Abstract

This paper describes an extension of the perturbation Monte Carlo method to model light transport when the phase function is arbitrarily perturbed. Current perturbation Monte Carlo methods allow perturbation of both the scattering and absorption coefficients, however, the phase function can not be varied. The more complex method we develop and test here is not limited in this way. We derive a rigorous perturbation Monte Carlo extension that can be applied to a large family of important biomedical light transport problems and demonstrate its greater computational efficiency compared with using conventional Monte Carlo simulations to produce forward transport problem solutions. The gains of the perturbation method occur because only a single baseline Monte Carlo simulation is needed to obtain forward solutions to other closely related problems whose input is described by perturbing one or more parameters from the input of the baseline problem. The new perturbation Monte Carlo methods are tested using tissue light scattering parameters relevant to epithelia where many tumors originate. The tissue model has parameters for the number density and average size of three classes of scatterers; whole nuclei, organelles such as lysosomes and mitochondria, and small particles such as ribosomes or large protein complexes. When these parameters or the wavelength is varied the scattering coefficient and the phase function vary. Perturbation calculations give accurate results over variations of ∼15–25% of the scattering parameters.

© 2013 OSA

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2012 (1)

C Zhu and Q Liu, “Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities.” J. Biomed. Opt.17010501 (2012).
[CrossRef] [PubMed]

2011 (1)

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomographycomputational efficiency,” Med. Phys.38, 5788–5798 (2011).
[CrossRef] [PubMed]

2010 (1)

Q. Wang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Condensed Monte Carlo modeling of reflectance from biological tissue with a single illuminationdetection fiber,” IEEE J. Sel. Top. Quantum Electron.16, 627–634 (2010).
[CrossRef]

2009 (3)

2008 (1)

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (1)

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

2005 (3)

J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett.18, 2442–2444 (2005).
[CrossRef]

P. Yalavarthy, K. Karlekar, H. Patel, R. Vasu, M. Pramanik, P. Mathias, B. Jain, and P. Gupta, “Experimental Investigation of Perturbation Monte-Carlo Based Derivative Estimation for Imaging Low-Scattering Tissue,” Opt. Express13, 985–997 (2005).
[CrossRef] [PubMed]

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

2004 (2)

2003 (1)

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt.8, 121–147 (2003).
[CrossRef] [PubMed]

2002 (2)

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures” J. Biomed. Opt.7, 378–387 (2002).
[CrossRef] [PubMed]

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (1)

M. Canpolat and J. R. Mourant, “High-angle scattering events strongly affect light collection in clinically relevant measurement geometries for light transport through tissue,” Phys. Med. Biol.45, 1127–1140 (2000).
[CrossRef] [PubMed]

1999 (1)

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

1998 (1)

1996 (2)

1994 (1)

1993 (1)

1974 (1)

A. Brunsting and P. F. Mullaney, “Differential light scattering from spherical mammalian cells,” Biophys. J.14, 439–453 (1974).
[CrossRef] [PubMed]

A‘Amar, O.

Aarnoudse, J. G.

Aaron, J.

Agrawal, A.

Q. Wang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Condensed Monte Carlo modeling of reflectance from biological tissue with a single illuminationdetection fiber,” IEEE J. Sel. Top. Quantum Electron.16, 627–634 (2010).
[CrossRef]

Aida, T.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures” J. Biomed. Opt.7, 378–387 (2002).
[CrossRef] [PubMed]

Amelink, A.

Atkinson, E. N.

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

Avrillier, S.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt.5, 377–388 (1996).
[CrossRef]

Backman, V.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Bartek, M.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

Bechtel, K.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Bender, J. E.

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

Bevilacqua, F.

Bigio, I. J.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boyer, J.

Brunsting, A.

A. Brunsting and P. F. Mullaney, “Differential light scattering from spherical mammalian cells,” Biophys. J.14, 439–453 (1974).
[CrossRef] [PubMed]

Canpolat, M.

