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Analysis of physiological parameters
in skin tumors by a scaleable Monte
Carlo simulation
Alejandro Garcia-Uribe, Lihong V. Wang
Alejandro Garcia-Uribe, Lihong V. Wang, "Analysis of physiological
parameters in skin tumors by a scaleable Monte Carlo simulation," Proc. SPIE
5695, Optical Interactions with Tissue and Cells XVI, (15 April 2005); doi:
10.1117/12.590308
Event: SPIE BiOS, 2005, San Jose, CA, United States
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Analysis of Physiological Parameters in Skin Tumors by a
Scaleable Monte Carlo Simulation
Alejandro Garcia-Uribe
1
, Lihong V. Wang
2,1
1
Department of Electrical Engi
neering, Texas A&M University
3128 TAMU, College St
ation, Texas 77843-3128
2
Department of Biomedical Engi
neering, Texas A&M University
3120 TAMU, College St
ation, Texas 77843-3120
ABSTRACT
This paper presents a study of the use of a single scaleable Monte Carlo simulation to estimate the physiological
parameters of skin lesions from data collected
in vivo
using spectroscopic oblique-inc
idence reflectometry. Spatio-
spectral data from 101 cases are separated into two groups based on their melanocytic conditions. Group-1 consists of
(a) cancerous basal cell carcinomas and squamous cell carcin
omas and (b) benign actinic keratoses and seborrheic
keratoses. Group-2 consists of (a) dysplastic nevi and (b) benign common nevi. Several physiological parameters are
estimated, such as the size distribution of the optical scatterers, the relative index of refraction of the scatterers, the tot
al
volume concentration of the scatterers, the concentration of the total hemoglobin and the oxygen saturation, and the
relative changes related to the values calculated from the neighboring healthy tissues. The most significant features are
then combined into one feature. The results show that for both groups the combined feature is significantly different for
the benign and cancerous cases than for the dysplastic cases. The ROC area was 0.9 and 0.86 for group-1 and group-2,
respectively.
Keywords
: Oblique incidence reflectometry,
Spectroscopy, Monte Carlo, Skin Cancer, Lesion classification,
Physiological origin
1. INTRODUCTION
Skin cancer is the most common of all cancers in humans, and its incidence has increased dramatically in recent years.
Malignant melanoma (MM) is the most serious type of skin cancer. Other types of skin cancer, such as basal cell
carcinoma (BCC) and squamous cell carcinoma (SCC), are ca
lled non-melanoma cancers. In the United States alone,
more than one million cases of non-melanoma skin cancer were diagnosed in 2003.
1
Melanoma accounted for about
54,200 cases, and it is responsible for about 7,600 of the 9,800 deaths due to skin cancer reported in 2003.
1
Oblique
incidence reflectometry has an advantage over the the cla
ssically used normal incidence method because it gathers
information specifically from the superficial layers of the sk
in. This is of particular importance since skin cancer is
usually present in the top layers of the skin tissue, and the deeper layers only add to the background noise in the signal.
2
Monte Carlo simulation was used to extract optical properties
from measured diffuse reflectance. The principles of
Monte Carlo simulation of photon transport have been thoroughly described by Wang et al.
3
The Monte Carlo method
is often used to solve the transport equation numerically, but it is too slow to be used repetitively in an inverse algorithm
for deducing optical properties. Assuming a semi-infinite homogeneous media,
4,5
a single scaleable Monte Carlo
simulation can be used to deduce the optical properties. Th
is scaleable simulation is possible because the Monte Carlo
simulation results for the reference values of the index of refraction
n
r
, the anisotropy factor
g
, the absorption
coefficients
μ
a
, and the scattering coefficient
μ
s
can be used to calculate the desired quantities for all possible absorption
coefficients
μ
a
by applying Beer's law.
5
The results can be scaled for all scattering coefficients
μ
s
'
while the refractive
index
n
r
and
g
are constants because different
μ
s
values change only the distances between the interaction points on the
photon paths.
