Abstract

We report on the nonlinear reconstruction of local absorption and fluorescence contrast in tissuelike scattering media from measured time-domain diffuse reflectance and transmittance of laser as well as laser-excited fluorescence radiation. Measurements were taken at selected source–detector offsets using slablike diffusely scattering and fluorescent phantoms containing fluorescent heterogeneities. Such measurements simulate in vivo data that would be obtained employing a scanning, time-domain fluorescence mammograph, where the breast is gently compressed between two parallel glass plates, and source and detector optical fibers scan synchronously at various source–detector offsets, allowing the recording of laser and fluorescence mammograms. The diffusion equations modeling the propagation of the laser and fluorescence radiation were solved in frequency domain by the finite element method simultaneously for several modulation frequencies using Fourier transformation and preprocessed experimental data. To reconstruct the concentration of the fluorescent contrast agent, the Born approximation including higher-order reconstructed photon densities at the excitation wavelength was used. Axial resolution was determined that can be achieved by various detection schemes. We show that remission measurements increase the depth resolution significantly.

© 2009 Optical Society of America

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  22. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. T. Köhler, R. Proksa, and T. Nielsen, “SNR-weighted ART applied to transmission tomography,” in Nuclear Science Symposium Conference Record (IEEE, 2003), pp. 2739-2742.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2009 (2)

2008 (2)

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

2007 (4)

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696-6716 (2007).
[CrossRef]

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced three-dimensional lifetime imaging: a phantom study,” Phys. Med. Biol. 52, 4155-4170 (2007).
[CrossRef]

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

2006 (1)

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol. 51, 3983-4001 (2006).
[CrossRef]

2005 (6)

E. Scherleitner and B. G. Zagar, “Optical tomography imaging based on higher order Born approximation of diffuse photon densitiy waves,” IEEE Trans. Instrum. Meas. 54, 1607-1611 (2005).
[CrossRef]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef]

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

2004 (1)

V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E 70, 056616 (2004).
[CrossRef]

2002 (1)

2001 (2)

2000 (1)

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388-417 (2000).
[CrossRef]

1999 (3)

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

M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999).
[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270-286 (1999).

1997 (1)

1995 (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef]

1993 (2)

S. R. Arridge, Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef]

A. Dax, “On row relaxation methods for large constrained least squares problems,” SIAM J. Sci. Comput. 14, 570-584 (1993).
[CrossRef]

1981 (1)

Y. Censor, “Row-action methods for huge and sparse systems and their applications,” SIAM Rev. 23, 444-466 (1981).
[CrossRef]

1907 (1)

G. Voronoi, “Nouvelles applications des paramètres continus à la théorie des formes quadratiques,” J. Reine Angew. Math. 133, 97-178 (1907).

Achilefu, S.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Akers, W.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Arridge, S.

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

Arridge, S. R.

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696-6716 (2007).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef]

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

M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef]

S. R. Arridge, Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef]

Bahner, M.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Bangerth, W.

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

Barbour, R. L.

Bontus, C.

Brambilla, M.

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

Brendel, B.

Censor, Y.

Y. Censor, “Row-action methods for huge and sparse systems and their applications,” SIAM Rev. 23, 444-466 (1981).
[CrossRef]

Chen, A. U.

Choe, R.

Corlu, A.

Cubbedu, R.

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

Culver, J. P.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Dax, A.

A. Dax, “On row relaxation methods for large constrained least squares problems,” SIAM J. Sci. Comput. 14, 570-584 (1993).
[CrossRef]

Delpy, D.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef]

Delpy, D. T.

S. R. Arridge, Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef]

Dierkes, T.

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

Durduran, T.

Ebert, B.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Gebauer, B.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef]

Gibson, J. J.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Godavarty, A.

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced three-dimensional lifetime imaging: a phantom study,” Phys. Med. Biol. 52, 4155-4170 (2007).
[CrossRef]

Graber, H. L.

Grosenick, D.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Hagen, A.

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Hartmann, R.

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

Hartov, A.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Hauff, P.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Hawrysz, D. J.

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388-417 (2000).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef]

S. R. Arridge, Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

Kanschat, G.

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

Kogel, C. A.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Köhler, T.

