Abstract

In this paper, a multilevel, hybrid regularization method is presented for fluorescent molecular tomography (FMT) based on the hp-finite element method (hp-FEM) with a continuous wave. The hybrid regularization method combines sparsity regularization and Landweber iterative regularization to improve the stability of the solution of the ill-posed inverse problem. In the first coarse mesh level, considering the fact that the fluorescent probes are sparsely distributed in the entire reconstruction region in most FMT applications, the sparse regularization method is employed to take full advantage of this sparsity. In the subsequent refined mesh levels, since the reconstruction region is reduced and the initial value of the unknown parameters is provided from the previous mesh, these mesh levels seem to be different from the first level. As a result, the Landweber iterative regularization method is applied for reconstruction. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are conducted to evaluate the performance of our method. The reconstructed results show the potential and feasibility of the proposed approach.

© 2012 Optical Society of America

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    [CrossRef]

2011 (1)

2010 (6)

X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

2009 (5)

2008 (4)

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35, 5703–5707 (2008).
[CrossRef]

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]

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (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]

2007 (3)

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15, 18300–18317 (2007).
[CrossRef]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587(2007).
[CrossRef]

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]

2006 (1)

2005 (3)

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]

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

A. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13, 9847–9857 (2005).
[CrossRef]

2004 (2)

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004).
[CrossRef]

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).

1999 (2)

R. Ramlau, “A modified Landweber method for inverse problems,” Numer. Funct. Anal. Optim. 20, 79–98 (1999).
[CrossRef]

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

1997 (1)

M. Ainsworth and B. Senior, “Aspects of an adaptive hp-finite element method: Adaptive strategy conforming approximation and efficient solvers,” Comput. Methods Appl. M 150, 65–87 (1997).
[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]

1951 (1)

L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624(1951).
[CrossRef]

Ahn, S.

Aikawa, E.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

Ainsworth, M.

M. Ainsworth and B. Senior, “Aspects of an adaptive hp-finite element method: Adaptive strategy conforming approximation and efficient solvers,” Comput. Methods Appl. M 150, 65–87 (1997).
[CrossRef]

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]

Andersson-Engels, S.

Arridge, S. R.

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Opt. Express 17, 3025–3035 (2009).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (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]

Axelsson, J.

Badea, C. T.

X. Zhang, C. T. Badea, and G. A. Johnson, “Three-dimensional reconstruction in free-space whole-body fluorescence tomography of mice using optically reconstructed surface and atlas anatomy,” J. Biomed. Opt. 14, 064010 (2009).
[CrossRef]

Bai, J.

D. Wang, X. Liu, Y. Chen, and J. Bai, “A novel finite-element-based algorithm for fluorescence molecular tomography of heterogeneous media,” IEEE Trans. Inf. Technol. Biomed. 13, 766–773 (2009).

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]

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15, 18300–18317 (2007).
[CrossRef]

Bangerth, W.

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]

Barber, W. C.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

Chatziioannou, A. F.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587(2007).
[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]

Chen, D.

Chen, N.

Chen, Y.

D. Wang, X. Liu, Y. Chen, and J. Bai, “A novel finite-element-based algorithm for fluorescence molecular tomography of heterogeneous media,” IEEE Trans. Inf. Technol. Biomed. 13, 766–773 (2009).

Cherry, S. R.

Cong, A.

de Kleine, R. H.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

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]

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).
[CrossRef]

Dogdas, B.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587(2007).
[CrossRef]

Dutta, J.

Feng, J.

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

Gambhir, S. S.

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]

Gao, F.

Gao, H.

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]

Graves, E. E.

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).

Gulsen, G.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

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]

Han, D.

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

Han, R.

He, X.

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]

Hou, Y.

Iwanczyk, J. S.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

Jiang, H.

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35, 5703–5707 (2008).
[CrossRef]

Johnson, G. A.

X. Zhang, C. T. Badea, and G. A. Johnson, “Three-dimensional reconstruction in free-space whole-body fluorescence tomography of mice using optically reconstructed surface and atlas anatomy,” J. Biomed. Opt. 14, 064010 (2009).
[CrossRef]

Joshi, A.

