Abstract

Optical tomography of small imaging domains holds great promise as the signal-to-noise ratio is usually high, and the achievable spatial resolution is much better than in large imaging domains. Emerging applications range from the imaging of joint diseases in human fingers to monitoring tumor growth or brain activity in small animals. In these cases, the diameter of the tissue under investigation is typically smaller than 3 cm, and the optical path length is only a few scattering mean-free paths. It is well known that under these conditions the widely applied diffusion approximation to the equation of radiative transfer (ERT) is of limited applicability. To accurately model light propagation in these small domains, the ERT has to be solved directly. We use the frequency-domain ERT to perform a sensitivity study for small imaging domains. We found optimal source-modulation frequencies for which variations in optical properties, size, and location of a tissue inhomogeneity lead to maximal changes in the amplitude and phase of the measured signal. These results will be useful in the design of experiments and optical tomographic imaging systems that probe small tissue volumes.

© 2007 Optical Society of America

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  1. B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).
  2. B. Chance, R. R. Alfano, and B. J. Tromberg, in Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE 3597, (1999).
  3. G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).
  4. A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
    [CrossRef]
  5. A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
    [CrossRef] [PubMed]
  6. A. H. Hielscher, "Optical tomographic imaging of small animals," Curr. Opin. Biotechnol. 16, 79-88 (2005).
    [CrossRef] [PubMed]
  7. O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
    [CrossRef]
  8. A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
    [CrossRef] [PubMed]
  9. A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
    [CrossRef]
  10. A. D. Klose and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 2: Inverse model," J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002).
    [CrossRef]
  11. A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
    [CrossRef]
  12. G. Abdoulaev and A. H. Hielscher, "Three-dimensional optical tomography with the equation of radiative transfer," J. Electron. Imaging 14, 594-560 (2003).
    [CrossRef]
  13. K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
    [CrossRef] [PubMed]
  14. K. Ren, G. Bal, and A. H. Hielscher, "Frequency domain optical tomography with the equation of radiative transfer," SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
    [CrossRef]
  15. S. R. Arridge and W. R. B. Lionheart, "Nonuniqueness in diffusion-based optical tomography," Opt. Lett. 23, 882-884 (1998).
    [CrossRef]
  16. T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, 2000 OSA Technical Digest Series (Optical Society of America, 2000), pp. 339-341.
  17. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, "Detection and characteriztion of optical inhomogeneities with diffuse photon density waves: a singal-to-noise analysis," Appl. Opt. 36, 75-92 (1997).
    [CrossRef] [PubMed]
  18. V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
    [CrossRef]
  19. M. J. Eppstein, F. Fedele, and J. P. Laible, "Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: Theory and vectorized imlementation," J. Comput. Phys. 187, 597-619 (2003).
    [CrossRef]
  20. L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 90, 70-83 (1941).
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  21. A. J. Welch and M. J. C. Van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995), Chap. 6.
  22. E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport, 2nd ed. (American Nuclear Society, 1993).
  23. R. Eymard, T. Gallouet, and R. Herbin, "Finite volume methods," in Handbook of Numerical Analysis VII, P. Ciarlet and J. L. Lions, eds., 2nd ed. (North-Holland, 2000).
    [CrossRef]
  24. Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math) J. Sci. Stat. Comput. 7, 856-869 (1986).
  25. T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
    [CrossRef]

2006 (1)

K. Ren, G. Bal, and A. H. Hielscher, "Frequency domain optical tomography with the equation of radiative transfer," SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
[CrossRef]

2005 (3)

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. H. Hielscher, "Optical tomographic imaging of small animals," Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

2004 (2)

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
[CrossRef] [PubMed]

2003 (4)

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

G. Abdoulaev and A. H. Hielscher, "Three-dimensional optical tomography with the equation of radiative transfer," J. Electron. Imaging 14, 594-560 (2003).
[CrossRef]

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

M. J. Eppstein, F. Fedele, and J. P. Laible, "Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: Theory and vectorized imlementation," J. Comput. Phys. 187, 597-619 (2003).
[CrossRef]

2002 (3)

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 2: Inverse model," J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002).
[CrossRef]

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

1999 (2)

B. Chance, R. R. Alfano, and B. J. Tromberg, in Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE 3597, (1999).

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

1998 (2)

S. R. Arridge and W. R. B. Lionheart, "Nonuniqueness in diffusion-based optical tomography," Opt. Lett. 23, 882-884 (1998).
[CrossRef]

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

1997 (1)

1993 (1)

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

1986 (1)

Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math) J. Sci. Stat. Comput. 7, 856-869 (1986).

