length is
equivalent to the partial mean optical path length of
the surface layer, i.e., the spatial sensitivity profile is
confined to the surface layer; ~2! at intermediate de-
tection positions ~$15 mm, #25 mm! the partial
mean optical path lengths of both the clear CSF and
the gray-matter layer increase with the detection po-
sition, and the spatial sensitivity profile spreads lat-
erally over the inner face of the surface layer and the
gray-matter layer; and ~3! at large detection positions
~$25 mm! the partial mean optical path lengths of
the surface and the gray-matter layer remain approx-
imately constant while that of the clear CSF layer
increases with the detection position. The spatial
sensitivity profile is distributed mainly around the
surfaces that face the clear CSF layer except for the
sites directly underneath the source and the detector.
It is apparent that once light reaches the clear CSF,
this layer starts to act as a conduit for the light that
reaches the distant detector. Because little absorp-
tion occurs in the clear CSF layer, the intensity of
detected light at large detection positions in the mod-
els with a clear CSF layer is much higher than that in
the three-layered model without the clear CSF layer.
The light that passes through the CSF layer only
grazes the surface and the gray-matter layers, which
therefore make little contribution to the optical path
length. Thus the partial mean optical path lengths
in the surface and the gray-matter layers increase
only slowly with detection position. It is also nota-
ble that the presence of the clear CSF layer signifi-
cantly reduces the light penetration into the deeper
white-matter layer. As shown in Fig. 4, the partial
mean optical path length of the white-matter layer in
the models with a clear CSF layer are almost negli-
gible whereas that in the three-layered model with-
out the clear CSF layer steeply increases beyond a
detection spacing of 40 mm. It should be empha-
sized here that the presence of the clear layer does
not prevent light penetration into white matter. In-
deed, the intensity of the detected light that has pen-
etrated into the white matter is probably similar to
that in the three-layered model; however, the in-
creased intensity of the light guided to the detector
through the CSF layer becomes the dominant com-
ponent of the signal. Because in the clear-layer
models, light penetration into the gray matter is pre-
dominantly confined to a shallow depth, the geometry
of both the sulci and the boundary between the gray-
and the white-matter layers only slightly affect the
partial mean optical path lengths and spatial sensi-
tivity profiles. In the case in which both the source
and the detector are placed along the axis of a slot,
the light does penetrate deeper, but even then, it is
still confined to the area around the sulcus and the
light does not penetrate the white matter.
From the FEM predictions of the partial optical
path lengths in the sophisticated brain model shown
in Fig. 4~d!, light detected at a spacing of 50 mm
spends approximately 65% of its path length in the
scalp and skull, 35% in the CSF, and 5% in the gray
matter, with very little white-matter component.
However, these ratios do not necessarily represent
the contribution of each layer to the change in the
output signal. The change in the output signal de-
pends not only on the partial mean optical path
length but also on the change in the absorption coef-
ficient. Any layer in which no absorption change
occurs does not contribute to the output signal, no
matter how long the light path length in it. Simi-
larly, the deeper area in which the partial mean op-
tical path length is much shorter than in the shallow
area can contribute significantly to the output signal
if the absorption change there is much greater than
that in the shallow area. This may explain why ab-
sorption changes caused by intracranial hemorrhage
can be detected with NIRS instruments even if they
occur in the white matter or in deeper areas of the
gray matter.
38
This sort of drastic absorption
change will also considerably affect the light propa-
gation in the head and hence alter both the partial
mean optical path lengths and the spatial sensitivity
profile. For example, it is easy to imagine that if the
CSF is replaced by blood in an epidural hemorrhage,
Fig. 9. Spatial sensitivity profiles with a detection fiber 30 mm
distant from the light source along the vertical ~ y! axis.
1 January 1997 y Vol. 36, No. 1 y APPLIED OPTICS 29
the CSF layer no longer works as a light guide. Ac-
cordingly the prediction of partial mean optical path
length and spatial sensitivity profile for the models in
this study cannot be used to analyze the signal con-
tribution and interrogated area in cases in which
drastic absorption changes occur in the head.
However, in most clinical NIRS studies, smaller
absorption changes, for example, those that are due
to mild hypoxia or changes in oxygenation state with
brain activity and so on, are normally monitored.
This sort of small absorption change should mini-
mally affect the light propagation in the head, and
hence the detected light distribution can be described
by the spatial sensitivity profiles shown in Figs. 6–9.
Because the change in the absorption coefficient de-
pends on the blood content and there is virtually no
absorption change in the CSF layer under normal
conditions, the contribution of the CSF layer to the
output signal is negligible. In this study the scalp
~typically 5 mm thick! and the skull ~typically 5 mm
thick! were combined into one surface layer, and the
partial optical path length of this combined layer is
much greater than that of all other layers. The
blood volume and hence the absorption coefficient of
the scalp is much higher than those of the skull;
however, in NIRS studies, the blood directly under
the NIRS optodes may often be squeezed out because
of optode pressure, thus reducing its contribution to
the total absorption change signal. The light in the
surface layer then passes through the skull, which,
because of its low blood volume, also contributes little
to any absorption change signal. This supposition is
further borne out by the spatial sensitivity profile,
which shows that this element of the signal arises
mainly from the inner skull table. In the brain the
blood volume in gray matter is approximately twice
as much as that in white matter,
39
and hence the
absorption change caused by oxygenation variation
in gray matter is generally greater than that in white
matter. Consequently, the actual contribution of
the absorption change in the gray matter to the
change in the detected NIRS signal is probably sig-
nificantly greater under normal conditions and it
probably reaches at least 20–30%. The success of
experimental studies of cerebral-evoked response in
adult humans provides further evidence for this
conclusion.
6,40–42
6. Conclusions
In this study the effect on NIR signals of the layered
surface tissues surrounding the brain in the adult
head have been investigated by both time-of-flight
measurements and mathematical predictions. The
clear CSF layer significantly affects light propagation
in the adult head once the spacing between source
and detector is greater than 15 mm. At large
source–detector spacing the detected light passes
mainly through the CSF layer and this forces the
sensitive region to be confined to a shallow section of
the gray matter. The partial mean optical path
lengths of both the surface and the gray-matter lay-
ers change only slowly once the detection position
exceeds 30 mm. This indicates that the contribution
of changes in absorption in the gray matter to the
NIRS signal is almost constant at these detection
positions and its contribution probably reaches 20%–
30%. Under these circumstances, it is difficult for
NIRS to detect small oxygenation changes in the
deeper areas of the gray and the white matter. The
geometries of the sulci and the boundary between the
gray- and the white-matter layers scarcely affect the
optical path in the adult head.
This work was supported by the Japan Society for
the Promotion of Science, Postdoctoral Fellowship for
Research Abroad to E. Okada from April 1995 to
March 1996, funding from the Engineering and Phys-
ical Research Council ~UK!~GRyK07386, GRy
G05100!, the Wellcome Trust, and Hamamatsu
Photonics KK. Some parts of these data were pre-
sented at a Society of Photo-Optical Instrumentation
Engineers’ Conference, “Photon Propagation in Tis-
sues: Quantitation and Clinical Studies using Con-
tinuous Wave, Time, and Frequency Domain
Technology” in Barcelona, Spain, in 1995.
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