Abstract

The Green’s function for diffusive wave propagation can be obtained by utilizing the representation theorems of the convolution type and the correlation type. In this work, the Green’s function is retrieved by making use of the Robin boundary condition and the representation theorems for diffusive media. The diffusive Green’s function between two detectors for photon flux is calculated by combining detector readings due to point light sources and utilizing virtual light sources at the detector positions in optical tomography. Two dimensional simulations for a circular region with eight sources and eight detectors located on the boundary are performed using a finite element method to demonstrate the feasibility of virtual sources. The most important potential application would be the replacement of noisy measurements with synthetic measurements that are provided by the virtual sources. This becomes an important issue in small animal and human studies. In addition, the same method may also be used to reduce the imaging time.

© 2013 Optical Society of America

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  47. T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol. 50, 4913–4930 (2005).
    [CrossRef]
  48. P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
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    [CrossRef]

2012 (1)

D. Halliday, A. Curtis, and K. Wapenaar, “Generalized PP+ PS= SS from seismic interferometry,” Geophys. J. Int. 189, 1015–1024 (2012).
[CrossRef]

2008 (5)

K. Wapenaar, E. Slob, and R. Snieder, “Seismic and electromagnetic controlled-source interferometry in dissipative media,” Geophys. Prospect. 56, 419–434 (2008).
[CrossRef]

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

M. B. Unlu and G. Gulsen, “Effects of the time dependence of a bioluminescent source on the tomographic reconstruction,” Appl. Opt. 47, 799–806 (2008).
[CrossRef]

M. B. Unlu, O. Birgul, and G. Gulsen, “A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (dce-dot),” Phys. Med. Biol. 53, 3189–3200 (2008).
[CrossRef]

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

2007 (4)

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

R. Snieder, “Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves,” J. Acoust. Soc. Am. 121, 2637–2643 (2007).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34, 4293–4301 (2007).
[CrossRef]

2006 (6)

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

K. Wapenaar, E. Slob, and R. Snieder, “Unified Green’s function retrieval by cross correlation,” Phys. Rev. Lett. 97, 234301 (2006).
[CrossRef]

B. W. Pogue, “Near-infrared characterization of disease via vascular permeability probes,” Acad. Radiol. 13, 1–3 (2006).
[CrossRef]

R. Snieder, “Retrieving the Green’s function of the diffusion equation from the response to a random forcing,” Phys. Rev. E 74, 0466201 (2006).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

2005 (4)

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

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

B. J. Tromberg, “Optical scanning and breast cancer,” Acad. Radiol. 12, 923–924 (2005).
[CrossRef]

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

2004 (1)

K. Wapenaar, “Retrieving the elastodynamic Green’s function of an arbitrary inhomogeneous medium by cross correlation,” Phys. Rev. Lett. 93, 254301 (2004).
[CrossRef]

2003 (3)

M. Campillo and A. Paul, “Long-range correlations in the diffuse seismic coda,” Science 299, 547–549 (2003).
[CrossRef]

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

2002 (3)

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

R. Weaver and O. Lobkis, “On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons,” Ultrasonics 40, 435–439 (2002).
[CrossRef]

2001 (3)

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[CrossRef]

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

2000 (2)

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

H. Dehghani, S. R. Arridge, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1670 (2000).
[CrossRef]

1999 (2)

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

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

1998 (2)

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

S. Thomsen and D. Tatman, “Physiological and pathological factors of human breast disease that can influence optical diagnosis,” Ann. N.Y. Acad. Sci. 838, 171–193 (1998).
[CrossRef]

1997 (1)

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef]

1995 (2)

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

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

1993 (1)

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

1992 (1)

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef]

1988 (1)

A. D. Hoop and H. Stam, “Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems,” Wave Motion 10, 479–489 (1988).
[CrossRef]

Abdoulaev, G. S.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Arridge, S. R.

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

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

H. Dehghani, S. R. Arridge, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1670 (2000).
[CrossRef]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

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

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef]

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

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef]

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Austin, T.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

Berger, A. J.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Beuthan, J.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Bevilacqua, F.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Birgul, O.

