Analysis of nonlinear relation for skin
hemoglobin imaging
Manami Kobayashi, Yasunobu Ito, Naofumi Sakauchi, Ichiro Oda, Ikuo Konishi,
and Yoshio Tsunazawa
Technology Research Laboratory, Shimadzu Corporation,
380-1, Horiyamashita, Hadano, Kanagawa, 259-1304, Japan
[email protected]
http://www.shimadzu.com/
Abstract: This paper discusses the accuracy of the optical determination of
the oxygenated and deoxygenated hemoglobin content of human skin under
the influence of a melanin layer for a multi-wavelengths imager. The
relation between the nonlinear results by Monte Carlo simulation (MCS)
and the modified Lambert Beer’s law (MLB) is also clarified, emphasizing
the importance of the absolute values of skin pigments and their influence
on the mean path-length used in MLB. The fitting procedure of the MCS
data to the actual skin spectra is shown to obtain the absolute values. It is
also shown that once the proper mean path-lengths have been determined,
MLB can be used fairly well within an accuracy of 80% compared with
MCS. Images of oxygenated hemoglobin with a newly-developed fourwavelength camera are presented to demonstrate the advantages of a multiwavelength system.
2001 Optical Society of America
OCIS codes: (170.0170) Medical optics and biotechnology, (170.3880) Medical and biological
imaging
References and links
1.
2.
3.
4.
5.
6.
7.
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9.
10.
11.
12.
San Wan, R. Rox Anderson and John A. Parrish, "Analytical modeling for the optical properties of the skin
with in vitro and in vivo applications," Photochem. Photobiol. 34, 493-499 (1981).
R. Rox Anderson, B. S. and John A. Parrish M. D., "The optics of human skin," J. Invest. Dermatol. 77, 1319 (1981).
I. V. Meglinsky and S.J. Matcher, "Analysis of reflectance spectra for skin oxygenation measurements," in
Controlling of the Optical Properties, V. V. Tuchin, J. Lademann, Editors, Proc. SPIE 4162, 46-53 (2000).
I. V. Meglinsky and S.J. Matcher, "Modelling the sampling volume for skin blood oxygenation
measurements," Med. Biol. Eng. Comput. 39, 44-50 (2001).
M. Shimada, Y. Masuda, M. Y. Yamada, M. Itoh, M. Takahashi and T. Yatagai, "Explanation of human
skin color by multiple linear regression analysis based on the Modified Lambert-Beer law," Optical Review
7, 348-352 (2000).
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Transactions On Biomedical Engineering 36, 1146-1154 (1989).
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EMHO I," Phys.Med. Biol. 34, 1883-1900 (1989).
G. B. Hanna, D. J. Newton, D. K. Harrison, J.J. F. Belch and P. T. McCollum, "Use of lightguide
spectrophotometry to quantify skin oxygenation in a variable model of venous hypertension," Br. J. Surg.
82, 1352-1356 (1995).
Y. Kakihana, M. Kessler, D. Alexandre J, and A. Krug, "Stable and reliable measurement of intracapillary
hemoglobin-oxygenation in human skin by EMPHO II," SPIE 2979, 378-389 (1997).
N. Tsumura, H. Haneishi and Y. Miyake, "Independent -component analysis of skin color image," J. Opt.
Soc. Am. A 16, 2169-2176 (1999).
N. Tsumura, H. Haneishi and Y. Miyake, "Independent component analysis of spectral absorbance image in
human skin," Optical Review 7, 479-482 (2000).
N. Tsumura, M. Kawabuchi, H. Haneishi and Y. Miyake, "Mapping pigmentation in human skin by multivisible-spectral imaging by inverse optical scattering technique," IS&T/ SID's 8th Color Imaging
Conference, Color Science, Systems and Appl. 81-84 (2000).
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(C) 2001 OSA
Received October 23, 2001; Revised December 10, 2001
17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 802
13.
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16.
W. G. Zijlstra, A. Buursma and W. P. Meeuwsen-van der Roest , "Absorption spectra of human fetal and
adult oxyhemoglobin, de-oxyhemoglobin, carboxyhemoglobin, and methemoglobin", CLIN. CHEM. 37,
1633-1638 (1991).
B. C. Wilson and G. Adam, "A Monte Carlo model for the absorption and flux distributions of light in
tissue," Med. Phys. 10, 824-830 (1987).
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through tissue from direct time of flight measurement," Phys. Med. Biol. 33, 1433-1442 (1988).
M. Kobayashi, Y. Ito, N. Sakauchi, I. Oda, I. Konishi, and Y. Tunazawa, "Optical imaging of hemoglobin
distribution in human skin," in Photon Migration, Optical Coherence Tomography, and Microscopy, Stefan
Anderson-Engels, Michael Kaschke, Editor, Proc. SPIE 4431, (now printed)
1. Introduction
