A finite-element-based reconstruction method for 3D fluorescence tomography
Optics Express, Vol. 13, Issue 24, pp. 9847-9857 (2005)
http://dx.doi.org/10.1364/OPEX.13.009847
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Abstract
In this paper, we propose a dual-excitation-mode methodology for three-dimensional (3D) fluorescence molecular tomography (FMT). For this modality, an effective reconstruction algorithm is developed to reconstruct fluorescent yield and lifetime using finite element techniques. In the steady state mode, a direct linear relationship is established between measured optical data on the body surface of a small animal and the unknown fluorescent yield inside the animal, and the reconstruction of fluorescent yield is formulated as a linear least square minimization problem. In the frequency domain mode, based on localization results of the fluorescent probe obtained using the first mode, the reconstruction of fluorescent lifetime is transformed into a relatively simple optimization problem. This algorithm helps overcome the ill-posedness with FMT. The effectiveness of the proposed method is numerically demonstrated using a heterogeneous mouse chest phantom, showing good accuracy, stability, noise characteristics and computational efficiency.
© 2005 Optical Society of America
1. Introduction
1 . A. B. Milstein , S. O. , K. J. Webb , C. A. Bouman , Q. Zhang , D. A. Boas , and R. P. Milane , “ Fluorescence optical diffusion tomography ,” Appl. Opt. 42 , 3081 – 3094 ( 2003 ). [CrossRef] [PubMed]
2 . G. Choy , P. Choyke , and S. K. Libutti , “ Current advances in molecular imaging: noninvasive in vivo bioluminescent and fluorescent optical Imaging in Cancer Research ,” Mol. Imag. 2 , 303 – 312 ( 2003 ). [CrossRef]
3 . V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weissleder , “ Looking and listening to light: the evolution of whole-body photonic imaging ,” Nature Biotech. 23 , 313 – 320 ( 2005 ). [CrossRef]
4 . V. Ntziachristos and R. Weissleder , “ Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation ,” Opt. Lett. 26 , 893 – 895 ( 2001 ). [CrossRef]
5 . M. A. O’Leary , D. A. Boas , X. D. Li , B. Chance , and A. G. Yodh , “ Fluorescence lifetime imaging in turbid media ,” Opt. Lett. 21 , 158 – 160 ( 1996 ). [CrossRef] [PubMed]
6 . A. D. Klose and A. H. Hielscher , “ Fluorescence tomography with simulated data based on the equation of radiative transfer ,” Opt. Lett. 28 , 1019 – 1021 ( 2003 ). [CrossRef] [PubMed]
7 . 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 ( 2004 ). [CrossRef]
8 . H. Jiang , “ Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations ,” Appl. Opt. 37 , 5337 – 5343 ( 1998 ). [CrossRef]
9 . A. B. Milstein , J. J. Stott , S. Oh , D. A. Boas , and R. P. Millane , “ Fluorescence optical diffusion tomography using multiple-frequency data ,” J. Opt. Soc. Am. A 21 , 1035 – 1049 ( 2004 ). [CrossRef]
10 . 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 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402 [CrossRef] [PubMed]
11 . S. Lam , F. Lesage , and X. Intes , “ Time domain fluorescent diffuse optical tomography: analytical expressions ,” Opt. Express 13 , 2263 – 2275 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2263 . [CrossRef] [PubMed]
12 . A. Godavarty , E. M. Sevick-Muraca , and M. J. Eppstein , “ Three-dimensional fluorescence lifetime tomography ,” Med. Phys. 32 , 992 – 1000 ( 2005 ). [CrossRef] [PubMed]
3 . V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weissleder , “ Looking and listening to light: the evolution of whole-body photonic imaging ,” Nature Biotech. 23 , 313 – 320 ( 2005 ). [CrossRef]
12 . A. Godavarty , E. M. Sevick-Muraca , and M. J. Eppstein , “ Three-dimensional fluorescence lifetime tomography ,” Med. Phys. 32 , 992 – 1000 ( 2005 ). [CrossRef] [PubMed]
13 . W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE 5535 , 679 – 686 ( 2004 ). [CrossRef]
14 . W. Cong , G. Wang , and D. Kumar , et al. , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express 13 , 6756 – 6771 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 . [CrossRef] [PubMed]
15 . G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys. 31 , 2289 – 2299 ( 2004 ). [CrossRef] [PubMed]
2. Methodology
2.1. Diffusion models
16 . 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]
17 . E. Shives , Y. Xu , and H. Jiang , “ Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye ,” Opt. Express 10 , 1557 – 1562 ( 2002 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1557 . [PubMed]
