Abstract

A promising method to incorporate tissue structural information into the reconstruction of diffusion-based fluorescence imaging is introduced. The method regularizes the inversion problem with a Laplacian-type matrix, which inherently smoothes pre-defined tissue, but allows discontinuities between adjacent regions. The technique is most appropriately used when fluorescence tomography is combined with structural imaging systems. Phantom and simulation studies were used to illustrate significant improvements in quantitative imaging and linearity of response with the new algorithm. Images of an inclusion containing the fluorophore Lutetium Texaphyrin (Lutex) embedded in a cylindrical phantom are more accurate than in situations where no structural information is available, and edge artifacts which are normally prevalent were almost entirely suppressed. Most importantly, spatial priors provided a higher degree of sensitivity and accuracy to fluorophore concentration, though both techniques suffer from image bias caused by excitation signal leakage. The use of spatial priors becomes essential for accurate recovery of fluorophore distributions in complex tissue volumes. Simulation studies revealed an inability of the “no-priors” imaging algorithm to recover Lutex fluorescence yield in domains derived from T1 weighted images of a human breast. The same domains were reconstructed accurately to within 75% of the true values using prior knowledge of the internal tissue structure. This algorithmic approach will be implemented in an MR-coupled fluorescence spectroscopic tomography system, using the MR images for the structural template and the fluorescence data for region quantification.

©2007 Optical Society of America

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  1. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yeild and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36,2260–2272 (1997).
    [Crossref] [PubMed]
  2. H. B. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite- element-based algorithm and simulations,” Appl. Opt. 37,5337–5343 (1998).
    [Crossref]
  3. D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2,388–417 (2000).
    [Crossref]
  4. M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
    [Crossref] [PubMed]
  5. A. B. Milstein, O. Seungseok, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomograhy,” Appl. Opt. 42,3081–3094 (2003).
    [Crossref] [PubMed]
  6. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26,893–895 (2001).
    [Crossref]
  7. V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29,803–809 (2002).
    [Crossref] [PubMed]
  8. 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]
  9. A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
    [Crossref] [PubMed]
  10. R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissue with noncontact measurements,” IEEE Trans. Med. Imaging 23,492–500 (2004).
    [Crossref] [PubMed]
  11. S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
    [Crossref]
  12. A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
    [Crossref]
  13. B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
    [Crossref]
  14. X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
    [Crossref] [PubMed]
  15. M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
    [Crossref] [PubMed]
  16. P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).
  17. G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
    [Crossref]
  18. K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
    [Crossref] [PubMed]
  19. M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
    [Crossref]
  20. A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
    [Crossref] [PubMed]
  21. H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
    [Crossref] [PubMed]
  22. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20,299–309 (1993).
    [Crossref] [PubMed]
  23. K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22,691–701 (1995).
    [Crossref] [PubMed]
  24. S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Finite-element-method calculations,” Appl. Opt. 34,8026–8037 (1995).
    [Crossref] [PubMed]
  25. A. Borsic, W. R. B. Lionheart, and C. N. McLeod, “Generation of anisotropic-smoothness regularization filters for EIT,” IEEE Trans. Med. Imaging 21,579–587 (2002).
    [Crossref] [PubMed]
  26. B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).
  27. K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35,3447–3458 (1996).
    [Crossref] [PubMed]
  28. K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
    [Crossref] [PubMed]
  29. M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori boundary information,” Phys. Med. Biol. 44,2703–2722 (1999).
    [Crossref] [PubMed]
  30. B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
    [Crossref] [PubMed]
  31. S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
    [Crossref] [PubMed]
  32. T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, “Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging,” Opt. Lett. 26,822–824 (2001).
    [Crossref]
  33. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38,2950–2961 (1999).
    [Crossref]
  34. S. Jiang, B. W. Pogue, T. O. McBride, and K. D. Paulsen, “Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom,” J. Biomed. Opt. 8,308–315 (2003).
    [Crossref] [PubMed]
  35. B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11,0411021–04110216 (2006).
    [Crossref]

2006 (4)

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11,0411021–04110216 (2006).
[Crossref]

2005 (3)

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
[Crossref] [PubMed]

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
[Crossref]

A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
[Crossref]

2004 (5)

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissue with noncontact measurements,” IEEE Trans. Med. Imaging 23,492–500 (2004).
[Crossref] [PubMed]

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

2003 (5)

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

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]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).

