February  2016, 10(1): 227-246. doi: 10.3934/ipi.2016.10.227

Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography

1. 

Department of Applied Physics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland

2. 

Department of Computer Science, University College London, Gower Street, London WC1E 6BT, United Kingdom

3. 

Department of Mathematics, University of Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142

4. 

Center for Nanoscience and Technology, Istituto Italiano di Tecnologia, Dept of Physics, Politecnico di Milano, 20133 Milan, Italy

5. 

University of Eastern Finland, Department of Applied Physics, P.O.Box 1627, 70211 Kuopio

Received  October 2014 Revised  March 2015 Published  February 2016

In fluorescence diffuse optical tomography (fDOT), the reconstruction of the fluorophore concentration inside the target body is usually carried out using a normalized Born approximation model where the measured fluorescent emission data is scaled by measured excitation data. One of the benefits of the model is that it can tolerate inaccuracy in the absorption and scattering distributions that are used in the construction of the forward model to some extent. In this paper, we employ the recently proposed Bayesian approximation error approach to fDOT for compensating for the modeling errors caused by the inaccurately known optical properties of the target in combination with the normalized Born approximation model. The approach is evaluated using a simulated test case with different amount of error in the optical properties. The results show that the Bayesian approximation error approach improves the tolerance of fDOT imaging against modeling errors caused by inaccurately known absorption and scattering of the target.
Citation: Meghdoot Mozumder, Tanja Tarvainen, Simon Arridge, Jari P. Kaipio, Cosimo D'Andrea, Ville Kolehmainen. Approximate marginalization of absorption and scattering in fluorescence diffuse optical tomography. Inverse Problems & Imaging, 2016, 10 (1) : 227-246. doi: 10.3934/ipi.2016.10.227
References:
[1]

S. R. Arridge, Optical tomography in medical imaging,, Inv. Probl., 15 (1999). doi: 10.1088/0266-5611/15/2/022. Google Scholar

[2]

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen and M. Vauhkonen, Approximation errors and model reduction with an application in optical diffusion tomography,, Inv. Probl., 22 (2006), 175. doi: 10.1088/0266-5611/22/1/010. Google Scholar

[3]

D. Calvetti, J. P. Kaipio and E. Somersalo, Aristotelian prior boundary conditions,, Int. J. Math., 1 (2006), 63. Google Scholar

[4]

D. Calvetti and E. Somersalo, An Introduction to Bayesian Scientific Computing Ten Lectures on Subjective Computing,, Springer, (2007). Google Scholar

[5]

W. F. Cheong, S. A. Prahl and A. J. Welch, A review of the optical properties of biological tissues,, IEEE J. Quant. Electron., 26 (1990), 2166. doi: 10.1109/3.64354. Google Scholar

[6]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. Arridge, M. D. Schnall and A. G. Yodh, Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,, Opt. Exp., 15 (2007). doi: 10.1364/OE.15.006696. Google Scholar

[7]

T. Correia, N. Ducros, C. D'Andrea, M. Schweiger and S. Arridge, Quantitative fluorescence diffuse optical tomography in the presence of heterogeneities,, Opt. Lett., 38 (2013), 1903. doi: 10.1364/OL.38.001903. Google Scholar

[8]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, D. N. Pattanayak, B. Chance and A. G. Yodh, Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,, Med. Phys., 30 (2003), 235. doi: 10.1118/1.1534109. Google Scholar

[9]

S. C. Davis, K. S. Samkoe, J. A. O'Hara, S. L. Gibbs-Strauss, H. L. Payne, P. J. Hoopes, K. D. Paulsen and B. W. Pogue, MRI-coupled fluorescence tomography quantifies EGFR activity in brain tumors,, Acad. Radiol., 17 (2010), 271. doi: 10.1016/j.acra.2009.11.001. Google Scholar

[10]

B. Dogdas, D. Stout, A. Chatziioannou and R. M. Leahy, Digimouse: A 3D whole body mouse atlas from ct and cryosection data,, Phys. Med. Biol., 52 (2007), 577. doi: 10.1088/0031-9155/52/3/003. Google Scholar

[11]

S. J. Erickson, S. L. Martinez, J. DeCerce, A. Romero, L. Caldera and A. Godavarty, Three-dimensional fluorescence tomography of human breast tissues in vivo using a hand-held optical imager,, Phys. Med. Biol., 58 (2013). Google Scholar

