Abstract

A stochastic image reconstruction methodology is proposed for solving the highly ill-posed inverse bioluminescent source problem in light-scattering media. The unknown source distribution is expressed in terms of a set of linearly independent source basis functions. The bioluminescent boundary flux originating from each source basis function is computed prior to image reconstruction by solving the equation of radiative transfer. The misfit between the measured and the predicted boundary flux is described by an error function, which is iteratively minimized by stochastically sampling the global parameter space of all basis functions. Selection and alteration mechanisms, which can be guided by evolutionary principles found in nature, lead to new stochastic samples of source distributions for the next iteration cycle. A least-squares-error solution, representing the sought image of the unknown source distribution, is obtained after convergence. Numerical experiments demonstrate the feasibility of reconstructing bioluminescent source distributions in tissuelike media.

© 2007 Optical Society of America

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2006 (3)

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220, 441-470 (2006).
[CrossRef]

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

W. Han, W. Cong, and G. Wang, "Mathematical theory and numerical analysis of bioluminescence tomography," Inverse Probl. 22, 1659-1675 (2006).
[CrossRef]

2005 (7)

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, 6756-6771 (2005).
[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, 4225-4241 (2005).
[CrossRef] [PubMed]

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

D. K. Welsh and S. A. Kay, "Bioluminescence imaging in living organisms," Curr. Opin. Biotechnol. 16, 73-78 (2005).
[CrossRef] [PubMed]

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

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. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured," J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

2004 (3)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "In vivo fluorescence molecular imaging with a radiative transfer model," Mol. Imaging 3, 230 (2004).

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, "Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models," Mol. Imaging 3, 9-23 (2004).
[CrossRef] [PubMed]

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

2002 (3)

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, "A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method," Med. Phys. 29, 2013-2023 (2002).
[CrossRef] [PubMed]

R. Elaloufi, R. Carminati, and J.-J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. Soc. Am. A 4, S103-S108 (2002).

H.-G. Beyer and H.-P. Schwefel, "Evolution strategies," Nat. Comput. 1, 3-52 (2002).
[CrossRef]

2001 (2)

B. Chen, K. Stamnes, and J. J. Stamnes, "Validity of the diffusion approximation in bio-optical imaging," Appl. Opt. 40, 6356-6366 (2001).
[CrossRef]

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]

2000 (1)

1998 (2)

A. D. Kim and A. Ishimaru, "Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer," Appl. Opt. 37, 5313-5319 (1998).
[CrossRef]

A. M. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef] [PubMed]

1997 (1)

1996 (1)

1995 (1)

1994 (1)

C. E. Siewert, "A radiative-transfer inverse-source problem for a sphere," J. Quant. Spectrosc. Radiat. Transf. 52, 157-160 (1994).
[CrossRef]

1993 (1)

C. E. Siewert, "An inverse source problem in radiative transfer," J. Quant. Spectrosc. Radiat. Transf. 50, 603-609 (1993).
[CrossRef]

1990 (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

1989 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1975 (1)

E. W. Larsen, "The inverse source problem in radiative transfer," J. Quant. Spectrosc. Radiat. Transf. 15, 1-5 (1975).
[CrossRef]

1953 (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Alcouffe, R. E.

A. M. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef] [PubMed]

Alexandrakis, G.

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

Aydin, E. D.

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, "A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method," Med. Phys. 29, 2013-2023 (2002).
[CrossRef] [PubMed]

Bading, J. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Bal, G.

G. Bal and A. Tamasan, "Inverse source problem in transport equations" (manuscript in preparation).

Barbour, R. L.

A. M. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef] [PubMed]

Beuthan, J.

Beyer, H.-G.

H.-G. Beyer and H.-P. Schwefel, "Evolution strategies," Nat. Comput. 1, 3-52 (2002).
[CrossRef]

Bolin, F. P.

Bouma, B. E.

Brezinski, M. E.

Cable, M. D.

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]

Carminati, R.

R. Elaloufi, R. Carminati, and J.-J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. Soc. Am. A 4, S103-S108 (2002).

