Abstract

In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green’s functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
  29. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010).
    [CrossRef]
  30. A. Kienle and M. S. Patterson, “Improved solution of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A14, 246–524 (1997).
    [CrossRef]
  31. V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998).
    [CrossRef]
  32. R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol.46, 3043–3050 (2001).
    [CrossRef] [PubMed]
  33. M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  37. F. Martelli, A. Sassaroli, A. Pifferi, A. Torricelli, L. Spinelli, and G. Zaccanti, “Heuristic Green’s function of the time dependent radiative transfer equation for a semi-infinite medium,” Opt. Express15, 18168–18175 (2007).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  41. A. Sassaroli, F. Martelli, and S. Fantini, “Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries,” Appl. Opt.48, D62–D73 (2009).
    [CrossRef] [PubMed]
  42. A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results,” J. Opt. Soc. Am. A27, 1723–1742 (2010).
    [CrossRef]
  43. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt.37, 7392–7400 (1998).
    [CrossRef]

2011 (1)

A. Liemert and A. Kienle, “Analytical solution of the radiative transfer equation for the infinite-space fluence,” Phys. Rev. A83, 015804 (2011).
[CrossRef]

2010 (5)

M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010).
[CrossRef]

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010).
[CrossRef]

A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results,” J. Opt. Soc. Am. A27, 1723–1742 (2010).
[CrossRef]

A. Liemert and A. Kienle, “Analytical solutions of the simplified spherical harmonics equations,” Opt. Lett.35, 3507–3509 (2010).
[CrossRef] [PubMed]

2009 (2)

A. Sassaroli, F. Martelli, and S. Fantini, “Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries,” Appl. Opt.48, D62–D73 (2009).
[CrossRef] [PubMed]

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
[CrossRef] [PubMed]

2008 (2)

2007 (2)

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

F. Martelli, A. Sassaroli, A. Pifferi, A. Torricelli, L. Spinelli, and G. Zaccanti, “Heuristic Green’s function of the time dependent radiative transfer equation for a semi-infinite medium,” Opt. Express15, 18168–18175 (2007).
[CrossRef] [PubMed]

2006 (3)

A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. I. Theory,” J. Opt. Soc. Am. A48, 2105–2118 (2006).
[CrossRef]

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E74, 031908 (2006).
[CrossRef]

2005 (2)

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202, 323–345 (2005).
[CrossRef]

2004 (1)

2003 (3)

2002 (2)

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol.13, 195–208 (2002).

2001 (5)

D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001).
[CrossRef] [PubMed]

M. Sadoqi, P. Riseborough, and S. Kumar, “Analytical models of time resolved fluorescence spectroscopy in tissues,” Phys. Med. Biol.46, 2725–2743 (2001).
[CrossRef] [PubMed]

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett.26, 893–895 (2001).
[CrossRef]

D. Hattery, V. Chernomordik, M. Loew, I. Gannot, and A. Gandjbakhche, “Analytical solutions for time-resolved imaging in a turbid medium such as tissue,” Opt. Express16, 13188–13202 (2001).

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol.46, 3043–3050 (2001).
[CrossRef] [PubMed]

1998 (4)

H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt.37, 5337–5343 (1998).
[CrossRef]

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt.37, 7392–7400 (1998).
[CrossRef]

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998).
[CrossRef]

G. A. Wagnieres, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol.68, 603–632 (1998).
[PubMed]

1997 (3)

I. J. Bigio and J. R. Mourant, “Ultraviolet and visible spectroscopies for tissue diagnostics: fluorescence spectroscopy and elastic-scattering spectroscopy,” Phys. Med. Biol.42, 803–814 (1997).
[CrossRef] [PubMed]

A. Kienle and M. S. Patterson, “Improved solution of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A14, 246–524 (1997).
[CrossRef]

J. C. J. Paasschens, “Solution of the time-dependent Boltzmann equation,” Phys. Rev. E56, 1135–1141 (1997).
[CrossRef]

1996 (3)

1995 (1)

C. L. Hutchinson, J. R. Lakowicz, and E. Sevick-Muraca, “Fluorescence lifetime-based sensing in tissues: A computational study,” NeuroImage68, 1574–1582 (1995).