M. B. Unlu, O. Birgul, and G. Gulsen, “A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (dce-dot),” Phys. Med. Biol. 53, 3189–3200 (2008).
[CrossRef]

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

Bluestone, A. Y.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Boas, D. A.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

Brooksby, B.

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

Butler, J.

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Camara-Rey, O.

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Campillo, M.

M. Campillo and A. Paul, “Long-range correlations in the diffuse seismic coda,” Science 299, 547–549 (2003).
[CrossRef]

Cerussi, A.

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

Cerussi, A. E.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

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B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Compton, M.

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

Cong, W.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

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B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
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S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef]

Crum, W. R.

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Culver, J. P.

Curtis, A.

D. Halliday, A. Curtis, and K. Wapenaar, “Generalized PP+ PS= SS from seismic interferometry,” Geophys. J. Int. 189, 1015–1024 (2012).
[CrossRef]

Dehghani, H.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

H. Dehghani, S. R. Arridge, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1670 (2000).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

Delpy, D. T.

H. Dehghani, S. R. Arridge, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1670 (2000).
[CrossRef]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
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S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
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Diamond, S. G.

P. Giacometti and S. G. Diamond, “Diffuse optical tomography for brain imaging: continuous wave instrumentation and linear analysis methods,” in Optical Methods and Instrumentation in Brain Imaging and Therapy (Springer, 2013), pp. 57–85.

Dunn, J. F.

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

Durkin, A.

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

Everdell, N.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

Fehler, M.

G. Melo, A. Malcolm, and M. Fehler, “Comparison of microearthquake locations using seismic interferometry principles,” in SEG Technical Program Expanded Abstracts 2012 (Society of Exploration Geophysicists, 2012), pp. 1–5.

Fokkema, J. T.

J. T. Fokkema and P. M. van den Berg, Seismic Applications of Acoustic Reciprocity (Elsevier, 1993).

Fox, N.

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Giacometti, P.

P. Giacometti and S. G. Diamond, “Diffuse optical tomography for brain imaging: continuous wave instrumentation and linear analysis methods,” in Optical Methods and Instrumentation in Brain Imaging and Therapy (Springer, 2013), pp. 57–85.

Gibson, A.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

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]

Gratton, E.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Gulsen, G.

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

M. B. Unlu, O. Birgul, and G. Gulsen, “A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (dce-dot),” Phys. Med. Biol. 53, 3189–3200 (2008).
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M. B. Unlu and G. Gulsen, “Effects of the time dependence of a bioluminescent source on the tomographic reconstruction,” Appl. Opt. 47, 799–806 (2008).
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M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

Halliday, D.

D. Halliday, A. Curtis, and K. Wapenaar, “Generalized PP+ PS= SS from seismic interferometry,” Geophys. J. Int. 189, 1015–1024 (2012).
[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]

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

Hielscher, A. H.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Hill, D. L. G.

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Hiraoka, M.

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

Holboke, M. J.

Holcombe, R. F.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

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A. D. Hoop and H. Stam, “Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems,” Wave Motion 10, 479–489 (1988).
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Hsiang, D.

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

Jakubowski, D.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Jiang, H.

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

B. W. Pogue, H. Jiang, K. D. Paulsen, and U. L. Osterberg, “Frequency-domain diffuse optical tomography of breast tissue: detector size and imaging geometry,” in Proceedings of the IEEE Conference on Engineering in Medicine and Biology Society (IEEE, 1997), p. 2745.

Jiang, S.

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

Kaipio, J. P.

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

Klose, A. D.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Koehler, T.

T. Nielsen, T. Koehler, M. van der Mark, and G. t’Hooft, “Fully 3D reconstruction of attenuation for diffuse optical tomography using a finite element model,” in Proceedings of IEEE Conference on Nuclear Science (IEEE, 2005), p. 2283.

Kolehmainen, V.

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

Lasker, J.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Lewis, E.

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Lin, Y.

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

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R. Weaver and O. Lobkis, “On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons,” Ultrasonics 40, 435–439 (2002).
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[CrossRef]

Lv, Y.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Magazov, S.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

Malcolm, A.

