Abstract

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

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2010 (6)

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]

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]

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]

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]

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]

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]

2009 (4)

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]

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]

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]

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]

2008 (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]

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]

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]

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[CrossRef] [PubMed]

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]

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]

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]

2007 (4)

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]

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]

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]

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]

2006 (1)

2005 (2)

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]

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]

2004 (1)

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]

2001 (1)

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]

2000 (1)

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]

1998 (1)

1996 (1)

1993 (1)

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]

1992 (1)

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]

1991 (1)

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]

1989 (1)

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]

Aikawa, E.

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]

Ale, A.

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]

Arridge, S. R.

Badea, C. T.

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]

Boas, D. A.

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]

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]

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]

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]

Boverman, G.

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]

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]

Bradley, C. P.

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]

Brooks, D. H.

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]

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]

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]

Brukilacchio, T. J.

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]

Butler, J.

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]

Carpenter, C.

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]

Carpenter, C. M.

Cerussi, A.

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]

Chaves, T.

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]

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]

Cherry, S. R.

Chorlton, M.

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]

Cole, J. H.

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]

Custo, A.

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]

Dan, I.

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]

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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).
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de Kleine, R. H.

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]

Dehghani, H.

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]

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]

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]

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]

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]

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).
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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).
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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).
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Durkin, A.

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).
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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).
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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).
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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).
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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]

Forero, J.

Freyer, M.

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).
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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).
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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).
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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]

Goldstein, S. A.

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]

Grimson, W. E.

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).
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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).
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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]

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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]

Hoopes, P. J.

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]

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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).
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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).
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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]

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Isaacson, D.

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).
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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).
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Johnson, G. A.

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).
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[PubMed]

Kaufman, P. A.

Kirsch, D. G.

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]

Kogel, C.

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]

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]

Kolehmainen, V.

Kopans, D. B.

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]

Kreider, J. M.

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]

Leblond, F.

Li, A.

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]

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]

Li, C.

Liu, W.

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]

Lynch, D. R.

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]

Mehta, R.

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]

Mesquita, R.

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]

Miller, E. L.

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]

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]

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]

Modre, R.

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]

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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]

Morris, M. D.

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]

Niedre, M. J.

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]

Nissila, I.

Ntziachristos, V.

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]

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]

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]

O’Hara, J. A.

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]

Okunieff, P.

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).
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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]

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]

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]

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]

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]

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]

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]

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]

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]

Payne, H. L.

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]

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R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
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Pogue, B. W.

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Poplack, S. P.

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]

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]

Pullan, A. J.

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]

Qi, J.

Rafferty, E.

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]

Rucker, W.

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]

Samkoe, K. S.

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]

Sarantopoulos, A.

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]

Schulmerich, M. V.

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]

Schulz, R. B.

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]

Schweiger, M.

Shah, N.

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]

Sobel, E. S.

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]

Soehngen, E.

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]

Soho, S.

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]

Song, X.

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]

Srinivasan, S.

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]

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]

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]

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]

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]

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]

Stott, J. J.

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]

Sullivan, J. M.

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]

Tilg, B.

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]

Tosteson, T. D.

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]

Tromberg, B. J.

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]

Tsuzuki, D.

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]

Vaupel, P.

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]

Wach, P.

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]

Wang, G.

Wang, X.

Weaver, J. B.

Weissleder, R.

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]

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[CrossRef] [PubMed]

Wells, W.

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]

Wells, W. A.

Wilson, B. C.

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]

Wu, T.

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]

Wu, Z.

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]

Wyman, D. R.

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]

Yalavarthy, P. K.

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]

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]

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]

Yuan, Z.

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]

Zacharopoulos, A.

Zacharopoulos, A. D.

Zhang, Q.

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]

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]

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]

Zhang, X.

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]

Zientkowska, M.