M. Canpolat and J. R. Mourant, “High-angle scattering events strongly affect light collection in clinically relevant measurement geometries for light transport through tissue,” Phys. Med. Biol.45, 1127–1140 (2000).
[CrossRef] [PubMed]

Carpenter, S.

J. Ramachandran, T. Powers, S. Carpenter, A. Garcia-Lopez, J. P. Freyer, and J. R. Mourant, “Light Scattering and microarchitectural differences between tumorigenic and non-tumorigenic cell models of tissue,” Opt. Express15, 4039–4053 (2007).
[CrossRef] [PubMed]

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures” J. Biomed. Opt.7, 378–387 (2002).
[CrossRef] [PubMed]

Chang, S. K.

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

Chen, J.

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomographycomputational efficiency,” Med. Phys.38, 5788–5798 (2011).
[CrossRef] [PubMed]

J. Chen and X. Intes, “Time-gated perturbation Monte Carlo for whole body functional imaging in small animals,” Opt. Express17, 19566–19579 (2009).
[CrossRef] [PubMed]

Dassel, A. C. M.

de Mul, F. F. M.

Drezek, R. A.

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

Dunn, A.

Feld, M.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Feld, M. S.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Fitzmaurice, M.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Follen, M.

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

Foster, T. H.

J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett.18, 2442–2444 (2005).
[CrossRef]

Freyer, J. P.

Fulghum, S.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Garcia-Lopez, A.

Gelbard, E.

J. Spanier and E. Gelbard, Monte Carlo Principles and Neutron Transport Problems (Addison-Wesley, 1969).

Gélébart, B.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt.5, 377–388 (1996).
[CrossRef]

Goertzel, G.

G. Goertzel and M. K. Kalos, “Monte Carlo methods in transport problems,” Appendix 2 in Progress in Nuclear Energy, Vol 2, Series 1, D. J. Hughes, J. E. Sanders, and J. Horowitz, eds. (Pergamon Press, 1958).

Gomes, A. J.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Graaff, R.

Grant, P. E.

Guerra, A.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures” J. Biomed. Opt.7, 378–387 (2002).
[CrossRef] [PubMed]

Gupta, P.

Hayakawa, C.

I. Seo, J. You, C. Hayakawa, and V. Venugopalan, “Perturbation and differential Monte Carlo Methods for measurement of optical properties in a layered epithelial tissue model,” J. Biomed. Opt.12, 014030 (2007).
[CrossRef] [PubMed]

C. Hayakawa, J. Spanier, F. Bevilacqua, A. Dunn, J. You, B. Tromberg, and V. Venugopalan, “Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues,” Opt. Lett.26, 1335–1337 (2001).
[CrossRef]

Heiskala, J.

Hielscher, A. H.

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Intes, X.

J. Chen and X. Intes, “Comparison of Monte Carlo methods for fluorescence molecular tomographycomputational efficiency,” Med. Phys.38, 5788–5798 (2011).
[CrossRef] [PubMed]

J. Chen and X. Intes, “Time-gated perturbation Monte Carlo for whole body functional imaging in small animals,” Opt. Express17, 19566–19579 (2009).
[CrossRef] [PubMed]

Jain, B.

Jameel, M.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Johnson, T. M.

J. R. Mourant, T. M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J. P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures” J. Biomed. Opt.7, 378–387 (2002).
[CrossRef] [PubMed]

J. R. Mourant, T. M. Johnson, and J. P. Freyer, “Characterizing mammalian cells and cell phantoms by polarized backscattering fiber-optic measurements,” Appl. Opt.40, 5114–5123 (2001).
[CrossRef]

Kalos, M. K.

G. Goertzel and M. K. Kalos, “Monte Carlo methods in transport problems,” Appendix 2 in Progress in Nuclear Energy, Vol 2, Series 1, D. J. Hughes, J. E. Sanders, and J. Horowitz, eds. (Pergamon Press, 1958).

Karlekar, K.

Kim, Y. L.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Koelink, M. H.

Kromine, A.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Kumar, G.

