Abstract

In this work we describe the development of a program that simulates the propagation of photons through refractive and reflecting optical components such as lenses, mirrors and stops that includes a biological tissue sample as the main issue to be investigated in order to get a simulated value of light distribution, in particular, of the unscattered light. The analysis of the photons that travel through the sample is based on the program Monte Carlo Multi-Layered with some modifications that consider a Gaussian beam as initial source of light. Position, directional cosines and weight of photons exiting the turbid media are used to propagate them through an optical system. As a mean of validation of the program, we selected a typical optical system for measurement of collimated transmittance. Therefore, several tests were carried out to find the optical system that gives the theoretical collimated transmittance at different values of the optical properties of the turbid media. Along this validation, the optimal experimental configuration is found. Using this results, a comparison between the simulated optimal configuration and the experimental set-up was done, by using a colloidal suspension as a turbid media.

© 2015 Optical Society of America

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References

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    [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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2013 (1)

2012 (1)

2011 (1)

B. Morales and S. Vázquez, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis. 57(4), 375–381 (2011).

2010 (1)

2006 (1)

M. Friebel, A. Roggan, G. Müller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. 11(3), 034021 (2006).
[Crossref] [PubMed]

2003 (1)

L. Quan, Z. Changfang, and R. Nirmala, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8(2), 223–236 (2003).

1998 (1)

1997 (1)

A. M. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, and M. J. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65(2), 366–373 (1997).
[Crossref] [PubMed]

1995 (3)

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995).
[Crossref] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, “MCML- Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

A. M. Nilsson, R. Berg, and S. Andersson-Engels, “Measurements of the optical properties of tissue in conjunction with photodynamic therapy,” Appl. Opt. 34(21), 4609–4619 (1995).
[Crossref] [PubMed]

1994 (1)

L. Wang and S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39(12), 2349–2354 (1994).
[Crossref] [PubMed]

1993 (1)

1990 (1)

S. Avrillier, E. Tinet, and E. Delettre, “Monte Carlo simulation of collimated beam transmission through turbid media,” J. Phys. 51(22), 2521–2542 (1990).
[Crossref]

Alerstam, E.

Andersson-Engels, S.

Atencio, J. A.

Avrillier, S.

S. Avrillier, E. Tinet, and E. Delettre, “Monte Carlo simulation of collimated beam transmission through turbid media,” J. Phys. 51(22), 2521–2542 (1990).
[Crossref]

Berg, R.

Changfang, Z.

L. Quan, Z. Changfang, and R. Nirmala, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8(2), 223–236 (2003).

Delettre, E.

S. Avrillier, E. Tinet, and E. Delettre, “Monte Carlo simulation of collimated beam transmission through turbid media,” J. Phys. 51(22), 2521–2542 (1990).
[Crossref]

Friebel, M.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. 11(3), 034021 (2006).
[Crossref] [PubMed]

Hammer, M.

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995).
[Crossref] [PubMed]

Han, T. D.

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML- Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

L. Wang and S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39(12), 2349–2354 (1994).
[Crossref] [PubMed]

Jacques, Steven L.

Lihong Wang and Steven L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (1998).

Lilge, L.

Liu, D. L.

Liu, Q.

Lo, W. C.

Lucassen, G. W.

A. M. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, and M. J. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65(2), 366–373 (1997).
[Crossref] [PubMed]

Meinke, M.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. 11(3), 034021 (2006).
[Crossref] [PubMed]

Morales, B.

B. Morales and S. Vázquez, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis. 57(4), 375–381 (2011).

Morales Cruzado, B.

Müller, G.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. 11(3), 034021 (2006).
[Crossref] [PubMed]

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995).
[Crossref] [PubMed]

Nilsson, A. M.

Nirmala, R.

L. Quan, Z. Changfang, and R. Nirmala, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8(2), 223–236 (2003).

Prahl, S. A.

Quan, L.

L. Quan, Z. Changfang, and R. Nirmala, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8(2), 223–236 (2003).

Roggan, A.

M. Friebel, A. Roggan, G. Müller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. 11(3), 034021 (2006).
[Crossref] [PubMed]

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995).
[Crossref] [PubMed]

Rose, J.

Schweitzer, D.

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995).
[Crossref] [PubMed]

Sturesson, C.

Tinet, E.

S. Avrillier, E. Tinet, and E. Delettre, “Monte Carlo simulation of collimated beam transmission through turbid media,” J. Phys. 51(22), 2521–2542 (1990).
[Crossref]

van Gemert, M. J.

A. M. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, and M. J. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65(2), 366–373 (1997).
[Crossref] [PubMed]

van Gemert, M. J. C.

Vázquez, S.

B. Morales and S. Vázquez, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis. 57(4), 375–381 (2011).

Verkruysse, W.

A. M. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, and M. J. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65(2), 366–373 (1997).
[Crossref] [PubMed]

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML- Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

L. Wang and S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39(12), 2349–2354 (1994).
[Crossref] [PubMed]

Wang, Lihong

Lihong Wang and Steven L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (1998).

Welch, A. J.