G. Melo, A. Malcolm, and M. Fehler, “Comparison of microearthquake locations using seismic interferometry principles,” in SEG Technical Program Expanded Abstracts 2012 (Society of Exploration Geophysicists, 2012), pp. 1–5.

McBride, T. O.

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

Meek, J.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

Mehta, R.

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

Melo, G.

G. Melo, A. Malcolm, and M. Fehler, “Comparison of microearthquake locations using seismic interferometry principles,” in SEG Technical Program Expanded Abstracts 2012 (Society of Exploration Geophysicists, 2012), pp. 1–5.

Nalcioglu, O.

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

Netz, U.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Nielsen, T.

T. Nielsen, T. Koehler, M. van der Mark, and G. t’Hooft, “Fully 3D reconstruction of attenuation for diffuse optical tomography using a finite element model,” in Proceedings of IEEE Conference on Nuclear Science (IEEE, 2005), p. 2283.

Ntziachristos, V.

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34, 4293–4301 (2007).
[CrossRef]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

Nwaigwe, C.

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

Okada, E.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

Osterberg, U. L.

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

B. W. Pogue, H. Jiang, K. D. Paulsen, and U. L. Osterberg, “Frequency-domain diffuse optical tomography of breast tissue: detector size and imaging geometry,” in Proceedings of the IEEE Conference on Engineering in Medicine and Biology Society (IEEE, 1997), p. 2745.

Paul, A.

M. Campillo and A. Paul, “Long-range correlations in the diffuse seismic coda,” Science 299, 547–549 (2003).
[CrossRef]

Paulsen, K. D.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

B. W. Pogue, H. Jiang, K. D. Paulsen, and U. L. Osterberg, “Frequency-domain diffuse optical tomography of breast tissue: detector size and imaging geometry,” in Proceedings of the IEEE Conference on Engineering in Medicine and Biology Society (IEEE, 1997), p. 2745.

Pogue, B. W.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

B. W. Pogue, “Near-infrared characterization of disease via vascular permeability probes,” Acad. Radiol. 13, 1–3 (2006).
[CrossRef]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).
[CrossRef]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

B. W. Pogue, H. Jiang, K. D. Paulsen, and U. L. Osterberg, “Frequency-domain diffuse optical tomography of breast tissue: detector size and imaging geometry,” in Proceedings of the IEEE Conference on Engineering in Medicine and Biology Society (IEEE, 1997), p. 2745.

Poplack, S.

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

Qin, C.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Ramanujam, N.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Razansky, D.

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34, 4293–4301 (2007).
[CrossRef]

Schnabel, J.

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Schweiger, M.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef]

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

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

Shafiiha, R.

M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

Shah, N.

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Slob, E.

K. Wapenaar, E. Slob, and R. Snieder, “Seismic and electromagnetic controlled-source interferometry in dissipative media,” Geophys. Prospect. 56, 419–434 (2008).
[CrossRef]

K. Wapenaar, E. Slob, and R. Snieder, “Unified Green’s function retrieval by cross correlation,” Phys. Rev. Lett. 97, 234301 (2006).
[CrossRef]

Snieder, R.

K. Wapenaar, E. Slob, and R. Snieder, “Seismic and electromagnetic controlled-source interferometry in dissipative media,” Geophys. Prospect. 56, 419–434 (2008).
[CrossRef]

R. Snieder, “Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves,” J. Acoust. Soc. Am. 121, 2637–2643 (2007).
[CrossRef]

R. Snieder, “Retrieving the Green’s function of the diffusion equation from the response to a random forcing,” Phys. Rev. E 74, 0466201 (2006).
[CrossRef]

K. Wapenaar, E. Slob, and R. Snieder, “Unified Green’s function retrieval by cross correlation,” Phys. Rev. Lett. 97, 234301 (2006).
[CrossRef]

Soho, S.

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

Stam, H.

A. D. Hoop and H. Stam, “Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems,” Wave Motion 10, 479–489 (1988).
[CrossRef]

Stewart, M.

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

t’Hooft, G.

T. Nielsen, T. Koehler, M. van der Mark, and G. t’Hooft, “Fully 3D reconstruction of attenuation for diffuse optical tomography using a finite element model,” in Proceedings of IEEE Conference on Nuclear Science (IEEE, 2005), p. 2283.

