Abstract

In vivo bioluminescence imaging (BLI) has played a more and more important role in biomedical research of small animals. Bioluminescence tomography (BLT) further translates the BLI optical information into three-dimensional bioluminescent source distribution, which could greatly facilitate applications in related studies. Although the diffusion approximation (DA) is one of the most widely-used forward models, higher-order approximations are still needed for in vivo small animal imaging. In this work, as a higher-order approximation theory, the performance of the simplified spherical harmonics approximation (SPN) in BLT is evaluated thoroughly on heterogeneous mouse models. In the numerical validations, the SPN based results demonstrate better imaging quality compared with diffusion approximation heterogeneously under various source locations over wide optical domain. In what follows, heterogeneous experimental BLT reconstructions using in vivo mouse further evaluate the capability of the higher-order method for practical biomedical applications.

© 2010 Optical Society of America

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2010 (2)

. K. Liu, J. Tian, D. Liu, C-H. Qin, J-T. Liu, S-P. Zhu, Z-J. Chang, X. Yang, and M. Xu, “Spectrally resolved three dimension bioluminescence tomography with a level set strategy,” J. Opt. Soc. Amer. A 27,1413-1423 (2010).
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2009 (5)

. M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using threedimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54,2493–2509 (2009).
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. Y-J. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrallyresolved bioluminescence tomography with the three-order simplified spherical harmonics approximation,” Phys. Med. Biol. 50,4225–4241 (2009).

. D. Hyde, R. Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-β plaques in a murine Alzheimer’s disease model,” NeuroImage 44,1304–1311 (2009).
[CrossRef]

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. 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. Imaging2009, doc. ID 960573 (2009).
[CrossRef] [PubMed]

2008 (5)

. 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] [PubMed]

. 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]

. J. Tian, J. Bai, X-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

. C-H. Qin, J. Tian, X. Yang, K. Liu, G-R. Yan, J-C. Feng, Y-J. 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/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

2007 (4)

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

. Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol. 52,5569–5585 (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]

. S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol. 18,79–86 (2007).
[CrossRef]

2006 (6)

. 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]

. 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]

. G. Gulsen, O. Birgul, M. B. Unlu, R. Shafiiha, and O. Nalcioglu, “Combined diffuse optical tomography (DOT) and MRI system for cancer imaging in small animals,” Technol. Cancer Res. Treat. 5,351–363 (2006).
[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]

. A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys. 220,441–470 (2006).
[CrossRef]

2005 (5)

. 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]

. 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. Weisslder, “Looking and listening to light: the evolution of whole body photonic imaging,” Nat. Biotechnol. 23,313–320 (2005).
[CrossRef] [PubMed]

. H. Li, J. Tian, F-P. Zhu, W-X. 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 the monte carlo method,” Acad. Radiol. 11,1029–1038 (2005).
[CrossRef]

2004 (3)

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

. X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[CrossRef] [PubMed]

. 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]

2003 (1)

. R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9,123–128 (2003).
[CrossRef] [PubMed]

2002 (1)

. 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. Radiat. Spectrosc. Transfer 72,691–713 (2002).
[CrossRef]

2001 (2)

. B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of lightemitting probes,” J. Biomed. Opt. 6,432–440 (2001).
[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).
[CrossRef] [PubMed]

1999 (3)

. H. Dehghani, D. Delpy, and S. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44,2897–2906 (1999).
[CrossRef]

. S. R. Arridge, “Optical tomography in medical imaging,” Inv. Prob. 15,R41–R93 (1999).
[CrossRef]

. H. B. Jiang, “Optical image reconstruction based on the third-order diffusion equations,” Opt. Express 4,241–246 (1999), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-4-8-241.
[CrossRef] [PubMed]

1998 (2)

. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43,1285–1302 (1998).
[CrossRef] [PubMed]

. O. Dorn, “Transportłbacktransport method for optical tomography,” Inv. Prob. 14,1107–1130 (1998).
[CrossRef]

1993 (1)

Alcouffe, R. E.

. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43,1285–1302 (1998).
[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.

