Abstract

Imaging of oxygen in tissue in three dimensions can be accomplished by using the phosphorescence quenching method in combination with diffuse optical tomography. We experimentally demonstrate the feasibility of tomographic imaging of oxygen by phosphorescence lifetime. Hypoxic phantoms were immersed in a cylinder with scattering solution equilibrated with air. The phantoms and the medium inside the cylinder contained near-infrared phosphorescent probe(s). Phosphorescence at multiple boundary sites was registered in the time domain at different delays (td) following the excitation pulse. The duration of the excitation pulse (tp) was regulated to optimize the contrast in the images. The reconstructed integral intensity images, corresponding to delays td, were fitted exponentially to give the phosphorescence lifetime image, which was converted into the three-dimensional image of oxygen concentrations in the volume. The time-independent diffusion equation and the finite element method were used to model the light transport in the medium. The inverse problem was solved by the recursive maximum entropy method. We provide what we believe to be the first example of oxygen imaging in three dimensions using long-lived phosphorescent probes and establish the potential of these probes for diffuse optical tomography.

© 2006 Optical Society of America

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  59. Similar porphyrin-dendrimers have been described in S. A. Vinogradov, "Arylamide dendrimers with flexible linkers via haloacyl halide method," Org. Lett. 7, 1761-1764 (2005).
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    [CrossRef]

2006 (1)

2005 (9)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "The inverse source problem based on the radiative transfer equation in optical molecular imaging," J. Comput. Phys. 202, 323-345 (2005).
[CrossRef]

G. Zacharakis, H. Kambara, H. Shih, J. Ripoll, J. Grimm, Y. Saeki, R. Weissleder, and V. Ntziachristos, "Volumetric tomography of fluorescent proteins through small animals in vivo," Proc. Natl. Acad. Sci. U.S.A. 102, 18252-18257 (2005).
[CrossRef] [PubMed]

G. B. Arden, R. L. Sidman, W. Arap, and R. O. Schlingemann, "Spare the rod and spoil the eye," Br. J. Ophthamol. 89, 764-769 (2005).
[CrossRef]

F. Pena and A. M. Ramirez, "Hypoxia-induced changes in neuronal network properties," Mol. Neurobiol. 32, 251-283 (2005).
[CrossRef] [PubMed]

O. S. Finikova, A. V. Cheprakov, and S. A. Vinogradov, "Synthesis and luminescence of soluble meso-unsubstituted tetrabenzo- and tetranaphtho[2,3]porphyrins," J. Org. Chem. 70, 9562-9572 (2005), and references therein.
[CrossRef] [PubMed]

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

A. Douiri, M. Schweiger, J. Railey, and S. Arridge, "Local diffusion regularization method for optical tomography reconstruction using robust statistics," Opt. Lett. 30, 2439-2441 (2005), and references therein.
[CrossRef] [PubMed]

L. S. Ziemer, W. M. F. Lee, S. A. Vinogradov, C. Sehgal, and D. F. Wilson, "Oxygen distribution in murine tumors: characterization using oxygen-dependent quenching of phosphorescence," J. Appl. Physiol. 98, 1503-1510 (2005).
[CrossRef]

Similar porphyrin-dendrimers have been described in S. A. Vinogradov, "Arylamide dendrimers with flexible linkers via haloacyl halide method," Org. Lett. 7, 1761-1764 (2005).
[CrossRef] [PubMed]

2004 (3)

V. Y. Soloviev, D. F. Wilson, and S. A. Vinogradov, "Phosphorescence lifetime imaging in turbid media: the inverse problem and experimental image reconstruction," Appl. Opt. 43, 564-574 (2004).
[CrossRef] [PubMed]

D. M. Ferriero, "Medical progress--neonatal brain injury," New Eng. J. Med. 351, 1985-1995 (2004).
[CrossRef] [PubMed]

V. A. Markel, "Modified spherical harmonics method for solving the radiative transport equation," Waves Random Media 14, L13-L19 (2004).
[CrossRef]

2003 (5)

A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical diffusion tomography," Appl. Opt. 42, 3081-3094 (2003).
[CrossRef] [PubMed]

S. M. Evans and C. J. Koch, "Prognostic significance of tumor oxygenation in humans," Cancer Lett. 195, 1-16 (2003).
[CrossRef] [PubMed]

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, "The role of diffuse optical spectroscopy in the clinical management of breast cancer," Dis. Markers 19, 95-105 (2003).