1941 (1)

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 90, 70-83 (1941).
[CrossRef]

Abdoulaev, G.

G. Abdoulaev and A. H. Hielscher, "Three-dimensional optical tomography with the equation of radiative transfer," J. Electron. Imaging 14, 594-560 (2003).
[CrossRef]

Abdoulaev, G. S.

Alfano, R. R.

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

B. Chance, R. R. Alfano, and B. J. Tromberg, in Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE 3597, (1999).

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Arridge, S.

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Arridge, S. R.

Backhaus, M.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Bal, G.

K. Ren, G. Bal, and A. H. Hielscher, "Frequency domain optical tomography with the equation of radiative transfer," SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
[CrossRef]

K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
[CrossRef] [PubMed]

Barbieri, B.

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

Beuthan, J.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
[CrossRef]

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Boas, D. A.

Burmester, G. R.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

Chance, B.

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

B. Chance, R. R. Alfano, and B. J. Tromberg, in Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE 3597, (1999).

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, "Detection and characteriztion of optical inhomogeneities with diffuse photon density waves: a singal-to-noise analysis," Appl. Opt. 36, 75-92 (1997).
[CrossRef] [PubMed]

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Chen, Y.

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

D'Amico, E.

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

Dorn, O.

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

Eppstein, M. J.

M. J. Eppstein, F. Fedele, and J. P. Laible, "Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: Theory and vectorized imlementation," J. Comput. Phys. 187, 597-619 (2003).
[CrossRef]

Eymard, R.

R. Eymard, T. Gallouet, and R. Herbin, "Finite volume methods," in Handbook of Numerical Analysis VII, P. Ciarlet and J. L. Lions, eds., 2nd ed. (North-Holland, 2000).
[CrossRef]

Fedele, F.

M. J. Eppstein, F. Fedele, and J. P. Laible, "Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: Theory and vectorized imlementation," J. Comput. Phys. 187, 597-619 (2003).
[CrossRef]

Gallouet, T.

R. Eymard, T. Gallouet, and R. Herbin, "Finite volume methods," in Handbook of Numerical Analysis VII, P. Ciarlet and J. L. Lions, eds., 2nd ed. (North-Holland, 2000).
[CrossRef]

Gratton, E.

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Greenstein, J. L.

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 90, 70-83 (1941).
[CrossRef]

Henyey, L. G.

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 90, 70-83 (1941).
[CrossRef]

Herbin, R.

R. Eymard, T. Gallouet, and R. Herbin, "Finite volume methods," in Handbook of Numerical Analysis VII, P. Ciarlet and J. L. Lions, eds., 2nd ed. (North-Holland, 2000).
[CrossRef]

Hermann, K. G.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

Hielscher, A. H.

K. Ren, G. Bal, and A. H. Hielscher, "Frequency domain optical tomography with the equation of radiative transfer," SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
[CrossRef]

A. H. Hielscher, "Optical tomographic imaging of small animals," Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
[CrossRef] [PubMed]

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

G. Abdoulaev and A. H. Hielscher, "Three-dimensional optical tomography with the equation of radiative transfer," J. Electron. Imaging 14, 594-560 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 2: Inverse model," J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

Hueber, D.

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

Intes, X.

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

Kaschke, M.

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Klose, A.

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Klose, A. D.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 2: Inverse model," J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002).
[CrossRef]

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

Laible, J. P.

M. J. Eppstein, F. Fedele, and J. P. Laible, "Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: Theory and vectorized imlementation," J. Comput. Phys. 187, 597-619 (2003).
[CrossRef]

Lewis, E. E.

