OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 12, Iss. 22 — Nov. 1, 2004
  • pp: 5402–5417

Adaptive finite element based tomography for fluorescence optical imaging in tissue

Amit Joshi, Wolfgang Bangerth, and Eva M. Sevick-Muraca  »View Author Affiliations

Optics Express, Vol. 12, Issue 22, pp. 5402-5417 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (1727 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A three-dimensional fluorescence-enhanced optical tomography scheme based upon an adaptive finite element formulation is developed and employed to reconstruct fluorescent targets in turbid media from frequency-domain measurements made in reflectance geometry using area excitation illumination. The algorithm is derived within a Lagrangian framework by treating the photon diffusion model as a constraint to the optimization problem. Adaptively refined meshes are used to separately discretize maps of the forward/adjoint variables and the unknown parameter of fluorescent yield. A truncated Gauss-Newton method with simple bounds is used as the optimization method. Fluorescence yield reconstructions from simulated measurement data with added Gaussian noise are demonstrated for one and two fluorescent targets embedded within a 512ml cubical tissue phantom. We determine the achievable resolution for the area-illumination/area-detection reflectance measurement geometry by reconstructing two 0.4cm diameter spherical targets placed at at a series of decreasing lateral spacings. The results show that adaptive techniques enable the computationally efficient and stable solution of the inverse imaging problem while providing the resolution necessary for imaging the signals from molecularly targeting agents.

© 2004 Optical Society of America

OCIS Codes
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5280) Medical optics and biotechnology : Photon migration

ToC Category:
Research Papers

Original Manuscript: September 7, 2004
Revised Manuscript: October 18, 2004
Published: November 1, 2004

Amit Joshi, Wolfgang Bangerth, and Eva Sevick-Muraca, "Adaptive finite element based tomography for fluorescence optical imaging in tissue," Opt. Express 12, 5402-5417 (2004)

