Abstract

Bioluminescence imaging (BLI) makes it possible to elucidate molecular and cellular signatures to better understand the effects of human disease in small animal models in vivo. The unambiguous three-dimensional bioluminescent source information obtained by bioluminescence tomography (BLT) could further facilitate its applications in biomedicine. However, to the best of our knowledge, the existing gradient-type reconstruction methods in BLT are inefficient, and often require a relatively small volume of interest (VOI) for feasible results. In this paper, a fast generalized graph cuts based reconstruction method for BLT is presented, which is to localize the bioluminescent source in heterogeneous mouse tissues via max-flow/min-cut algorithm. Since the original graph cuts theory can only handle graph-representable problem, the quadratic pseudo-boolean optimization is incorporated to make the graph representable and tractable, which is called generalized graph cuts (GGC). The internal light source can be reconstructed from the whole domain, so a priori knowledge of VOI can be avoided in this method. In the simulation validations, the proposed method was validated in a heterogeneous mouse atlas, and the source can be localized reliably and efficiently by GGC; and compared with gradient-type method, the proposed method is about 25-50 times faster. Moreover, the experiments for sensitivity to the measurement errors of tissue optical properties demonstrate that, the reconstruction quality is not much affected by mismatch of parameters. In what follows, in vivo mouse BLT reconstructions further demonstrated the potential and effectiveness of the generalized graph cut based reconstruction method.

© 2010 Optical Society of America

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2009 (3)

2008 (4)

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography," Phys. Med. Biol. 53,3921-3942 (2008).
[CrossRef] [PubMed]

G.-R. Yan, J. Tian, S.-P. Zhu, Y.-K. Dai, and C.-H. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," J. X-Ray Sci. and Technol. 16,225-234 (2008).

R. Weissleder and M. J. Pittet, "Imaging in the era of molecular oncology," Nature 452,580-589 (2008).
[CrossRef]

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, "Molecular imaging in drug development," Nat. Rev. Drug Discov. 7,591-607 (2008).
[CrossRef] [PubMed]

2007 (4)

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007:1-12 (2007).
[CrossRef]

J. Virostko, A. C. Powers, and E. D. Jansen, "Validation of luminescent source reconstruction using single-view spectrally resolved bioluminescence images," App. Opt. 46,2540-2547 (2007).
[CrossRef]

V. Kolmogorov and C. Rother, "Minimizing nonsubmodular functions with graph cuts-a review," IEEE Trans. Patt. Anal. and Mach. Intell. 9,1274-1279 (2007).
[CrossRef]

2006 (7)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system," Phys. Med. Biol. 51,2045-2053 (2006).
[CrossRef] [PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, "Spectrally resolved bioluminescence optical tomography," Opt. Lett. 31,365-367 (2006).
[CrossRef] [PubMed]

W.-X. Cong, D. Kumar, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

G. Wang, W.-X. Cong, K. Durairaj, X. Qian, H-O. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, "In vivo mouse studies with bioluminescence tomography," Opt. Express 14,7801-7809 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7801.
[CrossRef] [PubMed]

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, "Iterative reconstruction method for light emitting sources based on the diffusion equation," Med. Phys. 33, 61-68 (2006).
[CrossRef] [PubMed]

Y.-J. Lv, J. Tian, G. Wang, W.-X. Cong, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

G. Wang, H.-O. Shen, W.-X. Cong, S. Zhao, and G.-W. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-18-6756.
[CrossRef] [PubMed]

2005 (4)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

W.-X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?id=140930.
[CrossRef] [PubMed]

2004 (5)

M. Jiang and G. Wang, "Image reconstruction for bioluminescence tomography," Proc. SPIE,  5535,335-351 (2004).
[CrossRef]

X. Gu, Q. Zhang, L. Larcom, and H.-B. Jiang, "Three dimensional bioluminescence tomography with model based reconstruction," Opt. Express 12,3996-4000 (2004), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-12-17-3996.
[CrossRef] [PubMed]

G. Wang, Y. Li, and M. Jiang, "Uniqueness theorems in bioluminescence tomography," Med. Phys. 31,2289-2299 (2004).
[CrossRef] [PubMed]

