Abstract

We propose a digital spectral separation (DSS) system and methods to extract spectral information optimally from a weak multispectral signal such as in the bioluminescent imaging (BLI) studies. This system utilizes our newly invented spatially-translated spectral-image mixer (SSM), which consists of dichroic beam splitters, a mirror, and a DSS algorithm. The DSS approach overcomes the shortcomings of the data acquisition scheme used for the current BLI systems. Primarily, using our DSS scheme, spectral information will not be filtered out. Accordingly, truly parallel multi-spectral multi-view acquisition is enabled for the first time to minimize experimental time and optimize data quality. This approach also permits recovery of the bioluminescent signal time course, which is useful to study the kinetics of multiple bioluminescent probes using multi-spectral bioluminescence tomography (MSBT).

© 2008 Optical Society of America

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  1. R. Weissleder and V. Ntziachristos, "Shedding light onto live molecular targets," Nat. Med. 9, 123-128 (2003).
    [CrossRef] [PubMed]
  2. V. Ntziachristos, J. Ripoll, L. H. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole-body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
    [CrossRef] [PubMed]
  3. M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, J. H. Rao, "Self-illuminating quantum dot conjugates for in vivo imaging," Nat. Biotechnol. 24, 339-343 (2006).
    [CrossRef] [PubMed]
  4. C. Kuo, O. Conquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Imaging. 4, 370 (2005).
  5. C. Kuo, H. Xu, and B. Rice, "Improved techniques in Diffuse Luminescent Tomography on whole animal meshes," in "Annual Meeting of The Society for Molecular Imaging," Hawaii, 2006.
  6. C. Kuo, O. Conquoz, T. Troy, H. Xu, and B. Rice, "Three-dimensional reconstruction of in Vivo Bioluminescent sources based on multi-spectral imaging," J. Biomed. Opt. 12, 024007 (Apr. 19, 2007).
    [CrossRef]
  7. G. Wang, E. A. Hoffman, and G. McLennan, "Systems and methods for bioluminescent computed tomographic reconstruction," US Patent Application. No. 10/791140, 2002.
  8. G. Wang,  et al., "Development of the first bioluminescent CT scanner," Radiology 229, 566 (2003).
  9. W. X. Cong,  et al., "Practical reconstruction method for bioluminescence tomography," Opt. Express. 13, 6756-6771 (2005).
    [CrossRef] [PubMed]
  10. A. Cong and G. Wang, "Multi-spectral bioluminescence tomography: Methodology and simulation," Int. J. Biomed. Imaging ID57614 (2006).
    [CrossRef]
  11. W. Cong and G. Wang, "Boundary integral method for bioluminescence tomography," J. Biomed. Opt. 11, 020503 (2006).
    [CrossRef] [PubMed]
  12. W. Cong,  et al., "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33, 679-686 (2006).
    [CrossRef] [PubMed]
  13. G. Wang,  et al., "In vivo mouse studies with bioluminescence tomography," Opt. Express. 147801-7809 (2006).
    [CrossRef] [PubMed]
  14. W. Cong, A. Cong, H. Shen, Y. Liu, and G. Wang, "Flux vector formulation for photon propagation in the biological tissue," Opt. Lett. 32, 2837-2839 (2007).
    [CrossRef] [PubMed]
  15. V. Ntziachristos, "Fluorescence molecular imaging," Annu. Rev. Biomed. Eng. 8, 1-33 (2006).
    [CrossRef] [PubMed]
  16. G. Wang, Y. Li, and M. Jiang, "Uniqueness theorems in bioluminescence tomography," Med. Phys. 31, 2289-2299 (2004).
    [CrossRef] [PubMed]
  17. W. Han, W. Cong, and G. Wang, "Mathematical study and numerical simulation ofmultispectral bioluminescence tomography," Int. J. Biomed. Imaging ID54390 (2006).
    [CrossRef]
  18. G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "3D bioluminescence imaging by use of a combined optical-PET tomographic system: A computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
    [CrossRef] [PubMed]
  19. A. J. Chaudhari,  et al., "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
    [CrossRef] [PubMed]
  20. H. Dehghani,  et al., "Spectrally resolved bioluminescence optical tomography," Opt. Lett. 31, 365-367 (2006).
    [CrossRef] [PubMed]
  21. X. Qian, R. Svensson, X. Y. Ying, H. Shen, W. Cong, M. Henry, G. Wang, "Measurement of temperature-dependent bioluminescent spectra in Vivo," in "Annual Meeting of The Society for Molecular Imaging," Providence, Rhode Island, (2007).
  22. H. Lang and C. Bouwhuis, "Optical system for a color television camera," USA patent: 3202039, (1961).
  23. K. Hideo Hoshuyama, "Color separation device of solid-state image sensor," USA patent: US 7,138,663 B2, (2003).
  24. H. Macleod, Thin Film Optical Filters, (Taylor and Francis, Philadelphia, PA, 2001).
  25. G. Wang, H. Shen, D. Kumar, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multi-view and multi-spectral data," Int. J. Biomed. Imaging. ID58601, (2006).
    [CrossRef]
  26. C. Lawson and R. Hanson, "Solving least squares problems," (Prentice-Hall, Englewood Cliffs, 1974).
  27. A. Bjorck, "Numerical Method for Least Squares Problems," (SIAM, Philadelphia, PA, 1996).
  28. J. Cantarella and M. Piatex, "Tsnnls a sparse nonnegative least-squares solver," http://www.cs.dug.edu/ Epiatek/ tsnnls/, (2004).
  29. R. Storn and K. Price, "Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces," J. Global Optim. 11, 341-359 (1997).
    [CrossRef]
  30. K. Price, R. Storn, and J. Lampinen, Differential evolution: a practical approach to global optimization (Springer, Berlin, 2004).
  31. V. Feoktistov, Differential evolution : in search of solutions (Springer, New York, 2006).
  32. A. Cong, W. Cong, H. Shen, et al., "Bioluminescence tomography using genetic algorithm," working paper, 2007.