. H. Dehghani, D. Delpy, and S. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44,2897–2906 (1999).
[CrossRef]

Arridge, S. R.

. S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol. 18,79–86 (2007).
[CrossRef]

. S. R. Arridge, “Optical tomography in medical imaging,” Inv. Prob. 15,R41–R93 (1999).
[CrossRef]

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-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

Bao, S-L.

. J. Tian, J. Bai, X-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

Barbour, R. L.

. A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43,1285–1302 (1998).
[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. Radiat. Spectrosc. Transfer 72,691–713 (2002).
[CrossRef]

Birgul, O.

. G. Gulsen, O. Birgul, M. B. Unlu, R. Shafiiha, and O. Nalcioglu, “Combined diffuse optical tomography (DOT) and MRI system for cancer imaging in small animals,” Technol. Cancer Res. Treat. 5,351–363 (2006).
[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).
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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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. Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol. 52,5569–5585 (2007).
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. Y-J. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrallyresolved bioluminescence tomography with the three-order simplified spherical harmonics approximation,” Phys. Med. Biol. 50,4225–4241 (2009).

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. D. Hyde, R. Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-β plaques in a murine Alzheimer’s disease model,” NeuroImage 44,1304–1311 (2009).
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. Y. Lin, H. Gao, O. Nalcioglu, and G. Gulsen, “Fluorescence diffuse optical tomography with functional and anatomical a priori information: feasibility study,” Phys. Med. Biol. 52,5569–5585 (2007).
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. D. Hyde, R. Kleine, S. A. MacLaurin, E. Miller, D. H. Brooks, T. Krucker, and V. Ntziachristos, “Hybrid FMT-CT imaging of amyloid-β plaques in a murine Alzheimer’s disease model,” NeuroImage 44,1304–1311 (2009).
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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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. 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]

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. 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).
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. 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).
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. Y-J. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrallyresolved bioluminescence tomography with the three-order simplified spherical harmonics approximation,” Phys. Med. Biol. 50,4225–4241 (2009).

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. K. Liu, J. Tian, D. Liu, C-H. Qin, J-T. Liu, S-P. Zhu, Z-J. Chang, X. Yang, and M. Xu, “Spectrally resolved three dimension bioluminescence tomography with a level set strategy,” J. Opt. Soc. Amer. A 27,1413-1423 (2010).
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. K. Liu, J. Tian, Y-J. Lu, C-H. Qin, S-P. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18,3732-3745 (2010), http: //www.opticsinfobase.org/abstract.cfm?uri=oe-18-4-3732.
[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. Imaging2009, doc. ID 960573 (2009).
[CrossRef] [PubMed]

. Y-J. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrallyresolved bioluminescence tomography with the three-order simplified spherical harmonics approximation,” Phys. Med. Biol. 50,4225–4241 (2009).

. J. Tian, J. Bai, X-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

. 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).

. C-H. Qin, J. Tian, X. Yang, K. Liu, G-R. Yan, J-C. Feng, Y-J. 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/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

. Y-J. Lv, J. Tian, H. Li,W-X. Cong, G. Wang,W-X. Yang, C-H. Qin, andM. 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]

. H. Li, J. Tian, F-P. Zhu, W-X. 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 the monte carlo method,” Acad. Radiol. 11,1029–1038 (2005).
[CrossRef]

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]

Unlu, M. B.

. G. Gulsen, O. Birgul, M. B. Unlu, R. Shafiiha, and O. Nalcioglu, “Combined diffuse optical tomography (DOT) and MRI system for cancer imaging in small animals,” Technol. Cancer Res. Treat. 5,351–363 (2006).
[PubMed]

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]

van Gemert, M. J. C.

Vishwanath, K.

. M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using threedimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol. 54,2493–2509 (2009).
[CrossRef] [PubMed]

Wang, G.

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

. 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, 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]

. H. Li, J. Tian, F-P. Zhu, W-X. 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 the monte carlo method,” Acad. Radiol. 11,1029–1038 (2005).
[CrossRef]

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

Wang, L. V.