Y Montiel, S. V.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML- Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

Zhu, C.

Appl. Opt. (3)

Biomed. Opt. Express (2)

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML- Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47(2), 131–146 (1995).
[Crossref] [PubMed]

J. Biomed. Opt. (2)

L. Quan, Z. Changfang, and R. Nirmala, “Experimental validation of Monte Carlo modeling of fluorescence in tissues in the UV-visible spectrum,” J. Biomed. Opt. 8(2), 223–236 (2003).

M. Friebel, A. Roggan, G. Müller, and M. Meinke, “Determination of optical properties of human blood in the spectral range 250 to 1100 nm using Monte Carlo simulations with hematocrit-dependent effective scattering phase functions,” J. Biomed. Opt. 11(3), 034021 (2006).
[Crossref] [PubMed]

J. Phys. (1)

S. Avrillier, E. Tinet, and E. Delettre, “Monte Carlo simulation of collimated beam transmission through turbid media,” J. Phys. 51(22), 2521–2542 (1990).
[Crossref]

Opt. Express (1)

Photochem. Photobiol. (1)

A. M. Nilsson, G. W. Lucassen, W. Verkruysse, S. Andersson-Engels, and M. J. van Gemert, “Changes in optical properties of human whole blood in vitro due to slow heating,” Photochem. Photobiol. 65(2), 366–373 (1997).
[Crossref] [PubMed]

Phys. Med. Biol. (2)

M. Hammer, A. Roggan, D. Schweitzer, and G. Müller, “Optical properties of ocular fundus tissues-an in vitro study using the double-integrating-sphere technique and inverse Monte Carlo simulation,” Phys. Med. Biol. 40(6), 963–978 (1995).
[Crossref] [PubMed]

L. Wang and S. L. Jacques, “Error estimation of measuring total interaction coefficients of turbid media using collimated light transmission,” Phys. Med. Biol. 39(12), 2349–2354 (1994).
[Crossref] [PubMed]

Rev. Mex. Fis. (1)

B. Morales and S. Vázquez, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis. 57(4), 375–381 (2011).

Other (7)

ZEMAX Development Corporation, ZEMAX Optical Design Program User's Guide (2003).

Lambda Research Corporation, TracePro 5.0 User’s Manual (2009).

“ http://www.scatlab.org ”, November 2011.

Lihong Wang and Steven L. Jacques, Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C (1998).

W. J. Smith, Modern Optical Engineering, 4th ed. (SPIE PRESS, 2008).

W. T. Welford, Aberration of Optical Systems (Finite Ray tracing, 1991) Chap. 4.

H. C. van de Hulst, Multiple Light Scattering (Academic Press, New York, 1980), Vol. 1.

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Figures (8)

Fig. 1
Fig. 1 Schematic representation of the “photon propagation program in an optical-biological system”.
Fig. 2
Fig. 2 A) On the left is shown the experimental set-up for reflectance measurements and on the right is outlined the experimental set-up for transmittance measurements. B) Experimental set-up for collimated transmittance measurements. The elements in the array are identified as follows: 1) Laser, 2) Neutral optical density filter, 3) sample 4) Integrating Sphere, 5) detector, 6) voltmeter and 7) pinholes
Fig. 3
Fig. 3 Result of Monte Carlo simulation for the laser beam intensity profile at the entrance (black) and exit (red) surfaces of a turbid slab when the waist of the beam, w, is varied. Both profiles were normalized at the maximum intensity value.
Fig. 4
Fig. 4 A) Simulation of collimated transmittance, Tc of a sample with scattering coefficient of 25 cm−1, as a function of the distance, d, between pinhole 1 and 2 for the optical set up shown in Fig. 2B. B) Result for the simulation of collimated transmittance, Tc, as a function of the distance, d, between pinhole 1 and 2 at several values of the scattering coefficient. Inset: Dependence of minimum distance between pinholes required to get a reliable result of Tc with the scattering coefficient.
Fig. 5
Fig. 5 Plots on the left represent a linear fit of ln(Tc) when the thickness of the slab is the independent variable while plots on the right represent a linear fit of ln(Tc) when the scattering coefficient, μs, of the slab is the independent variable.
Fig. 6
Fig. 6 a) Comparison between the scattering coefficient used in MCML simulation µs-teo and the scattering coefficient µs-sim recovered from the linear fit of ln(Tc) as function of the thickness and b) plot of the comparison between th e thickness tteo used in the MCML simulation and the thickness recovered from the linear fit of ln(Tc) as a function of the scattering coefficient.
Fig. 7
Fig. 7 A) Collimated transmittance “Tc” versus the anisotropy factor “g” at different values of μs when the sample is considered as a non-absorbing medium. B)Collimated transmittance “Tc” versus the absorption coefficient.
Fig. 8
Fig. 8 Result of the comparison between the experimental dependence of “Tc” versus “µs” and its simulation by mean of the developed program.

Equations (4)

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r=ω ln( 1χ ) 2
S( r )= 2 π ω 2 exp( 2 r 2 ω 2 )
R= r std R r R 0 R 1 R 0
T= T t T 0 T 1 T 0

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