Abstract

A valuable method is described to analyze time-domain optical mammograms measured in the slab-like geometry of the slightly compressed female breast with a method based on linear perturbation theory including edge correction. Perturbations in scattering and absorption coefficients were mapped applying a computationally efficient point model.

© 2005 Optical Society of America

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  1. E.B. de Haller, "Time-resolved transillumination and optical tomography," J. Biomed. Opt. 1, 7-17 (1996).
    [CrossRef]
  2. G. Mitic, J. Kölzer, J. Otto, E. Plies, G. Sölkner, W. Zinth, "Time-gated transillumination, of biological tissues and tissuelike phantoms," Appl. Opt. 33, 6699-6710 (1994).
    [CrossRef] [PubMed]
  3. J.B. Fishkin, P.T.C. So, A.E. Cerussi, S. Fantini, M.A. Franceschini, E. Gratton, "Frequency domain method for measuring spectral properties in multiple-scattering media: methemoglobin spectra in a tissuelike phantom," Appl. Opt. 34, 1143-1155 (1995).
    [CrossRef] [PubMed]
  4. H. Heusmann, J. Kölzer, G. Mitic, "Characterization of female breasts in vivo by time resolved and spectroscopic measurements in near infrared spectroscopy, �??J. Biomed. Opt. 1, 425-434 (1996).
    [CrossRef]
  5. S. Fantini, S.A. Franceschini, G. Gaida, E. Gratton, H. Jess, W.W. Mantulin, K.T. Moesta, P.M. Schlag, M. Kaschke, "Frequency-domain optical mammography: Edge effects correction," Med. Phys. 23, 149-157 (1996).
    [CrossRef] [PubMed]
  6. J.B. Fishkin, O. Coquoz, E.R. Anderson, M. Brenner, B.J. Tromberg, "Frequency domain photon migration measurements of normal and malignant tissue optical properties in a human subject," Appl. Opt. 36, 10-20 (1997).
    [CrossRef] [PubMed]
  7. M.A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W.W. Mantulin, M. Seeber, P.M. Schlag, M. Kaschke, "Freuqency-domain techniques enhance optical mammography, Initial clinical results,�?? Proc. Natl. Acad. Sci. USA 94, 6468-6473 (1997).
    [CrossRef] [PubMed]
  8. B.W. Pogue, M. Testorf, T. McBride, U. Osterberg, K. Paulsen, "Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection," Opt. Express 1, 391-403 (1997).
    [CrossRef] [PubMed]
  9. D. Grosenick, H. Wabnitz, H.H. Rinneberg, K.T. Moesta, P.M Schlag, "Development of a time-domain optical mammograph and first in-vivo applications," Appl. Opt. 38, 2927-2943 (1999).
    [CrossRef]
  10. R. Cubeddu, A. Pifferi, P. Taroni, A. Toricelli, G. Valentini, "Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of the human breast," Appl. Phys. Lett. 74, 874-876 (1999).
    [CrossRef]
  11. A.E. Cerussi, D. Jakubowski, N. Shah, F. Bevilacqua, R. Lanning, A.J. Berger, D. Hsiang, J. Butler, R.F. Holcomb, B.J. Tromberg, "Spectroscopy enhances the information content of optical mammography," J. Biomed. Opt. 7, 60-71 (2002).
    [CrossRef] [PubMed]
  12. D. Grosenick, K.T. Moesta, H. Wabnitz, J. Mucke, C. Stroszcynski, R. Macdonald, P.M. Schlag, H.H. Rinneberg, " Time-domain optical mammography: initial clinical results on detection and characterization of breast tumors," Appl. Opt. 42, 3170-3186 (2003).
    [CrossRef] [PubMed]
  13. A. Pifferi, P. Taroni, A. Toricelli, F. Messina, R. Cubeddu, �??Four-wavelength, time-resolved optical mammography in the 680-980 nm range,�?? Opt. Lett. 28, 1138-1140 (2003).
    [CrossRef] [PubMed]
  14. D.B. Jakubowski, A.E. Cerussi, F. Bevilacqua, N. Shah, D. Hsiang, J. Butler, B.J. Tromberg, "Monitoring neoadjuvant chemotherapy in breast cancer using quantitative optical spectroscopy: a case study," J. Biomed. Opt. 9, 230-238 (2004).
    [CrossRef] [PubMed]
  15. B.W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T.D. Tosteson, S.P. Poplack, 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, 541-552 (2004).
