Abstract

We develop discontinuous Galerkin framework for solving direct and inverse problems in fluorescence diffusion optical tomography in turbid media. We show the advantages and the disadvantages of this method by comparing it with previously developed framework based on the finite volume discretization. The reconstruction algorithm was used with time-gated experimental dataset acquired by imaging a highly scattering cylindrical phantom concealing small fluorescent tubes. Optical parameters, quantum yield and lifetime were simultaneously reconstructed. Reconstruction results are presented and discussed.

© 2010 OSA

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2010 (2)

2009 (6)

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48, 28–36 (2009).

V. Gaind, K. J Webb, S. Kularatne, and C. A. Bouman, “Towards in vivo imaging of intramolecular fluorescence resonance energy transfer parameters,” J. Opt. Soc. Am. A 26, 1805–1813 (2009).

J. McGinty, V. Y. Soloviev, K. B. Tahir, R. Laine, D. W. Stuckey, J. V. Hajnal, A. Sardini, P. M. W. French, and S. R. Arridge, “Three-dimensional imaging of Förster resonance energy transfer in heterogeneous turbid media by tomographic fluorescent lifetime imaging,” Opt. Lett. 34, 2772–2774 (2009).

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

S. R. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

2008 (2)

2007 (3)

2006 (5)

V. Y. Soloviev and L. V. Krasnosselskaia, “Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography,” Appl. Opt. 45, 2828–2837 (2006).

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Non-contact fluorescence optical tomography with scanning patterned illumination,” Opt. Express 14, 6516–6534 (2006).

A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, “Time resolved fluorescence tomography of turbid media based on lifetime contrast,” Opt. Express 14, 12255–12270 (2006).

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176–4183 (2006).

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

2005 (2)

2004 (2)

D. L. Andrews and D. S. Bradshaw, “Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach,” Eur. J. Phys. 25, 845–858 (2004).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

2003 (2)

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D: Appl. Phys. 36, 1675–1681 (2003).

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-Space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).

2002 (1)

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys. 35, R61–R76 (2002).

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).

1997 (3)

F. Bassi and S. Rebay, “A high-order accurate discontinuous finite elements method for the numerical solution of the compressible Navier-Stokes equations,” J. Comp. Phys. 131, 267–279 (1997).

S. B. Colak, D. G. Papaioannou, G. W. 't Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, and N. A. A. J. van Asten, “Tomographic image reconstruction from optical projection in light-diffusing media,” Appl. Opt. 36, 180–213 (1997).

M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585–1605 (1997).

1996 (1)

1995 (2)

S. R. Arridge and M. Schweiger, “Photon measurement density functions, Part II: Finite Element results,” Appl. Opt. 34, 8026–8037 (1995).

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).

1993 (1)

S. Kaczmarz, “Approximate solution of system of linear equations,” Internat. J. Control 57, 1269–1271 (1993).

1905 (1)

A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).

Achilefu, S.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

Akers, W.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

Andersson-Engels, S.

Andrews, D. L.

D. L. Andrews and D. S. Bradshaw, “Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach,” Eur. J. Phys. 25, 845–858 (2004).

Arridge, S. R.

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48, 28–36 (2009).

S. R. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

J. McGinty, V. Y. Soloviev, K. B. Tahir, R. Laine, D. W. Stuckey, J. V. Hajnal, A. Sardini, P. M. W. French, and S. R. Arridge, “Three-dimensional imaging of Förster resonance energy transfer in heterogeneous turbid media by tomographic fluorescent lifetime imaging,” Opt. Lett. 34, 2772–2774 (2009).

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescent imaging in turbid media,” Appl. Opt. 47, 2303–2311 (2008).

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034–2036 (2007).

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).

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).

S. R. Arridge and M. Schweiger, “Photon measurement density functions, Part II: Finite Element results,” Appl. Opt. 34, 8026–8037 (1995).

Avrillier, S.

Bacskai, B. J.

Bangerth, W.

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Non-contact fluorescence optical tomography with scanning patterned illumination,” Opt. Express 14, 6516–6534 (2006).

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

Bassi, A.

Bassi, F.

F. Bassi and S. Rebay, “A high-order accurate discontinuous finite elements method for the numerical solution of the compressible Navier-Stokes equations,” J. Comp. Phys. 131, 267–279 (1997).

Boas, D. A.

Bouman, C. A.

Boverman, G.

Bradshaw, D. S.