S. Jiang, B. W. Pogue, T. O. McBride, and K. D. Paulsen, “Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom,” J. Biomed. Opt. 8,308–315 (2003).
[Crossref] [PubMed]

A. B. Milstein, O. Seungseok, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomograhy,” Appl. Opt. 42,3081–3094 (2003).
[Crossref] [PubMed]

2002 (3)

A. Borsic, W. R. B. Lionheart, and C. N. McLeod, “Generation of anisotropic-smoothness regularization filters for EIT,” IEEE Trans. Med. Imaging 21,579–587 (2002).
[Crossref] [PubMed]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
[Crossref] [PubMed]

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29,803–809 (2002).
[Crossref] [PubMed]

2001 (2)

2000 (2)

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2,388–417 (2000).
[Crossref]

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

1999 (2)

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38,2950–2961 (1999).
[Crossref]

M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori boundary information,” Phys. Med. Biol. 44,2703–2722 (1999).
[Crossref] [PubMed]

1998 (1)

1997 (3)

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yeild and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36,2260–2272 (1997).
[Crossref] [PubMed]

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

1996 (1)

1995 (3)

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Finite-element-method calculations,” Appl. Opt. 34,8026–8037 (1995).
[Crossref] [PubMed]

K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22,691–701 (1995).
[Crossref] [PubMed]

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. 20,299–309 (1993).
[Crossref] [PubMed]

Achilefu, S.

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
[Crossref]

Arridge, S. R.

M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori boundary information,” Phys. Med. Biol. 44,2703–2722 (1999).
[Crossref] [PubMed]

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Finite-element-method calculations,” Appl. Opt. 34,8026–8037 (1995).
[Crossref] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20,299–309 (1993).
[Crossref] [PubMed]

Bloch, S. R.

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
[Crossref]

Boas, D. A.

Borsic, A.

A. Borsic, W. R. B. Lionheart, and C. N. McLeod, “Generation of anisotropic-smoothness regularization filters for EIT,” IEEE Trans. Med. Imaging 21,579–587 (2002).
[Crossref] [PubMed]

Bouman, C. A.

Brooksby, B.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

Carpenter, C. M.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

Chance, B.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
[Crossref] [PubMed]

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

Chen, A. U.

Culver, J. P.

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
[Crossref]

Dehghani, H.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

Delpy, D. T.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20,299–309 (1993).
[Crossref] [PubMed]

Doyley, M.

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

Ehrenberg, B.

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

Eppstein, M. J.

A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
[Crossref]

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
[Crossref] [PubMed]

Fan, Q.

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Gibson, J. J.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

Godavarty, A.

A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
[Crossref]

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
[Crossref] [PubMed]

Graves, 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]

Gurfinkel, M.

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

Guven, M.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
[Crossref] [PubMed]

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

Hawrysz, D. J.

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
[Crossref] [PubMed]

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2,388–417 (2000).
[Crossref]

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20,299–309 (1993).
[Crossref] [PubMed]

Intes, X.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
[Crossref] [PubMed]

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

Jiang, H.

K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35,3447–3458 (1996).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22,691–701 (1995).
[Crossref] [PubMed]

Jiang, H. B.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

H. B. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite- element-based algorithm and simulations,” Appl. Opt. 37,5337–5343 (1998).
[Crossref]

Jiang, S.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, and K. D. Paulsen, “Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom,” J. Biomed. Opt. 8,308–315 (2003).
[Crossref] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, “Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging,” Opt. Lett. 26,822–824 (2001).
[Crossref]

K. D., P.

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

Kessel, D.

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Kogel, C.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

Kostenich, G.

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

Kral, V.

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

Lionheart, W. R. B.

A. Borsic, W. R. B. Lionheart, and C. N. McLeod, “Generation of anisotropic-smoothness regularization filters for EIT,” IEEE Trans. Med. Imaging 21,579–587 (2002).
[Crossref] [PubMed]

Luo, Y.