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport, 2nd ed. (American Nuclear Society, 1993).

Lionheart, W. R. B.

Masters, B.

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

McBride, T. O.

T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, 2000 OSA Technical Digest Series (Optical Society of America, 2000), pp. 339-341.

Miller, W. F.

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport, 2nd ed. (American Nuclear Society, 1993).

Moa-Anderson, B.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Müller, G.

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Müller, G. A.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

Netz, U.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
[CrossRef]

O'Leary, M. A.

Österberg, U. L.

T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, 2000 OSA Technical Digest Series (Optical Society of America, 2000), pp. 339-341.

Paulsen, K. D.

T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, 2000 OSA Technical Digest Series (Optical Society of America, 2000), pp. 339-341.

Pogue, B. W.

T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, 2000 OSA Technical Digest Series (Optical Society of America, 2000), pp. 339-341.

Ren, K.

K. Ren, G. Bal, and A. H. Hielscher, "Frequency domain optical tomography with the equation of radiative transfer," SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
[CrossRef]

K. Ren, G. S. Abdoulaev, G. Bal, and A. H. Hielscher, "Algorithm for solving the equation of radiative transfer in the frequency domain," Opt. Lett. 29, 578-580 (2004).
[CrossRef] [PubMed]

Saad, Y.

Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math) J. Sci. Stat. Comput. 7, 856-869 (1986).

Scheel, A. K.

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Schultz, M. H.

Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math) J. Sci. Stat. Comput. 7, 856-869 (1986).

Sevick-Muraca, E. M.

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

Svanberg, S.

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Tamura, M.

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

Tao, T.

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

Toronov, V.

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

Tromberg, B. J.

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

B. Chance, R. R. Alfano, and B. J. Tromberg, in Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE 3597, (1999).

van der Zee, P.

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

Van Gemert, M. J. C.

A. J. Welch and M. J. C. Van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995), Chap. 6.

Webb, A.

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

Welch, A. J.

A. J. Welch and M. J. C. Van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995), Chap. 6.

Yodh, A. G.

Zhang, J.

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

Ann. Rheum. Dis. (1)

A. K. Scheel, M. Backhaus, A. D. Klose, B. Moa-Anderson, U. Netz, K. G. Hermann, J. Beuthan, G. A. Müller, G. R. Burmester, and A. H. Hielscher, "First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints," Ann. Rheum. Dis. 64, 239-245 (2005).
[CrossRef]

Appl. Opt. (1)

Astrophys. J. (1)

L. G. Henyey and J. L. Greenstein, "Diffuse radiation in the galaxy," Astrophys. J. 90, 70-83 (1941).
[CrossRef]

Curr. Opin. Biotechnol. (1)

A. H. Hielscher, "Optical tomographic imaging of small animals," Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

Inverse Probl. (2)

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

A. D. Klose and A. H. Hielscher, "Quasi-Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

J. BioMed. Opt. (1)

T. Tao, Y. Chen, J. Zhang, X. Intes, and B. Chance, "Analysis on performance and optimization of frequency-domain near-infrared instruments," J. BioMed. Opt. 7, 643-649 (2002).
[CrossRef]

J. Comput. Phys. (1)

M. J. Eppstein, F. Fedele, and J. P. Laible, "Coupled complex adjoint sensitivities for frequency-domain fluorescence tomography: Theory and vectorized imlementation," J. Comput. Phys. 187, 597-619 (2003).
[CrossRef]

J. Electron. Imaging (1)

G. Abdoulaev and A. H. Hielscher, "Three-dimensional optical tomography with the equation of radiative transfer," J. Electron. Imaging 14, 594-560 (2003).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (2)

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 1: Forward model," J. Quant. Spectrosc. Radiat. Transfer 72, 691-713 (2002).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer. part 2: Inverse model," J. Quant. Spectrosc. Radiat. Transfer 72, 715-732 (2002).
[CrossRef]

Med. Phys. (1)

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

Opt. Express (1)