D. L. Andrews and D. S. Bradshaw, “Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach,” Eur. J. Phys. 25, 845–858 (2004).

Brambilla, M.

Chance, B.

Chandrasekhar, S.

S. Chandrasekhar, in Radiative Transfer (Dover Publications, New York, 1960).

Colak, S. B.

Comelli, D.

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D: Appl. Phys. 36, 1675–1681 (2003).

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys. 35, R61–R76 (2002).

Cubeddu, R.

Culver, J. P.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

D'Andrea, C.

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48, 28–36 (2009).

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescent imaging in turbid media,” Appl. Opt. 47, 2303–2311 (2008).

A. Bassi, A. Farina, C. D'Andrea, A. Pifferi, G. Valentini, and R. Cubeddu, “Portable, large-bandwidth time-resolved system for diffuse optical spectroscopy,” Opt. Express 15, 14482–14487 (2007).

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D: Appl. Phys. 36, 1675–1681 (2003).

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys. 35, R61–R76 (2002).

Davis, D. M.

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

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, 1779–1792 (1995).

Dunn, A. K.

Dunsby, C.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Eddington, A. S.

A. S. Eddington, in The Internal Constitution of the Stars (Cambridge University Press, Cambridge, 1926).

Elson, D. S.

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Farina, A.

French, P. M. W.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

J. McGinty, V. Y. Soloviev, K. B. Tahir, R. Laine, D. W. Stuckey, J. V. Hajnal, A. Sardini, P. M. W. French, and S. R. Arridge, “Three-dimensional imaging of Förster resonance energy transfer in heterogeneous turbid media by tomographic fluorescent lifetime imaging,” Opt. Lett. 34, 2772–2774 (2009).

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034–2036 (2007).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Gaind, V.

Galletly, N.

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Gao, F.

Grosenick, D.

Hajnal, J. V.

Hares, J. D.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

He, H.

Hesthaven, J. S.

J. S. Hesthaven and T. Warburton, in Nodal Discontinuous Garlerkin Methods, Algorithms, Analysis, and Applications (Springer, New York, 2008).

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, 1779–1792 (1995).

Hooft, G. W. 't

Hwan, K.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

Joshi, A.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Non-contact fluorescence optical tomography with scanning patterned illumination,” Opt. Express 14, 6516–6534 (2006).

Kaczmarz, S.

S. Kaczmarz, “Approximate solution of system of linear equations,” Internat. J. Control 57, 1269–1271 (1993).

Kellett, P. A.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

Krasnosselskaia, L. V.

Kularatne, S.

Kumar, A. T. N.

Laine, R.

Lakowicz, J. R.

J. R. Lakowicz, in Principles of Fluorescence Spectroscopy (Plenum Press, New York, 1999).

Lanigan, P. M. P.

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Li, J.

Li, X. D.

Low, P. S.

MacDonald, R.

McCann, F.

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

McGinty, J.

J. McGinty, V. Y. Soloviev, K. B. Tahir, R. Laine, D. W. Stuckey, J. V. Hajnal, A. Sardini, P. M. W. French, and S. R. Arridge, “Three-dimensional imaging of Förster resonance energy transfer in heterogeneous turbid media by tomographic fluorescent lifetime imaging,” Opt. Lett. 34, 2772–2774 (2009).

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034–2036 (2007).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Melissen, J. B. M.

Möller, M.

Munro, I.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Neil, M. A. A.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034–2036 (2007).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

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Nocedal, J.

J. Nocedal and S. J. Wright, in Numerical Optimization (Springer-Verlag Inc., New York, 1999).

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R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

Ntziachristos, V.

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-Space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).

O'Leary, M. A.

Onfelt, B.

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Paasschens, J. C. J.

Papaioannou, D. G.

Patwardhan, S. V.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

Pifferi, A.

Poulet, P.

Rasmussen, J. C.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

Raymond, S. B.

Rebay, S.

F. Bassi and S. Rebay, “A high-order accurate discontinuous finite elements method for the numerical solution of the compressible Navier-Stokes equations,” J. Comp. Phys. 131, 267–279 (1997).

Requejo-Isidro, J.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

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J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-Space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).

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B. Rivière, in Discontinuous Galerkin Methods for solving elliptic and parabolic equations (SIAM, Philadelphia, 2008).

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S. R. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

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V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescent imaging in turbid media,” Appl. Opt. 47, 2303–2311 (2008).

