Abstract

We study the performance of a previously proposed perturbation theory for the diffusion equation in frequency and time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography. We have derived approximate formulas for calculating higher order self- and mixed path length moments, up to the fourth order, which can be used in general diffusive media regardless of geometry and initial distribution of the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is used to extend the validity of the theory to a wider range of absorption contrasts between defects and background. By using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries for the cases of single and multiple absorbing defects having sizes of interest (d=4–10 mm, where d is the diameter of the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximants and Monte Carlo simulations) was within 10% for absorption contrasts Δμa≤0.2 mm−1 for alternating current data, and usually to within 1° for Δμa≤0.1 mm−1 for phase data. In time domain, the average discrepancy in the temporal range of interest (a few nanoseconds) was 2%–3% for Δμa≤0.06 mm−1. The proposed method is an effective fast forward problem solver: all the time-domain results presented in this work were obtained with a computational time of less than about 15 s with a Pentium IV 1.66 GHz personal computer.

© 2010 Optical Society of America

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2009 (7)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

A. Sassaroli, F. Martelli, S. Fantini, “Fourth order perturbation theory for the diffusion equation: continuous wave results for absorbing defects,” Proc. SPIE 7174, 717402 (2009).
[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]

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17, 3884–3902 (2009).
[CrossRef]

Y. Yu, N. Liu, A. Sassaroli, and S. Fantini, “Near-infrared spectral imaging of the female breast for quantitative oximetry in optical tomography,” Appl. Opt. 48, D225–D235 (2009).
[CrossRef]

K. G. Phillips and S. L. Jacques, “Solution of transport equations in layered media with refractive index mismatch using the PN-method,” J. Opt. Soc. Am. A 26, 2147–2162 (2009).
[CrossRef]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17, 20178–20190 (2009).
[CrossRef]

2008 (1)

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

2007 (1)

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

2006 (6)

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef]

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

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

B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E 74, 031908 (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. 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]

2005 (1)

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

2003 (2)

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, “Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method,” Phys. Rev. E 67, 056623 (2003).
[CrossRef]

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

2002 (2)

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]

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

2001 (6)

1999 (1)

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

1998 (1)

1997 (5)

1996 (1)

G. A. Baker and P. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, 1996).

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: Analytical solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).
[CrossRef]

1993 (1)

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

1992 (1)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

1989 (1)

Abdoulaev, G.

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

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001).
[CrossRef]

Anday, E.

Arridge, S. R.

S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef]

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

Baker, G. A.

G. A. Baker and P. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, 1996).

Bal, G.

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

Bangerth, W.

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

Barbour, R. L.

Bluestone, A. Y.

Boas, D. A.

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17, 20178–20190 (2009).
[CrossRef]

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef]

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Express 1, 404–413 (1997).
[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: Analytical solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).
[CrossRef]

Boden, S.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Boverman, G.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

Brooks, D. H.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

Butler, J.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Cerussi, A.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Chance, B.

Chaves, T.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

Chernomordik, V.

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

Choe, R.

Choi, J. H.

Contini, D.

Cubeddu, R.

Cucchiara, B. L.

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Dehghani, H.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Del Bianco, S.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, “Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method,” Phys. Rev. E 67, 056623 (2003).
[CrossRef]

Delpy, D. T.

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

Detre, J. A.

Diamond, S. G.

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef]

Durduran, T.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Edlow, B. L.

Eker, C.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Espinoza, J.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Fang, Q.

Fantini, S.

Fishkin, J.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Foster, T. H.

Franceschini, M. A.

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef]

Gandjbakhche, A.

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

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.

Graves-Morris, P.

G. A. Baker and P. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, 1996).

Greenberg, J. H.

Grosenick, D.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

Hattery, D. W.

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

Haux, D.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Hebden, J. C.

S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef]

Hielscher, A. H.

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

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001).
[CrossRef]

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

Hiraoka, M.

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

Hornung, R.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Hull, E. L.

Huppert, T. J.

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef]

Jacques, S. L.

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]

Joseph, D. K.

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[CrossRef]

Joshi, A.

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

Kasner, S. E.

Kempf, F.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Kim, M. N.

Klose, A. D.

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

Kummrow, A.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

Li, A.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

Li, C.

Liu, N.

Long, H.

Macdonald, R.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

Markel, V. A.

Martelli, F.

McBride, T. O.

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]

Miller, E. L.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

Moesta, K. T.

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

Nioka, S.

