Abstract

Bioluminescence tomography (BLT) poses a typical ill-posed inverse problem with a large number of unknowns and a relatively limited number of boundary measurements. It is indispensable to incorporate a priori information into the inverse problem formulation in order to obtain viable solutions. In the paper, Bayesian approach has been firstly suggested to incorporate multiple types of a priori information for BLT reconstruction. Meanwhile, a generalized adaptive Gaussian Markov random field (GAGMRF) prior model for unknown source density estimation is developed to further reduce the ill-posedness of BLT on the basis of finite element analysis. Then the distribution of bioluminescent source can be acquired by maximizing the log posterior probability with respect to a noise parameter and the unknown source density. Furthermore, the use of finite element method makes the algorithm appropriate for complex heterogeneous phantom. The algorithm was validated by numerical simulation of a 3-D micro-CT mouse atlas and physical phantom experiment. The reconstructed results suggest that we are able to achieve high computational efficiency and accurate localization of bioluminescent source.

© 2009 Optical Society of America

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2009

S. Zhu, J. Tian, G. Yan, C. Qin and J. Liu, "An experimental cone-beam micro-CT system for small animal imaging," Proc. SPIE 7258, 72582S (2009).
[CrossRef]

2008

2007

2006

2005

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]

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]

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

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

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]

A. P. Gibson, J. C. Hebden, and S. R. Arridge "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50R1-R43 (2005).
[CrossRef] [PubMed]

2004

X. Gu, Q. Zhang, L. Larcom, and H. 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]

Z. Paroo, R. A. Bollinger, D. A. Braascb, E. Ricber, and D. R. Corey, "Validating Bioluminescence Imaging as a High-Throughput, Quantitiative Modality for Assesing Tumor Burden," Mol. Imaging 3, 117-124 (2004).
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

2003

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30901-911 (2003).
[CrossRef] [PubMed]

T. F. Massoud and S. S. Gambhir, "Molecular imaging in living subjects: seeing fundamental biological processes in a new light," Genes Dev. 17, 545-580 (2003).
[CrossRef] [PubMed]

2002

C. H. Contag and M. H. Bachmann, "Advances in bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235-260 (2002).
[CrossRef] [PubMed]

E. G. Birgin, J. M. Martinez, "Large-scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients," Comput. Optim. Appl. 23, 101-125, (2002).
[CrossRef]

2001

E. G. Birgin, J. M. Martinez, "A box-constrained optimization algorithm with negative curvature directions and spectral projected gradients," Computing, Sup. 15, 49-60 (2001).
[CrossRef]

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, "Nonlinear multigrid algorithms for bayesian optical diffusion tomography," IEEE Trans. Image Process. 10, 909-922, (2001).
[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]

1999

1997

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, "Model-based image reconstruction from time-resolved diffusion data," Proc. SPIE 3034, 369-380 (1997).
[CrossRef]

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

C. A. Bouman and K. Sauer, "A generalized Gaussian imaging model for edge-preserving MAP estimation," IEEE Trans. Image Process. 2, 296-310 (1993).
[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]

Alexandrakis, G.

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]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50R1-R43 (2005).
[CrossRef] [PubMed]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, 41-93 (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 for modeling photon transport in tissue," Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Bachmann, M. H.

C. H. Contag and M. H. Bachmann, "Advances in bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235-260 (2002).
[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]

Bai, J.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Bao, S.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Birgin, E. G.

E. G. Birgin, J. M. Martinez, "Large-scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients," Comput. Optim. Appl. 23, 101-125, (2002).
[CrossRef]

E. G. Birgin, J. M. Martinez, "A box-constrained optimization algorithm with negative curvature directions and spectral projected gradients," Computing, Sup. 15, 49-60 (2001).
[CrossRef]

Bollinger, R. A.

Z. Paroo, R. A. Bollinger, D. A. Braascb, E. Ricber, and D. R. Corey, "Validating Bioluminescence Imaging as a High-Throughput, Quantitiative Modality for Assesing Tumor Burden," Mol. Imaging 3, 117-124 (2004).
[CrossRef] [PubMed]

Bouman, C. A.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, "Nonlinear multigrid algorithms for bayesian optical diffusion tomography," IEEE Trans. Image Process. 10, 909-922, (2001).
[CrossRef]

J. C. Ye, K. J. Webb, and C. A. Bouman, "Optical diffusion tomography by iterative coordinate descent optimization in a Bayesian framework," J. Opt. Soc. Am. A 16, 2400-2412 (1999).
[CrossRef]

C. A. Bouman and K. Sauer, "A generalized Gaussian imaging model for edge-preserving MAP estimation," IEEE Trans. Image Process. 2, 296-310 (1993).
[CrossRef] [PubMed]

Braascb, D. A.