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-Space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).

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A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).

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S. R. Arridge and M. Schweiger, “Photon measurement density functions, Part II: Finite Element results,” Appl. Opt. 34, 8026–8037 (1995).

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A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Non-contact fluorescence optical tomography with scanning patterned illumination,” Opt. Express 14, 6516–6534 (2006).

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

Skoch, J.

Sobolev, V. V.

V. V. Sobolev, A Treatise on Radiative Transfer (D. Van Nostrand Company, Inc, Princeton, 1963).

Soloviev, V. Y.

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48, 28–36 (2009).

J. McGinty, V. Y. Soloviev, K. B. Tahir, R. Laine, D. W. Stuckey, J. V. Hajnal, A. Sardini, P. M. W. French, and S. R. Arridge, “Three-dimensional imaging of Förster resonance energy transfer in heterogeneous turbid media by tomographic fluorescent lifetime imaging,” Opt. Lett. 34, 2772–2774 (2009).

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescent imaging in turbid media,” Appl. Opt. 47, 2303–2311 (2008).

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034–2036 (2007).

V. Y. Soloviev and L. V. Krasnosselskaia, “Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography,” Appl. Opt. 45, 2828–2837 (2006).

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176–4183 (2006).

Stamm, H.

Sterenborg, H. J. C. M.

Stuckey, D. W.

Svensson, T.

Swartling, J.

Tadi, M.

M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585–1605 (1997).

Tahir, K. B.

Talbot, C. B.

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

Taroni, P.

Torricelli, A.

Treanor, B.

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

Tualle, J. M.

Valentini, G.

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48, 28–36 (2009).

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescent imaging in turbid media,” Appl. Opt. 47, 2303–2311 (2008).

A. Bassi, A. Farina, C. D'Andrea, A. Pifferi, G. Valentini, and R. Cubeddu, “Portable, large-bandwidth time-resolved system for diffuse optical spectroscopy,” Opt. Express 15, 14482–14487 (2007).

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D: Appl. Phys. 36, 1675–1681 (2003).

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys. 35, R61–R76 (2002).

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J. S. Hesthaven and T. Warburton, in Nodal Discontinuous Garlerkin Methods, Algorithms, Analysis, and Applications (Springer, New York, 2008).

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J. Nocedal and S. J. Wright, in Numerical Optimization (Springer-Verlag Inc., New York, 1999).

Yamada, Y.

Ye, Y.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

Yodh, A. G.

Zhang, L.

Zhao, H.

Appl. Opt. (8)

F. Gao, J. Li, L. Zhang, P. Poulet, H. Zhao, and Y. Yamada, “Simultaneous fluorescence yield and lifetime tomography from time-resolved transmittances of small-animal-sized phantom,” Appl. Opt. 49, 3163–3172 (2010).

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384–7391 (2007).

V. Y. Soloviev, C. D'Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48, 28–36 (2009).

V. Y. Soloviev, C. D'Andrea, M. Brambilla, G. Valentini, R. B. Schulz, R. Cubeddu, and S. R. Arridge, “Adjoint time domain method for fluorescent imaging in turbid media,” Appl. Opt. 47, 2303–2311 (2008).

S. R. Arridge and M. Schweiger, “Photon measurement density functions, Part II: Finite Element results,” Appl. Opt. 34, 8026–8037 (1995).

S. B. Colak, D. G. Papaioannou, G. W. 't Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, and N. A. A. J. van Asten, “Tomographic image reconstruction from optical projection in light-diffusing media,” Appl. Opt. 36, 180–213 (1997).

V. Y. Soloviev and L. V. Krasnosselskaia, “Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography,” Appl. Opt. 45, 2828–2837 (2006).

A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. MacDonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J. M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. 44, 2104–2114 (2005).

Astrophys. J. (1)

A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).

Eur. J. Phys. (1)

D. L. Andrews and D. S. Bradshaw, “Virtual photons, dipole fields and energy transfer: a quantum electrodynamical approach,” Eur. J. Phys. 25, 845–858 (2004).

Internat. J. Control (1)

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Inverse Probl. (3)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).

S. R. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585–1605 (1997).

J. Biomed. Opt. (1)

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).

J. Comp. Phys. (1)

F. Bassi and S. Rebay, “A high-order accurate discontinuous finite elements method for the numerical solution of the compressible Navier-Stokes equations,” J. Comp. Phys. 131, 267–279 (1997).