Diffuse reflection spectroscopy for skin is expected to have various applications for
noninvasive diagnosis. In particular, recent advances in CCD detectors will facilitate the use
of imaging spectroscopy for detecting local changes in oxygenated and deoxygenated
hemoglobin, which are related to peripheral circulation diseases or injuries of the skin. In the
visible wavelength range between 500 nm and 620 nm, optically absorbing pigments are
limited to oxygenated hemoglobin and deoxygenated hemoglobin and melanin. Therefore, the
development of a method that can extract the contents of three components from the obtained
reflection spectrum of the skin is required. However, skin has a complex multi-layered
structure and has strong optical scattering; the relation between the pigment concentration and
measurable optical absorbance become nonlinear, which is not easy to predict. Many
researchers have tried to solve this problem through a variety of approaches.
San Wan et al. (1981)1) and R. Rox Anderson et al. (1981)2) used the Kubelka Munk
approach to deal with nonlinear diffuse reflection from the skin. I.V. Meglinsky et al.3) 4) used
the Monte Carlo technique to determine where the skin signal comes from and to simulate
human skin spectra assuming seven skin layers. M. Shimada et al.5) discussed the use of
modified Lambert-Beer's law combined with multiple linear regression analysis. M. J. C. Van
Gemert et al. (1989) 6) summarized the optical properties of human skin, which can be used as
the basic data to understand skin optics.
K. H. Frank et al. (1989)7), G. B. Hanna et al. (1995)8) and Y. Kakihana et al. (1997)9)
reported skin hemoglobin oxygenation and its concentration using a micro lightguide
spectrophotometer. N. Tsumura et al. discussed the imaging technology of hemoglobin and
melanin using independent-component analysis10) 11) or using an inverse optical scattering
technique by multi-spectral camera 12).
The present paper reports on a new fitting method for extracting the contents of three
components from the actual skin spectra. The Monte Carlo simulation (MCS) of the threelayered skin model is described to obtain nonlinear relations between the absorbance and
concentration to be used for fitting. Then, the relation between the nonlinear MCS and the
linear modified Lambert Beer’s law (MLB) is discussed. Finally, a series of typical images of
oxygenated hemoglobin for the human foot, during and after arterial occlusion, are presented
to demonstrate the advantages of the multi-wavelength system for skin analysis.
2. Human skin spectra to determine the absolute concentration of oxygenated and
deoxygenated hemoglobin and melanin by fitting
The actual skin spectra, to be used in subsequent fitting analyses for finding absolute
concentrations of hemoglobin and melanin, were measured using a spectrophotometer. Fig.
1(a) and (b) present the reflection spectra of the skin from the forearms of three Japanese
volunteers. The ordinate of the spectra is the absorbance; i.e. log (Ro/R), where R is the
amount of reflected light from a sample and Ro is that from barium sulfate powder as a white
reference. Fig. 1(a) is for volunteer No.1 at rest as well as with varied skin oxygenation, while
Fig. 1(b) is for volunteers No. 2 and No. 3 only at rest. In Fig. 1(a), in addition to the rest
condition, a heating or occlusion action was employed to give various hemoglobin
concentrations and saturations. First, the skin surface was heated to 43.5°C to increase the
amount of oxygenated hemoglobin (oxyHb) and to decrease deoxygenated hemoglobin
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17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 803
(deoxyHb). Secondly, the upper arm was occluded by a cuff at a pressure of 200 mmHg;
closing both veins and arteries to decrease [oxyHb] and to increase [deoxyHb]. Finally, the
pressure was released to reverse this change.
absorbance
1
(a)
2
3
4
absorbance
wavelength(nm)
(b)
wavelength(nm)
Fig.1. Skin spectra of human forearm to be used for fitting.
The curved lines are the measured spectra and the six points on each spectrum represent the
absorbance points obtained by fitting.
(a): Skin spectra of volunteer No.1 with varied states of hemoglobin. 1: at rest, 2: after heating, 3:
after occlusion, 4: after release. (b): Skin spectra of three volunteers. 1: volunteer No.1 at rest, same
as 1in Fig.1.(a), 5: volunteer No.2 at rest , 6: volunteer No.3 at rest.
3. Monte Carlo simulation and the result of fitting
