Practical reconstruction method for bioluminescence tomography

Wenxiang Cong; Ge Wang; Durairaj Kumar; Yi Liu; Ming Jiang; Lihong V. Wang; Eric A. Hoffman; Geoffrey McLennan; Paul B. McCray; Joseph Zabner; Alexander Cong

doi:10.1364/OPEX.13.006756

Practical reconstruction method for bioluminescence tomography

Wenxiang Cong, Ge Wang, Durairaj Kumar, Yi Liu, Ming Jiang, Lihong V. Wang, Eric A. Hoffman, Geoffrey McLennan, Paul B. McCray, Joseph Zabner, and Alexander Cong

Optics Express
Vol. 13,
Issue 18,
pp. 6756-6771
(2005)
•https://doi.org/10.1364/OPEX.13.006756

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Wenxiang Cong, Ge Wang, Durairaj Kumar, Yi Liu, Ming Jiang, Lihong V. Wang, Eric A. Hoffman, Geoffrey McLennan, Paul B. McCray, Joseph Zabner, and Alexander Cong, "Practical reconstruction method for bioluminescence tomography," Opt. Express 13, 6756-6771 (2005)

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Related Topics
Table of Contents Category
- Research Papers
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Tomography (110.6960)
- Image reconstruction techniques (170.3010)
- Spectroscopy, fluorescence and luminescence (170.6280)

About this Article
History
- Original Manuscript: July 11, 2005
- Revised Manuscript: August 16, 2005
- Manuscript Accepted: August 18, 2005
- Published: September 5, 2005

Accessible

Open Access

Abstract

Bioluminescence tomography (BLT) is used to localize and quantify bioluminescent sources in a small living animal. By advancing bioluminescent imaging to a tomographic framework, it helps to diagnose diseases, monitor therapies and facilitate drug development. In this paper, we establish a direct linear relationship between measured surface photon density and an unknown bioluminescence source distribution by using a finite-element method based on the diffusion approximation to the photon propagation in biological tissue. We develop a novel reconstruction algorithm to recover the source distribution. This algorithm incorporates a priori knowledge to define the permissible source region in order to enhance numerical stability and efficiency. Simulations with a numerical mouse chest phantom demonstrate the feasibility of the proposed BLT algorithm and reveal its performance in terms of source location, density, and robustness against noise. Lastly, BLT experiments are performed to identify the location and power of two light sources in a physical mouse chest phantom.

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References

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|
Author
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Publication

S. Bhaumik and S. S. Gambhir, “Optical imaging of Renilla luciferase reporter gene expression in living mice,” Proc. Natl. Acad. Sci. USA 99, 377–382 (2002).
[Crossref]
C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]
P. Ray, A.M. Wu, and S.S. Gambhir, “Optical bioluminescence and positron emission tomography imaging of a novel fusion reporter gene in tumor xenografts of living mice,” Cancer Res. 63, 1160–1165 (2003).
[PubMed]
W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6, 432–440 (2001).
[Crossref] [PubMed]
J. Welch and M. J. C. van Gemert, Optical and Thermal response of laser-irradiated tissue (Plenum Press, New York,1995).
A.D. Klose, V. Ntziachristos, and A.H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[Crossref]
V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]
R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with non-contact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
[Crossref]
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]
J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A 22, 546–551 (2005).
[Crossref]
T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]
M. Gurfinkel, T. S. Pan, and E. M. Sevick-Muraca, “Determination of optical properties in semi-infinite turbid media using imaging measurements of frequency-domain photon migration obtained with an intensified charge-coupled device,” J. Biomed. Opt. 9, 1336–1346 (2004).
[Crossref] [PubMed]
M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]
G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).
G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[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]
X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]
J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis ( Wiley, New York,1976).
M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: Boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
[Crossref] [PubMed]
S. S. Rao, The finite element method in engineering (Butterworth-Heinemann, Boston,1999).
S. C. Brenner and R. L. Scott, The Mathematical Theory of Finite Elements (Springer, Berlin-Heidelberg-New York,1994).
J. C. Ye, K. J. Webb, C. A. Bouman, and R. P. Millane, “Optical diffusion tomography by iterative-coordinate-descent optimization in a Bayesian framework,” J. Opt. Soc. Am. A 16, 2400–2412 (1999).
[Crossref]
P. E. Gill, W. Murray, and M. Wright, Practical Optimization (Academic Press, New York, 1981).
T. Chen, “Digital Camera System Simulator and applications,” Ph. D. Thesis, Stanford University (2003).
S. Holder, Electrical Impedance Tomography (Institute of Physics Publishing, Bristol and Philadelphia,2005).

