Theoretical and numerical analysis on multispectral bioluminescence tomography

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 72, Issue 1, 2007, Pages 67-85

  Han, Weimin ^a   Wang, Ge ^b  

^a UNIVERSITY OF IOWA   (United States)

^b Medical Center Boulevard   (United States)

Author keywords

Convergence; Error estimates; Multiple optical reporters; Multispectral bioluminescence tomography; Numerical solution; Optical molecular imaging; Well posedness

Indexed keywords

ERRORS; ESTIMATION; IMAGING TECHNIQUES; NUMERICAL ANALYSIS; TOMOGRAPHY;

ERROR ESTIMATES; MULTISPECTRAL BIOLUMINESCENCE TOMOGRAPHY; NUMERICAL SOLUTION; OPTICAL MOLECULAR IMAGING; WELL-POSEDNESS;

BIOLUMINESCENCE;

EID: 33846694122     PISSN: 02724960     EISSN: 14643634     Source Type: Journal    
DOI: 10.1093/imamat/hxl031     Document Type: Article

References (26)

1. Arridge, S. R., Schweiger, M., Hiraoka, M. & Delpy, D. T. (1993) A finite element approach for modeling photon transport in tissue. Med. Phys., 20, 299-309.
2. Atkinson, K. & Han, W. (2005) Theoretical Numerical Analysis: A Functional Analysis Framework, 2nd edn. Texts in Applied Mathematics, vol. 39. New York: Springer.
3. Bassingthwaighte, J. B. (2000) Strategies for the physiome project. Ann. Biomed. Eng., 28, 1043-1058.
4. Brenner, S. C. & Scott, L. R. (2002) The Mathematical Theory of Finite Element Methods, 2nd edn. New York: Springer.
5. Ciarlet, P. G. (1978) The Finite Element Method for Elliptic Problems. Amsterdam: North Holland.
6. Cong, A. X. & Wang, G. (2006) Multispectral bioluminescence tomography: methodology and simulation. Int. J. Biomed. Imaging, 2006, 1-7.
7. Cong, W. X., Wang, G., Kumar, D., Liu, Y., Jiang, M., Wang, L. H., Hoffman, E. A., McLennan, G., McCray, P. B., Zabner, J. & Cong, A. (2005) A practical reconstruction method for bioluminescence tomography. Opt. Express, 13, 6756-6771.
8. Contag, C. H. & Ross, B. D. (2002) It's not just about anatomy: In vivo bioluminescence imaging as an eyepiece into biology. J. Magn. Reson. Imaging, 16, 378-387.
9. Crampin, E. J., Halstead, M., Hunter, P., Nielson, P., Noble, D., Smith, N. & Tawhai, M. (2004) Computational physiology and the physiome project. Exp. Physiol., 89, 1-26.
10. Engl, H. W., Hanke, M. & Neubauer, A. (1996) Regularization of Inverse Problems. Dordrecht: Kluwer Academic Publishers.
11. Evans, L. C. (1998) Partial Differential Equations. Providence, RI: American Mathematical Society.
12. Grisvard, P. (1985) Elliptic Problems in Nonsmooth Domains. Boston, MA: Pitman.
13. Han, W., Cong, W. X. & Wang, G. (2006) Mathematical theory and numerical analysis of bioluminescence tomography. Inverse Probl., 22, 1659-1675.
14. Han, W., Cong, W. X. & Wang, G. Mathematical study and numerical simulation of multispectral bioluminescence tomography. Int. J. Biomed. Imaging (to appear).
15. Lions, J. L. (1971) Optimal Control of Systems Governed by Partial Differential Equations. Berlin: Springer.
16. Niziachristos, V., Tung, C. H., Bremer, C. & Weissleder, R. (2002) Fluorescence molecular tomography resolves protease activity in vivo. Nat. Med., 8, 757-761.
17. Ntziachristos, V., Ripoll, J., Wang, L. V. & Weissleder, R. (2005) Looking and listening to light: The evolution of whole-boday photonic imaging. Nat. Biotechnol., 23, 313-320.
18. Schweiger, M., Arridge, S. R., Hiraoka, M. & Delpy, D. T. (1995) The finite element method for the propagation of light in scattering media: boundary and source conditions. Med. Phys., 22, 1779-1792.
19. Wang, G., Hoffman, E. A., McLennan, G., Wang, L. V., Suter, M. & Meinel, J. F. (2003) Development of the first bioluminescent CT scanner. Radiology, 229, 566.
20. Wang, G., Jaszczak, R. & Basilion, J. (2005) Towards molecular imaging. IEEE Trans. Med. Imaging, 24, 829-831.
21. Wang, G., Li, Y. & Jiang, M. (2004) Uniqueness theorems in bioluminescence tomography. Med. Phys., 31, 2289-2299.
22. Weissleder, R. & Mahmood, U. (2001) Molecular imaging. Radiology, 219, 316-333.
23. Weissleder, R. & Ntziachristos, V. (2003) Shedding light onto live molecular targets. Nat. Med., 9, 123-128.
24. Tikhonov, A. N. (1963) Regularization of incorrectly posed problems. Sov. Dokl., 4, 1624-1627.
25. Zerhouni, E. (2003) Medicine, the NIH roadmap. Science, 302, 63-72.
26. Zhao, H., Doyle, T. C., Coquoz, O., Kalish, F., Rice, B. W. & Contag, C. H. (2005) Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo. J. Biomed. Opt., 10, 041210/1-041210/9.