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Modelling the sampling volume for skin
blood oxygenation measurements
I. V. Meglinsky
1,2
S. J. Matcher
1
1
School of Physics, University of Exeter, Exeter, UK
2
School of Engineering, Cranfiels Universirty, Cranfield, UK
AbstractÐThe absolute quanti®ed measurement of haemoglobin skin blood saturation
from collected re¯ectance spectra of the skin is complicated by the fact that the blood
content of tissues can vary both in the spatial distribution and in the amount. These
measurements require an understanding of which vascular bed is primarily respon-
sible for the detected signal. Knowing the spatial detector depth sensitivity makes it
possible to ®nd the best range of different probe geometries for the measurements of
signal from the required zones and group of vessels inside the skin. To facilitate this, a
Monte Carlo simulation has been developed to estimate the sampling volume offered
by ®bre-optic probes with a small source-detector spacing (in the current report
250 mm, 400 mm and 800 mm). The optical properties of the modelled medium are
taken to be the optical properties of the Caucasian type of skin tissue in the visible
range of the spectrum. It is shown that, for a small source-detector separation (800 mm
and smaller), rough boundaries between layers of different refractive index can play a
signi®cant role in skin optics. Wavy layer interfaces produce a deeper and more
homogeneous distribution of photons within the skin and tend to suppress the direct
channelling of photons from source to detector. The model predicts that a probe
spacing of 250 mm samples primarily epidermal layers and papillary dermis, whereas
spacings of 400±800 mm sample upper blood net dermis and dermis.
KeywordsÐSampling volume, Light scattering, Human skin, Monte Carlo simulation,
Skin blood oxygenation, Multi-layered media
1 Introduction
SINCE CHANCE introduced the two-wavelength method
(CHANCE,1954),tissuespectraphotometryhasbeenwidely
applied to different biomedical investigations. Nowadays,
optical techniques are most popular for these investigations
because light in the visible (l400±770 nm) and near-infrared
(NIR) (l770±1400 nm) spectral regions makes it possible to
monitor changes in microcirculation and haemoglobin oxygen
saturation essentially in real time and non-invasively. The results
ofsuchmeasurementswithindifferentareasoftheskinshed
light on a broad range of physiological processes that occur
within various skin diseases, such as venous ulcers, skin
necrosis, interstitial oedema etc.
As an object of investigation by optical techniques, skin
represents a complex heterogeneous medium consisting of
distinct layers: epidermis, dermis and subcutaneous fat. These
layers contain the chromophores, including DNA, urocanic acid
(UCA), amino acids, elastin, collagen, kerratin, NADH, melanin
and their precursors and metabolites, whereas the major contri-
bution to light absorption in the visible and NIR spectral regions
arises from oxy- and deoxy-haemoglobin (contained in blood),
melaninandwater(FEATHERetal.,1981;YOUNG,1997).
Recently, the possibility of using optical re¯ectance
spectroscopy to measure non-invasively skin haemoglobin
saturation SO
2
(HANNAetal.,1995)(de®nedastheratioof
oxygenated to total haemoglobin present in the blood
compartment being observed) was introduced. For given
carbon dioxide tension and pH, this quantity should bear a
®xed relationship to blood pO
2
.
However, the absolute quanti®ed measurements of haemo-
globin skin blood oxygen saturation from collected re¯ectance
spectra of the skin are complicated by the fact that the blood
content of tissues can vary both in the amount and in the spatial
distribution. These measurements require an understanding of
which vascular bed is primarily responsible for the detected
signal. This problem is well known in the related ®eld of laser
Doppler¯owmetry(JAKOBSSONandNILSSON,1993;DEMUL
etal.,1995).
