Abstract

We describe a novel method for localizing a fluorescent inclusion in a homogeneous turbid medium through the use of time-resolved techniques. Based on the calculation of the mean time of the fluorescence curves, the method does not require a priori knowledge of either the fluorescence lifetime or the mean time of the instrument response function since it adopts a differential processing approach. Theoretical expressions were validated and experiments for assessing the accuracy of localization were carried out on liquid optical phantoms with a small fluorescent inclusion. The illumination and detection optical fibers were immersed in the medium to achieve infinite medium geometry as required by the model used. The experimental setup consisted of a time-correlated single-photon counting system. Submillimeter accuracy was achieved for the localization of the inclusion.

© 2007 Optical Society of America

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  1. C. Bremer, V. Ntziachristos, and R. Weissleder, "Optical-based molecular imaging: contrast agents and potential medical applications," Eur. Rad. 13, 231-243 (2003).
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2006 (2)

2005 (5)

S. Lam, F. Lesage, and X. Intes, "Time domain fluorescent diffuse optical tomography: analytical expressions," Opt. Express 13, 2263-2275 (2005).
[CrossRef] [PubMed]

A. T. N. Kumar, J. Skoch, B. J. Bacskai, D. A. Boas, and A. K. Dunn, "Fluorescence-lifetime-based tomography for turbid media," Opt. Lett. 30, 3347-3349 (2005).
[CrossRef]

B. Ballou, L. A. Ernst, and A. S. Waggoner, "Fluorescence imaging of tumors in vivo," Curr. Med. Chem. 12, 795-805 (2005).
[CrossRef] [PubMed]

K. Licha and C. Olbrich, "Optical imaging in drug discovery and diagnostic applications," Adv. Drug Del. Rev. 57, 1087-1108 (2005).
[CrossRef]

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (2)

2001 (1)

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Opt. 9, 112-147 (1998).
[CrossRef]

1997 (1)

1996 (1)

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

1994 (2)

E. M. Sevick-Muraca and C. L. Burch, "Origin of phosphorescence signals reemitted from tissues," Opt. Lett. 19, 1928-1930 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. Oleary, 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. U.S.A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

1992 (1)

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

Arridge, S. R.

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

Bacskai, B. J.

Ballou, B.

B. Ballou, L. A. Ernst, and A. S. Waggoner, "Fluorescence imaging of tumors in vivo," Curr. Med. Chem. 12, 795-805 (2005).
[CrossRef] [PubMed]

Berger, M.

Boas, D. A.

A. T. N. Kumar, J. Skoch, B. J. Bacskai, D. A. Boas, and A. K. Dunn, "Fluorescence-lifetime-based tomography for turbid media," Opt. Lett. 30, 3347-3349 (2005).
[CrossRef]

D. A. Boas, M. A. Oleary, 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. U.S.A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

Bonner, R. F.

Bremer, C.

C. Bremer, V. Ntziachristos, and R. Weissleder, "Optical-based molecular imaging: contrast agents and potential medical applications," Eur. Rad. 13, 231-243 (2003).

Burch, C. L.

Chance, B.

D. A. Boas, M. A. Oleary, 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. U.S.A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

Cope, M.

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

Cubeddu, R.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

Da Silva, A.

Delpy, D. T.

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

Dinten, J.-M.

Dunn, A. K.

Eppstein, M. J.

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

Ernst, L. A.

B. Ballou, L. A. Ernst, and A. S. Waggoner, "Fluorescence imaging of tumors in vivo," Curr. Med. Chem. 12, 795-805 (2005).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

Godavarty, A.

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

Grosenick, D.

Hall, D.

Intes, X.

Kumar, A. T. N.

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Opt. 9, 112-147 (1998).
[CrossRef]

Laidevant, A.

Lam, S.

Lesage, F.

Licha, K.

K. Licha and C. Olbrich, "Optical imaging in drug discovery and diagnostic applications," Adv. Drug Del. Rev. 57, 1087-1108 (2005).
[CrossRef]

Liebert, A.