V. Kolmogorov and R. Zabih, "What energy functions can be minimized via graph cuts?" IEEE Trans. Patt. Anal. and Mach. Intell. 26,147-159 (2004).
[CrossRef]

Y. Boykov and V. Kolmogorov, "An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision," IEEE Trans. Patt. Anal. and Mach. Intell. 26,1124-1137 (2004).
[CrossRef]

2001 (3)

Y. Boykov, O. Veksler, and R. Zabih, "Efficient approximate energy minimization via graph cuts," IEEE Trans. Patt. Anal. and Mach. Intell. 20,1222-1239 (2001).
[CrossRef]

V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, "Diffuse optical tomography of highly heterogeneous media," IEEE Trans. Med. Imaging 20,470-478 (2001).
[CrossRef] [PubMed]

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light emitting probes," J. Biomed. Opt. 6,432-440 (2001).
[CrossRef] [PubMed]

1988 (1)

A. V. Goldberg and R. E. Tarjan, "A new approach to the maximum-flow problem," J. ACM 35,921-940 (1988).
[CrossRef]

1984 (1)

P. L. Hammer, P. Hansen, and B. Simeone, "Roof duality, complementation and persistency in quadratic 0-1 optimization," Math. Program. 28,121-155 (1984).
[CrossRef]

1956 (1)

L. Ford and D. Fulkerson, "Maximal flow through a network," Canad. J. Math. 8,309-404 (1956).
[CrossRef]

Ahn, S.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography," Phys. Med. Biol. 53,3921-3942 (2008).
[CrossRef] [PubMed]

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system," Phys. Med. Biol. 51,2045-2053 (2006).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

Antich, P. P.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, "Iterative reconstruction method for light emitting sources based on the diffusion equation," Med. Phys. 33, 61-68 (2006).
[CrossRef] [PubMed]

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Blake, A.

V. Lempitsky, C. Rother, S. Roth, and A. Blake, "Fusion moves for markov random field optimization," IEEE Trans. Patt. Anal. and Mach. Intell., in press.

Bouman, C. A.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography," Phys. Med. Biol. 53,3921-3942 (2008).
[CrossRef] [PubMed]

Boykov, Y.

Y. Boykov and V. Kolmogorov, "An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision," IEEE Trans. Patt. Anal. and Mach. Intell. 26,1124-1137 (2004).
[CrossRef]

Y. Boykov, O. Veksler, and R. Zabih, "Efficient approximate energy minimization via graph cuts," IEEE Trans. Patt. Anal. and Mach. Intell. 20,1222-1239 (2001).
[CrossRef]

Cable, M. D.

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light emitting probes," J. Biomed. Opt. 6,432-440 (2001).
[CrossRef] [PubMed]

Chance, B.

V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, "Diffuse optical tomography of highly heterogeneous media," IEEE Trans. Med. Imaging 20,470-478 (2001).
[CrossRef] [PubMed]

Chatziioannou, A. F.

Y.-J. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman and A. F. Chatziioannou, "Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework," Opt. Express 17,16681-16695 (2009), http://www.opticsinfobase.org/abstract.cfm?URI=oe-17-19-16681.
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system," Phys. Med. Biol. 51,2045-2053 (2006).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50,4225-4241 (2005).
[CrossRef] [PubMed]

Chaudhari, A. J.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography," Phys. Med. Biol. 53,3921-3942 (2008).
[CrossRef] [PubMed]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Cong, A.

Cong, W.-X.

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

G. Wang, H.-O. Shen, W.-X. Cong, S. Zhao, and G.-W. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-18-6756.
[CrossRef] [PubMed]

Y.-J. Lv, J. Tian, G. Wang, W.-X. Cong, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

W.-X. Cong, D. Kumar, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

G. Wang, W.-X. Cong, K. Durairaj, X. Qian, H-O. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, "In vivo mouse studies with bioluminescence tomography," Opt. Express 14,7801-7809 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7801.
[CrossRef] [PubMed]

W.-X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?id=140930.
[CrossRef] [PubMed]

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Coquoz, O.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007:1-12 (2007).
[CrossRef]

Dai, Y.-K.