V. Toronov, E. D'Amico, D. Hueber, E. Gratton, B. Barbieri, and A. Webb, "Optimization of the signal-to-noise ratio of frequency-domain instrument for near-infrared spectro-imaging of the human brain," Opt. Express 11, 2117-2729 (2003).
[CrossRef]

Opt. Lett. (2)

Phys. Med. Biol. (1)

A. H. Hielscher, A. Klose, A. K. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, and J. Beuthan, "Sagittal laser optical tomography for imaging of rheumatoid finger joints," Phys. Med. Biol. 49, 1147-1163 (2004).
[CrossRef] [PubMed]

Proc. SPIE (3)

B. Chance, R. R. Alfano, B. J. Tromberg, M. Tamura, and E. M. Sevick-Muraca, in Optical Tomography and Spectroscopy of Tissue VI, Proc. SPIE 5693 (2005).

B. Chance, R. R. Alfano, and B. J. Tromberg, in Optical Tomography and Spectroscopy of Tissue III, Proc. SPIE 3597, (1999).

G. Müller, B. Chance, R. R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, in Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIE IS11 (1993).

SIAM (1)

Y. Saad and M. H. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAM (Soc. Ind. Appl. Math) J. Sci. Stat. Comput. 7, 856-869 (1986).

SIAM J. Sci. Comput. (1)

K. Ren, G. Bal, and A. H. Hielscher, "Frequency domain optical tomography with the equation of radiative transfer," SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
[CrossRef]

Other (4)

T. O. McBride, B. W. Pogue, U. L. Österberg, and K. D. Paulsen, "Separation of absorption and scattering heterogeneities in NIR tomographic imaging of tissue," in Biomedical Topical Meetings, 2000 OSA Technical Digest Series (Optical Society of America, 2000), pp. 339-341.

A. J. Welch and M. J. C. Van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995), Chap. 6.

E. E. Lewis and W. F. Miller, Computational Methods of Neutron Transport, 2nd ed. (American Nuclear Society, 1993).

R. Eymard, T. Gallouet, and R. Herbin, "Finite volume methods," in Handbook of Numerical Analysis VII, P. Ciarlet and J. L. Lions, eds., 2nd ed. (North-Holland, 2000).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Geometric setup for numerical simulation, the diameter of the cylinder D = 2 cm, and height H = 2 cm. The source is identified by the letter S and the detectors by circles.

Fig. 2
Fig. 2

(a) Amplitude and (b) phase delay as well as (c) S N R A C and (d) S N R ϕ of a homogeneous cylinder at modulation frequencies from 100 to 1000 MHz. Here 1 to 6 refer to the detectors arranged around the boundary, 1 being the closest detector to the source and 6 the farthest from the source (see also Fig. 1).

Fig. 3
Fig. 3

(a) Signal amplitude sensitivity ( δ A C ) , (b) phase sensitivity ( δ ϕ ) , (c) S S N R A C , and (d) S S N R ϕ of the reference case listed in Table 1. Here 1 to 6 refer to the detectors arranged around the boundary, 1 being the closest detector to the source and 6 the farthest from the source (see also Fig. 1).

Fig. 4
Fig. 4

(a) S S N R A C and (b) S S N R ϕ with varied strengths of absorption perturbation, 1.2 μ a , 1.5 μ a , 2.0μ a .

Fig. 5
Fig. 5

(a) S S N R A C and (b) S S N R ϕ with varied sizes of absorption perturbation, r = 0.15, 0.25, and 0.35 cm.

Fig. 6
Fig. 6

(a) S S N R A C and (b) S S N R ϕ by moving the location of absorption perturbation O O = 0.0 , 0.25, and 0.50 cm.

Fig. 7
Fig. 7

(a) Signal amplitude sensitivity ( δ A C ) and (b) phase sensitivity ( δ ϕ ) and as well as (c) S S N R A C , and (d) S S N R ϕ of the reference case listed in Table 2. Here 1 to 6 refer to the detectors arranged around the boundary, 1 being the closest detector to the source and 6 the farthest from the source (see also Fig. 1).

