Abstract

We present a novel fluorescent tomography algorithm to estimate the spatial distribution of fluorophores and the fluorescence lifetimes from surface time resolved measurements. The algorithm is a hybridization of the level set technique for recovering the distributions of distinct fluorescent markers with a gradient method for estimating their lifetimes. This imaging method offers several advantages compared to more traditional pixel-based techniques as, for example, well defined boundaries and a better resolution of the images. The numerical experiments show that our imaging method gives rise to accurate reconstructions in the presence of data noise and fluorescence background even for complicated fluorophore distributions in several-centimiter-thick biological tissue.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. Ntziachristos, "Fluorescence molecular imaging," Annu. Rev. Biomed. Eng. 8, 1-33 (2006).
    [CrossRef] [PubMed]
  2. O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
    [CrossRef]
  3. S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
    [CrossRef]
  4. M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, "Reconstructing absorption and diffusion shape profiles in optical tomography using a level set technique," Opt. Lett. 31, 471-473 (2006).
    [CrossRef] [PubMed]
  5. P. Gonzalez-Rodriguez, A. D. Kim, and M. Moscoso, "Reconstructing a thin absorbing obstacle in a half space of tissue," J. Opt. Soc. Am. A 24, 3456-3466 (2007).
    [CrossRef]
  6. E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimiter resolution for small animal imaging," Med. Phys. 30, 901 (2003).
    [CrossRef] [PubMed]
  7. R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
    [CrossRef] [PubMed]
  8. 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]
  9. A. D. Kim and M. Moscoso, "Radiative transport theory for optical molecular imaging," Inverse Probl. 22, 23-42 (2006).
    [CrossRef]
  10. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, "Fluorescence lifetime imaging in turbid media," Opt. Lett. 21, 158-160 (1996).
    [CrossRef] [PubMed]
  11. E. Shives, Y. Xu, and H. Jiang, "Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye," Opt. Express 10, 1557-1562 (2002).
    [PubMed]
  12. A. B. Milstein, J. J. Stott, S. Oh, D. A. Boas, R. P. Millane, C. A. Bouman, and K. J. Webb, "Fluorescence optical diffusion tomography using multiple-frequency data," J. Opt. Soc. Am. A 21, 1035-1049 (2004).
    [CrossRef]
  13. A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
    [CrossRef] [PubMed]
  14. B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227 (1997).
    [CrossRef]
  15. G. M. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, "Complete-angle projection diffuse optical tomography by use of early photons," Opt. Lett. 30, 409-411 (2005).
    [CrossRef] [PubMed]
  16. S. Lam, F. Lesage, and X. Intes, "Time domain fluorescent diffuse optical tomography: analytical expressions," Opt. Express 13, 2263-2275 (2005).
    [CrossRef] [PubMed]
  17. S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
    [CrossRef] [PubMed]
  18. A. T. N. Kumar, J. Skoch, B. J. Bacskai, D. A. Boas, and A. K. Dunn, "Fluorescence-lifetime-based tomography for turbid media," Opt. Lett. 30, 3347-3349 (2005).
    [CrossRef]
  19. A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, "Time resolved fluorescence tomography of turbid media based on lifetime contrast," Opt. Express 14, 12255-12270 (2006).
    [CrossRef] [PubMed]
  20. A. T. N. Kumar, S. B. Raymond, B. J. Bacskai, and D. A. Boas, "Comparison of frequency-domain and timedomain fluorescence lifetime tomography," Opt. Lett. 33, 470-472 (2008).
    [CrossRef] [PubMed]
  21. F. Santosa, "A Level set approach for inverse problems involving obstacles," ESAIM Control, Optimization and Calculus of Variations 1, 17-33 (1996).
    [CrossRef]
  22. O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
    [CrossRef]
  23. N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
    [CrossRef] [PubMed]
  24. S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys. 79, 12-49 (1988).
    [CrossRef]
  25. F. Santosa, "A level set approach for inverse problems involving obstacles," ESAIM Control, Optim. Calculus Variations 1, 17-33 (1996).
    [CrossRef]
  26. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, "Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media," Appl. Opt. 36, 2260-2272 (1997).
    [CrossRef] [PubMed]
  27. J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE. Trans. Biomed. Eng. 44, 810 (1997).
    [CrossRef] [PubMed]
  28. H. Jiang, "Frequency-Domain Fluorescent Diffusion Tomography: A Finite-Element-Based Algorithm and Simulations," Appl. Opt. 37, 5337-5343 (1998).
    [CrossRef]
  29. V. Ntziachristos and R. Weissleder, "Charge-coupled-device based scanner for tomography of fluorescent nearinfrared probes in turbid media," Med. Phys. 29, 803 (2002).
    [CrossRef] [PubMed]
  30. A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R.P Millane, "Fluorescence Optical Diffusion Tomography," Appl. Opt. 42, 3081-3094 (2003).
    [CrossRef] [PubMed]
  31. A. D. Kim and J. B. Keller, "Light propagation in biological tissue," J. Opt. Soc. Am. A 20, 92-98 (2003).
    [CrossRef]
  32. A. D. Kim and M. Moscoso, "Beam propagation in sharply peaked forward scattering media," J. Opt. Soc. Am. A 21, 797-803 (2004).
    [CrossRef]
  33. A. D. Kim and P. Tranquilli, "Numerical solution of a boundary value problem for the Fokker-Planck equation with variable coefficients," J. Quant. Spectrosc. Radiat. Transfer 109, 727-740 (2007).
  34. D. A´ lvarez, O. Dorn, N. Irishina, and M. Moscoso, "Crack reconstructions using a level-set strategy," J. Comput. Phys. (to be published).