1994 (1)

1992 (1)

S. Andersson-Engels and B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol.3, 66–79 (1992).

Alianelli, L.

Andersson-Engels, S.

J. Swartling, A. Pifferi, A. M. K. Enejder, and S. Andersson-Engels, “Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues,” J. Opt. Soc. Am. A20, 714–727 (2003).
[CrossRef]

S. Andersson-Engels and B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol.3, 66–79 (1992).

Arridge, S. R.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010).
[CrossRef]

Bigio, I. J.

I. J. Bigio and J. R. Mourant, “Ultraviolet and visible spectroscopies for tissue diagnostics: fluorescence spectroscopy and elastic-scattering spectroscopy,” Phys. Med. Biol.42, 803–814 (1997).
[CrossRef] [PubMed]

Blumetti, C.

Boas, D. A.

Bouman, C. A.

Braichotte, D. R.

D. R. Braichotte, J. F. Savary, P. Monnier, and H. E. van den Bergh, “Optimizing light dosimetry in photodynamic theraphy of early stage carcinomas of the esophagus using fluorescence spectroscopy,” Laser Surg. Med.19, 340–346 (1996).
[CrossRef]

Bremer, C.

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol.13, 195–208 (2002).

Carder, K. L.

Chance, B.

Chernomordik, V.

Choe, R.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010).
[CrossRef]

Chu, M.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
[CrossRef] [PubMed]

Comelli, D.

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

Contini, D.

Cubeddu, R.

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

D’Andrea, C.

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

Dehghani, H.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
[CrossRef] [PubMed]

Del Bianco, S.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. ZaccantiLight Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, Bellingham, 2010).
[CrossRef] [PubMed]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010).
[CrossRef]

Enejder, A. M. K.

Erdmann, R.

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Fantini, S.

Farrel, T. J.

D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001).
[CrossRef] [PubMed]

Gandjbakhche, A.

Gannot, I.

Gao, G.

Graaff, R.

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol.46, 3043–3050 (2001).
[CrossRef] [PubMed]

Grosenick, D.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

Hattery, D.

He, H.

Hielscher, A. H.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202, 323–345 (2005).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative tranfer,” Opt. Lett.28, 1019–1021 (2003).
[CrossRef] [PubMed]

Hutchinson, C. L.

C. L. Hutchinson, J. R. Lakowicz, and E. Sevick-Muraca, “Fluorescence lifetime-based sensing in tissues: A computational study,” NeuroImage68, 1574–1582 (1995).

Hyde, D. E.

D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001).
[CrossRef] [PubMed]

Ismaelli, A.

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt.37, 7392–7400 (1998).
[CrossRef]

F. Martelli, S. Del Bianco, A. Ismaelli, and G. ZaccantiLight Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, Bellingham, 2010).
[CrossRef] [PubMed]

Jiang, H.

Kaipio, J.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

Kienle, A.

Klose, A. D.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202, 323–345 (2005).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative tranfer,” Opt. Lett.28, 1019–1021 (2003).
[CrossRef] [PubMed]

Kolehmainen, V.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

Kumar, S.

M. Sadoqi, P. Riseborough, and S. Kumar, “Analytical models of time resolved fluorescence spectroscopy in tissues,” Phys. Med. Biol.46, 2725–2743 (2001).
[CrossRef] [PubMed]

Kummrow, A.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

Lakowicz, J. R.

C. L. Hutchinson, J. R. Lakowicz, and E. Sevick-Muraca, “Fluorescence lifetime-based sensing in tissues: A computational study,” NeuroImage68, 1574–1582 (1995).

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, New York, 2006).
[CrossRef]

Li, X. D.

Liebert, A.

A. Liebert, H. Wabnitz, N. Żołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express16, 13188–13202 (2008).
[CrossRef] [PubMed]

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Liemert, A.

A. Liemert and A. Kienle, “Analytical solution of the radiative transfer equation for the infinite-space fluence,” Phys. Rev. A83, 015804 (2011).
[CrossRef]

A. Liemert and A. Kienle, “Analytical solutions of the simplified spherical harmonics equations,” Opt. Lett.35, 3507–3509 (2010).
[CrossRef] [PubMed]

Loew, M.

Lu, Y.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

Macdonald, R.

