Abstract

In this paper, after a critical review of the literature, we present two forward solvers and a new methodology for description of photon migration in the presence of totally absorbing inclusions embedded in diffusive media in both time and CW domains. The first forward solver is a heuristic approach based on a higher order perturbation theory applied to the diffusion equation (DE) [denoted eighth-order perturbation theory (EOPT)]. The second forward solver [denoted eighth-order perturbation theory with the equivalence relation (EOPTER) ] is obtained by combining the EOPT solver with the adoption of the equivalence relation (ER) [J. Biomed. Opt. 18, 066014 (2013)]. These forward solvers can possibly overcome some evident limitations of previous approaches like the theory behind the so-called banana-shape regions or exact analytical solutions of the DE in the presence of highly or totally absorbing inclusions. We also propose the ER to reformulate the problem of a totally absorbing inclusion in terms of another inclusion having a finite absorption contrast and a re-scaled volume. For instance, we have shown how this approach can indeed be used to simulate black inclusions with the Born approximation. By means of comparisons with the results of Monte Carlo simulations, we have shown that the EOPTER solver can model totally absorbing inclusions with an error smaller than about 10%, whereas the EOPT solver shows an error smaller than about 20%, showing a performance largely better than that observed with solvers proposed previously.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2013 (2)

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

2010 (2)

2009 (2)

2006 (2)

2005 (1)

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

2003 (2)

2001 (2)

S. Carraresi, T. S. M. Shatir, F. Martelli, and G. Zaccanti, “Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration,” Appl. Opt. 40, 4622–4632 (2001).
[CrossRef]

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 46, 3043–3050 (2001).
[CrossRef]

2000 (1)

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

1998 (2)

1997 (2)

1996 (1)

1995 (1)

1994 (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

’t Hooft, G. W.

Alianelli, L.

Amelink, A.

Arridge, S. R.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Blumetti, C.

Boas, D. A.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Carraresi, S.

Chance, B.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

X. D. Zhu, S. Wei, S. C. Feng, and B. Chance, “Analysis of a diffuse-photon-density wave in multiple-scattering media in the presence of a small spherical object,” J. Opt. Soc. Am. A 13, 494–499 (1996).
[CrossRef]

S. Feng, F. Zeng, and B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Choe, R.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Christiaanse, T.

Contini, D.

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
[CrossRef]

Corlu, A.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Cubeddu, R.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11, 853–867 (2003).
[CrossRef]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, and R. Cubeddu, “Experimental test of a perturbation model for time-resolved imaging in diffusive media,” Appl. Opt. 42, 3145–3153 (2003).
[CrossRef]

Czerniecki, B. J.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Danesini, G.

Del Bianco, S.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media (SPIE, 2010).

DeMichele, A.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Di Ninni, P.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Durduran, T.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Fantini, S.

Feng, S.

Feng, S. C.

Fraker, D. L.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Franceschini, M. A.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Graaff, R.

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 46, 3043–3050 (2001).
[CrossRef]

Gratton, E.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Grosicka-Koptyra, M.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Hebden, J.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Hueber, D. M.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Ismaelli, A.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962).

Jacques, S. L.

Jelzow, A.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Kacprzak, M.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Kofinas, A. D.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Konecky, S. D.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Lee, K.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Liebert, A.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Macdonald, R.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

Magazov, S.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Martelli, F.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results,” J. Opt. Soc. Am. A 27, 1723–1742 (2010).
[CrossRef]

A. Sassaroli, F. Martelli, and S. Fantini, “Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries,” Appl. Opt. 48, D62–D73 (2009).
[CrossRef]

A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. I. Theory,” J. Opt. Soc. Am. A 23, 2105–2118 (2006).
[CrossRef]

A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. II. Continuous-wave results,” J. Opt. Soc. Am. A 23, 2119–2131 (2006).
[CrossRef]

S. Carraresi, T. S. M. Shatir, F. Martelli, and G. Zaccanti, “Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration,” Appl. Opt. 40, 4622–4632 (2001).
[CrossRef]

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
[CrossRef]

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media (SPIE, 2010).

Maulik, D.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Mazurenka, M.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Milej, D.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Ostermeyer, M. R.

Paasschens, J. C. J.

Pifferi, A.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11, 853–867 (2003).
[CrossRef]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, and R. Cubeddu, “Experimental test of a perturbation model for time-resolved imaging in diffusive media,” Appl. Opt. 42, 3145–3153 (2003).
[CrossRef]

Rinzema, K.

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 46, 3043–3050 (2001).
[CrossRef]

Rosen, M. A.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

Rosenfeld, W.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Sassaroli, A.

Sawosz, P.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Shatir, T. S. M.

Spinelli, L.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11, 853–867 (2003).
[CrossRef]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, and R. Cubeddu, “Experimental test of a perturbation model for time-resolved imaging in diffusive media,” Appl. Opt. 42, 3145–3153 (2003).
[CrossRef]

Stankovic, M. R.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Steinkellner, O.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Sterenborg, H. J. C. M.

Stubblefield, P. G.

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

Taroni, P.

Torricelli, A.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11, 853–867 (2003).
[CrossRef]

L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, and R. Cubeddu, “Experimental test of a perturbation model for time-resolved imaging in diffusive media,” Appl. Opt. 42, 3145–3153 (2003).
[CrossRef]

Wabnitz, A.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Wabnitz, H.

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

Wei, S.

