RTE-based bioluminescence tomography: A theoretical study

References

• Thakur, M, and Lentle, BC, 2006. Report of a summit on molecular imaging, Radiology 236 (2006), pp. 753–755.
   Web of Science ®Google Scholar
• Weissleder, R, and Ntziachristos, V, 2003. Shedding light onto live molecular targets, Nat. Med. 9 (2003), pp. 123–128.
   PubMed Web of Science ®Google Scholar
• Jaffer, FA, and Weissleder, R, 2005. Molecular imaging in the clinical arena, JAMA 293 (2005), pp. 855–862.
   PubMed Web of Science ®Google Scholar
• Rice and, BW, Cable, MD, and Nelson, MB, 2001. In vivo imaging of light-emitting probes, J. Biomed. Opt. 6 (2001), pp. 432–440.
   PubMed Web of Science ®Google Scholar
• Contag, CH, and Ross, BD, 2002. It's not just about anatomy: In vivo bioluminescence imaging as an eyepiece into biology, J. Magn. Resonance Imaging 16 (2002), pp. 378–387.
   PubMed Web of Science ®Google Scholar
• Ray, P, Wu, AM, and Gambhir, SS, 2003. Optical bioluminescence and positron emission tomography imaging of a novel fusion reporter gene in tumor xenografts of living mice, Cancer Res. 63 (2003), pp. 1160–1165.
   PubMed Web of Science ®Google Scholar
• Ntziachristos, V, Ripoll, J, Wang, LV, and Weissleder, R, 2005. Looking and listening to light: The evolution of whole-body photonic imaging, Nat. Biotechnol. 23 (2005), pp. 313–320.
   PubMed Web of Science ®Google Scholar
• Wang, G, Hoffman, EA, McLennan, G, Wang, LV, Suter, M, and Meinel, J, 2003. Development of the first bioluminescent CT scanner, Radiology 229 (P) (2003), p. 566.
   Google Scholar
• Henyey, L, and Greenstein, J, 1941. Diffuse radiation in the galaxy, Astrophysi. J. 93 (1941), pp. 70–83.
   Web of Science ®Google Scholar
• Natterer, F, and Wübbeling, F, 2001. Mathematical Methods in Image Reconstruction. Philadelphia: SIAM; 2001.
   Google Scholar
• Han, W, Cong, W-X, and Wang, G, 2006. Mathematical theory and numerical analysis of bioluminescence tomography, Inverse Probl. 22 (2006), pp. 1659–1675.
   Web of Science ®Google Scholar
• Han, W, Cong, W-X, Kazmi, K, and Wang, G, 2007. Bioluminescence tomography with optimized optical parameters, Inverse Probl. 23 (2007), pp. 1215–1228.
   Web of Science ®Google Scholar
• Han, W, and Wang, G, 2007. Theoretical and numerical analysis on multispectral bioluminescence tomography, IMA J. Appl. Math. 72 (2007), pp. 67–85.
   Web of Science ®Google Scholar
• Cheng, X-L, Gong, R-F, and Han, W, 2008. A new general mathematical framework for bioluminescence tomography, Comput. Methods Appli. Mech. Eng. 197 (2008), pp. 524–535.
   Web of Science ®Google Scholar
• Han, W, Shen, H, Kazmi, K, Cong, WX, and Wang, G, 2009. Studies of a mathematical model for temperature-modulated bioluminescence tomography, Appl. Anal. 88 (2009), pp. 193–213.
   Web of Science ®Google Scholar
• Han, W, and Wang, G, 2008. Bioluminescence tomography: Biomedical background, mathematical theory, and numerical approximation, J. Comput. Math. 26 (2008), pp. 324–335.
   PubMed Web of Science ®Google Scholar
• Anikonov, DS, 1998. Comparison of two mathematical models in radiative transfer theory, Dokl. Math. 58 (1998), pp. 136–138.
   Google Scholar
• Bal, G, and Tamasan, A, 2007. Inverse source problems in transport equations, SIAM J. Math. Anal. 39 (2007), pp. 57–76.
   Web of Science ®Google Scholar
• Stefanov, P, and Uhlmann, G, 2008. An inverse source problem in optical molecular imaging, Anal. PDE 1 (2008), pp. 115–126.
   Web of Science ®Google Scholar
• Dierkes, T, Dorn, O, Natterer, F, Palamodov, V, and Sielschott, H, 2002. Fréchet derivatives for some bilinear inverse problems, SIAM J. Appl. Math. 62 (2002), pp. 2092–2113.
   Web of Science ®Google Scholar
• Isakov, V, 2006. Inverse Problems for Partial Differential Equations, . New York: Springer; 2006.
   Google Scholar
• Banks, HT, and Kunisch, K, 1989. Estimation Techniques for Distributed Parameter Systems. Boston: Birkhäuser; 1989.
   Google Scholar
• Agoshkov, V, 1998. Boundary Value Problems for Transport Equations. Boston: Birkhäuser; 1998.
   Google Scholar
• Germogenova, TA, 1969. Generalized solutions of boundary value transport problems, USSR Math. Comput. Math. Phys. 9 (1969), pp. 605–625.
   Google Scholar
• Atkinson, K, and Han, W, 2009. "Theoretical Numerical Analysis: A Functional Analysis Framework, ". In: Texts in Applied Mathematics,, . Vol. 39. New York: Springer-Verlag; 2009.
   Google Scholar
• Ciarlet, PG, 1978. The Finite Element Method for Elliptic Problems. Amsterdam: North-Holland; 1978.
   Google Scholar
• Brenner, SC, and Scott, LR, 2008. The Mathematical Theory of Finite Element Methods, . New York: Springer; 2008.
   Google Scholar
• Atkinson, K, 1982. Numerical integration on the sphere, J. Austral. Math. Soc. (Ser. B) 23 (1982), pp. 332–347.
   Web of Science ®Google Scholar
• Leopardi, P, 2006. A partition of the unit sphere into regions of equal area and small diameter, Electron. Trans. Numer. Anal. 25 (2006), pp. 309–327.
   Web of Science ®Google Scholar
• Tikhonov, AN, 1963. Regularization of incorrectly posed problems, Sov. Dokl. 4 (1963), pp. 1624–1627.
   Google Scholar
• Engl, HW, Hanke, M, and Neubauer, A, 1996. Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers; 1996.
   Google Scholar
• Lewis, EE, and Miller, WF, 1984. Computational Methods of Neutron Transport. New York: John Wiley & Sons; 1984.
   Google Scholar