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]

Acad. Radiol. (1)

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]

Ann. Biomed. Eng. (1)

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]

Appl. Opt. (2)

Cancer Res. (1)

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]

Finite Elem. Anal. Des. (1)

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]

IEEE Trans. Biomed. Eng. (1)

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]

IEEE Trans. Med. Imaging (3)

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]

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]

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]

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[CrossRef]

J. Biomed. Opt. (5)

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]

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]

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]

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]

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]

Lasers Med. Sci. (1)

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]

Med. Phys. (3)

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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]

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]

Nature (1)

R. Weissleder and M. J. Pittet, “Imaging in the era of molecular oncology,” Nature 452(7187), 580–589 (2008).
[CrossRef] [PubMed]

Neuroimage (1)

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]

Opt. Express (5)

Opt. Lett. (2)

Philos. Transact. A Math. Phys. Eng. Sci. (1)

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]

Phys. Med. Biol. (1)

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]

Proc. Natl. Acad. Sci. U.S.A. (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]

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).
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Figures (8)

Fig. 1
Fig. 1

A schematic showing steps from medical image data to obtaining a volumetric mesh for computation with examples from breast data. These steps have to be routinely performed before image reconstruction can be done for 3D multi-modality optical imaging. Methods for image segmentation vary between applications; here thresholding and region-growing techniques were applied for breast tissue. Surface rendering is automatically generated by many open source softwares, but getting a reliable volume mesh can be time-consuming and more difficult to automate.

Fig. 2
Fig. 2

Schematic of a two-layered region in 2D having homogeneous distribution of optical properties in region I and heterogeneous distribution in region II.

Fig. 3
Fig. 3

Surface renderings of the six test cases used in this study are shown, with two-three regions created. Clockwise from top left, the six test cases show cases (1) the outer breast contour and tumor created from clinical MRI (2) outer breast and simulated spherical inclusion (3) Outer breast, sphere and tumor (4) Outer breast, larger sphere and tumor (5) Outer breast and two spherical inclusions and (6) Outer breast, fibroglandular and tumor tissues.

Fig. 4
Fig. 4

Logarithm of photon fluence obtained using coupled FE-BEM for a single source in test cases 1, and 6. Left: Results from test case 1 showing outer boundary; Middle: inner tumor boundary by making outer surface transparent; Right: Results from test case 6 for inner tissues.

Fig. 5
Fig. 5

Comparison of (a) logarithm of intensity and (b) phase at the detector locations on the boundary ( = 240 measurement points) obtained from BEM, FEM and coupled FE-BEM for test case 1.

Fig. 6
Fig. 6

2-D cross-sections along the center of the interior spherical inclusion in test case 2 for μ a (left column) and logarithm of fluence (right column). The background was always homogeneous. Top row shows cross-section of sphere for a homogeneous domain (1:1 contrast between sphere and background), Middle row shows 2:1 contrast between sphere and background and bottom row shows a spatially varying distribution in the sphere (2:1 varying). As expected the fluence decreases with increasing heterogeneity.

Fig. 7
Fig. 7

Ratio of computational time of coupled FE-BEM to stand-alone FEM for the six test cases, plotted as a function of % surface to volume nodes (top) from the respective meshes (Ns/N) where Ns is the number of boundary nodes in the coupled mesh and N is the number of nodes in the FEM mesh and % surface area to volume ratio (bottom) of the total tissue domain.

Fig. 8
Fig. 8

Ratio of computational time of coupled FE-BEM model to BEM for the six test cases, plotted as a function of % surface to volume nodes (top) of the interior tissue (Nb/Nv) where Nb is the number of nodes on boundary of interior tissue and Nv is the number of volume nodes of interior tissue, and % surface area to volume ratio (ISA/IV) (bottom) of the interior tissue domain.

Tables (1)

Tables Icon

Table 1 Mesh sizes for the different test cases used in the simulations. The first two columns of mesh sizes correspond to the coupled FE-BEM and the last two columns correspond to mesh sizes for BEM and FEM