2005 (3)

A.D. Klose, V. Ntziachristos, and A.H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[Crossref]

J. Ripoll, D. Yessayan, G. Zacharakis, and V. Ntziachristos, “Experimental determination of photon propagation in highly absorbing and scattering media,” J. Opt. Soc. Am. A 22, 546–551 (2005).
[Crossref]

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]

2004 (5)

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[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]

X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]

R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with non-contact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
[Crossref]

M. Gurfinkel, T. S. Pan, and E. M. Sevick-Muraca, “Determination of optical properties in semi-infinite turbid media using imaging measurements of frequency-domain photon migration obtained with an intensified charge-coupled device,” J. Biomed. Opt. 9, 1336–1346 (2004).
[Crossref] [PubMed]

2003 (2)

P. Ray, A.M. Wu, and S.S. Gambhir, “Optical bioluminescence and positron emission tomography imaging of a novel fusion reporter gene in tumor xenografts of living mice,” Cancer Res. 63, 1160–1165 (2003).
[PubMed]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

2002 (3)

S. Bhaumik and S. S. Gambhir, “Optical imaging of Renilla luciferase reporter gene expression in living mice,” Proc. Natl. Acad. Sci. USA 99, 377–382 (2002).
[Crossref]

C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]

2001 (1)

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

1999 (1)

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

1993 (1)

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]

1992 (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref] [PubMed]

Arridge, S. R.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[Crossref] [PubMed]

Bachmann, M. H.

C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]

Bhaumik, S.

S. Bhaumik and S. S. Gambhir, “Optical imaging of Renilla luciferase reporter gene expression in living mice,” Proc. Natl. Acad. Sci. USA 99, 377–382 (2002).
[Crossref]

Bouman, C. A.

Bremer, C.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]

Brenner, S. C.

S. C. Brenner and R. L. Scott, The Mathematical Theory of Finite Elements (Springer, Berlin-Heidelberg-New York,1994).

Cable, M. D.

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

Chance, B.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]

Chen, T.

T. Chen, “Digital Camera System Simulator and applications,” Ph. D. Thesis, Stanford University (2003).

Cong, A.

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]

Cong, W.

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]

Contag, C.

C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]

Delpy, D. T.

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]

Duderstadt, J. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis ( Wiley, New York,1976).

Farrell, T. J.

Gambhir, S. S.

S. Bhaumik and S. S. Gambhir, “Optical imaging of Renilla luciferase reporter gene expression in living mice,” Proc. Natl. Acad. Sci. USA 99, 377–382 (2002).
[Crossref]

Gambhir, S.S.

Gemert, M. J. C. van

J. Welch and M. J. C. van Gemert, Optical and Thermal response of laser-irradiated tissue (Plenum Press, New York,1995).

Gill, P. E.

P. E. Gill, W. Murray, and M. Wright, Practical Optimization (Academic Press, New York, 1981).

Gu,, X.

X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]

Gurfinkel, M.

Guven, M.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]

Hamilton, L. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis ( Wiley, New York,1976).

Hielscher, A.H.

Hiraoka, M.

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]

Hoffman, E. A.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Holder, S.

S. Holder, Electrical Impedance Tomography (Institute of Physics Publishing, Bristol and Philadelphia,2005).

Intes, X.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]

Jiang, H.

X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]

Jiang, M.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[Crossref] [PubMed]

Klose, A.D.

Kumar, D.

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]

Larcom, L.

X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]

Li, Y.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[Crossref] [PubMed]

Liu, Y.

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]

McLennan, G.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Meinel, J.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Millane, R. P.

Murray, W.

P. E. Gill, W. Murray, and M. Wright, Practical Optimization (Academic Press, New York, 1981).

Nelson, M. B.

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

Ntziachristos, V.

R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with non-contact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
[Crossref]

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]

Pan, T. S.

Patterson, M. S.

Rao, S. S.

S. S. Rao, The finite element method in engineering (Butterworth-Heinemann, Boston,1999).

Ray, P.

Rice, W.

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

Ripoll, J.

R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with non-contact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
[Crossref]

Schultz, R.

R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with non-contact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
[Crossref]

Schweiger, M.

