Abstract

We present an algorithm for simultaneous reconstruction of optical parameters, quantum yield, and lifetime in turbid media with embedded fluorescent inclusions. This algorithm is designed in the Fourier domain as an iterative solution of a system of differential equations of the Helmholtz type and does not involve full ill-conditioned matrix computations. The approach is based on allowing the unknown optical parameters, quantum yield, and lifetime to depend on the Fourier spectral parameter. The algorithm was applied to a time-gated experimental data set acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Relatively accurate reconstruction demonstrates the potential of the method.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2008

2007

2006

V. Y. Soloviev and L. V. Krasnosselskaia, “Consideration of a spread out source in problems of near infrared optical tomography,” Appl. Opt. 45, 4765-4775 (2006).
[CrossRef] [PubMed]

F. Gao, H. Zhao, Y. Tanikawa, and Y. Yamada, “A linear, featured-data scheme for image reconstruction in time-domain fluorescence molecular tomography,” Opt. Express 14, 7109-7124 (2006).
[CrossRef] [PubMed]

A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, “Time resolved fluorescence tomography of turbid media based on lifetime contrast,” Opt. Express 14, 12255-12270 (2006).
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310(2006).
[CrossRef] [PubMed]

J. Ripoll and V. Ntziachristos, “From finite to infinite volumes: removal of boundaries in diffuse wave imaging,” Phys. Rev. Lett. 96, 173903 (2006).
[CrossRef] [PubMed]

V. Y. Soloviev and L. V. Krasnosselskaia, “Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography,” Appl. Opt. 45, 2828-2837 (2006).
[CrossRef] [PubMed]

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176-4183(2006).
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Non-contact fluorescence optical tomography with scanning patterned illumination,” Opt. Express 14, 6516-6534 (2006).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, “Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique,” Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

2005

2004

2003

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2003).
[CrossRef]

2002

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

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

1999

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

1998

1997

M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585-1605 (1997).
[CrossRef]

1996

1995

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

1993

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

Achhilefu, S.

Andersson-Engels, S.

Arridge, S.

Arridge, S. R.

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescence imaging in turbid media,” Appl. Opt. 47, 2303-2311 (2008).
[CrossRef] [PubMed]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. R. Arridge, M. D. Schnall, and A. G. Yodh, “Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696-6716 (2007).
[CrossRef] [PubMed]

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M.A. A. Neil, P.M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384-7391 (2007).
[CrossRef] [PubMed]

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034-2036 (2007).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, O. Dorn, A. Zacharopoulos, and V. Kolehmainen, “Reconstructing absorption and diffusion shape profiles in optical tomography by a level set technique,” Opt. Lett. 31, 471-473 (2006).
[CrossRef] [PubMed]

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

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

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

Avrillier, S.

Bacskai, B. J.

Bangerth, W.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310(2006).
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Non-contact fluorescence optical tomography with scanning patterned illumination,” Opt. Express 14, 6516-6534 (2006).
[CrossRef] [PubMed]

Bassi, A.

Bloch, S. R.

Boas, D. A.

Boverman, G.

Brambilla, M.

Bremer, C.

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

Chance, B.

Choe, R.

Comelli, D.

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2003).
[CrossRef]

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Corlu, A.

Cubeddu, R.

Culver, J. P.

D'Andrea, C.

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescence imaging in turbid media,” Appl. Opt. 47, 2303-2311 (2008).
[CrossRef] [PubMed]

A. Bassi, A. Farina, C. D'Andrea, A. Pifferi, G. Valentini, and R. Cubeddu, “Portable, large-bandwidth time-resolved system for diffuse optical spectroscopy,” Opt. Express 15, 14482-14487 (2007).
[CrossRef] [PubMed]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2003).
[CrossRef]

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

Dayel, M. J.

Delpy, D. T.

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

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

Dorn, O.

Dowling, K.

Dunn, A. K.

Durduran, T.

Dymoke-Bradshaw, A. K. L.

Elson, D. S.

Farina, A.

French, M. W.

French, P. M. W.

Gao, F.

Grosenick, D.

Hajnal, J. V.

Hares, J. D.

He, H.

Hiraoka, M.

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

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

Hwan, K.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310(2006).
[CrossRef] [PubMed]

Joshi, A.

Kim, A. D.

Kolehmainen, V.

Konecky, S. D.

Krasnosselskaia, L. V.

Kumar, A. T. N.

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy, (Plenum, 1999).

Lee, J. H.

Lee, K.

Lesselier, D.

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

Lever, M. J.

Li, X. D.

Loudon, R.

R. Loudon, The Quantum Theory of Light (Oxford U. Press, 1983).

Macdonald, R.

Markel, V. A.

McGinty, J.

Möller, M.

Moscoso, M.

Neil, A. A.

Neil, M. A. A.

Nghiem, H. L.

Ntziachristos, V.

J. Ripoll and V. Ntziachristos, “From finite to infinite volumes: removal of boundaries in diffuse wave imaging,” Phys. Rev. Lett. 96, 173903 (2006).
[CrossRef] [PubMed]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

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

O'Leary, M. A.

Panasyuk, G. Y.

Patwardhan, S. V.

Pifferi, A.

Rasmussen, J. C.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310(2006).
[CrossRef] [PubMed]

Raymond, S. B.

Ripoll, J.

J. Ripoll and V. Ntziachristos, “From finite to infinite volumes: removal of boundaries in diffuse wave imaging,” Phys. Rev. Lett. 96, 173903 (2006).
[CrossRef] [PubMed]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

Rosen, M. A.

Sardini, A.

Schnall, M. D.

Schotland, J. C.

Schulz, R. B.

Schweiger, M.

Sevick-Muraca, E. M.