2009 (1)

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

2008 (1)

2007 (2)

P. Gonzalez-Rodriguez, A. D. Kim, and M. Moscoso, "Reconstructing a thin absorbing obstacle in a half space of tissue," J. Opt. Soc. Am. A 24, 3456-3466 (2007).
[CrossRef]

A. D. Kim and P. Tranquilli, "Numerical solution of a boundary value problem for the Fokker-Planck equation with variable coefficients," J. Quant. Spectrosc. Radiat. Transfer 109, 727-740 (2007).

2006 (5)

2005 (6)

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

G. M. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, "Complete-angle projection diffuse optical tomography by use of early photons," Opt. Lett. 30, 409-411 (2005).
[CrossRef] [PubMed]

S. Lam, F. Lesage, and X. Intes, "Time domain fluorescent diffuse optical tomography: analytical expressions," Opt. Express 13, 2263-2275 (2005).
[CrossRef] [PubMed]

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

A. T. N. Kumar, J. Skoch, B. J. Bacskai, D. A. Boas, and A. K. Dunn, "Fluorescence-lifetime-based tomography for turbid media," Opt. Lett. 30, 3347-3349 (2005).
[CrossRef]

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 (3)

2003 (3)

2002 (2)

E. Shives, Y. Xu, and H. Jiang, "Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye," Opt. Express 10, 1557-1562 (2002).
[PubMed]

V. Ntziachristos and R. Weissleder, "Charge-coupled-device based scanner for tomography of fluorescent nearinfrared probes in turbid media," Med. Phys. 29, 803 (2002).
[CrossRef] [PubMed]

1999 (1)

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

1998 (2)

1997 (3)

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, "Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media," Appl. Opt. 36, 2260-2272 (1997).
[CrossRef] [PubMed]

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE. Trans. Biomed. Eng. 44, 810 (1997).
[CrossRef] [PubMed]

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227 (1997).
[CrossRef]

1996 (3)

F. Santosa, "A Level set approach for inverse problems involving obstacles," ESAIM Control, Optimization and Calculus of Variations 1, 17-33 (1996).
[CrossRef]

F. Santosa, "A level set approach for inverse problems involving obstacles," ESAIM Control, Optim. Calculus Variations 1, 17-33 (1996).
[CrossRef]

M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, "Fluorescence lifetime imaging in turbid media," Opt. Lett. 21, 158-160 (1996).
[CrossRef] [PubMed]

1988 (1)

S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys. 79, 12-49 (1988).
[CrossRef]

Achilefu, S.

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

Alfano, R. R.

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227 (1997).
[CrossRef]

Arridge, S. R.

Bacskai, B. J.

Barbour, R. L.

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE. Trans. Biomed. Eng. 44, 810 (1997).
[CrossRef] [PubMed]

Bloch, S.

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

Boas, D. A.

Bouman, C. A.

Boverman, G.

Chance, B.

Chang, J.

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE. Trans. Biomed. Eng. 44, 810 (1997).
[CrossRef] [PubMed]

Chen, A. U.

Das, B. B.

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227 (1997).
[CrossRef]

Dorn, O.