Lam, S.

Lau, C.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Liu, Q

C Zhu and Q Liu, “Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities.” J. Biomed. Opt.17010501 (2012).
[CrossRef] [PubMed]

Liu, Q.

Liu, Y.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

MacAulay, C.

Malpica, A.

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

Manoharan, R.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Mathias, P.

McGee, S.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Metsäranta, M.

Mirabal, Y. N.

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

Mirkovic, J.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Mourant, J. R.

Mullaney, P. F.

A. Brunsting and P. F. Mullaney, “Differential light scattering from spherical mammalian cells,” Biophys. J.14, 439–453 (1974).
[CrossRef] [PubMed]

Myakov, A.

Nieman, L.

Palcic, B.

Patel, H.

Paulsen, K. D.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

Perelman, L. T.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Pfefer, J.

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

Pfefer, T. J.

Q. Wang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Condensed Monte Carlo modeling of reflectance from biological tissue with a single illuminationdetection fiber,” IEEE J. Sel. Top. Quantum Electron.16, 627–634 (2010).
[CrossRef]

Pogue, P. W.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

Pollari, M.

Powers, T.

Pramanik, M.

Qu, J.

Ramachandran, J.

Ramanujam, N.

Reif, R.

Richards-Kortum, R.

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

Richards-Kortum, R. R.

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt.8, 121–147 (2003).
[CrossRef] [PubMed]

Rogers, J. D.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Roy, H. K.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Šcepanovic, O.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Schmitt, J.

Seo, I.

I. Seo, J. You, C. Hayakawa, and V. Venugopalan, “Perturbation and differential Monte Carlo Methods for measurement of optical properties in a layered epithelial tissue model,” J. Biomed. Opt.12, 014030 (2007).
[CrossRef] [PubMed]

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Spanier, J.

Sterenborg, H.

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B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt.5, 377–388 (1996).
[CrossRef]

Tromberg, B.

Tualle, J. M.

B. Gélébart, E. Tinet, J. M. Tualle, and S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt.5, 377–388 (1996).
[CrossRef]

Tunnell, J.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Turzhitsky, V. M.

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

Utzinger, U.

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt.8, 121–147 (2003).
[CrossRef] [PubMed]

Van Dam, J.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Vasu, R.

Venugopalan, V.

I. Seo, J. You, C. Hayakawa, and V. Venugopalan, “Perturbation and differential Monte Carlo Methods for measurement of optical properties in a layered epithelial tissue model,” J. Biomed. Opt.12, 014030 (2007).
[CrossRef] [PubMed]

C. Hayakawa, J. Spanier, F. Bevilacqua, A. Dunn, J. You, B. Tromberg, and V. Venugopalan, “Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues,” Opt. Lett.26, 1335–1337 (2001).
[CrossRef]

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C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Wang, A. M. J.

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

Wang, N. S.

Q. Wang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Condensed Monte Carlo modeling of reflectance from biological tissue with a single illuminationdetection fiber,” IEEE J. Sel. Top. Quantum Electron.16, 627–634 (2010).
[CrossRef]

Wang, Q.

Q. Wang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Condensed Monte Carlo modeling of reflectance from biological tissue with a single illuminationdetection fiber,” IEEE J. Sel. Top. Quantum Electron.16, 627–634 (2010).
[CrossRef]

Wang, X.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

Wells, W.

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

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J. D. Wilson and T. H. Foster, “Mie theory interpretations of light scattering from intact cells,” Opt. Lett.18, 2442–2444 (2005).
[CrossRef]

Yalavarthy, P.

You, J.

I. Seo, J. You, C. Hayakawa, and V. Venugopalan, “Perturbation and differential Monte Carlo Methods for measurement of optical properties in a layered epithelial tissue model,” J. Biomed. Opt.12, 014030 (2007).
[CrossRef] [PubMed]

C. Hayakawa, J. Spanier, F. Bevilacqua, A. Dunn, J. You, B. Tromberg, and V. Venugopalan, “Perturbation Monte Carlo methods to solve inverse photon migration problems in heterogeneous tissues,” Opt. Lett.26, 1335–1337 (2001).
[CrossRef]

Yu, C.-C.