3.1 Description of Monte Carlo simulation (MCS) and skin model
The purpose of the MCS is to obtain skin data for fitting by calculating the amount of
reflected light from the skin as a function of the concentrations of three pigments: oxyHb,
deoxyHb and melanin existing in the respective layers. Fig.2 presents a three-layered skin
model used in the MCS6). Layer1 (epidermis) contains melanin, layer2 (dermis) contains
oxyHb and deoxyHb, and layer3 (subcutaneous tissue) contains lipid. The depth of the three
layers is assumed to be 0.06 mm, 1.00 mm, and 28.94 mm, respectively. Layer3 is sufficiently
thick because the MCS photons only migrate down to the shallow part of this layer.
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lipid µa= 0.003
Layer3
µs= 12
(Subcutaneous
g = 0.90
tissue)
1.0
28.94
Fig.2. Skin model with three layers used in the MCS.
Absorptivities of melanin ((mg/mL)-1· cm-1)
Layer2
(Dermis)
melanin
oxyHb
deoxyHb
Absorptivities of hemoglobin (mM-1· cm-1)
Layer1
(Epidermis)
Depth
(mm)
0.06
70
oxyHb
deoxyHb
melanin
60
50
40
30
20
10
0
450
500
550
600
650
wavelength(nm)
700
750
Fig.3. Absorptivities of oxyHb and deoxyHb (mM-1· cm-1)
after four times multiplied from the report of
W. G. Zijlstra et al. 13) and absorptivities of melanin
((mg/mL)-1· cm-1)
In order to reduce the number of variables, an absorption coefficient µa (mm-1) of layer2 was
used in place of using two variables: concentration of oxyHb or [oxyHb] and the
concentration of deoxyHb or [deoxyHb], noting that both the pigments are contained in the
same layer. So the µa of layer2 is defined as:
µ a = ln 10 ⋅ (ε oxyHb ⋅ [oxyHb] + ε deoxyHb ⋅ [ deoxyHb]) / 10,
(1)
where εoxyHb and εdeoxyHb are the millimolar absorptivities in the unit of mM-1·cm-1, [oxyHb]
and [deoxyHb] are in mM. Thus, the diffusely reflected amount of light is calculated as a
function of µa and the melanin concentration for six wavelengths. The refractive index of
three-layers is assumed to be 1.34. The εoxyHb and εdeoxyHb are taken from the report of W. G.
Zijlstra et al.(1991) 13) and are shown in Fig.3 after being multiplied four times, because their
molar weight is based on one of four subunits of a full hemoglobin molecule. The
absorptivities of melanin ((mg/mL) -1·cm-1) are determined by our measurement and are also
given in Fig.3. The scattering coefficients µs and the anisotropy factor g of layer1 and 2 are
the values; µs: 41 - 60, g: 0.768 - 0.823 depending on the wavelength according to the data
reported by M. J .C Gemert et al. (1989) 6). The CS program used here is coded based on
the method of B. C. Wilson and G. Adam (1987)14).
3.2 Result of MCS
Fig.4 shows the nonlinear relation obtained by the MCS as the basic data for fitting. The four
graphs correspond to the relation for 512 nm, 557 nm, 581 nm, and 619 nm, respectively. The
ordinate (Z-axis) of the graph represents the absorbance by MCS. The absorbance is defined
as log (I /Ir), where I is the intensity of light illuminated and Ir is that reflected. The X-axis
represents the µa (mm-1) of layer2, which is related to the concentration of oxyHb and
deoxyHb by equation (1). The Y-axis directly represents the concentration of melanin
(mg/mL). The surface plot of (X, Y, Z) forms a curved surface, therefore, when the
concentration of the hemoglobin or melanin varies, the point (X, Y, Z) will move on the curved
surface. The four red dots and yellow and blue dots on the graph stand for actual skin data
obtained by the fitting procedure.
0
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17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 805
absorbance
absorbance
6
3
5
2
1
4
[melanin]
(mg / mL)
6
3
5
2
1
µa(mm-1)
[melanin]
(mg / mL)
µa(mm-1)
4
absorbance
absorbance
Fig.3. Result of MCS dependence of absorption coefficient µa of the second layer (X-axis:
mm-1) and concentration of melanin (Y-axis: mg/ml) on the absorbance (Z-axis) for 512nm,
557nm, 581nm and 619nm. The scale of X-axis for 619nm is 1/10 of that for other three
wavelengths due to weak hemoglobin absorption. The points 1 to 6 on the figure correspond
to actual skin spectra described in section 2.3.
6
5
2 3
4
6
[melanin]
(mg / mL)
3
5
1
1
2
4
[melanin]
(mg / mL)
µa(mm-1)
µa(mm-1)
Fig.4. Nonlinear relation obtained by MCS to be used for fitting at four wavelengths
The dependence of the absorbance (Z-axis) on the absorption coefficient µa of the layer 2 (X-axis: mm-1)
and on the concentration of melanin (Y-axis: mg/mL) for 512 nm, 557 nm, 581 nm and 619 nm. The scale