G.-R. Yan, J. Tian, S.-P. Zhu, Y.-K. Dai, and C.-H. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," J. X-Ray Sci. and Technol. 16,225-234 (2008).

Darvas, F.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography," Phys. Med. Biol. 53,3921-3942 (2008).
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Dehghani, H.

Dinkelborg, L. M.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, "Molecular imaging in drug development," Nat. Rev. Drug Discov. 7,591-607 (2008).
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Durairaj, K.

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L. Ford and D. Fulkerson, "Maximal flow through a network," Canad. J. Math. 8,309-404 (1956).
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L. Ford and D. Fulkerson, "Maximal flow through a network," Canad. J. Math. 8,309-404 (1956).
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J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, "Molecular imaging in drug development," Nat. Rev. Drug Discov. 7,591-607 (2008).
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A. V. Goldberg and R. E. Tarjan, "A new approach to the maximum-flow problem," J. ACM 35,921-940 (1988).
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Hammer, P. L.

P. L. Hammer, P. Hansen, and B. Simeone, "Roof duality, complementation and persistency in quadratic 0-1 optimization," Math. Program. 28,121-155 (1984).
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Hansen, P.

P. L. Hammer, P. Hansen, and B. Simeone, "Roof duality, complementation and persistency in quadratic 0-1 optimization," Math. Program. 28,121-155 (1984).
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Herschman, H.

Hielscher, A. H.

V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, "Diffuse optical tomography of highly heterogeneous media," IEEE Trans. Med. Imaging 20,470-478 (2001).
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Hoffman, E.

Jansen, E. D.

J. Virostko, A. C. Powers, and E. D. Jansen, "Validation of luminescent source reconstruction using single-view spectrally resolved bioluminescence images," App. Opt. 46,2540-2547 (2007).
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Jiang, H.-B.

Jiang, M.

W.-X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?id=140930.
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M. Jiang and G. Wang, "Image reconstruction for bioluminescence tomography," Proc. SPIE,  5535,335-351 (2004).
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G. Wang, Y. Li, and M. Jiang, "Uniqueness theorems in bioluminescence tomography," Med. Phys. 31,2289-2299 (2004).
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Jiang, S.

Kolmogorov, V.

V. Kolmogorov and C. Rother, "Minimizing nonsubmodular functions with graph cuts-a review," IEEE Trans. Patt. Anal. and Mach. Intell. 9,1274-1279 (2007).
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Y. Boykov and V. Kolmogorov, "An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision," IEEE Trans. Patt. Anal. and Mach. Intell. 26,1124-1137 (2004).
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V. Kolmogorov and R. Zabih, "What energy functions can be minimized via graph cuts?" IEEE Trans. Patt. Anal. and Mach. Intell. 26,147-159 (2004).
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Kumar, D.

Kuo, C.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007:1-12 (2007).
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Larcom, L.

Leahy, R. M.

S. Ahn, A. J. Chaudhari, F. Darvas, C. A. Bouman, and R. M. Leahy, "Fast iterative image reconstruction methods for fully 3D multispectral bioluminescence tomography," Phys. Med. Biol. 53,3921-3942 (2008).
[CrossRef] [PubMed]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
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Lempitsky, V.

V. Lempitsky, C. Rother, S. Roth, and A. Blake, "Fusion moves for markov random field optimization," IEEE Trans. Patt. Anal. and Mach. Intell., in press.

Lewis, M. A.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, "Iterative reconstruction method for light emitting sources based on the diffusion equation," Med. Phys. 33, 61-68 (2006).
[CrossRef] [PubMed]

Li, H.

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
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Y.-J. Lv, J. Tian, G. Wang, W.-X. Cong, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
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Li, Y.

G. Wang, Y. Li, and M. Jiang, "Uniqueness theorems in bioluminescence tomography," Med. Phys. 31,2289-2299 (2004).
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Liu, J.-T.

Liu, Y.

Lu, Y.-J.

Luo, J.

Lv, Y.-J.