Fig. 8
Fig. 8

(a) S S N R A C and (b) S S N R ϕ with varied strengths of scattering perturbation, 1.2 μ s , 1.5 μ s , 2.0μ s .

Fig. 9
Fig. 9

(a) S S N R A C and (b) S S N R ϕ with varied sizes of scattering perturbation, r = 0.15, 0.25, and 0.35 cm.

Fig. 10
Fig. 10

(a) S S N R A C and (b) S S N R ϕ by moving the location of scattering perturbation, O O = 0.0 , 0.25, and 0.50 cm.

Tables (2)

Tables Icon

Table 1 Summary of Different Cases Used for Sensitivity Analysis with Absorption Perturbations

Tables Icon

Table 2 Summary of Different Cases Used for Sensitivity Analysis with Scattering Perturbations

Equations (25)

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

[ i ω v + θ + μ t ( x ) ] ψ ( x , θ ) μ s ( x )
× S 2 k ( θ θ ) ψ ( x , θ ) d θ = 0 in   D × S 2
ψ ( x , θ ) = q ( x , θ ) o n Γ .
Γ ± = { ( x , θ ) D × S 2   such  t h a t ± θ ν ( x ) > 0 } ,
k ( θ θ ) = 1 g 2 ( 1 + g 2 2 g   cos   ϕ ) 3 / 2 ,
J ( x d ) = S + 2 θ ν ( x d ) ψ ( x d , θ ) d θ .
δ J ( x d ) ( δ μ a , δ μ s ) = S + 2 θ ν ( x d ) δ ψ ( x d , θ ) d θ .
( i ω v + θ + μ t ( x ) ) δ ψ ( x , θ ) = μ s ( x ) S 2 k ( θ θ ) δ ψ ( x , θ ) d θ ( δ μ a ( x ) + δ μ s ( x ) ) ψ ( x , θ ) + δ μ s ( x ) S 2 k ( θ θ ) ψ ( x , θ ) × d θ ,
δ ψ ( x , θ ) = 0   on   Γ .
( i ω v θ + μ t ( x ) ) G ( x , θ ; x d , θ d ) = μ s ( x ) S 2 k ( θ θ ) × G ( x , θ ; x d , θ d ) × d θ ,
G ( x , θ ; x d , θ d ) = δ ( θ θ d ) δ ( x x d ) on   Γ + .
δ ψ ( x d , θ d ) = X G ( x , θ ; x d , θ d ) [ ( δ μ a ( x ) + δ μ s ( x ) ) ψ ( x , θ ) + δ μ s ( x ) × S 2 k ( θ θ ) ψ ( x , θ ) d θ ] d x d θ ,
δ J ( x d ) ( δ μ a , δ μ s ) = D ( Φ a ( x ; x d ) δ μ a ( x ) + Φ s ( x ; x d ) δ μ s ( x ) ) d x ,
Φ a ( x ; x d ) = S + 2 θ d ν S 2 G ( x , θ ; x d , θ d ) ψ ( x , θ ) d θ d θ d ,
Φ s ( x ; x d ) = S + 2 θ d ν S 2 G ( x , θ ; x d , θ d ) × ( ψ ( x , θ ) S 2 k ( θ θ ) ψ ( x , θ ) d θ ) × d θ d θ d .
A Ψ = S Ψ + Q ,
J ( x d ) ( μ a , μ s ) = A C   exp ( i ϕ ) .
δ J ( x d ) ( δ μ a , δ μ s ) = A C t   exp ( i ϕ t ) A C h   exp ( i ϕ h ) ,
σ D C D C ,
σ A C D C ,
σ ϕ 1 A C / σ A C A C D C ,
S N R A C ( ω ) = A C σ A C A C D C ,
S N R ϕ ( ω ) = ϕ σ ϕ ϕ σ A C / A C ϕ S N R A C .
S S N R A C ( ω ) = δ A C σ A C A C t A C h D C ,
S S N R ϕ ( ω ) = δ ϕ σ ϕ ( ϕ t ϕ h ) S N R A C .

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