[12]

Q. Fang, Digimouse atlas FEM mesh,, , (). Google Scholar

[13]

E. E. Graves, J. Ripoll, R. Weissleder and V. Ntziachristos, A submillimeter resolution fluorescence molecular imaging system for small animal imaging,, Med. Phys., 30 (2003), 901. doi: 10.1118/1.1568977. Google Scholar

[14]

J. Heino and E. Somersalo, A modelling error approach for the estimation of optical absorption in the presence of anisotropies,, Phys. Med. Biol., 49 (2004), 4785. doi: 10.1088/0031-9155/49/20/009. Google Scholar

[15]

J. Heino, E. Somersalo and J. Kaipio, Compensation for geometric mismodelling by anisotropies in optical tomography,, Opt. Express, 13 (2005), 296. doi: 10.1364/OPEX.13.000296. Google Scholar

[16]

J. Huttunen and J. Kaipio, Approximation errors in nostationary inverse problems,, Inv. Probl. Imag., 1 (2007), 77. doi: 10.3934/ipi.2007.1.77. Google Scholar

[17]

J. Huttunen and J. Kaipio, Approximation error analysis in nonlinear state estimation with an application to state-space identification,, Inv. Probl., 23 (2007), 2141. doi: 10.1088/0266-5611/23/5/019. Google Scholar

[18]

A. Ishimaru, Wave Propagation and Scattering in Random Media,, Academic, (1997). doi: 10.1109/9780470547045. Google Scholar

[19]

S. L. Jacques, Optical properties of biological tissues: A review,, Phys. Med. Biol., 58 (2013). doi: 10.1088/0031-9155/58/11/R37. Google Scholar

[20]

J. Kaipio and V. Kolehmainen, Approximate marginalization over modelling errors and uncertainites in inverse problems,, in Bayesian Theory and Applications (eds. P. Damien, (2013), 644. doi: 10.1093/acprof:oso/9780199695607.003.0032. Google Scholar

[21]

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems,, Springer, (2005). Google Scholar

[22]

J. Kaipio and E. Somersalo, Statistical inverse problems: Discretization, model reduction and inverse crimes,, J. Comput. Appl. Math., 198 (2007), 493. doi: 10.1016/j.cam.2005.09.027. Google Scholar

[23]

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J. M. Dinten, P. Peltié, J. L. Coll and P. Rizo, In vivo mice lung tumor follow-up with fluorescence diffuse optical tomography,, J. Biomed. Opt., 13 (2008). doi: 10.1117/1.2884505. Google Scholar

[24]

V. Kolehmainen, M. Schweiger, I. Nissilä, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Approximation errors and model reduction in three-dimensional diffuse optical tomography,, J. Opt. Soc. Am. A., 26 (2009), 2257. doi: 10.1364/JOSAA.26.002257. Google Scholar

[25]

V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Marginalization of uninteresting distributed parameters in inverse problems - application to diffuse optical tomography,, Int. J. Uncertainty Quantification, 1 (2011), 1. doi: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10. Google Scholar

[26]

V. Kolehmainen, A. Vanne, S. Siltanen, S. Jarvenpaa, J. Kaipio, M. Lassas and M. Kalke, Parallelized bayesian inversion for three-dimensional dental x-ray imaging,, IEEE Trans. Med. Imag., 25 (2006), 218. doi: 10.1109/TMI.2005.862662. Google Scholar

[27]

A. Lehikoinen, S. Finsterle, A. Voutilainen, L. M. Heikkinen, M. Vauhkonen and J. P. Kaipio, Approximation errors and truncation of computational domains with application to geophysical tomography,, Inv. Probl. Imag., 1 (2007), 371. doi: 10.3934/ipi.2007.1.371. Google Scholar

[28]

C. Lieberman, K. Willcox and O. Ghattas, Parameter and state model reduction for large-scale statistical inverse problems,, SIAM J. Sci. Comput., 32 (2010), 2523. doi: 10.1137/090775622. Google Scholar

[29]

Y. Lin, H. Yan, O. Nalcioglu and G. Gulsen, Quantitative fluorescence tomography with functional and structural a priori information,, Appl. Opt., 48 (2009), 1328. doi: 10.1364/AO.48.001328. Google Scholar