Tarvainen, T.

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

Tatman, D.

S. Thomsen and D. Tatman, “Physiological and pathological factors of human breast disease that can influence optical diagnosis,” Ann. N.Y. Acad. Sci. 838, 171–193 (1998).
[CrossRef]

Thomsen, S.

S. Thomsen and D. Tatman, “Physiological and pathological factors of human breast disease that can influence optical diagnosis,” Ann. N.Y. Acad. Sci. 838, 171–193 (1998).
[CrossRef]

Tian, J.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Tromberg, B.

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Tromberg, B. J.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

B. J. Tromberg, “Optical scanning and breast cancer,” Acad. Radiol. 12, 923–924 (2005).
[CrossRef]

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Unlu, M. B.

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

M. B. Unlu, O. Birgul, and G. Gulsen, “A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (dce-dot),” Phys. Med. Biol. 53, 3189–3200 (2008).
[CrossRef]

M. B. Unlu and G. Gulsen, “Effects of the time dependence of a bioluminescent source on the tomographic reconstruction,” Appl. Opt. 47, 799–806 (2008).
[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

van den Berg, P. M.

J. T. Fokkema and P. M. van den Berg, Seismic Applications of Acoustic Reciprocity (Elsevier, 1993).

van der Mark, M.

T. Nielsen, T. Koehler, M. van der Mark, and G. t’Hooft, “Fully 3D reconstruction of attenuation for diffuse optical tomography using a finite element model,” in Proceedings of IEEE Conference on Nuclear Science (IEEE, 2005), p. 2283.

Varela, M.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

Vauhkonen, M.

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

Vishwanath, K.

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

Wang, G.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Wapenaar, K.

D. Halliday, A. Curtis, and K. Wapenaar, “Generalized PP+ PS= SS from seismic interferometry,” Geophys. J. Int. 189, 1015–1024 (2012).
[CrossRef]

K. Wapenaar, E. Slob, and R. Snieder, “Seismic and electromagnetic controlled-source interferometry in dissipative media,” Geophys. Prospect. 56, 419–434 (2008).
[CrossRef]

K. Wapenaar, E. Slob, and R. Snieder, “Unified Green’s function retrieval by cross correlation,” Phys. Rev. Lett. 97, 234301 (2006).
[CrossRef]

K. Wapenaar, “Retrieving the elastodynamic Green’s function of an arbitrary inhomogeneous medium by cross correlation,” Phys. Rev. Lett. 93, 254301 (2004).
[CrossRef]

Weaver, R.

R. Weaver and O. Lobkis, “On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons,” Ultrasonics 40, 435–439 (2002).
[CrossRef]

Weaver, R. L.

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[CrossRef]

Wells, W. A.

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

Xu, M.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Yalavarthy, P. K.

Yang, W.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (2007).
[CrossRef]

Yodh, A. G.

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Opt. Lett. 26, 701–703 (2001).
[CrossRef]

Zhu, H.

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

Acad. Radiol. (3)

B. J. Tromberg, “Optical scanning and breast cancer,” Acad. Radiol. 12, 923–924 (2005).
[CrossRef]

B. W. Pogue, “Near-infrared characterization of disease via vascular permeability probes,” Acad. Radiol. 13, 1–3 (2006).
[CrossRef]

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol. 8, 211–218 (2001).
[CrossRef]

Adv. Exp. Med. Biol. (1)

B. W. Pogue, H. Zhu, C. Nwaigwe, T. O. McBride, U. L. Osterberg, K. D. Paulsen, and J. F. Dunn, “Hemoglobin imaging with hybrid magnetic resonance and near-infrared diffuse tomography,” Adv. Exp. Med. Biol. 530, 215–224 (2003).
[CrossRef]

Ann. N.Y. Acad. Sci. (1)

S. Thomsen and D. Tatman, “Physiological and pathological factors of human breast disease that can influence optical diagnosis,” Ann. N.Y. Acad. Sci. 838, 171–193 (1998).
[CrossRef]

Appl. Opt. (1)

Breast Cancer Res. (1)

B. J. Tromberg, A. Cerussi, N. Shah, M. Compton, A. Durkin, D. Hsiang, J. Butler, and R. Mehta, “Imaging in breast cancer: diffuse optics in breast cancer: detecting tumors in pre-menopausal women and monitoring neoadjuvant chemotherapy,” Breast Cancer Res. 7, 279–285 (2005).
[CrossRef]

Disease Markers (1)

A. H. Hielscher, A. Y. Bluestone, G. S. Abdoulaev, A. D. Klose, J. Lasker, M. Stewart, U. Netz, and J. Beuthan, “Near-infrared diffuse optical tomography,” Disease Markers 18, 313–337 (2002).