    [CrossRef] [PubMed]
  16. P. Taroni, G. Danesini, A. Toricelli, A. Pifferi,L. Spinelli, R. Cubeddu, "Clinical trial of time-resolved optical mammography at 4 wavelengths between 683 and 975 nm," J. Biomed. Opt. 9, 464-473 (2004).
    [CrossRef] [PubMed]
  17. B.W. Pogue, T.O. McBride, U.L. Osterberg, K. Paulsen, "Comparison of imaging geometries for diffuse optical tomography of tissue," Opt. Express 4, 270-286 (1999).
    [CrossRef] [PubMed]
  18. S.R. Arridge, Inverse Problems (15, R41-R93 ,1999).
  19. J.C. Hebden, H. Veenstra, H. Dehghani, E.M.C. Hillman, M. Schweiger, S.R. Arridge, D.T. Delpy, "Three-dimensional time-resolved optical tomography of a conical breast phantom," Appl. Opt. 40, 3278- 3287 (2001).
    [CrossRef]
  20. V. Ntziachristos, A.G. Yodh, M. Schnall, B. Chance, "Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc. Natl. Acad. Sci. 97, 2767-2772 (2000).
    [CrossRef] [PubMed]
  21. B. Brooksby, S. Jiang, H. Dehghani, B.W. Pogue, K.D. Paulsen, C. Kogel, M. Doyley, J.B. Weaver, S.P. Poplack, "Magnetic resonance-guided near-infrared tomography of the breast," Rev. Sci. Instr. 75, 5262- 5270 (2004).
    [CrossRef]
  22. A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, "Use of nonlinear perturbation approach for invivo breast lesion characterization by multiwavelength time-resolved optical mammography," Opt. Exp. 11, 853-867 (2003).
    [CrossRef]
  23. L. Spinelli , A. Torircelli, A. Pifferi, P. Taroni, R. Cubeddu, "Experimental test of a novel perturbation model for time resolved imaging in diffusive media," Appl. Opt. 42, 3145-3153 (2003).
    [CrossRef] [PubMed]
  24. D. Grosenick, H. Wabnitz, K.T. Moesta, J. Mucke, M. Möller, C. Stroszcynski, J. Stö�?el, B. Wassermann, P.M. Schlag, and H.H. Rinneberg, "Concentration and oxygen saturation of haemoglobin of 50 breast tumours determined by time-domain optical mammography," Phys. Med. Biol. 49, 1165-1181 (2004).
    [CrossRef] [PubMed]
  25. S.R. Arridge, P. van der Zee, M. Cope, D.T Delpy , "Reconstruction methods for infra-red absorption imaging," in Proc. SPIE vol. 1431, "Time resolved Spectroscopy and Imaging of Tissues," 204-215 (1991).
    [CrossRef]
  26. J.C. Hebden, S.R. Arridge, "Imaging through scattering media by the use of an analytical method of perturbation amplitudes in the time domain," Appl. Opt. 35, 6788-6796 (1996).
    [CrossRef] [PubMed]
  27. M. Morin, S. Verreault, A. Mailloux, J. Frechette, S. Chatingy, Y. Painchaud, P. Beaudry, "Inclusion characterization in a scattering slab with time-resolved transmittance measurements: perturbation analysis," Appl. Opt. 39, 2840-2852 (2000).
    [CrossRef]
  28. S. Carraresi, T.S.M. Shatir, F. Martelli, G. Zaccanti, "Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration," Appl. Opt. 40, 4622-4632 (2001).
    [CrossRef]
  29. S.R. Arridge, "Photon-measurement density functions. Part I: Analytical forms," Appl. Opt. 34, 7395-7409 (1995).
    [CrossRef] [PubMed]
  30. S. Feng, F.-A. Zeng, B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," Appl. Opt. 34, 3826-3837 (1995).
    [CrossRef] [PubMed]
  31. W.H. Press, S.A. Teukolsky, V.T. Vetterling, B.P. Flannery, Numerical Recipes in C, (Cambridge University Press, 1997).
  32. D. Grosenick, K.Th. Moesta, M. Möller, J. Mucke, H. Wabnitz, J. Gebauer, C. Stroszcynski, B. Wassermann, P.M. Schlag, H. Rinneberg, "Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients," Phys. Med. Biol. 50, 2429-2449 (2005).
    [CrossRef] [PubMed]
  33. D. Grosenick, H. Wabnitz, K.Th. Moesta, , J. Mucke, P.M. Schlag, H. Rinneberg, "Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas," Phys. Med. Biol. 50, 2451-2468 (2005).
    [CrossRef] [PubMed]

