Abstract

Monte Carlo (MC) simulations are frequently used to simulate the radial distribution of remitted fluorescence light from tissue surfaces upon pencil beam excitation to gather information about influences of different tissue parameters. Here, the “weighted direct emission method” (WDEM) is proposed, which uses a weighted MC simulation approach for both excitation and fluorescence photons, and is compared to four other methods in terms of accuracy and speed, and using a broad range of tissue-relevant optical parameters. The WDEM is 5.2× faster on average than a fixed weight MC approach while still preserving its accuracy. Additional gain of speed can be achieved by implementing it on graphics processing units.

© 2013 Optical Society of America

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2011

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

G. Hennig, H. Stepp, and A. Johansson, “Photobleaching-based method to individualize irradiation time during interstitial 5-aminolevulinic acid photodynamic therapy,” Photodiagnosis Photodyn. Ther. 8, 275–281 (2011).
[CrossRef]

J. Hegyi, V. Hegyi, T. Ruzicka, P. Arenberger, and C. Berking, “New developments in fluorescence diagnostics,” J. Dtsch. Dermatol. Ges. 9, 368–372 (2011).
[CrossRef]

2010

2009

N. Baddour, “Operational and convolution properties of two-dimensional Fourier transforms in polar coordinates,” J. Opt. Soc. Am. A 26, 1767–1777 (2009).
[CrossRef]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17, 20178–20190 (2009).
[CrossRef]

A. A. Tanbakuchi, A. R. Rouse, and A. F. Gmitro, “Monte Carlo characterization of parallelized fluorescence confocal systems imaging in turbid media,” J. Biomed. Opt. 14, 044024 (2009).
[CrossRef]

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[CrossRef]

2008

A. Liebert, H. Wabnitz, N. Zolek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express 16, 13188–13202 (2008).
[CrossRef]

G. M. Palmer and N. Ramanujam, “Monte-Carlo-based model for the extraction of intrinsic fluorescence from turbid media,” J. Biomed. Opt. 13, 024017 (2008).
[CrossRef]

2007

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

2006

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145–167 (2006).
[CrossRef]

I. Georgakoudi, “The color of cancer,” J. Lumin. 119–120, 75–83 (2006).
[CrossRef]

2005

2003

2002

K. Vishwanath, B. Pogue, and M. A. Mycek, “Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods,” Phys. Med. Biol. 47, 3387–3405 (2002).
[CrossRef]

1998

1997

R. J. Crilly, W. F. Cheong, B. Wilson, and J. R. Spears, “Forward-adjoint fluorescence model: Monte Carlo integration and experimental validation,” Appl. Opt. 36, 6513–6519(1997).
[CrossRef]

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21, 166–178 (1997).
[CrossRef]

1996

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef]

1995

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

1989

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

1987

H. F. Johnson, “An improved method for computing a discrete Hankel transform,” Comput. Phys. Commun. 43, 181–202(1987).
[CrossRef]

1983

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 (1983).
[CrossRef]

1949

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
[CrossRef]

1941

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Adam, G.

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 (1983).
[CrossRef]

Alerstam, E.

Andersson-Engels, S.

Arenberger, P.

J. Hegyi, V. Hegyi, T. Ruzicka, P. Arenberger, and C. Berking, “New developments in fluorescence diagnostics,” J. Dtsch. Dermatol. Ges. 9, 368–372 (2011).
[CrossRef]

Arifler, D.

Averbuch, A.

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145–167 (2006).
[CrossRef]

Avrillier, S.

Ayers, F. R.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[CrossRef]

Baddour, N.

Baumgartner, R.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Beck, T.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Berking, C.

J. Hegyi, V. Hegyi, T. Ruzicka, P. Arenberger, and C. Berking, “New developments in fluorescence diagnostics,” J. Dtsch. Dermatol. Ges. 9, 368–372 (2011).
[CrossRef]

Bevilacqua, F.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[CrossRef]

Beyer, W.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Boas, D. A.

Burke, G.

Chan, E.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21, 166–178 (1997).
[CrossRef]

Chang, S. K.

Cheong, W. F.

Coifman, R. R.

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145–167 (2006).
[CrossRef]

Conde, O. M.

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

Crilly, R. J.

Criswell, G.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21, 166–178 (1997).
[CrossRef]

Cuccia, D. J.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[CrossRef]

Donoho, D. L.

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145–167 (2006).
[CrossRef]

Durkin, A. J.

D. J. Cuccia, F. Bevilacqua, A. J. Durkin, F. R. Ayers, and B. J. Tromberg, “Quantitation and mapping of tissue optical properties using modulated imaging,” J. Biomed. Opt. 14, 024012 (2009).
[CrossRef]

Elad, M.

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145–167 (2006).
[CrossRef]

Enejder, A. M.