[30]

A. Martin, J. Aguirre, A. Sarasa-Renedo, D. Tsoukatou, A. Garofalakis, H. Meyer, C. Mamalaki, J. Ripoll and A. M. Planas, Imaging changes in lymphoid organs in vivo after brain ischemia with three-dimensional fluorescence molecular tomography in transgenic mice expressing green fluorescent protein in T lymphocytes,, Mol. Imag., 7 (2008). Google Scholar

[31]

M. Mozumder, T. Tarvainen, S. R. Arridge, J. Kaipio and V. Kolehmainen, Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach,, Biomed. Opt. Express, 4 (2013), 2015. doi: 10.1364/BOE.4.002015. Google Scholar

[32]

M. Mozumder, T. Tarvainen, J. P. Kaipio, S. R. Arridge and V. Kolehmainen, Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography,, J. Opt. Soc. Am. A, 31 (2014), 1847. doi: 10.1364/JOSAA.31.001847. Google Scholar

[33]

A. Nissinen, L. Heikkinen and J. Kaipio, Approximation errors in electrical impedance tomography - an experimental study,, Meas. Sci. Technol., 19 (2008). Google Scholar

[34]

A. Nissinen, L. M. Heikkinen, V. Kolehmainen and J. P. Kaipio, Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography,, Meas. Sci. Technol., 20 (2009). doi: 10.1088/0957-0233/20/10/105504. Google Scholar

[35]

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Looking and listening to light: The evolution of whole-body photonic imaging,, Nat. Biotech., 23 (2005), 313. doi: 10.1038/nbt1074. Google Scholar

[36]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson and R. Weissleder, Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 12294. doi: 10.1073/pnas.0401137101. Google Scholar

[37]

V. Ntziachristos, C. H. Tung, C. Bremer and R. Weissleder, Fluorescence molecular tomography resolves protease activity in vivo,, Nat. Med., 8 (2002), 757. doi: 10.1038/nm729. Google Scholar

[38]

V. Ntziachristos and R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,, Opt. Lett., 26 (2001), 893. doi: 10.1364/OL.26.000893. Google Scholar

[39]

S. Patwardhan, S. Bloch, S. Achilefu and J. Culver, Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,, Opt. Express, 13 (2005), 2564. doi: 10.1364/OPEX.13.002564. Google Scholar

[40]

S. Pursiainen, Two-stage reconstruction of a circular anomaly in electrical impedance tomography,, Inv. Probl., 22 (2006), 1689. doi: 10.1088/0266-5611/22/5/010. Google Scholar

[41]

T. J. Rudge, V. Y. Soloviev and S. R. Arridge, Fast image reconstruction in fluoresence optical tomography using data compression,, Opt. Lett., 35 (2010), 763. doi: 10.1364/OL.35.000763. Google Scholar

[42]

H. Rue and L. Held, Gaussian Markov Random Fields: Theory and Applications,, Monographs on Statistics and Applied Probability, (2005). doi: 10.1201/9780203492024. Google Scholar

[43]

R. Schulz, J. Ripoll and V. Ntziachristos, Experimental fluorescence tomography of tissues with noncontact measurements,, IEEE Trans. Med. Imag., 23 (2004), 492. doi: 10.1109/TMI.2004.825633. Google Scholar

[44]

M. Schweiger, S. R. Arridge and I. Nissilä, Gauss-Newton method for image reconstruction in diffuse optical tomography,, Phys. Med. Biol., 50 (2005), 2365. doi: 10.1088/0031-9155/50/10/013. Google Scholar

[45]

A. Seppanen, A. Voutilainen and J. P. Kaipio, State estimation in process tomography - reconstruction of velocity fields using eit,, Inv. Probl., 25 (2009). doi: 10.1088/0266-5611/25/8/085009. Google Scholar

[46]

H. Shih and V. Ntziachristos, In vivo characterization of Her-2/neu carcinogenesis in mice using fluorescence molecular tomography,, Proc. Biomed. Opt., (2006). doi: 10.1364/BIO.2006.TuC1. Google Scholar

[47]

M. Solomon, B. R. White, R. E. Nothdruft, W. Akers, G. Sudlow, A. T. Eggebrecht, S. Achilefu and J. P. Culver, Video-rate fluorescence diffuse optical tomography for in vivo sentinel lymph node imaging,, Biomed. Opt. Express, 2 (2011), 3267. doi: 10.1364/BOE.2.003267. Google Scholar