18 . R. C. Haskell , L. O. Svaasand , T. T. Tsay , T. C. Feng , M. S. McAdams , and B. J. Tromberg , “ Boundary conditions for the diffusion equation in radiative transfer ,” J. Opt. Soc. Am. A 11 , 2727 – 2741 ( 1994 ). [CrossRef]
19 . 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 conditons ,”, Med. Phys. 22 , 1779 – 1792 ( 1995 ). [CrossRef] [PubMed]
19 . 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 conditons ,”, Med. Phys. 22 , 1779 – 1792 ( 1995 ). [CrossRef] [PubMed]
20 . A. Godavarty , M. J. Eppstein , C. Zhang , S. Theru , A. B. Thompson , M. Gurfinkel , and E. M. Sevick-Muraca , “ Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera ,” Phys. Med. Biol. 48 , 1701 – 1720 ( 2003 ). [CrossRef] [PubMed]
1 . A. B. Milstein , S. O. , K. J. Webb , C. A. Bouman , Q. Zhang , D. A. Boas , and R. P. Milane , “ Fluorescence optical diffusion tomography ,” Appl. Opt. 42 , 3081 – 3094 ( 2003 ). [CrossRef] [PubMed]
8 . H. Jiang , “ Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations ,” Appl. Opt. 37 , 5337 – 5343 ( 1998 ). [CrossRef]
2.2. Reconstruction method
16 . 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]
19 . 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 conditons ,”, Med. Phys. 22 , 1779 – 1792 ( 1995 ). [CrossRef] [PubMed]
2.2.1. Reconstruction of fluorescent yield
2.2.2. Reconstruction of fluorescent lifetime
3. Simulations and results
3.1. Numerical experiments setup
9 . A. B. Milstein , J. J. Stott , S. Oh , D. A. Boas , and R. P. Millane , “ Fluorescence optical diffusion tomography using multiple-frequency data ,” J. Opt. Soc. Am. A 21 , 1035 – 1049 ( 2004 ). [CrossRef]
14 . W. Cong , G. Wang , and D. Kumar , et al. , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express 13 , 6756 – 6771 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 . [CrossRef] [PubMed]
3.2. Single fluorescent target
3.3. Two fluorescent targets
4. Discussion and conclusion
21 . J. R. Mansfield , K. W. Gossage , C. C. Hoyt , and R. M. Levenson , ” Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging ,” J. Biomed. Opt. 10 , 041207 ( 2005 ). [CrossRef]
Acknowledgments
References and links
1 . | A. B. Milstein , S. O. , K. J. Webb , C. A. Bouman , Q. Zhang , D. A. Boas , and R. P. Milane , “ Fluorescence optical diffusion tomography ,” Appl. Opt. 42 , 3081 – 3094 ( 2003 ). [CrossRef] [PubMed] |
2 . | G. Choy , P. Choyke , and S. K. Libutti , “ Current advances in molecular imaging: noninvasive in vivo bioluminescent and fluorescent optical Imaging in Cancer Research ,” Mol. Imag. 2 , 303 – 312 ( 2003 ). [CrossRef] |
3 . | V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weissleder , “ Looking and listening to light: the evolution of whole-body photonic imaging ,” Nature Biotech. 23 , 313 – 320 ( 2005 ). [CrossRef] |
4 . | V. Ntziachristos and R. Weissleder , “ Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation ,” Opt. Lett. 26 , 893 – 895 ( 2001 ). [CrossRef] |
5 . | M. A. O’Leary , D. A. Boas , X. D. Li , B. Chance , and A. G. Yodh , “ Fluorescence lifetime imaging in turbid media ,” Opt. Lett. 21 , 158 – 160 ( 1996 ). [CrossRef] [PubMed] |
6 . | A. D. Klose and A. H. Hielscher , “ Fluorescence tomography with simulated data based on the equation of radiative transfer ,” Opt. Lett. 28 , 1019 – 1021 ( 2003 ). [CrossRef] [PubMed] |
7 . | 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 ( 2004 ). [CrossRef] |
8 . | H. Jiang , “ Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations ,” Appl. Opt. 37 , 5337 – 5343 ( 1998 ). [CrossRef] |
9 . | A. B. Milstein , J. J. Stott , S. Oh , D. A. Boas , and R. P. Millane , “ Fluorescence optical diffusion tomography using multiple-frequency data ,” J. Opt. Soc. Am. A 21 , 1035 – 1049 ( 2004 ). [CrossRef] |
10 . | 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 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402 [CrossRef] [PubMed] |
11 . | S. Lam , F. Lesage , and X. Intes , “ Time domain fluorescent diffuse optical tomography: analytical expressions ,” Opt. Express 13 , 2263 – 2275 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2263 . [CrossRef] [PubMed] |
12 . | A. Godavarty , E. M. Sevick-Muraca , and M. J. Eppstein , “ Three-dimensional fluorescence lifetime tomography ,” Med. Phys. 32 , 992 – 1000 ( 2005 ). [CrossRef] [PubMed] |
13 . | W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE 5535 , 679 – 686 ( 2004 ). [CrossRef] |
14 . | W. Cong , G. Wang , and D. Kumar , et al. , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express 13 , 6756 – 6771 ( 2005 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 . [CrossRef] [PubMed] |