Appl. Opt. (12)

G. Mitic, J. Kölzer, J. Otto, E. Plies, G. Sölkner, W. Zinth, "Time-gated transillumination, of biological tissues and tissuelike phantoms," Appl. Opt. 33, 6699-6710 (1994).
[CrossRef] [PubMed]

J.B. Fishkin, O. Coquoz, E.R. Anderson, M. Brenner, B.J. Tromberg, "Frequency domain photon migration measurements of normal and malignant tissue optical properties in a human subject," Appl. Opt. 36, 10-20 (1997).
[CrossRef] [PubMed]

J.B. Fishkin, P.T.C. So, A.E. Cerussi, S. Fantini, M.A. Franceschini, E. Gratton, "Frequency domain method for measuring spectral properties in multiple-scattering media: methemoglobin spectra in a tissuelike phantom," Appl. Opt. 34, 1143-1155 (1995).
[CrossRef] [PubMed]

S. Feng, F.-A. Zeng, B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," Appl. Opt. 34, 3826-3837 (1995).
[CrossRef] [PubMed]

S.R. Arridge, "Photon-measurement density functions. Part I: Analytical forms," Appl. Opt. 34, 7395-7409 (1995).
[CrossRef] [PubMed]

J.C. Hebden, S.R. Arridge, "Imaging through scattering media by the use of an analytical method of perturbation amplitudes in the time domain," Appl. Opt. 35, 6788-6796 (1996).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, H.H. Rinneberg, K.T. Moesta, P.M Schlag, "Development of a time-domain optical mammograph and first in-vivo applications," Appl. Opt. 38, 2927-2943 (1999).
[CrossRef]

M. Morin, S. Verreault, A. Mailloux, J. Frechette, S. Chatingy, Y. Painchaud, P. Beaudry, "Inclusion characterization in a scattering slab with time-resolved transmittance measurements: perturbation analysis," Appl. Opt. 39, 2840-2852 (2000).
[CrossRef]

J.C. Hebden, H. Veenstra, H. Dehghani, E.M.C. Hillman, M. Schweiger, S.R. Arridge, D.T. Delpy, "Three-dimensional time-resolved optical tomography of a conical breast phantom," Appl. Opt. 40, 3278- 3287 (2001).
[CrossRef]

S. Carraresi, T.S.M. Shatir, F. Martelli, G. Zaccanti, "Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration," Appl. Opt. 40, 4622-4632 (2001).
[CrossRef]

L. Spinelli , A. Torircelli, A. Pifferi, P. Taroni, R. Cubeddu, "Experimental test of a novel perturbation model for time resolved imaging in diffusive media," Appl. Opt. 42, 3145-3153 (2003).
[CrossRef] [PubMed]

D. Grosenick, K.T. Moesta, H. Wabnitz, J. Mucke, C. Stroszcynski, R. Macdonald, P.M. Schlag, H.H. Rinneberg, " Time-domain optical mammography: initial clinical results on detection and characterization of breast tumors," Appl. Opt. 42, 3170-3186 (2003).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

R. Cubeddu, A. Pifferi, P. Taroni, A. Toricelli, G. Valentini, "Noninvasive absorption and scattering spectroscopy of bulk diffusive media: An application to the optical characterization of the human breast," Appl. Phys. Lett. 74, 874-876 (1999).
[CrossRef]

in Proc. SPIE (1)

