Abstract

Accurate determination of in-vivo light fluence rate is critical for preclinical and clinical studies involving photodynamic therapy (PDT). The light fluence distribution in tissue depends on both the tissue optical properties and the incident field size. This study compares the longitudinal light fluence distribution inside biological tissue in the central axis of circular uniform light field with different radii for a range of in-vivo tissue optical properties (absorption coefficients (µa) between 0.01 and 1 cm−1 and reduced scattering coefficients (µs’) between 2 and 40 cm−1). This was done using Monte-Carlo simulations for a semi-infinite turbid medium in an air-tissue interface. The end goal is to develop simple analytical expressions that would fit the results from the Monte Carlo simulation for circular beams with different radii. A 6-parameter model (ϕ/ϕair=(1beλ1d)(C2eλ2d+C3eλ3d)) can be used to fit MC simulation. Each of these parameters (b, C2, C3, λ1, λ2, and λ3) is expressed as a function of tissue optical properties and beam radius. These results can then be compared against the existing expressions in the literature for broad beam for analysis in both accuracy and applicable range. The analytical function can be used as rapid guide in PDT to calculate in vivo light fluence distribution for known tissue optical properties.

© 2016 Optical Society of America

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Corrections

Yi Hong Ong and Timothy C. Zhu, "Analytic function for predicting light fluence rate of circular fields on a semi-infinite turbid medium: erratum," Opt. Express 24, 30494-30494 (2016)
https://www.osapublishing.org/oe/abstract.cfm?uri=oe-24-26-30494

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  11. T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
    [Crossref] [PubMed]
  12. M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
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    [Crossref] [PubMed]
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  21. S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” Proc. SPIE 5, 102–111 (1989).
  22. T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
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  23. T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
    [Crossref] [PubMed]
  24. A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
    [Crossref]
  25. C. B. Simone and K. A. Cengel, “Photodynamic Therapy for Lung Cancer and Malignant Pleural Mesothelioma,” Semin. Oncol. 41(6), 820–830 (2014).
    [Crossref] [PubMed]
  26. T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
    [Crossref] [PubMed]
  27. S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
    [Crossref] [PubMed]

2016 (1)

H. Qiu, M. M. Kim, R. Penjweini, and T. C. Zhu, “Macroscopic singlet oxygen modeling for dosimetry of Photofrin-mediated photodynamic therapy: an in-vivo study,” J. Biomed. Opt. 21(8), 088002 (2016).
[Crossref] [PubMed]

2014 (1)

C. B. Simone and K. A. Cengel, “Photodynamic Therapy for Lung Cancer and Malignant Pleural Mesothelioma,” Semin. Oncol. 41(6), 820–830 (2014).
[Crossref] [PubMed]

2013 (2)

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013).
[Crossref] [PubMed]

2011 (1)

J. L. Sandell and T. C. Zhu, “A review of in-vivo optical properties of human tissues and its impact on PDT,” J. Biophotonics 4(11-12), 773–787 (2011).
[Crossref] [PubMed]

2009 (1)

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

2008 (1)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

2006 (1)

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

2005 (1)

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol. 50(10), 2291–2311 (2005).
[Crossref] [PubMed]

2004 (2)

T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
[Crossref] [PubMed]

T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
[Crossref] [PubMed]

2003 (1)

T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
[Crossref] [PubMed]

2002 (1)

A. Dimofte, T. C. Zhu, S. M. Hahn, and R. A. Lustig, “In vivo light dosimetry for motexafin lutetium-mediated PDT of recurrent breast cancer,” Lasers Surg. Med. 31(5), 305–312 (2002).
[Crossref] [PubMed]

2000 (1)

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

1998 (1)

S. L. Jacques, “Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues,” Photochem. Photobiol. 67(1), 23–32 (1998).
[Crossref] [PubMed]

1997 (1)

W. M. Star, “Light dosimetry in vivo,” Phys. Med. Biol. 42(5), 763–787 (1997).
[Crossref] [PubMed]

1996 (2)

J. P. Marijnissen and W. M. Star, “Calibration of isotropic light dosimetry probes based on scattering bulbs in clear media,” Phys. Med. Biol. 41(7), 1191–1208 (1996).
[Crossref] [PubMed]

C. M. Gardner, S. L. Jacques, and A. J. Welch, “Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation,” Lasers Surg. Med. 18(2), 129–138 (1996).
[Crossref] [PubMed]

1995 (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]

1992 (2)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19(4), 879–888 (1992).
[Crossref] [PubMed]

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

1990 (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

1989 (2)

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

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
[Crossref] [PubMed]

1983 (1)

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[Crossref] [PubMed]

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(6), 824–830 (1983).
[Crossref] [PubMed]

Baas, P.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Bieda, M.