5
2. SPECTRAL IMAGING SYSTEM
Our oblique incidence diffuse reflectance spectroscopy (OIDRS
) system is illustrated in Figure 1. A white light is
coupled to a single optical fiber that delivers light to the sample to be irradiated. As indicated in Figure 1, the source
Optical Interactions with Tissue and Cells XVI, edited by Steven L. Jacques,
William P. Roach, Proc. of SPIE Vol. 5695 (SPIE, Bellingham, WA, 2005)
1605-7422/05/$15 · doi: 10.1117/12.590308
122
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fiber delivers the light while a linear array of 13 fibers (200
μ
m diameter low-OH optical fibers) collects the diffusely
reflected light. The output of the connecting interface is pl
aced at the object plane of th
e imaging spectrograph (Oriel
MS257). With the probe placed normal to the surface of the sample, the source fiber is oriented at a 45 degree angle of
incidence. The spectrograph generates the light spectrum and
projects it onto a CCD camera (Princeton instrument Inc.
1530P) to form a spatio-spectral image as shown in Figure 2. In this figure the horizontal axis reflects the spatial
location as seen by the fibers, and the vertical axis represents the spectral distribution of the light from each fiber.
Figure 1. Diffuse Reflectance Spectroscopic Imaging System.
The image acquisition for our studies was performed at the University of Texas MD Anderson Cancer Center. The
suspicious lesions were divided into two groups. Group 1 corresponded to the non-melanoma cases consisting of
cancerous basal and squamous cell carcinomas and benign seborrhoeic keratosis. Group 2 consisted of pre-cancerous
dysplastic nevi and benign common, compound and junctional nevi. These groups were chosen since in each group the
benign cases resemble their respective cancerous cases making diagnosis difficult.
6
For the group-1 classifier, 304
spectral images were collected from 36 cases (13 cancerous and 23 benign), which consisted of 152 spectral images
from the lesions and the same number of images from neighboring healthy tissues. For the group-2 classifier, 522
spectral images from 65 cases (36 dysplasia and 29 benign) were collected, 261 images from the skin lesions and 182
images from neighboring healthy tissues.
Figure 2. Sample spatio-spectral image.
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3. SCALABLE MONTE-CARLO
The algorithm is briefly summarized here. A single reference initial Monte Carlo simulation was run with a fixed
anisotropy factor
g
at 0.9. The pre-calculated time-resolved diffuse reflectance
R
r
(
x,y
,
t
) was computed for reference
parameters
μ
ar
and
μ
sr
and saved in a computer file. The time-resolved diffuse reflectance
R
(
x,y,t
) for any new
parameters,
μ
a
and
μ
', was calculated based on the following relationship:
()
()
−
−
=
t
n
c
t
y
x
R
t
y
x
R
sr
s
ar
a
sr
s
sr
s
sr
s
r
sr
s
μ
μ
μ
μ
μ
μ
μ
μ
μ
μ
μ
μ
exp
,
,
,
,
3
(1)
where
c
is the speed of light in a vacuum and
n
is the index of refraction of the tissue. Since the perpendicular distance
y
o
=1.2mm
between any collection fiber and the source fiber is constant,
R
(
x,t
) was obtained by first scaling in the y
direction. The corresponding steady-stat
e diffuse reflectance was calculated by
∫
∞
=
0
)
,
(
)
(
dt
t
x
R
x
R
(2)
The absorption spectra
μ
a
(
λ
) can be represented by
7
abg
mel
mel
de
de
ox
ox
a
C
C
C
μ
λ
ε
λ
ε
λ
ε
λ
μ
+
+
+
=
)
(
)
(
)
(
)
(
(3)
where
μ
a
(cm
–1
) is the absorption coefficient;
λ
is the wavelength;
ε
ox
(
λ
),
ε
de
(
λ
), and
ε
mel
(
λ
) are the known extinction
coefficients, (cm
–1
mM
–1
) of oxy-hemoglobin, deoxy-hemoglobin, and melanin;
C
ox
,
C
de
, and
C
mel
are the concentrations
(mM) of oxy-hemoglobin, deoxyhemoglobin, and melanin; and
μ
abg
is the absorption coeffi
cient caused by the local
tissue components other than hemoglobins and melanin. The size distribution of the optical scatterers
f
(
φ
) can be
calculated from the reduce scattering coefficient
8
μ
s
‘=
μ
s
[1-
g
] using the following relationship:
φ
φ
φ
λ
φ
λ
φ
λ
μ
d
f
n
g
n
Q
C
s
s
s
)
(
2
)]
,
,
(
1
)[
,
,
(
3
)
(
'
0
∫
∞
−
=
(4)
where
C
s
is the total volume concentration of the scatterers;
Q
s
() is the scattering efficiency;
φ
is the diameter of the
scatterers, and
g
() is the scattering anisotropy.