2007 (2)

C. Kuo, O. Conquoz, T. Troy, H. Xu, and B. Rice, "Three-dimensional reconstruction of in Vivo Bioluminescent sources based on multi-spectral imaging," J. Biomed. Opt. 12, 024007 (Apr. 19, 2007).
[CrossRef]

W. Cong, A. Cong, H. Shen, Y. Liu, and G. Wang, "Flux vector formulation for photon propagation in the biological tissue," Opt. Lett. 32, 2837-2839 (2007).
[CrossRef] [PubMed]

2006 (6)

V. Ntziachristos, "Fluorescence molecular imaging," Annu. Rev. Biomed. Eng. 8, 1-33 (2006).
[CrossRef] [PubMed]

H. Dehghani,  et al., "Spectrally resolved bioluminescence optical tomography," Opt. Lett. 31, 365-367 (2006).
[CrossRef] [PubMed]

W. Cong and G. Wang, "Boundary integral method for bioluminescence tomography," J. Biomed. Opt. 11, 020503 (2006).
[CrossRef] [PubMed]

W. Cong,  et al., "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33, 679-686 (2006).
[CrossRef] [PubMed]

G. Wang,  et al., "In vivo mouse studies with bioluminescence tomography," Opt. Express. 147801-7809 (2006).
[CrossRef] [PubMed]

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, J. H. Rao, "Self-illuminating quantum dot conjugates for in vivo imaging," Nat. Biotechnol. 24, 339-343 (2006).
[CrossRef] [PubMed]

2005 (5)

C. Kuo, O. Conquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Imaging. 4, 370 (2005).

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

W. X. Cong,  et al., "Practical reconstruction method for bioluminescence tomography," Opt. Express. 13, 6756-6771 (2005).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "3D bioluminescence imaging by use of a combined optical-PET tomographic system: A computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
[CrossRef] [PubMed]

A. J. Chaudhari,  et al., "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

2004 (1)

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

2003 (2)

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

G. Wang,  et al., "Development of the first bioluminescent CT scanner," Radiology 229, 566 (2003).

1997 (1)