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

Zhu, C

C Zhu and Q Liu, “Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities.” J. Biomed. Opt.17010501 (2012).
[CrossRef] [PubMed]

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Zonios, G.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt.31, 6628–6637 (1999).
[CrossRef]

Appl. Opt (1)

V. M. Turzhitsky, A. J. Gomes, Y. L. Kim, Y. Liu, A. Kromine, J. D. Rogers, M. Jameel, H. K. Roy, and V. Backman, “Measuring mucosal blood supply in vivo with a polarization-gating probe,” Appl. Opt, 47, 6046–6057 (2008).
[CrossRef] [PubMed]

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IEEE J. Sel. Top. Quantum Electron. (1)

Q. Wang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Condensed Monte Carlo modeling of reflectance from biological tissue with a single illuminationdetection fiber,” IEEE J. Sel. Top. Quantum Electron.16, 627–634 (2010).
[CrossRef]

J. Biomed. Opt. (8)

I. Seo, J. You, C. Hayakawa, and V. Venugopalan, “Perturbation and differential Monte Carlo Methods for measurement of optical properties in a layered epithelial tissue model,” J. Biomed. Opt.12, 014030 (2007).
[CrossRef] [PubMed]

C Zhu and Q Liu, “Hybrid method for fast Monte Carlo simulation of diffuse reflectance from a multilayered tissue model with tumor-like heterogeneities.” J. Biomed. Opt.17010501 (2012).
[CrossRef] [PubMed]

C. Lau, O. Šcepanović, J. Mirkovic, S. McGee, C.-C. Yu, S. Fulghum, M. Wallace, J. Tunnell, K. Bechtel, and M. Feld, “Re-evaluation of model-based light-scattering spectroscopy for tissue spectroscopy,” J. Biomed. Opt.14, 024031 (2009).
[CrossRef] [PubMed]

A. M. J. Wang, J. E. Bender, J. Pfefer, U. Utzinger, and R. A. Drezek, “Depth-sensitive reflectance measurements using obliquely oriented fiber probes,” J. Biomed. Opt.10, 044017 (2005).
[CrossRef]

U. Utzinger and R. R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt.8, 121–147 (2003).
[CrossRef] [PubMed]

Y. N. Mirabal, S. K. Chang, E. N. Atkinson, A. Malpica, M. Follen, and R. Richards-Kortum, “Reflectance spectroscopy for in vivo detection of cervical precancer,” J. Biomed. Opt.7587–594 (2002).
[CrossRef] [PubMed]

M. Bartek, X. Wang, W. Wells, K. D. Paulsen, and P. W. Pogue, “Estimation of subcellular particle size histograms with electron microscopy for prediction of optical scattering in breast tissue,” J. Biomed. Opt.6, 064007 (2006).
[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

a) Scatterers per volume as a function of scatter radius. b) The phase function for the baseline MC simulation of epithelial tissue at 620 nm.

Fig. 2
Fig. 2

Source and detector setup for this study. The yellow fiber in the middle represents the photon source and 1, 2, 3, 4 represent detectors.

Fig. 3
Fig. 3

Comparison of pMC estimates of reflectance with independent cMC simulations results when the concentration of single size scatterers is perturbed. Each panel is for a different collection fiber shown in Fig. 2. Error bars are standard errors of the mean.

Fig. 4
Fig. 4

Comparison of pMC estimates of reflectance with estimates of reflectance obtained from independent cMC simulations when the radius of a single size distribution is perturbed. Error bars are standard errors of the mean.

Fig. 5
Fig. 5

Comparison of pMC estimates of reflectance with independent cMC simulations results when wavelength is perturbed. The scattering particles had a radius of 447.5 nm. Each panel is for a different collection fiber shown in Fig. 2. Error bars are standard errors of the mean.