T. Nielsen, B. Brendel, R. Ziegler, M. van Beek, F. Uhlemann, C. Bontus, and T. Köhler, “Linear image reconstruction for a diffuse optical mammography system in a non-compressed geometry using scattering fluid,” Appl. Opt. 48, D1-D13 (2009).
[CrossRef]

T. Köhler, R. Proksa, and T. Nielsen, “SNR-weighted ART applied to transmission tomography,” in Nuclear Science Symposium Conference Record (IEEE, 2003), pp. 2739-2742.

Licha, K.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

M, M.

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

Macdonald, R.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Markel, V. A.

V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E 70, 056616 (2004).
[CrossRef]

V. A. Markel and J. C. Schotland, “Scanning paraxial optical tomography,” Opt. Lett. 27, 1123-1125 (2002).
[CrossRef]

McBride, T. O.

Meaney, P. M.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Moesta, K. T.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Möller, M.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Mucke, J.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Nielsen, T.

T. Nielsen, B. Brendel, R. Ziegler, M. van Beek, F. Uhlemann, C. Bontus, and T. Köhler, “Linear image reconstruction for a diffuse optical mammography system in a non-compressed geometry using scattering fluid,” Appl. Opt. 48, D1-D13 (2009).
[CrossRef]

T. Köhler, R. Proksa, and T. Nielsen, “SNR-weighted ART applied to transmission tomography,” in Nuclear Science Symposium Conference Record (IEEE, 2003), pp. 2739-2742.

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Nothdurft, R. E.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Ntziachristos, V.

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol. 51, 3983-4001 (2006).
[CrossRef]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef]

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]

Osterberg, U. L.

Paithankar, D. Y.

Patterson, M. S.

Patwardhan, S. V.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Paulsen, K. D.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270-286 (1999).

Pei, Y.

Perlitz, C.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Pifferi, A.

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

Pogue, B. W.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270-286 (1999).

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]

Poplack, S. P.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Proksa, R.

T. Köhler, R. Proksa, and T. Nielsen, “SNR-weighted ART applied to transmission tomography,” in Nuclear Science Symposium Conference Record (IEEE, 2003), pp. 2739-2742.

Rinneberg, H.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Ripoll, J.

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef]

Rosen, M. A.

Roy, R.

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced three-dimensional lifetime imaging: a phantom study,” Phys. Med. Biol. 52, 4155-4170 (2007).
[CrossRef]

Scherleitner, E.

E. Scherleitner and B. G. Zagar, “Optical tomography imaging based on higher order Born approximation of diffuse photon densitiy waves,” IEEE Trans. Instrum. Meas. 54, 1607-1611 (2005).
[CrossRef]

Schirner, M.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Schlag, P.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

Schlag, P. M.

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Schnall, M. D.

Scholle, F.-D.

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

Schotland, J. C.

V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E 70, 056616 (2004).
[CrossRef]

V. A. Markel and J. C. Schotland, “Scanning paraxial optical tomography,” Opt. Lett. 27, 1123-1125 (2002).
[CrossRef]

Schweiger,

S. R. Arridge, Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef]

Schweiger, M.

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696-6716 (2007).
[CrossRef]

M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef]

Sevick-Muraca, E. M.

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced three-dimensional lifetime imaging: a phantom study,” Phys. Med. Biol. 52, 4155-4170 (2007).
[CrossRef]

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388-417 (2000).
[CrossRef]

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]

Soho, S. K.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Soubret, A.

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol. 51, 3983-4001 (2006).
[CrossRef]

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef]

Spinelli, L.

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

Stadelhoff, C.

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Steinkellner, O.

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

Stroszczynski, C.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Torricelli, A.

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

Tosteson, T. D.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Uhlemann, F.

van Beek, M.

Voronoi, G.

G. Voronoi, “Nouvelles applications des paramètres continus à la théorie des formes quadratiques,” J. Reine Angew. Math. 133, 97-178 (1907).

Wabnitz, H.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Wassermann, B.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

Weissleder, R.

Wells, W. A.

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Wübbeler, G.

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

Ye, Y.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Yodh, A. G.

Zagar, B. G.

E. Scherleitner and B. G. Zagar, “Optical tomography imaging based on higher order Born approximation of diffuse photon densitiy waves,” IEEE Trans. Instrum. Meas. 54, 1607-1611 (2005).
[CrossRef]

Ziegler, R.

