Abstract

Optical imaging and tomography in tissues can facilitate the quantitative study of several important chromophores and fluorophores. Several theoretical models have been validated for diffuse photon propagation in highly scattering and low-absorbing media that describe the optical appearance of tissues in the near-infrared (NIR) region. However, these models are not generally applicable to quantitative optical investigations in the visible because of the significantly higher tissue absorption in this spectral region compared with that in the NIR. We performed photon measurements through highly scattering and absorbing media for ratios of the absorption coefficient to the reduced scattering coefficient ranging approximately from zero to one. We examined experimentally the performance of the absorption-dependent diffusion coefficient defined by Aronson and Corngold [ J. Opt. Soc. Am. A 16, 1066 ( 1999)] for quantitative estimations of photon propagation in the low- and high-absorption regimes. Through steady-state measurements we verified that the transmitted intensity is well described by the diffusion equation by considering a modified diffusion coefficient with a nonlinear dependence on the absorption. This study confirms that simple analytical solutions based on the diffusion approximation are suitable even for high-absorption regimes and shows that diffusion-approximation-based models are valid for quantitative measurements and tomographic imaging of tissues in the visible.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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2003 (3)

R. Elaloufi, R. Carminati, J.-J. Greffet, “Definition of the diffusion coefficient in scattering and absorbing media,” J. Opt. Soc. Am. A 20, 678–685 (2003).
[CrossRef]

R. Weissleder, V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[CrossRef] [PubMed]

2002 (5)

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

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

V. Ntziachristos, R. Weissleder, “CCD-based scanner for three-dimensional fluorescence-mediated diffuse optical tomography of small animals,” Med. Phys. 29, 803–809 (2002).
[CrossRef] [PubMed]

W. Cai, M. Xu, M. Lax, R. R. Alfano, “Diffusion coefficient depends on time, not on absorption,” Opt. Lett. 27, 731–733 (2002).
[CrossRef]

R. Elaloufi, R. Carminati, J.-J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4, S103–S108 (2002).
[CrossRef]

2001 (2)

R. Graaff, K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 23, 3043–3050 (2001).
[CrossRef]

R. Weissleder, U. Mahmood, “Special review: molecular imaging,” Radiology 219, 316–333 (2001).
[CrossRef] [PubMed]

2000 (2)

C. H. Contag, D. Jenkins, P. R. Contag, R. S. Negrin, “Use of reporter genes for optical measurements of neoplastic disease in vivo,” Neoplasia 2, 41–52 (2000).
[CrossRef] [PubMed]

R. Graaff, J. J. Ten Bosch, “Diffusion coefficient in photon diffusion theory,” Opt. Lett. 25, 43–45 (2000).
[CrossRef]

1999 (6)

R. Aronson, N. Corngold, “Photon diffusion coefficient in an absorbing medium,” J. Opt. Soc. Am. A 16, 1066–1071 (1999).
[CrossRef]

D. J. Durian, J. Rudnick, “Spatially resolved backscattering: implementation of extrapolation boundary condition and exponential source,” J. Opt. Soc. Am. A 16, 837–844 (1999).
[CrossRef]

I. Delfino, M. Lepore, P. L. Indovina, “Experimental tests of different solutions to the diffusion equation for optical characterization of scattering media by time-resolved transmittance,” Appl. Opt. 38, 4228–4236 (1999).
[CrossRef]

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

U. Mahmood, C. Tung, A. Bogdanov, R. Weissleder, “Near infrared optical imaging system to detect tumor protease activity,” Radiology 213, 866–870 (1999).
[CrossRef] [PubMed]

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

1998 (2)

1997 (7)

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

A. Y. Polishchuk, S. Gutman, M. Lax, R. R. Alfano, “Photon-density modes beyond the diffusion approximation: a scalar wave-diffusion equation,” J. Opt. Soc. Am. A 14, 230–234 (1997).
[CrossRef]

M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
[CrossRef] [PubMed]

T. Nakai, G. Nishimura, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

K. Furutsu, “Pulse wave scattering by an absorber and integrated attenuation in the diffusion approximation,” J. Opt. Soc. Am. A 14, 267–274 (1997).
[CrossRef]

T. Durduran, A. G. Yodh, B. Chance, D. A. Boas, “Does the photon-diffusion coefficient depend on absorption?” J. Opt. Soc. Am. A 14, 3358–3365 (1997).
[CrossRef]

1995 (2)

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).
[CrossRef]

1994 (1)

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

1991 (2)

I. Kuscer, N. J. McCormick, “Some analytical results for radiative transfer in thick atmospheres,” Transp. Theory Stat. Phys. 20, 351–381 (1991).
[CrossRef]

H. J. van Staveren, C. J. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemer, “Light Scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
[CrossRef] [PubMed]

1990 (1)

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 65, 2210–2211 (1990).
[CrossRef]

1989 (1)

1988 (1)

I. Freund, M. Kaveh, M. Rosenbluh, “Dynamic multiple scattering: ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988).
[CrossRef] [PubMed]

1984 (2)

1980 (1)

1978 (1)

1965 (1)

J. A. Nelder, R. Mead, “A Simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

1948 (1)

G. Holte, “On a method of calculating the density of neutrons emitted form a point source in an infinite medium,” Ark. Mat., Astron. Fys. 35A, 1–9 (1948).

