Abstract

Reconstruction algorithms are presented for a two-step solution of the bioluminescence tomography (BLT) problem. In the first step, a priori anatomical information provided by x-ray computed tomography or by other methods is used to solve the continuous wave (cw) diffuse optical tomography (DOT) problem. A Taylor series expansion approximates the light fluence rate dependence on the optical properties of each region where first and second order direct derivatives of the light fluence rate with respect to scattering and absorption coefficients are obtained and used for the reconstruction. In the second step, the reconstructed optical properties at different wavelengths are used to calculate the Green’s function of the system. Then an iterative minimization solution based on the L1 norm shrinks the permissible regions where the sources are allowed by selecting points with higher probability to contribute to the source distribution. This provides an efficient BLT reconstruction algorithm with the ability to determine relative source magnitudes and positions in the presence of noise.

© 2010 OSA

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  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(3), 313–320 (2005).
    [CrossRef] [PubMed]
  2. R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
    [PubMed]
  3. J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
    [CrossRef] [PubMed]
  4. J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
    [CrossRef] [PubMed]
  5. C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
    [CrossRef] [PubMed]
  6. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993).
    [CrossRef] [PubMed]
  7. 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(11), 1779–1792 (1995).
    [CrossRef] [PubMed]
  8. H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt. 37(22), 5337–5343 (1998).
    [CrossRef] [PubMed]
  9. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
    [CrossRef] [PubMed]
  10. X. Gu, Q. Zhang, L. Larcom, and H. Jiang, “Three-dimensional bioluminescence tomography with model-based reconstruction,” Opt. Express 12(17), 3996–4000 (2004).
    [CrossRef] [PubMed]
  11. G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
    [CrossRef] [PubMed]
  12. W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005).
    [CrossRef] [PubMed]
  13. N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
    [CrossRef] [PubMed]
  14. H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
    [CrossRef] [PubMed]
  15. D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantification of bioluminescence images of point source objects using diffusion theory models,” Phys. Med. Biol. 51(15), 3733–3746 (2006).
    [CrossRef] [PubMed]
  16. C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
    [CrossRef] [PubMed]
  17. 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(26), 18300–18317 (2007).
    [CrossRef] [PubMed]
  18. P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
    [CrossRef] [PubMed]
  19. Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009).
    [CrossRef] [PubMed]
  20. P. Mohajerani, A. A. Eftekhar, J. Huang, and A. Adibi, “Optimal sparse solution for fluorescent diffuse optical tomography: theory and phantom experimental results,” Appl. Opt. 46(10), 1679–1685 (2007).
    [CrossRef] [PubMed]
  21. N. Cao, A. Nehorai, and M. Jacobs, “Image reconstruction for diffuse optical tomography using sparsity regularization and expectation-maximization algorithm,” Opt. Express 15(21), 13695–13708 (2007).
    [CrossRef] [PubMed]
  22. J. F. Claerbout and F. Muir, “Robust modeling with erratic data,” Geophysics 38(5), 826–844 (1973).
    [CrossRef]
  23. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 41–93 (1999).
    [CrossRef]
  24. A. D. Klose, “Transport-theory-based stochastic image reconstruction of bioluminescence sources,” J. Opt. Soc. Am. A 24(6), 1601–1608 (2007).
    [CrossRef]
  25. H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
    [CrossRef] [PubMed]
  26. L. J. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics, (IEEE Press, New York, 1998).
  27. G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system,” Phys. Med. Biol. 51(8), 2045–2053 (2006).
    [CrossRef] [PubMed]
  28. 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(17), 4225–4241 (2005).
    [CrossRef] [PubMed]
  29. S. A. Prahl, http://omlc.ogi.edu/spectra/index.html (Oregon Medical Laser Clinic) (2001).
  30. R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
    [PubMed]

2009 (2)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009).
[CrossRef] [PubMed]

2008 (2)

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[CrossRef] [PubMed]

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

2007 (6)

2006 (4)

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef] [PubMed]