In the current paper, we report the results of our initial
theoretical investigation of the degree of signal localisation to
the upper layers of skin (especially the capillary loops). A small
source-detector separation in required owing to the shallow
spatial location of skin capillary loops (only about 100 mm
under the skin surface); hence, we cannot reliably apply the
diffusionapproximationoftransporttheoryforthisstudy(YOO
etal.,1990),andonlytheMonteCarlotechniquecanprovidea
realistic model of light propagation in biological tissues. These
reasons lead us to choose the Monte Carlo method, which is
well-known for its accuracy and simplicity of application to
complexmulti-layeredmedia(HIRAOKAetal.,1993;JACQUES
andWANG,1995;PRAHLetal.,1989).
Correspondence should be addressed to Dr I.V. Meglinsky;
e-mail:i.meglinski@cranfield.ac.uk
44
Medical & Biological Engineering & Computing, 2001, 39 (1): 44-50
2 Computational model of the skin
Following earlier work aimed at computational modelling of
theskin(PRAHLetal.,1989;TUCHINetal.,1994;JACQUESand
WANG,1995),letusconsidertheskinasathree-dimensional
half-in®nite medium divided into several layers with varying
opticalproperties(Fig.1).
The ®rst layer in our model corresponds to a layer of
desquamating ¯attened dead cells, mainly containing keratin,
which is 20 mm thick and known as the stratum corneum. The
second layer we call `living epidermis'. It is 80 mm thick and is
assumed to contain primarily living cells: a fraction of
dehydrated cells, laden cells with keratohyalin granules,
columnar cells and also melanin dust, small melanin granules
and melanosoms. Given the inhomogeneous distribution of the
bloodvesselsandskincapillarieswithintheskin,wesub-
divide the dermis into four different layers, with different
blood volumes. These layers are the papillary dermis
(150 mm thick), upper blood net dermis (80 mm thick), dermis
(1500 mm thick) and deep blood net dermis (170 mm thick).
The deepest layer in our model is the subcutaneous fat
(6000mmthick)(seeFig.1).
Of course, some variability in thickness is expected from
region to region of the body and between individuals, and
histological evidence suggests this can be of the order of
30±40%(STENN,1988;ODLAND,1991;RYAN,1991).
However, we assume that these values for layer thickness are
typical of Caucasian adults.
The different structure and blood content of these skin layers
affect their optical properties, which is very important for our
optical model. The optical properties of the simulated skin layers
are m
a
absorption coef®cient, m
s
scattering coef®cient,
gscattering anisotropy factor and nrefractive index. To
try to represent the observed histological structure of real skin
(seeFig.1),wemodeltheboundariesofthelayersasperiodic
surfaces(Fig.2)
Bkx;yZkx0;y0Akx sinokyxfkx
akx sino0
kxyf0
kxAky sinoky yfky
aky sino0
kyyf0
ky 1
where B
k
(x,y) is the depth of the klayer at (x,y); Z
k
(x
0
,y
0
)is
the mean depth of the boundary; kis the layer index; A
kx
,A
ky
,
a
kx
,a
ky
are amplitude coef®cients; o
kx
,o
ky
,o0
kx
,o0
ky
are
scale lengths of the roughness; and f
kx
,f
ky
,f0
kx
,f0
ky
are arbitrary
phase offsets, respectively, in the x- and y-directions. The values
of these parameters, presented in Table 1, produce boundaries
comparablewiththeobservedstructureofrealskin(MAIBACH
andLOWE,1987;CORCUFFetal.,1993;HOLBROOK,1991;
ODLAND,1991;STENN,1988;RYAN,1991;SERUPandJEMEC,
1995).Suchboundariesareclosertothestructureofobserved
histological sections than plane boundaries (see Fig. 1). This can
be important, as the statistics of photon re¯ections at the
boundaries will be affected.
The optical properties of the layers presented in Table 2 are
taken from the literature and correspond to a wavelength of
600nm(SHEUPLEIN,1964;ANDERSONandPARRISH,1982;
CHEONGetal.,1990;DUCK,1990;NILSSONandNILSSON,
1998;RAJADHYAKSHAandZAVISLAN,1998;TUCHIN,1998;
SCHMITTandKUMAR,1998;SIMPSONetal.,1998;DOORNBOS
etal.,1999).