S.R. Arridge, P. van der Zee, M. Cope, D.T Delpy , "Reconstruction methods for infra-red absorption imaging," in Proc. SPIE vol. 1431, "Time resolved Spectroscopy and Imaging of Tissues," 204-215 (1991).
[CrossRef]

J. Biomed. Opt. (6)

A.E. Cerussi, D. Jakubowski, N. Shah, F. Bevilacqua, R. Lanning, A.J. Berger, D. Hsiang, J. Butler, R.F. Holcomb, B.J. Tromberg, "Spectroscopy enhances the information content of optical mammography," J. Biomed. Opt. 7, 60-71 (2002).
[CrossRef] [PubMed]

D.B. Jakubowski, A.E. Cerussi, F. Bevilacqua, N. Shah, D. Hsiang, J. Butler, B.J. Tromberg, "Monitoring neoadjuvant chemotherapy in breast cancer using quantitative optical spectroscopy: a case study," J. Biomed. Opt. 9, 230-238 (2004).
[CrossRef] [PubMed]

B.W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T.D. Tosteson, S.P. Poplack, 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, 541-552 (2004).
[CrossRef] [PubMed]

P. Taroni, G. Danesini, A. Toricelli, A. Pifferi,L. Spinelli, R. Cubeddu, "Clinical trial of time-resolved optical mammography at 4 wavelengths between 683 and 975 nm," J. Biomed. Opt. 9, 464-473 (2004).
[CrossRef] [PubMed]

E.B. de Haller, "Time-resolved transillumination and optical tomography," J. Biomed. Opt. 1, 7-17 (1996).
[CrossRef]

H. Heusmann, J. Kölzer, G. Mitic, "Characterization of female breasts in vivo by time resolved and spectroscopic measurements in near infrared spectroscopy, �??J. Biomed. Opt. 1, 425-434 (1996).
[CrossRef]

Med. Phys. (1)

S. Fantini, S.A. Franceschini, G. Gaida, E. Gratton, H. Jess, W.W. Mantulin, K.T. Moesta, P.M. Schlag, M. Kaschke, "Frequency-domain optical mammography: Edge effects correction," Med. Phys. 23, 149-157 (1996).
[CrossRef] [PubMed]

Opt. Exp. (1)

A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, "Use of nonlinear perturbation approach for invivo breast lesion characterization by multiwavelength time-resolved optical mammography," Opt. Exp. 11, 853-867 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Med. Biol. (3)

D. Grosenick, H. Wabnitz, K.T. Moesta, J. Mucke, M. Möller, C. Stroszcynski, J. Stö�?el, B. Wassermann, P.M. Schlag, and H.H. Rinneberg, "Concentration and oxygen saturation of haemoglobin of 50 breast tumours determined by time-domain optical mammography," Phys. Med. Biol. 49, 1165-1181 (2004).
[CrossRef] [PubMed]

D. Grosenick, K.Th. Moesta, M. Möller, J. Mucke, H. Wabnitz, J. Gebauer, C. Stroszcynski, B. Wassermann, P.M. Schlag, H. Rinneberg, "Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients," Phys. Med. Biol. 50, 2429-2449 (2005).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, K.Th. Moesta, , J. Mucke, P.M. Schlag, H. Rinneberg, "Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas," Phys. Med. Biol. 50, 2451-2468 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. (1)

V. Ntziachristos, A.G. Yodh, M. Schnall, B. Chance, "Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc. Natl. Acad. Sci. 97, 2767-2772 (2000).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

M.A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W.W. Mantulin, M. Seeber, P.M. Schlag, M. Kaschke, "Freuqency-domain techniques enhance optical mammography, Initial clinical results,�?? Proc. Natl. Acad. Sci. USA 94, 6468-6473 (1997).
[CrossRef] [PubMed]

Rev. Sci. Instr. (1)

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

Other (2)

S.R. Arridge, Inverse Problems (15, R41-R93 ,1999).

W.H. Press, S.A. Teukolsky, V.T. Vetterling, B.P. Flannery, Numerical Recipes in C, (Cambridge University Press, 1997).