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]

Scott, R. L.

S. C. Brenner and R. L. Scott, The Mathematical Theory of Finite Elements (Springer, Berlin-Heidelberg-New York,1994).

Sevick-Muraca, E. M.

Suter, M.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Tung, C.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]

Wang, G.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31, 2289–2299 (2004).
[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]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Wang, L. V.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Webb, K. J.

Weissleder, R.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]

Welch, J.

J. Welch and M. J. C. van Gemert, Optical and Thermal response of laser-irradiated tissue (Plenum Press, New York,1995).

Wilson, B.

Wright, M.

P. E. Gill, W. Murray, and M. Wright, Practical Optimization (Academic Press, New York, 1981).

Wu, A.M.

Yazici, B.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]

Ye, J. C.

Yessayan, D.

Zacharakis, G.

Zhang, Q.

X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]

Annu. Rev. Biomed. Eng. (1)

C. Contag and M. H. Bachmann, “Advances in Bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4, 235–260 (2002).
[Crossref] [PubMed]

Cancer Res. (1)

IEEE Trans. Med. Imag. (1)

R. Schultz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with non-contact measurements,” IEEE Trans. Med. Imag. 23, 492–500 (2004).
[Crossref]

J. Biomed. Opt. (2)

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

J. Comput. Phys. (1)

J. Opt. Soc. Am. A (2)

Med. Phys. (4)

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]

Nat. Med. (1)

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002).
[Crossref] [PubMed]

Opt. Express (1)

X. Gu,, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12, 3996–4000 (2004).
[Crossref]

Phys. Med. Biol. (1)

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50, 2837–2858 (2005).
[Crossref] [PubMed]

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

S. Bhaumik and S. S. Gambhir, “Optical imaging of Renilla luciferase reporter gene expression in living mice,” Proc. Natl. Acad. Sci. USA 99, 377–382 (2002).
[Crossref]

Proc. SPIE (1)

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]

Radiology (1)

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, “Development of the first bioluminescent CT scanner,” Radiology 229(P), 566 (2003).

Other (7)

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor analysis ( Wiley, New York,1976).

J. Welch and M. J. C. van Gemert, Optical and Thermal response of laser-irradiated tissue (Plenum Press, New York,1995).

S. S. Rao, The finite element method in engineering (Butterworth-Heinemann, Boston,1999).

S. C. Brenner and R. L. Scott, The Mathematical Theory of Finite Elements (Springer, Berlin-Heidelberg-New York,1994).

P. E. Gill, W. Murray, and M. Wright, Practical Optimization (Academic Press, New York, 1981).

T. Chen, “Digital Camera System Simulator and applications,” Ph. D. Thesis, Stanford University (2003).

S. Holder, Electrical Impedance Tomography (Institute of Physics Publishing, Bristol and Philadelphia,2005).

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Fig. 1. Numerical simulation for BLT reconstruction of one source. (a) The true source distribution in the left lung consisting of 6 volume elements and having a homogeneous density of 200.0pico-Watts/mm³, and (b) the counterpart reconstructed from the surface data corrupted by 10% Gaussian noise. The average density error is 0.5%.

Download Full Size | PPT Slide | PDF

Fig. 2. Numerical simulation for BLT reconstruction of two sources in the left and right lungs, respectively. (a) The true source distribution with a density of 200.0pico-Watts/mm³ for each source, and (b) the counterparts reconstructed from the surface data corrupted by 10% Gaussian noise. The average density error is 3%.

Download Full Size | PPT Slide | PDF

Fig. 3. Numerical simulation for BLT reconstruction of two sources in the left lung. (a) The true source distribution with density 200.0pico-Watts/mm³ for both the sources, and (b) the counterparts reconstructed from the surface data corrupted by 10% Gaussian noise. The average density error is 5%.

Download Full Size | PPT Slide | PDF

Fig. 4. Numerical simulation for BLT reconstruction of three sources: two in the left lung and one in the right lung. (a) The true source distribution in which each source consists of several volume elements and has density 200.0pico-Watts/mm³, and (b) the counterparts reconstructed from the surface data corrupted by 10% Gaussian noise. The average density error is 3%.