Kirsch, A.

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer-Verlag, 1996).

Kirsch, D. G.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

Landweber, L.

L. Landweber, “An iteration formula for Fredholm integral equations of the first kind,” Am. J. Math. 73, 615–624(1951).
[CrossRef]

Leahy, R. M.

Li, C.

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).
[CrossRef]

Liang, J.

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).
[CrossRef]

Lin, Y.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

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]

Liu, F.

Liu, J.

J. Liu, Regularization Methods to Ill-Posed Problem and Its Applications (Science Press, 2005).

Liu, K.

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

Liu, X.

D. Wang, X. Liu, Y. Chen, and J. Bai, “A novel finite-element-based algorithm for fluorescence molecular tomography of heterogeneous media,” IEEE Trans. Inf. Technol. Biomed. 13, 766–773 (2009).

Lv, Y.

Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

Ma, X.

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

Mao, J.

Mitchell, G. S.

Nalcioglu, O.

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

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]

Naser, M. A.

Niedre, M. J.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

Ntziachristos, V.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

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

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).

Patterson, M. S.

Qin, C.

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

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R. Ramlau, “A modified Landweber method for inverse problems,” Numer. Funct. Anal. Optim. 20, 79–98 (1999).
[CrossRef]

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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).
[CrossRef]

Rasmussen, J. C.

Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

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

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A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Opt. Express 17, 3025–3035 (2009).
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[CrossRef]

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M. Ainsworth and B. Senior, “Aspects of an adaptive hp-finite element method: Adaptive strategy conforming approximation and efficient solvers,” Comput. Methods Appl. M 150, 65–87 (1997).
[CrossRef]

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Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004).
[CrossRef]

Shen, H.

Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

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B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587(2007).
[CrossRef]

Svenmarker, P.

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Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35, 5703–5707 (2008).
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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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D. Wang, X. Liu, Y. Chen, and J. Bai, “A novel finite-element-based algorithm for fluorescence molecular tomography of heterogeneous media,” IEEE Trans. Inf. Technol. Biomed. 13, 766–773 (2009).

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15, 18300–18317 (2007).
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Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

A. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13, 9847–9857 (2005).
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Wang, L. V.

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

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Weissleder, R.

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

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

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).

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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).
[CrossRef]

Yamada, Y.

Yan, X.

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]

Yang, X.

Yu, J.

Zacharopoulos, A. D.

Zhang, B.

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

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X. Zhang, C. T. Badea, and G. A. Johnson, “Three-dimensional reconstruction in free-space whole-body fluorescence tomography of mice using optically reconstructed surface and atlas anatomy,” J. Biomed. Opt. 14, 064010 (2009).
[CrossRef]

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Zhu, B.

Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
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[CrossRef]

Biomed. Opt. Express (1)

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M. Ainsworth and B. Senior, “Aspects of an adaptive hp-finite element method: Adaptive strategy conforming approximation and efficient solvers,” Comput. Methods Appl. M 150, 65–87 (1997).
[CrossRef]

Curr. Mol. Med. (1)

E. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004).

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

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]

IEEE Trans. Biomed. Eng. (1)

D. Han, J. Tian, K. Liu, J. Feng, B. Zhang, X. Ma, and C. Qin, “Sparsity promoting tomographic fluorescence imaging with simplified spherical harmonics approximation,” IEEE Trans. Biomed. Eng. 57, 2564–2567 (2010).
[CrossRef]

IEEE Trans. Inf. Technol. Biomed. (1)

D. Wang, X. Liu, Y. Chen, and J. Bai, “A novel finite-element-based algorithm for fluorescence molecular tomography of heterogeneous media,” IEEE Trans. Inf. Technol. Biomed. 13, 766–773 (2009).