Ma, G.

Macdonald, R.

Moller, M.

Nossal, R.

Ntziachristos, V.

C. Bremer, V. Ntziachristos, and R. Weissleder, "Optical-based molecular imaging: contrast agents and potential medical applications," Eur. Rad. 13, 231-243 (2003).

V. Ntziachristos and R. Weissleder, "Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation," Opt. Lett. 26, 893-895 (2001).
[CrossRef]

Olbrich, C.

K. Licha and C. Olbrich, "Optical imaging in drug discovery and diagnostic applications," Adv. Drug Del. Rev. 57, 1087-1108 (2005).
[CrossRef]

Oleary, M. A.

D. A. Boas, M. A. Oleary, 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. U.S.A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

O'Leary, M. A.

M. A. O'Leary, Imaging with Diffuse Photon Density Waves (U. Pennsylvania Press, 1996).

Pifferi, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Opt. 9, 112-147 (1998).
[CrossRef]

Rinneberg, H.

Sevick-Muraca, E. M.

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

E. M. Sevick-Muraca and C. L. Burch, "Origin of phosphorescence signals reemitted from tissues," Opt. Lett. 19, 1928-1930 (1994).
[CrossRef] [PubMed]

Skoch, J.

Taroni, P.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

Torricelli, A.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

Valentini, G.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

Wabnitz, H.

Waggoner, A. S.

B. Ballou, L. A. Ernst, and A. S. Waggoner, "Fluorescence imaging of tumors in vivo," Curr. Med. Chem. 12, 795-805 (2005).
[CrossRef] [PubMed]

Wang, Y.

Weiss, G. H.

Weissleder, R.

C. Bremer, V. Ntziachristos, and R. Weissleder, "Optical-based molecular imaging: contrast agents and potential medical applications," Eur. Rad. 13, 231-243 (2003).

V. Ntziachristos and R. Weissleder, "Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation," Opt. Lett. 26, 893-895 (2001).
[CrossRef]

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Opt. 9, 112-147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Opt. 9, 112-147 (1998).
[CrossRef]

Yodh, A. G.

D. A. Boas, M. A. Oleary, 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. U.S.A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

Yuan, B.

Zhu, Q.

Adv. Drug Del. Rev. (1)

K. Licha and C. Olbrich, "Optical imaging in drug discovery and diagnostic applications," Adv. Drug Del. Rev. 57, 1087-1108 (2005).
[CrossRef]

Appl. Opt. (3)

Curr. Med. Chem. (1)

B. Ballou, L. A. Ernst, and A. S. Waggoner, "Fluorescence imaging of tumors in vivo," Curr. Med. Chem. 12, 795-805 (2005).
[CrossRef] [PubMed]

Eur. Rad. (1)

C. Bremer, V. Ntziachristos, and R. Weissleder, "Optical-based molecular imaging: contrast agents and potential medical applications," Eur. Rad. 13, 231-243 (2003).

Med. Phys. (2)

A. Godavarty, E. M. Sevick-Muraca, and M. J. Eppstein, "Three-dimensional fluorescence lifetime tomography," Med. Phys. 32, 992-1000 (2005).
[CrossRef] [PubMed]

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, "Experimental test of theoretical models for time-resolved reflectance," Med. Phys. 23, 1625-1633 (1996).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (4)

Phys. Med. Biol. (1)

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

Proc. Natl. Acad. Sci. U.S.A. (1)

D. A. Boas, M. A. Oleary, 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. U.S.A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

SIAM J. Opt. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM J. Opt. 9, 112-147 (1998).
[CrossRef]

Other (1)

M. A. O'Leary, Imaging with Diffuse Photon Density Waves (U. Pennsylvania Press, 1996).

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Figures (9)

Fig. 1
Fig. 1

(Color online) Illustration of the experimental setup.

Fig. 2
Fig. 2

(Color online) Experimental data for an inclusion z = 0.74   cm above the fibers (solid line) and data for a measurement without the fluorescent inclusion (dashed line). The fibers are separated by 0 .2   cm and at a depth of 2 .5   cm in a liquid optical phantom.