T. Nielsen, B. Brendel, R. Ziegler, M. van Beek, F. Uhlemann, C. Bontus, and T. Köhler, “Linear image reconstruction for a diffuse optical mammography system in a non-compressed geometry using scattering fluid,” Appl. Opt. 48, D1-D13 (2009).
[CrossRef]

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

R. Ziegler, “Modeling photon transport and reconstruction of optical properties for perfromance assessment of laser and fluorescence mammographs and analysis of clinical data,” Ph.D. dissertation (Free University of Berlin, 2008), http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000005928.

ACM Trans. Math. Softw. (1)

W. Bangerth, R. Hartmann, and G. Kanschat, “deal.II--a general-purpose object-oriented finite element library,” ACM Trans. Math. Softw. 33, 24 (2007).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Instrum. Meas. (1)

E. Scherleitner and B. G. Zagar, “Optical tomography imaging based on higher order Born approximation of diffuse photon densitiy waves,” IEEE Trans. Instrum. Meas. 54, 1607-1611 (2005).
[CrossRef]

IEEE Trans. Med. Imaging (1)

A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24, 1377-1386 (2005).
[CrossRef]

Inverse Probl. (1)

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

J. Biomed. Opt. (1)

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

J. Fluoresc. (1)

C. Perlitz, K. Licha, F.-D. Scholle, B. Ebert, M. Bahner, P. Hauff, K. T. Moesta, and M. Schirner, “Comparison of two tricarbocyanine-based dyes for fluorescence optical imaging,” J. Fluoresc. 15, 443-454 (2005).
[CrossRef]

J. Reine Angew. Math. (1)

G. Voronoi, “Nouvelles applications des paramètres continus à la théorie des formes quadratiques,” J. Reine Angew. Math. 133, 97-178 (1907).

Med. Phys. (2)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef]

S. R. Arridge, Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef]

Neoplasia (1)

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2, 388-417 (2000).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Opto-electron. Rev. (1)

H. Rinneberg, D. Grosenick, K. T. Moesta, H. Wabnitz, J. Mucke, G. Wübbeler, R. Macdonald, and P. Schlag, “Detection and characterization of breast tumors by time-domain scanning optical mammography,” Opto-electron. Rev. 16, 147-162 (2008).
[CrossRef]

Phys. Med. Biol. (6)

R. Roy, A. Godavarty, and E. M. Sevick-Muraca, “Fluorescence-enhanced three-dimensional lifetime imaging: a phantom study,” Phys. Med. Biol. 52, 4155-4170 (2007).
[CrossRef]

T. Dierkes, D. Grosenick, K. T. Moesta, M. Möller, P. M. Schlag, H. Rinneberg, and S. Arridge, “Reconstruction of optical properties of phantom and breast lesion in vivo from paraxial scanning data,” Phys. Med. Biol. 50, 2519-2542 (2005).
[CrossRef]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef]

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef]

M. Schweiger and S. R. Arridge, “Application of temporal filters to time resolved data in optical tomography,” Phys. Med. Biol. 44, 1699-1717 (1999).
[CrossRef]

A. Soubret and V. Ntziachristos, “Fluorescence molecular tomography in the presence of background fluorescence,” Phys. Med. Biol. 51, 3983-4001 (2006).
[CrossRef]

Phys. Rev. E (1)

V. A. Markel and J. C. Schotland, “Symmetries, inversion formulas, and image reconstruction for optical tomography,” Phys. Rev. E 70, 056616 (2004).
[CrossRef]

Radiology (Oak Brook, Ill.) (1)

S. P. Poplack, T. D. Tosteson, W. A. Wells, B. W. Pogue, P. M. Meaney, A. Hartov, C. A. Kogel, S. K. Soho, J. J. Gibson, and K. D. Paulsen, “Electromagnetic breast imaging: results of a pilot study in women with abnormal mammograms,” Radiology (Oak Brook, Ill.) 243, 350-359 (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Brambilla, L. Spinelli, A. Pifferi, A. Torricelli, and R. Cubbedu, “Time-resolved scanning system for double reflectance and transmittance fluorescence imaging of diffusive media,” Rev. Sci. Instrum. 79, 013103 (2008).
[CrossRef]

SIAM J. Sci. Comput. (1)

A. Dax, “On row relaxation methods for large constrained least squares problems,” SIAM J. Sci. Comput. 14, 570-584 (1993).
[CrossRef]

SIAM Rev. (1)

Y. Censor, “Row-action methods for huge and sparse systems and their applications,” SIAM Rev. 23, 444-466 (1981).
[CrossRef]

Other (4)

O. Steinkellner, A. Hagen, C. Stadelhoff, D. Grosenick, R. Macdonald, H. Rinneberg, R. Ziegler, and T. Nielsen, “Recording of artifact-free reflection data with a laser and fluorescence scanning mammograph for improved axial resolution,” in Biomedical Optics/Digital Holography and Three-Dimensional Imaging/Laser Applications to Chemical, Security and Environmental Analysis on CD-ROM (Optical Society of America, 2008), BMD 45.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, 1978).