[48]

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 (2009), 28. doi: 10.1364/AO.48.000028. Google Scholar

[49]

Y. Tan and H. Jiang, Diffuse optical tomography guided quantitative fluorescence molecular tomography,, Appl. Opt., 47 (2008), 2011. doi: 10.1364/AO.47.002011. Google Scholar

[50]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. R. Arridge and J. P. Kaipio, An approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,, Inv. Probl., 26 (2010). doi: 10.1088/0266-5611/26/1/015005. Google Scholar

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S. V. D. Ven, A. Wiethoff, T. Nielsen, B. Brendel, M. V. D. Voort, R. Nachabe, M. Mark, M. Beek, L. Bakker, L. Fels, S. Elias, P. Luijten and W. Mali, A novel fluorescent imaging agent for diffuse optical tomography of the breast: First clinical experience in patients,, Mol. Imag. Biol., 12 (2010), 343. Google Scholar

show all references

References:
[1]

S. R. Arridge, Optical tomography in medical imaging,, Inv. Probl., 15 (1999). doi: 10.1088/0266-5611/15/2/022. Google Scholar

[2]

S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Somersalo, T. Tarvainen and M. Vauhkonen, Approximation errors and model reduction with an application in optical diffusion tomography,, Inv. Probl., 22 (2006), 175. doi: 10.1088/0266-5611/22/1/010. Google Scholar

[3]

D. Calvetti, J. P. Kaipio and E. Somersalo, Aristotelian prior boundary conditions,, Int. J. Math., 1 (2006), 63. Google Scholar

[4]

D. Calvetti and E. Somersalo, An Introduction to Bayesian Scientific Computing Ten Lectures on Subjective Computing,, Springer, (2007). Google Scholar

[5]

W. F. Cheong, S. A. Prahl and A. J. Welch, A review of the optical properties of biological tissues,, IEEE J. Quant. Electron., 26 (1990), 2166. doi: 10.1109/3.64354. Google Scholar

[6]

A. Corlu, R. Choe, T. Durduran, M. A. Rosen, M. Schweiger, S. Arridge, M. D. Schnall and A. G. Yodh, Three-dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,, Opt. Exp., 15 (2007). doi: 10.1364/OE.15.006696. Google Scholar

[7]

T. Correia, N. Ducros, C. D'Andrea, M. Schweiger and S. Arridge, Quantitative fluorescence diffuse optical tomography in the presence of heterogeneities,, Opt. Lett., 38 (2013), 1903. doi: 10.1364/OL.38.001903. Google Scholar

[8]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, D. N. Pattanayak, B. Chance and A. G. Yodh, Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging,, Med. Phys., 30 (2003), 235. doi: 10.1118/1.1534109. Google Scholar

[9]

S. C. Davis, K. S. Samkoe, J. A. O'Hara, S. L. Gibbs-Strauss, H. L. Payne, P. J. Hoopes, K. D. Paulsen and B. W. Pogue, MRI-coupled fluorescence tomography quantifies EGFR activity in brain tumors,, Acad. Radiol., 17 (2010), 271. doi: 10.1016/j.acra.2009.11.001. Google Scholar

[10]

B. Dogdas, D. Stout, A. Chatziioannou and R. M. Leahy, Digimouse: A 3D whole body mouse atlas from ct and cryosection data,, Phys. Med. Biol., 52 (2007), 577. doi: 10.1088/0031-9155/52/3/003. Google Scholar

[11]

S. J. Erickson, S. L. Martinez, J. DeCerce, A. Romero, L. Caldera and A. Godavarty, Three-dimensional fluorescence tomography of human breast tissues in vivo using a hand-held optical imager,, Phys. Med. Biol., 58 (2013). Google Scholar

[12]

Q. Fang, Digimouse atlas FEM mesh,, , (). Google Scholar

[13]

E. E. Graves, J. Ripoll, R. Weissleder and V. Ntziachristos, A submillimeter resolution fluorescence molecular imaging system for small animal imaging,, Med. Phys., 30 (2003), 901. doi: 10.1118/1.1568977. Google Scholar

[14]

