Abstract

The recent application of tomographic methods to three-dimensional imaging through tissue by use of light often requires modeling of geometrically complex diffuse–nondiffuse boundaries at the tissue–air interface. We have recently investigated analytical methods to model complex boundaries by means of the Kirchhoff approximation. We generalize this approach using an analytical approximation, the N-order diffuse-reflection boundary method, which considers higher orders of interaction between surface elements in an iterative manner. We present the general performance of the method and demonstrate that it can improve the accuracy in modeling complex boundaries compared with the Kirchhoff approximation in the cases of small diffuse volumes or low absorption. Our observations are also contrasted with exact solutions. We furthermore investigate optimal implementation parameters and show that a second-order approximation is appropriate for most in vivo investigations.

© 2003 Optical Society of America

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2002

2001

J. Ripoll, V. Ntziachristos, R. Carminati, M. Nieto-Vesperinas, “The Kirchhoff approximation for diffusive waves,” Phys. Rev. E 64, 051917 (2001).
[CrossRef]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

V. Ntziachristos, B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41–46 (2001).

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

2000

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97, 2767–2772 (2000).

1999

1998

V. Ntziachristos, X. H. Ma, B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

1997

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

1996

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, March1996, pp. 16–22 .

E. B. Haller, “Time-resolved transillumination and optical tomography,” J. Biomed. Opt. 1, 7–17 (1996).
[CrossRef] [PubMed]

1995

1994

R. Haskell, B. Tromberg, L. Svaasand, T. Tsay, T. Feng, M. Mcadams, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994).
[CrossRef]

K. Davey, I. Rosindale, “An iterative solution scheme for systems of boundary element equations,” Int. J. Numer. Methods Eng. 37, 1399–1411 (1994).
[CrossRef]

1993

1992

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

1991

1989

Alfano, R. R.

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, March1996, pp. 16–22 .

Aronson, R.

Arridge, S. R.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

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

S. R. Arridge, “Photon measurement density functions. Part I: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

Beckmann, P.

P. Beckmann, in Progress in Optics VI, E. Wolf, ed. (North-Holland, Amsterdam, 1961), pp. 55–69.

Beer, G.

G. Beer, J. O. Watson, Introduction to Finite and Boundary Element Methods for Engineers (Wiley, Chichester, UK, 1992).

Benaron, D. A.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Beuthan, J.

A. Klose, A. H. Hielscher, K. M. Hanson, J. Beuthan, “Two- and three-dimensional optical tomography of finger joints for diagnostics of rheumatoid arthritis,” in Photon Propagation in Tissues IV, D. A. Benaron, B. Chance, M. Ferrari, M. Kohl, eds., Proc. SPIE3566, 151–160 (1998).
[CrossRef]

Boas, D.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Boas, D. A.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Bolster, M. B.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

Brebbia, C. A.

C. A. Brebbia, J. Dominguez, Boundary Elements, An Introductory Course (MacGraw-Hill, New York, 1989).

Bremer, C.

V. Ntziachristos, C. Tung, C. Bremer, R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nature Med. 8, 757–760 (2002).
[CrossRef] [PubMed]

V. Ntziachristos, C. Bremer, E. E. Graves, J. Ripoll, R. Weissleder, “In vivo tomographic imaging of near-infrared fluorescent probes,” Mol. Imag. 1, 82–88 (2002).
[CrossRef]

Carminati, R.

J. Ripoll, V. Ntziachristos, R. Carminati, M. Nieto-Vesperinas, “The Kirchhoff approximation for diffusive waves,” Phys. Rev. E 64, 051917 (2001).
[CrossRef]

J. Ripoll, M. Nieto-Vesperinas, R. Carminati, “Spatial resolution of diffuse photon density waves,” J. Opt. Soc. Am. A 16, 1466–1476 (1999).
[CrossRef]

Chance, B.

V. Ntziachristos, B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41–46 (2001).

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97, 2767–2772 (2000).

V. Ntziachristos, X. H. Ma, B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

A. G. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

Cheong, W. F.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Davey, K.

K. Davey, I. Rosindale, “An iterative solution scheme for systems of boundary element equations,” Int. J. Numer. Methods Eng. 37, 1399–1411 (1994).
[CrossRef]

Dehghani, H.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Delpy, D. T.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Dominguez, J.

C. A. Brebbia, J. Dominguez, Boundary Elements, An Introductory Course (MacGraw-Hill, New York, 1989).

Fantini, S.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Feng, T.

Frahm, J.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Franceschini, M. A.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Gaida, G.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Gayen, S. K.

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, March1996, pp. 16–22 .

Gratton, E.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Graves, E. E.