T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
[Crossref] [PubMed]

Bjärngard, B. E.

T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
[Crossref] [PubMed]

Busch, T. M.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Cengel, K.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

Cengel, K. A.

C. B. Simone and K. A. Cengel, “Photodynamic Therapy for Lung Cancer and Malignant Pleural Mesothelioma,” Semin. Oncol. 41(6), 820–830 (2014).
[Crossref] [PubMed]

Chen, Q.

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

Chopp, M.

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

Culligan, M.

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

Dereski, M. O.

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

Dimofte, A.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol. 50(10), 2291–2311 (2005).
[Crossref] [PubMed]

T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
[Crossref] [PubMed]

T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, S. M. Hahn, and R. A. Lustig, “In vivo light dosimetry for motexafin lutetium-mediated PDT of recurrent breast cancer,” Lasers Surg. Med. 31(5), 305–312 (2002).
[Crossref] [PubMed]

Edmonds, C. E.

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19(4), 879–888 (1992).
[Crossref] [PubMed]

Finlay, J.

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

Finlay, J. C.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol. 50(10), 2291–2311 (2005).
[Crossref] [PubMed]

T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
[Crossref] [PubMed]

Fraker, D. L.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Friedberg, J. S.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

Gardner, C. M.

C. M. Gardner, S. L. Jacques, and A. J. Welch, “Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation,” Lasers Surg. Med. 18(2), 129–138 (1996).
[Crossref] [PubMed]

Glatstein, E.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Hahn, S. M.

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
[Crossref] [PubMed]

T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, S. M. Hahn, and R. A. Lustig, “In vivo light dosimetry for motexafin lutetium-mediated PDT of recurrent breast cancer,” Lasers Surg. Med. 31(5), 305–312 (2002).
[Crossref] [PubMed]

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Hetzel, F. W.

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

Hsi, A.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Jacques, S. L.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

S. L. Jacques, “Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues,” Photochem. Photobiol. 67(1), 23–32 (1998).
[Crossref] [PubMed]

C. M. Gardner, S. L. Jacques, and A. J. Welch, “Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation,” Lasers Surg. Med. 18(2), 129–138 (1996).
[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]

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
[Crossref] [PubMed]

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

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 5, 102–111 (1989).

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
[Crossref] [PubMed]

Kim, M. M.

H. Qiu, M. M. Kim, R. Penjweini, and T. C. Zhu, “Macroscopic singlet oxygen modeling for dosimetry of Photofrin-mediated photodynamic therapy: an in-vivo study,” J. Biomed. Opt. 21(8), 088002 (2016).
[Crossref] [PubMed]

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

R. Penjweini, M. M. Kim, B. Liu, and T. C. Zhu, “Evaluation of the 2-(1-Hexyloxyethyl)-2-devinyl pyropheophorbide (HPPH) mediated photodynamic therapy by macroscopic singlet oxygen modeling,” J. Biophotonics, published online Sept 22 (2016).

Liang, X.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

Liu, B.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

R. Penjweini, M. M. Kim, B. Liu, and T. C. Zhu, “Evaluation of the 2-(1-Hexyloxyethyl)-2-devinyl pyropheophorbide (HPPH) mediated photodynamic therapy by macroscopic singlet oxygen modeling,” J. Biophotonics, published online Sept 22 (2016).

Liu, Q.

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013).
[Crossref] [PubMed]

Lustig, R. A.

T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, S. M. Hahn, and R. A. Lustig, “In vivo light dosimetry for motexafin lutetium-mediated PDT of recurrent breast cancer,” Lasers Surg. Med. 31(5), 305–312 (2002).
[Crossref] [PubMed]

Marijnissen, J. P.

J. P. Marijnissen and W. M. Star, “Calibration of isotropic light dosimetry probes based on scattering bulbs in clear media,” Phys. Med. Biol. 41(7), 1191–1208 (1996).
[Crossref] [PubMed]

Menon, C.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Meo, J. L.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

Metz, J.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Mick, R.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Murrer, L. H.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Patterson, M. S.

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19(4), 879–888 (1992).
[Crossref] [PubMed]

Penjweini, R.

H. Qiu, M. M. Kim, R. Penjweini, and T. C. Zhu, “Macroscopic singlet oxygen modeling for dosimetry of Photofrin-mediated photodynamic therapy: an in-vivo study,” J. Biomed. Opt. 21(8), 088002 (2016).
[Crossref] [PubMed]

R. Penjweini, M. M. Kim, B. Liu, and T. C. Zhu, “Evaluation of the 2-(1-Hexyloxyethyl)-2-devinyl pyropheophorbide (HPPH) mediated photodynamic therapy by macroscopic singlet oxygen modeling,” J. Biophotonics, published online Sept 22 (2016).

Pogue, B. W.

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

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

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
[Crossref] [PubMed]

Putt, M.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Qiu, H.

H. Qiu, M. M. Kim, R. Penjweini, and T. C. Zhu, “Macroscopic singlet oxygen modeling for dosimetry of Photofrin-mediated photodynamic therapy: an in-vivo study,” J. Biomed. Opt. 21(8), 088002 (2016).
[Crossref] [PubMed]

Rodriguez, C.

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Rodriguez, C. E.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Rubin, S. C.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Sandell, J. L.

J. L. Sandell and T. C. Zhu, “A review of in-vivo optical properties of human tissues and its impact on PDT,” J. Biophotonics 4(11-12), 773–787 (2011).
[Crossref] [PubMed]

Shin, D.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Simone, C. B.

C. B. Simone and K. A. Cengel, “Photodynamic Therapy for Lung Cancer and Malignant Pleural Mesothelioma,” Semin. Oncol. 41(6), 820–830 (2014).
[Crossref] [PubMed]

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

Smith, D.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Spitz, F.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Star, W. M.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

W. M. Star, “Light dosimetry in vivo,” Phys. Med. Biol. 42(5), 763–787 (1997).
[Crossref] [PubMed]

J. P. Marijnissen and W. M. Star, “Calibration of isotropic light dosimetry probes based on scattering bulbs in clear media,” Phys. Med. Biol. 41(7), 1191–1208 (1996).
[Crossref] [PubMed]

Vulcan, T. G.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

Wang, H. W.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[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]

Welch, A. J.

C. M. Gardner, S. L. Jacques, and A. J. Welch, “Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation,” Lasers Surg. Med. 18(2), 129–138 (1996).
[Crossref] [PubMed]

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

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

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
[Crossref] [PubMed]

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19(4), 879–888 (1992).
[Crossref] [PubMed]

Wilson, B. C.

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[Crossref] [PubMed]

Xiao, Y.

T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
[Crossref] [PubMed]

Yodh, A.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Yodh, A. G.

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

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.

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013).
[Crossref] [PubMed]

Zhu, T.

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

Zhu, T. C.

H. Qiu, M. M. Kim, R. Penjweini, and T. C. Zhu, “Macroscopic singlet oxygen modeling for dosimetry of Photofrin-mediated photodynamic therapy: an in-vivo study,” J. Biomed. Opt. 21(8), 088002 (2016).
[Crossref] [PubMed]

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

J. L. Sandell and T. C. Zhu, “A review of in-vivo optical properties of human tissues and its impact on PDT,” J. Biophotonics 4(11-12), 773–787 (2011).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

A. Dimofte, J. C. Finlay, and T. C. Zhu, “A method for determination of the absorption and scattering properties interstitially in turbid media,” Phys. Med. Biol. 50(10), 2291–2311 (2005).
[Crossref] [PubMed]

T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
[Crossref] [PubMed]

T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
[Crossref] [PubMed]

T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, S. M. Hahn, and R. A. Lustig, “In vivo light dosimetry for motexafin lutetium-mediated PDT of recurrent breast cancer,” Lasers Surg. Med. 31(5), 305–312 (2002).
[Crossref] [PubMed]

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

R. Penjweini, M. M. Kim, B. Liu, and T. C. Zhu, “Evaluation of the 2-(1-Hexyloxyethyl)-2-devinyl pyropheophorbide (HPPH) mediated photodynamic therapy by macroscopic singlet oxygen modeling,” J. Biophotonics, published online Sept 22 (2016).

Clin. Cancer Res. (1)

S. M. Hahn, D. L. Fraker, R. Mick, J. Metz, T. M. Busch, D. Smith, T. Zhu, C. Rodriguez, A. Dimofte, F. Spitz, M. Putt, S. C. Rubin, C. Menon, H. W. Wang, D. Shin, A. Yodh, and E. Glatstein, “A phase II trial of intraperitoneal photodynamic therapy for patients with peritoneal carcinomatosis and sarcomatosis,” Clin. Cancer Res. 12(8), 2517–2525 (2006).
[Crossref] [PubMed]

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]

IEEE J. Quantum Electron. (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26(12), 2166–2185 (1990).
[Crossref]

J. Biomed. Opt. (3)

S. L. Jacques and B. W. Pogue, “Tutorial on diffuse light transport,” J. Biomed. Opt. 13(4), 041302 (2008).
[Crossref] [PubMed]

C. Zhu and Q. Liu, “Review of Monte Carlo modeling of light transport in tissues,” J. Biomed. Opt. 18(5), 050902 (2013).
[Crossref] [PubMed]

H. Qiu, M. M. Kim, R. Penjweini, and T. C. Zhu, “Macroscopic singlet oxygen modeling for dosimetry of Photofrin-mediated photodynamic therapy: an in-vivo study,” J. Biomed. Opt. 21(8), 088002 (2016).
[Crossref] [PubMed]

J. Biophotonics (1)

J. L. Sandell and T. C. Zhu, “A review of in-vivo optical properties of human tissues and its impact on PDT,” J. Biophotonics 4(11-12), 773–787 (2011).
[Crossref] [PubMed]

Lasers Surg. Med. (4)

C. M. Gardner, S. L. Jacques, and A. J. Welch, “Light transport in tissue: Accurate expressions for one-dimensional fluence rate and escape function based upon Monte Carlo simulation,” Lasers Surg. Med. 18(2), 129–138 (1996).
[Crossref] [PubMed]

T. G. Vulcan, T. C. Zhu, C. E. Rodriguez, A. Hsi, D. L. Fraker, P. Baas, L. H. Murrer, W. M. Star, E. Glatstein, A. G. Yodh, and S. M. Hahn, “Comparison between isotropic and nonisotropic dosimetry systems during intraperitoneal photodynamic therapy,” Lasers Surg. Med. 26(3), 292–301 (2000).
[Crossref] [PubMed]

A. Dimofte, T. C. Zhu, S. M. Hahn, and R. A. Lustig, “In vivo light dosimetry for motexafin lutetium-mediated PDT of recurrent breast cancer,” Lasers Surg. Med. 31(5), 305–312 (2002).
[Crossref] [PubMed]

M. Keijzer, S. L. Jacques, S. A. Prahl, and A. J. Welch, “Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams,” Lasers Surg. Med. 9(2), 148–154 (1989).
[Crossref] [PubMed]

Med. Phys. (3)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19(4), 879–888 (1992).
[Crossref] [PubMed]

B. C. Wilson and G. Adam, “A Monte Carlo model for the absorption and flux distributions of light in tissue,” Med. Phys. 10(6), 824–830 (1983).
[Crossref] [PubMed]

T. C. Zhu, B. E. Bjärngard, Y. Xiao, and M. Bieda, “Output ratio in air for MLC shaped irregular fields,” Med. Phys. 31(9), 2480–2490 (2004).
[Crossref] [PubMed]

Photochem. Photobiol. (2)

S. L. Jacques, “Light Distributions from Point, Line and Plane Sources for Photochemical Reactions and Fluorescence in Turbid Biological Tissues,” Photochem. Photobiol. 67(1), 23–32 (1998).
[Crossref] [PubMed]

Q. Chen, B. C. Wilson, M. O. Dereski, M. S. Patterson, M. Chopp, and F. W. Hetzel, “Effects of light beam size on fluence distribution and depth of necrosis in superficially applied photodynamic therapy of normal rat brain,” Photochem. Photobiol. 56(3), 379–384 (1992).
[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

Proc SPIE (1)

T. C. Zhu, M. M. Kim, X. Liang, B. Liu, J. L. Meo, J. C. Finlay, A. Dimofte, C. Rodriguez, C. B. Simone, K. Cengel, and J. S. Friedberg, “Real-time treatment feedback guidance of Pleural PDT,” Proc SPIE 8568, 85680O (2013).
[Crossref] [PubMed]

Proc SPIE Int Soc Opt Eng (2)

T. C. Zhu, J. C. Finlay, A. Dimofte, and S. M. Hahn, “Light Dosimetry at Tissue Surfaces for Oblique Incident Circular Fields,” Proc SPIE Int Soc Opt Eng 5315, 113–124 (2004).
[Crossref] [PubMed]

T. C. Zhu, A. Dimofte, S. M. Hahn, and R. A. Lustig, “Light dosimetry at tissue surfaces for small circular fields,” Proc SPIE Int Soc Opt Eng 4952, 56–67 (2003).
[Crossref] [PubMed]

Proc. SPIE (2)

A. Dimofte, T. C. Zhu, J. Finlay, M. Culligan, C. E. Edmonds, J. S. Friedberg, K. Cengel, and S. M. Hahn, “In-vivo Light Dosimetry for Pleural PDT,” Proc. SPIE 7164, 71640A (2009).
[Crossref]

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Semin. Oncol. (1)

C. B. Simone and K. A. Cengel, “Photodynamic Therapy for Lung Cancer and Malignant Pleural Mesothelioma,” Semin. Oncol. 41(6), 820–830 (2014).
[Crossref] [PubMed]

Other (2)

F. H. Attix, Introduction to Radiological Physics and Radiation Dosimetry (1st. John Wiley & Sons, 1983), Chap. 3.

R. Penjweini, M. M. Kim, B. Liu, and T. C. Zhu, “Evaluation of the 2-(1-Hexyloxyethyl)-2-devinyl pyropheophorbide (HPPH) mediated photodynamic therapy by macroscopic singlet oxygen modeling,” J. Biophotonics, published online Sept 22 (2016).

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Figures (11)

