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Mont-Carlo simulation of OCT
structural images of subcutaneous
blood vessels
Petrov D.A., Potlov A.Yu.,
Proskurin S.G.
Biomedical engineering,
TSTU, Russia
http://bmt.tstu.ru/
http://spros.tamb.ru/
[email protected]
Saratov Fall Meeting 2016
Abstract
•
•
•
•
A method of optical coherence tomography (OCT) structural images simulation
using the Monte Carlo method with the help of multithreaded computation is
described. Simulated structural images of subcutaneous blood vessel are
presented.
Biological object inner structure simulated with set of cubic volumetric shapes
based on the experimental results. B-scans of the inner structure are
demonstrated instead of analytical representation of the boundary geometry.
Effectiveness of the described simulation technique is checked by the comparison
of the simulated and experimentally acquired A-scans.
For this purpose, the biological object is considered as a set of 3D elements that
allow simulation of media, structure of which cannot be described analytically.
Each element is characterized by its refractive index and anisotropy, scattering and
absorption coefficients.
The probability of reflection on the interface of elements with different refractive
indices is determined using Fresnel equations. The photon mean free path is
calculated using total attenuation coefficient. The possibility of simulation and
visualization of biological objects with high scattering, such as blood vessels and
blood flow was demonstrated.
Voxel representation
Biological object inner structure simulation based on voxels and analytical expressions
Object structure simulation
Biological object inner structure simulation based on the experimental B-scan
Simulation algorithm
Photon packet launching
x w cos A d ,
Photon packet start position:
i
0
1
i
y w sin ,
z 0,
i
0
1
0
i
where
w
0
- beam waist,
- azimuthal angle A - current A-scan index
0
i
- uniformly distributed random number between 0 and 1
x
,
r z
y
u
,
r z
z
u
,
r z
u
x
Photon packet initial position:
2
2
f
y
2
2
f
f
z
2
2
f
where
r w , z
0
f
- focal distance
Photon packet launching
And energy absorption
Step size of photon packet :
s
1
where
s
ln( )
s
- scattering coefficient
Photon packet energy absorption calculated using Beer-Lambert law:
W W exp( s)
0
where
a
- absorption coefficient
W
a
- statistical weight of photon packet
Scattering
As a photon travels, free path distance direction of its propagation is changed as
sin (u u cos u sin )
u
'
x
z
y
1 u
x
z
sin (u u cos u sin )
u
'
y
z
x
1 u
y
u cos ,
x
2
2
u cos ,
y
z
u 1 u sin cos u cos
'
z
2
z
z
where - scattering angle, 2 - azimuthal scattering angle,
u , u , u - directional cosines.
x
y
z
Voxel boundary intersection
Voxel – photon packet intersection calculated using Smith algorithm:
zd z
если u 0
u
db
,
zz
если u 0
u
y
z
y
z
y
z
с
с
y
z
z
с
y
с
z
yd y
если u 0
u
db
,
y y
если u 0
u
xd x
если u 0
x
db
,
xx
если u 0
x
y
с
x
x
z
x
с
x
z
db , db , db - distances to voxel boundary plane, xс , yс , zс - current photon location ,
x
y
d ,d ,d
x
y
z
z
- Voxel facet length,
Distances db , db , db are compared, and the minimal value represents the distance to
the closest voxel boundary.
x
y
z
Photon detection
When photon exits tissue its weight added to intensity of the image according to
2z L
W exp
l
I'
i
i, j
c
2
2 (2 z L )
cos
if u ; r d; 2 z L l ,
0, else
I'
- structural image pixel intensity
- wave length
l
- coherence length
- fiber acceptance angle
i, j
c
i
z
i
d
- detector radius
r
L
- distance from center of detector to point where photon exits tissue
i
- Photon path length in object arm
c
Subcutaneous vessel structure
Experimental subcutaneous blood vessel image
Object structure used in simulation
Optical properties of the layers
Layer
s (см 1 )
n
g
a (см 1 )
Stratum corneum
320
0,2
0,9
1,49
Upper epidermis
63
0,3
0,93
1,37
Epidermis
120
0,6
0,87
1,38
Dermis
90
0,8
0,9
1,36
Lower dermis
110
1.1
0,9
1,35
Blood
650
2
0.995
1.37
Vessel wall
2.8
0.9
0.95
1.38
MC simulated images
Simulated images of subcutaneous blood vessel with (right)
and without (left) speckle influence.
Correlation with experimental data is between 0.85 and 0.9
Size of the image is 2x2 mm in all cases
A-scans comparison
The biggest difference located at the stratum corneum – air boundary
Conclusion
Described simulation technique allows to simulate OCT of
biological object with high precision.
This is because the structure of an object is reconstructed
using information taken from experimental data.
High efficiency is provided both for simulation with and
without presence of speckles.
Some inconsistency may occur due to choose of inaccurate
optical properties of the simulated object.
Future work will be focused on other types of tissues and
light source properties.
References
1.
Kirillin M., Meglinski I., Kuzmin V., Sergeeva E., Myllylä R. Opt. Express,
18(21), P. 21714 (2010).
2.
Proskurin S.G., Quantum Electronics, 42 (6), P. 495-499 (2012).
http://iopscience.iop.org/1063-7818/42/6/A05/
3.
Petrov D.A. Galeb K.E.S. Proskurin S.G., Fundamental Research, 5(2), P.
275-278 (2016)
http://fundamental-research.ru/ru/article/view?id=40288
4.
Petrov D.A., Abdulkareem S.N., Ghaleb K.E.S., Proskurin S.G., Journal of
Biomedical Photonics & Engineering, 2(2) – P. 020302-1 (2016)
http://journals.ssau.ru/index.php/JBPE/article/view/2363
5.
Proskurin S.G., Potlov A.Yu., Frolov S.V., Patent, RU 147284 U1 (2014)
6.
Potlov A.Yu., Proskurin S.G., Frolov S.V., Registered Software, 2014662539
(2014)