Fig. 3
Fig. 3

(Color online) Geometry for measurements above the inclusion.

Fig. 4
Fig. 4

(Color online) Measured data for different positions of the inclusion beneath the fibers from 0.24 to 0 .74   cm by steps of 0 .1   cm . The interfiber distance was 0 .2   cm . Amplitudes are arbitrarily represented because the input power was not constant.

Fig. 5
Fig. 5

(Color online) Mean time (calculated from the measurements and subtracted from the mean time of the IRF: t signal t IRF as a function of the depth of the inclusion for measurements above the inclusion.

Fig. 6
Fig. 6

(Color online) Comparison between a measurement for z = 0.74   cm and two simulations ( τ = 1.02 , dashed line; τ = 0.96 , solid line) calculated with Eq. (1) and convolved with the IRF. Curves are normalized to the same area.

Fig. 7
Fig. 7

(Color online) Representation of the grid of detectors and their numbers in the scanning. For each detector, the emission fiber is located 0.2   cm in the x direction.

Fig. 8
Fig. 8

(Color online) Experimental differential mean times (cross line) and those calculated from the fit (circle line) for the 25 measurements above the inclusion at 0.24 cm depth.

Fig. 9
Fig. 9

(Color online) Experimental mean time as a function of total photon path r s r + r r d , with r being the result from the fit, for an inclusion at 0.24   cm depth.

Tables (4)

Tables Icon

Table 1 Phantom Optical Properties and Cy5 Fluorophore Decay Lifetime

Tables Icon

Table 2 Results of the Inversion Formula Eq. (11) for τ = 0.96 ns and τ = 1.02 ns

Tables Icon

Table 3 Results of the Fit for a 0.2 cm Step 5 × 5 Grid of Acquisitions Centered above the Inclusion at (0, 0) for Various z Locations with a 0.1 cm Step

Tables Icon

Table 4 Results of the Fit for a 0.2 cm Step 5 × 5 Grid of Acquisitions Centered at (0, 0) for Different x Locations of the Inclusion

Equations (14)

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S f ( r s r , t ) = α 0 t ϕ x ( r s r , t t 0 ) 1 τ exp ( t t τ ) d t ,
ϕ fluo ( r s r , r r d , t ) = α 0 t S f ( r s r , t , t 0 ) ϕ m ( r r d , t t ) d t = α 0 t 0 t ϕ x ( r s r , t t 0 ) 1 τ exp ( t t τ ) × ϕ m ( r r d , t t ) d t d t .
ϕ fluo ( r s r , r r d , t ) = α 0 t d t e r s r + r r d r s r r r d 1 [ 4 π c ( t t e ) ] 3 / 2 × exp [ μ a c ( t t e ) ] × exp [ ( r s r + r r d ) 2 4 c D ( t t e ) ] exp ( t e / τ ) τ ,
t = t g ( t ) d t g ( t ) d t .
Φ fluo ( r s r , r r d , ω ) = α exp [ i k ( r s r + r r d ) ] r s r r r d 1 1 + i ω τ ,
t = i Φ ω | ω = 0 × 1 Φ ( ω ) | ω = 0 ,
t theo = r s r + r r d 2 c μ a D + τ .
signal fluo = measure fluo T fluo T I L measure I L .
t signal = t theo + t IRF .
t signal = r s r + r r d 2 c μ a D + τ + t I R F .
z = [ ( c μ a D ) 2 ( t signal τ t IRF ) 2 ( d / 2 ) 2 ] 1 / 2 ,
Δ t signal , i = t signal , i min ( t signal , i ) , i [ 1 , N ] = r s r , i + r r d , i 2 c μ a D r s r , min + r r d , min 2 c μ a D .
χ 2 ( x , y , z ) = i ( Δ t signal , i Δ t theo , i ) 2 .
Δ t theo , i = t theo , i t theo , j , i [ 1 , N ] ,

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