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

.D(r)Φ(r,ω)+( μ a (r)+ iω c )Φ(r,ω)=q(r,ω)
D(r)= 1 ( 3( μ a (r)+ μ s ' (r)) )
Φ(r,ω)+ D α Φ n | dΩ =0
DΦ, ϕ j + ( μ a + iω c )Φ, ϕ j = q, ϕ j
DΦ, ϕ j D Φ n ϕ j ds+ ( μ a + iω c )Φ, ϕ j =0
( D i ϕ i , ϕ j + ( μ a + iω c ) i ϕ i , ϕ j ) i=1 N v Φ i =( ϕ i ϕ j ds ) i=1 N v D i Φ i n
[A](Φ)=[B]( D Φ n )
A kl = D ϕ k ϕ l + ( μ a + iω c ) ϕ k ϕ l B kl = ϕ k ϕ l
( A bb A bi A ib A ii ){ Φ b Φ i }=( B bb 0 0 0 ){ D Φ n | Γ b 0 } { Φ b Φ i }=( A I bb A I bi A I ib A I ii )( B bb 0 0 0 ){ D Φ n | b 0 }
Φ b =[A I b b ] B bb ( D Φ n | b )
. D l Φ k l 2 Φ= q 0 (r,ω)
( μ a (r)+ iω c )= k l 2
D l 2 G(r, r i ) k l 2 G(r, r i )=δ(r r i )
G i (r,ri)= exp( k l | r r i | D l ) 4π D l | r r i | ,3D
c i Φ i + D l G i n Φ D l Φ n G i = q 0 , G i
c i Φ i + D l G i n Φds D l Φ n G i ds= q 0 , G i
[ A ˜ ]{ Φ i }[ B ˜ ]{ D l Φ n }={ Q ˜ i }
A ˜ i,j = c i δ ij + D l G i n ψ j ds B ˜ i,j = G i ψ j ds Q ˜ i = q 0 , G i
( A ˜ aa +α B ˜ aa A ˜ ab B ˜ ab A ˜ ba +α B ˜ ba A ˜ bb B ˜ bb ){ Φ a Φ b D Φ n | b }={ Q ˜ a Q ˜ b }
Φ b  (FEM)= Φ b  (BEM) D Φ n | b  (FEM) =  D Φ n | b  (BEM)
( A ˜ aa +α B ˜ aa A ˜ ab B ˜ ab A ˜ ba +α B ˜ ba A ˜ bb B ˜ bb ){ Φ a A I bb B bb D Φ n | b D Φ n | b }={ Q ˜ a Q ˜ b } ( A ˜ aa +α B ˜ aa A ˜ ab A I bb B bb B ˜ ab A ˜ ba +α B ˜ ba A ˜ bb A I bb B bb B ˜ bb ){ Φ a D Φ n | b }={ Q ˜ a Q ˜ b }
( A ˜ aa A ˜ ab A ˜ ba A ˜ bb ){ Φ a Φ b }( B ˜ aa B ˜ ab B ˜ ba B ˜ bb ){ D I Φ n | a D I Φ n | a b }={ Q ˜ a Q ˜ b }
( A ˜ aa A ˜ ab B ˜ aa B ˜ ab A ˜ ba A ˜ bb B ˜ ba B ˜ bb ){ Φ a Φ b D I Φ n | a D I Φ n | b }={ Q ˜ a Q ˜ b }
( A ˜ aa A ˜ ab B ˜ aa B ˜ ab A ˜ ba A ˜ bb B ˜ ba B ˜ bb ){ Φ a Φ b α Φ a D I Φ n | b }={ Q ˜ a Q ˜ b } ( A ˜ aa +α B ˜ aa A ˜ ab B ˜ ab A ˜ ba +α B ˜ ba A ˜ bb B ˜ bb ){ Φ a Φ b D I Φ n | b }={ Q ˜ a Q ˜ b }
( A ˜ aaI +α B ˜ aaI A ˜ abI B ˜ abI A ˜ ba +α B ˜ baI A ˜ bbI A ˜ bbII A ˜ cbII B ˜ bbI B ˜ bbII B ˜ cbII A ˜ bcII A ˜ ccII B ˜ bcII B ˜ ccII ){ Φ aI Φ bI D I Φ n | bI Φ cII D II Φ n | cII }={ Q ˜ aI Q ˜ bI 0 0 }
( A ˜ aaI +α B ˜ aaI A ˜ abI B ˜ abI A ˜ ba +α B ˜ baI A ˜ bbI A ˜ bbII A ˜ cbII B ˜ bbI B ˜ bbII B ˜ cbII A ˜ bcII A ˜ ccII B ˜ bcII B ˜ ccII ){ Φ aI Φ bI D I Φ n | bI A I cc B cc D II Φ n | cII D II Φ n | cII }={ Q ˜ aI Q ˜ bI 0 0 } ( A ˜ aaI +α B ˜ aaI A ˜ abI B ˜ abI A ˜ ba +α B ˜ baI A ˜ bbI B ˜ bbI A ˜ bbII B ˜ bbII A ˜ bcII A I cc B cc B ˜ bcII A ˜ cbII B ˜ cbII A ˜ ccII A I cc B cc B ˜ ccII ){ Φ aI Φ bI D I Φ n | bI D II Φ n | cII }={ Q ˜ aI Q ˜ bI 0 0 }

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