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, "Reconstructing absorption and diffusion shape profiles in optical tomography using a level set technique," Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

Dunn, A. K.

Eppstein, M. J.

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

Gandjbakhche, A.

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

Godavarty, A.

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

Gonzalez-Rodriguez, P.

Graber, H. L.

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE. Trans. Biomed. Eng. 44, 810 (1997).
[CrossRef] [PubMed]

Graves, E. E.

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimiter resolution for small animal imaging," Med. Phys. 30, 901 (2003).
[CrossRef] [PubMed]

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]

Intes, X.

Irishina, N.

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

Jiang, H.

Keller, J. B.

Kim, A. D.

A. D. Kim and P. Tranquilli, "Numerical solution of a boundary value problem for the Fokker-Planck equation with variable coefficients," J. Quant. Spectrosc. Radiat. Transfer 109, 727-740 (2007).

P. Gonzalez-Rodriguez, A. D. Kim, and M. Moscoso, "Reconstructing a thin absorbing obstacle in a half space of tissue," J. Opt. Soc. Am. A 24, 3456-3466 (2007).
[CrossRef]

A. D. Kim and M. Moscoso, "Radiative transport theory for optical molecular imaging," Inverse Probl. 22, 23-42 (2006).
[CrossRef]

A. D. Kim and M. Moscoso, "Beam propagation in sharply peaked forward scattering media," J. Opt. Soc. Am. A 21, 797-803 (2004).
[CrossRef]

A. D. Kim and J. B. Keller, "Light propagation in biological tissue," J. Opt. Soc. Am. A 20, 92-98 (2003).
[CrossRef]

Klose, A. D.

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]

Kolehmainen, V.

Kumar, A. T. N.

Lam, S.

Lesage, F.

S. Lam, F. Lesage, and X. Intes, "Time domain fluorescent diffuse optical tomography: analytical expressions," Opt. Express 13, 2263-2275 (2005).
[CrossRef] [PubMed]

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

Lesselier, D.

O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

Li, X. D.

Liang, K.

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

Liu, F.

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227 (1997).
[CrossRef]

McIntosh, L.

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

Millane, R. P

Millane, R. P.

Milstein, A. B.

Moscoso, M.

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

P. Gonzalez-Rodriguez, A. D. Kim, and M. Moscoso, "Reconstructing a thin absorbing obstacle in a half space of tissue," J. Opt. Soc. Am. A 24, 3456-3466 (2007).
[CrossRef]

A. D. Kim and M. Moscoso, "Radiative transport theory for optical molecular imaging," Inverse Probl. 22, 23-42 (2006).
[CrossRef]

A. D. Kim and M. Moscoso, "Beam propagation in sharply peaked forward scattering media," J. Opt. Soc. Am. A 21, 797-803 (2004).
[CrossRef]

Ntziachristos, V.

V. Ntziachristos, "Fluorescence molecular imaging," Annu. Rev. Biomed. Eng. 8, 1-33 (2006).
[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]

G. M. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, "Complete-angle projection diffuse optical tomography by use of early photons," Opt. Lett. 30, 409-411 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimiter resolution for small animal imaging," Med. Phys. 30, 901 (2003).
[CrossRef] [PubMed]

V. Ntziachristos and R. Weissleder, "Charge-coupled-device based scanner for tomography of fluorescent nearinfrared probes in turbid media," Med. Phys. 29, 803 (2002).
[CrossRef] [PubMed]

O’Leary, M. A.

Oh, S.

Osher, S.

S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys. 79, 12-49 (1988).
[CrossRef]

Paithankar, D. Y.

Patterson, M. S.

Pogue, B. W.

Raymond, S. B.

Ripoll, J.

G. M. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, "Complete-angle projection diffuse optical tomography by use of early photons," Opt. Lett. 30, 409-411 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimiter resolution for small animal imaging," Med. Phys. 30, 901 (2003).
[CrossRef] [PubMed]

Santosa, F.

F. Santosa, "A Level set approach for inverse problems involving obstacles," ESAIM Control, Optimization and Calculus of Variations 1, 17-33 (1996).
[CrossRef]

F. Santosa, "A level set approach for inverse problems involving obstacles," ESAIM Control, Optim. Calculus Variations 1, 17-33 (1996).
[CrossRef]

Schulz, R. B.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

Schweiger, M.

Sethian, J. A.