I. B. Rietveld, E. Kim, and S. A. Vinogradov, "Dendrimers with tetrabenzoporphyrin cores: near-infrared phosphors for in vivo oxygen imaging," Tetrahedron 59, 3821-3831 (2003).
[CrossRef]

V. Y. Soloviev, D. F. Wilson, and S. A. Vinogradov, "Phosphorescence lifetime imaging in turbid media: the forward problem," Appl. Opt. 42, 113-123 (2003).
[CrossRef] [PubMed]

2002 (6)

E. Shives, Y. Xu, and H. Jiang, "Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye," Opt. Express 10, 1557-1562 (2002).
[PubMed]

V. V. Rozhkov, D. F. Wilson, and S. A. Vinogradov, "Phosphorescent Pd porphyrin-dendrimers: tuning core accessibility by varying the hydrophobicity of the dendritic matrix," Macromolecules 35, 1991-1993 (2002).
[CrossRef]

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

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer--Part 1: Forward model," J. Quant. Spectrosc. Radiat. Transf. 72, 691-713 (2002).
[CrossRef]

I. Dunphy, S. A. Vinogradov, and D. F. Wilson, "Oxyphor R2 and G2: phosphors for measuring oxygen by oxygen-dependent quenching of phosphorescence," Anal. Biochem. 310, 191-198 (2002).
[CrossRef] [PubMed]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, "Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography," Proc. Natl. Acad. Sci. U.S.A. 99, 9619-9624 (2002).
[CrossRef] [PubMed]

2001 (3)

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, and D. F. Wilson, "Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples," Rev. Sci. Instrum. 72, 3396-3406 (2001).
[CrossRef]

B. W. Pogue, S. Geimer, T. O. McBride, S. D. Jiang, U. L. Osterberg, and K. D. Paulsen, "Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction," Appl. Opt. 40, 588-600 (2001).
[CrossRef]

J. R. Ballinger, "Imaging hypoxia in tumors," Semin. Nucl. Med. 31, 321-329 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (2)

A. A. Istratov and O. F. Vyvenko, "Exponential analysis in physical phenomena," Rev. Sci. Instrum. 70, 1233-1257 (1999).
[CrossRef]

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

1998 (1)

1997 (3)

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

J. H. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, and M. Fabiani, "Measurements of scattering and absorption changes in muscle and brain," Phil. Trans. R. Soc. London , Ser. B 352, 727-735 (1997).
[CrossRef]

1996 (2)

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, and D. F. Wilson, "Noninvasive imaging of the distribution of oxygen in tissue in vivo using near-infrared phosphors," Biophys. J. 70, 1609-1617 (1996).
[CrossRef] [PubMed]

M. A. O'Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, "Fluorescence lifetime imaging in turbid media," Opt. Lett. 21, 158-160 (1996).
[CrossRef] [PubMed]

1994 (2)

1993 (2)

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

H. W. Engl and G. Landl, "Convergence rates for maximum-entropy regularization," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 30, 1509-1536 (1993).

1992 (1)

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

1988 (1)

W. L. Rumsey, J. M. Vanderkooi, and D. F. Wilson, "Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue," Science 241, 1649-1651 (1988).
[CrossRef] [PubMed]

1987 (1)

J. M. Vanderkooi, G. Maniara, T. J. Green, and D. F. Wilson, "An optical method for measurement of dioxygen concentration based on quenching of phosphorescence," J. Biol. Chem 262, 5476-5482 (1987).
[PubMed]

1985 (1)

A. K. Livesey and J. Skilling, "Maximum entropy theory," Acta Crystal. A41, 113-122 (1985).
[CrossRef]

1984 (1)

J. Skilling and R. K. Bryan, "Maximum entropy image reconstruction: general algorithm," Mon. Not. R. Astron. Soc. 211, 111-124 (1984).

1978 (1)

J. G. McWhirter and E. R. Pike, "On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind," J. Phys. 11, 1729-1745 (1978).
[CrossRef]

1972 (1)

R. I. Shrager, "Quadratic programming for nonlinear regression," Commun. ACM 15, 41-45 (1972).
[CrossRef]

Apreleva, S. V.

Arap, W.

G. B. Arden, R. L. Sidman, W. Arap, and R. O. Schlingemann, "Spare the rod and spoil the eye," Br. J. Ophthamol. 89, 764-769 (2005).
[CrossRef]

Arden, G. B.

G. B. Arden, R. L. Sidman, W. Arap, and R. O. Schlingemann, "Spare the rod and spoil the eye," Br. J. Ophthamol. 89, 764-769 (2005).
[CrossRef]

Arridge, S.

Arridge, S. R.

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

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

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

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

Arsenin, V.

A. Tikhonov and V. Arsenin, Solutions of Ill-Posed Problems (Wiley, London, 1977).

Atwater, B. W.

J. Saltiel and B. W. Atwater, "Spin-statistical factors in diffusion controlled reactions," in Advances in Photochemistry, D. H. Volman, G. S. Hammond, and K. Gollnick, eds. (Wiley, 1988) pp. 1-90.
[CrossRef]

Ballinger, J. R.