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[CrossRef] [PubMed]

D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantification of bioluminescence images of point source objects using diffusion theory models,” Phys. Med. Biol. 51(15), 3733–3746 (2006).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system,” Phys. Med. Biol. 51(8), 2045–2053 (2006).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

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(3), 313–320 (2005).
[CrossRef] [PubMed]

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

2004 (2)

2002 (1)

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

2001 (1)

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

1999 (2)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[CrossRef] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 41–93 (1999).
[CrossRef]

1998 (1)

1997 (1)

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

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(11), 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(2), 299–309 (1993).
[CrossRef] [PubMed]

1973 (1)

J. F. Claerbout and F. Muir, “Robust modeling with erratic data,” Geophysics 38(5), 826–844 (1973).
[CrossRef]

Adibi, A.

Alexandrakis, G.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system,” Phys. Med. Biol. 51(8), 2045–2053 (2006).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Antich, P. P.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 41–93 (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(11), 1779–1792 (1995).
[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(2), 299–309 (1993).
[CrossRef] [PubMed]

Bachmann, M. H.

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

Bai, J.

Bao, S.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

Beliles, R. P.

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

Brown, R. P.

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

Cao, N.

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

Chan, T. F.

Chatziioannou, A. F.

Y. Lu, X. Zhang, A. Douraghy, D. Stout, J. Tian, T. F. Chan, and A. F. Chatziioannou, “Source reconstruction for spectrally-resolved bioluminescence tomography with sparse a priori information,” Opt. Express 17(10), 8062–8080 (2009).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system,” Phys. Med. Biol. 51(8), 2045–2053 (2006).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Chen, N.

Claerbout, J. F.

J. F. Claerbout and F. Muir, “Robust modeling with erratic data,” Geophysics 38(5), 826–844 (1973).
[CrossRef]

Comsa, D. C.

D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantification of bioluminescence images of point source objects using diffusion theory models,” Phys. Med. Biol. 51(15), 3733–3746 (2006).
[CrossRef] [PubMed]

Cong, A.

Cong, W.

Contag, C. H.

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

Coquoz, O.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[CrossRef] [PubMed]

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef] [PubMed]

Dehghani, H.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[CrossRef] [PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef] [PubMed]

Delp, M. D.

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

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(11), 1779–1792 (1995).
[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(2), 299–309 (1993).
[CrossRef] [PubMed]

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(7), 591–607 (2008).
[CrossRef] [PubMed]

Douraghy, A.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

Eftekhar, A. A.

Farrell, T. J.

D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantification of bioluminescence images of point source objects using diffusion theory models,” Phys. Med. Biol. 51(15), 3733–3746 (2006).
[CrossRef] [PubMed]

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(7), 591–607 (2008).
[CrossRef] [PubMed]

Gu, X.

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[CrossRef] [PubMed]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11), 1779–1792 (1995).
[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(2), 299–309 (1993).
[CrossRef] [PubMed]

Hoffman, E. A.

Huang, J.

Jacobs, M.

Jiang, H.

Jiang, M.

Jiang, S.

Klose, A. D.

A. D. Klose, “Transport-theory-based stochastic image reconstruction of bioluminescence sources,” J. Opt. Soc. Am. A 24(6), 1601–1608 (2007).
[CrossRef]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[CrossRef] [PubMed]

Kumar, D.

Kuo, C.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[CrossRef] [PubMed]

Larcom, L.

Lewis, M. A.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[CrossRef] [PubMed]

Li, Y.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

Liang, W.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

Lindstedt, S. L.

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

Liu, Y.

Lu, Y.

Mahmood, U.

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

McCray, P. B.

McLennan, G.

Mohajerani, P.

Muir, F.

J. F. Claerbout and F. Muir, “Robust modeling with erratic data,” Geophysics 38(5), 826–844 (1973).
[CrossRef]

Nehorai, A.

Ntziachristos, 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(3), 313–320 (2005).
[CrossRef] [PubMed]

Patterson, M. S.