Z. Paroo, R. A. Bollinger, D. A. Braascb, E. Ricber, and D. R. Corey, "Validating Bioluminescence Imaging as a High-Throughput, Quantitiative Modality for Assesing Tumor Burden," Mol. Imaging 3, 117-124 (2004).
[CrossRef] [PubMed]

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]

Chatziioannou, A. F.

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.

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]

Cheng, J.

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.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

Cong, W.

M. Jiang, T. Zhou, J. Cheng, W. Cong, and G. Wang, "Image reconstruction for bioluminescence tomography from partial measurement," Opt. Express 15,11095-11116 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11095.
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 524497-4512 (2007).
[CrossRef] [PubMed]

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14, 7852-7871 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7852.
[CrossRef] [PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. 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]

Y. Lv, J. Tian, W. Cong, G. Wang, 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. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Contag, C. H.

C. H. Contag and M. H. Bachmann, "Advances in bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235-260 (2002).
[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).
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Corey, D. R.

Z. Paroo, R. A. Bollinger, D. A. Braascb, E. Ricber, and D. R. Corey, "Validating Bioluminescence Imaging as a High-Throughput, Quantitiative Modality for Assesing Tumor Burden," Mol. Imaging 3, 117-124 (2004).
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S. S. Saquib, K. M. Hanson, and G. S. Cunningham, "Model-based image reconstruction from time-resolved diffusion data," Proc. SPIE 3034, 369-380 (1997).
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G. Yan, J. Tian, S. Zhu, Y. Dai, and C. Qin, "Fast cone-beam CT image reconstruction using GPU hardware," IJ. X-Ray Sci.Technol. 16, 225-234 (2008).

Darvas, F.

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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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).
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Economou, E. N.

Feng, J.

Gambhir, S. S.

T. F. Massoud and S. S. Gambhir, "Molecular imaging in living subjects: seeing fundamental biological processes in a new light," Genes Dev. 17, 545-580 (2003).
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D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
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E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30901-911 (2003).
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Gu, X.

Hanson, K. M.

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, "Model-based image reconstruction from time-resolved diffusion data," Proc. SPIE 3034, 369-380 (1997).
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A. P. Gibson, J. C. Hebden, and S. R. Arridge "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50R1-R43 (2005).
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Hielscher, A. H.

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).
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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).
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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).
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Hoffman, E.

Hoffman, E. A.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
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Hyde, D.

Jia, K.

Jiang, H.

Jiang, M.

M. Jiang, T. Zhou, J. Cheng, W. Cong, and G. Wang, "Image reconstruction for bioluminescence tomography from partial measurement," Opt. Express 15,11095-11116 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11095.
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W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
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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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Kioussis, D.

Klose, A. D.

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]

Kumar, D.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

Larcom, L.

Lasser, T.

Leahy, R. M.

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]

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. Lv, J. Tian, W. Cong, G. Wang, 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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H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Li, Y.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
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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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Liang, W.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
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Liu, J.

S. Zhu, J. Tian, G. Yan, C. Qin and J. Liu, "An experimental cone-beam micro-CT system for small animal imaging," Proc. SPIE 7258, 72582S (2009).
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Liu, K.

Liu, Y.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
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Luo, J.

Lv, Y.

Mamalaki, C.

Martinez, J. M.

E. G. Birgin, J. M. Martinez, "Large-scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients," Comput. Optim. Appl. 23, 101-125, (2002).
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E. G. Birgin, J. M. Martinez, "A box-constrained optimization algorithm with negative curvature directions and spectral projected gradients," Computing, Sup. 15, 49-60 (2001).
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T. F. Massoud and S. S. Gambhir, "Molecular imaging in living subjects: seeing fundamental biological processes in a new light," Genes Dev. 17, 545-580 (2003).
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McCray, P. B.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

McLennan, G.

G. Wang, W. Cong, K. Durairaj, X. Qian, H. 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. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

Meyer, H.

Millane, R. P.

J. C. Ye, C. A. Bouman, K. J. Webb, and R. P. Millane, "Nonlinear multigrid algorithms for bayesian optical diffusion tomography," IEEE Trans. Image Process. 10, 909-922, (2001).
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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]

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).
[CrossRef] [PubMed]

Ntziachristos, V.