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Malik, Z.

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

Maloux, C.

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

Matejka, P.

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

McBride, T. O.

McLeod, C. N.

A. Borsic, W. R. B. Lionheart, and C. N. McLeod, “Generation of anisotropic-smoothness regularization filters for EIT,” IEEE Trans. Med. Imaging 21,579–587 (2002).
[Crossref] [PubMed]

Meaney, P.

K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
[Crossref] [PubMed]

Miles, D. R.

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Millane, R. P.

Milstein, A. B.

Monnier, P.

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

Moskowitz, M.

K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
[Crossref] [PubMed]

Ntziachristos, V.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissue with noncontact measurements,” IEEE Trans. Med. Imaging 23,492–500 (2004).
[Crossref] [PubMed]

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]

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29,803–809 (2002).
[Crossref] [PubMed]

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26,893–895 (2001).
[Crossref]

Orenstein, A.

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

Osterberg, U. L.

Paithankar, D. Y.

Patterson, M.

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11,0411021–04110216 (2006).
[Crossref]

Patterson, M. S.

Patwardhan, S. V.

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
[Crossref]

Paulsen, K. D.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, and K. D. Paulsen, “Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom,” J. Biomed. Opt. 8,308–315 (2003).
[Crossref] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, “Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging,” Opt. Lett. 26,822–824 (2001).
[Crossref]

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38,2950–2961 (1999).
[Crossref]

K. D. Paulsen and H. Jiang, “Enhanced frequency-domain optical image reconstruction in tissues through total-variation minimization,” Appl. Opt. 35,3447–3458 (1996).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22,691–701 (1995).
[Crossref] [PubMed]

K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
[Crossref] [PubMed]

Pogue, B.

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11,0411021–04110216 (2006).
[Crossref]

Pogue, B. W.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

S. Jiang, B. W. Pogue, T. O. McBride, and K. D. Paulsen, “Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom,” J. Biomed. Opt. 8,308–315 (2003).
[Crossref] [PubMed]

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, “Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging,” Opt. Lett. 26,822–824 (2001).
[Crossref]

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38,2950–2961 (1999).
[Crossref]

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yeild and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36,2260–2272 (1997).
[Crossref] [PubMed]

Poplack, S. P.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

T. O. McBride, B. W. Pogue, S. Jiang, U. L. Osterberg, K. D. Paulsen, and S. P. Poplack, “Initial studies of in vivo absorbing and scattering heterogeneity in near-infrared tomographic breast imaging,” Opt. Lett. 26,822–824 (2001).
[Crossref]

Pouckova, P.

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

Prewitt, J.

Radu, A.

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

Ripoll, J.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissue with noncontact measurements,” IEEE Trans. Med. Imaging 23,492–500 (2004).
[Crossref] [PubMed]

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]

Roitman, L.

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

Roy, R.

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

Schulz, R. B.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissue with noncontact measurements,” IEEE Trans. Med. Imaging 23,492–500 (2004).
[Crossref] [PubMed]

Schweiger, M.

M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori boundary information,” Phys. Med. Biol. 44,2703–2722 (1999).
[Crossref] [PubMed]

S. R. Arridge and M. Schweiger, “Photon-measurement density functions. Part2: Finite-element-method calculations,” Appl. Opt. 34,8026–8037 (1995).
[Crossref] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20,299–309 (1993).
[Crossref] [PubMed]

Sessler, J. L.

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

Seungseok, O.

Sevick-Muraca, E. M.

A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
[Crossref]

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
[Crossref] [PubMed]

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2,388–417 (2000).
[Crossref]

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yeild and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36,2260–2272 (1997).
[Crossref] [PubMed]

Soho, S.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

Srinivasan, S.

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

Sullican, J.

K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
[Crossref] [PubMed]

Synytsya, A.

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

Thompson, A. B.

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

Tosteson, T. D.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

van den Bergh, H.

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

Vishwanath, K.

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

Volka, K.

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

Wagnieres, G.

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

Weaver, J.

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

Weaver, J. B.

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

Webb, K. J.