V. Ntziachristos, C. Bremer, E. E. Graves, J. Ripoll, R. Weissleder, “In vivo tomographic imaging of near-infrared fluorescent probes,” Mol. Imag. 1, 82–88 (2002).
[CrossRef]

Grosenick, D.

Haller, E. B.

E. B. Haller, “Time-resolved transillumination and optical tomography,” J. Biomed. Opt. 1, 7–17 (1996).
[CrossRef] [PubMed]

Hanson, K. M.

A. Klose, A. H. Hielscher, K. M. Hanson, J. Beuthan, “Two- and three-dimensional optical tomography of finger joints for diagnostics of rheumatoid arthritis,” in Photon Propagation in Tissues IV, D. A. Benaron, B. Chance, M. Ferrari, M. Kohl, eds., Proc. SPIE3566, 151–160 (1998).
[CrossRef]

Haskell, R.

Hebden, J. C.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Hielscher, A. H.

A. Klose, A. H. Hielscher, K. M. Hanson, J. Beuthan, “Two- and three-dimensional optical tomography of finger joints for diagnostics of rheumatoid arthritis,” in Photon Propagation in Tissues IV, D. A. Benaron, B. Chance, M. Ferrari, M. Kohl, eds., Proc. SPIE3566, 151–160 (1998).
[CrossRef]

Hillman, E. M. C.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Hintz, S. R.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Hirth, C.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Iftimia, N.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

Ishimaru, A.

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

Jess, H.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Jiang, H.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

Kachoyan, B. J.

Kak, A.

A. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Kaschke, M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Kermit, E. L.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Key, L. L.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

Kleinschmidt, A.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Klose, A.

A. Klose, A. H. Hielscher, K. M. Hanson, J. Beuthan, “Two- and three-dimensional optical tomography of finger joints for diagnostics of rheumatoid arthritis,” in Photon Propagation in Tissues IV, D. A. Benaron, B. Chance, M. Ferrari, M. Kohl, eds., Proc. SPIE3566, 151–160 (1998).
[CrossRef]

Lu, T.

Ma, X. H.

V. Ntziachristos, X. H. Ma, B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

Macaskill, C.

Mantulin, W. W.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Mcadams, M.

McBride, T. O.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Moesta, K.

Moesta, K. T.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Nieto-Vesperinas, M.

Ntziachristos, V.

V. Ntziachristos, C. Tung, C. Bremer, R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nature Med. 8, 757–760 (2002).
[CrossRef] [PubMed]

J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527–529 (2002).
[CrossRef]

V. Ntziachristos, J. Ripoll, R. Weissleder, “Would near-infrared fluorescence signals propagate through large human organs for clinical studies?” Opt. Lett. 27, 333–335 (2002).
[CrossRef]

V. Ntziachristos, C. Bremer, E. E. Graves, J. Ripoll, R. Weissleder, “In vivo tomographic imaging of near-infrared fluorescent probes,” Mol. Imag. 1, 82–88 (2002).
[CrossRef]

V. Ntziachristos, B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41–46 (2001).

J. Ripoll, V. Ntziachristos, R. Carminati, M. Nieto-Vesperinas, “The Kirchhoff approximation for diffusive waves,” Phys. Rev. E 64, 051917 (2001).
[CrossRef]

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97, 2767–2772 (2000).

V. Ntziachristos, X. H. Ma, B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

V. Ntziachristos, “Concurrent diffuse optical tomography, spectroscopy and magnetic resonance of breast cancer,” Ph.D. dissertation (University of Philadelphia, Philadelphia, Pa., 2000).

O’Leary, M. A.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Obrig, H.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Adam Hilger, Bristol, 1991).

Osterberg, U. L.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Osterman, K. S.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Patterson, M. S.

Paulsen, K. D.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Pogue, B. W.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Poplack, S. P.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Rinneberg, H.

Ripoll, J.

Rosindale, I.

K. Davey, I. Rosindale, “An iterative solution scheme for systems of boundary element equations,” Int. J. Numer. Methods Eng. 37, 1399–1411 (1994).
[CrossRef]

Sanchez-Gil, J. A.

Schlag, P.

Schlag, P. M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Schmidt, F. E. W.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Schnall, M.

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97, 2767–2772 (2000).

Schweiger, M.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Seeber, M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

Slaney, M.

A. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Stevenson, D. K.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Svaasand, L.

Tromberg, B.

Tsay, T.

Tung, C.

V. Ntziachristos, C. Tung, C. Bremer, R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nature Med. 8, 757–760 (2002).
[CrossRef] [PubMed]

van Houten, J. C.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Villringer, A.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

Wabnitz, H.

Watson, J. O.