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

J. Phys D.: Appl Phys. (1)

J. McGinty, J. Requejo-Isidro, I. Munro, C. B. Talbot, P. A. Kellett, J. D. Hares, C. Dunsby, M. A. A. Neil, and P. M. W. French, “Signal-to-noise characterization of time-gated intensifiers used for wide-field time-domain FLIM,” J. Phys D.: Appl Phys. 42, 135103 (2009).

J. Phys. D.: Appl. Phys. (1)

C. Dunsby, P. M. P. Lanigan, J. McGinty, D. S. Elson, J. Requejo-Isidro, I. Munro, N. Galletly, F. McCann, B. Treanor, B. Onfelt, D. M. Davis, M. A. A. Neil, and P. M. W. French, “An electronically tuneable ultrafast laser source applied to fluorescence imaging and fluorescence lifetime imaging microscopy,” J. Phys. D.: Appl. Phys. 37, 3296–3303 (2004).

J. Phys. D: Appl. Phys. (2)

R. Cubeddu, D. Comelli, C. D'Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys. 35, R61–R76 (2002).

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D: Appl. Phys. 36, 1675–1681 (2003).

Med. Phys. (3)

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299–1310 (2006).

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).

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176–4183 (2006).

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-Space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).

Other (8)

V. V. Sobolev, A Treatise on Radiative Transfer (D. Van Nostrand Company, Inc, Princeton, 1963).

J. Nocedal and S. J. Wright, in Numerical Optimization (Springer-Verlag Inc., New York, 1999).

B. Rivière, in Discontinuous Galerkin Methods for solving elliptic and parabolic equations (SIAM, Philadelphia, 2008).

J. S. Hesthaven and T. Warburton, in Nodal Discontinuous Garlerkin Methods, Algorithms, Analysis, and Applications (Springer, New York, 2008).

P. S. Mohan, V. Y. Soloviev, and S. R. Arridge, “Discontinuous Galerkin method for the forward modelling in optical diffusion tomography,” Int. J. Numer. Meth. Engng. to appear, (2010).

J. R. Lakowicz, in Principles of Fluorescence Spectroscopy (Plenum Press, New York, 1999).

A. S. Eddington, in The Internal Constitution of the Stars (Cambridge University Press, Cambridge, 1926).

S. Chandrasekhar, in Radiative Transfer (Dover Publications, New York, 1960).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Phantom; (b) Surface mesh; (c) Mesh slice showing internal mesh structure.

Fig. 2.
Fig. 2.

(a) Image recorded by the CCD camera; (b) corrected image; (c) computed energy density on the surface of a homogeneous cylinder. Intensities of all images are scaled by 105. Images are shown at ω = 0. The source is located on the opposite side of visible part of the surface.

Fig. 3.
Fig. 3.

Functions fi . These functions are used for computing fluorescence and optical parameters. Each row corresponds to a projection angle. Only 3 angles are shown. Each column corresponds to a particular parameter according Eqs. (14)–(18).

Fig. 4.
Fig. 4.

Reconstruction results. First, second, and third rows show slices at y = 40mm; 50mm; and 60mm respectively. First column shows reconstructed reduced scattering coefficient μ s , second column shows the absorption coefficient μa , third - the fluorescence efficiency ημa , and fourth - the lifetime τ.

Fig. 5.
Fig. 5.

Reconstruction results based on the Finite Volume discretization at y = 40mm; 50mm; and 60mm respectively. First column shows reconstructed reduced scattering coefficient μ s , second column shows the absorption coefficient μa , third - the fluorescence efficiency ημa , and fourth - the lifetime τ.

Equations (55)