Weissleder, R.

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]

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29,803–809 (2002).
[Crossref] [PubMed]

V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. 26,893–895 (2001).
[Crossref]

Woodburn, K. W.

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Yalavarthy, P. K.

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

Yazici, B.

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
[Crossref] [PubMed]

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

Young, S. W.

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Zellweger, M.

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

Zhang, C.

A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
[Crossref]

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

Zhang, Q.

Acad. Radiol. (1)

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, and K. D. Paulsen, “In vivo hemoglobin and water concentrations, oxygen saturation, and scattering estimates from near-infrared breast tomography using spectral reconstruction,” Acad. Radiol. 13,195–202 (2006).
[Crossref] [PubMed]

Appl. Opt. (6)

IEEE J. STQE (1)

B. Brooksby, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Near infrared (NIR) tomography breast image reconstruction with a priori structural information from MRI: algorithm development for reconstructing heterogeneities,” IEEE J. STQE 9,199–209 (2003).

IEEE Trans. Med. (1)

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, C. M. Carpenter, H. B. Jiang, and K. D. Paulsen, “Structural information within regularization matrices improves near infrared diffuse optical tomography,” IEEE Trans. Med. Imaging In review (2006).

IEEE Trans. Med. Imaging (3)

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissue with noncontact measurements,” IEEE Trans. Med. Imaging 23,492–500 (2004).
[Crossref] [PubMed]

A. Borsic, W. R. B. Lionheart, and C. N. McLeod, “Generation of anisotropic-smoothness regularization filters for EIT,” IEEE Trans. Med. Imaging 21,579–587 (2002).
[Crossref] [PubMed]

K. D. Paulsen, P. Meaney, M. Moskowitz, and J. Sullican, “A dual mesh for finite element based reconstruction algorithms,” IEEE Trans. Med. Imaging 14,504–514 (1995).
[Crossref] [PubMed]

J. Biomed. Opt. (3)

S. Jiang, B. W. Pogue, T. O. McBride, and K. D. Paulsen, “Quantitative analysis of near-infrared tomography: sensitivity to the tissue-simulating precalibration phantom,” J. Biomed. Opt. 8,308–315 (2003).
[Crossref] [PubMed]

B. Pogue and M. Patterson, “Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry,” J. Biomed. Opt. 11,0411021–04110216 (2006).
[Crossref]

A. Godavarty, A. B. Thompson, R. Roy, M. Gurfinkel, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies,” J. Biomed. Opt. 9,488–496 (2004).
[Crossref] [PubMed]

Med. Phys. (4)

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29,803–809 (2002).
[Crossref] [PubMed]

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]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20,299–309 (1993).
[Crossref] [PubMed]

K. D. Paulsen and H. Jiang, “Spatially varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22,691–701 (1995).
[Crossref] [PubMed]

Neoplasia (1)

D. J. Hawrysz and E. M. Sevick-Muraca, “Developments toward diagnostic breast cancer imaging using near-infrared optical measurements and fluorescent contrast agents,” Neoplasia 2,388–417 (2000).
[Crossref]

Opt. Exp. (1)

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distribution in mice,” Opt. Exp. 13,2564–2577 (2005).
[Crossref]

Opt. Lett. (2)

Photochem. & Photobiol. (3)

A. Synytsya, V. Kral, P. Matejka, P. Pouckova, K. Volka, and J. L. Sessler, “Biodistribution assessment of a lutetium(III) texaphyrin analogue in tumor-bearing mice using NIR Fourier-transform Raman spectroscopy,” Photochem. & Photobiol. 79,453–460 (2004).
[Crossref] [PubMed]

G. Kostenich, A. Orenstein, L. Roitman, Z. Malik, and B. Ehrenberg, “In vivo photodynamic therapy with the new near-IR absorbing water soluble photosensitizer lutetium texaphyrin and a high intensity pulsed light delivery system,” Photochem. & Photobiol. 39,36–42 (1997).
[Crossref]