Geophys. J. Int. (1)

D. Halliday, A. Curtis, and K. Wapenaar, “Generalized PP+ PS= SS from seismic interferometry,” Geophys. J. Int. 189, 1015–1024 (2012).
[CrossRef]

Geophys. Prospect. (1)

K. Wapenaar, E. Slob, and R. Snieder, “Seismic and electromagnetic controlled-source interferometry in dissipative media,” Geophys. Prospect. 56, 419–434 (2008).
[CrossRef]

Inverse Probl. (1)

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

J. Acoust. Soc. Am. (1)

R. Snieder, “Extracting the Green’s function of attenuating heterogeneous acoustic media from uncorrelated waves,” J. Acoust. Soc. Am. 121, 2637–2643 (2007).
[CrossRef]

J. Biomed. Opt. (4)

A. Cerussi, N. Shah, D. Hsiang, A. Durkin, J. Butler, and B. J. Tromberg, “In vivo absorption, scattering, and physiologic properties of 58 malignant breast tumors determined by broadband diffuse optical spectroscopy,” J. Biomed. Opt. 11, 044005 (2006).
[CrossRef]

M. B. Unlu, Y. Lin, O. Birgul, O. Nalcioglu, and G. Gulsen, “Simultaneous in vivo dynamic magnetic resonance-diffuse optical tomography for small animal imaging,” J. Biomed. Opt. 13, 060501 (2008).
[CrossRef]

T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, “Multispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast,” J. Biomed. Opt. 7, 72–79 (2002).
[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiiha, G. Gulsen, and O. Nalcioglu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

Med. Phys. (7)

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

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef]

B. J. Tromberg, B. W. Pogue, K. D. Paulsen, A. G. Yodh, D. A. Boas, and A. E. Cerussi, “Assessing the future of diffuse optical imaging technologies for breast cancer management,” Med. Phys. 35, 2443–2451 (2008).
[CrossRef]

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

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef]

D. Razansky and V. Ntziachristos, “Hybrid photoacoustic fluorescence molecular tomography using finite-element-based inversion,” Med. Phys. 34, 4293–4301 (2007).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (7)

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef]

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

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, “Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation,” Phys. Med. Biol. 52, 4497–4512 (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]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach,” Phys. Med. Biol. 48, 2713–2727 (2003).
[CrossRef]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

M. B. Unlu, O. Birgul, and G. Gulsen, “A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (dce-dot),” Phys. Med. Biol. 53, 3189–3200 (2008).
[CrossRef]

Phys. Rev. E (1)

R. Snieder, “Retrieving the Green’s function of the diffusion equation from the response to a random forcing,” Phys. Rev. E 74, 0466201 (2006).
[CrossRef]

Phys. Rev. Lett. (3)

K. Wapenaar, “Retrieving the elastodynamic Green’s function of an arbitrary inhomogeneous medium by cross correlation,” Phys. Rev. Lett. 93, 254301 (2004).
[CrossRef]

K. Wapenaar, E. Slob, and R. Snieder, “Unified Green’s function retrieval by cross correlation,” Phys. Rev. Lett. 97, 234301 (2006).
[CrossRef]

R. L. Weaver and O. I. Lobkis, “Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies,” Phys. Rev. Lett. 87, 134301 (2001).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. USA 104, 4014–4019 (2007).
[CrossRef]

Rev. Sci. Instrum. (1)

B. Chance, M. Cope, E. Gratton, N. Ramanujam, and B. Tromberg, “Phase measurement of light absorption and scatter in human tissue,” Rev. Sci. Instrum. 69, 3457 (1998).
[CrossRef]