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef] [PubMed]

D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantification of bioluminescence images of point source objects using diffusion theory models,” Phys. Med. Biol. 51(15), 3733–3746 (2006).
[CrossRef] [PubMed]

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[CrossRef] [PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef] [PubMed]

Pogue, B. W.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[CrossRef] [PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31(3), 365–367 (2006).
[CrossRef] [PubMed]

Rannou, F. R.

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system,” Phys. Med. Biol. 51(8), 2045–2053 (2006).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Rhomberg, L. R.

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

Rice, B. W.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[CrossRef] [PubMed]

Richer, E.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[CrossRef] [PubMed]

Ripoll, J.

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(3), 313–320 (2005).
[CrossRef] [PubMed]

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11), 1779–1792 (1995).
[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(2), 299–309 (1993).
[CrossRef] [PubMed]

Slavine, N. V.

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[CrossRef] [PubMed]

Song, X.

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

Stout, D.

Tian, J.

Troy, T. L.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[CrossRef] [PubMed]

van Bruggen, N.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[CrossRef] [PubMed]

Wang, D.

Wang, G.

Wang, H.

Wang, L. V.

W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L. V. Wang, E. A. Hoffman, G. McLennan, P. B. McCray, J. Zabner, and A. Cong, “Practical reconstruction method for bioluminescence tomography,” Opt. Express 13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

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(3), 313–320 (2005).
[CrossRef] [PubMed]

Weissleder, R.

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(3), 313–320 (2005).
[CrossRef] [PubMed]

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Willmann, J. K.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7(7), 591–607 (2008).
[CrossRef] [PubMed]

Xu, H.

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[CrossRef] [PubMed]

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[CrossRef] [PubMed]

Yan, X. P.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

Yang, X.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

Zabner, J.

Zhang, Q.

Zhang, X.

Annu. Rev. Biomed. Eng. (1)

C. H. Contag and M. H. Bachmann, “Advances in in vivo bioluminescence imaging of gene expression,” Annu. Rev. Biomed. Eng. 4(1), 235–260 (2002).
[CrossRef] [PubMed]

Appl. Opt. (2)

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25(6), 711–732 (2009).
[CrossRef] [PubMed]

Geophysics (1)

J. F. Claerbout and F. Muir, “Robust modeling with erratic data,” Geophysics 38(5), 826–844 (1973).
[CrossRef]

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

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27(5), 48–57 (2008).
[CrossRef] [PubMed]

IEEE Trans. Med. Imaging (1)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient-based iterative image reconstruction scheme for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18(3), 262–271 (1999).
[CrossRef] [PubMed]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 41–93 (1999).
[CrossRef]

J. Biomed. Opt. (1)

C. Kuo, O. Coquoz, T. L. Troy, H. Xu, and B. W. Rice, “Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging,” J. Biomed. Opt. 12(2), 024007 (2007).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Med. Phys. (5)

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography,” Med. Phys. 34(6), 2085–2098 (2007).
[CrossRef] [PubMed]

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).
[CrossRef] [PubMed]

N. V. Slavine, M. A. Lewis, E. Richer, and P. P. Antich, “Iterative reconstruction method for light emitting sources based on the diffusion equation,” Med. Phys. 33(1), 61–68 (2006).
[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(2), 299–309 (1993).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22(11), 1779–1792 (1995).
[CrossRef] [PubMed]

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(3), 313–320 (2005).
[CrossRef] [PubMed]

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(7), 591–607 (2008).
[CrossRef] [PubMed]

Opt. Express (5)

Opt. Lett. (1)

Phys. Med. Biol. (3)

D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantification of bioluminescence images of point source objects using diffusion theory models,” Phys. Med. Biol. 51(15), 3733–3746 (2006).
[CrossRef] [PubMed]

G. Alexandrakis, F. R. Rannou, and A. F. Chatziioannou, “Effect of optical property estimation accuracy on tomographic bioluminescence imaging: simulation of a combined optical-PET (OPET) system,” Phys. Med. Biol. 51(8), 2045–2053 (2006).
[CrossRef] [PubMed]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Radiology (1)