3 Method
The method for simulating the sampling volume for the
different ®bre-optic probe geometries is based on the random
simulation of a large number of possible trajectories of photons
stratum corneum
living epidermis
dermis
subcutaneous fat
Fig. 1 Skin structure
Y
X
Z
0
Fig. 2 This surface plot shows the mathematical form used to
describe the junction between skin layers in our model,
corresponding to a cross-section of a real image of the
epidermal boundary
45
as they travel through the highly scattering medium. The
simulation consists of a sequential random walk of photon
packets between scattering events from the site of photon
injection into the medium to the site where the photon leaves
the medium. The random path length that a photon packet moves
for step iis given by
liÿlnxi
ms
2
where x
i
is a uniformly distributed random number between 0
and 1. After injection into the medium, a software-generated
random number is used to determine the distance propagated
before the photon packet encounters the next scattering centre.
The scattering event is then simulated by the generation of two
randompropagationanglesjandy,whichdescribethenew
direction in which the photon packet then travels. The whole
process is repeated until the photon packet either exits the tissue
or is lost within the medium. The principles of this method have
beenwidelydescribed(CASHWELLandEVERETT,1959;MEIER
etal.,1978;PRAHLetal.,1989;JACQUESandWANG,1995;
WANGetal.,1995).
In our model, we have taken into account the internal
re¯ection of the scattered radiation on the medium boundary
by allowing the incident photon packet to split into a re¯ected
andtransmittedpart(VANDERZEE,1992).Theweightofthese
re¯ected and transmitted parts of the photon packet are attenu-
atedaccordingtotheFresnelre¯ectioncoef®cients(BORNand
WOLF,1986)
Ra
nk1ÿnk
nk1nk
2
if a0
1
2
sin2aÿat
sin2aattan2aÿat
tan2aat
hi
if 0 <a<sinÿ1nk1
nk
1 if sinÿ1nk1
nk
<a<90
8
>
>
>
>
<
>
>
>
>
:3
where the symbols are de®ned in Fig. 3.
Thus, in the absence of absorption, the probability of
collecting a photon on the detector is described as follows:
W0Win1ÿR0a Q
B
p1
Rpa4
where W
in
is the initial weight of the photon packet, Bis the
number of times the photon packet undergoes a partial re¯ection
on the medium boundary, R
p
(a) is the Fresnel re¯ection coef®-
cient for the pth photon±boundary interaction, and R
0
(a) is the
Fresnel re¯ection coef®cient for the initial photon packet±
boundary interaction, when the photon packet enters the
medium.
To decide whether a photon is re¯ected or transmitted at
internallayerboundariesinthemedium(k60),wefollowthe
procedureofJACQUESandWANG(1995),i.e.comparearandom
number x
B
uniformly distributed between 0 and 1 to R(a) (3) and
allow either re¯ection or transmission of the photon if x
B
is
smaller or bigger than R(a), respectively.
The simulation of an individual photon packet is stopped if its
statistical weight falls below 0.001, or if it moves away from the
source by more than 1000 scattering mean free-paths, or if the
total number of scattering events exceeds 10 000. The total
number of detected photon packets N
ph
(usually 10
5
±10
7
) used
foreachsimulationisde®nedbeforethesimulation(KIENLE
etal.,1996).Theindividualtrajectoryofeachdetectedphoton
packet are stored in a data ®le, requiring a large amount of disk
memory (typically several hundred megabytes).