J. R. Ballinger, "Imaging hypoxia in tumors," Semin. Nucl. Med. 31, 321-329 (2001).
[CrossRef] [PubMed]

Barbour, R. L.

J. H. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

Beuthan, J.

A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, "Optical tomography using the time-independent equation of radiative transfer--Part 1: Forward model," J. Quant. Spectrosc. Radiat. Transf. 72, 691-713 (2002).
[CrossRef]

Boas, D. A.

Bouman, C. A.

Bryan, R. K.

J. Skilling and R. K. Bryan, "Maximum entropy image reconstruction: general algorithm," Mon. Not. R. Astron. Soc. 211, 111-124 (1984).

Burch, C. L.

Butler, J.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, "The role of diffuse optical spectroscopy in the clinical management of breast cancer," Dis. Markers 19, 95-105 (2003).

Case, M. C.

M. C. Case and P. F. Zweifel, Linear Transport Theory (Addison-Wesley, 1967).

Cerussi, A. E.

N. Shah, A. E. Cerussi, D. Jakubowski, D. Hsiang, J. Butler, and B. J. Tromberg, "The role of diffuse optical spectroscopy in the clinical management of breast cancer," Dis. Markers 19, 95-105 (2003).

Chance, B.

Chang, J. H.

J. H. Chang, H. L. Graber, and R. L. Barbour, "Imaging of fluorescence in highly scattering media," IEEE Trans. Biomed. Eng. 44, 810-822 (1997).
[CrossRef] [PubMed]

Chen, A.

A. Chen and E. M. Sevick-Muraca, "On the use of phophorescent and fluorescent dyes for lifetime-based imaging within tissues," in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, B. Chance and A. A. Alfano, eds. (SPIE Press, 1997), pp. 129-138.
[PubMed]

Cheprakov, A. V.

O. S. Finikova, A. V. Cheprakov, and S. A. Vinogradov, "Synthesis and luminescence of soluble meso-unsubstituted tetrabenzo- and tetranaphtho[2,3]porphyrins," J. Org. Chem. 70, 9562-9572 (2005), and references therein.
[CrossRef] [PubMed]

Christakos, G.

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The phosphorescence quantum yield Phi(r) at the point r inside the medium is dependent on the local concentration of the quencher (oxygen) and is proportional to the phosphorescence lifetime τ(r). The quantum yield in the absence of the quencher Phi0 is the same for all probe molecules throughout the volume, provided that the probe molecules do not interact with the environment. Dendritically protected phosphorescent probes are designed to exclude such interactions. They have been shown to retain their photophysical properties in physiological environments, e.g., in the blood serum and interstitial fluid.

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Figures (4)

Fig. 1
Fig. 1

Phosphorescent probes (a) Oxyphor G2, (b) Oxyphor G3, and (c) their absorption and emission spectra.

Fig. 2
Fig. 2

(Color online) Simulation of dependence of contrast ratio κ on pulse duration t p for different delays t d . Two volumes with pO 2 ( 1 ) = 50   mm   Hg - 1 ( τ 1 = 25 μ s ) and pO 2 ( 2 ) = 10   mm   Hg - 1 ( τ 2 = 91 μ s ) , containing equal amounts of phosphorescent probe ( k q = 700   mm   Hg - 1 s - 1 , τ 0 = 250 μ s ) , were equally excited by a rectangular pulse of duration t p . Delays t d (start of the data integration) correspond to the moments of time when the intensity of the decay with longer lifetime ( τ 2 ) was reduced n times: t d ( n ) = τ 2   ln ( n ) .

Fig. 3
Fig. 3

(Color online) Numerical simulation and recovery of phosphorescence lifetime distributions in the scattering cylinder (dimensions in millimeters). Dots on the periphery of the cylinder correspond to the positions of the source and detector sites. Only cross sections (xz plane) of complete 3D images are shown. (a) Integral intensity images recovered by the MEM from the data obtained at different delays t d (shown above the images in microseconds). Data set (a) was produced using a 70 μs excitation pulse ( t p = 70 μ s ) , SNR = 135 . Lifetime images (b) and (c) were obtained by fitting the intensity images either (b) including all the images in the series, t d = 13 472 μ s , or (c) ignoring the images taken at shorter delays t d = 36 472 μ s . The lifetime scale (microseconds) is shown on the left in pseudocolor. Images (b) and (c) were produced using excitation pulses of different lengths ( t p = 10 , 70 , and 250 μ s ).