Chatziioannou, A. F.

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

Chaudhari, A. J.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Chen, B.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Cherry, S. R.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Cong, A.

Cong, W.

Contag, C. H.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

Conti, P. S.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Coquoz, O.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

Darvas, F.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Davis, S. C.

de Oliveira, C. R. E.

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, "A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method," Med. Phys. 29, 2013-2023 (2002).
[CrossRef] [PubMed]

Decraemer, W. F.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured," J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Dehghani, H.

Dirckx, J. J. J.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured," J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Doyle, T. C.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

Elaloufi, R.

R. Elaloufi, R. Carminati, and J.-J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. Soc. Am. A 4, S103-S108 (2002).

Ference, R. J.

Fujimotot, J. G.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Goddard, A. J. H.

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, "A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method," Med. Phys. 29, 2013-2023 (2002).
[CrossRef] [PubMed]

Greffet, J.-J.

R. Elaloufi, R. Carminati, and J.-J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. Soc. Am. A 4, S103-S108 (2002).

Han, W.

W. Han, W. Cong, and G. Wang, "Mathematical theory and numerical analysis of bioluminescence tomography," Inverse Probl. 22, 1659-1675 (2006).
[CrossRef]

Hee, M. R.

Hielscher, A. H.

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]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "In vivo fluorescence molecular imaging with a radiative transfer model," Mol. Imaging 3, 230 (2004).

A. H. Hielscher, A. D. Klose, and J. Beuthan, "Evolution strategies for optical tomographic characterization of homogeneous media," Opt. Express 7, 507-518 (2000).
[CrossRef] [PubMed]

Hielscher, A. M.

A. M. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef] [PubMed]

Hoenders, B. J.

Hoffman, E. A.

Ishimaru, A.

Jekic-McMullen, D.

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, "Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models," Mol. Imaging 3, 9-23 (2004).
[CrossRef] [PubMed]

Jiang, M.

Jiang, S.

Kalish, F.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

Kay, S. A.

D. K. Welsh and S. A. Kay, "Bioluminescence imaging in living organisms," Curr. Opin. Biotechnol. 16, 73-78 (2005).
[CrossRef] [PubMed]

Kim, A. D.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Klose, A. D.

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220, 441-470 (2006).
[CrossRef]

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]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "In vivo fluorescence molecular imaging with a radiative transfer model," Mol. Imaging 3, 230 (2004).

A. H. Hielscher, A. D. Klose, and J. Beuthan, "Evolution strategies for optical tomographic characterization of homogeneous media," Opt. Express 7, 507-518 (2000).
[CrossRef] [PubMed]

Kumar, D.

Kuypers, L. C.

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured," J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

Larsen, E. W.

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220, 441-470 (2006).
[CrossRef]

E. W. Larsen, "The inverse source problem in radiative transfer," J. Quant. Spectrosc. Radiat. Transf. 15, 1-5 (1975).
[CrossRef]

Leahy, R. M.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Li, H.

Li, Y.

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

Liu, Y.

McCray, P. B.

McLennan, G.

Metropolis, N.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Moats, R. A.

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

Nash, S. G.

S. G. Nash, Linear and Nonlinear Programming (McGraw-Hill, 1996).

Nelson, M. B.

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]

Nocedal, J.

J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 1999).
[CrossRef]

Ntziachristos, V.

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]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "In vivo fluorescence molecular imaging with a radiative transfer model," Mol. Imaging 3, 230 (2004).

Paulsen, K. D.

Pogue, B. W.

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Preuss, L. E.

Rannou, F. R.

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

Rice, B.

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N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Rosenbluth, M.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

Sambucetti, L.

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, "Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models," Mol. Imaging 3, 9-23 (2004).
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[CrossRef]

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[CrossRef]

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A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

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J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 1999).
[CrossRef]

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Zabner, J.

Zhao, H.