N. Dehiolanis, T. Lasser, D. Hyde, A. Soubret, J. Ripoll, and V. Ntziachristos, "Free-space fluorescence molecular tomography utilizing 360? geometry projections," Opt. Lett. 32, 382-384 (2007).
[CrossRef]

H. Meyer, A. Garofalakis, G. Zacharakis, S. Psycharakis, C. Mamalaki, D. Kioussis, E. N. Economou, V. Ntziachristos, and J. Ripoll, "Noncontact optical imaging in mice with full angular coverage and automatic surface extraction," Appl. Opt. 46, 3617-3627 (2007).
[CrossRef] [PubMed]

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

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]

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30901-911 (2003).
[CrossRef] [PubMed]

Paroo, Z.

Z. Paroo, R. A. Bollinger, D. A. Braascb, E. Ricber, and D. R. Corey, "Validating Bioluminescence Imaging as a High-Throughput, Quantitiative Modality for Assesing Tumor Burden," Mol. Imaging 3, 117-124 (2004).
[CrossRef] [PubMed]

Psycharakis, S.

Qian, X.

Qin, C.

S. Zhu, J. Tian, G. Yan, C. Qin and J. Liu, "An experimental cone-beam micro-CT system for small animal imaging," Proc. SPIE 7258, 72582S (2009).
[CrossRef]

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

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, "Galerkin-based meshless methods for photon transport in the biological tissue," Opt. Express 16, 20317-20333 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, "An optimal permissible source region strategy for multispectral bioluminescence tomography," Opt. Express 16, 15640-15654 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15640.
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 524497-4512 (2007).
[CrossRef] [PubMed]

Qin, D.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Rannou, F. R.

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]

Ricber, E.

Z. Paroo, R. A. Bollinger, D. A. Braascb, E. Ricber, and D. R. Corey, "Validating Bioluminescence Imaging as a High-Throughput, Quantitiative Modality for Assesing Tumor Burden," Mol. Imaging 3, 117-124 (2004).
[CrossRef] [PubMed]

Rice, B. W.

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.

H. Meyer, A. Garofalakis, G. Zacharakis, S. Psycharakis, C. Mamalaki, D. Kioussis, E. N. Economou, V. Ntziachristos, and J. Ripoll, "Noncontact optical imaging in mice with full angular coverage and automatic surface extraction," Appl. Opt. 46, 3617-3627 (2007).
[CrossRef] [PubMed]

N. Dehiolanis, T. Lasser, D. Hyde, A. Soubret, J. Ripoll, and V. Ntziachristos, "Free-space fluorescence molecular tomography utilizing 360? geometry projections," Opt. Lett. 32, 382-384 (2007).
[CrossRef]

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

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30901-911 (2003).
[CrossRef] [PubMed]

Saquib, S. S.

S. S. Saquib, K. M. Hanson, and G. S. Cunningham, "Model-based image reconstruction from time-resolved diffusion data," Proc. SPIE 3034, 369-380 (1997).
[CrossRef]

Sauer, K.

C. A. Bouman and K. Sauer, "A generalized Gaussian imaging model for edge-preserving MAP estimation," IEEE Trans. Image Process. 2, 296-310 (1993).
[CrossRef] [PubMed]

Schweiger, 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 for modeling photon transport in tissue," Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Shen, H.

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]

Soubret, A.

Tan, Y.

Tanikawa, Y.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Tian, J.

S. Zhu, J. Tian, G. Yan, C. Qin and J. Liu, "An experimental cone-beam micro-CT system for small animal imaging," Proc. SPIE 7258, 72582S (2009).
[CrossRef]

C. Qin, J. Tian, X. Yang, K. Liu, G. Yan, J. Feng, Y. Lv, and M. Xu, "Galerkin-based meshless methods for photon transport in the biological tissue," Opt. Express 16, 20317-20333 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

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

J. Feng, K. Jia, G. Yan, S. Zhu, C. Qin, Y. Lv, and J. Tian, "An optimal permissible source region strategy for multispectral bioluminescence tomography," Opt. Express 16, 15640-15654 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15640.
[CrossRef] [PubMed]

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, "Multimodality molecular imaging," IEEE Eng. Med. Biol. Mag. 27, 48-57 (2008).
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 524497-4512 (2007).
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, 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]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Wang, G.

Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, and M. Xu, "Spectrally resolved bioluminescence tomography with adaptive finite element: methodology and simulation," Phys. Med. Biol. 524497-4512 (2007).
[CrossRef] [PubMed]

M. Jiang, T. Zhou, J. Cheng, W. Cong, and G. Wang, "Image reconstruction for bioluminescence tomography from partial measurement," Opt. Express 15,11095-11116 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-18-11095.
[CrossRef] [PubMed]

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, "Temperature-modulated bioluminescence tomography," Opt. Express 14, 7852-7871 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-17-7852.
[CrossRef] [PubMed]

Y. Lv, J. Tian, W. Cong, G. Wang, 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, W. Cong, K. Durairaj, X. Qian, H. 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. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

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

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Wang, L. V.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6765-6771 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=OPEX-13-18-6756.
[CrossRef]

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

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A Mouse Optical Simulation Environment (MOSE) to Investigate Bioluminescent Phenomena in the Living Mouse with Monte Carlo Method," Acad. Radiol. 11, 1029-1038 (2004).
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Figures (9)

Fig. 1.
Fig. 1.