R. Ziegler, “Modeling photon transport and reconstruction of optical properties for perfromance assessment of laser and fluorescence mammographs and analysis of clinical data,” Ph.D. dissertation (Free University of Berlin, 2008), http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000005928.

T. Köhler, R. Proksa, and T. Nielsen, “SNR-weighted ART applied to transmission tomography,” in Nuclear Science Symposium Conference Record (IEEE, 2003), pp. 2739-2742.

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Figures (6)

Fig. 1
Fig. 1

Laboratory setup for time-resolved measurements in slab geometry (top view with coordinate system). TCSPC, time-correlated single photon counting.

Fig. 2
Fig. 2

(Left) Photo of the lesion-simulating delrin twin cone filled with background scattering fluid and additional Omocyanine fluorescent dye. (Right) Schematic top view of phantom indicating the three selected lesion positions A, B, and C inside the cuvette at x = y = 0 and z = 1.5 cm , z = 2.2 cm , and z = 3 cm , respectively. The plane z = 0 corresponds to the entrance face of the phantom.

Fig. 3
Fig. 3

Scheme of the nonlinear reconstruction of the spatial distribution of optical properties and fluorescent dye concentration, initialized with a homogeneous distribution at iteration σ = 0 . Numbers in circles correspond to the detailed description of the steps of the reconstruction algorithm given in the text.

Fig. 4
Fig. 4

Schematic view of different source–detector geometries with a lesion near the entrance face of the slab, i.e., at position x = y = 0 , z = 2.2 cm (position B, Fig. 2). The source and the detector fibers are scanned in tandem keeping source–detector offsets fixed. The step size amounted to 5 mm , sampling a total of 17 source positions across the front face. (a) Projection-shadow geometry. (b) Slab fan-beam geometry. (c) Slab reflection and transmission geometry.

Fig. 5
Fig. 5

Reconstruction of three-dimensional dye concentration Δ c ( x ) = c ( x ) c 0 of fluorescent dye of the delrin twin cone indicated by circle and located at position B ( x = y = 0 , z = 2.2 cm ) . Dye concentration Δ c ( x ) is given in min / max scaling in the x z plane ( y = 0 , top row) and in the y z plane ( x = 0 , bottom row) through the center of the lesion. The three images of each row correspond to the source–detector combinations shown in Fig. 4: (left) projection-shadow geometry, (middle) slab fan-beam geometry, and (right) reflection and transmission geometry. Line profiles along x = y = 0 and absolute values for the middle and right image are shown in Fig. 6.

Fig. 6
Fig. 6

Line profiles of three-dimensional reconstruction of (left)  μ a ( x = 0 , y = 0 , z ) and of fluorescent dye concentration c ( x = 0 , y = 0 , z ) for the three different twin-cone positions A (no symbol), B (star), and C (triangle). Full lines correspond to reconstructions using both remittance ( z = 0 ) and transmittance ( z = 6 cm ) data; dashed lines are obtained from transmittance data only. The horizontal dash-dot line shows the background value μ a 0 of the absorption coefficient (left) and the background dye concentration c 0 (right), respectively. The vertical arrows indicate the three positions (A, B, C) of the heterogeneity.