Fig. 4
Fig. 4

(Color online) Experimental image reconstructions in a cylinder. xz cross sections of complete 3D images are shown (dimensions in millimeters). Excitation pulse was 200 μ s long ( t p = 200 μ s ) . (a) Oxygen image and (b) phosphorescence lifetime image of a phantom ( τ 2 = 190 μ s , pO 2 = 0.2   Torr , Oxyphor G2) in solution with a low background ( τ 1 < 5 μ s ) . Lifetime image was recovered using a series of MEM-reconstructed phosphorescence intensity images (e), with the first image (not shown in the figure) taken after a delay t d 1 = 27 μ s . (c) and (d) Lifetime images of the phantom ( τ 2 = 170 μ s ) in solution with strong background phosphorescence ( τ 1 = 45 μ s , Oxyphor G3). Lifetime image obtained from intensity images taken after delays (c) t d 1 = 20 μ s and (d) t d 1 = 60 μ s .

Equations (42)

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τ 0 / τ = I 0 / I = 1 + k q × τ 0 × pO 2 ,
k ( r , λ ex ) U ex ( r , t ) + [ μ a t ( r , λ ex ) + μ a p ( r , λ ex ) ]
× U ex ( r , t ) + 1 c U ex ( r , t ) t = q ex ( m s , t ) ,
k ( r , λ p ) U p ( r , t ) + μ a t ( r , λ p ) U p ( r , t )
+ 1 c U p ( r , t ) t = q p ( r s , t ) ,
k ( r , λ ) = 1 3 [ μ a ( r , λ ) + μ s ( r , λ ) ] ,
μ s ( r , λ ) = μ s ( r , λ ) ( 1 p 1 ) ,
U ( m ) + 2 k ( m ) A U ( m ) n 0 = 0 ,
q ex ( m s , t ) = δ ( m m s ) δ ( t t 0 ) .
q p ( r s , t ) = U ex ( r s , t ) μ a p ( r s , λ ex ) ϕ 0 δ ( r r s ) exp [ - t τ ( r s ) ] .
S ex ( r s ) = U ex ( r s , t ) d t .
− ∇ k ( r , λ ex ) U ex ( r ) + [ μ a t ( r , λ ex ) + μ a p ( r , λ ex ) ] U ex ( r )
=  q ex ( m s ) ,
− ∇ k ( r , λ p ) U p ( r ) + μ a p ( r , λ p ) U p ( r ) = q p ( r s ) ,
U ( r , m s , m d , t ) = ϕ ( r ) μ a p ( r , λ ex ) U ex ( m s , r ) U p ( r , m d ) × exp [ - t - t 0 τ ( r ) ] d r ,
M ( m d , t d ) = 2 A t d Γ ( m d , t ) d t ,
Γ ( m d , t ) = 1 2 A U ( m d , t ) ,
U ( m s , m d , t ) = V K ( r , m s , m d ) q [ I 0 ( r ) , τ ( r ) , t ] d 3 r ,
K ( r , m s , m d ) = U ex ( m s , r ) U p ( r , m d ) .
q [ I 0 ( r ) , τ ( r ) , t ] = I 0 ( r ) exp [ - t τ ( r ) ] ,
I 0 ( r ) = ϕ 0 μ a p ( r , λ ex ) ,
M ( m s , m d , t d ) = V K ( r , m s , m d ) t d q [ I 0 ( r ) , τ ( r ) , t ] × d t d 3 r ,
P ( r , t d ) = t d I 0 ( r ) exp [ - t τ ( r ) ] d t = τ ( r ) I 0 ( r ) exp [ - t d τ ( r ) ] ,
M ( m s , m d , t d ) = V K ( r , m s , m d ) P ( r , t d ) d 3 r ,
g ( r , t ) = c × τ ( r ) exp [ - t τ ( r ) ] ,
m = Kp + η
f ( x ) = n p n K ( p n , x ) ,
χ 2 = 1 M i 1 σ i 2 [ f ( x i ) m i ] 2 ,
χ 2 = 1 2 ( p , H p ) ( g o , p ) + i m i 2 σ i 2 ,
H m n = 2 M i 1 σ i 2 K m ( x i ) K n ( x i )
g n o = 2 M i 1 σ i 2 K n ( x i ) m i .
Z = ( g o , p ) 1 2 ( p , H p ) ,
S = n p n  ln   p n b n = ( p , l ) ,
Q = S β χ 2 .
Q = γ Q = χ 2 + γ S = Z γ ( p , l ) = ( g o , p ) 1 2 ( p , H p ) γ ( p , l ) = ( g o , p ) 1 2 [ p , ( H + νΔ ) p ] ,
Δ n n = ln ( p n / b n ) p n ,
Δ m n = 0 ; m n .
δ = 1 2 χ 2 χ 2 S S ,
C ( t d ) = τ 2 τ 1  exp ( τ 2 τ 1 τ 1 τ 2 t d ) .
I ( t ) = o t L ( t ) I 0   exp ( - t t τ ) d t ,
R ( t p ) = τ 2 [ 1 exp ( - t p τ 2 ) ] τ 1 [ 1 exp ( - t p τ 1 ) ] .
κ ( t p , t d ) = R ( t p ) C ( t d ) .

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