A. Liebert, H. Wabnitz, N. Żołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express16, 13188–13202 (2008).
[CrossRef] [PubMed]

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Machida, M.

M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010).
[CrossRef]

Markel, V. A.

M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010).
[CrossRef]

Martelli, F.

Millane, R. P.

Milstein, A. B.

Möller, M.

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Monnier, P.

D. R. Braichotte, J. F. Savary, P. Monnier, and H. E. van den Bergh, “Optimizing light dosimetry in photodynamic theraphy of early stage carcinomas of the esophagus using fluorescence spectroscopy,” Laser Surg. Med.19, 340–346 (1996).
[CrossRef]

Mourant, J. R.

I. J. Bigio and J. R. Mourant, “Ultraviolet and visible spectroscopies for tissue diagnostics: fluorescence spectroscopy and elastic-scattering spectroscopy,” Phys. Med. Biol.42, 803–814 (1997).
[CrossRef] [PubMed]

Ntziachristos, V.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202, 323–345 (2005).
[CrossRef]

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol.13, 195–208 (2002).

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett.26, 893–895 (2001).
[CrossRef]

O’Leary, M. A.

Obrig, H.

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Oh, S.

Paasschens, J. C. J.

J. C. J. Paasschens, “Solution of the time-dependent Boltzmann equation,” Phys. Rev. E56, 1135–1141 (1997).
[CrossRef]

Panasyuk, G. Y.

M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010).
[CrossRef]

Patterson, M.

D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001).
[CrossRef] [PubMed]

M. Patterson and B. Pogue, “Mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissues,” Appl. Opt.33, 1963–1974 (1994).
[CrossRef] [PubMed]

Patterson, M. S.

Pifferi, A.

Pogue, B.

Rasmussen, J. C.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

Reinersman, P. N.

Rinneberg, H.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Rinzema, K.

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol.46, 3043–3050 (2001).
[CrossRef] [PubMed]

Riseborough, P.

M. Sadoqi, P. Riseborough, and S. Kumar, “Analytical models of time resolved fluorescence spectroscopy in tissues,” Phys. Med. Biol.46, 2725–2743 (2001).
[CrossRef] [PubMed]

Sadoqi, M.

M. Sadoqi, P. Riseborough, and S. Kumar, “Analytical models of time resolved fluorescence spectroscopy in tissues,” Phys. Med. Biol.46, 2725–2743 (2001).
[CrossRef] [PubMed]

Sassaroli, A.

Savary, J. F.

D. R. Braichotte, J. F. Savary, P. Monnier, and H. E. van den Bergh, “Optimizing light dosimetry in photodynamic theraphy of early stage carcinomas of the esophagus using fluorescence spectroscopy,” Laser Surg. Med.19, 340–346 (1996).
[CrossRef]

Schlag, P. M.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

Schotland, J. C.

M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010).
[CrossRef]

Sevick-Muraca, E.

C. L. Hutchinson, J. R. Lakowicz, and E. Sevick-Muraca, “Fluorescence lifetime-based sensing in tissues: A computational study,” NeuroImage68, 1574–1582 (1995).

Sevick-Muraca, E. M.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

Shen, H.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

Spinelli, L.

Star, W. M.

G. A. Wagnieres, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol.68, 603–632 (1998).
[PubMed]

Steinbrink, J.

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Swartling, J.

Taroni, P.

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

Tarvainen, T.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

Torricelli, A.

Tromberg, B. J.

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998).
[CrossRef]

Valentini, G.

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

van den Bergh, H. E.

D. R. Braichotte, J. F. Savary, P. Monnier, and H. E. van den Bergh, “Optimizing light dosimetry in photodynamic theraphy of early stage carcinomas of the esophagus using fluorescence spectroscopy,” Laser Surg. Med.19, 340–346 (1996).
[CrossRef]

Vauhkonen, M.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

Venugopalan, V.

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998).
[CrossRef]

Villinger, A.

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Vishwanath, K.

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
[CrossRef] [PubMed]

Wabnitz, H.

A. Liebert, H. Wabnitz, N. Żołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express16, 13188–13202 (2008).
[CrossRef] [PubMed]

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

Wagnieres, G. A.