J. Heino and E. Somersalo, A modelling error approach for the estimation of optical absorption in the presence of anisotropies,, Phys. Med. Biol., 49 (2004), 4785. doi: 10.1088/0031-9155/49/20/009. Google Scholar

[15]

J. Heino, E. Somersalo and J. Kaipio, Compensation for geometric mismodelling by anisotropies in optical tomography,, Opt. Express, 13 (2005), 296. doi: 10.1364/OPEX.13.000296. Google Scholar

[16]

J. Huttunen and J. Kaipio, Approximation errors in nostationary inverse problems,, Inv. Probl. Imag., 1 (2007), 77. doi: 10.3934/ipi.2007.1.77. Google Scholar

[17]

J. Huttunen and J. Kaipio, Approximation error analysis in nonlinear state estimation with an application to state-space identification,, Inv. Probl., 23 (2007), 2141. doi: 10.1088/0266-5611/23/5/019. Google Scholar

[18]

A. Ishimaru, Wave Propagation and Scattering in Random Media,, Academic, (1997). doi: 10.1109/9780470547045. Google Scholar

[19]

S. L. Jacques, Optical properties of biological tissues: A review,, Phys. Med. Biol., 58 (2013). doi: 10.1088/0031-9155/58/11/R37. Google Scholar

[20]

J. Kaipio and V. Kolehmainen, Approximate marginalization over modelling errors and uncertainites in inverse problems,, in Bayesian Theory and Applications (eds. P. Damien, (2013), 644. doi: 10.1093/acprof:oso/9780199695607.003.0032. Google Scholar

[21]

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems,, Springer, (2005). Google Scholar

[22]

J. Kaipio and E. Somersalo, Statistical inverse problems: Discretization, model reduction and inverse crimes,, J. Comput. Appl. Math., 198 (2007), 493. doi: 10.1016/j.cam.2005.09.027. Google Scholar

[23]

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J. M. Dinten, P. Peltié, J. L. Coll and P. Rizo, In vivo mice lung tumor follow-up with fluorescence diffuse optical tomography,, J. Biomed. Opt., 13 (2008). doi: 10.1117/1.2884505. Google Scholar

[24]

V. Kolehmainen, M. Schweiger, I. Nissilä, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Approximation errors and model reduction in three-dimensional diffuse optical tomography,, J. Opt. Soc. Am. A., 26 (2009), 2257. doi: 10.1364/JOSAA.26.002257. Google Scholar

[25]

V. Kolehmainen, T. Tarvainen, S. R. Arridge and J. P. Kaipio, Marginalization of uninteresting distributed parameters in inverse problems - application to diffuse optical tomography,, Int. J. Uncertainty Quantification, 1 (2011), 1. doi: 10.1615/Int.J.UncertaintyQuantification.v1.i1.10. Google Scholar

[26]

V. Kolehmainen, A. Vanne, S. Siltanen, S. Jarvenpaa, J. Kaipio, M. Lassas and M. Kalke, Parallelized bayesian inversion for three-dimensional dental x-ray imaging,, IEEE Trans. Med. Imag., 25 (2006), 218. doi: 10.1109/TMI.2005.862662. Google Scholar

[27]

A. Lehikoinen, S. Finsterle, A. Voutilainen, L. M. Heikkinen, M. Vauhkonen and J. P. Kaipio, Approximation errors and truncation of computational domains with application to geophysical tomography,, Inv. Probl. Imag., 1 (2007), 371. doi: 10.3934/ipi.2007.1.371. Google Scholar

[28]

C. Lieberman, K. Willcox and O. Ghattas, Parameter and state model reduction for large-scale statistical inverse problems,, SIAM J. Sci. Comput., 32 (2010), 2523. doi: 10.1137/090775622. Google Scholar

[29]

Y. Lin, H. Yan, O. Nalcioglu and G. Gulsen, Quantitative fluorescence tomography with functional and structural a priori information,, Appl. Opt., 48 (2009), 1328. doi: 10.1364/AO.48.001328. Google Scholar

[30]

A. Martin, J. Aguirre, A. Sarasa-Renedo, D. Tsoukatou, A. Garofalakis, H. Meyer, C. Mamalaki, J. Ripoll and A. M. Planas, Imaging changes in lymphoid organs in vivo after brain ischemia with three-dimensional fluorescence molecular tomography in transgenic mice expressing green fluorescent protein in T lymphocytes,, Mol. Imag., 7 (2008). Google Scholar