. 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]

. 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).
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. H. Li, J. Tian, F-P. Zhu, W-X. 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 the monte carlo method,” Acad. Radiol. 11,1029–1038 (2005).
[CrossRef]

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).
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Weissleder, R.

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

. R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9,123–128 (2003).
[CrossRef] [PubMed]

Welch, A. J.

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]

Wright, S.

. S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol. 18,79–86 (2007).
[CrossRef]

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.

. K. Liu, J. Tian, D. Liu, C-H. Qin, J-T. Liu, S-P. Zhu, Z-J. Chang, X. Yang, and M. Xu, “Spectrally resolved three dimension bioluminescence tomography with a level set strategy,” J. Opt. Soc. Amer. A 27,1413-1423 (2010).
[CrossRef]

. C-H. Qin, J. Tian, X. Yang, K. Liu, G-R. Yan, J-C. Feng, Y-J. 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/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

Yan, G-R.

. 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. Imaging2009, doc. ID 960573 (2009).
[CrossRef] [PubMed]

. C-H. Qin, J. Tian, X. Yang, K. Liu, G-R. Yan, J-C. Feng, Y-J. 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/abstract.cfm?URI=oe-16-25-20317.
[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).

Yan, X-P.

. J. Tian, J. Bai, X-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

Yang, W.

Yang, W-X.

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

Yang, X.

. K. Liu, J. Tian, D. Liu, C-H. Qin, J-T. Liu, S-P. Zhu, Z-J. Chang, X. Yang, and M. Xu, “Spectrally resolved three dimension bioluminescence tomography with a level set strategy,” J. Opt. Soc. Amer. A 27,1413-1423 (2010).
[CrossRef]

. J. Tian, J. Bai, X-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

. C-H. Qin, J. Tian, X. Yang, K. Liu, G-R. Yan, J-C. Feng, Y-J. 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/abstract.cfm?URI=oe-16-25-20317.
[CrossRef] [PubMed]

Yazici, B.

. X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
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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).
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Yuan, Z.

. Z. Yuan, X-H. Hu and JiangH-B , “A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography,” Phys. Med. Biol. 54,65–88 (2009).
[CrossRef]

Zabner, J.

Zhang, X.

Zhu, F-P.

. H. Li, J. Tian, F-P. Zhu, W-X. 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 the monte carlo method,” Acad. Radiol. 11,1029–1038 (2005).
[CrossRef]

Zhu, S-P.

. K. Liu, J. Tian, Y-J. Lu, C-H. Qin, S-P. Zhu, and X. Zhang, “A fast bioluminescent source localization method based on generalized graph cuts with mouse model validations,” Opt. Express 18,3732-3745 (2010), http: //www.opticsinfobase.org/abstract.cfm?uri=oe-18-4-3732.
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. K. Liu, J. Tian, D. Liu, C-H. Qin, J-T. Liu, S-P. Zhu, Z-J. Chang, X. Yang, and M. Xu, “Spectrally resolved three dimension bioluminescence tomography with a level set strategy,” J. Opt. Soc. Amer. A 27,1413-1423 (2010).
[CrossRef]

. 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. Imaging2009, doc. ID 960573 (2009).
[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).

Acad. Radiol. (1)

. H. Li, J. Tian, F-P. Zhu, W-X. 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 the monte carlo method,” Acad. Radiol. 11,1029–1038 (2005).
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Appl. Opt. (1)

IEEE Eng. Med. Biol. (1)

. J. Tian, J. Bai, X-P. Yan, S-L. Bao, Y-H. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. 27,48–57 (2008).

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).
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. 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).
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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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Nature (1)

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. 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.
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. 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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. X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
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. S. A. Prahl, Oregon Medical Laser Clinic, 2001, http://omlc.ogi.edu/spectra/index.html.

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Figures (8)

Fig. 1
Fig. 1

(a) The mouse phantom scanned by the CT component in our dual-modality in vivo imaging system. (b) The heterogeneous mouse torso used for reconstructions, which contains main organs such as heart, lungs, liver, spleen and muscle. The mouse torso was discreted into volumetric mesh with 5747 nodes and 31245 tetrahedral elements with 940 nodes on the surface.

