Fluorescence lifetime optical tomography with discontinuous Galerkin discretisation scheme

doi:10.1364/BOE.1.000998

Fluorescence lifetime optical tomography with discontinuous Galerkin discretisation scheme

Vadim Y. Soloviev, Cosimo D'Andrea, P. Surya Mohan, Gianluca Valentini, Rinaldo Cubeddu, and Simon R. Arridge »View Author Affiliations

Biomedical Optics Express, Vol. 1, Issue 3, pp. 998-1013 (2010)
http://dx.doi.org/10.1364/BOE.1.000998

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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.

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(290.0290) Scattering : Scattering
(290.7050) Scattering : Turbid media

ToC Category:
Image Reconstruction and Inverse Problems

History
Original Manuscript: August 19, 2010
Revised Manuscript: September 7, 2010
Manuscript Accepted: September 12, 2010
Published: September 20, 2010

Citation
Vadim Y. Soloviev, Cosimo D'Andrea, P. Surya Mohan, Gianluca Valentini, Rinaldo Cubeddu, and Simon R. Arridge, "Fluorescence lifetime optical tomography with discontinuous Galerkin discretisation scheme," Biomed. Opt. Express 1, 998-1013 (2010)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-1-3-998

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References

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).
M. A. O'Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
A. T. N. Kumar, J. Skoch, B. J. Bacskai, D. A. Boas, and A. K. Dunn, “Fluorescence-lifetime-based tomography for turbid media,” Opt. Lett. 30, 3347–3349 (2005).
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).
L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express 16, 7214–7223 (2008).
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, 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).
J. R. Lakowicz, in Principles of Fluorescence Spectroscopy (Plenum Press, New York, 1999).
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).
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. 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).
V. Gaind, S. Kularatne, P. S. Low, and K. J. Webb, “Deep-tissue imaging of intramolecular fluorescence resonance energy-transfer parameters,” Opt. Lett. 35, 1314–1316 (2010).
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).
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).
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).
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. 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. V. Sobolev, A Treatise on Radiative Transfer (D. Van Nostrand Company, Inc, Princeton, 1963).
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).
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).
M. Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585–1605 (1997).
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. Kaczmarz, “Approximate solution of system of linear equations,” Internat. J. Control 57, 1269–1271 (1993).
J. Nocedal and S. J. Wright, in Numerical Optimization (Springer-Verlag Inc., New York, 1999).
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).
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).
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).
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).
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).
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).
J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-Space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett. 91, 103901 (2003).
A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).
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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[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).

[2] M. A. O'Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).

[3] A. T. N. Kumar, J. Skoch, B. J. Bacskai, D. A. Boas, and A. K. Dunn, “Fluorescence-lifetime-based tomography for turbid media,” Opt. Lett. 30, 3347–3349 (2005).

[4] 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).

[5] L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express 16, 7214–7223 (2008).

[6] 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).

[7] 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).

[8] 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).

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

[10] 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).

[11] 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).

[12] 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).

[13] V. Gaind, S. Kularatne, P. S. Low, and K. J. Webb, “Deep-tissue imaging of intramolecular fluorescence resonance energy-transfer parameters,” Opt. Lett. 35, 1314–1316 (2010).

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

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

[16] 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).

[17] 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).

[18] 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).

[19] 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).

[20] 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).

[21] 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).

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

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

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

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

[26] 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).

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

[28] 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).

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

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

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

[32] 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).

[33] 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).

[34] 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).

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

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

[37] 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).

[38] 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).

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

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

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

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

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Fluorescence lifetime optical tomography with discontinuous Galerkin discretisation scheme