Equations (31)

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· D ( x ) Φ ( x , x s , ω ) μ a ( x ) Φ ( x , x s , ω ) i ω v Φ ( x , x s , ω ) = q 0 ( x , x s , ω ) ,
Φ ˜ ( x , x s , t ) = ( 1 / 2 π ) + Φ ( x , x s , ω ) e + i ω t d ω .
· D f ( x ) Φ f ( x , x s , ω ) μ a f ( x ) Φ f ( x , x s , ω ) i ω v Φ f ( x , x s , ω ) = η μ a dye ( x ) 1 + i ω τ Φ ( x , x s , ω ) .
[ Φ ( x , x s , ω ) + 2 1 + K 1 K n · D ( x ) Φ ( x , x s , ω ) ] Ω ( ξ ) = 0 ,
ln ( Φ ( x d i , x s i , ω ) Φ 0 ( x d i , x s i , ω ) Φ 0 sim ( x d i , x s i , ω ) Φ σ sim ( x d i , x s i , ω ) ) = v Ω δ μ a σ ( x ) G σ ( x d i , x , ω ) G σ ( x , x s i , ω ) G σ ( x d i , x s i , ω ) d Ω v Ω δ D σ ( x ) G σ ( x d i , x , ω ) G σ ( x , x s i , ω ) G σ ( x d i , x s i , ω ) · d Ω ,
μ a σ ( x ) = μ a 0 + 0 m < σ δ μ a m ( x ) , D σ ( x ) = D 0 + 0 m < σ δ D m ( x ) .
q 0 σ ( x , x s i , ω ) = 1 v S σ ( x , x s i ) ,
S σ ( x , x s i ) = ( 1 σ src 2 π ) 3 exp ( ( x x s i σ ) 2 / 2 σ src 2 ) .
y = ( ln ( Φ ( x d 1 , x s 1 , ω 1 ) Φ 0 ( x d 1 , x s 1 , ω 1 ) Φ 0 sim ( x d 1 , x s 1 , ω 1 ) Φ σ sim ( x d 1 , x s 1 , ω 1 ) ) ln ( Φ ( x d 1 , x s 1 , ω 1 ) Φ 0 ( x d 1 , x s 1 , ω 1 ) Φ 0 sim ( x d 1 , x s 1 , ω 1 ) Φ σ sim ( x d 1 , x s 1 , ω 1 ) ) ln ( Φ ( x d k , x s k , ω 1 ) Φ 0 ( x d k , x s k , ω 1 ) Φ 0 sim ( x d k , x s k , ω 1 ) Φ σ sim ( x d k , x s k , ω 1 ) ) ln ( Φ ( x d k , x s k , ω 1 ) Φ 0 ( x d k , x s k , ω 1 ) Φ 0 sim ( x d k , x s k , ω 1 ) Φ σ sim ( x d k , x s k , ω 1 ) ) ln ( Φ ( x d k , x s k , ω p ) Φ 0 ( x d k , x s k , ω p ) Φ 0 sim ( x d k , x s k , ω p ) Φ σ sim ( x d k , x s k , ω p ) ) ln ( Φ ( x d k , x s k , ω p ) Φ 0 ( x d k , x s k , ω p ) Φ 0 sim ( x d k , x s k , ω p ) Φ σ sim ( x d k , x s k , ω p ) ) ) .
A = ( a 1 σ ( x 1 , ω 1 ) ... a 1 σ ( x N , ω 1 ) a ^ 1 σ ( x 1 , ω 1 ) ... a ^ 1 σ ( x N , ω 1 ) a 1 σ ( x 1 , ω 1 ) ... a 1 σ ( x N , ω 1 ) a ^ 1 σ ( x 1 , ω 1 ) ... a ^ 1 σ ( x N , ω 1 ) a k σ ( x 1 , ω 1 ) ... a k σ ( x N , ω 1 ) a ^ k σ ( x 1 , ω 1 ) ... a ^ k σ ( x N , ω 1 ) a k σ ( x 1 , ω 1 ) ... a k σ ( x N , ω 1 ) a ^ k σ ( x 1 , ω 1 ) ... a ^ k σ ( x N , ω 1 ) a k σ ( x 1 , ω p ) ... a k σ ( x N , ω p ) a ^ k σ ( x 1 , ω p ) ... a ^ k σ ( x N , ω p ) a k σ ( x 1 , ω p ) ... a k σ ( x N , ω p ) a ^ k σ ( x 1 , ω p ) ... a ^ k σ ( x N , ω p ) ) ,
a i σ ( x , ω ) = v G σ ( x d i , x , ω ) G σ ( x d i , x s i , ω ) G σ ( x , x s i , ω ) w ( x )
a ^ i σ ( x , ω ) = v G σ ( x d i , x , ω ) · G σ ( x , x s i , ω ) G σ ( x d i , x s i , ω ) w ( x )
Φ f ( x d i , x s i , ω ) Φ ( x d i , x s i , ω ) = v η ϵ dye ln 10 1 + i ω τ Ω c ( x ) G f σ c ( x d i , x , ω ) G σ c ( x , x s i , ω ) G σ c ( x d i , x s i , ω ) d Ω ,
v Ω μ a dye ( x ) G σ c ( x d i x , ω ) G σ c ( x , x s i , ω ) G σ c ( x d i , x s i , ω ) d Ω
Φ f ( x d i , x s i , ω ) Φ ( x d i , x s i , ω ) = η 1 + i ω τ Δ Φ ( x d i , x s i , ω ) Φ ( x d i , x s i , ω ) .
A = ( a 1 f ( x 1 , ω 1 ) ... a 1 f ( x N , ω 1 ) a 1 f ( x 1 , ω 1 ) ... a 1 f ( x N , ω 1 ) a k f ( x 1 , ω 1 ) ... a k f ( x N , ω 1 ) a k f ( x 1 , ω 1 ) ... a k f ( x N , ω 1 ) a k f ( x 1 , ω p ) ... a k f ( x N , ω p ) a k f ( x 1 , ω p ) ... a k f ( x N , ω p ) ) ,
a i f ( x , ω ) = v η ϵ dye ln 10 1 + i ω τ G f σ c ( x d i , x , ω ) G σ c ( x d i , x s i , ω ) G σ c ( x , x s i , ω ) w ( x ) ,
y = ( Φ f ( x d 1 , x s 1 , ω 1 ) Φ ( x d 1 , x s 1 , ω 1 ) Φ f ( x d 1 , x s 1 , ω 1 ) Φ ( x d 1 , x s 1 , ω 1 ) Φ f ( x d k , x s k , ω 1 ) Φ ( x d k , x s k , ω 1 ) Φ f ( x d 1 , x s 1 , ω 1 ) Φ ( x d 1 , x s 1 , ω 1 ) Φ f ( x d k , x s k , ω p ) Φ ( x d k , x s k , ω p ) Φ f ( x d k , x s k , ω p ) Φ ( x d k , x s k , ω p ) ) .
A = ( A n j ) n I , j J ,
b = ( b j ) j J .
b j l + 1 = b j l + r ( i , ω q ) A i l j Δ y i l m A i l m ,
r ( i , ω q ) = σ 0 err σ err ( i , ω q ) ,
ln ( Φ ( x d i , x s i , ω q ) Φ 0 sim ( x d i , x s i , ω q ) Φ 0 ( x d i , x s i , ω q ) Φ σ sim ( x d i , x s i , ω q ) )
A i j = A i j γ j ,
b j = b j / γ j ,
R d i , s i = ( Φ meas ( x d i , x s i , ω q ) ) ave , NA ( Φ 0 meas ( x d i , x s i , ω q ) ) ave ,
( Φ ( x d i , x s i , ω q ) ) ( Φ 0 ( x d i , x s i , ω q ) ) = 1 R d i , s i Φ meas ( x d i , x s i , ω q ) Φ 0 meas ( x d i , x s i , ω q ) ,
( Φ f meas ( x d i , x s i , ω q ) Φ meas ( x d i , x s i , ω q ) ) ave , NA = R d i , s i f Φ f sim ( x d i , x s i , ω q ) Φ 0 sim ( x d i , x s i , ω q ) ,
Φ f ( x d i , x s i , ω q ) Φ ( x d i , x s i , ω q ) = 1 R d i , s i f Φ f meas ( x d i , x s i , ω q ) Φ meas ( x d i , x s i , ω q ) ,
Φ f 0 sim ( x d i , x s i , ω q ) / Φ 0 sim ( x d i , x s i , ω q )
Φ f ( x d i , x s i , ω q ) Φ ( x d i , x s i , ω q ) Φ f 0 sim ( x d i , x s i , ω q ) Φ 0 sim ( x d i , x s i , ω q ) = 1 R d i , s i f ( Φ f meas ( x d i , x s i , ω q ) Φ meas ( x d i , x s i , ω q ) ( Φ f meas ( x d i , x s i , ω q ) Φ meas ( x d i , x s i , ω q ) ) avg , NA ) = v η ϵ dye ln 10 1 + i ω q τ Δ c ( x ) G f σ c ( x d i , x s i , ω q ) G σ c ( x , x s i , ω q ) G σ c ( x d i , x s i , ω q ) d Ω ,

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