Q
s
() and
g
() were calculated using Mie Theory.
9
The Mitochondria, other cytoplasmic organelles and structures wi
thin the cell nuclei, are expected to be significant light
scatterers.
10,11
The average effective size of the scattering centers is assumed to correlate well with the size of the cell
nuclei. Because our OIDR system provides diffuse reflectan
ce for multiple wavelengths, we can fit the entire spatio-
spectral image for a spectra
μ
a
(
λ
) and
μ
s
(
λ
). To simplify the inverse problem, the scattering spectra
μ
s
(
λ
) is linearized
and represented by the equation
s
s
s
b
m
+
≈
λ
λ
μ
)
(
over a range of wavelength from 517nm to 604 nm. The fitted
parameters that define
μ
a
(
λ
) are the concentrations of
C
ox
,
C
de
, and
C
mel
directly. An example of the clinical data and the
corresponding fitted image is shown in figure 3.
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(a)
(b)
Figure 3. (a) Clinical spatio-spectral
image. (b) Fitted spatio-spectral image.
The estimated linear
s
s
s
b
m
+
≈
λ
λ
μ
)
(
was used later to calculate the size distribution of the optical scatters
f
(
φ
) using Eq.
4.
f
(
φ
) is assumed to be a Gaussian distribution N(
μ,σ
). The oxygen saturation
SO
2
and the concentration of total
hemoglobin
C
Hb
were computed based on the equations:
)
/(
2
de
ox
ox
C
C
C
SO
+
=
and
de
ox
Hb
C
C
C
+
=
.
The concentrations of
C
ox
,
C
de
, and
C
mel
, their derived physiological parameters and the size distributions of
f
(
φ
) were
estimated from the average spatio-spectral image for all skin lesions (L) and their corresponding average image from
neighboring healthy tissue (H). The extracted values from th
e neighboring healthy tissues were used as a reference, or
for normalization, to eliminate any back
ground artifacts appearing in the lesion images. Figure 4 shows the normalized
oxygen saturation
SO
2
and the mean and standard deviation of the size distributions of the optical scatters.
(a)
(b)
Figure 4. (a) Physiological parameters Group-1. (b) Physiological parameters Group-2
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These 3 physiological parameters for each case were combined into a single value.
12
This final single value was used to
calculate the receiver operating characteristic curve (ROC). The ROC curve describes the relationship between the true
positives and the false positives for different threshold values on a scatter plot. The abscissa of the ROC curve is 1–
specificity, and its ordinate is sensitivity. Sensitivity indicates the fraction of correctly identified positive cases among
all positive cases. The area under the ROC curve is a reflection of how effective the feature is at distinguishing between
the classes. The ROC area is 0.9 and 0.86 for group-1 and group-2, respectively. Figure 5 shows the ROC curve for
group-1 and group-2, respectively.
(a)
(b)
Figure 5. (a) ROC Group-1. (b) ROC Group-2
4. CONCLUSIONS
The results show that the expected value of the size distributions of the scatters
f
(
φ
) in the cancerous and dysplasia cases
is larger than that in the benign cases. The cancerous lesions in group-1 have a lower average relative oxygen saturation
SO
2
than the benign lesions. Also dysplastic nevi cases present lower relative SO
2
than common nevi. The lower
oxygen saturation in cancerous and dysplastic nevi lesions can be related to abnormal blood supply and distribution and
metabolic abnormalities.
5. ACKNOWLEDGMENT
This project is sponsored by NIH grant R01 CA106728. Wang’s email is LWang@tamu.edu.
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