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2COMPARISON OF LSCI AND TR-LSCI USING MONTE CARLO SIMULATION
ARSENII FASHCHEVSKII1, QING XIA2, YANWEN XU2, VALERY TUCHIN1,3,4, DAN ZHU2 AND
DONGYU LI5
1Saratov State University, Russia; 2Britton Chance Center for Biomedical Photonics- MoE Key Laboratory for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics- Advanced Biomedical Imaging Facility, Huazhong University of
Science and Technology, Wuhan, Hubei, China;
3Tomsk State University, Russia; 4Institute of Precision Mechanics and Control, FRC "Saratov Scientific Centre of the RAS," Saratov, Russia; 5School of Optical Electronic Information, Huazhong University of Science and Technology, Wuhan, Hubei,
China
ABSTRACT
One of the methods of studying biological tissue using light is laser speckle contrast imaging (LSCI). The essence of the method is to visualize and analyze the speckle pattern that occurs when laser radiation is scattered on small structures of biological tissue. The conventional method works with light reflected from an object. This method works well for a relatively thin object or the surface layers of an object. LSCI is used for in vivo blood flow studies. The sizes of microstructures in biological tissues are comparable to the wavelength of incident radiation, therefore, according to the theory of Mie, light is mainly scattered forward. For thicker objects or when examining deeper layers of biological tissue, you can use the transmitted LSCI (TR-LSCI) method [1]. Before proceeding to field experiments, mathematical and computer modeling of such method of studying biological tissue should be carried out. In this paper, the Monte Carlo (MC) method was used to simulate the passage of light. The schemes of LSCI and TR-LSCI techniques are shown in fig. 1.
A
detected light
Figure 1: schemes of (a) LSCI and (b) TR-LSCI.
To evaluate and compare these two techniques, computer and mathematical modeling can be used as a first approximation. The following assumptions have been made to study the behavior of light in biological tissue: 1) light is a stream of photon particles; 2) when a photon collides with particles, it undergoes one of two states: absorption or scattering; 3) when passing from a medium with one optical density to a medium with another optical density, the photon is either elastically reflected, absorbed, or passes into the next medium in accordance with the law Snell.
The 2D MC simulation is used as a computer model of the passage of light, designed to simulate random processes. It can be used to trace the trajectory of each photon.
For modeling, it is necessary to know the following optical properties of an object: ^a — absorption coefficient, — scattering coefficient, n — refractive index and g — anisotropy factor. They are needed to evaluate transport free mean path of photon in medium, scattering angle, probability of scattering and absorption of photon.
Transport free mean path is:
L = -Miliil (1),
Va+Vs
where ^ — random number from 0 to 1.
For simulation, a photon has a certain weight, which is responsible for its absorption and scattering. If the initial weight of the photon is W, then every time the photon interacts with the medium, it changes according to the following law:
W = W--^W (2),
Va+Vs
as soon as weight of photon reach a critical mean Wcrit photon is absorbed.
The angle of scattering is defined by:
9 = 9nad + arccos(\^ + ^ - L-g-2gf2) ] ' if 9 (3),
Ufc- 1, if g*0
where <2 — random number from 0 to 1.