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

Appl. Opt. (4)

Curr. Opin. Biotechnol. (1)

D. K. Welsh and S. A. Kay, "Bioluminescence imaging in living organisms," Curr. Opin. Biotechnol. 16, 73-78 (2005).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, "A review of the optical properties of biological tissue," IEEE J. Quantum Electron. 26, 2166-2185 (1990).
[CrossRef]

Inverse Probl. (1)

W. Han, W. Cong, and G. Wang, "Mathematical theory and numerical analysis of bioluminescence tomography," Inverse Probl. 22, 1659-1675 (2006).
[CrossRef]

J. Biomed. Opt. (3)

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]

H. Zhao, T. C. Doyle, O. Coquoz, F. Kalish, B. W. Rice, and C. H. Contag, "Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo," J. Biomed. Opt. 10, 041210-01 (2005).
[CrossRef]

J. J. J. Dirckx, L. C. Kuypers, and W. F. Decraemer, "Refractive index of tissue measured," J. Biomed. Opt. 10, 044014 (2005).
[CrossRef]

J. Chem. Phys. (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller, "Equation of state calculations by fast computing machines," J. Chem. Phys. 21, 1087-1092 (1953).
[CrossRef]

J. Comput. Phys. (2)

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]

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220, 441-470 (2006).
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R. Elaloufi, R. Carminati, and J.-J. Greffet, "Time-dependent transport through scattering media: from radiative transfer to diffusion," J. Opt. Soc. Am. A 4, S103-S108 (2002).

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[CrossRef]

C. E. Siewert, "An inverse source problem in radiative transfer," J. Quant. Spectrosc. Radiat. Transf. 50, 603-609 (1993).
[CrossRef]

C. E. Siewert, "A radiative-transfer inverse-source problem for a sphere," J. Quant. Spectrosc. Radiat. Transf. 52, 157-160 (1994).
[CrossRef]

Med. Phys. (2)

E. D. Aydin, C. R. E. de Oliveira, and A. J. H. Goddard, "A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method," Med. Phys. 29, 2013-2023 (2002).
[CrossRef] [PubMed]

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

Mol. Imaging (2)

T. Troy, D. Jekic-McMullen, L. Sambucetti, and B. Rice, "Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models," Mol. Imaging 3, 9-23 (2004).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, "In vivo fluorescence molecular imaging with a radiative transfer model," Mol. Imaging 3, 230 (2004).

Nat. Comput. (1)

H.-G. Beyer and H.-P. Schwefel, "Evolution strategies," Nat. Comput. 1, 3-52 (2002).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Med. Biol. (3)

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

A. J. Chaudhari, F. Darvas, J. R. Bading, R. A. Moats, P. S. Conti, D. J. Smith, S. R. Cherry, and R. M. Leahy, "Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging," Phys. Med. Biol. 50, 5421-5441 (2005).
[CrossRef] [PubMed]

A. M. Hielscher, R. E. Alcouffe, and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-1302 (1998).
[CrossRef] [PubMed]

Science (1)

S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Other (6)

H.-P. Schwefel, Evolution and Optimum Seeking (Wiley, 1995).

G. Bal and A. Tamasan, "Inverse source problem in transport equations" (manuscript in preparation).

S. G. Nash, Linear and Nonlinear Programming (McGraw-Hill, 1996).

J. Nocedal and S. J. Wright, Numerical Optimization (Springer, 1999).
[CrossRef]

V. V. Tuchin, Handbook of Optical Biomedical Diagnostics (SPIE, 2002).

A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

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Figures (7)

Fig. 1
Fig. 1

Schematic of SIR approach. The boundary flux J + for a given set of source basis functions b m is calculated prior to image reconstruction (first stage). The image reconstruction process (second stage) is a global optimization scheme that stochastically samples the unknown parameter space of θ by iteratively minimizing an error function Φ ( θ ) . The reconstructed source distribution is obtained after convergence in global parameter space.

Fig. 2
Fig. 2

Reconstructed source power density distribution m = 1 M θ m b m ( r ) (photons s 1 cm 3 ) for single sources at different depths of (a) 0.5 cm , (b) 0.7 cm , and (c) 0.9 cm from medium boundary.