Sort:  Journal  |  Reset  


  1. M. G. Pomper, �??Molecular Imaging: An Overview,�?? Acad. Radiol. 8, 1141�??1153 (2001). [CrossRef] [PubMed]
  2. M. A. O�??Leary, D. A. Boas, B. Chance, and A. Yodh, �??Reradiation and imaging of diffuse photon density waves using fluorescent inhomogeneities,�?? J. Luminescence 60, 281�??286 (1994). [CrossRef]
  3. J. Wu, Y. Wang, L. Perleman, I. Itzkan, R. R. Desai, and M. S. Feld, �??Time resolved multichannel imaging of fluorescent objects embedded in turbid media,�?? Opt. Lett. 20, 489�??491 (1995). [CrossRef] [PubMed]
  4. E. L. Hull, M. G. Nichols, and T. H. Foster, �??Localization of Luminescent Inhomogeneities in Turbid Media with Spatially Resolved Measurements of CW Diffuse Luminescence Emittance,�?? Appl. Opt. 37, 2755�??2765 (1998). [CrossRef]
  5. J. C. Schotland, �??Continuous wave diffusion imaging,�?? J. Opt. Soc. Am. A 14(275�??279) (1997).
  6. M. A. O�??Leary, D. A. Boas, B. Chance, and A. G. Yodh, �??Fluorescence lifetime imaging in turbid media,�?? Opt. Lett. 20, 426�??428 (1996). [CrossRef]
  7. E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, �??A submillimeter resolution fluorescence molecular imaging system for small animal imaging,�?? Med. Phys. 30, 901�??911 (2003). [CrossRef] [PubMed]
  8. V. Ntziachristos and R. Weissleder, �??Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,�?? Opt. Lett. 26(12), 893�??895 (2001). [CrossRef]
  9. V. Chernomordik, D. Hattery, I. Gannot, and A. H. Gandjbakhche, �??Inverse method 3-D reconstruction of localized in vivo fluorescence-application to Sjøgren syndrome,�?? IEEE J. Sel. Top. Quantum Electron. 54, 930�??935 (1999).
  10. H. Quan and Z. Guo, �??Fast 3-D Optical Imaging With Transient Fluorescence Signals,�?? Opt. Express 12(3), 449�??457 (2004). <a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-449">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-3-449</a> [CrossRef]
  11. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, �??Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media,�?? Appl. Opt. 36(10), 2260�??2272 (1997). [CrossRef]
  12. R. Roy and E. M. Sevick-Muraca, �??Truncated Newton�??s Optimization Schemes for Absorption and Fluorescence Optical Tomography: part(1) theory and formulation,�?? Opt. Express 4(10), 353�??371 (1999). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-353">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-4-10-353</a> [CrossRef]
  13. H. Jiang, �??Frequency-domain fluorescent diffusion tomography: a finite element based algorithm and simulations,�?? Appl. Opt. 37(22), 5337�??5343 (1998). [CrossRef]
  14. M. J. Eppstein, D. E. Dougherty, T. L. Troy, and E. M. Sevick-Muraca, �??Biomedical optical tomography using dynamic parametrization and Bayesian conditioning on photon migration measurements,�?? Appl. Opt. 38(10), 2138�??2150 (1998).
  15. M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, �??Three dimensional near infrared fluorescence tomography with Bayesian methodologies for image reconstruction from sparse and noisy data sets,�?? Proc. Nat. Acad. Sci. 99, 9619�??9624 (2002). [CrossRef] [PubMed]
  16. A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, �??Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,�?? Phys. Med. Biol. 48, 1701�??1720 (2003). [CrossRef] [PubMed]
  17. A. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. Boas, and R. P. Milane, �??Fluorescence Optical Diffusion Tomography,�?? Appl. Opt. 42(16), 3061�??3094 (2003).
  18. J. P. Houston, S. Ke,W.Wang, C. Li, and E. M. Sevick-Muraca, �??Optical and nuclear image quality analysis with invivo NIR fluorescence and conventional gamma images acquired using a dual labeled tumor targeting probe,�?? J. Biomed. Opt. (submitted) (2004).
  19. W. Bangerth, �??Adaptive Finite Element Methods for the Identification of Distributed Coefficients in Partial Differential Equations,�?? Ph.D. thesis, University of Heidelberg (2002).
  20. W. Bangerth, �??A framework for the adaptive finite element solution of large inverse problems. I. Basic techniques,�?? Tech. Rep. 04-39, ICES, University of Texas at Austin (2004).
  21. E. M. Sevick-Muraca, E. Kuwana, A. Godavarty, J. P. Houston, A. B. Thompson, and R. Roy, Near Infrared Fluorescence Imaging and Spectroscopy in Random Media and Tissues, chap. 33, Biomedical Photonics Handbook (CRC Press, 2003).