G. A. Wagnieres, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol.68, 603–632 (1998).
[PubMed]

Wang, G.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

Wassermann, B.

B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E74, 031908 (2006).
[CrossRef]

Webb, K. J.

Weissleder, R.

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol.13, 195–208 (2002).

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett.26, 893–895 (2001).
[CrossRef]

Wilson, B.

D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001).
[CrossRef] [PubMed]

Wilson, B. C.

G. A. Wagnieres, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol.68, 603–632 (1998).
[PubMed]

S. Andersson-Engels and B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol.3, 66–79 (1992).

Yodh, A. G.

You, J. S.

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998).
[CrossRef]

Zaccanti, G.

Zhang, L.

Zhang, Q.

Zhao, H.

Zhu, B.

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

Zolek, N.

Appl. Opt. (7)

Eur. Radiol. (1)

V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol.13, 195–208 (2002).

J. Cell. Pharmacol. (1)

S. Andersson-Engels and B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol.3, 66–79 (1992).

J. Comput. Phys. (1)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202, 323–345 (2005).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Phys. A: Math. Theor. (1)

M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010).
[CrossRef]

J. Phys. D: Appl. Phys. (1)

R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002).
[CrossRef]

Laser Surg. Med. (1)

D. R. Braichotte, J. F. Savary, P. Monnier, and H. E. van den Bergh, “Optimizing light dosimetry in photodynamic theraphy of early stage carcinomas of the esophagus using fluorescence spectroscopy,” Laser Surg. Med.19, 340–346 (1996).
[CrossRef]

NeuroImage (2)

A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006).
[CrossRef] [PubMed]

C. L. Hutchinson, J. R. Lakowicz, and E. Sevick-Muraca, “Fluorescence lifetime-based sensing in tissues: A computational study,” NeuroImage68, 1574–1582 (1995).

Opt. Express (4)

Opt. Lett. (4)

Photochem. Photobiol. (1)

G. A. Wagnieres, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol.68, 603–632 (1998).
[PubMed]

Phys. Med. Biol. (7)

I. J. Bigio and J. R. Mourant, “Ultraviolet and visible spectroscopies for tissue diagnostics: fluorescence spectroscopy and elastic-scattering spectroscopy,” Phys. Med. Biol.42, 803–814 (1997).
[CrossRef] [PubMed]

D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001).
[CrossRef] [PubMed]

M. Sadoqi, P. Riseborough, and S. Kumar, “Analytical models of time resolved fluorescence spectroscopy in tissues,” Phys. Med. Biol.46, 2725–2743 (2001).
[CrossRef] [PubMed]

Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005).
[CrossRef] [PubMed]

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol.46, 3043–3050 (2001).
[CrossRef] [PubMed]

M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009).
[CrossRef] [PubMed]

Phys. Rev. A (1)

A. Liemert and A. Kienle, “Analytical solution of the radiative transfer equation for the infinite-space fluence,” Phys. Rev. A83, 015804 (2011).
[CrossRef]

Phys. Rev. E (4)

J. C. J. Paasschens, “Solution of the time-dependent Boltzmann equation,” Phys. Rev. E56, 1135–1141 (1997).
[CrossRef]

V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998).
[CrossRef]

B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E74, 031908 (2006).
[CrossRef]

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007).
[CrossRef]

Rep. Prog. Phys. (1)

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010).
[CrossRef]

Other (2)

F. Martelli, S. Del Bianco, A. Ismaelli, and G. ZaccantiLight Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, Bellingham, 2010).
[CrossRef] [PubMed]

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, New York, 2006).
[CrossRef]

Supplementary Material (1)

» Media 1: PDF (45 KB)     

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Figures (4)

Fig. 1
Fig. 1

Diagram of a photon path from the source to the fluorophore and from the fluorophore to the detector.

Fig. 2
Fig. 2

Fluorescence TR reflectance signal received from a slab 2000 mm thick at ρ =15 mm. The absorption and the reduced scattering coefficient of the background medium are equal to 0.01 and 1. mm−1, respectively, at both the emission and the excitation wavelengths. The fluorophore is a sphere centered at (7.5, 0, 7.5) mm and with a volume V′ = 1.25 mm3. The absorption coefficient of the fluorophore at excitation wavelength is μaf = 0.002 mm−1. The refractive index of the medium and of the external is 1.4.