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
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Y.-J. Lv, J. Tian, G. Wang, W.-X. Cong, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
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Machado, H. B.

McCray, P.

McLennan, G.

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
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Nelson, M. B.

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light emitting probes," J. Biomed. Opt. 6,432-440 (2001).
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Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, "Diffuse optical tomography of highly heterogeneous media," IEEE Trans. Med. Imaging 20,470-478 (2001).
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Patterson, M. S.

Paulsen, K. D.

Pittet, M. J.

R. Weissleder and M. J. Pittet, "Imaging in the era of molecular oncology," Nature 452,580-589 (2008).
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Pogue, B. W.

Powers, A. C.

J. Virostko, A. C. Powers, and E. D. Jansen, "Validation of luminescent source reconstruction using single-view spectrally resolved bioluminescence images," App. Opt. 46,2540-2547 (2007).
[CrossRef]

Qian, X.

Qin, C.-H.

J.-C. Feng, K.-B. Jia, C.-H. Qin, G.-R. Yan, S.-P. Zhu, X. Zhang, J.-T. Liu, and J. Tian, "Three-dimensional Bioluminescence Tomography based on Bayesian Approach," Opt. Express 17,16834-16848 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-19-16834.
[CrossRef] [PubMed]

S.-P. Zhu, J. Tian, G.-R. Yan, C.-H. Qin, and J.-C. Feng, "Cone beam micro-CT system for small animal imaging and performance evaluation," Int. J. Biomed. Imaging, doc. ID 960573 (2009).

G.-R. Yan, J. Tian, S.-P. Zhu, Y.-K. Dai, and C.-H. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," J. X-Ray Sci. and Technol. 16,225-234 (2008).

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
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Rannou, F. R.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system," Phys. Med. Biol. 51,2045-2053 (2006).
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G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study," Phys. Med. Biol. 50,4225-4241 (2005).
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Rice, B. W.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007:1-12 (2007).
[CrossRef]

B. W. Rice, M. D. Cable, and M. B. Nelson, "In vivo imaging of light emitting probes," J. Biomed. Opt. 6,432-440 (2001).
[CrossRef] [PubMed]

Richer, E.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, "Iterative reconstruction method for light emitting sources based on the diffusion equation," Med. Phys. 33, 61-68 (2006).
[CrossRef] [PubMed]

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

Roth, S.

V. Lempitsky, C. Rother, S. Roth, and A. Blake, "Fusion moves for markov random field optimization," IEEE Trans. Patt. Anal. and Mach. Intell., in press.

Rother, C.

V. Kolmogorov and C. Rother, "Minimizing nonsubmodular functions with graph cuts-a review," IEEE Trans. Patt. Anal. and Mach. Intell. 9,1274-1279 (2007).
[CrossRef]

V. Lempitsky, C. Rother, S. Roth, and A. Blake, "Fusion moves for markov random field optimization," IEEE Trans. Patt. Anal. and Mach. Intell., in press.

Shen, H.-O.

Shen, H-O.

Simeone, B.

P. L. Hammer, P. Hansen, and B. Simeone, "Roof duality, complementation and persistency in quadratic 0-1 optimization," Math. Program. 28,121-155 (1984).
[CrossRef]

Sinn, P.

Slavine, N. V.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, "Iterative reconstruction method for light emitting sources based on the diffusion equation," Med. Phys. 33, 61-68 (2006).
[CrossRef] [PubMed]

Smith, D. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging" Phys. Med. Biol. 50,5421-5441 (2005).
[CrossRef] [PubMed]

Stout, D.

Tarjan, R. E.

A. V. Goldberg and R. E. Tarjan, "A new approach to the maximum-flow problem," J. ACM 35,921-940 (1988).
[CrossRef]

Tian, J.

S.-P. Zhu, J. Tian, G.-R. Yan, C.-H. Qin, and J.-C. Feng, "Cone beam micro-CT system for small animal imaging and performance evaluation," Int. J. Biomed. Imaging, doc. ID 960573 (2009).