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

= ( 2 π ) ξ ( θ ) ( θ + θ ) d θ + ϒ ,
θ = ς ( ω ) d ω V χ θ ( r ) ( e θ u θ 2 + h θ v θ 2 ) d 3 r .
ξ ( θ ) = Σ 0 n < N δ ( θ θ n ) ,
χ θ ( r ) = Σ 0 m < M a m δ ( r r θ m ) , ς ( ω ) = Σ 0 l < L δ ( ω ω l ) ,
θ = Re ς ( ω ) ψ θ , Λ u θ ρ θ c d ω
+ Re ς ( ω ) φ θ , Λ ν θ q u θ d ω .
Λ = · κ + σ ,
κ = [ 3 ( μ s + μ a + i ω c ) ] 1 ,
σ = μ a ( 1 + i ω c μ a ) ,
q = η μ a ( 1 + i ω τ ) 1 .
ϒ ( x ) = Σ 1 i 4 α i ς ( ω ) x k + 1 i x k i 2 d ω ,
Λ u θ = ρ θ c ; Λ v θ = q u θ ,
Λ φ θ * = 2 χ θ ( r ) ( h θ * v θ * ) ,
Λ ψ θ * = 2 χ θ ( r ) ( e θ * u θ * ) + q φ θ * ,
x k + 1 i = x k i + ( 1 α i ) ( 2 π ) ξ ( θ ) f i ( θ , x k ) d θ ,
f 1 = 3 Re [ κ 2 ( φ θ * · v θ + ψ θ * · u θ ) ] ,
f 2 = Re ( φ θ * v θ + ψ θ * u θ ) + η f 3 ,
f 3 = Re ϑ , f 4 = ω Im ( q ϑ ) ,
ϑ = ( 1 + i ω τ ) 1 φ θ * u θ .
x k + 1 i = [ x s , k i + ( 1 α i ) f i ( θ s , x k ) ] + ( 1 α i ) Σ n = s + 1 N 1 f i ( θ n , x k ) ,
x s + 1 , k i = x s , k i + ( 1 α i ) f i ( θ s , x s , k ) .
· q + σ u = ρ c ,
q = κ u .
I c 4 π u + 3 c 4 π q · s .
u = u i ϕ i , ρ = ρ i ϕ i .
w j + κ a i j u i + σ b i j u i = b i j ρ i c .
w j = V ( q · n ) ϕ j d 2 r ,
a i j = V ( ϕ i · ϕ j ) d 3 r ,
b i j = V ϕ i ϕ j d 3 r .
[ u ] = u u , { u } = ( 1 2 ) ( u + u ) ,
[ q ] = q q , { q } = ( 1 2 ) ( q + q ) ,
w j + w j = V [ q ϕ j ] · n d 2 r .
w j + w j = V ( { q } [ ϕ j ] + [ q ] { ϕ j } ) · n d 2 r .
w j + w j = V { κ u i ϕ i } · n [ ϕ j ] d 2 r .
w j = u i f ij + u i f i j ,
f ij = 1 2 κ V ϕ j n · ϕ i d 2 r ,
f i j = 1 2 κ V ϕ j n · ϕ i d 2 r .
w j = 1 3 ( 1 γ 1 + γ ) u i Ω ϕ i ϕ j d 2 r .
v j + v j = β V { κ ϕ j } · n [ u ] d 2 r + δ V [ ϕ j ] [ u ] d 2 r ,
v j = u i e i j + u i e i j ,
e i j = β 2 κ V ϕ i n · ϕ j d 2 r + δ V ϕ i ϕ j d 2 r ,
e i j = β 2 κ V ϕ i n · ϕ j d 2 r δ V ϕ i ϕ j d 2 r .
ϕ i = 1 8 ( 1 ± ξ ) ( 1 ± η ) ( 1 ± ζ ) ,
g i j = v l m n · ϕ l ξ ϕ m η ϕ j ϕ i d ξ d η ,
h i j = v l m ϕ l ξ ϕ m η ϕ i ϕ j d ξ d η ,
a i j = λ lmn ϕ l ξ ϕ m η ϕ n ζ ϕ i · ϕ j d ξ d η d ζ ,
b i j = λ lmn ϕ l ξ ϕ m η ϕ n ζ ϕ i ϕ j d ξ d η d ζ ,
λ lmn = r l · ( r m × r n ) ; v lm = n · ( r l × r m ) .
u ¯ = 1 8 Σ 0 i < 8 u i ; ρ ¯ = 1 8 Σ 0 i < 8 ρ i ,
cos θ dI ( ρ , θ ) d ρ = I ( ρ , θ ) B ( ρ ) ,
B ( ρ ) = 1 2 0 π I ( ρ , θ ) sin θ d θ ,
B ( ρ ) = 1 2 [ I 1 ( ρ ) + I 2 ( ρ ) ] .
B ( ρ ) = F ( 1 2 + ρ ) ,
I ( 0 , θ ) = 0 B ( ρ ) exp ( ρ cos θ ) d ρ cos θ = F ( 1 2 + cos θ ) .
u r V = 3 c ( 1 + γ 1 γ ) I ( 0 , θ ) 1 2 + cos θ .

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