Fig. 3
Fig. 3

Identical to Fig. 2 except for the Fluorescence CW reflectance.

Fig. 4
Fig. 4

Comparison between hybrid model and Monte Carlo results for the fluorescence TR reflectance signal received from a slab 2000 mm thick with the receiver at ρ = 30 mm. The reduced scattering coefficient of the background medium is assumed at the emission and the excitation wavelength equal to 0.5 mm−1. The absorption coefficient of the background medium is 0.01 mm−1 in Fig. a), and 0 in Fig. b). In the MC simulations four different values of the volume and of the absorption of the fluorophore have been considered (for each case we have Vμaf = 0.01 mm2): V′ = 10 mm3, μaf = 0.001 mm−1; V′ = 100 mm3, μaf = 0.0001 mm−1; V′ = 500 mm3, μaf = 0.00002 mm−1, and V′ = 1000 mm3, μaf = 0.00001 mm−1. The fluorophore is assumed by a sphere centered at (15, 0, 15) mm. The refractive index of the medium and of the external is 1.4. The hybrid model is calculated with Eq. (11) and with the partial current boundary condition, and it has been implemented using the RTE solution for the infinite medium.

Equations (17)

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

[ 1 v t + μ a + μ a f D 2 ] Φ ( r , t ) = q ( r , t ) ,
[ 1 v e t + μ a e + μ a f e D e 2 ] Φ e ( r , t ) = q e ( r , t ) ,
d P f ( r , t ) = G ( r s , r , μ a + μ a f , μ s + μ s f , n , t ) μ a f η ( λ , λ e ) d 3 r d λ e d t ,
q e ( r , t ) = μ a f τ η ( λ , λ e ) d λ e 0 t exp [ ( t t ) τ ] G ( r s , r , μ a + μ a f , μ s + μ s f , n , t ) d t ,
[ 1 v e t + μ a e + μ a f e D e 2 ] Φ e ( r , t ) μ a f τ η e 0 t exp [ ( t t ) τ ] G ( r s , r , t ) d t = 0 ,
Φ e ( r , t ) = 0 t V q e ( r , t ) G e ( r , r , μ a e + μ a f e , μ s e + μ s f e , n e , t t ) d r d t ,
Φ e 0 ( r , t ) = μ a f η e 0 t V G ( r s , r , t ) G e ( r , r , , t t ) d r d t .
Φ e ( r , t ) = Φ e 0 ( r , t ) * 1 τ exp ( t / τ ) .
{ G ( r s , r , μ a + μ a f , μ s + μ s f , n , t ) G ( r s , r , μ a , μ s , n , t ) G e ( r , r , μ a e + μ a e f , μ s e + μ s e f , n e , t t ) G e ( r , r , μ a e , μ s e , n e , t t ) G ( r s , r , μ a , μ s , n , t ) G ( r s , r , μ a , μ s , n , t ) , r , r V G e ( r , r , μ a e , μ s e , n e , t t ) G e ( r , r , μ a e , μ s e , n e , t t ) , r , r V
Φ e 0 ( r , t ) = μ a f η e V 0 t G ( r s , r , μ a , μ s , n , t ) G e ( r , r , μ a e , μ s e , n e , t t ) d t ,
Φ e ( r , t ) = μ a f η e τ V 0 t 0 t exp [ ( t t ) τ ] G ( r s , r , μ a , μ s , n , t ) × G e ( r , r , μ a e , μ s e , n e , t t ) d t d t .
Φ e ( r ) = μ a f η e V G ( r s , r , μ a , μ s , n ) G e ( r , r , μ a e , μ s e , n e ) .
q ( r , t ) = q 0 D C ( r ) + q 0 A C ( r ) exp ( i ω t ) ,
Φ A C ( r , t ) = Φ A C 0 exp ( i ω t ) .
[ ( i ω ) / v + μ a + μ a f D 2 ] Φ A C 0 ( r ) = q 0 ( r ) .
R ( ρ , t ) = D z Φ ( ρ , z = 0 , t ) ,
R ( ρ , t ) = 1 2 A Φ ( ρ , z = 0 , t ) ,

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