1941 (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Aalders, M.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

Alfano, R. R.

Aronson, R.

Arridge, S. R.

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

Bassani, M.

Beek, J.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

Benaron, D. A.

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

Blokland, P.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

Boas, D. A.

Bogdanov, A.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

U. Mahmood, C. Tung, A. Bogdanov, R. Weissleder, “Near infrared optical imaging system to detect tumor protease activity,” Radiology 213, 866–870 (1999).
[CrossRef] [PubMed]

Bremer, C.

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

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

Cai, W.

Carminati, R.

R. Elaloufi, R. Carminati, J.-J. Greffet, “Definition of the diffusion coefficient in scattering and absorbing media,” J. Opt. Soc. Am. A 20, 678–685 (2003).
[CrossRef]

R. Elaloufi, R. Carminati, J.-J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4, S103–S108 (2002).
[CrossRef]

Case, K. M.

K. M. Case, F. Hoffmann, G. Placzek, Introduction to the Theory of Neutron Diffusion (Los Alamos Scientific Laboratory, Los Alamos, N.M., 1953).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1967).

Chance, B.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Contag, C. H.

C. H. Contag, D. Jenkins, P. R. Contag, R. S. Negrin, “Use of reporter genes for optical measurements of neoplastic disease in vivo,” Neoplasia 2, 41–52 (2000).
[CrossRef] [PubMed]

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

Contag, P. R.

C. H. Contag, D. Jenkins, P. R. Contag, R. S. Negrin, “Use of reporter genes for optical measurements of neoplastic disease in vivo,” Neoplasia 2, 41–52 (2000).
[CrossRef] [PubMed]

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

Contini, D.

Corngold, N.

Delfino, I.

Dennery, P.

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

Durduran, T.

Durian, D. J.

Eames, B.

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

Elaloufi, R.

R. Elaloufi, R. Carminati, J.-J. Greffet, “Definition of the diffusion coefficient in scattering and absorbing media,” J. Opt. Soc. Am. A 20, 678–685 (2003).
[CrossRef]

R. Elaloufi, R. Carminati, J.-J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4, S103–S108 (2002).
[CrossRef]

Freund, I.

I. Freund, M. Kaveh, M. Rosenbluh, “Dynamic multiple scattering: ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988).
[CrossRef] [PubMed]

Furutsu, K.

Graaff, R.

R. Graaff, K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 23, 3043–3050 (2001).
[CrossRef]

R. Graaff, J. J. Ten Bosch, “Diffusion coefficient in photon diffusion theory,” Opt. Lett. 25, 43–45 (2000).
[CrossRef]

Graves, E. E.

E. E. Graves, J. Ripoll, R. Weissleder, V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[CrossRef] [PubMed]

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

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Greffet, J.-J.

R. Elaloufi, R. Carminati, J.-J. Greffet, “Definition of the diffusion coefficient in scattering and absorbing media,” J. Opt. Soc. Am. A 20, 678–685 (2003).
[CrossRef]

R. Elaloufi, R. Carminati, J.-J. Greffet, “Time-dependent transport through scattering media: from radiative transfer to diffusion,” J. Opt. A, Pure Appl. Opt. 4, S103–S108 (2002).
[CrossRef]

Gutman, S.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Hoffmann, F.

K. M. Case, F. Hoffmann, G. Placzek, Introduction to the Theory of Neutron Diffusion (Los Alamos Scientific Laboratory, Los Alamos, N.M., 1953).

Holte, G.

G. Holte, “On a method of calculating the density of neutrons emitted form a point source in an infinite medium,” Ark. Mat., Astron. Fys. 35A, 1–9 (1948).

Indovina, P. L.

Ishimaru, A.

Ito, S.

Jenkins, D.

C. H. Contag, D. Jenkins, P. R. Contag, R. S. Negrin, “Use of reporter genes for optical measurements of neoplastic disease in vivo,” Neoplasia 2, 41–52 (2000).
[CrossRef] [PubMed]

Kaveh, M.

I. Freund, M. Kaveh, M. Rosenbluh, “Dynamic multiple scattering: ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988).
[CrossRef] [PubMed]

Kuscer, I.