Ettori, D.

Fang, Q.

Gardner, C.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21, 166–178 (1997).
[CrossRef]

Gelebart, B.

Georgakoudi, I.

I. Georgakoudi, “The color of cancer,” J. Lumin. 119–120, 75–83 (2006).
[CrossRef]

Gmitro, A. F.

A. A. Tanbakuchi, A. R. Rouse, and A. F. Gmitro, “Monte Carlo characterization of parallelized fluorescence confocal systems imaging in turbid media,” J. Biomed. Opt. 14, 044024 (2009).
[CrossRef]

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Han, T. D.

Harris, B. T.

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

Hegyi, J.

J. Hegyi, V. Hegyi, T. Ruzicka, P. Arenberger, and C. Berking, “New developments in fluorescence diagnostics,” J. Dtsch. Dermatol. Ges. 9, 368–372 (2011).
[CrossRef]

Hegyi, V.

J. Hegyi, V. Hegyi, T. Ruzicka, P. Arenberger, and C. Berking, “New developments in fluorescence diagnostics,” J. Dtsch. Dermatol. Ges. 9, 368–372 (2011).
[CrossRef]

Hennig, G.

G. Hennig, H. Stepp, and A. Johansson, “Photobleaching-based method to individualize irradiation time during interstitial 5-aminolevulinic acid photodynamic therapy,” Photodiagnosis Photodyn. Ther. 8, 275–281 (2011).
[CrossRef]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Israeli, M.

A. Averbuch, R. R. Coifman, D. L. Donoho, M. Elad, and M. Israeli, “Fast and accurate polar Fourier transform,” Appl. Comput. Harmon. Anal. 21, 145–167 (2006).
[CrossRef]

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, 131–146 (1995).
[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

S. L. Jacques, “Monte Carlo simulations of fluorescence in turbid media,” in Handbook of Biomedical Fluorescence, M. A. Mycek and B. W. Pogue, eds. (Marcel-Dekker, 2003).

Johansson, A.

G. Hennig, H. Stepp, and A. Johansson, “Photobleaching-based method to individualize irradiation time during interstitial 5-aminolevulinic acid photodynamic therapy,” Photodiagnosis Photodyn. Ther. 8, 275–281 (2011).
[CrossRef]

Johnson, H. F.

H. F. Johnson, “An improved method for computing a discrete Hankel transform,” Comput. Phys. Commun. 43, 181–202(1987).
[CrossRef]

Keijzer, M.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

Kienle, A.

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef]

Kim, A.

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

Kollias, N.

Y. P. Sinichkin, N. Kollias, G. I. Zonios, S. R. Utz, and V. V. Tuchin, “Reflectance and fluorescence spectroscopy of human skin in vivo,” in Handbook of Optical Biomedical Diagnostics, V. V. Tuchin, ed. (SPIE, 2002), pp. 725–785.

Leblond, F.

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

Liebert, A.

Lilge, L.

Lo, W. C.

Macdonald, R.

Metropolis, N.

N. Metropolis and S. Ulam, “The Monte Carlo method,” J. Am. Stat. Assoc. 44, 335–341 (1949).
[CrossRef]

Mycek, M. A.

K. Vishwanath, B. Pogue, and M. A. Mycek, “Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods,” Phys. Med. Biol. 47, 3387–3405 (2002).
[CrossRef]

Palmer, G. M.

G. M. Palmer and N. Ramanujam, “Monte-Carlo-based model for the extraction of intrinsic fluorescence from turbid media,” J. Biomed. Opt. 13, 024017 (2008).
[CrossRef]

Patterson, M. S.

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef]

Paulsen, K. D.

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

Pfaller, C.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Pfefer, J.

A. J. Welch, C. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21, 166–178 (1997).
[CrossRef]

Pifferi, A.

Pogue, B.

K. Vishwanath, B. Pogue, and M. A. Mycek, “Quantitative fluorescence lifetime spectroscopy in turbid media: comparison of theoretical, experimental and computational methods,” Phys. Med. Biol. 47, 3387–3405 (2002).
[CrossRef]

Pogue, B. W.

Prahl, S. A.

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE IS 5, 102–111 (1989).

Ramanujam, N.

G. M. Palmer and N. Ramanujam, “Monte-Carlo-based model for the extraction of intrinsic fluorescence from turbid media,” J. Biomed. Opt. 13, 024017 (2008).
[CrossRef]

Richards-Kortum, R.

Roberts, D. W.

P. A. Valdes, A. Kim, F. Leblond, O. M. Conde, B. T. Harris, K. D. Paulsen, B. C. Wilson, and D. W. Roberts, “Combined fluorescence and reflectance spectroscopy for in vivo quantification of cancer biomarkers in low- and high-grade glioma surgery,” J. Biomed. Opt. 16, 116007 (2011).
[CrossRef]

Rose, J.