R. Storn and K. Price, "Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces," J. Global Optim. 11, 341-359 (1997).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

V. Ntziachristos, "Fluorescence molecular imaging," Annu. Rev. Biomed. Eng. 8, 1-33 (2006).
[CrossRef] [PubMed]

J. Biomed. Opt. (2)

W. Cong and G. Wang, "Boundary integral method for bioluminescence tomography," J. Biomed. Opt. 11, 020503 (2006).
[CrossRef] [PubMed]

C. Kuo, O. Conquoz, T. Troy, H. Xu, and B. Rice, "Three-dimensional reconstruction of in Vivo Bioluminescent sources based on multi-spectral imaging," J. Biomed. Opt. 12, 024007 (Apr. 19, 2007).
[CrossRef]

J. Global Optim. (1)

R. Storn and K. Price, "Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces," J. Global Optim. 11, 341-359 (1997).
[CrossRef]

Med. Phys. (2)

W. Cong,  et al., "A Born-type approximation method for bioluminescence tomography," Med. Phys. 33, 679-686 (2006).
[CrossRef] [PubMed]

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

Mol. Imaging. (1)

C. Kuo, O. Conquoz, T. Troy, D. Zwarg, and B. Rice, "Bioluminescent tomography for in vivo localization and quantification of luminescent sources from a multiple-view imaging system," Mol. Imaging. 4, 370 (2005).

Nat. Biotechnol. (2)

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

M. K. So, C. J. Xu, A. M. Loening, S. S. Gambhir, J. H. Rao, "Self-illuminating quantum dot conjugates for in vivo imaging," Nat. Biotechnol. 24, 339-343 (2006).
[CrossRef] [PubMed]

Nat. Med. (1)

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

Opt. Express. (2)

W. X. Cong,  et al., "Practical reconstruction method for bioluminescence tomography," Opt. Express. 13, 6756-6771 (2005).
[CrossRef] [PubMed]

G. Wang,  et al., "In vivo mouse studies with bioluminescence tomography," Opt. Express. 147801-7809 (2006).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Med. Biol. (2)

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, "3D bioluminescence imaging by use of a combined optical-PET tomographic system: A computer simulation feasibility study," Phys. Med. Biol. 50, 4225-4241 (2005).
[CrossRef] [PubMed]

A. J. Chaudhari,  et al., "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Radiology (1)

G. Wang,  et al., "Development of the first bioluminescent CT scanner," Radiology 229, 566 (2003).

Other (15)

G. Wang, E. A. Hoffman, and G. McLennan, "Systems and methods for bioluminescent computed tomographic reconstruction," US Patent Application. No. 10/791140, 2002.

C. Kuo, H. Xu, and B. Rice, "Improved techniques in Diffuse Luminescent Tomography on whole animal meshes," in "Annual Meeting of The Society for Molecular Imaging," Hawaii, 2006.

A. Cong and G. Wang, "Multi-spectral bioluminescence tomography: Methodology and simulation," Int. J. Biomed. Imaging ID57614 (2006).
[CrossRef]

W. Han, W. Cong, and G. Wang, "Mathematical study and numerical simulation ofmultispectral bioluminescence tomography," Int. J. Biomed. Imaging ID54390 (2006).
[CrossRef]

K. Price, R. Storn, and J. Lampinen, Differential evolution: a practical approach to global optimization (Springer, Berlin, 2004).

V. Feoktistov, Differential evolution : in search of solutions (Springer, New York, 2006).

A. Cong, W. Cong, H. Shen, et al., "Bioluminescence tomography using genetic algorithm," working paper, 2007.

X. Qian, R. Svensson, X. Y. Ying, H. Shen, W. Cong, M. Henry, G. Wang, "Measurement of temperature-dependent bioluminescent spectra in Vivo," in "Annual Meeting of The Society for Molecular Imaging," Providence, Rhode Island, (2007).