Fig. 1
Fig. 1 (a) Setup geometry for Monte-Carlo simulation for a semi-infinite turbid medium. The light fluence rate is calculated along the central-axis on the center of the field. (b) Pencil beam setup is actually used for the Monte Carlo simulation. The ring scoring voxel has radius width dr and thickness dz at depth z and radius r in a cylindrical geometry. (c) Simplified setup geometry for Monte-Carlo simulation for a semi-infinite turbid medium in a water-tissue interface, where n1 = 1.33 for water, n2 = 1.4 for tissue and n0 is always 1.
Fig. 2
Fig. 2 Light fluence rate ϕ/ ϕ air for tissue optical properties ( μ a , μ s ' ) = (a) (0.01, 2), (b) (0.1, 10), (c) (0.5, 10), and (d) (1, 40) cm−1 and ratio of the index of refraction, n2/n1 = 1.4. Solid lines are MC simulations. Dashed lines in (a) and (b) are 6-parameters fits using Eq. (3) for small circular fields and dotted lines are 4-parameters fits using Eq. (4) for broad beam. Dashed lines in (c) and (d) are for 4-parameters fits using Eq. (4). The curves in each plot are for seven different beam radii, from bottom to top, r = 0.5, 0.75, 1, 1.5, 2, and 3 cm for small fields, and 8 cm for broad beam.
Fig. 3
Fig. 3 Radius dependence of light fluence rate ϕ/ ϕ air above tissue surface (n2/n1 = 1.4)
Fig. 4
Fig. 4 Fitting results between the 4 parameters (b, C2, λ1eff, and λ2eff) and the diffuse reflectance (Rd) for broad beams with air-tissue interface (n2/n1 = 1.4) and water-tissue interface (n2/n1 = 1.053). Solid lines are Eqs. (6)-(9) and dotted lines are Eqs. (20)-(23) for their respective parameters. Black circles and diamonds represent fitting results using 4 parameters from Table 6 and Table 7, respectively. Red triangles represent parameters using formulas from Ref [6]. R2 refers to the goodness of fit between the fitting results of each parameter to their respective equation.
Fig. 5
Fig. 5 Relationship between Rd and a´/(1-a´). R2 refers to the goodness of fit between the MC calculated Rd and Eqs. (19) and (24). Solid and dotted lines are Eqs. (19) and (24) respectively. Circles represent MC simulation results for air-tissue interface (n2/n1 = 1.4) while diamonds represent MC simulation results for water-tissue interface (n2/n1 = 1.053).
Fig. 6
Fig. 6 Fitting results between the 4 and 6 parameters (b, C2, C3, λ1/µeff, λ2/µeff, and λ3) and the optical properties (µa, µs) for circular beams with radii = 0.5 cm, 0.75 cm, 1 cm and 8 cm and refractive index mismatch, n2/n1 = 1.4. Black solid lines are Eqs. (6)-(9) while the red, blue and green lines are Eqs. (11)-(16) for their respective parameters. Circles with their respective color represent MC fitting results using 4 or 6 parameters from Tables 3 to 6.
Fig. 7
Fig. 7 Relationship between parameters b, C2, λ1/µeff, and λ2/µeff using Eqs. (11)–(14) and beam radius.
Fig. 8
Fig. 8 ϕ/ ϕ air for (a) broad beam and (b) small diameter circular beams for three tissue optical properties (µa, µs) = (i) (1, 40), (ii) (0.1, 10), and (iii) (0.01, 2) cm−1. Solid lines are MC simulations. Dotted lines are fittings using Eqs. (6)–(9) for (a) and Eqs. (11)–(16) for (b). Dashed line are 4 parameters fits for (a) and 6 parameters fits for (b). Black lines in (b) correspond to beam with radius = 0.5 cm, blue lines correspond to beam with radius = 0.75 cm, and red lines correspond to beam with radius = 1 cm.
Fig. 9
Fig. 9 Relative deviation of the fitting results to the MC simulation data for (a) broad beam and (b) small diameter circular beam for three tissue optical properties (μa, μs’) = (i) (1, 40), (ii) (0.1, 10), and (iii) (0.01, 2) cm−1. Data for (i) and (ii) are vertically shifted for clarity: + 25% for (ii) and + 30% for (i) for (a) and + 10% for (ii) and + 16% for (i) for (b), respectively. Black lines in (b) correspond to beam with radius = 0.5 cm, blue lines correspond to beam with radius = 0.75 cm, and red lines correspond to beam with radius = 1 cm.
Fig. 10
Fig. 10 ϕ/ ϕ air for (a) broad beam with MC simulation and 4-parameter fitting using Eqs. (6)–(9) without the buildup term and (b) small diameter circular beam with MC simulation and 6-parameters fitting using Eqs. (11)–(16) without the buildup region for three tissue optical properties (μa, μs’) = (i) (1, 40), (ii) (0.1, 10), and (iii) (0.01, 2) cm−1. Black lines in (b) correspond to beam with radius = 0.5 cm, blue lines correspond to beam with radius = 0.75 cm, and red lines correspond to beam with radius = 1 cm.
Fig. 11
Fig. 11 (a) Relative deviation of the 4-parameters fitting using Eqs. (6)–(9) without the buildup term to the MC simulation data for broad beam. Relative standard deviation of 6-parameters fitting using Eqs. (11)–(16) without the buildup term to the MC simulation data for (b) 1-cm beam, (c) 1.5-cm beam and (d) 2-cm beam.

Tables (7)

Tables Icon

Table 1 Summary of maximum relative deviation (%) of the 6-parameter fitting using Eqs. (11)–(16) to the MC calculated ϕ/ ϕ air for optical properties (μa, μs’) used in model training. Maximum relative deviation of 4 parameters fit for broad beam (radius = 8 cm) using Eqs. (6)–(9) are shown in bracket.

Tables Icon

Table 2 Summary of maximum relative deviation (%) of the 6-parameter fitting using Eqs. (11)–(16) to the MC calculated ϕ/ ϕ air for optical properties (μa, μs’) not used in model training. Maximum relative deviation of 4 parameters fit for broad beam (radius = 8 cm) using Eqs. (6)–(9) are shown in bracket.