I. Kuscer, N. J. McCormick, “Some analytical results for radiative transfer in thick atmospheres,” Transp. Theory Stat. Phys. 20, 351–381 (1991).
[CrossRef]

Lax, M.

Lepore, M.

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 65, 2210–2211 (1990).
[CrossRef]

Mahmood, U.

R. Weissleder, U. Mahmood, “Special review: molecular imaging,” Radiology 219, 316–333 (2001).
[CrossRef] [PubMed]

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

U. Mahmood, C. Tung, A. Bogdanov, R. Weissleder, “Near infrared optical imaging system to detect tumor protease activity,” Radiology 213, 866–870 (1999).
[CrossRef] [PubMed]

Martelli, F.

McCormick, N. J.

I. Kuscer, N. J. McCormick, “Some analytical results for radiative transfer in thick atmospheres,” Transp. Theory Stat. Phys. 20, 351–381 (1991).
[CrossRef]

Mead, R.

J. A. Nelder, R. Mead, “A Simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Moes, C. J.

Mullins, J. I.

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
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Nakai, T.

T. Nakai, G. Nishimura, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Negrin, R. S.

C. H. Contag, D. Jenkins, P. R. Contag, R. S. Negrin, “Use of reporter genes for optical measurements of neoplastic disease in vivo,” Neoplasia 2, 41–52 (2000).
[CrossRef] [PubMed]

Nelder, J. A.

J. A. Nelder, R. Mead, “A Simplex method for function minimization,” Comput. J. 7, 308–313 (1965).
[CrossRef]

Nishimura, G.

T. Nakai, G. Nishimura, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Ntziachristos, V.

E. E. Graves, J. Ripoll, R. Weissleder, V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[CrossRef] [PubMed]

R. Weissleder, V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

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

V. Ntziachristos, R. Weissleder, “CCD-based scanner for three-dimensional fluorescence-mediated diffuse optical tomography of small animals,” Med. Phys. 29, 803–809 (2002).
[CrossRef] [PubMed]

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

Oshiro, M.

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

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Pickering, J.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
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K. M. Case, F. Hoffmann, G. Placzek, Introduction to the Theory of Neutron Diffusion (Los Alamos Scientific Laboratory, Los Alamos, N.M., 1953).

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Posthumus, P.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
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R. Graaff, K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 23, 3043–3050 (2001).
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K. Rinzema, L. H. P. Murrer, W. M. Star, “Direct experimental verification of light transport theory in an optical phantom,” J. Opt. Soc. Am. A 15, 2078–2088 (1998).
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Ripoll, J.

E. E. Graves, J. Ripoll, R. Weissleder, V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[CrossRef] [PubMed]

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

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I. Freund, M. Kaveh, M. Rosenbluh, “Dynamic multiple scattering: ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988).
[CrossRef] [PubMed]

Rudnick, J.

Spilman, S. D.

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

Star, W. M.

Sterenborg, H.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

Stevenson, D. K.

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

Tamura, M.

T. Nakai, G. Nishimura, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Ten Bosch, J. J.

Tung, C.

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

U. Mahmood, C. Tung, A. Bogdanov, R. Weissleder, “Near infrared optical imaging system to detect tumor protease activity,” Radiology 213, 866–870 (1999).
[CrossRef] [PubMed]

Tung, C. H.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

van Gemer, M. J. C.

van Gemert, M.

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

van Marle, J.

van Staveren, H. J.

Weissleder, R.

E. E. Graves, J. Ripoll, R. Weissleder, V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[CrossRef] [PubMed]

R. Weissleder, V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

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

V. Ntziachristos, R. Weissleder, “CCD-based scanner for three-dimensional fluorescence-mediated diffuse optical tomography of small animals,” Med. Phys. 29, 803–809 (2002).
[CrossRef] [PubMed]

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

R. Weissleder, U. Mahmood, “Special review: molecular imaging,” Radiology 219, 316–333 (2001).
[CrossRef] [PubMed]

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

U. Mahmood, C. Tung, A. Bogdanov, R. Weissleder, “Near infrared optical imaging system to detect tumor protease activity,” Radiology 213, 866–870 (1999).
[CrossRef] [PubMed]

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S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
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K. Rinzema, L. H. P. Murrer, W. M. Star, “Direct experimental verification of light transport theory in an optical phantom,” J. Opt. Soc. Am. A 15, 2078–2088 (1998).
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Med. Phys. (2)

V. Ntziachristos, R. Weissleder, “CCD-based scanner for three-dimensional fluorescence-mediated diffuse optical tomography of small animals,” Med. Phys. 29, 803–809 (2002).
[CrossRef] [PubMed]