R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology 219(2), 316–333 (2001).
[PubMed]

Toxicol. Ind. Health (1)

R. P. Brown, M. D. Delp, S. L. Lindstedt, L. R. Rhomberg, and R. P. Beliles, “Physiological parameter values for physiologically based pharmacokinetic models,” Toxicol. Ind. Health 13(4), 407–484 (1997).
[PubMed]

Other (2)

S. A. Prahl, http://omlc.ogi.edu/spectra/index.html (Oregon Medical Laser Clinic) (2001).

L. J. Volakis, A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics, (IEEE Press, New York, 1998).

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Figures (7)

Fig. 1
Fig. 1

Flowchart for iterative solution of the optical properties reconstruction.

Fig. 2
Fig. 2

Schematic of the object used in the simulation illustrating 6 different regions: E1 is the skin, E2 is the bowel, E3 and E4 are the kidneys, E5 is the bone and E6 is adipose tissue. The source-detectors setup is also shown in the figure; 16 sources (one is indicated by the star) uniformly distributed are used and associated with every source 48 detectors forming an approximately 270° of view; the total number of data readings are 16x48 which is 768.

Fig. 6
Fig. 6

BLT reconstruction of one bioluminescence Gaussian source localized in the left kidney; 3% Gaussian noise is added. (a) The actual source with a total power of 0.4845 nW. (b) The reconstructed source with a total power 0.2397 nW. (c) The reconstructed source with a total power 0.4975 nW when the actual source power used is 0.969 nW.

Fig. 4
Fig. 4

Comparisons between the actual and reconstructed optical properties of different tissue regions, see Fig. 2, at 600 nm in the heterogeneous object and percentage relative error. Gaussian noise with standard deviation of 1% is added and the reconstruction model considers the 1st order approximation (the Jacobian). (a) and (b) show the actual (blue line with circles) and reconstructed (red line with stars) scattering and absorption coefficients in different regions, and (c) and (d) show the relative errors in the reconstructed scattering and absorption coefficients.

Fig. 5
Fig. 5

(a) and (b) show comparisons between the actual (blue lines with circles) and reconstructed (red lines with stars) scattering and absorption coefficients of different tissue regions at 600 nm in the heterogeneous object using the first order approximation (the Jacobian); the Gaussian noise added is 3%. (c) and (d) Show the same results using the second order approximation (the Hessian).

Fig. 3
Fig. 3

Flowchart for iterative solution of the bioluminescence sources reconstruction algorithm.

Fig. 7
Fig. 7

BLT reconstruction of two bioluminescence Gaussian sources localized in the left and right kidneys with added 3% Gaussian noise. The actual sources are shown in (a), (c), and (e), while the corresponding reconstructed sources are shown in (b), (d), and (f) respectively. The two sources have the same strength in (a) and (b) and the total powers of the actual left and right sources are 0.96907 and 0.97743 nW and the left and right reconstructed sources are 0.260 nW and 0.22 nW, respectively. (c) and (d) Show the results when the left source power is the double the right source power; and the total powers of the actual left and right sources are 0.96907 and 0.4887 nW and the left and right reconstructed sources are 0.236 nW and 0.117 nW, respectively. (e) and (f) Show the case when the right source power is double the left one; The total powers of the actual left and right sources are 0.4845 and 0.9774 and the left and right reconstructed sources are 0.1431 nW and 0.2329 nW, respectively.