Skoch, J.

Sobolev, V. V.

V. V. Sobolev, A Treatise on Radiative Transfer (Van Nostrand, 1963).

Soloviev, V. Y.

Stamm, H.

Sterenborg, H. J. C. M.

Svensson, T.

Swartling, J.

Tadi, M.

M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585-1605 (1997).
[CrossRef]

Tahir, K. B.

Tanikawa, Y.

Taroni, P.

Torricelli, A.

Tualle, J. M.

Tung, C.

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

Valentini, G.

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescence imaging in turbid media,” Appl. Opt. 47, 2303-2311 (2008).
[CrossRef] [PubMed]

A. Bassi, A. Farina, C. D'Andrea, A. Pifferi, G. Valentini, and R. Cubeddu, “Portable, large-bandwidth time-resolved system for diffuse optical spectroscopy,” Opt. Express 15, 14482-14487 (2007).
[CrossRef] [PubMed]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2003).
[CrossRef]

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

van Veen, R. L. P.

Wabnitz, H.

Wang, Z. M.

Weissleder, R.

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

Whelan, M.

Yamada, Y.

Yodh, A. G.

Zacharopoulos, A.

Zhang, L.

Zhao, H.

Appl. Opt.

Inverse Probl.

O. Dorn and D. Lesselier, “Level set methods for inverse scattering,” Inverse Probl. 22, R67-R131 (2006).
[CrossRef]

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

M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585-1605 (1997).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. D

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D 35, R61-R76 (2002).
[CrossRef]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2003).
[CrossRef]

Med. Phys.

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176-4183(2006).
[CrossRef] [PubMed]

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

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310(2006).
[CrossRef] [PubMed]

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

Nat. Med.

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

Opt. Express

S. V. Patwardhan, S. R. Bloch, S. Achhilefu, and J. P. Culver “Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,” Opt. Express 13, 2564-2577 (2005).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

Typical Fourier transformed fluorescent images obtained from time-gated images taken by the CCD camera. The top row shows real parts, the bottom row shows imaginary parts.

Fig. 2
Fig. 2

(a) Diagram of the phantom. Background values of the absorption and reduced scattering coefficient are μ a = 0.01 mm 1 and μ s = 0.83 mm 1 . Tube A contains fluorophore. Its absorption coefficient is the same as that of the background and its reduced scattering coefficient is twice lower than the background value, i.e., μ s 0.4 mm 1 . Tube B contains an absorber only. Its absorption is 4 times higher than the background value, i.e., μ a = 0.04 mm 1 . The diameter of tubes A and B is 4 mm and their height is 100 mm . Tube C was filled with fluorophore only. It has background values of μ a and μ s . Its diameter is 3 mm and its length is 50 mm . (b) Hexahedral mesh used in computations.

Fig. 3
Fig. 3

Reconstruction results. First, second, and third rows show slices at y = 40 , 50, and 60 mm , respectively. The first column shows reconstructed quantum yield, the second column shows lifetime, the third shows the diffusion coefficient, and the fourth shows the absorption coefficient.

Equations (28)

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I = 0 n < N I n ,
I n = ς ( ω ) d ω V χ n ( r ) ( | e n u n | 2 + | h n - υ n | 2 ) d 3 r ,
χ n ( r ) = 0 m < M δ ( r r m , n ) ,
ς ( ω ) = 0 l < L δ ( ω ω l ) ,
Λ u n = ϱ n / c ,
Λ = · κ + μ a + i ω / c .
κ = 1 3 ( μ s + μ a ) ,
( u n + 3 γ κ n · u n ) | V = 0 ,
Λ υ n = q u n
q = μ a η 1 + i ω τ .
T = 0 n < N ( I n + J n ) ,
J n = Re ς ( ω ) ( ψ n , Λ u n ϱ n / c ) d ω + Re ς ( ω ) ( φ n , Λ υ n q u n ) d ω ,
H = T d ω V x ω T α ^ x ω d 3 r + d ω V x T β ^ x d 3 r ,
Y ( ω , Δ ω ) d ω ,
Y ( ω , Δ ω ) = V x T ( ω ) β ^ x ( ω + Δ ω ) d 3 r ,
{ Λ l u n , l = ϱ n , l / c , Λ l υ n , l = q l u n , l ,
{ Λ l φ n , l * = 2 χ n ( r ) ( h n , l * υ n , l * ) , Λ l ψ n , l * = 2 χ n ( r ) ( e n , l * u n , l * ) + q l φ n , l * .
Δ x l + 1 j = Δ x l j + ξ j f j ( x l ) + Δ ω β j ξ j x j ,
f 1 = Re 0 n < N ( φ n , l * · υ n , l + ψ n , l * · u n , l ) ,
f 2 = Re 0 n < N ( φ n , l * υ n , l + ψ n , l * u n , l ) + η l R e ϑ l ,
f 3 = μ a , l Re ϑ l , f 4 = ω l Im ( q l ϑ l ) ,
ϑ l = ( 1 + i ω l τ l ) 1 0 n < N φ n , l * u n , l .
0 < ξ j f j Δ x l j f j 2 + ϵ ,
0 < ξ j | ( f j , Δ x l j ) | f j 2 + ϵ .
0 n < N V χ n ( r ) ( | e n , l u n , l | 2 + | h n , l υ n , l | 2 ) d 3 r + Δ ω Y l
s n , l = θ ( ω l ) exp ( i ω l Δ t / 2 ) sinc ( ω l Δ t / 2 ) δ ( r r n ) ,
a l n ( χ n g n , l , e n , l ) n ( χ n g n , l , g n , l ) .
t 0 ( l ) = 1 ω l arctan ( Im a l Re a l ) .

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