[31]

M. Mozumder, T. Tarvainen, S. R. Arridge, J. Kaipio and V. Kolehmainen, Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach,, Biomed. Opt. Express, 4 (2013), 2015. doi: 10.1364/BOE.4.002015. Google Scholar

[32]

M. Mozumder, T. Tarvainen, J. P. Kaipio, S. R. Arridge and V. Kolehmainen, Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography,, J. Opt. Soc. Am. A, 31 (2014), 1847. doi: 10.1364/JOSAA.31.001847. Google Scholar

[33]

A. Nissinen, L. Heikkinen and J. Kaipio, Approximation errors in electrical impedance tomography - an experimental study,, Meas. Sci. Technol., 19 (2008). Google Scholar

[34]

A. Nissinen, L. M. Heikkinen, V. Kolehmainen and J. P. Kaipio, Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography,, Meas. Sci. Technol., 20 (2009). doi: 10.1088/0957-0233/20/10/105504. Google Scholar

[35]

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Looking and listening to light: The evolution of whole-body photonic imaging,, Nat. Biotech., 23 (2005), 313. doi: 10.1038/nbt1074. Google Scholar

[36]

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, L. Josephson and R. Weissleder, Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,, Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 12294. doi: 10.1073/pnas.0401137101. Google Scholar

[37]

V. Ntziachristos, C. H. Tung, C. Bremer and R. Weissleder, Fluorescence molecular tomography resolves protease activity in vivo,, Nat. Med., 8 (2002), 757. doi: 10.1038/nm729. Google Scholar

[38]

V. Ntziachristos and R. Weissleder, Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,, Opt. Lett., 26 (2001), 893. doi: 10.1364/OL.26.000893. Google Scholar

[39]

S. Patwardhan, S. Bloch, S. Achilefu and J. Culver, Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,, Opt. Express, 13 (2005), 2564. doi: 10.1364/OPEX.13.002564. Google Scholar

[40]

S. Pursiainen, Two-stage reconstruction of a circular anomaly in electrical impedance tomography,, Inv. Probl., 22 (2006), 1689. doi: 10.1088/0266-5611/22/5/010. Google Scholar

[41]

T. J. Rudge, V. Y. Soloviev and S. R. Arridge, Fast image reconstruction in fluoresence optical tomography using data compression,, Opt. Lett., 35 (2010), 763. doi: 10.1364/OL.35.000763. Google Scholar

[42]

H. Rue and L. Held, Gaussian Markov Random Fields: Theory and Applications,, Monographs on Statistics and Applied Probability, (2005). doi: 10.1201/9780203492024. Google Scholar

[43]

R. Schulz, J. Ripoll and V. Ntziachristos, Experimental fluorescence tomography of tissues with noncontact measurements,, IEEE Trans. Med. Imag., 23 (2004), 492. doi: 10.1109/TMI.2004.825633. Google Scholar

[44]

M. Schweiger, S. R. Arridge and I. Nissilä, Gauss-Newton method for image reconstruction in diffuse optical tomography,, Phys. Med. Biol., 50 (2005), 2365. doi: 10.1088/0031-9155/50/10/013. Google Scholar

[45]

A. Seppanen, A. Voutilainen and J. P. Kaipio, State estimation in process tomography - reconstruction of velocity fields using eit,, Inv. Probl., 25 (2009). doi: 10.1088/0266-5611/25/8/085009. Google Scholar

[46]

H. Shih and V. Ntziachristos, In vivo characterization of Her-2/neu carcinogenesis in mice using fluorescence molecular tomography,, Proc. Biomed. Opt., (2006). doi: 10.1364/BIO.2006.TuC1. Google Scholar

[47]

M. Solomon, B. R. White, R. E. Nothdruft, W. Akers, G. Sudlow, A. T. Eggebrecht, S. Achilefu and J. P. Culver, Video-rate fluorescence diffuse optical tomography for in vivo sentinel lymph node imaging,, Biomed. Opt. Express, 2 (2011), 3267. doi: 10.1364/BOE.2.003267. Google Scholar

[48]

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 (2009), 28. doi: 10.1364/AO.48.000028. Google Scholar

[49]

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