Fig. 6
Fig. 6

Comparison of pMC estimates of reflectance with independent cMC simulations results when wavelength is perturbed. The scattering particles had a radius of 100 nm.

Fig. 7
Fig. 7

Scattering parameters used in the MC simulations incorporating only one scatterer size. Top left: μs. Top right: μs. Bottom left: anisotropy coefficient g, Bottom right: g on an expanded scale.

Fig. 8
Fig. 8

The number density of each of the distributions in Table 1 is varied. a) Ns for the smallest size distribution is varied. b) Ns for the middle size distribution is varied. c) Ns for the large size distribution is varied. Errors are standard error of the mean. Only cMC results for fiber 1 are shown for clarity. Similarly, only pMC results for one or two fibers are shown.

Fig. 9
Fig. 9

The mean radii of individual groups of scatterers are perturbed; a) distribution 1, b) distribution 2, and c) distribution 3 in Table 1. Only cMC results for fiber 1 are shown for clarity. Similarly, pMC results are shown for only some fibers. The range of the ”Fraction of Photons Collected” is different in panel a) from all other graphs of ”Fraction of Photons Collected”. The error bars are standard errors of the mean.

Fig. 10
Fig. 10

Comparison of pMC estimates of reflectance across wavelengths with calculations of reflectance obtained from independent cMC simulations of tissue.

Fig. 11
Fig. 11

Scattering parameters for the simulation results shown in Figs. 8, 9 and 10.

Tables (2)

Tables Icon

Table 1 Distributions of scatter sizes in the tissue model

Tables Icon

Table 2 Range of parameter variation for <1% error in pMC reflectance calculation

Equations (24)

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

L k ( x ) = 1 x σ k 2 π e ( ln x ln x ¯ k ) 2 2 ( σ k ) 2
μ s , k = N k a b L k ( x ) C sca ( x ) d x
f = k = 1 m μ s , k μ s f k
μ s = k = 1 m μ s , k .
Φ ( r , ω ) ω = μ t Φ ( r , ω ) + μ s 4 π Φ ( r , ω ) f ( ω ω ) d ω + Q ( r , ω )
Ψ ( P ) = Γ K ( P , P ) Ψ ( P ) d P + S ( P )
K ( r , ω r , ω ) = f ( ω ω ) T ( r r , ω )
T ( r r , ω ) = μ s ( r ) e μ s ( r ) l
Ψ ( r , ω ) = μ t ( r ) Φ ( r , ω ) .
S ( r , ω ) = T ( r r , ω ) Q ( r , ω ) d r
I = Γ d ( P ) Ψ ( P ) d P
ξ ( C i ) = { 1 if C i results in a detected photon 0 otherwise .
I = Γ d ( P ) Ψ ( P ) d P = ξ d M .
I = i = 1 n ξ ( C i ) M ( C i )
I ^ = i = 0 n ξ ( C i ) M ^ ( C i )
ξ ^ ( C i ) = ξ ( C i ) M ^ ( C i ) M ( C i )
I ^ = i = 0 n ξ ^ ( C i ) M ( C i ) .
M ^ α ( C i ) M ( C i ) = ( T ^ α T ) m = 1 j ( K ^ α , m K m )
K = f ( ω ω ) μ s exp ( μ s l )
K ^ = f ^ ( ω ω ) μ ^ s exp ( μ ^ s l ) .
0 L s μ s e μ s l d l = e μ s L s + 1
ξ ^ = ξ ( μ ^ s μ s ) e ( μ ^ s μ s ) l 0 ( m = 1 j 1 f ^ ( θ m ) f ( θ m ) μ ^ s μ s e ( μ ^ s μ s ) l m ) f ^ ( θ j ) f ( θ j ) e ( μ ^ s μ s ) L s
ξ ^ = ξ ( μ ^ s μ s ) j exp [ ( μ ^ s μ s ) L ] ( m = 1 j f ^ ( θ m ) f ( θ m ) )
size parameter = 2 π r n medium / λ

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