Abstract

Bioluminescence tomography (BLT) has become a powerful tool for whole-body small animal imaging. In this contribution, an adaptive improved element free Galerkin method (IEFGM) is presented to perform a quantitative reconstruction of the internal light source using quasi- or multi-spectral information, which not only can avoid the time-consuming mesh generation but also can reduce the ill-posedness of BLT effectively. In the algorithm, the reconstruction can be largely enhanced by an adaptive technology based on a posteriori error estimation. Finally, the numerical and physical phantom experiment results show that the bioluminescent source can be recovered accurately.

© 2009 Optical Society of America

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  1. 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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    [CrossRef]

2008 (5)

2007 (2)

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

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]

2006 (3)

2005 (6)

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

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]

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

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 13,6756-6771 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6756.
[CrossRef] [PubMed]

2004 (1)

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

2000 (1)

P. R. Johnston and R. M. Gulrajani, "Selecting the corner in the L-curve approach to Tikhonov regularization," IEEE T.Bio-Med. Eng. 47,1293-1296 (2000).
[CrossRef]

1998 (1)

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5,207-241 (1998).
[CrossRef]

1995 (1)

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]

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]

Arridge, S. R.

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

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]

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

Bao, S.

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

Belytschko, T.

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5,207-241 (1998).
[CrossRef]

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]

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.

Contag, C. H.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

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.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

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).
[CrossRef] [PubMed]

Davis, S. C.

Dehghani, H.

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).
[CrossRef] [PubMed]

Dolbow, J.

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5,207-241 (1998).
[CrossRef]

Doyle, T. C.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

Dubey, P.

Feng, J.

Gao, F.

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]

Gibson, A. P.

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

Gulrajani, R. M.

P. R. Johnston and R. M. Gulrajani, "Selecting the corner in the L-curve approach to Tikhonov regularization," IEEE T.Bio-Med. Eng. 47,1293-1296 (2000).
[CrossRef]

Han, W. M.

W. M. Han and G. Wang, "Theoretical and numerical analysis on multispectral bioluminescence tomography," IMA J. Appl. Math. 72,1-19 (2006).
[CrossRef]

Hebden, J. C.

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

Hiraoka, 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]

Hoffman, E. A.

Jia, K.

Jiang, M.

Jiang, S.

Johnston, P. R.

P. R. Johnston and R. M. Gulrajani, "Selecting the corner in the L-curve approach to Tikhonov regularization," IEEE T.Bio-Med. Eng. 47,1293-1296 (2000).
[CrossRef]

Kalish, F.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

Kumar, D.

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]

Li, H.

Li, Y.

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

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

Liang, W.

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

Liu, K.

Liu, Y.

Luo, J.

Lv, Y.

McCray, P. B.

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).
[CrossRef] [PubMed]

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]

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Qin, C.

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/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]

C. Qin, J. Tian, Y. Lv, and W. Yang, "Three-dimensional bioluminescent source reconstruction method based on nodes of adaptive FEM," Proc. SPIE 6916,69161K (2008).
[CrossRef]

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

Rice, B. W.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

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]

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]

Shen, H.

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]

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.

Wang, G.

Wang, L. V.

Wang, Y.

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]

Xu, M.

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/abstract.cfm?URI=oe-16-25-20317.
[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 analysis: methodology and simulation," Phys. Med. Biol. 52,4497-4512 (2007).
[CrossRef] [PubMed]

Yan, G.

Yan, X. P.

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

Yang, W.

C. Qin, J. Tian, Y. Lv, and W. Yang, "Three-dimensional bioluminescent source reconstruction method based on nodes of adaptive FEM," Proc. SPIE 6916,69161K (2008).
[CrossRef]

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

Yang, X.

Zabner, J.

Zhao, H.

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]

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10,041210 (2005).
[CrossRef]

Zhu, S.

Arch. Comput. Methods Eng. (1)

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5,207-241 (1998).
[CrossRef]

Bio-Med. Eng. (1)

P. R. Johnston and R. M. Gulrajani, "Selecting the corner in the L-curve approach to Tikhonov regularization," IEEE T.Bio-Med. Eng. 47,1293-1296 (2000).
[CrossRef]

IEEE Eng. Med. Biol. Mag. (1)

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

IMA J. Appl. Math. (1)

W. M. Han and G. Wang, "Theoretical and numerical analysis on multispectral bioluminescence tomography," IMA J. Appl. Math. 72,1-19 (2006).
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Figures (5)

Fig. 1.
Fig. 1.

The flowchart of the proposed algorithm.

Fig. 2.
Fig. 2.

Numerical phantom experiment using multi-spectral data. (a) A heterogeneous phantom with two light sources; (b) Transverse view of the reconstructed result without adaptive technique; (c) The recovered sources after node refinement. The black square indicates the actual source position.

Fig. 3.
Fig. 3.

Numerical phantom experiment using quasi-spectral information. (a) The reconstructed result without adaptive technique; (b) The recovered sources after node refinement.

Fig. 4.
Fig. 4.

Imaging system and resinous phantom. (a) The polyoxymethylene phantom; (b) The non-contact imaging system; (c) The middle cross-section of the phantom.

Fig. 5.
Fig. 5.

Physical phantom experiment. (a), (b) and (c) The reconstructed source using single, two and three bands measurement respectively.

Tables (5)

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Table 1. Optical properties of the numerical phantom in different multi-spectral ranges.

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Table 2. Comparison between the actual and reconstructed sources in multi-spectral case.

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Table 3. Optical properties of the numerical phantom in different quasi-spectrums.

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Table 4. Comparison between the actual and reconstructed sources in quasi-spectral case.

Tables Icon

Table 5. Optical parameters for the physical phantom.

Equations (13)

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· ( D ( x , λ ) Φ ( x , λ ) ) + μ a ( x , λ ) Φ ( x , λ ) = S ( x , λ ) ( x Ω )
Φ ( x , λ ) + 2 A ( x ; n , n ' ) D ( x , λ ) ( v ( x ) · Φ ( x , λ ) ) = 0 ( x Ω )
N i ( x ) = p T ( x ) G 1 ( x ) H i ( x )
M l ( x ) = i = 1 N n N i ( x ) N l ( x i ) 1
Γ = [ N 1 ( x 1 ) N 2 ( x 1 ) N N n ( x 1 ) N 1 ( x 2 ) N 2 ( x 2 ) N N n ( x 2 ) N 1 ( x N n ) N 2 ( x N n ) N N n ( x N n ) ]
Φ ( x , λ k ) i = 1 N n Φ ( x i , λ k ) M i ( x , λ k ) S ( x , λ k ) i = 1 N n S ( x i , λ k ) M i ( x , λ k )
Ω ( D ( x , λ ) ( Φ ( x , λ ) ) · ( Ψ ( x , λ ) ) + μ a ( x , λ ) Φ ( x , λ ) Ψ ( x , λ ) ) d x
+ Ω 1 2 A ( x ; n , n ' ) Φ ( x , λ ) Ψ ( x , λ ) d x = Ω S ( x , λ ) Ψ ( x , λ ) d x
M k Φ k = F k S k
Φ k meas = A K S k
Φ meas = AS
Φ meas = [ Φ 1 meas Φ 2 meas Φ τ meas ] , A = [ ω 1 A 1 ω 2 A 2 ω τ A τ ]
min 0 S S sup { AS Φ meas Λ + α S T S }

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