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

J. Biomed. Opt. (2)

X. Zhang, C. T. Badea, and G. A. Johnson, “Three-dimensional reconstruction in free-space whole-body fluorescence tomography of mice using optically reconstructed surface and atlas anatomy,” J. Biomed. Opt. 14, 064010 (2009).
[CrossRef]

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a trimodality system: in vivo validation,” J. Biomed. Opt. 15, 040503 (2010).
[CrossRef]

Med. Phys. (2)

Y. Tan and H. Jiang, “DOT guided fluorescence molecular tomography of arbitrarily shaped objects,” Med. Phys. 35, 5703–5707 (2008).
[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]

Nat. Biotechnol. (1)

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

Nat. Rev. Drug Discov. (1)

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]

Numer. Funct. Anal. Optim. (1)

R. Ramlau, “A modified Landweber method for inverse problems,” Numer. Funct. Anal. Optim. 20, 79–98 (1999).
[CrossRef]

Opt. Express (10)

Y. Lin, W. C. Barber, J. S. Iwanczyk, W. Roeck, O. Nalcioglu, and G. Gulsen, “Quantitative fluorescence tomography using a combined tri-modality FT/DOT/XCT system,” Opt. Express 18, 7835–7850 (2010).
[CrossRef]

X. He, J. Liang, X. Wang, J. Yu, X. Qu, X. Wang, Y. Hou, D. Chen, F. Liu, and J. Tian, “Sparse reconstruction for quantitative bioluminescence tomography based on the incomplete variables truncated conjugate gradient method,” Opt. Express 18, 24825–24841 (2010).
[CrossRef]

F. Gao, H. J. Zhao, Y. Tanikawa, and Y. Yamada, “A linear, featured-data scheme for image reconstruction in time-domain fluorescence molecular tomography,” Opt. Express 14, 7109–7124 (2006).
[CrossRef]

A. D. Zacharopoulos, P. Svenmarker, J. Axelsson, M. Schweiger, S. R. Arridge, and S. Andersson-Engels, “A matrix-free algorithm for multiple wavelength fluorescence tomography,” Opt. Express 17, 3025–3035 (2009).
[CrossRef]

X. Song, D. Wang, N. Chen, J. Bai, and H. Wang, “Reconstruction for free-space fluorescence tomography using a novel hybrid adaptive finite element algorithm,” Opt. Express 15, 18300–18317 (2007).
[CrossRef]

A. Cong and G. Wang, “A finite-element-based reconstruction method for 3D fluorescence tomography,” Opt. Express 13, 9847–9857 (2005).
[CrossRef]

D. Han, J. Tian, S. Zhu, J. Feng, C. Qin, B. Zhang, and X. Yang, “A fast reconstruction algorithm for fluorescence molecular tomography with sparsity regularization,” Opt. Express 18, 8630–8646 (2010).
[CrossRef]

R. Han, J. Liang, X. Qu, Y. Hou, N. Ren, J. Mao, and J. Tian, “A source reconstruction algorithm based on adaptive hp-FEM for bioluminescence tomography,” Opt. Express 17, 14481–14494 (2009).
[CrossRef]

C. Li, G. S. Mitchell, J. Dutta, S. Ahn, R. M. Leahy, and S. R. Cherry, “A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design,” Opt. Express 17, 7571–7585 (2009).
[CrossRef]

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004).
[CrossRef]

Phys. Med. Biol. (4)

Y. Lv, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol. 55, 4625–4645 (2010).
[CrossRef]

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]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52, 577–587(2007).
[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]

Proc. Natl. Acad. Sci. USA (1)

M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. USA 105, 19126–19131 (2008).
[CrossRef]

Other (2)

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems (Springer-Verlag, 1996).

J. Liu, Regularization Methods to Ill-Posed Problem and Its Applications (Science Press, 2005).

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Figures (12)

Fig. 1.
Fig. 1.

Different reconstruction regions at different mesh levels, where the red cylinder is the fluorescent target. (a) The reconstruction region for the first mesh consists of the entire mouse torso. (b) The green zone is the reconstruction region at the second level. (c) The green zone is the reconstruction region at the third level.

Fig. 2.
Fig. 2.

Our prototype FMT imaging system. (1) Laser, (2) optical scanner, (3) phantom, (4) rotational stage, (5) CCD camera. The components of the system are shown as described in Subsection 2.C.