Table 1 Values of parameters de®ned in eqn 1 and used in our simulation
kBoundary between layers A
kx
,A
ky
,mm(p=o)
kx
,mm(p=o)
ky
,mmZ
k
(x
0
,y
0
), mm
0 air ± startum corneum (skin surface) 2 100 150 0
1 startum corneum ± living epidermis 2.5 80 80 20
2 living epidermis ± papillary dermis 20 50 45 100
3 papillary dermis ± upper blood net dermis 2 20 40 200
4 upper blood net dermis ± dermis 2 20 50 280
5 dermis ± deep blood net dermis 2 20 50 1900
6 deep blood net dermis ± subcutaneous fat 5 20 50 2100
7 subcutaneous fat ± other tissues 5 25 30 8000
α
αt
medium k
nk
nk+1
medium k+1
Fig. 3 The diagram represents the re¯ected and transmitted parts of
the photon packet on the medium boundary. Here, aand a
t
are the angles of the photon packet incidence on the layer
boundary and transmittance, respectively, k and k 1 show
the direction of the photon packet±boundary crossing and
indicate the medium layers (0 corresponds to the ambient
medium); nis the refractive index
Table 2 Optical properties of skin model (l600 nm, Caucasian
skin)
kSkin layer m
s
,mm
ÿ1
m
a
,mm
ÿ1
gn
1 stratum corneum 100 0.02 0.9 1.53
2 living epidermis 40 0.015 0.85 1.34
3 papillary dermis 30 0.07 0.8 1.4
4 upper blood net dermis 35 0.1 0.9 1.39
5 dermis 20 0.07 0.76 1.4
6 deep blood net dermis 35 0.1 0.95 1.39
7 subcutaneous fat 15 0.03 0.8 1.44
The refractive index of air is n
0
1
46
According to the microscopic Beer±Lambert law, we include
absorption of photons within the medium layers by recalculating
the statistical weight of each photon packet according to the
length of its trajectory within the layer. Thus, the ®nal weight of
the photon packet on the detector is described as follows:
Wa;jW0exp ÿP
M
i1
mariljri
5
where Mis the number of voxels in the simulated volume, and
m
a
(r
i
) and l
j
(r
i
) are, respectively, the absorption coef®cient and
the path length traversed by the jth photon packet in voxel iat
position r
i
.
The sampling volume, i.e. spatial distribution of detector
depth sensitivity Q(r
m
), is de®ned as the gradient of optical
density with respect to absorption coef®cient m
a
at each pixel r
m
inthemedium(HIRAOKAetal.,1993;ARRIDGE,1995)
Qrmÿ @
@marmln I
I0
X
Nph
j1
Wa;jljrm
X
Nph
j1
Wa;j
hlrmi 6
Here, IPNph
j1Wa;j;Wa;jis the statistical weight of the jth
detected photon (eqn 5); l
j
(r
m
) is the path length traversed by the
jth photon packet in the mth pixel at a position r
m
; and hl(r
m
)iis
theweightedmeanofthepathlengthtraversedbyeachphoton
through pixel m. In the current simulation, we consider the
distribution Q(r
m
) as a function of xand zonly, where xis the
horizontal axis referred to the centre-to-centre line between
source and detector, and zis the depth direction; i.e., Q(x,z)
represents a two-dimensional cross-section map through the 3D
distribution Q(r
m
).Itcanbeshown(HIRAOKAetal.,1993;
ARRIDGE,1995;OKADAetal.,1997)thatthisquantityequalsthe
mean path length travelled by photons within the cell at r. Hence,
in our simulation, Q(r
m
) is calculated directly from the photon
history data.
4 Results and discussion
Simulated spatial distributions of detector depth sensitivity in
the case of wavy interfaces between the layers are presented in
Figs4a,candeandarecomparedwiththeresultsofsimulations
with¯atlayerboundaryinterfacesinFigs4b,dandf.Thephoton
history has been calculated using 10
4
detected photon packets
for each model, and the calculation time on a Silicon Graphics
RS00 Indy workstation took about 1 h for 10
3
photon packets.
The source-detector ®bre spacing (800 mm, 400 mm and 250 mm
(centre-to-centre)) and diameters (200 mm and 50 mm, respec-
tively) were largely determined by the practicalities of the ®bre-
optic probe design and manufacture. The sizes of the grid cells
usedinthesimulationwerechosentobe10mminthex-,y-,and
z-directions.