H. Lang and C. Bouwhuis, "Optical system for a color television camera," USA patent: 3202039, (1961).

K. Hideo Hoshuyama, "Color separation device of solid-state image sensor," USA patent: US 7,138,663 B2, (2003).

H. Macleod, Thin Film Optical Filters, (Taylor and Francis, Philadelphia, PA, 2001).

G. Wang, H. Shen, D. Kumar, X. Qian, and W. Cong, "The first bioluminescence tomography system for simultaneous acquisition of multi-view and multi-spectral data," Int. J. Biomed. Imaging. ID58601, (2006).
[CrossRef]

C. Lawson and R. Hanson, "Solving least squares problems," (Prentice-Hall, Englewood Cliffs, 1974).

A. Bjorck, "Numerical Method for Least Squares Problems," (SIAM, Philadelphia, PA, 1996).

J. Cantarella and M. Piatex, "Tsnnls a sparse nonnegative least-squares solver," http://www.cs.dug.edu/ Epiatek/ tsnnls/, (2004).

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Figures (9)

Fig. 1.
Fig. 1.

Bioluminescent intensity change over time at 37°C using the Xenogen IVIS 100 in a transgenic mouse injected with 150mg/kg D-luciferin [21].

Fig. 2.
Fig. 2.

Two spectral components are separated, shifted and mixed using a dichroic coating and a mirror.

Fig. 3.
Fig. 3.

Optical imaging model for an SSM device.

Fig. 4.
Fig. 4.

Four-view DSS prototype.

Fig. 5.
Fig. 5.

Comparison of the workflow of our DSS system and the current BLI system.

Fig. 6.
Fig. 6.

Static DSS simulation with a real bioluminescent view of a mouse. (a) Original mouse bioluminescent view, (b) two spectral components q (upper) and p (lower), (c) two composite images M′ (upper) and M (lower) captured by DSS, (d) two recovered spectral components q′ (upper) and p′ (lower), and (e) the recombined image p′+q′.

Fig. 7.
Fig. 7.

Dynamic DSS simulation with a two spectral 1D image. (a) Spectral components p and q and the recovered results p′ and q′, and (b) dynamic functions p(t) and q(t) as well as the recovered time-courses p′(t) and q′(t) respectively.

Fig. 8.
Fig. 8.

Static DSS simulation with ray tracing data and imperfect coefficients. (a) System configuration of the forward ray tracing for a SSM component, (b) line images formed on the CCD as simulated via ray tracing, (c) the spatial shift due to the SSM, (d) the spectral components p and q and recovered counterpart p′ and q′,

Fig. 9.
Fig. 9.

Digital spectral separation (DSS) in one shot. (a) Eight-view design in the two-component case, (b) twelve-view design in the three-component case.

Equations (9)

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

a l ( 1 a ) 2 p + b 2 ( 1 b ) l q for l = 1 , ,
l = t + 1 a l ( 1 a ) 2 p + b 2 ( 1 b ) l q = a 1 + t ( 1 a ) p + b ( 1 b ) 1 + t q
M k = p k + q ( k i ) for k = 1 , , n + i
[ A A ]   [ p q ] = [ M M ]
{ M k = p k + q k M k = a p k + ( 1 b ) q k + l = 0 t a l ( 1 a ) 2 p ( k ( l + 1 ) i ) + b 2 ( 1 b ) l q ( k ( l + 1 ) i )
M k ( l ) = ( p k ( 1 ) + + p k ( l ) ) + ( p k i l ( l + 1 ) + + p k i l ( m ) )
min AX B 2 2 for X > 0
{ M k ( 0 ) = p k + q k   M k ( 1 ) = p k ( 1 ) + q k i ( 1 ) = t p ( 1 ) p k + t q ( 1 ) q k i M k ( L 1 ) = p k ( L 1 ) + q k ( L 1 ) = t p ( L 1 ) p k + t q ( L 1 ) q k M k ( L ) = p k ( L ) + q k i ( L ) = t p ( L ) p k + t q ( L ) q k i
{ M k = p k + q k M k = a p k + ( 1 b ) q k + l = 0 1 a l ( 1 a ) 2 p ( k ( l + 1 ) i ) + b 2 ( 1 b ) l q ( k ( l 1 ) i )

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