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: Analytical solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).
[CrossRef]

Obrig, H.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Osterberg, U. L.

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]

Ostermeyer, M. R.

Ovetsky, Y.

Paasschens, J. C. J.

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

Patterson, M. S.

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[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]

Phillips, K. G.

Pidikiti, D.

Pifferi, A.

Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[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]

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]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Putt, M. E.

Ren, K.

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

Rinneberg, H.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[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]

Sassaroli, A.

Schlag, P. M.

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

Schmitz, C. H.

Schotland, J. C.

Schweiger, M.

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

Shah, N.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Shah, Q.

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]

Spinelli, L.

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Steinbrink, J.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Taroni, P.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Thomas, R.

Toronov, V.

Torricelli, A.

Tromberg, B.

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Turray, T.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

Villringer, A.

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Wabnitz, H.

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

Wassermann, B.

B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E 74, 031908 (2006).
[CrossRef]

Webb, A.

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]

Wilson, B. C.

Wolf, M.

Wolf, U.

Worden, K.

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Yamada, Y.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, “Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method,” Phys. Rev. E 67, 056623 (2003).
[CrossRef]

Yodh, A. G.

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17, 3884–3902 (2009).
[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: Analytical solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).
[CrossRef]

Yu, G.

Yu, Y.

Zaccanti, G.

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, “Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method,” Phys. Rev. E 67, 056623 (2003).
[CrossRef]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[CrossRef]

Zhang, Q.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

Zhou, C.

Zhou, S.

Appl. Opt. (4)

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Inverse Probl. (1)

W. Bangerth and A. Joshi, “Adaptive finite element methods for the solution of inverse problems in optical tomography,” Inverse Probl. 24, 034011 (2008).
[CrossRef]

J. Biomed. Opt. (3)

V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjbakhche, “Quantification of optical properties of a breast tumor using random walk theory,” J. Biomed. Opt. 7, 80–87 (2002).
[CrossRef]

M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, “Diffuse optical imaging of the whole head,” J. Biomed. Opt. 11, 054007 (2006).
[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]

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

Magn. Reson. Imaging (1)

J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, “Illuminating the BOLD signal: combined fMRI-fNIRS studies,” Magn. Reson. Imaging 24, 495–505 (2006).
[CrossRef]

Med. Phys. (2)

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

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

Opt. Express (7)

D. A. Boas, “A fundamental limitation of linearized algorithms for diffuse optical tomography,” Opt. Express 1, 404–413 (1997).
[CrossRef]

B. Chance, E. Anday, S. Nioka, S. Zhou, H. Long, K. Worden, C. Li, T. Turray, Y. Ovetsky, D. Pidikiti, and R. Thomas, “A novel method for fast imaging of brain function, non-invasively, with light,” Opt. Express 2, 411–423 (1998).
[CrossRef]

A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Barbour, and A. H. Hielscher, “Three-dimensional optical tomography of hemodynamics in the human head,” Opt. Express 9, 272–286 (2001).
[CrossRef]

V. Toronov, A. Webb, J. H. Choi, M. Wolf, U. Wolf, and E. Gratton, “Study of local cerebral hemodynamics by frequency-domain near-infrared spectroscopy and correlation with simultaneously acquired functional magnetic resonance imaging,” Opt. Express 9, 417–427 (2001).
[CrossRef]

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

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17, 3884–3902 (2009).
[CrossRef]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17, 20178–20190 (2009).
[CrossRef]

Phys. Med. Biol. (3)

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50, 3941–3956 (2005).
[CrossRef]

S. R. Arridge and J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef]

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 (4)

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

D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E 76, 061908 (2007).
[CrossRef]

B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E 74, 031908 (2006).
[CrossRef]

F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, “Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method,” Phys. Rev. E 67, 056623 (2003).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (2)

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: Analytical solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).
[CrossRef]

N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fishkin, R. Hornung, and B. Tromberg, “Noninvasive functional optical spectroscopy of human breast tissue,” Proc. Natl. Acad. Sci. U.S.A. 98, 4420–4425 (2001).
[CrossRef]

Proc. SPIE (1)

A. Sassaroli, F. Martelli, S. Fantini, “Fourth order perturbation theory for the diffusion equation: continuous wave results for absorbing defects,” Proc. SPIE 7174, 717402 (2009).
[CrossRef]

SIAM J. Sci. Comput. (USA) (1)

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

Other (2)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).

G. A. Baker and P. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, 1996).

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