Tables (1)

Tables Icon

Table 1 Optical properties for each region in the heterogeneous object calculated at three different wavelengths. The values of the scattering and absorption coefficients are given in (mm−1)

Equations (24)

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[ ( x κ ( x , y ; λ ) x + y κ ( x , y ; λ ) y ) + ( μ a ( x , y ; λ ) + i ω c ) ] φ ( x , y ; λ ; ω ) = q ( x , y ; λ ; ω ) ,
κ ( x , y ; λ ) = 1 3 ( μ a ( x , y ; λ ) + μ s ( x , y ; λ ) ) ,
φ ( x , y ; λ ; ω ) + 2 κ ( x , y ; λ ) A n ^ ( x , y ) . φ ( x , y ; λ ; ω ) = 0 ,
A = ( 2 / ( 1 R 0 ) ) 1 + | cos θ c | 3 1 | cos θ c | 2 ,
[ K ] N × N φ N × 1 = [ q ] N × 1 ,
φ d = φ d 0 + i φ d u i δ μ i + 1 2 i , j 2 φ d μ i μ j δ μ i δ μ j + ,
δ μ = [ δ μ s 1 δ μ s N δ μ a 1 δ μ s N ] ,
φ d = φ d 0 + J d δ μ + 1 2 δ μ T H d δ μ
δ μ = ( J T J ) 1 ( J T ( δ φ 1 2 δ μ T H d δ μ ) ) ,
δ μ = ( J T J ) 1 ( J T ( δ φ 1 2 d = 1 N d δ μ T H d δ μ ) ) ,
J = [ φ 1 μ s 1 φ 1 μ s N φ 1 μ a 1 φ 1 μ a N φ N d μ s 1 φ N d μ s N φ N d μ a 1 φ N d μ a N ] ,
H d = [ 2 φ d μ s 1 2 2 φ d μ s 1 μ s N 2 φ d μ s 1 μ a 1 2 φ d μ s 1 μ a N 2 φ d μ s N μ s 1 2 φ d μ s N 2 2 φ d μ s N μ a 1 2 φ d μ s N μ a N 2 φ d μ a 1 μ s 1 2 φ d μ a 1 μ s N 2 φ d μ a 1 2 2 φ d μ a 1 μ a N 2 φ d μ a N μ s 1 2 φ d μ a N μ s N 2 φ d μ a N μ a 1 2 φ d μ a N 2 ]
φ k μ i | μ i = φ k ( μ i + Δ μ i ) φ k ( μ i Δ μ i ) 2 Δ μ i ,   μ i = μ s i  or  μ a i ,
2 φ k μ i 2 | μ i = φ k ( μ i + Δ μ i ) + φ k ( μ i Δ μ i ) 2 φ k ( μ i ) Δ μ i 2 2 φ k μ i μ j | μ i , μ j = 1 4 Δ μ i Δ μ j ( φ k ( μ i + Δ μ i , μ j + Δ μ j ) + φ k ( μ i Δ μ i , μ j Δ μ j ) φ k ( μ i + Δ μ i , μ j Δ μ j ) φ k ( μ i Δ μ i , μ j + Δ μ j ) )
μ s ( λ ) = a × λ b ,
μ a ( λ ) = S B ( x μ aHb ( λ ) + ( 1 x ) μ aHbO 2 ( λ ) ) + S W μ aW ( λ ) ,
[ ( x κ ( x , y ; λ ) x + y κ ( x , y ; λ ) y ) + μ a ( x , y ; λ ) ] G ( x , x ; y , y ; λ ) = δ ( x x ) δ ( y y )
φ ( x , y ; λ ) = x , y G ( x , x ; y , y ; λ ) s ( x , y ; λ ) d x d y
D G = I     G = D 1 ,
G p s = φ ,
s = ( G p T G p ) 1 G p T φ
min λ G p ( λ , R ) s ( R ) φ ( λ ) 1 s . t .     0 s s max s . t .      R Permissible Region
min λ G p ( λ ) s φ ( λ ) 1 + α s 0 ,
J 11 = log ( φ 1 ) μ s 1 | μ s = 2 μ a = 0.02 = [ log ( φ 1 ( 2.01 , 2 , , 2 ; 0.02 , , 0.02 ) ) log ( φ 1 ( 1.99 , 2 , , 2 ; 0.02 , , 0.02 ) ) ] / ( 2 × 0.01 )

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