Yodh, A. G.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Zaccanti, G.

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

S. Carraresi, T. S. M. Shatir, F. Martelli, and G. Zaccanti, “Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration,” Appl. Opt. 40, 4622–4632 (2001).
[CrossRef]

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37, 7392–7400 (1998).
[CrossRef]

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media (SPIE, 2010).

Zeng, F.

Zhu, X. D.

Zolek, N.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Zucchelli, L.

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Appl. Opt. (5)

Breast Cancer Res. Treat. (1)

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).

J. Biomed. Opt. (1)

F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013).
[CrossRef]

J. Matern. Fetal Med. (1)

M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).

J. Opt. Soc. Am. A (6)

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (1)

R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 46, 3043–3050 (2001).
[CrossRef]

Phys. Rev. E (1)

J. C. J. Paasschens, “Solution of the time-dependent Boltzmann equation,” Phys. Rev. E 56, 1135–1141 (1997).
[CrossRef]

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

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Proc. SPIE (1)

A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013).
[CrossRef]

Rep. Prog. Phys. (1)

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73, 076701 (2010).
[CrossRef]

Other (2)

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media (SPIE, 2010).

J. D. Jackson, Classical Electrodynamics (Wiley, 1962).

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Figures (8)

Fig. 1.
Fig. 1.

Comparison of the probability of a photon detected to “pass” through or “intersect” the region occupied by a black sphere of radius 2 mm placed inside a semi-infinite medium obtained with various solvers.

Fig. 2.
Fig. 2.

Mirror image sources inside the semi-infinite medium.

Fig. 3.
Fig. 3.

Time-resolved relative contrast |C(t)| for reflectance obtained with MC simulations, and with the EOPTER and the EOPT solvers for a black inclusion located inside a semi-infinite medium with μs=1mm1. The plots pertain to three different arrangements of detector and inclusion.

Fig. 4.
Fig. 4.

Time-resolved relative contrast |C(t)| for transmittance obtained with MC simulations, with the EOPTER and EOPT solvers for a black inclusion located inside a slab 40 mm thick slab with μs=1mm1. The plots pertain to three different arrangements of the inclusion [positions (xi,yi,zi)].

Fig. 5.
Fig. 5.

Comparison of time-resolved relative transmittance contrast |C(t)| obtained with MC simulations and with the EOPTER solver for a black inclusion located inside a slab 40 mm thick with μs=1mm1. The plots pertain to three arrangements of the inclusion [positions (xi,yi,zi)].

Fig. 6.
Fig. 6.

Comparison of CW reflectance contrast obtained with MC simulations and with the EOPT solver, the EOPTER solver, and the BAER solver for a black inclusion located inside a semi-infinite medium with μs=1mm1 and μa=0.01mm1.

Fig. 7.
Fig. 7.

Comparison of CW transmittance contrast obtained with MC simulations and with the EOPT solver, the EOPTER solver, and the BAER solver for a black inclusion located inside a slab 40 mm thick with μs=1mm1 and μa=0.01mm1.

Fig. 8.
Fig. 8.

Comparison of CW transmittance contrast for an inclusion with finite Δμa contrast obtained with MC simulations and with the EOPT solver for a slab 40 mm thick with μs=1mm1 and μa=0.01mm1.

Tables (2)

Tables Icon

Table 1. Positions of the Image Sources of the DE Solution for a Semi-infinite Medium

Tables Icon

Table 2. Coefficients kn and their Standard Deviations Calculated with MC Simulations by Average of Several Combinations of Optical Properties, Position, and Size of Inclusion, and Geometry

Equations (14)

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

S04πDexp(μeffr1)r1+q4πDexp(μeffa)a=0,
ΔΦΦ0(rs,rd)=ar1exp[μeff(r1a)]exp[μeff|rdr1|]|rdr1|exp(μeffrd)rd.
Pbs=ΔΦΦ0(rs,rd)|bs,
ΔΦΦ0(rs,rd)|BornliΔμa,
li=VΦ0(rs,r)Φ0(r,rd)dVΦ0(rs,rd)Φ0(rs,r1)Φ0(r1,rd)Φ0(rs,rd)V,
ΔΦΦ0(rs,rd)|Born=a33Dr1exp[μeffr1]exp[μeff|rdr1|]|rdr1|exp(μeffrd)rdΔμa.
ΔΦΦ0(rs,rd)|bs=ΔΦΦ0(rs,rd)|Born3Da2exp(μeffa)1Δμa.
Pbs=ΔΦΦ0(rs,rd)|bs=li3Da2exp(μeffa)=liVΦ0(r1,a).
limV0liV=13Dr1exp[μeffr1]exp[μeff|rdr1|]|rdr1|exp(μeffrd)rd=14πDlima01aΔΦΦ0(rs,rd)|bs.
D2Φ(r)=δ(rrs).
Φ(r)=14πD[1|rrs|(a/R)1|r(a2/R)k^|].
C(rs,rb,V,Δμa)=JJ0J0n=18(1)nn!lin(Δμa)n,
lin(rb)kn1li(rb)(VΦ0(ri,r)dr)n1lin(rb,t)kn1J0(rb,t){[J0(rb,τ)li(rb,τ)]j=1n1VΦ0(ri,r,τ)dr}(t)n2,
CPM,N(Δμa)=k=0Mak(Δμa)k/[1+j=0Nbj(Δμa)j].

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