Rouse, A. R.

A. A. Tanbakuchi, A. R. Rouse, and A. F. Gmitro, “Monte Carlo characterization of parallelized fluorescence confocal systems imaging in turbid media,” J. Biomed. Opt. 14, 044024 (2009).
[CrossRef]

Ruzicka, T.

J. Hegyi, V. Hegyi, T. Ruzicka, P. Arenberger, and C. Berking, “New developments in fluorescence diagnostics,” J. Dtsch. Dermatol. Ges. 9, 368–372 (2011).
[CrossRef]

Schuppler, M.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Schwarz, R. A.

Sinichkin, Y. P.

Y. P. Sinichkin, N. Kollias, G. I. Zonios, S. R. Utz, and V. V. Tuchin, “Reflectance and fluorescence spectroscopy of human skin in vivo,” in Handbook of Optical Biomedical Diagnostics, V. V. Tuchin, ed. (SPIE, 2002), pp. 725–785.

Spears, J. R.

Sroka, R.

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Stepp, H.

G. Hennig, H. Stepp, and A. Johansson, “Photobleaching-based method to individualize irradiation time during interstitial 5-aminolevulinic acid photodynamic therapy,” Photodiagnosis Photodyn. Ther. 8, 275–281 (2011).
[CrossRef]

H. Stepp, T. Beck, W. Beyer, C. Pfaller, M. Schuppler, R. Sroka, and R. Baumgartner, “Measurement of fluorophore concentration in turbid media by a single optical fiber,” Med. Laser Appl. 22, 23–34 (2007).
[CrossRef]

Swartling, J.

Tanbakuchi, A. A.

A. A. Tanbakuchi, A. R. Rouse, and A. F. Gmitro, “Monte Carlo characterization of parallelized fluorescence confocal systems imaging in turbid media,” J. Biomed. Opt. 14, 044024 (2009).
[CrossRef]

Tinet, E.

Tromberg, B. J.

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Figures (4)

Fig. 1.
Fig. 1.

Ratio μ a , x / ( μ a , x + μ s , x ) for the 18 sets of optical parameters (with low and high scattering coefficients each, LOW and HIGH, 9 each) is plotted against the optimal fluorescence emission probability P fl , opt for the WDEM, as well as the identity. Two overlapping points are indicated by solid symbols.

Fig. 2.
Fig. 2.

Remitted fluorescence per area F ( r ) , normalized by the number of excitation photons, for one set of optical parameters (aa, LOW, as indicated in Table 2) is shown in the upper panel. Three different methods, WDEM, WSEM, and RM are shown. The FEM is omitted as it shows a perfect overlap with the RM, and the DEM as it overlaps with the WDEM. In the lower panel, the relative residual of WSEM/WDEM and RM/WDEM is shown.

Fig. 3.
Fig. 3.

Effective simulation time relative to t eff ( DEM ) for the different methods is shown. For each method, on the left the results for low scattering coefficients (LOW) are shown, and on the right for high scattering coefficients (HIGH). Bars denote the mean simulation time, averaged over the 9 sets of optical parameters for low or high scattering coefficients (LOW and HIGH), and the error bars indicate the range. Please note the logarithmic y -axis scale.

Fig. 4.
Fig. 4.

Ratio of the total simulation time required by the CPU version and the GPU version is shown. The method WDEM was used to simulate fluorescence for 9 sets of optical parameters with low scattering coefficient (LOW, left bar for each set of optical parameters) and 9 sets of optical parameters with high scattering coefficient (HIGH, right bar for each set of optical parameters).

Tables (4)

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Table 1. Overview of the Methods Used for the Different Simulation Methods

Tables Icon

Table 2. List of the Simulation Input Optical Parameters Denoted by aa to cc, with Three Different Absorptiona,b and Scattering Coefficientsa,c, Respectively

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Table 3. Total Remitted Fluorescence in Percent, Normalized to the Excitation Photons, for the Five Different Methods for 18 Different Optical Parametersa Denoted by aa to cc

Tables Icon

Table 4. Comparison of the Results for the Different Methods

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

w a , x = μ a , x μ a , x + μ s , x w x .
w fl = w a , x γ · μ a , fl μ a , x 1 P fl .
w x * = ( w x w a , x ) 1 1 P fl ,
Φ x ( r , z ) = A x ( r , z ) V · μ a , x ,
F ( r ¯ ) = i = 1 n z Φ x ( r ¯ , z i ) * P m ( r ¯ , z i ) .
θ c = sin 1 n 0 n 1 .
P m ( r , z ) = c reverse A m ( r , z ) V · μ a , m ,
t eff = t sim min { SNR ( d ) } 2 .

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