J.-C. Feng, K.-B. Jia, C.-H. Qin, G.-R. Yan, S.-P. Zhu, X. Zhang, J.-T. Liu, and J. Tian, "Three-dimensional Bioluminescence Tomography based on Bayesian Approach," Opt. Express 17,16834-16848 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-19-16834.
[CrossRef] [PubMed]

G.-R. Yan, J. Tian, S.-P. Zhu, Y.-K. Dai, and C.-H. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," J. X-Ray Sci. and Technol. 16,225-234 (2008).

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Y.-J. Lv, J. Tian, G. Wang, W.-X. Cong, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Troy, T. L.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007:1-12 (2007).
[CrossRef]

van Bruggen, N.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, "Molecular imaging in drug development," Nat. Rev. Drug Discov. 7,591-607 (2008).
[CrossRef] [PubMed]

Veksler, O.

Y. Boykov, O. Veksler, and R. Zabih, "Efficient approximate energy minimization via graph cuts," IEEE Trans. Patt. Anal. and Mach. Intell. 20,1222-1239 (2001).
[CrossRef]

Virostko, J.

J. Virostko, A. C. Powers, and E. D. Jansen, "Validation of luminescent source reconstruction using single-view spectrally resolved bioluminescence images," App. Opt. 46,2540-2547 (2007).
[CrossRef]

Wang, G.

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
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G. Wang, H.-O. Shen, W.-X. Cong, S. Zhao, and G.-W. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14,7852-7871 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-13-18-6756.
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Y.-J. Lv, J. Tian, G. Wang, W.-X. Cong, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14,8211-8223 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

W.-X. Cong, D. Kumar, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

G. Wang, W.-X. Cong, K. Durairaj, X. Qian, H-O. Shen, P. Sinn, E. Hoffman, G. McLennan, and M. Henry, "In vivo mouse studies with bioluminescence tomography," Opt. Express 14,7801-7809 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7801.
[CrossRef] [PubMed]

W.-X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?id=140930.
[CrossRef] [PubMed]

M. Jiang and G. Wang, "Image reconstruction for bioluminescence tomography," Proc. SPIE,  5535,335-351 (2004).
[CrossRef]

G. Wang, Y. Li, and M. Jiang, "Uniqueness theorems in bioluminescence tomography," Med. Phys. 31,2289-2299 (2004).
[CrossRef] [PubMed]

Wang, L. V.

W.-X. Cong, D. Kumar, L. V. Wang, and G. Wang, "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33,679-686 (2006).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

W.-X. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. Hoffman, G. McLennan, P. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13,6756-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?id=140930.
[CrossRef] [PubMed]

Wei, G.-W.

Weisslder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weisslder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23,313-320 (2005).
[CrossRef] [PubMed]

Weissleder, R.

R. Weissleder and M. J. Pittet, "Imaging in the era of molecular oncology," Nature 452,580-589 (2008).
[CrossRef]

Willmann, J. K.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, "Molecular imaging in drug development," Nat. Rev. Drug Discov. 7,591-607 (2008).
[CrossRef] [PubMed]

Xu, H.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, "Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging," J. Biomed. Opt. 12,024007:1-12 (2007).
[CrossRef]

Xu, M.

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Yan, G.-R.

J.-C. Feng, K.-B. Jia, C.-H. Qin, G.-R. Yan, S.-P. Zhu, X. Zhang, J.-T. Liu, and J. Tian, "Three-dimensional Bioluminescence Tomography based on Bayesian Approach," Opt. Express 17,16834-16848 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-19-16834.
[CrossRef] [PubMed]

S.-P. Zhu, J. Tian, G.-R. Yan, C.-H. Qin, and J.-C. Feng, "Cone beam micro-CT system for small animal imaging and performance evaluation," Int. J. Biomed. Imaging, doc. ID 960573 (2009).

G.-R. Yan, J. Tian, S.-P. Zhu, Y.-K. Dai, and C.-H. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," J. X-Ray Sci. and Technol. 16,225-234 (2008).

Yang, W.

Yang, W.-X.

Y.-J. Lv, J. Tian, H. Li, W.-X. Cong, G. Wang, W.-X. Yang, C.-H. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Yodh, A. G.