E. E. Graves, J. Ripoll, R. Weissleder, V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003).
[CrossRef] [PubMed]

Mol. Imaging (1)

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

Mol. Microbiol. (1)

C. H. Contag, P. R. Contag, J. I. Mullins, S. D. Spilman, D. K. Stevenson, D. A. Benaron, “Photonic detection of bacterial pathogens in living hosts,” Mol. Microbiol. 18, 593–603 (1995).
[CrossRef] [PubMed]

Nat. Biotechnol. (1)

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near-infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

Nat. Med. (2)

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

R. Weissleder, V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

Neoplasia (1)

C. H. Contag, D. Jenkins, P. R. Contag, R. S. Negrin, “Use of reporter genes for optical measurements of neoplastic disease in vivo,” Neoplasia 2, 41–52 (2000).
[CrossRef] [PubMed]

Opt. Lett. (4)

Photochem. Photobiol. (1)

C. H. Contag, S. D. Spilman, P. R. Contag, M. Oshiro, B. Eames, P. Dennery, D. K. Stevenson, D. A. Benaron, “Visualizing gene expression in living mammals using a bioluminescent reporter,” Photochem. Photobiol. 66, 523–531 (1997).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

T. Nakai, G. Nishimura, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

R. Graaff, K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 23, 3043–3050 (2001).
[CrossRef]

J. Beek, P. Blokland, P. Posthumus, M. Aalders, J. Pickering, H. Sterenborg, M. van Gemert, “In vitro double-integrating-sphere optical properties of tissues between 630 and 1064 nm,” Phys. Med. Biol. 42, 2255–2261 (1997).
[CrossRef] [PubMed]

Phys. Rev. E (1)

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Phys. Rev. Lett. (2)

I. Freund, M. Kaveh, M. Rosenbluh, “Dynamic multiple scattering: ballistic photons and the breakdown of the photon-diffusion approximation,” Phys. Rev. Lett. 60, 1130–1133 (1988).
[CrossRef] [PubMed]

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media?” Phys. Rev. Lett. 65, 2210–2211 (1990).
[CrossRef]

Radiology (2)

U. Mahmood, C. Tung, A. Bogdanov, R. Weissleder, “Near infrared optical imaging system to detect tumor protease activity,” Radiology 213, 866–870 (1999).
[CrossRef] [PubMed]

R. Weissleder, U. Mahmood, “Special review: molecular imaging,” Radiology 219, 316–333 (2001).
[CrossRef] [PubMed]

Transp. Theory Stat. Phys. (1)

I. Kuscer, N. J. McCormick, “Some analytical results for radiative transfer in thick atmospheres,” Transp. Theory Stat. Phys. 20, 351–381 (1991).
[CrossRef]

Other (5)

K. M. Case, F. Hoffmann, G. Placzek, Introduction to the Theory of Neutron Diffusion (Los Alamos Scientific Laboratory, Los Alamos, N.M., 1953).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, New York, 1967).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

V. Tuchin, ed., Tissue Optics: Light Scattering Methods and Instruments for Medical Diagnosis, Vol. TT38 of Tutorial Texts on Optical Engineering (SPIE Press, Bellingham, Wash., 2000).

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Figures (2)

Fig. 1
Fig. 1

Retrieved absorption coefficient versus ink concentration for a slab of width 1 cm with μ s = 6   cm - 1 for the cases a ( μ a ,   μ s ) [see Eq. (6)] (solid circles), a = 0 [see Eq. (2)] (squares), and a = 1 [see Eq. (2)] (triangles). The solid curve represents a linear fit of the a ( μ a ,   μ s ) data.

Fig. 2
Fig. 2

Variation of the retrieved absorption coefficient for different anisotropy values ( g = 0.7 , 0.8, 0.9, and 0.95) versus ink concentration for a slab of width 1 cm with μ s = 12 cm - 1 . Results presented correspond to the difference between g = 0.7 and g = 0.8 (squares), g = 0.9 and g = 0.8 (solid circles), and g = 0.95 and g = 0.8 (triangles). For comparison we show the standard deviation when averaging the retrieved absorption coefficient for seven different source positions (solid squares) in the g = 0.8 case.

Tables (1)

Tables Icon

Table 1 Fitting Results a

Equations (7)

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

L d = D / μ a .
D = 1 3 ( μ s + a μ a ) ,
L d 2 ln L d + 1 / ( μ s + μ a ) L d - 1 / ( μ s + μ a ) = 1 μ s .
D = 1 3 ( μ s + 0.2 μ a ) ,
D = 1 3 ( μ s + μ a )   1 - 4 5         μ a μ s ( 1 + g ) + μ a - 1 .
a = 1 - 4 5   μ s + μ a μ s ( 1 + g ) + μ a .
l ext = C nd D ,

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