15 . | G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys. 31 , 2289 – 2299 ( 2004 ). [CrossRef] [PubMed] |
16 . | 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] |
17 . | E. Shives , Y. Xu , and H. Jiang , “ Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye ,” Opt. Express 10 , 1557 – 1562 ( 2002 ) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1557 . [PubMed] |
18 . | R. C. Haskell , L. O. Svaasand , T. T. Tsay , T. C. Feng , M. S. McAdams , and B. J. Tromberg , “ Boundary conditions for the diffusion equation in radiative transfer ,” J. Opt. Soc. Am. A 11 , 2727 – 2741 ( 1994 ). [CrossRef] |
19 . | 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 conditons ,”, Med. Phys. 22 , 1779 – 1792 ( 1995 ). [CrossRef] [PubMed] |
20 . | A. Godavarty , M. J. Eppstein , C. Zhang , S. Theru , A. B. Thompson , M. Gurfinkel , and E. M. Sevick-Muraca , “ Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera ,” Phys. Med. Biol. 48 , 1701 – 1720 ( 2003 ). [CrossRef] [PubMed] |
21 . | J. R. Mansfield , K. W. Gossage , C. C. Hoyt , and R. M. Levenson , ” Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging ,” J. Biomed. Opt. 10 , 041207 ( 2005 ). [CrossRef] |
OCIS Codes
(110.6960) Imaging systems : Tomography
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence
ToC Category:
Research Papers
History
Original Manuscript: September 6, 2005
Revised Manuscript: September 1, 2005
Published: November 28, 2005
Citation
Alexander Cong and Ge Wang, "A finite-element-based reconstruction method for 3D fluorescence tomography," Opt. Express 13, 9847-9857 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-24-9847
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References
- A. B. Milstein, S. O., K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Milane, “Fluorescence optical diffusion tomography,” Appl. Opt. 42, 3081–3094 (2003). [CrossRef] [PubMed]
- G. Choy, P. Choyke, and S. K. Libutti, “Current advances in molecular imaging: noninvasive in vivo bioluminescent and fluorescent optical Imaging in Cancer Research,” Mol. Imag. 2, 303–312 (2003). [CrossRef]
- V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nature Biotech. 23, 313–320 (2005). [CrossRef]
- V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26, 893–895 (2001). [CrossRef]
- M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996). [CrossRef] [PubMed]
- A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative transfer,” Opt. Lett. 28, 1019–1021 (2003). [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 (2004). [CrossRef]
- H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt. 37, 5337–5343 (1998). [CrossRef]
- A. B. Milstein, J. J. Stott, S. Oh, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomography using multiple-frequency data,” J. Opt. Soc. Am. A 21, 1035–1049 (2004). [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) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402</a> [CrossRef] [PubMed]
- S. Lam, F. Lesage, and X. Intes, “Time domain fluorescent diffuse optical tomography: analytical expressions,” Opt. Express 13, 2263–2275 (2005) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2263.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-7-2263.</a> [CrossRef] [PubMed]
- A. Godavarty, E. M. Sevick-Muraca and M. J. Eppstein, “Three-dimensional fluorescence lifetime tomography,” Med. Phys. 32, 992–1000 (2005). [CrossRef] [PubMed]
- W. Cong, D. Kumar, Y. Liu, A. Cong, and G.Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004). [CrossRef]
- W. Cong, G. Wang, D. Kumar, et al., “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13, 6756–6771 (2005) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756.</a> [CrossRef] [PubMed]
- G.Wang, Y. Li and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004). [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]
- E. Shives, Y. Xu, and H. Jiang, “Fluorescence lifetime tomography of turbid media based on an oxygen-sensitive dye,” Opt. Express 10, 1557–1562 (2002) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1557.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-26-1557.</a> [PubMed]
- R. C. Haskell, L. O. Svaasand, T. T. Tsay, T. C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994). [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 conditons,” Med. Phys. 22, 1779–1792 (1995). [CrossRef] [PubMed]
- A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003). [CrossRef] [PubMed]
- J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 041207 (2005). [CrossRef]
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