Fig. 3
Fig. 3

Reconstructed source power density distribution m = 1 M θ m b m ( r ) (photons s 1 cm 3 ) for two sources with different relative distances of (a) 0.75 cm , (b) 0.5 cm , and (c) 0.25 cm .

Fig. 4
Fig. 4

Source reconstruction in nonuniform tissue model. (a) Medium with nonuniform distribution of optical properties: (1) μ s = 44 cm 1 , μ a = 1.8 cm 1 , (2) μ s = 48 cm 1 , μ a = 2.4 cm 1 , (3) μ s = 64 cm 1 , μ a = 1.6 cm 1 , (4) μ s = 56 cm 1 , μ a = 1.2 cm 1 , (5) μ s = 32 cm 1 , μ a = 1.6 cm 1 , and (6) μ s = 48 cm 1 , μ a = 2.8 cm 1 . (b) Reconstructed source power density m = 1 M θ m b m ( r ) for two sources with relative distance of 0.5 cm inside medium. (c) Linear dependence of reconstructed source power W of left source in (b) with unit source power W 0 .

Fig. 5
Fig. 5

Transport-theory- and diffusion-theory-based image reconstructions of Q ( r ) . Tissuelike medium contained a single bioluminescent source with 10 9 photons s 1 cm 3 (square). (a) Medium with voidlike ring. (b) Image reconstruction based on the ERT. (c) Image reconstruction based on the diffusion equation.

Fig. 6
Fig. 6

Transport-theory- and diffusion-theory-based image reconstructions of Q ( r ) . Small tissuelike medium with diameter of 1 cm and large absorption of μ a = 2 cm 1 contained a bioluminescent source with power density of 10 9 photons s 1 cm 3 distributed along a narrow strip (rectangle). (a) Image reconstruction based on the ERT. (b) Image reconstruction based on the diffusion equation.

Fig. 7
Fig. 7

Reconstructed source power density of gradient-based method (Ref. [27]) and SIR approach. Tissuelike medium contained a single bioluminescent source with 10 9 photons s 1 cm 3 (original location is shown by square). (a) Image reconstruction with SIR method. (b)–(i) Gradient-based reconstruction starting from different initial guess Q 0 . (b) Q 0 = 0 , (c) Q 0 = 10 5 photons s 1 cm 3 , (d) Q 0 = 10 6 photons s 1 cm 3 , (e) Q 0 = 10 7 photons s 1 cm 3 , (f) Q 0 = 10 8 photons s 1 cm 3 , (g) Q 0 = 10 9 photons s 1 cm 3 , (h) Q 0 = 10 10 photons s 1 cm 3 , and (i) Q 0 = 10 11 photons s 1 cm 3 .

Equations (10)

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b m ( r ) = b ( x m , y m ) = { b , for 0 , else { ( x m 1 2 Δ x ) < x < ( x m + 1 2 Δ x ) ( y m 1 2 Δ y ) < y < ( y m + 1 2 Δ y ) ,
J + ( b m ) = Ω n > 0 [ 1 R ( Ω n ) ] ( Ω n ) ψ ( r , Ω ) d Ω ,
Ω ψ ( r , Ω ) + ( μ a + μ s ) ψ ( r , Ω ) = b m ( r ) 4 π + μ s 4 π p ( Ω Ω ) ψ ( r , Ω ) d Ω .
Ψ ( θ ) = 1 N n = 1 N ( Y n J n + ( θ ) ) 2 σ n 2
θ m λ = θ a μ + θ b μ 2 ,
θ ̂ m λ = θ m λ + N ( 0 , σ ̂ m λ ) .
σ ̂ m λ = σ m λ e τ N ( 0 , 1 ) .
1 3 ( μ a + ( 1 g ) μ s ) ϕ ( r ) + μ a ϕ ( r ) = b m ( r ) .
( 1 2 R 1 ) ϕ ( r ) 1 3 R 2 3 ( μ a + ( 1 g ) μ s ) n ϕ ( r ) = 0 .
J D + ( b m ) = ( 1 4 1 2 R 1 ) ϕ ( r ) 1 3 R 2 6 ( μ a + ( 1 g ) μ s ) n ϕ ( r ) .

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