S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys. 79, 12-49 (1988).
[CrossRef]

Sevick-Muraca, E. M.

Shives, E.

Skoch, J.

Soubret, A.

Stott, J. J.

Tranquilli, P.

A. D. Kim and P. Tranquilli, "Numerical solution of a boundary value problem for the Fokker-Planck equation with variable coefficients," J. Quant. Spectrosc. Radiat. Transfer 109, 727-740 (2007).

Turner, G. M.

Webb, K. J.

Weissleder, R.

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimiter resolution for small animal imaging," Med. Phys. 30, 901 (2003).
[CrossRef] [PubMed]

V. Ntziachristos and R. Weissleder, "Charge-coupled-device based scanner for tomography of fluorescent nearinfrared probes in turbid media," Med. Phys. 29, 803 (2002).
[CrossRef] [PubMed]

Xu, Y.

Yodh, A. G.

Zacharakis, G.

Zacharopoulos, A.

Zhang, Q.

Annu. Rev. Biomed. Eng. (1)

V. Ntziachristos, "Fluorescence molecular imaging," Annu. Rev. Biomed. Eng. 8, 1-33 (2006).
[CrossRef] [PubMed]

Appl. Opt. (3)

ESAIM Control, Optimization and Calculus of Variations (1)

F. Santosa, "A Level set approach for inverse problems involving obstacles," ESAIM Control, Optimization and Calculus of Variations 1, 17-33 (1996).
[CrossRef]

IEEE Trans. Biomed. Eng. (1)

N. Irishina, M. Moscoso, and O. Dorn, "Microwave imaging for early breast cancer detection using a shape-based strategy," IEEE Trans. Biomed. Eng. 56, 1143-1153 (2009).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (1)

R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23, 492-500 (2004).
[CrossRef] [PubMed]

IEEE. Trans. Biomed. Eng. (1)

J. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE. Trans. Biomed. Eng. 44, 810 (1997).
[CrossRef] [PubMed]

Inverse Probl. (4)

O. Dorn and D. Lesselier, "Level set methods for inverse scattering," Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

A. D. Kim and M. Moscoso, "Radiative transport theory for optical molecular imaging," Inverse Probl. 22, 23-42 (2006).
[CrossRef]

J. Biomed. Opt. (1)

S. Bloch, F. Lesage, L. McIntosh, A. Gandjbakhche, K. Liang, S. Achilefu, " Whole-body fluorescence lifetime imaging of a tumor-targeted near-infrared molecular probe in mice," J. Biomed. Opt. 10, 054003 (2005).
[CrossRef] [PubMed]

J. Comput. Phys. (3)

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]

S. Osher and J. A. Sethian, "Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys. 79, 12-49 (1988).
[CrossRef]

D. A´ lvarez, O. Dorn, N. Irishina, and M. Moscoso, "Crack reconstructions using a level-set strategy," J. Comput. Phys. (to be published).

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

J. Quant. Spectrosc. Radiat. Transfer (1)

A. D. Kim and P. Tranquilli, "Numerical solution of a boundary value problem for the Fokker-Planck equation with variable coefficients," J. Quant. Spectrosc. Radiat. Transfer 109, 727-740 (2007).

Med. Phys. (3)

V. Ntziachristos and R. Weissleder, "Charge-coupled-device based scanner for tomography of fluorescent nearinfrared probes in turbid media," Med. Phys. 29, 803 (2002).
[CrossRef] [PubMed]

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimiter resolution for small animal imaging," Med. Phys. 30, 901 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (5)

Optim. Calculus Variations (1)

F. Santosa, "A level set approach for inverse problems involving obstacles," ESAIM Control, Optim. Calculus Variations 1, 17-33 (1996).
[CrossRef]

Rep. Prog. Phys. (1)

B. B. Das, F. Liu, and R. R. Alfano, "Time-resolved fluorescence and photon migration studies in biomedical and model random media," Rep. Prog. Phys. 60, 227 (1997).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

First numerical experiment: a multi-object lifetime reconstruction. On the first row: reference fluorescence lifetime profile (left) and pixel by pixel reconstruction at the end of the first stage of the algorithm (right). On the second row: initial fluorescence lifetime profile for the second stage (left) and reconstructed profile at the 13 th iteration. On the third row: final fluorescence lifetime reconstruction (left) and evolution of the cost during the two stages of the algorithm.

Fig. 2.
Fig. 2.