V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, "Diffuse optical tomography of highly heterogeneous media," IEEE Trans. Med. Imaging 20,470-478 (2001).
[CrossRef] [PubMed]

Zabih, R.

V. Kolmogorov and R. Zabih, "What energy functions can be minimized via graph cuts?" IEEE Trans. Patt. Anal. and Mach. Intell. 26,147-159 (2004).
[CrossRef]

Y. Boykov, O. Veksler, and R. Zabih, "Efficient approximate energy minimization via graph cuts," IEEE Trans. Patt. Anal. and Mach. Intell. 20,1222-1239 (2001).
[CrossRef]

Zabner, J.

Zhang, Q.

Zhang, X.

Zhao, S.

Zhu, S.-P.

S.-P. Zhu, J. Tian, G.-R. Yan, C.-H. Qin, and J.-C. Feng, "Cone beam micro-CT system for small animal imaging and performance evaluation," Int. J. Biomed. Imaging, doc. ID 960573 (2009).

J.-C. Feng, K.-B. Jia, C.-H. Qin, G.-R. Yan, S.-P. Zhu, X. Zhang, J.-T. Liu, and J. Tian, "Three-dimensional Bioluminescence Tomography based on Bayesian Approach," Opt. Express 17,16834-16848 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-17-19-16834.
[CrossRef] [PubMed]

G.-R. Yan, J. Tian, S.-P. Zhu, Y.-K. Dai, and C.-H. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," J. X-Ray Sci. and Technol. 16,225-234 (2008).

App. Opt. (1)

J. Virostko, A. C. Powers, and E. D. Jansen, "Validation of luminescent source reconstruction using single-view spectrally resolved bioluminescence images," App. Opt. 46,2540-2547 (2007).
[CrossRef]

Canad. J. Math. (1)

L. Ford and D. Fulkerson, "Maximal flow through a network," Canad. J. Math. 8,309-404 (1956).
[CrossRef]

IEEE Trans. Med. Imaging (1)

V. Ntziachristos, A. H. Hielscher, A. G. Yodh, and B. Chance, "Diffuse optical tomography of highly heterogeneous media," IEEE Trans. Med. Imaging 20,470-478 (2001).
[CrossRef] [PubMed]

IEEE Trans. Patt. Anal. and Mach. Intell. (5)

V. Kolmogorov and R. Zabih, "What energy functions can be minimized via graph cuts?" IEEE Trans. Patt. Anal. and Mach. Intell. 26,147-159 (2004).
[CrossRef]

Y. Boykov and V. Kolmogorov, "An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision," IEEE Trans. Patt. Anal. and Mach. Intell. 26,1124-1137 (2004).
[CrossRef]

V. Kolmogorov and C. Rother, "Minimizing nonsubmodular functions with graph cuts-a review," IEEE Trans. Patt. Anal. and Mach. Intell. 9,1274-1279 (2007).
[CrossRef]

Y. Boykov, O. Veksler, and R. Zabih, "Efficient approximate energy minimization via graph cuts," IEEE Trans. Patt. Anal. and Mach. Intell. 20,1222-1239 (2001).
[CrossRef]

V. Lempitsky, C. Rother, S. Roth, and A. Blake, "Fusion moves for markov random field optimization," IEEE Trans. Patt. Anal. and Mach. Intell., in press.

Int. J. Biomed. Imaging (1)

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Figures (8)

Fig. 1:
Fig. 1:

An irregular directed graph and the cut. (a)A graph ***. (b)A cut on graph ***. It is noted that the mesh is constructed by tetrahedron elements, so graph used here is not regular any more and the adjacent connections of each node become very complex.

Fig. 2:
Fig. 2:

The GGC algorithmic structure used for BLT reconstruction.