K. W. Woodburn, Q. Fan, D. R. Miles, D. Kessel, Y. Luo, and S. W. Young, “Localization and efficacy analysis of the phototherapeutic lutetium texaphyrin (PCI-0123) in the murine EMT6 sarcoma model,” Photochem. & Photobiol. 65,410–415 (1997).
[Crossref] [PubMed]

Photochem. & Photobiol. B (1)

M. Zellweger, A. Radu, P. Monnier, H. van den Bergh, and G. Wagnieres, “Fluorescence pharmacokinetics of Lutetium Texaphyrin (PCI-0123, Lu-Tex) in the skin and in healthy and tumoral hamster cheek-pouch mucosa,” Photochem. & Photobiol. B 55,56–62 (2000).
[Crossref]

Phys. Med. Biol. (4)

X. Intes, C. Maloux, M. Guven, B. Yazici, and B. Chance, “Diffuse Optical tomography with physiological and spatial a priori constraints,” Phys. Med. Biol. 49,N155–N163 (2004).
[Crossref] [PubMed]

M. Guven, B. Yazici, X. Intes, and B. Chance, “Diffuse optical tomography with a priori anatomical information,” Phys. Med. Biol. 50,2837–2858 (2005).
[Crossref] [PubMed]

H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and P. K. D., “The effects of internal refractive index variation in near infrared optical tomography: A finite element modeling approach,” Phys. Med. Biol. 48,2713–2727 (2003).
[Crossref] [PubMed]

M. Schweiger and S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori boundary information,” Phys. Med. Biol. 44,2703–2722 (1999).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

B. Brooksby, B. W. Pogue, S. Jiang, H. Dehghani, S. Srinivasan, C. Kogel, T. D. Tosteson, J. Weaver, S. P. Poplack, and K. D. Paulsen, “Imaging breast adipose and fibroglandular tissue molecular signatures using hybrid MRI-guided near-infrared spectral tomography,” Proc. Natl. Acad. Sci. USA 103,8828–8833 (2006).
[Crossref] [PubMed]

M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: near-infrared fluorescence tomography,” Proc. Natl. Acad. Sci. USA 99,9619–9624 (2002).
[Crossref] [PubMed]

Radiol. (1)

A. Godavarty, M. J. Eppstein, C. Zhang, and E. M. Sevick-Muraca, “Detection of single and multiple targets in tissue phantoms with fluorescence-enhanced optical imaging: feasibility study,” Radiol. 235,148–154 (2005).
[Crossref]

Rev. Sci. Instrum. (1)

B. Brooksby, S. Jiang, C. Kogel, M. Doyley, H. Dehghani, J. B. Weaver, S. P. Poplack, B. W. Pogue, and K. D. Paulsen, “Magnetic resonance-guided near-infrared tomography of the breast,” Rev. Sci. Instrum. 75,5262–5270 (2004).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. An axial T1 weighted MR slice of a human breast is shown in (a), from which the test domain for simulation studies was derived. Darker regions indicate fibro-glandular tissue imbedded in adipose tissue indicated by lighter values. The image was acquired during a clinical exam with one of our MR-coupled NIR tomography systems and shows the indentations caused by the fiber optic probes. The test domain (b) was a discretization of the MR image thresholded into regions. The yellow anomaly was added to simulate a targeted cancerous tumor.

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Fig. 2.
Fig. 2. The normalized absorbance and fluorescence emission spectra of Lutetium Texaphyrin are shown.

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Fig. 3.
Fig. 3. The experimental spectrometer-based system depicted at left couples directly into the MR via 13 meter fiber optic bundles. Sixteen spectrometers are computer controlled for rapid image acquisition (left photograph). An animal interface (right photograph) is composed of a rodent MR coil custom built by Philips Research Hamburg to accommodate the optical fiber array for simultaneous MR and NIR fluorescence imaging.

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Fig. 4.
Fig. 4. An example of a pair of basis spectra for the excitation and fluorescence light (in counts/s as a function of CCD pixel number) is shown in (b). These spectra are recorded for each detector prior to imaging. In practice, the basis spectra are used to perform a least squares fit (a) to the spectrum measured for each source-detector pair to determine the relative contribution of the fluorescence and excitation light to the measured response.