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Fig. 5. Numerical simulation for BLT reconstruction of four sources. (a) Four bioluminescent source separations of 1mm between first and second, 2mm between second and third, and 3mm between third and fourth source with the density of 200.0 pico-Watts/mm³ for each source, and (b) the counterparts reconstructed from the surface data corrupted by 10% Gaussian noise. The source positions are accurately identified with their density being recovered to 196.1 pico-Watts/mm³, 184.7 pico-Watts/mm³, 175.1 pico-Watts/mm³ and 181.5 pico-Watts/mm³, respectively.

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Fig. 6. (a), (b) and (c) are the reconstructed source distributions (with unit pico-Watts/mm³) from the surface noise-free data subject to permissible source regions

Ω_{s}^{1}

Ω_{s}^{2}

and

Ω_{s}^{3}

, respectively. They are identical to the actual source in position and strength.

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Fig. 7. (a), (b) and (c) are the reconstructed source distribution (with unit pico-Watts/mm³) from the surface data corrupted by 5% Gaussian noise subject to permissible source regions

Ω_{s}^{1}

Ω_{s}^{2}

and

Ω_{s}^{3}

, respectively.

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Fig. 8. (a), (b) and (c) are the reconstructed source distributions (with unit pico-Watts/mm³) from the surface data corrupted by 10% Gaussian noise subject to permissible source regions

Ω_{s}^{1}

Ω_{s}^{2}

and

Ω_{s}^{3}

, respectively.

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Fig. 9. (a), (b) and (c) are the reconstructed source distribution (with unit pico-Watts/mm³), subject to permissible source regions

Ω_{s}^{1}

Ω_{s}^{2}

and

Ω_{s}^{3}

, respectively. The measured surface data are corrupted by 15% Gaussian noise.

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Fig. 10. Mouse Chest phantom. (a) A heterogeneous mouse phantom consisting of bone (B), heart (H), lungs (L), and muscle (M); (b) a middle cross-section through two hollow cylinders for hosting luminescent sources in the left lung. The four arrows show the direction of the CCD camera during data acquisition.

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Fig. 11. Comparison of experimental and computational photon density profiles for determination of the optical parameters of the phantom materials: (a) Muscle (M), (b) Lung (L), (c) Heart (H), and (d) Bone (B).

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Fig. 12. Luminescent views of the side surface covering cylindrical phantom taken using a CCD camera in four directions 90 degrees apart. (a) Front view, (b) Right view, (c) Back view, and (d) Left view.

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Fig. 13. (a) Finite element model for a middle portion of the mouse chest phantom. (b) Physical experiment on BLT reconstruction of two sources in the left lung of the mouse chest phantom. The difference between the reconstructed and real source centers was less than 1mm for both the sources at height 15.0mm. The maximum error of source power was about 18.5%.

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Fig. 14. Comparison between measured and computational photon density profiles along the detection circle on the phantom surface at heights (a) 10.6mm, (b) 15.9mm, and (c) 21.1mm, from the top surface of the model.

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Tables (3)

Table 1. Optical parameters for the numerical phantom

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Table 2. Relative error (%) with BLT results of total source power

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Table 3. Optical parameters of the mouse chest phantom.

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Equations (19)

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{\begin{matrix} - \nabla \cdot (D (x) ∇Φ (x)) + μ_{a} (x) Φ (x) = S (x) (x ∊ Ω) \\ D (x) = {(3 (μ_{a} (x) + (1 - g) μ_{s} (x)))}^{- 1} \end{matrix}

Φ (x) + 2 A (x; n, n′) D (x) (v (x) \cdot ∇Φ (x)) = 0 (x ∊ \partial Ω)

A (x; n, n′) \approx \frac{(1 + R (x))}{(1 - R (x))}

Q (x) = - D (x) (v \cdot ∇Φ (x)) = \frac{Φ (x)}{(2 A (x; n, n′))} (x ∊ \partial Ω) .

\int_{Ω} (D (x) (\nabla Φ (x)) \cdot (\nabla Ψ (x)) + μ_{a} (x) Φ (x) Ψ (x)) d x

+ \frac{\int_{\partial Ω} Φ (x) Ψ (x)}{(2 A (x; n, n')) d x} = \int_{Ω} S (x) Ψ (x) d x