Tables Icon

Table 3 Summary of the 6 fitting parameters (b, λ1, λ2, C2, λ3, C3) using Eq. (3) to the MC calculated ϕ/ϕair for 1-cm diameter circular beam for optical properties (µa, µs’) and index of refraction, n2/n1 = 1.4. MC calculated diffuse reflectance for broad beam, Rd, is also listed.

Tables Icon

Table 4 Summary of the 6 fitting parameters (b, λ1, λ2, C2, λ3, C3) using Eq. (3) to the MC calculated ϕ/ϕair for 1.5-cm diameter circular beam for optical properties (µa, µs’) and index of refraction, n2/n1 = 1.4.

Tables Icon

Table 5 Summary of the 6 fitting parameters (b, λ1, λ2, C2, λ3, C3) using Eq. (3) to the MC calculated ϕ/ϕair for 2-cm diameter circular beam for optical properties (µa, µs’) and index of refraction, n2/n1 = 1.4.

Tables Icon

Table 6 Summary of the 4 fitting parameters (b, λ1, λ2, C2) using Eq. (4) to the MC calculated ϕ/ϕair for broad beam for optical properties (µa, µs’) and index of refraction, n2/n1 = 1.4.

Tables Icon

Table 7 Summary of the 4 fitting parameters (b, λ1, λ2, C2) using Eq. (4) to the MC calculated ϕ/ϕair for broad beam for optical properties (µa, µs’) and index of refraction, n2/n1 = 1.053.

Equations (24)

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ϕ/ ϕ air = 0 R ρ n / N inc / μ a 2πrdr ,
ϕ/ ϕ air =1+2 r d ,
ϕ/ ϕ air =( 1b e λ 1 d )( C 2 e λ 2 d + C 3 e λ 3 d ),
ϕ/ ϕ air =( 1b e λ 1 d ) C 2 e λ 2 d ,
f= i=1 N ( 1 ϕ fit ( z i ,params ) ϕ MC ( z i ) ) 2 N( N1 ) ,
b=1.1541.025 R d 0.1823 ,
λ 1 μ eff =2.284 e 3.19 R d 1.81,
C 2 =5.996 R d +2.931,
λ 2 μ eff =3.039 R d 5 8.023 R d 4 +8.342 R d 3 4.306 R d 2 +1.144 R d +0.865,
ϕ/ ϕ air =1+2 R d .
b=( ( e 4.2r +0.63 )( 0.1 r 1.35 +0.28 ) e 7(1a') ) ( 1a' ) 0.1570.1 r 0.35 ,
λ 1 μ eff =( 0.33 e 0.96r +2.16 ) e ( 3.263.99 e 3.057r ) R d 1.8,
C 2 =6 R d +0.06 r 1.8 +2.945,
λ 2 μ eff =( 10.6 e 0.483r ) μ eff 0.236 e 0.434r +( 4.37 e 1.5r ) μ eff 1 ,
C 3 =( ( 8.2431.662r ) μ a 0.056 r 3.395 1.251 )( ( 0.802r+6.103 ) μ s ' ( 1.196 r 8.315 +0.212 ) +2.988 r 4.152 3.131 ),
λ 3 =( ( 300.005 r 11.44 ) μ a +( 3.392.404 r 3.402 ) ) ( 0.9730.0373 r 2.345 ) μ s ' ,
ϕ/ ϕ air =1+2 R d ( 1 e ( 0.56( μ a 0.4 +0.43 ) μ s ' 0.76 +0.34 )r ),
a'= μ s ' μ s ' + μ a .
R d =0.4843a'(1+ e 4.428 1a' ) e 2.65 1a' ,
b=0.9430.531 R d 0.1946 ,
λ 1 μ eff =1.572 e 3.19 R d +1.135× 10 9 e 26 R d 1.8,
C 2 =2.388 R d +2.992,
λ 2 μ eff =2.626 R d 5 7.451 R d 4 +8.436 R d 3 4.81 R d 2 +1.426 R d +0.812,
R d =0.5013a'(1+ e 2.789 1a' ) e 1.732 1a' ,

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