Science (1)

M. Campillo and A. Paul, “Long-range correlations in the diffuse seismic coda,” Science 299, 547–549 (2003).
[CrossRef]

Ultrasonics (1)

R. Weaver and O. Lobkis, “On the emergence of the Green’s function in the correlations of a diffuse field: pulse-echo using thermal phonons,” Ultrasonics 40, 435–439 (2002).
[CrossRef]

Wave Motion (1)

A. D. Hoop and H. Stam, “Time-domain reciprocity theorems for elastodynamic wave fields in solids with relaxation and their application to inverse problems,” Wave Motion 10, 479–489 (1988).
[CrossRef]

Other (7)

M. Schweiger, O. Camara-Rey, W. R. Crum, E. Lewis, J. Schnabel, S. R. Arridge, D. L. G. Hill, and N. Fox, “An inverse problem approach to the estimation of volume change,” Medical Image Computing and Computer-Assisted Intervention—MICCAI (Springer, 2005), pp. 616–623.

T. Nielsen, T. Koehler, M. van der Mark, and G. t’Hooft, “Fully 3D reconstruction of attenuation for diffuse optical tomography using a finite element model,” in Proceedings of IEEE Conference on Nuclear Science (IEEE, 2005), p. 2283.

G. Melo, A. Malcolm, and M. Fehler, “Comparison of microearthquake locations using seismic interferometry principles,” in SEG Technical Program Expanded Abstracts 2012 (Society of Exploration Geophysicists, 2012), pp. 1–5.

J. T. Fokkema and P. M. van den Berg, Seismic Applications of Acoustic Reciprocity (Elsevier, 1993).

B. W. Pogue, H. Jiang, K. D. Paulsen, and U. L. Osterberg, “Frequency-domain diffuse optical tomography of breast tissue: detector size and imaging geometry,” in Proceedings of the IEEE Conference on Engineering in Medicine and Biology Society (IEEE, 1997), p. 2745.

J. C. Hebden, M. Varela, S. Magazov, N. Everdell, A. Gibson, J. Meek, and T. Austin, “Diffuse optical imaging of the newborn infant brain,” Biomedical Imaging (ISBI), 2012 9th IEEE International Symposium, Barcelona, Spain, May2–5, 2012, (2012).

P. Giacometti and S. G. Diamond, “Diffuse optical tomography for brain imaging: continuous wave instrumentation and linear analysis methods,” in Optical Methods and Instrumentation in Brain Imaging and Therapy (Springer, 2013), pp. 57–85.

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Figures (5)

Fig. 1.
Fig. 1.

(a) Eight sources and eight detectors are uniformly distributed on the boundary of the circular region. (b) Finite element mesh used in the simulations.

Fig. 2.
Fig. 2.

Absorption map ( mm 1 ) of a circular region with an inclusion. Inclusion has an absorption coefficient twice the background and its center is located 10 mm away from the center of the circular region.

Fig. 3.
Fig. 3.

Simulation results for cases 1 and 2. In each figure, there are two curves. The first curve shows log amplitude data at detectors 2, 3, 4, 5, 6, 7, and 8 for a source placed at detector 1 (amp meas.). The second curve shows the log amplitude data if a virtual source is placed at detector 1 (amp calc.). For this case, detector readings are calculated using Eq. (24). Figures show (a) log amplitude data and (b) normalized log amplitude data. Normalization is performed by subtracting the highest detector reading from all other ones.

Fig. 4.
Fig. 4.

2D illustration of the distribution of the sources and detectors. Four sources and four detectors are linearly distributed on the boundary of the slab. s1, s2, s3, s4, and d1, d2, d3, d4 denote the sources and detectors, respectively. Virtual source was located at d1.

Fig. 5.
Fig. 5.

Solid curve shows log amplitude data readings of the detectors 2, 3, and 4 when an actual source is placed at detector 1. The dashed curve shows the log amplitude data reading of the same detectors when a virtual source is placed at 1.