Fig. 2
Fig. 2

The ratio of μ s / μ a between 390-1000 nm for the main organs in a mouse.

Fig. 3
Fig. 3

The reconstruction comparisons of 800 nm cases between SP3 and DA approximations in heterogeneous background. Figures (a)-(c) are the SP3-based reconstruction results when the source is located at (21.45, 33.65, 14.50), (18.50, 33.00, 14.50) and (23.50, 36.50, 14.50), respectively. Figures (d)-(f) are the counterparts with DA-based reconstruction. Cross-sections with red and green boundaries are the centre position of actual and reconstructed sources, respectively. All the reconstructed values above zero are displayed in the results.

Fig. 4
Fig. 4

The reconstruction comparisons of 670 nm cases between SP3 and DA approximations in heterogeneous background. Figures (a)-(c) are the SP3-based reconstruction results when the source is located at (21.45, 33.65, 14.50), (18.50, 33.00, 14.50) and (23.50, 36.50, 14.50), respectively. Figures (d)-(f) are the counterparts with DA-based reconstruction. Cross-sections with red and green boundaries are the centre position of actual and reconstructed sources, respectively. All the reconstructed values above zero are displayed in the results.

Fig. 5
Fig. 5

The reconstruction comparisons of 620 nm cases between SP3 and DA approximations in heterogeneous background. Figures (a)-(c) are the SP3-based reconstruction results when the source is located at (21.45, 33.65, 14.50), (18.50, 33.00, 14.50) and (23.50, 36.50, 14.50), respectively. Figures (d)-(f) are the counterparts with DA-based reconstruction. Cross-sections with red and green boundaries are the centre position of actual and reconstructed sources, respectively. All the reconstructed values above zero are displayed in the results.

Fig. 6
Fig. 6

The reconstruction comparisons of 670 nm cases between SP3 and DA approximations in heterogeneous background. Figures (a) and (b) are the SP3-based reconstruction results when the source is located at (19.00, 33.20, 20.70) in muscle below liver, and (22.50, 35.80, 12.00) in lung, respectively. Figures (c) and (d) are the counterparts with DA-based reconstruction. Cross-sections with red and green boundaries are the centre position of actual and reconstructed sources, respectively. All the reconstructed values above zero are displayed in the results.

Fig. 7
Fig. 7

The volumetric mesh of mouse in the experiment. (a) The heterogeneous mouse torso used for imaging reconstructions, including heart, lungs, liver, muscle, and bone. (b) The mapped photon distribution on the mouse surface from four views.

Fig. 8
Fig. 8

Comparisons of reconstruction results between the SP3 and DA models. The left-bottom and right-top figures are the results of SP3 and DA models in lateral cross sectional views, respectively, compared with the source location in the corresponding CT slices. It is noted that all the reconstructed values above zero in the slice are displayed for the results.

Tables (3)

Tables Icon

Table 1 The optical properties for 800, 670 and 620 nm absorption of the major organs. The units for μa and μ s are mm−1.

Tables Icon

Table 2 The result summary of both SP3 and DA models for the 800, 670 and 620 nm cases. Offset denotes the distance between reconstructed and actual centre of the bioluminescent sources.

Tables Icon

Table 3 Optical properties for each organ in the mouse. The units are mm−1.

Equations (9)