Fig. 3.
Fig. 3.

(a) Torso of the mouse atlas model with a cylindrical fluorescent target in the liver, (b) the plane of excitation sources at z=16.5mm. The black points in (b) represent the location of the isotropic point sources. For each excitation source, fluorescence is detected at the opposite side with a 120° FOV.

Fig. 4.
Fig. 4.

A comparison of the reconstruction results for a single fluorescent target between our method and by only using the sparsity regularization method at each mesh level. (a), (c), (e) are the transverse views of the reconstruction at z=16.4mm plane using the proposed method at the initial coarse mesh, refined mesh, and final mesh, respectively, with a threshold of 70% of the maximum value (the black circles denote the real target). (b), (d), (f) are corresponding results only using the sparsity regularization at each mesh.

Fig. 5.
Fig. 5.

The transverse view of the reconstructed results for a single target at z=16.4mm plane, based on a fixed mesh, which is the same as the final mesh in our method. (a) The sparsity regularization method. (b) The Landweber iterative regularization.

Fig. 6.
Fig. 6.

(a), (b), (c), and (d) are results for single target of the transverse views at the z=16.4mm plane using our method with 0%, 10%, 20%, and 40% of the Gaussian noise, respectively, where the black circles denote the real target.

Fig. 7.
Fig. 7.

Reconstruction comparisons between two sets of optical parameters at z=16.4mm. (a) The transverse view of the result of the optical parameters in case 1. (b) The transverse view of the result of the optical parameters in case 2. The black circles represent the real target.

Fig. 8.
Fig. 8.

Reconstruction results for double fluorescent targets embedded in the liver using our method. (a) The isosurface view of the results from the initial coarse mesh with node values greater than 70% of the maximum value. (b) Transverse view of the reconstruction at z=16.5mm in the same mesh, where the black circle represents the real fluorescent target. (c) and (d) are the results of the refined, second level mesh. (e) and (f) are the final results of the third level mesh.

Fig. 9.
Fig. 9.

Reconstructed results for two targets with different centers distances at z=16.4mm plane. (a), (b), (c), and (d) are the transverse views of reconstructed results using our method with centers distances of 4, 3, 2.5, and 2mm, respectively, where the black circles denote the real target.

Fig. 10.
Fig. 10.

Physical phantom. (a) The homogeneous physical phantom. (b) The 3D view of the single fluorescent target in the cubic phantom. (c) The xy view on the z=10mm plane, where the black dots represent the excitation point source positions. Four degrees show the direction of the CCD camera during data acquisition.

Fig. 11.
Fig. 11.

Surface data acquired by CCD from four views. (a) front view, (b) right view, (c) back view, (d) left view.

Fig. 12.
Fig. 12.

Reconstructed results of the cubic phantom with a single fluorescent target. (a) The isosurface view of the results with top 30% of the maximum value. The red cylinder is the real target while the green zone is the reconstructed target. (b) The transverse view of the reconstruction on the z=9.5mm plane. The black circle represents the real target.

Tables (8)

Tables Icon

Table 1. Optical Parameters of the Mouse Organs

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Table 2. Reconstructed Results for a Single Target on the Final Mesh

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Table 3. Quantitative Comparison Between Sparsity Regularization and Landweber Iterative Regularization Based on a Fixed Mesh

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Table 4. Optical Parameters of the Mouse Organs at 670nm and 710nm

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Table 5. Optical Parameters of the Mouse Organs at 780nm and 830nm

Tables Icon

Table 6. Quantitative Comparison Between the Two Sets of Optical Properties

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Table 7. Quantitative Results of Our Method for Double Targets on Final Mesh

Tables Icon

Table 8. Optical Parameters of the Homogeneous Cubic Phantom

Equations (4)

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

{·(Dx(r)Φx(r))μax(r)Φx(r)=Θδ(rrs)·(Dm(r)Φm(r))μam(r)Φm(r)=Φx(r)ημaf(r)(rΩ),
Φm=AX.
minX{AXΦm22+λ1X1},
Xiter+1=(Iλ2ATA)Xiter+λ2ATΦm,

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