The spatial distribution of detector depth sensitivity Q(x,z)
has units of millimetres, representing the average physical path
travelledbyphotonsinthepixellocatedat(x,z).Theasymmetry
in the distribution near the source and detector areas seen in
Figs4a±fisduetothedifferentsizeofthesourceanddetector
®bres. It is noteworthy here that, for all values of source±detector
spacing(seeFigs4a±f),thedetectorismostsensitivetothe
uppermost highly scattering and absorbing layer, the thickness
of which is 100 mm or less. In other words, the majority of the
incident radiation reaches only the ®rst layer of the skin. This
result agrees well with the known properties of skin, where the
stratum corneum and epidermis stop the majority of the light
incidentontheskinsurface(SLINEYandWOLBARSHT,1980;
TUCHIN,1998).
However, skin blood oxygenation measurements require us to
sample deeper layers of skin, because the capillary loops are
typically located at a depth of about 100±150 mm under the skin
surface. Increasing the source±detector spacing to 800 mm
increases the sampling volume, so that it reaches the middle of
thedermis(Figs4aandb).Thedetectedsignalshouldbe
collected now from the top part of the dermis, which includes
the capillary loops, small venules and arterioles. Decreasing the
source±detector spacing signi®cantly reduces the area over
whichthedetectorissensitive(seeFigs4eandf).
For the distribution of detector depth sensitivity Q(x,z) for the
mediumwith¯atlayerboundaryinterfaces(seeFigs3b,dandf)
along the boundaries of the ®rst two layers (in depth 0, 20, 100
and 200 mm) we can see small `channels' between the source and
detector areas. The simulations using wavy boundary interfaces
betweenlayerstendtosuppressthese`channels'(seeFigs4a,c
ande)andleadtophotonpacketsbeingdistributedmore
homogeneouslywithinthemedium(seeFig.4a).Comparing
the results of the simulations using wavy interfaces with those
using ¯at interfaces, we can see that the in¯uence of the wavy
boundaries is also pronounced in reducing the internal re¯ection
of photon packets on the medium surface. This is evident as a
suppression of the channels between source and detector (see
Figs4aandb,candd).
To compare the results quantitatively, it is better to consider
the mean partial optical path length
hlki
ÿ@ln I
I0
@ma;k
7
for each layer as a function of the source±detector spacing. Here
@ma;krepresents a perturbation to mathat occurs uniformly
throughout layer k.
An increase in blood content in a layer will tend to reduce the
overall path length in that layer; conversely, a decrease in blood
content will lengthen the path length in it. However, we believe
that the blood content used in our simulation is a reliable
estimate for the true blood volume in the skin tissues.
Fig.5showsthefractionoftotalpathlengthinthe®rst®ve
layersofbothmediawithwavy(Fig.5a)and¯at(Fig.5b)layer
boundariesasafunctionofthesource±detectorspacing.Itcanbe
seen that the fraction of total path length in the ®rst two layers
decreases as the source±detector spacing increases up to 800 mm
(seeFig.5),whereas,inotherlayers,themeanpathlength
increases with increasing source±detector spacing. It is evident
that, in the case of wavy boundaries, the photon packets
penetratedeeperintothemedium(seeFig.5a).
Thus, alteration of the photon re¯ection/refraction rules on the
layer boundaries of the medium alters the statistics of the photon
trajectories, an effect that becomes more distinct as the source±
detector spacing increases. In terms of photon propagation, the
wavy layer boundary interfaces and the refractive index
mismatch can be considered as an additional scattering
process, the anisotropy of which is different to the scattering
anisotropy of typical skin tissues. This could be important for the
accurate determination of skin tissue optical properties when the
source±detector spacing is small.