Φ (x) \approx Φ^{h} (x) = \sum_{k = 1}^{T} ϕ_{k} φ_{k} (x) when x ∊ Ω,

S (x) \approx S^{h} (x) = \sum_{k = 1}^{N_{s}} S_{k} γ_{k} (x) when x ∊ Ω

([K] + [C] + [B]) {Φ} = [M] {Φ} = [F] {S},

{\begin{matrix} k_{ij} = \int_{Ω} (D (x) (\nabla φ_{i} (x)) \cdot (\nabla φ_{i} (x)) d x \\ c_{ij} = \int_{Ω} μ_{a} (x) φ_{i} (x) φ_{j} (x) d x \\ f_{ij} = \int_{Ω} φ_{i} (x) γ_{j} (x) d x \\ b_{ij} = \frac{\int_{\partial Ω} φ_{i} (x) φ_{j} (x)}{(2 A (x : n, n')) d x} \end{matrix}

[\begin{matrix} M_{11} & M_{12} \\ M_{12}^{T} & M_{22} \end{matrix}] {\begin{matrix} Φ^{m} \\ Φ^{*} \end{matrix}} = [\begin{matrix} F_{11} & F_{12} \\ F_{21} & F_{22} \end{matrix}] {\begin{matrix} S^{p} \\ S^{*} \end{matrix}},

(M_{11} - M_{12} M_{22}^{- 1} M_{12}^{T}) Φ^{m} = (F_{11} - M_{12} M_{22}^{- 1} F_{21}) S^{p} .

Φ^{m} = {(M_{11} - M_{12} M_{22}^{- 1} M_{12}^{T})}^{- 1} (F_{11} - M_{12} M_{22}^{- 1} F_{21}) S^{p},

p_{k} = {(\frac{1}{2 π Φ_{k}^{meas}})}^{\frac{1}{2}} \exp [- \frac{{(Φ_{k}^{m} - Φ_{k}^{meas})}^{2}}{2 Φ_{k}^{meas}}]

p (S^{p}) = {(\frac{\det (W)}{π^{M}})}^{\frac{1}{2}} \exp [- \sum_{k = 1}^{M} \frac{{(Φ_{k}^{m} - Φ_{k}^{meas})}^{2}}{2 Φ_{k}^{meas}}],

Θ (S^{p}) = {(Φ^{m} - Φ^{meas})}^{T} W (Φ^{m} - Φ^{meas}) .

min_{U_{i} \geq s_{i} \geq 0} Θ (S^{p}) .

Ω_{s}^{1} = \{(x, y, z)| x < 0, 5.6 < z < 7.0, (x, y, z) ∊ L\},

Ω_{s}^{2} = \{(x, y, z)| x < 0, 5.6 < z < 8.0, (x, y, z) ∊ L\}

Material	Muscle (M)	Lung (L)	Heart (H)	Bone (B)
μ_a [mm^-1]	0.10	0.22	0.21	0.16
μ_s ′ [mm^-1]	1.20	2.30	2.00	1.28

Permissible region	Source	Noise (0%)	Noise (5%)	Noise (10%)	Noise (15%)
$Ω_{s}^{1}$	Source-1	1.0	5.0	13.0	4.8
$Ω_{s}^{1}$	Source-2	0.5	0.5	1.2	9.5
$Ω_{s}^{2}$	Source-1	1.0	5.1	9.1	14.1
$Ω_{s}^{2}$	Source-2	0.5	4.5	9.3	14.4
$Ω_{s}^{3}$	Source-1	7.0	4.2	13.2	24.1
$Ω_{s}^{3}$	Source-2	8.5	23.0	33.0	12.6

Material	Muscle (M)	Lung (L)	Heart (H)	Bone (B)
μ_a [mm^-1]	0.007	0.023	0.011	0.001
μ_s ′ [mm^-1]	1.031	2.000	1.096	0.060

Material	Muscle (M)	Lung (L)	Heart (H)	Bone (B)
μ_a [mm^-1]	0.10	0.22	0.21	0.16
μ_s ′ [mm^-1]	1.20	2.30	2.00	1.28

Permissible region	Source	Noise (0%)	Noise (5%)	Noise (10%)	Noise (15%)
$Ω_{s}^{1}$	Source-1	1.0	5.0	13.0	4.8
$Ω_{s}^{1}$	Source-2	0.5	0.5	1.2	9.5
$Ω_{s}^{2}$	Source-1	1.0	5.1	9.1	14.1
$Ω_{s}^{2}$	Source-2	0.5	4.5	9.3	14.4
$Ω_{s}^{3}$	Source-1	7.0	4.2	13.2	24.1
$Ω_{s}^{3}$	Source-2	8.5	23.0	33.0	12.6