Equations (26)

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

· D ( r ) ϕ ( r , t ) + μ a ϕ ( r , t ) + 1 c ϕ ( r , t ) t = q ( r , t ) ,
· D ( r ) ϕ ( r , ω ) + ( μ a i ω c ) ϕ ( r , ω ) = q ( r , ω ) ,
ϕ ( r , t ) = ϕ ( r , ω ) exp ( i ω t ) d ω ,
ϕ ( r d , ω ) + 2 ζ D ( r d ) ϕ ( r d , ω ) ν = 0
· D ( r ) ϕ * ( r , ω ) + ( μ a + i ω c ) ϕ * ( r , ω ) = q * ( r , ω )
( ϕ B * E A ϕ A Q B ) d V
( ϕ B * E A + ϕ A Q B ) d V
[ ( ϕ B * · D ϕ A ) ( ϕ A · D ϕ B * ) ] d V = [ ϕ B * ( μ a i ω c ) ϕ A ϕ A ( μ a + i ω c ) ϕ B * ] d V + [ ϕ B * q A ϕ A q B * ] d V
[ ( ϕ B * · D ϕ A ) + ( ϕ A · D ϕ B * ) ] d V = [ ϕ B * ( μ a i ω c ) ϕ A + ϕ A ( μ a + i ω c ) ϕ B * ] d V + [ ϕ B * q A + ϕ A q B * ] d V ,
ϕ B * · D ϕ A = · ( ϕ B * D ϕ A ) D ( ϕ B * ) · ( ϕ A )
ϕ A · D ϕ B * = · ( ϕ A D ϕ B * ) D ( ϕ A ) · ( ϕ B * )
[ ( D ϕ B * ϕ A ) ( D ϕ A ϕ B * ) ] d S = 2 i ω c ϕ B * ϕ A d V + [ ϕ B * q A ϕ A q B * ] d V
[ ( D ϕ B * ϕ A ) + ( D ϕ A ϕ B * ) ] d S = 2 μ a ϕ B * ϕ A d V 2 D ( ϕ B * ) · ( ϕ A ) d V + [ ϕ B * q A + ϕ A q B * ] d V .
D ( ϕ B * ) · ( ϕ A ) d V = 1 4 ζ 2 ϕ B * ϕ A D d V .
ϕ A ϕ B * + 2 ζ D ϕ A ν ϕ B * = 0
ϕ B * ϕ A + 2 ζ D ϕ B * ν ϕ A = 0 ,
ϕ A ϕ B * + ζ D ( ϕ B * ϕ A ) ν = 0 .
D ( ϕ B * ) · ( ϕ A ) d V = 1 4 ζ ( ϕ A ϕ B * ) ν d V = 1 4 ζ ϕ A ϕ B * d S .
ϕ B * q A d V ϕ A q B * d V = 2 i ω c ϕ B * ϕ A d V
ϕ B * q A d V + ϕ A q B * d V = 1 2 ζ ϕ B * ϕ A d S + 2 μ a ϕ B * ϕ A d V .
G * ( r A , r B , ω ) G ( r B , r A , ω ) = 2 i ω c G * ( r , r B , ω ) G ( r , r A , ω ) d V
G * ( r A , r B , ω ) + G ( r B , r A , ω ) = 1 2 ζ G * ( r , r B , ω ) G ( r , r A , ω ) d S + 2 μ a ( r ) G * ( r , r B , ω ) G ( r , r A , ω ) d V ,
G ( r A , r B , ω ) = 1 4 ζ G ( r A , r , ω ) G * ( r B , r , ω ) d S + μ a ( r ) G ( r A , r , ω ) G * ( r B , r , ω ) d V + i ω c G ( r A , r , ω ) G * ( r B , r , ω ) d V .
G Γ ( r A , r , ω ) = 1 2 ζ G ( r A , r , ω ) .
G Γ ( r A , r B , ω ) = 1 2 G Γ ( r A , r , ω ) ( G * ) Γ ( r B , r , ω ) d S + 2 ζ μ a ( r ) G Γ ( r A , r , ω ) ( G * ) Γ ( r B , r , ω ) d V + 2 i ζ ω c G Γ ( r A , r , ω ) ( G * ) Γ ( r B , r , ω ) d V .
G d v Γ 1 2 s = 1 N G d s Γ G v s Γ ,

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