The results also suggest that all probe spacings up to 800 mm
sample effectively the same vascular bed. If this is true, then the
wider probe spacing is desirable, as a larger absorption signal
from the blood is obtained. Also, each probe spacing should
yield the same value for haemoglobin concentration and satura-
tion. We are manufacturing a ®bre-optic probe that will allow
re¯ectance spectra to be gathered at all three spacings simulta-
neously. We can thus test this conclusion both in phantoms and
in real skin.
47
5 Summary
Inthispaper,wehaveproposedasimplenumericalmethodas
a tool for the optimisation of probe geometry, so that the probe is
preferentially sensitive to the optical properties at different
depthswithintheskin.Figs4and5presenttheresultsofthe
simulation of the spatial localisation of the detected signal in
multi-layered highly scattering complex medium with wavy and
¯at boundaries between the layers. Knowledge of this photon
signal localisation is very important for the clinical interpretation
of the results, as capillary loops are responsible for delivering
nutrients to the epidermis, whereas deeper vessels are primarily
thermoregulatory in function.
The results of the simulation show that, for the small
source±detector separation (800 mm and smaller), rough
boundaries between layers of different refractive indices can
900
800
700
600
500
400
300
100
200
0
depth, mµ
900
800
700
600
500
400
300
100
200
0
depth, mµ
-200 0200 400 600 800
horizontal axis, mµ
-200 0 200 400 600 800
horizontal axis, mµ
a b
900
800
700
600
500
400
300
100
200
0
depth, mµ
900
800
700
600
500
400
300
100
200
0
depth, mµ
-200 0 200 400
horizontal axis, mµ
-200 0 100 300
horizontal axis, mµ
c d
900
800
700
600
500
400
300
100
200
0
depth, mµ
900
800
700
600
500
400
300
100
200
0
depth, mµ
-300 0 100 300 500 600
horizontal axis, mµ
-300 0 200 300 400 500
horizontal axis, mµ
e f
-100 200 400 500 600 -100 100 300 500 600
-200 -100 100 -200 400200
10-1
10-2
10-3
10-4 Q(x, z)
Fig. 4 Two dimensional distributions of the spatial depth sensitivity for the wavy and ¯at interfaces between the layer boundaries of the skin
model for the various source-detector ®bre spacing. (a) and (b) 800mm; (c) and (d) 400 mm; (e) and ( f ) 250 mm (centre to centre). Source
anddetector®brediametersare200mm,and50mm,respectively,withnumericalaperture0.22.Theassumedopticalpropertiesofthe
mediumaregiveninTable2
48
play a signi®cant role in skin optics. Wavy layer interfaces
produce a deeper and more homogeneous distribution of
photons within the skin and tend to suppress the direct
channelling of photons from source to detector.
Our model predicts that a probe spacing of 250 mm
samples primarily the epidermal layers and papillary
dermis, whereas spacings of 400±800 mm sample the upper
blood net dermis and dermis. In a subsequent paper, we will
present experimental results obtained on real skin at all three
probe spacings to validate this prediction.
Acknowledgment Ð We acknowledge the ®nancial support of EPSRC
grant GR/L89433.
The authors would also like to thank Professor A. Shore and Dr P.
Collier for useful and helpful discussions concerning human skin
structure and it properties.
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Fig. 5 Fraction of total path length in the layers of modelling media: (a) for the medium with wavy layer boundary interfaces; (b) for the medium
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Author's biography
IGOR V. M EGLINSKY was born in Saratov, Russia,
in 1968. He received his BSc and MSc in Laser
Physics from the Department of Physics, Saratov
State University, Russia. After pre-doctoral
research at the Department of Biochemistry
and Biophysics, University of Pennsylvania,
USA, he obtained his PhD in Biophysics in
1997 from Saratov State University. Since
1998, he has been a research fellow at the
School of Physics, University of Exeter, Exeter.
He is currently lecturing at the School of Mechanical Engineering,
University of Cran®eld, Bedfordshire.
50