The view of mouse phantom. (a) Coronal and transverse image of micro-CT data; (b) Labelling of organs and tissues in the coronal and transverse planes; (c) Dorsal-ventral view of surface rendering of the separated organs and tissues: skin, skeleton, heart, lung and liver; (d) Left lateral view of surface rending of above five tissues.

Fig. 2.
Fig. 2.

(a) Heterogeneous phantom with muscle, bone, heart, liver and lung; (b) The mesh used in the tomographic algorithm; (c) The discretized mesh of the phantom used in MOSE.

Fig. 3.
Fig. 3.

Four views of the phantom surface with an angular of 90 degrees. Red lines denote the isoline of the surface light power. (a) Front view; (b) Right view; (c) Back view and (d) Left view.

Fig. 4.
Fig. 4.

BLT Reconstruction with the proposed algorithm. (a) The three-dimensional rendering of the reconstructed result. (b), (c) and (d) are three different slices of the reconstruction which are selected to illustrate the result in more detail. (c) is through the actual source’s center; (b) and (d) are perpendicular to the z-axis direction off the actual source’s center about ±0.5 mm. The black circle denotes the actual source.

Fig. 5.
Fig. 5.

BLT reconstruction with different σ and p. (a) and (b) Noise level was 30dB, and for (c) and (d), (e) and (f) was 20dB and 10dB, respectively. From (a) to (f), p gradually reduced and its value was 2, 1.8, 1.6, 1.4, 1.2, 1.1, respectively. The cross-section is through the actual source’s center. The black circle denotes the actual source.

Fig. 6.
Fig. 6.

Reconstruction results with two sources. The green mesh denotes the surface mesh of the 3D mouse phantom and the red sphere is the actual source. (a) BLT reconstruction in case of I, and (b) The BLT reconstruction in case of II.

Fig. 7.
Fig. 7.

Experimental setup and phantom. (a) The sketch of the free-space BLT system; (b) The phantom with one light source and (c) The middle cross-section of the phantom. The four degrees show the direction for data acquisition with the CCD camera. The black circle denotes the actual source.

Fig. 8.
Fig. 8.

The photon energy distribution on the surface of the phantom detected by the CCD camera. (a) 0°, (b) 90°, (c) 180° and (d) 270°.

Fig. 9.
Fig. 9.

Reconstructed result. (a) The mesh used in reconstruction. (b) The reconstructed result with proposed algorithm.

Tables (4)

Tables Icon

Table 1. Optical parameters of the real mouse [19]

Tables Icon

Table 2. Quantitative reconstructed results with and without Bayesian approach.

Tables Icon

Table 3. Quantitative results with different σ and p.

Tables Icon

Table 4. Quantitative BLT reconstruction results in case of two sources

Equations (21)

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

· (D(r)Φ(r))+μa(r)Φ(r)=x(r)(rΩ)
Φ(r)+2A(r;n,n)D(r)(v(r)·Φ(r))=0(rΩ)
A (r;n,n')1+R(r)1R(r)
Q(r)=D(r)(v(r)·Φ(r))=Φ(r)2A(r;n,n)(rΩ)
x̂MAP = arg max logx0 ρ (xy)
= argmaxx0 {logρ(yx)+logρ(x)}
x̂MAP = argmaxlogx0 ρ (xy,C)
= argmaxx0 {logρ(yx,C)+logρ(xC)}
x̂MAP = arg·maxlogx0 ρ (xy,C,PS)
= argmaxx0 {logρ(yx,C,PS)+logρ(xC,PS)}
x̂MAP = argmaxx0 {logρ(yx)+logρ(xC,PS)}
ρ (yx)=1(πα)MΛ1exp[yf(x)Λ2α]
Λii Φimeas (i=1,2,,M).
p(xC,PS)=1σNz(p)exp[1pi,jNbijxixjp]
arg max x0 maxα{1αyf(x)Λ2Mlogα1pi,jNbijxixjp}
α = 1M yf (x)Λ2
x̂=argmaxx0{MMlog(1Myf(x)Λ2)1pi,jNbijxixjp}
l (x)=Mlog(yf(x)Λ2)1pi,jNbijxixjp
α̂=1Myf(x̂)Λ2
x̂=argmaxx0{1α̂yf(x)Λ21pi,jNbijxixjp}
φ = 4.94×104·pixel+1.48×102

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