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Figures (6)

Fig 1.
Fig 1.

Geometry for perturbation analysis. In our calculations a sphere is assumed although arbitrary shapes can be considered as well. The point model accounts only for the influence of a perturbation in the center of the sphere with radius 10 mm. The full calculation accounts for the whole volume V of the lesion (black area).

Fig. 2.
Fig. 2.

Number of mammograms corrected by a shape correction factor S according to Eq. (5). Most mammograms do not need this correction (S = 1), since the scan did not extend far enough to the edge of the breast.

Fig. 3.
Fig. 3.

Effect of thickness correction on absorption mammograms derived by perturbation theory (patient #75, invasive ductal carcinoma, λ = 785 nm); (a, b) craniocaudal projection, tumor at x = -0.25 cm and y = 7.25 cm, μ a0 = 0.032 cm-1; (a) with thickness correction, edge correction factor W = 0.49 cm-1, S = 0.47, tumor absorption μa = 0.088 cm-1 from exact calculation; (b) without edge thickness correction, (c, d) mediolateral projection, same tumor at x = -2.0 cm, y = 8.0 cm; μ a0 = 0.032 cm-1; (c) with thickness correction, edge correction factor W= 0.8 cm-1, S = 1.07 , tumor absorption μa = 0.072 cm-1 from exact calculation; (d) without edge correction. Absorption coefficients exceeding the gray scale are marked black.

Fig. 4.
Fig. 4.

Comparison of absorption mammograms (a, b) generated by perturbation calculations (point model) and imaging photon counts in the late-time window for absorption contrast (patient #38, λ = 785nm, craniocaudal projection, μ a0 = 0.032 cm-1). (a) map of the absorption coefficient without amplitude and shape corrections (cf.Eq.(4)); (b) same mammogram but with amplitude scaling and shape correction (W = 0.848 cm-1, S = 0.825) applied, tumor at x = 3 cm, y = 5.25 cm, tumor absorption μa = 0.10 cm-1 from exact calculation; (c) reciprocal number (N81) of photons in the late-time window in relative units.

Fig. 5.
Fig. 5.

Comparison of optical mammogram generated by perturbation calculations (point model) and time-window imaging for scattering contrast (patient #98, cyst at x = 2.5 cm and y = 2 cm, λ = 785 nm, craniocaudal projection, μ a0 = 0.059 cm-1, μ s0 = 11.7 cm-1). (a) Map of the reduced scattering coefficient employing amplitude and shape corrections (W = 0.88 cm-1, S = 0.63), reduced scattering coefficient μs ′ = 7.2 cm-1 of cyst from exact perturbation calculation; (b) reciprocal number (arbitrary units) of photons in the early time window N11 showing artifacts from absorption features; (c) map of absorption coefficient calculated with point model as in (a).

Fig. 6.
Fig. 6.

Distribution of tumor optical properties (linear perturbation theory, cf. Eq.(1,2), λ = 785 nm). Relative change (a) of absorption coefficient and (b) of reduced scattering coefficient with respect to background optical properties for a number of patients (n=18). No clear trend is observed for the scattering whereas absorption is always increased.

Equations (6)

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T tot ( t ) = T 0 ( t ) + δ μ a f shape a ( t ) + δD f shape D ( t )
f shape a , D ( t ) = V K a , D ( r r s , t ; μ a 0 , D 0 , r d r s ) d 3 r .
f ˜ shape a , D ( t ) = K a , D ( ( r d r s ) / 2 , t ; μ a 0 , D 0 , r d r s ) 4 π r 3 3
N fit theo ( x , y , t ; d ) = { T 0 ( d , t ) * R ( t ) max [ T 0 ( d , t ) * R ( t ) ] + δ μ a ( x , y ) f ˜ shape a ( d , t ) + δD ( x , y ) f ˜ shape D ( d , t ) * R ( t ) max [ T 0 ( d , t ) * R ( t ) ] }
d n = d 0 S ( d 0 d n FM )
N fit theo , corr ( x , y , t ; d ) = N fit theo ( x , y , t ; d ) exp { W ( d 0 d ) }

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