Fig. 3:
Fig. 3:

The comparison of tomographic results between GGC and gradient-type method when the bioluminescent source is located at about the mouse torso center and no measurement error of tissue optical properties exists. (a) Mouse phantom captured by CT imaging system. (b) Mouse torso used for reconstructions and the 3D tomographic results based on GGC on the whole region of torso (4614 nodes). The arrow points to the reconstructed source in liver. (c)-(f) The results in 2D of the proposed method for 536, 1097, 3453 and 4614 nodes in the corresponding VOIs (Table 2), respectively. (g)-(j) are the counterparts with the gradient-type method. All the reconstructed values above zero in the slices are displayed in the results. The filled patch is the reconstructed source, and the other is the real one.

Fig. 4:
Fig. 4:

Time cost comparisons between GGC and a gradient-type method for BLT reconstructions. The grid used here contains 486 nodes on the surface of the mouse atlas. The execution time of the proposed method grows much more slowly with the number of nodes than that of the latter.

Fig. 5:
Fig. 5:

The tomography results based on GGC on the whole region when the bioluminescent source is located at about the half-radius of the mouse torso and no measurement error of tissue optical properties exists. (a) The results in 3D. All the reconstructed values above zero in the slices are displayed in the results. (b) The corresponding results in 2D.

Fig. 6:
Fig. 6:

The tomographic results with the proposed method in view of sensitivity to optical property errors based on GGC. (a) and (c) The reconstructed results corresponding to +50% and -50% optical property errors for all tissues respectively when the bioluminescent sources were located at about half-radius position in the mouse torso. (b) and (d) The reconstructed results corresponding to +50% and -50% optical property errors for all tissues respectively when the bioluminescent sources were located at about center of the mouse torso. All the reconstructed values above zero in the slices are displayed in the results.

Fig. 7:
Fig. 7:

The mouse profile and the mesh. (a) The mouse profile in bioluminescence imaging. (b) The volumetric mesh of the mouse torso used for imaging reconstructions and the mapped photon distribution on the mouse surface.

Fig. 8:
Fig. 8:

The experimental BLT reconstructions with the proposed method. The results are shown in lateral and vertical cross sectional views, compared with the source location in the corresponding CT slices. It is noted that all the reconstructed values above zero in the slices are displayed for the results.

Tables (4)

Tables Icon

Table 1: Optical properties for each organ in the mouse atlas. The units are mm -1.

Tables Icon

Table 2: The volume of interest used the in comparisons.

Tables Icon

Table 3: Comparisons of reconstruction results between GGC and a gradient-type method. Loc. Error denotes the distance between the center of real source and the center of reconstructed one.

Tables Icon

Table 4: Reconstruction results with different source locations and measurement errors of tissue optical properties. All the results were reconstructed on the whole region.

Equations (13)

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

· ( D ( r ) ( Φ ( r ) ) + μ a ( r ) Φ ( r ) = ∈** ( r ) ( r Ω )
Φ ( r ) + 2 κ ( r , n , n ' ) D ( r ) ( v ( r ) · Φ ( r ) ) = 0 ( r Ω )
V ( r ) = D ( r ) ( v ( r ) · Φ ( r ) ) = Φ ( r ) 2 κ ( r , n , n ' )
*** = Φ
min E ( *** ) = min *** b 2 + λ *** 2
E ( *** ) = *** b 2 + λ *** 2 = θ const + i θ i ( x i ) + ( i , j ) θ i j ( x i , x j )
= [ m 1 , m 2 , , m N ]
{ θ const = b T b θ i ( x i ) = ( m i T m i + λ ) x i 2 2 ( b T m i ) x i θ i j ( x i , x j ) = 2 ( m i T m j ) x i x j
θ i j ( 0 , 0 ) + θ i j ( 1 , 1 ) θ i j ( 0 , 1 ) + θ i j ( 1 , 0 )
θ i j ( 0 , 0 ) + θ i j ( 1 , 1 ) > θ i j ( 0 , 1 ) + θ i j ( 1 , 0 )
E ' ( *** , *** ̅ ) = θ const + 1 2 i [ θ i ( x i ) + θ i ( 1 x i ) ]
+ 1 2 ( i , j ) Sub [ θ i j ( x i , x j ) + θ i j ( 1 x i , 1 x j ) ]
+ 1 2 ( i , j ) Super [ θ i j ( x i , 1 x j ) + θ i j ( 1 x i , x j ) ]

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