of the X-axis for 619 nm is 1/10 of that for the other three wavelengths due to the weak absorption of
hemoglobin at 619 nm. Points 1 to 6 on the figure correspond to the actual skin spectra by fitting; points 1
to 4: volunteer No.1, 1 (at rest), 2 (after heating), 3 (after occlusion), 4 (after release), point 5: volunteer
No2 (at rest), point 6: volunteer No2 (at rest)
In order to use the above relation in the fitting, the absorbance (Z) of MCS is presented by
a cubic function (2) of X and Y for each wavelength.
Z = AX 3 + BX 2Y + CXY 2 + DY 3 + EX 2 + FXY + GY 2 + HX + IY + J ,
(2)
where X is µa (mm-1) as defined in equation (1) and Y is the concentration of melanin:
[melanin]. The coefficients A to J are the numerically determined constants except for J, and
are shown in table 1. The last term J is the offset that is common to all wavelengths. Then the
fitting procedure can be stated to minimize the sum S
S=
∑ [abs(i ) − Z (i )] ,
6
2
(3)
i =1
by adjusting the four variables [oxyHb], [deoxyHb], [melanin] and J (offset). In the equation
(3), abs(i) means the absorbance of the skin spectra at ith wavelength.
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Table 1 Coefficients of a cubic function
AX 3 + BX 2Y + CXY
512 nm
0.05033
0.01044
0.00420
0.00279
-0.27797
-0.06629
-0.04386
0.55663
0.33067
0.00000
A
B
C
D
E
F
G
H
I
J
557 nm
0.01130
0.00321
0.00208
0.00162
-0.11430
-0.03516
-0.02758
0.40462
0.23649
0.00000
2
+ DY 3 + EX
568 nm
0.01083
0.00291
0.00189
0.00153
-0.11235
-0.03263
-0.02558
0.40695
0.22114
0.00000
2
+ FXY + GY 2 + HX + IY + J
581 nm
0.00974
0.00272
0.00163
0.00143
-0.10712
-0.03038
-0.02334
0.40942
0.20483
0.00000
619 nm
2.58236
0.08862
0.00931
0.00092
-2.78521
-0.12906
-0.01637
1.35687
0.16636
0.00000
700 nm
-74.45105
0.75300
0.00931
0.00050
3.14482
-0.19244
-0.00930
1.52055
0.11640
0.00000
3.3 Results of fitting to actual human spectra
The four variables obtained by the fitting are shown in Table 2. This table presents [totalHb]
(the sum of [oxyHb] and [deoxyHb]) and oxygen saturation SO2 (100[oxyHb] / [totalHb]), in
addition to the four variables. “Max error” listed at the bottom of the table, stands for the
maximum of absorbance residues after fitting. This is the maximum difference between the
solid curves and the six points in Fig.1.
Table 2 Concentration of oxyHb, deoxyHb and melanin obtained by fitting.
Related values (offset, totalHb and SO2) are also shown.
volunteer
No.1
(at rest)
[oxyHb]
22.7
µM
[deoxyHb]
10.2
µΜ
[melanin ] mg/mL
0.53
offset
absorbance
0.225
[totalHb]
32.9
µM
SO2
%
69.1
max error absorbance 0.0119
unit
(after
heating)
50.5
5.0
0.42
0.236
55.5
91.0
0.0109
(after
(after
occlusion) release)
36.4
65.7
39.2
8.2
0.41
0.34
0.237
0.248
75.6
73.8
48.1
88.9
0.0184
0.0115
5
6
volunteer volunteer
No.2
No.3
(at rest) (at rest)
27.9
36.9
10.4
23.7
0.67
0.95
0.150
0.234
38.3
60.6
72.8
60.8
0.0116 0.0095
4. Derivation of modified Lambert-Beer's law from the cubic equation
The modified Lambert-Beer’s law15) (MLB) was proposed to improve the original LambertBeer’s law by introducing a concept of mean path-length. The mean path-length, d is the
average path-length of traveling photons due to multiple scattering. The MLB is usually
written in the formula
∆Z = doxyHb ⋅ ε oxyHb ⋅ ∆[oxyHb] + ddeoxyHb ⋅ ε deoxyHb ⋅ ∆[deoxyHb] + dmelanin ⋅ ε melanin ⋅ ∆[melanin] + ∆J ,
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(4)
Received October 23, 2001; Revised December 10, 2001
17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 807
where ∆Z is the change in absorbance caused by changes in the respective concentrations of
∆[oxyHb], ∆[deoxyHb], and ∆[melanin] and doxyHb, ddeoxyHb and dmelanin are the d values for
oxyHb, deoxyHb and melanin, respectively. A method of relating the nonlinear relation
obtained by MCS with the MLB follows.
Since the absorbance Z is the function of [oxyHb], [deoxyHb], [melanin] and J, in Eq. (2)
the change in absorbance ∆Z is written as
∆Z =
∂Z
∂Z
∂Z
∆[oxyHb] +
∆[deoxyHb] +
∆[melanin] + ∆J ,
∂[oxyHb]
∂[deoxyHb]
∂[melanin]
(5)
as the first order approximation.
The multiplying factors such as ∂Ζ / ∂[oxyHb] in Eq.(5) are presented by the following
formulas, remembering that X =µa and µa is presented by Eq.(1),
∂Z
∂Z
∂X
∂Z ln 10
=
⋅
=
⋅
ε oxyHb ,
∂[oxyHb] ∂X ∂[oxyHb] ∂X 10
(6)
∂Z
∂Z
∂X
∂Z ln 10
=
⋅
=
⋅
ε deoxyHb ,
∂[ deoxyHb ] ∂X ∂[ deoxyHb ] ∂X 10
(7)
∂Z
∂Z
=
,
∂[melanin] ∂Y
(8)
By comparing (4) and (5) in combination with (6)(7)(8), we have as the mean path-lengths for
the three pigments,
 ∂Z
ln10 
,
∂
X
10 