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{ ϕ i ( r ) k = 1 N ϕ i , k ν k ( r ) ( 1 a ) X ( r ) k = 1 N x k ν k ( r ) ( 1 b )
{ k = 1 N ϕ 1 , k [ Ω ( 1 3 μ a 1 ν j ( r ) ν k ( r ) + μ a ν j ( r ) ν k ( r ) ) d r Ω E 11 3 μ a 1 ν j ( r ) ν k ( r ) d r ] k = 1 N ϕ 2 , k [ Ω 2 μ a 3 ν j ( r ) ν k ( r ) d r + Ω E 12 3 μ a 1 ν j ( r ) ν k ( r ) d r ] = k = 1 N x k Ω ν j ( r ) ν k ( r ) d r ( 2 a ) k = 1 N ϕ 2 , k [ Ω ( 1 7 μ a 3 ν j ( r ) ν k ( r ) + ( 4 9 μ a + 5 9 μ a 2 ) ν j ( r ) ν k ( r ) ) d r Ω E 22 7 μ a 3 ν j ( r ) ν k ( r ) d r ] k = 1 N ϕ 1 , k [ Ω 2 μ a 3 ν j ( r ) ν k ( r ) d r + Ω E 21 7 μ a 3 ν j ( r ) ν k ( r ) d r ] = 2 3 k = 1 N x k Ω ν j ( r ) ν k ( r ) d r ( 2 b )
{ E 11 = ( D 1 μ a 3 ( 1 8 + C 2 ) + 1 + B 2 7 μ a 3 ( 1 2 + A 1 ) ) / ( 1 + B 1 3 μ a 1 1 + B 2 7 μ a 3 D 1 μ a 3 D 2 μ a 1 ) ( 3 a ) E 12 = ( 1 + B 2 7 μ a 3 ( 1 8 + C 2 ) D 1 μ a 3 ( 7 24 + A 2 ) ) / ( 1 + B 1 3 μ a 1 1 + B 2 7 μ a 3 D 1 μ a 3 D 2 μ a 1 ) ( 3 b ) E 21 = ( 1 + B 1 3 μ a 1 ( 1 8 + C 2 ) D 2 μ a 1 ( 1 2 + A 1 ) ) / ( 1 + B 1 3 μ a 1 1 + B 2 7 μ a 3 D 1 μ a 3 D 2 μ a 1 ) ( 3 c ) E 22 = ( D 2 μ a 1 ( 1 8 + C 1 ) 1 + B 1 3 μ a 1 ( 7 24 + A 2 ) ) / ( 1 + B 1 3 μ a 1 1 + B 2 7 μ a 3 D 1 μ a 3 D 2 μ a 1 ) ( 3 d )
[ M 11 M 12 M 21 M 22 ] [ ϕ 1 ϕ 2 ] = [ B 0 0 B ] [ X 2 3 X ]
{ M 11 j k = Ω ( 1 3 μ a 1 ν j ( r ) ν k ( r ) + μ a ν j ( r ) ν k ( r ) ) d r Ω E 11 3 μ a 1 ν j ( r ) ν k ( r ) d r ( 5 a ) M 12 j k = Ω E 12 3 μ a 1 ν j ( r ) ν k ( r ) d r ( 5 b ) M 21 j k = Ω 2 μ a 3 ν j ( r ) ν k ( r ) d r Ω E 21 7 μ a 3 ν j ( r ) ν k ( r ) d r ( 5 c ) M 22 j k = Ω ( 1 7 μ a 3 ν j ( r ) ν k ( r ) + ( 4 9 μ a + 5 9 μ a 2 ) ν j ( r ) ν k ( r ) ) d r Ω E 22 7 μ a 3 ν j ( r ) ν k ( r ) d r ( 5 d ) B j k = Ω ν j ( r ) ν k ( r ) d r ( 5 e )
{ ϕ 1 = [ M 12 1 M 11 M 22 1 M 21 ] 1 [ M 12 1 + 2 3 M 22 1 ] B X ( 6 a ) ϕ 2 = [ M 11 1 M 12 M 21 1 M 22 ] 1 [ M 11 1 + 2 3 M 21 1 ] B X ( 6 b )
J + = β 1 ϕ 1 + β 2 ϕ 2 = ( β 1 [ M 12 1 M 11 M 22 1 M 21 ] 1 [ M 12 1 + 2 3 M 22 1 ] + β 2 [ M 11 1 M 12 M 21 1 M 22 ] 1 [ M 11 1 + 2 3 M 21 1 ] ) B X = M X
{ β 1 = 1 4 + J 0 0.5 + J 1 3 μ a 1 E 11 J 3 7 μ a 3 E 21 ( 8 a ) β 2 = 1 16 2 3 J 0 + 1 3 J 2 0.5 + J 1 3 μ a 1 E 12 J 3 7 μ a 3 E 22 ( 8 b )
E ( X ) = M X J + , meas 2 + λ X 2

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