G. Beer, J. O. Watson, Introduction to Finite and Boundary Element Methods for Engineers (Wiley, Chichester, UK, 1992).

Weissleder, R.

V. Ntziachristos, J. Ripoll, R. Weissleder, “Would near-infrared fluorescence signals propagate through large human organs for clinical studies?” Opt. Lett. 27, 333–335 (2002).
[CrossRef]

V. Ntziachristos, C. Bremer, E. E. Graves, J. Ripoll, R. Weissleder, “In vivo tomographic imaging of near-infrared fluorescent probes,” Mol. Imag. 1, 82–88 (2002).
[CrossRef]

V. Ntziachristos, C. Tung, C. Bremer, R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nature Med. 8, 757–760 (2002).
[CrossRef] [PubMed]

J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527–529 (2002).
[CrossRef]

Wells, W. A.

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Wilson, B. C.

Xu, Y.

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

Yevick, D. O.

Yodh, A. G.

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97, 2767–2772 (2000).

A. G. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Breast Cancer Res.

V. Ntziachristos, B. Chance, “Probing physiology and molecular function using optical imaging: applications to breast cancer,” Breast Cancer Res. 3, 41–46 (2001).

Int. J. Numer. Methods Eng.

K. Davey, I. Rosindale, “An iterative solution scheme for systems of boundary element equations,” Int. J. Numer. Methods Eng. 37, 1399–1411 (1994).
[CrossRef]

Inverse Probl.

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

J. Biomed. Opt.

E. B. Haller, “Time-resolved transillumination and optical tomography,” J. Biomed. Opt. 1, 7–17 (1996).
[CrossRef] [PubMed]

J. Cereb. Blood Flow Metab.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, D. K. Stevenson, “Noninvasive functional imaging of human brain using light,” J. Cereb. Blood Flow Metab. 20, 469–477 (2000).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Mol. Imag.

V. Ntziachristos, C. Bremer, E. E. Graves, J. Ripoll, R. Weissleder, “In vivo tomographic imaging of near-infrared fluorescent probes,” Mol. Imag. 1, 82–88 (2002).
[CrossRef]

Nature Med.

V. Ntziachristos, C. Tung, C. Bremer, R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nature Med. 8, 757–760 (2002).
[CrossRef] [PubMed]

Opt. Lett.

Opt. Photon. News

S. K. Gayen, R. R. Alfano, “Emerging optical biomedical imaging techniques,” Opt. Photon. News, March1996, pp. 16–22 .

Optics Express

Y. Xu, N. Iftimia, H. Jiang, L. L. Key, M. B. Bolster, “Imaging of in vitro and in vivo bones and joints with continuous-wave diffuse optical tomography,” Optics Express 8, 447–451 (2001).
[CrossRef] [PubMed]

Phys. Med. Biol.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46, 1117–1130 (2001).
[CrossRef] [PubMed]

Phys. Rev. E

J. Ripoll, V. Ntziachristos, R. Carminati, M. Nieto-Vesperinas, “The Kirchhoff approximation for diffusive waves,” Phys. Rev. E 64, 051917 (2001).
[CrossRef]

Phys. Rev. Lett.

M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef] [PubMed]

Phys. Today

A. G. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. U.S.A. 94, 6468–6473 (1997).

V. Ntziachristos, A. G. Yodh, M. Schnall, B. Chance, “Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement,” Proc. Natl. Acad. Sci. U.S.A. 97, 2767–2772 (2000).

Radiography

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg, K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast,” Radiography 218, 261–266 (2001).

Rev. Sci. Instrum.

V. Ntziachristos, X. H. Ma, B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instrum. 69, 4221–4233 (1998).
[CrossRef]

Other

A. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

P. Beckmann, in Progress in Optics VI, E. Wolf, ed. (North-Holland, Amsterdam, 1961), pp. 55–69.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Adam Hilger, Bristol, 1991).

M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Pergamon, New York, 1996).

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

G. Beer, J. O. Watson, Introduction to Finite and Boundary Element Methods for Engineers (Wiley, Chichester, UK, 1992).

C. A. Brebbia, J. Dominguez, Boundary Elements, An Introductory Course (MacGraw-Hill, New York, 1989).

V. Ntziachristos, “Concurrent diffuse optical tomography, spectroscopy and magnetic resonance of breast cancer,” Ph.D. dissertation (University of Philadelphia, Philadelphia, Pa., 2000).

A. Klose, A. H. Hielscher, K. M. Hanson, J. Beuthan, “Two- and three-dimensional optical tomography of finger joints for diagnostics of rheumatoid arthritis,” in Photon Propagation in Tissues IV, D. A. Benaron, B. Chance, M. Ferrari, M. Kohl, eds., Proc. SPIE3566, 151–160 (1998).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Scattering geometry.