doxyHb = 
 ∂Z
ln10 
,
∂
X
10 

ddeoxyHb = 
 ∂Z
1 
.

∂
Y
ε
melanin

dmelanin = 
(9)
Partial derivatives by X and Y in (9) are given from Eq.(2) as follows;.
∂Z
= 3AX 2 + 2BXY + CY 2 + 2EX + FY + H ,
∂X
(10)
∂Z
= BX2 + 2CXY + 3DY2 + FX + 2GY + I.
∂Y
(11)
In order to determine ∂Z / ∂X and ∂Z / ∂Y in (10) and (11) we have to specify the values of
X and Y of a proper subject. Thus, the calculated mean path-lengths for volunteer No.1 (at
rest) and for volunteer No.3 (at rest) are shown in Table 3.
Table 3 Mean path-length of layer1 (dmelanin) and layer2 (doxyHb, ddeoxyHb)
(a) Determined mean path-length (mm) of volunteer No.1
dmelanin
512 nm
0.286
557 nm
0.314
568 nm
0.321
581 nm
0.329
619 nm
0.342
700 nm
0.359
doxyHb, ddeoxyHb
1.000
0.731
0.738
0.746
2.635
3.352
(b) Determined mean path-length (mm) of volunteer No.3
dmelanin
512 nm
0.246
557 nm
0.270
568 nm
0.277
581 nm
0.285
619 nm
0.307
700 nm
0.332
doxyHb, ddeoxyHb
0.792
0.576
0.587
0.606
2.190
3.242
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Using the mean path-length of volunteer No.1 in Table 3, Eq.(4) can be numerically
calculated, becoming a simultaneous equation
 ∆Z (512nm) 