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Fig. 5.
Fig. 5. Target and recovered values of μa,x, μ ′ s,x, μa,m, μ ′ s,m, and fluorescence yield, ημaf, for reconstruction implementations using no prior information and with spatial prior information. In this case, the simulated cancer region is near the edge, which is known to be easier to recover without spatial priors. The image scales are at right.

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Fig. 6.
Fig. 6. Target and recovered values of μa,x, μ ′ s,x, μa,m, μ ′ s,m, and fluorescence yield, ημaf, for reconstruction implementations using no priors and spatial priors. In this case, the simulated tumor region is near the center of the imaging domain, which is known to be more difficult to recover accurately. Image scales are at right.

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Fig. 7.
Fig. 7. Cross sectional plots of fluorescence yield are shown for the simulated imaging domains in (a) the case with an object near the edge and (b) the case with an object near the center. In both cases, the cross section is in the y-direction just off center from x = 0. The solid line represents the target value, the small dotted line the recovered value using a no-priors based algorithm, and the dashed line the recovered value using spatially guided reconstruction.

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Fig. 8.
Fig. 8. Recovered images of fluorescence yield are shown for varying concentrations of Lutex. The 14 mm diameter fluorescent inclusion was embedded in a 55 mm diameter solid epoxy tissue simulating phantom. Images were generated from the same data using algorithms based on no-priors and spatial soft prior implementations.

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Fig. 9.
Fig. 9. A narrower colorbar-scale version of the 0.3125 μM Lutex phantom images shown in Fig. 8 further illustrates the improvement in image accuracy for the spatially guided algorithm.

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Tables (2)

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Table 1. Chromophore concentrations and scattering parameter values assigned to the mesh regions in the simulation studies

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Table 2. Target and recovered fluorescence yield regional contrasts for the images in Figs. 4 and 5.

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Equations (16)

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

− ∇ ∙ κ x ( r ) ∇ Φ x r ω + ( μ a x ( r ) + i ω c ( r ) ) Φ x r ω = q 0 r ω
− ∇ ∙ κ m ( r ) ∇ Φ m r ω + ( μ a m ( r ) + i ω c ( r ) ) Φ m r ω = Φ x r ω η μ a f ( r ) 1 − i ω τ ( r ) 1 + [ ω τ ( r ) ] 2
Φ x , m ξ ω + 2 A n ̂ ∙ κ x , m ( ξ ) ∇ Φ x , m ξ ω = 0
A = 2 ( 1 − R 0 ) − 1 + ∣ cos θ c ∣ 3 1 − ∣ cos θ c ∣ 2
( K x ( κ ) + C x ( μ a x + i ω c ( r ) ) + 1 2 A F x ) Φ x = Q 0
( K m ( κ ) + C m ( μ a m + i ω c ( r ) ) + 1 2 A F m ) Φ m = − Q m
K x , m ij = ∫ Ω κ x , m ( r ) ∇ u i ( r ) . ∇ u j ( r ) d n r
C x , m ij = ∫ Ω ( μ a x , m ( r ) + i ω c ( r ) ) u i ( r ) u j ( r ) d n r
F x , m ij = ∮ ∂ Ω u i ( r ) u j ( r ) d n − 1 r
Q 0 i = ∫ Ω u i ( r ) q 0 ( r ) d n r
Q m i = ∫ Ω u i ( r ) [ Φ x r ω η μ a f ( r ) 1 − j ω τ ( r ) 1 + [ ω τ ( r ) ] 2 ] d n r
χ 2 = ∑ i = 1 N M ( Φ x i Meas − Φ x i C ) 2 + λ ∑ j = 1 N N I ( μ x j − μ x 0 ) 2
Δ μ x = [ J T J + λ I ] − 1 J T ( Φ x Meas − Φ x C )
χ 2 = ∑ i = 1 N M ( Φ x i Meas − Φ x i C ) 2 + β ∑ j = 1 N N ( L ( μ x j − μ x 0 ) ) 2
Δ μ x = [ J T J + β L T L ] − 1 J T ( Φ x Meas − Φ x C )
S = ∑ i = 1 N [ y i − ( a F ( λ i ) + b G ( λ i ) ) ] 2

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