  22. A. Godavarty, D. J. Hawrysz, R. Roy, E. M. Sevick-Muraca, and M. J. Eppstein, �??Influence of the refractive index-mismatch at the boundaries measured in fluorescenceenhanced frequency-domain photon migration imaging,�?? Opt. Express 10(15), 650�??653 (2002).<a href=" http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-653"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-15-653</a>
  23. A. B. Thompson and E. M. Sevick-Muraca, �??NIR fluorescence contrast enhanced imaging with ICCD homodyne detection: measurement precision and accuracy,�?? J. Biomed. Opt. 8, 111�??120 (2002). [CrossRef]
  24. A. Joshi, W. Bangerth, and E. Sevick-Muraca, �??Adaptive finite element methods for fluorescence enhanced frequency domain optical tomography: Forward imaging problem,�?? in International Symposium on Biomedical Imaging, pp. 1103�??1106 (IEEE, 2004).
  25. R. A. Adams, Sobolev Spaces (Academic Press, 1975).
  26. A. N. Tikhonov and V. Y. Arsenin, eds., Solution of Ill-Posed Problems (Winston, Washington, DC, 1977).
  27. S. R. Arridge and M. Schweiger, �??A Gradient Based Optimization Scheme for Optical Tomography,�?? Opt. Express 2(6), 213�??225 (1998). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213"> http://www.opticsexpress.org/abstract.cfm?URI=OPEX-2-6-213</a> [CrossRef]
  28. L. Beilina, �??Adaptive Hybrid FEM/FDM Methods for Inverse Scattering Problems,�?? Ph.D. thesis, Chalmers University of Technology (2002).
  29. R. Becker, H. Kapp, and R. Rannacher, �??Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept,�?? SIAM J. Contr. Optim. 39, 113�??132 (2000). [CrossRef]
  30. R. Luce and S. Perez, �??Parameter identification for an elliptic partial differential equation with distributed noisy data,�?? Inverse Problems 15, 291�??307 (1999). [CrossRef]
  31. D. G. Luenberger, Optimization by Vector Space Methods (John Wiley, 1969).
  32. J. Nocedal and S. J. Wright, Numerical Optimization, Springer Series in Operations Research (Springer, New York, 1999). [CrossRef]
  33. S. C. Brenner and R. L. Scott, The Mathematical Theory of Finite Elements (Springer, Berlin-Heidelberg-New York, 1994).
  34. R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh Refinement Techniques (Wiley/Teubner, New York, Stuttgart, 1996).
  35. W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations (Birkhäuser Verlag, 2003).
  36. M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, �??Adaptive Mesh Refinement techniques for Electrical Impedence Tomography,�?? Physiological Measurement 22, 91�??96 (2001). [CrossRef] [PubMed]
  37. M. Molinari, B. H. Blott, S. J. Cox, and G. J. Daniell, �??Optimal Imaging with Adaptive Mesh Refinement in Electrical Impedence Tomography,�?? Physiological Measurement 23, 121�??128 (2002). [CrossRef] [PubMed]
  38. R. Becker and R. Rannacher, �??An optimal control approach to error estimation and mesh adaptation in finite element methods,�?? Acta Numerica 10, 1�??102 (2001). [CrossRef]
  39. H. Ben Ameur, G. Chavent, and J. Jaffrè, �??Refinement and coarsening indicators for adaptive parametrization: application to the estimation of hydraulic transmissivities,�?? Inverse Problems 18, 775�??794 (2002). [CrossRef]
  40. A.-A. Grimstad, H. Krüger, T. Mannseth, G. Naevdal, and H. Urkedal, �??Adaptive selection of parameterization for reservoir history matching,�?? in ECMOR VIII: 8th European Conference on the Mathematics of Oil Recovery, Freiberg, Germany, pp. E�??46 (European Association of Geoscientists and Engineers (EAGE), 2002).
  41. R. Li, W. Liu, H. Ma, and T. Tang, �??Adaptive finite element approximation for distributed elliptic optimal control problems,�?? SIAM J. Control Optim. 41, 1321�??1349 (2002). [CrossRef]
  42. D. W. Kelly, J. P. d. S. R. Gago, O. C. Zienkiewicz, and I. Babuška, �??A posteriori error analysis and adaptive processes in the finite element method: Part I�??Error Analysis,�?? Int. J. Num. Meth. Engrg. 19, 1593�??1619 (1983). [CrossRef]
  43. W. Bangerth, R. Hartmann, and G. Kanschat, deal.II Differential Equations Analysis Library, Technical Reference (2004). <a href= "http://www.dealii.org/">http://www.dealii.org/</a>
  44. A. Thompson, �??Development of a new optical imaging modality for detection of fluorescence enhanced disease,�?? Ph.D. thesis, Texas A & M University (2003).
  45. M. Huang and Q. Zhu, �??Dual-mesh optical tomography reconstruction method with a depth correction that uses a priori ultrasound information,�?? Appl. Opt. 43(8), 1654�??1662 (2004). [CrossRef]
  46. X. Gu, Y. Xu, and H. Jiang, �??Mesh-based enhancement schemes in diffuse optical tomography,�?? Med. Phys. 30(5), 861�??869 (2003). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited