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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 1, Iss. 2 — Sep. 1, 2010
  • pp: 398–413

A coupled finite element-boundary element method for modeling Diffusion equation in 3D multi-modality optical imaging

Subhadra Srinivasan, Hamid R. Ghadyani, Brian W. Pogue, and Keith D. Paulsen  »View Author Affiliations

Biomedical Optics Express, Vol. 1, Issue 2, pp. 398-413 (2010)

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Three dimensional image reconstruction for multi-modality optical spectroscopy systems needs computationally efficient forward solvers with minimum meshing complexity, while allowing the flexibility to apply spatial constraints. Existing models based on the finite element method (FEM) require full 3D volume meshing to incorporate constraints related to anatomical structure via techniques such as regularization. Alternate approaches such as the boundary element method (BEM) require only surface discretization but assume homogeneous or piece-wise constant domains that can be limiting. Here, a coupled finite element-boundary element method (coupled FE-BEM) approach is demonstrated for modeling light diffusion in 3D, which uses surfaces to model exterior tissues with BEM and a small number of volume nodes to model interior tissues with FEM. Such a coupled FE-BEM technique combines strengths of FEM and BEM by assuming homogeneous outer tissue regions and heterogeneous inner tissue regions. Results with FE-BEM show agreement with existing numerical models, having RMS differences of less than 0.5 for the logarithm of intensity and 2.5 degrees for phase of frequency domain boundary data. The coupled FE-BEM approach can model heterogeneity using a fraction of the volume nodes (4-22%) required by conventional FEM techniques. Comparisons of computational times showed that the coupled FE-BEM was faster than stand-alone FEM when the ratio of the number of surface to volume nodes in the mesh (Ns/Nv) was less than 20% and was comparable to stand-alone BEM ( ± 10%).

© 2010 OSA

OCIS Codes
(170.3010) Medical optics and biotechnology : Image reconstruction techniques
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging

ToC Category:
Image Reconstruction and Inverse Problems

Original Manuscript: June 1, 2010
Revised Manuscript: July 21, 2010
Manuscript Accepted: July 23, 2010
Published: August 2, 2010

Virtual Issues
Optical Imaging and Spectroscopy (2010) Biomedical Optics Express

Subhadra Srinivasan, Hamid R. Ghadyani, Brian W. Pogue, and Keith D. Paulsen, "A coupled finite element-boundary element method for modeling Diffusion equation in 3D multi-modality optical imaging," Biomed. Opt. Express 1, 398-413 (2010)

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  1. R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008). [CrossRef] [PubMed]
  2. A. Cerussi, D. Hsiang, N. Shah, R. Mehta, A. Durkin, J. Butler, and B. J. Tromberg, “Predicting response to breast cancer neoadjuvant chemotherapy using diffuse optical spectroscopy,” Proc. Natl. Acad. Sci. U.S.A. 104(10), 4014–4019 (2007). [CrossRef] [PubMed]
  3. M. V. Schulmerich, J. H. Cole, K. A. Dooley, M. D. Morris, J. M. Kreider, S. A. Goldstein, S. Srinivasan, and B. W. Pogue, “Noninvasive Raman tomographic imaging of canine bone tissue,” J. Biomed. Opt. 13(2), 020506 (2008). [CrossRef]
  4. C. M. Carpenter, B. W. Pogue, S. Jiang, H. Dehghani, X. Wang, K. D. Paulsen, W. A. Wells, J. Forero, C. Kogel, J. B. Weaver, S. P. Poplack, and P. A. Kaufman, “Image-guided optical spectroscopy provides molecular-specific information in vivo: MRI-guided spectroscopy of breast cancer hemoglobin, water, and scatterer size,” Opt. Lett. 32(8), 933–935 (2007). [CrossRef] [PubMed]
  5. M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. U.S.A. 105(49), 19126–19131 (2008). [CrossRef] [PubMed]
  6. M. Schweiger and S. R. Arridge, “Comparison of two- and three-dimensional reconstruction methods in optical tomography,” Appl. Opt. 37(31), 7419–7428 (1998). [CrossRef] [PubMed]
  7. P. K. Yalavarthy, D. R. Lynch, B. W. Pogue, H. Dehghani, and K. D. Paulsen, “Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems,” Med. Phys. 35(5), 1682–1697 (2008). [CrossRef] [PubMed]
  8. M. Schweiger, O. Dorn, A. Zacharopoulos, I. Nissila, and S. R. Arridge, “3D level set reconstruction of model and experimental data in Diffuse Optical Tomography,” Opt. Express 18(1), 150–164 (2010). [CrossRef] [PubMed]
  9. G. Boverman, E. L. Miller, D. H. Brooks, D. Isaacson, Q. Fang, and D. A. Boas, “Estimation and statistical bounds for three-dimensional polar shapes in diffuse optical tomography,” IEEE Trans. Med. Imaging 27(6), 752–765 (2008). [CrossRef] [PubMed]
  10. A. D. Zacharopoulos, M. Schweiger, V. Kolehmainen, and S. R. Arridge, “3D shape based reconstruction of experimental data in Diffuse Optical Tomography,” Opt. Express 17(21), 18940–18956 (2009). [CrossRef] [PubMed]
  11. S. Srinivasan, B. W. Pogue, H. Dehghani, F. Leblond, and X. Intes, “Data subset algorithm for computationally efficient reconstruction of 3-D spectral imaging in diffuse optical tomography,” Opt. Express 14(12), 5394–5410 (2006). [CrossRef] [PubMed]
  12. Q. Zhang, T. J. Brukilacchio, A. Li, J. J. Stott, T. Chaves, E. Hillman, T. Wu, M. Chorlton, E. Rafferty, R. H. Moore, D. B. Kopans, and D. A. Boas, “Coregistered tomographic x-ray and optical breast imaging: initial results,” J. Biomed. Opt. 10(2), 024033–0240339 (2005). [CrossRef] [PubMed]
  13. 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(3), 271–276 (2010). [CrossRef] [PubMed]
  14. R. B. Schulz, A. Ale, A. Sarantopoulos, M. Freyer, E. Soehngen, M. Zientkowska, and V. Ntziachristos, “Hybrid system for simultaneous fluorescence and x-ray computed tomography,” IEEE Trans. Med. Imaging 29(2), 465–473 (2010). [CrossRef] [PubMed]
  15. C. Li, G. Wang, J. Qi, and S. R. Cherry, “Three-dimensional fluorescence optical tomography in small-animal imaging using simultaneous positron-emission-tomography priors,” Opt. Lett. 34(19), 2933–2935 (2009). [CrossRef] [PubMed]
  16. K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35(19), 3447–3458 (1996). [CrossRef]
  17. P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” Opt. Express 15(13), 8043–8058 (2007). [CrossRef] [PubMed]
  18. Z. Yuan, Q. Zhang, E. S. Sobel, and H. Jiang, “Tomographic x-ray-guided three-dimensional diffuse optical tomography of osteoarthritis in the finger joints,” J. Biomed. Opt. 13(4), 044006 (2008). [CrossRef] [PubMed]
  19. D. Hyde, E. L. Miller, D. H. Brooks, and V. Ntziachristos, “Data specific spatially varying regularization for multimodal fluorescence molecular tomography,” IEEE Trans. Med. Imaging 29(2), 365–374 (2010). [CrossRef] [PubMed]
  20. C. M. Carpenter, S. Srinivasan, B. W. Pogue, and K. D. Paulsen, “Methodology development for three-dimensional MR-guided near infrared spectroscopy of breast tumors,” Opt. Express 16(22), 17903–17914 (2008). [CrossRef] [PubMed]
  21. G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005). [CrossRef] [PubMed]
  22. S. Srinivasan, B. W. Pogue, C. Carpenter, P. K. Yalavarthy, and K. D. Paulsen, “A boundary element approach for image-guided near-infrared absorption and scatter estimation,” Med. Phys. 34(11), 4545–4557 (2007). [CrossRef] [PubMed]
  23. X. Zhang, C. T. Badea, and G. A. Johnson, “Three-dimensional reconstruction in free-space whole-body fluorescence tomography of mice using optically reconstructed surface and atlas anatomy,” J. Biomed. Opt. 14(6), 064010 (2009). [CrossRef] [PubMed]
  24. A. Custo, D. A. Boas, D. Tsuzuki, I. Dan, R. Mesquita, B. Fischl, W. E. Grimson, and W. Wells, “Anatomical atlas-guided diffuse optical tomography of brain activation,” Neuroimage 49(1), 561–567 (2010). [CrossRef] [PubMed]
  25. B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes,” J. Biomed. Opt. 9(3), 541–552 (2004). [CrossRef] [PubMed]
  26. J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys Med Biol (2006).
  27. P. Vaupel, F. Kallinowski, and P. Okunieff, “Blood flow, oxygen and nutrient supply, and metabolic microenvironment of human tumors: a review,” Cancer Res. 49(23), 6449–6465 (1989). [PubMed]
  28. A. Ishimaru, Wave propagation and scattering in random media (Academic Press, Inc., New York, 1978), Vol. 1.
  29. M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. models of radiation transport and their application,” Lasers Med. Sci. 6(2), 155–168 (1991). [CrossRef]
  30. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20(2), 299–309 (1993). [CrossRef] [PubMed]
  31. D. R. Lynch, Numerical partial differential equations for environmental scientists and engineers (Springer, 2005).
  32. C. A. Brebbia and J. Dominguez, Boundary elements: an introductory course.
  33. http://materialise.com/materialise/view/en/92078-Mimics.html , retrieved.
  34. S. Srinivasan, C. Carpenter, B. W. Pogue, and K. D. Paulsen, “Image-guided near infrared spectroscopy using boundary element method: phantom validation,” in SPIE 2009 BiOS Biomedical Optics Symposium: Multimodal Biomedical Imaging IV, 2009)
  35. H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, “Numerical modelling and image reconstruction in diffuse optical tomography,” Philos. Transact. A Math. Phys. Eng. Sci. 367(1900), 3073–3093 (2009). [CrossRef] [PubMed]
  36. H. Ghadyani, J. M. Sullivan, and Z. Wu, “Boundary recovery for delaunay tetrahedral meshes using local topological transformations,” Finite Elem. Anal. Des. 46(1-2), 74–83 (2010). [CrossRef] [PubMed]
  37. C. P. Bradley, G. M. Harris, and A. J. Pullan, “The computational performance of a high-order coupled FEM/BEM procedure in electropotential problems,” IEEE Trans. Biomed. Eng. 48(11), 1238–1250 (2001). [CrossRef] [PubMed]
  38. H. Ammari, ed., Modeling and computations in electromagnetics (Springer, 2007).
  39. G. Fischer, B. Tilg, R. Modre, G. J. Huiskamp, J. Fetzer, W. Rucker, and P. Wach, “A bidomain model based BEM-FEM coupling formulation for anisotropic cardiac tissue,” Ann. Biomed. Eng. 28(10), 1229–1243 (2000). [CrossRef] [PubMed]
  40. K. D. Paulsen and W. Liu, “Memory and operations count scaling of coupled finite element and boundary element systems of equations,” Int. J. Numer. Methods Eng. 33(6), 1289–1303 (1992). [CrossRef]

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