Fig. 2
Fig. 2

Computation times of the BEM (in minutes) versus the KA with FFTs (in seconds) and the DRBM (0.01 s). Results were obtained from a Pentium III running at 650 MHz, with 256 Mb RAM.

Fig. 3
Fig. 3

Computation times (in minutes) of the BEM versus four different orders of the DRBM. Results for the BEM for a large number of surface points were found by extrapolation, owing to the high computational cost. Results were obtained from a Pentium III running at 650 MHz, with 256 Mb RAM.

Fig. 4
Fig. 4

Geometry used for the simulation of diffuse optical tomography. Circles represent sources (27 with 0.05-mm spacing); crosses represent detectors (27 with 0.05-mm spacing).

Fig. 5
Fig. 5

Convergence of the DRBM for different orders for the cases: μa=0.2 cm-1, μs=10 cm-1, τ=1 (solid curve); μa=0.02 cm-1, μs=10 cm-1, τ=1 (dotted–dashed curve); μa=0.02 cm-1, μs=10 cm-1, τ=2 (dashed curve); μa=0.02 cm-1, μs=5 cm-1, τ=2 (circles).

Fig. 6
Fig. 6

Error convergence versus order and relaxation parameter τ for the case μa=0.2 cm-1, μs=10 cm-1. Modulation frequency ω=0.

Fig. 7
Fig. 7

Reconstruction of simulated geometry in Fig. 4 with use of the optimized relaxation parameter τ [see Eq. (14)] and the exact Green function: (a) μa=0.02 cm-1, μs=10 cm-1 and (b) μa=0.2 cm-1, μs=10 cm-1; the DRBM for (c) fourth order, μa=0.02 cm-1, μs=10 cm-1 and (d) second order, μa=0.2 cm-1, μs=10 cm-1; and the KA (first-order DRBM) for (e) μa=0.02 cm-1, μs=10 cm-1 and (f) μa=0.2 cm-1, μs=10 cm-1. See Fig. 8 for the errors corresponding to (c) and (d), where we see that, to obtain good reconstructions, the error must be under 5%. Modulation frequency ω=0.

Fig. 8
Fig. 8

Convergence of the DRBM and the iterative BEM for the cases presented in Figs. 7(c) and 7(d). The actual reconstruction values are marked with circles. Modulation frequency ω=0.

Fig. 9
Fig. 9

Effect of using the exact Green function (BEM) but approximating the geometry of Fig. 4. For optical properties μa=0.02 cm-1, μs=10 cm-1: (a) Ellipse, (b) slab. For optical properties μa=0.2 cm-1, μs=10 cm-1: (c) an ellipse, (d) a slab. Modulation frequency ω=0.

Equations (14)

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

g(κ|r-r|)=exp(iκ|r-r|)D|r-r|,
G(rs, rd)=g(κ|rs-rd|)-14πSg(κ|r-rd|)n+1CndD g(κ|r-rd|)G(rs, r)dS,
U(rd)=14πVΦ(r)G(r, rd)dr,rdV.
Rnd(K)=iCndDκ2-K2+1iCndDκ2-K2-1,
GKA(rs, rp)=-+[1+Rnd(K)]g˜(K, Z¯)exp(iKR¯)dK,
GKA(rs, rd)=g(κ|rs-rd|)-14πp=1Ng(κ|rp-rd|)np+1CndD g(κ|rp-rd|)×GKA(rs, rp)ΔS(rp).
GDRBM(1)(rs, rp)=[g(R¯, Z¯)-g(R¯, Z¯+CndD)].
GDRBM(1)(rs, rd)=g(κ|rs-rd|)-14πp=1Ng(κ|rp-rd|)np+1CndD g(κ|rp-rd|)ΔS(rp)×[g(R¯, Z¯)-g(R¯, Z¯+CndD)].
ddtU+G  U=U(inc),
U(N)=U(N-1)-τG  U(N-1)+τU(inc).
GDRBM(N)(rs, rk)=GDRBM(N-1)(rs, rk)-τg(κ|rs-rk|)+τ 14πp=1Ng(κ|rp-rk|)np+1CndD g(κ|rp-rk|)×GDRBM(N-1)(rs, rk)ΔS(rp).
GDRBM(N)(rs, rd)=g(κ|rs-rd|)-14πp=1Ng(κ|rp-rd|)np+1CndD g(κ|rp-rd|)×GDRMB(N)(rs, rp)ΔS(rp).
error(N)=1Ndi=1Nd1-UDRBM(N)UBEM21/2,
τ=2 imag{κ}W+1,

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