The probability of reflection and refraction of a photon at the boundary of two media must be written for two cases, provided that light passes from a medium with a lower optical density to a medium with a higher optical density (n1<n2) and vice versa (n1>n2). At ni<n2, the probability of reflection at the boundary of the layer corresponds to the Fresnel reflection energy coefficient:
R
— GS)2 <4>-
The probabilities of reflection and refraction depend on random number <3 the values of which are from 0 to 1 as:
(Reflection, if <f3 < R [Refraction, if <f3 > R
At n1>n2, the probability of reflection depends on the angle of incidence of the photon at the interface of the layers:
Ocrít — sin 1
(Reflection, if 9 > 9crit [Refraction, if 9 < 9crit
We compared two multilayer structures consisting of plane-parallel layers acts as a model of the sample of the studied biological tissue.The optical and geometric parameters of the first structure are taken from studies [1, 2, 3]. The object is like a sandwich and consists of 8 layers: stratum corneum (d=20^m), epidermis (d=80^m), dermis (d=520^m), blood (d=50^m), dermis (d=520^m), blood (d=25^m), epidermis (d=80^m), stratum corneum (d=20^m) (d is a geometrical thickness of a layer). The total thickness of the first sample is D1 = 1315 ^m .The optical and geometric parameters and the order of the layers are shown in Table 1. The second sample consist of 8 layers: stratum corneum (d=20^m), epidermis (d=80^m), blood (d=25^m), dermis (d=520^m), blood (d=50^m), dermis (d=520^m), epidermis (d=80^m), stratum corneum (d=20^m). The total thickness of the second sample is D2 = 1315 ^m. The optical and geometric parameters and the order of the layers are shown in Table 2.
Table 1: order of layers of 1st sample and their optical and geometric properties at the wavelength ^=633 nm.
Layer n ^a,cm_1 g
Stratum cornea [1] 1,50 175,00 0,15 0,90 20
Epidermis [1] 1,42 54,6 1,06 0,80 80
Dermis [2] 1,39 53,62 6,52 0,72 520
Blood [3] 1,35 400 15,20 0,97 50
Dermis [2] 1,39 53,62 6,52 0,72 520
Blood [3] 1,35 400 15,20 0,97 25
Epidermis [1] 1,42 54,6 1,06 0,80 80
Stratum cornea [1] 1,50 175,00 0,15 0,90 20
Table 2: order of layers of 2n sample and their optical and geometric properties at the wavelength ^=633 nm.
Layer n ^s,cm_1 Ha,cm_1 g
Stratum cornea [1] 1,50 175,00 0,15 0,90 20
Epidermis [1] 1,42 54,6 1,06 0,80 80
Blood [3] 1,35 400 15,20 0,97 25
Dermis [2] 1,39 53,62 6,52 0,72 520
Blood [3] 1,35 400 15,20 0,97 50
Dermis [2] 1,39 53,62 6,52 0,72 520
Epidermis [1] 1,42 54,6 1,06 0,80 80
Stratum cornea [1] 1,50 175,00 0,15 0,90 20
Heatmaps and traces of MC simulations are shown in fig. 1,2. And the statistical data is shown in Table 3.
s s D
Figure 2: Monte Carlo simulation for 1st sample of (a) TR-LSCI and (b) LSCI technologies, S - source, D -
detector.
S S D
Figure 3: Monte Carlo simulation for 2nd sample of (a) TR-LSCI and (b) LSCI technologies, S - source, D -
detector.
Table 3: amount and percentage of transmitted and reflected (back scattered) photons.
Sample Amount of photons Amount of transmitted Amount of reflected Percentage of transmitted. % Percentage of reflected, %
Sample 1 107 137 85226 0.001 0.852
Sample 2 163 84706 0.002 0.847
Thus, using Monte Carlo simulation, it is shown that the number of photons that passed through the biological tissue and were detected is significantly less than reflected. Nevertheless, the penetration depth of conventional LSCI is less than TR-LSC and does not allow visualizing some structures of the biological tissue.
REFERENCES
[1] Li D. Y. et al. Transmissive-detected laser speckle contrast imaging for blood flow monitoring in thick tissue: from Monte Carlo simulation to experimental demonstration //Light: Science & Applications.
Vol. 10., №. 1., p. 241, 2021.
[2] Bashkatov, Alexey N., Elina A. Genina, and Valery V. Tuchin. Optical properties of skin, subcutaneous, and muscle tissues: a review. Journal of Innovative Optical Health Sciences pp. 9-38, 2011.
[3] Tuchin, Valery V., ed. Handbook of photonics for biomedical science. CRC Press, p. 811 2010.