 ∆Z (557nm) 
 ∆Z (581nm) 


 ∆Z (619nm) 


=
 2.2581

 2.7706
 3.7557

 0.4444

2.2485
3.8677
2.6657
2.1528
0.2763
0.1984
0.1717
0.1465
1  ∆[oxyHb] 
 

1  ∆[ deoxyHb] 
,
⋅
1  ∆[melanin] 
 


∆J
1 

(12)
which is the MLB equation that we intended to derive.
By solving Eq.(12), we have finally Eq.(13), which converts a set of changes in
absorbance at four wavelengths to a set of changes in ∆[oxyHb], ∆[deoxyHb] and ∆[melanin].
 ∆[oxyHb] 


 ∆[deoxyHb] 
 ∆[ melanin] 




∆J


=
 - 0.0306

 - 0.2090
 8.2882


 - 0.7509
- 0.1185
 ∆Z (512nm) 
 

0.4021 - 0.2529 
0.7097 - 0.3840 - 0.1166   ∆Z (557nm) 
.
⋅
1.1331 - 5.3358 - 4.0855   ∆Z (581nm) 
- 1.6411
1.4300
1.9621
(13)
 

 

  ∆Z (619 nm) 
If the X and Y values of volunteer No.3 are adopted, Eqs.(12) and (13) change to
 ∆Z (512nm) 


 ∆Z (557nm) 
 ∆Z (581nm) 


 ∆Z (619nm) 


 ∆[oxyHb] 


 ∆[deoxyHb] 
 ∆[ melanin] 




∆J


=
 1.7883

 2.1802
 3.0513

 0.3695

=
 - 0.0236

 - 0.2694
 9.7175


 - 0.7871
1.7807
3.0435
2.1657
1.7897
0.2376
0.1707
0.1485
0.1315
- 0.1451
1  ∆[oxyHb] 
 

1  ∆[deoxyHb] 
,
⋅
1  ∆[ melanin] 
 


∆J
1 

(12 - 1)
 ∆Z (512nm) 
 

0.4834 - 0.3146 
0.9441 - 0.4949 - 0.1798   ∆Z (557nm) 
⋅
.
2.0209 - 6.5057 - 5.2327   ∆Z (581nm) 
- 1.9019
1.5627
2.1262
(13 - 1)
 

 

  ∆Z (619nm) 
5. Hemoglobin images for the human foot with a new four-wavelength optical imager
We developed a four-wavelength imaging system to detect changes in the oxygenated and
deoxygenated hemoglobin in the skin.16) The detector part consists of a CCD camera and a
filter assembly for wavelength selection, and the light source part consists of a halogen or
LED lamp. The filter assembly is made up of four interference filters set at a speed of 0.7
sec/filter. The selected wavelengths are 512 nm, 557 nm, 581 nm and 619 nm, which are the
A
B
C
D
E
F
Fig.5. Distribution of ∆[oxyHb] in foot obtained with a new four-wavelength imager
Six successive images of ∆[oxyHb] starting from just before the release of occlusion.
Distribution of [oxyHb] just before occlusion is taken to be zero (green) as the reference
A: just before the release of occlusion (at the end of occlusion period of 5 minutes), B: 6 sec
after the release, C: after 13 sec, D: after 26 sec, E: after 40 sec, F: after 105 sec.
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(µM)
Received October 23, 2001; Revised December 10, 2001
17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 809
same as described in the above simulation. With this system, four images are obtained every 3
seconds and many sets of four images can be saved on a computer during a series of
measurements.
In order to demonstrate the system’s advantages, an arterial occlusion was performed on
the skin of human foot of a healthy volunteer. A cuff was fixed at the neck of the left foot.
After resting for over 10 minutes, the cuff pressure was increased to 200 mmHg and
maintained for 5 minutes so as to stop both venous and arterial blood flow, then the occlusion
was released to re-start the blood flow. The camera was operated continuously during the
above procedure and four wavelength images of the foot were obtained every 3 to 5 seconds.
Then, these images were transformed into the image of [oxyHb] using the MLB method
equation (13).
The test results are shown in the six images, from A to F in Fig.5, which visualizes rapid
change in the local distribution of [oxyHb] starting from the end of a 5 minute occlusion. As a
reference, the distribution of [oxyHb] just before occlusion was taken to be zero (green).
When the amount of [oxyHb] increases, the color becomes red and it becomes blue when
[oxyHb] decreases below zero. Figure A shows the image taken at the end of a five minute
occlusion. The image is blue because it is the most deoxygenated situation. Figure B is the
situation 6 seconds after the release of the occlusion when the blood had started to flow again.
The increase in [oxyHb] was found to start at the position indicated with the arrow at the inner
side of the foot. Figures C, D and E are the images at 13, 26, and 40 seconds after release,
respectively. In figure C, D and E, the area showing increased [oxyHb] extends wider and
wider, finally reaching maximum in figure E. Then it decreases again in figure F from the area
indicated by the arrow. Finally, [oxyHb] gradually returns to the original level (green)
although the figure is not shown here.
6 Discussion
6.1 Discussion on the fitting result
From the fitting result given in table 2, we can see the total skin hemoglobin concentration at
rest ranges from 33 to 61 µM and the oxygen saturation ranges from 61% to 73% for the three
volunteers. After heating, there is a remarkable increase in total skin hemoglobin up to 56 µM
and an increase in oxygen saturation up to 91% for volunteer No.1. This increase is due to
arterialization of the skin and is considered to be qualitatively reasonable. After occlusion, a
further increase is found in total hemoglobin to 76 µM in addition to a rapid decrease in
oxygen saturation down to 48%. After release, a rapid increase in oxygen saturation up to
89%(at the maximum point) is found again due to the re-start of blood circulation. The
behavior of the oxyHb and deoxyHb during the occlusion-release procedure was also
reasonable.
The amount of melanin ranges from 0.5 to 0.95 mg/mL for the three volunteers. The
quantitative values of oxyHb, deoxyHb and melanin obtained by fitting may change
depending on the MCS model (assumed thickness of layers) and the values of the scattering
coefficient and g factor.
There is another noteworthy feature concerning the change in melanin concentration
during the heating or occlusion-release procedure. In the melanin data shown in table 2, there
is significant variation in the values of columns 1, 2, 3 and 4, starting from 0.53 to 0.34
mg/mL. Because melanin is thought to be stable against these procedures, such variations are
not reasonable. The cause of the variation could be due to the discrepancy in optical properties
adopted in MCS or some error in measurement, etc. Further research is required to determine
the cause of these variations.
6.2 Comparison of MLB with MCS
In order to obtain absolute concentrations, a fitting procedure based on the MCS is required.
On the other hand, where the changes in concentration from a particular value are concerned,
both the MCS and the MLB are applicable, although in the latter case, the importance of
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absolute values are still emphasized to determine the mean path-length. The following
discussion considers the accuracy of MLB compared with MCS, after a set of mean pathlengths has once been determined. As you can see in table 3, the mean path-length in the MLB
equation varies depending on the X and Y of the subject. So, in this discussion the three cases
are compared; the MCS and MLB with two different mean path-lengths. The MLB result with
the path-length for volunteer No.1 is referred to as MLB(1), and that for volunteer No.3 is
referred to as MLB(2).
Fig.6 represents the results of the comparison. The four graphs show the differences
among these three methods for the changes in [oxyHb], [deoxyHb], [totalHb], and [melanin].
The three bars in a group stand for the result with MCS, MLB(1), and MLB(2), respectively.
The numbers attached on the abscissa, 1 to 6, correspond to the numbers of the columns (1 to
6) in table 2, which describes the type of subject and the situation of the skin.
All the values in Fig.6 are the difference of the data for columns from “2” to “6” and a
common data for column “1.” Note here that all the bars at column “1” are zero, since the
values of volunteer No.1 (at rest) are regarded to be the reference.
Difference values with MCS are taken directly from table 2, as the values in the columns
“2” to “6” subtracted by a common value in the column “1.”
On the other hand, difference values with MLB(1), or MLB(2) are obtained by Eq.(13) or
(13-1) using ∆Z(512 nm), ∆Z(557 nm), ∆Z(581 nm) and ∆Z(619 nm), which are the difference
in original absorbance between the spectra of 2, 3, 4, 5 or 6 and the common spectrum 1 for
volunteer No.1 in Fig.1.
There are some differences in MCS and MLB(1) and MLB(2) with respect to the changes
in [oxyHb], [deoxyHb] and [totalHb]. However, these differences in the three methods are
found in less than 20% of the changes in MCS, so MLB is a useful method as far as the
relative changes are concerned.
A
D
∆ [deoxyHb] (µM)
∆ [oxyHb] (µM)
∆ [totalHb] (µM)
B
Number of column
C
∆ [melanin] (mg / mL)
Number of column
D
Number of column
Number of column
Fig.6. Comparison of MCS and MLB with two different mean path-lengths
MLB result with the path-length for volunteer No.1 is referred to as MLB(1), and that with volunteer
No.3 is referred to as MLB(2), since the MLB results depend on the path-length for respective
subjects. The graphs A, B, C and D show the difference of three methods MCS, MLB(1) and
MLB(2) in the changes in [oxyHb], [deoxyHb], [totalHb], and [melanin] respectively, calculated for
the same original data. The numbers attached on the abscissa; 1:volunteer No.1 (at rest), 2: after heat,
3: after occlusion, 4: after release, 5: volunteer No.2, 6: volunteer No.3. The values at number 1 are
zero, since the values of the volunteer No.1 (at rest) are taken as the reference.
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Received October 23, 2001; Revised December 10, 2001
17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 811
In addition, an interesting fact is observed in the trends of the MLB(1), MCS and MLB(2).
MLB(2) tends to exhibit the largest changes while MCS lies in the middle and MLB(1) shows
the smallest changes. This is understood if we note in Fig.4 that point 6 always shows higher
absorbance than point 1. Remember, point 1 corresponds to MLB(1), and point 6 corresponds
to MLB(2). And, also note that higher absorbance causes a smaller slope on the surface and
this smaller slope results in a smaller mean path-length. Comparison of tables 3(a) and 3(b)
supports this fact. Finally, a smaller mean path-length causes larger numerical factors in
equations (13) and (13-1). Thus, the differences of 20% appearing in Fig. 6 are due to the
variation of absorbance of the skin.
7. Conclusion
A systematic analysis was conducted to show the relation between the nonlinear results from
the Monte Carlo simulation (MCS) and the results from the modified Lambert Beer’s law
(MLB). The importance of the absolute concentrations of skin pigments are emphasized to
determine the mean path-lengths required in MLB. The result of the MCS with a three-layered
skin model were presented by a cubic function and the absolute concentrations of skin
pigments were obtained by the fitting procedure to the actual skin spectra. Thus, the obtained
[totalHb] at rest ranged from 33 to 61 µM and the oxygen saturation ranged from 61% to 73%
for the three volunteers. The mean path-lengths of the dermis layer were from 0.5 to 1 mm for
wavelengths less than 581 nm and about 3 mm for 619 nm. It is also shown that once the
proper mean path-lengths are determined, the MLB could be used fairly well within an
accuracy of 80% compared with the MCS. A series of ∆[oxyHb] images was displayed to
demonstrate the effectiveness of the four-wavelength camera. They presented local change in
skin oxygenation due to blood flow during a blood occlusion and release procedure. This
system could be applied to evaluate peripheral vascular diseases, skin injuries and skin
grafting.
8. Acknowledgements
The authors wish to thank Dr. Hayashi Shimadzu Corporation and Dr. Eda KARC, CRL for
their helpful support. We also wish to thank Dr. Tsumura Chiba University for the fruitful
discussions concerning skin optics.
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Received October 23, 2001; Revised December 10, 2001
17 December 2001 / Vol. 9, No. 13 / OPTICS EXPRESS 812