Second numerical experiment: a T-shape fluorescence lifetime profile. Form left to right: reference fluorescence lifetime profile, final reconstruction at the end of the first stage (pixel by pixel reconstruction), and final fluorescence lifetime reconstruction at the end of our algorithm.

Fig. 3.
Fig. 3.

Third numerical experiment: testing the spatial resolution. Form left to right: reference fluorescence lifetime profile, final reconstruction at the end of the first stage (pixel by pixel reconstruction) and final fluorescence lifetime reconstruction at the end of the algorithm.

Equations (50)

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

1vUxrttDx2Uxrt+(μax+μaxm)Uxrt=δ(rrs)δ(tt0)
1vUmrttDm2Umrt+μamUmrt=Sxmrt.
Dx=12[(1g)μsx+(μax+μaxm)],Dm=12[(1g)μsm+μam].
Sxmrt=ητ(r)μaxm(r)0te(tt)τ(r)Uxrtdt
Ux,mrt+π2Dx,mUx,mrtn̂=0,rΩ,
Ux,mr0=0rΩ.
G˜jl=DU˜mn̂,
μaxm(r)={μa,inxminsideS,whereϕ(r)0,0outsideS,whereϕ(r)>0.
=f(r;ξ)
(ϕ(ξ))=12(μaxm[ϕ(ξ)])22,
(ϕ(ξ))=Gj(ξ)G˜j,
Gj=DUmn̂
ddξ=μaxmμaxmϕdϕdξ=<gradμ,μaxmϕdϕdξ>P=
Ω d r gradμ (r;ξ) μa,inxm δ (ϕ) f rξ ,
f(r;ξ)=gradμ(r;ξ)forallrΩ.
gradμ(r;ξ)=ητ(r)0TdtWrt0tdte(tt)τ(r)Uxrt,
1vWrttDm2Wrt+μamWrt=0
Wrt=T=0
Wrt=(μaxm[ϕ])whererΩ.
ϕ(n+1)=ϕ(n)+Δξ(n)f(n)(r),ϕ(0)=ϕ0,
τ(n+1)(r)=τ(n)(r)+Δτ(r),
Δτ(r)=ημaxm(r)(τ(n)(r))20TdtWrt0tdt(1+ttτ(n)(r))e(tt)τ(n)(r)Uxrt,
Δτp=SpdrΔτ(r).
(μaxm;Z,W)=(μaxm)
0TdtΩdrA Z rt {1vUxrttDx2Uxrt+(μax+μaxm)Uxrtδ(rrs)δ(tt0)}
0TdtΩdrB W rt {1vUmrttDm2Umrt+μamUmrtS(rt)}
δ=μaxmδμaxmUxδUxUmδUm.
UxδUx=0,
UmδUm=0.
UxδUx=(μaxm,Ux+δUx,Um)(μaxm,Ux,Um)=
0T dt Ω d r Z {1vδUxtDx2δUx+(μax+μaxm)δUx} .
UxδUx=0TdtΩdrδUx{1vZtDx2Z+(μax+μaxm)Z},
Zrt=T=0inΩand,Zrt=0onΩ.
1vZtDx2Z+(μax+μaxm)Z=0.
Zrt=0forallrΩ,andt[0,T].
UmδUm=(μaxm,Ux,Um+δUm)(μaxm,Ux,Um)=
0T dt Ω d r W {1vδUmtDm2δUm+μamδUm} ,
UmδUm=0TdtΩdrδUm{1vWtDm2W+μamW},
Wrt=T=0inΩand,Wrt=(μaxm)onΩ.
1vWtDm2W+μamW=0,
δ=δ=μaxmδμaxm=<gradμ,δμaxm>P,
δ=<gradμ,δμaxm>P=Ωdr0TdtWSμaxmδμaxm,
gradμ(r)=ητ(r)0TdtWrt0tdte(tt)τ(r)Uxrt.
[τ]Δτ=[τ],
Δτ=R[τ]*(R[τ]R[τ]*)1R[τ],
Δτ=R[τ]*R[τ].
𝓙[τ+Δτ]=𝓙[τ]+<gradτ𝓙,Δτ>Pδ𝓙+O(ΔτP2)=
𝓙[τ]+<R[τ]*R[τ],Δτ>P+O(ΔτP2).
gradτ=R[τ]*R[τ].
gradτ𝓙(r)=0TdtWrtSτ rt ,

Metrics