Abstract

In order for diffuse optical tomography to realize its potential of obtaining quantitative images of spatially varying optical properties within random media, several potential experimental systematic errors must be overcome. One of these errors is the calibration of the emitter strength and detector efficiency/gain. While in principle these parameters can be determined accurately prior to an imaging experiment, slight fluctuations will cause significant image artifacts. For this reason, it is necessary to consider including their calibration as part of the inverse problem for image reconstruction. In this paper, we show that this can be done successfully in a linear reconstruction model with simulated continuous-wave data. The technique is general for frequency and time domain data.

© Optical Society of America

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  1. S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden and F. A. Kuijpers,"Clinical Optical Tomography and NIR Spectroscopy for Breast Cancer Detection," IEEE Journal of Selected Topics in Quantum Electronics 5, 1143-1158 (1999).
    [CrossRef]
  2. S. Fantini, M. A. Franceschini, E. Gratton, D. Hueber, W. Rosenfeld, D. Maulik, P. G. Stubblefield and M. R. Stankoivic,"Non-invasive optical imaging of the piglet brain in real time," Opt. Express 4, 308-314 (1999).
    [CrossRef] [PubMed]
  3. V. Ntziachristos, A. G. Yodh, M. Schnall and B. Chance,"Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc Natl Acad Sci U S A 97, 2767-72 (2000).
    [CrossRef] [PubMed]
  4. M. A. Franceschini, V. Toronov, M. Filiaci, E. Gratton and S. Fanini,"On-line optical imaging of the human brain with 160-ms temporal resolution," Opt. Express 6, 49-57 (2000).
    [CrossRef] [PubMed]
  5. B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman and U. L. Osterberg, "Hemoglobin imaging of breast tumors with near-infrared tomography," Radiology 214, (in press).
  6. S. R. Arridge,"Optical Tomography in medical imaging," Inverse Problems 15, R41-R93 (1999).
    [CrossRef]
  7. J. C. Hebden, E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy and S. R. Arridge,"Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data," Opt. Lett. 24, 334-336 (1999).
    [CrossRef]
  8. M. Schweiger and S. R. Arridge,"Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys Med Biol 44, 2703-21 (1999).
    [CrossRef] [PubMed]
  9. V. Kolehmainen, M. Vauhkonen, J. P. Kaipio and S. R. Arridge,"Recovery of Piecewise constant coefficients in optical diffusion tomography," Opt. Express 7, 468-480 (2000).
    [CrossRef] [PubMed]
  10. M. A. O'Leary, D. A. Boas, B. Chance and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography," Opt. Lett. 20, 426-428 (1995).
    [CrossRef]
  11. S. R. Arridge, M. Schweiger, M. Hiraoka and D. T. Delpy, "Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging," in Photon Migration and Imaging in Random Media and Tissues, B. Chance and R. R. Alfano, SPIE 1888, 360-371 (1993).
  12. M. Schweiger, S. R. Arridge and D. T. Delpy,"Application of the finite-element method for the forward and inverse models in optical tomography," J. Mathematical Imaging and Vision 3, 263-283 (1993).
    [CrossRef]
  13. S. R. Arridge and M. Schweiger, "Inverse Methods for Optical Tomography," in Information Processing in Medical Imaging (IPMI'93 Proceedings), Lecture Notes in Computer Science, (Springer-Verlag, 1993).
  14. 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]
  15. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego 1978).
  16. M. S. Patterson, B. Chance and B. C. Wilson, "Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
    [CrossRef] [PubMed]
  17. R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams and B. J. Tromberg,"Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
    [CrossRef]
  18. K. Furutsu and Y. Yamada, "Diffusion approximation for a dissipative random medium and the applications," Phys. Rev. E 50, 3634 (1994).
    [CrossRef]
  19. T. Durduran, B. Chance, A. G. Yodh and D. A. Boas, "Does the photon diffusion coefficient depend on absorption?," J. Opt. Soc. Am. A 14, 3358-3365 (1997).
    [CrossRef]
  20. D. J. Durian, "The diffusion coefficient depends on absorption," Opt. Lett. 23, 1502-1504 (1998).
    [CrossRef]
  21. R. Aronson and N. Corngold, "Photon diffusion coefficient in an absorbing medium," J. Opt. Soc. Am. A 16, 1066-1071 (1999).
    [CrossRef]
  22. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York 1988).
  23. S. R. Arridge, M. Cope and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-60 (1992).
    [CrossRef] [PubMed]
  24. H. Dehghani, D. C. Barber and I. Basarab-Horwath, "Incorporating a priori anatomical information into image reconstruction in electrical impedance tomography," Physiol. Meas. 20, 87-102 (1999).
    [CrossRef] [PubMed]
  25. V. Kolehmainen, M. Vauhkonen, P. A. Karjalainen and J. P. Kaipio,"Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns," Physiol Meas 18, 289-303 (1997).
    [CrossRef] [PubMed]

Other (25)

S. B. Colak, M. B. van der Mark, G. W. Hooft, J. H. Hoogenraad, E. S. van der Linden and F. A. Kuijpers,"Clinical Optical Tomography and NIR Spectroscopy for Breast Cancer Detection," IEEE Journal of Selected Topics in Quantum Electronics 5, 1143-1158 (1999).
[CrossRef]

S. Fantini, M. A. Franceschini, E. Gratton, D. Hueber, W. Rosenfeld, D. Maulik, P. G. Stubblefield and M. R. Stankoivic,"Non-invasive optical imaging of the piglet brain in real time," Opt. Express 4, 308-314 (1999).
[CrossRef] [PubMed]

V. Ntziachristos, A. G. Yodh, M. Schnall and B. Chance,"Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc Natl Acad Sci U S A 97, 2767-72 (2000).
[CrossRef] [PubMed]

M. A. Franceschini, V. Toronov, M. Filiaci, E. Gratton and S. Fanini,"On-line optical imaging of the human brain with 160-ms temporal resolution," Opt. Express 6, 49-57 (2000).
[CrossRef] [PubMed]

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman and U. L. Osterberg, "Hemoglobin imaging of breast tumors with near-infrared tomography," Radiology 214, (in press).

S. R. Arridge,"Optical Tomography in medical imaging," Inverse Problems 15, R41-R93 (1999).
[CrossRef]

J. C. Hebden, E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy and S. R. Arridge,"Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data," Opt. Lett. 24, 334-336 (1999).
[CrossRef]

M. Schweiger and S. R. Arridge,"Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys Med Biol 44, 2703-21 (1999).
[CrossRef] [PubMed]

V. Kolehmainen, M. Vauhkonen, J. P. Kaipio and S. R. Arridge,"Recovery of Piecewise constant coefficients in optical diffusion tomography," Opt. Express 7, 468-480 (2000).
[CrossRef] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance and A. G. Yodh, "Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography," Opt. Lett. 20, 426-428 (1995).
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka and D. T. Delpy, "Performance of an iterative reconstruction algorithm for near infrared absorption and scatter imaging," in Photon Migration and Imaging in Random Media and Tissues, B. Chance and R. R. Alfano, SPIE 1888, 360-371 (1993).

M. Schweiger, S. R. Arridge and D. T. Delpy,"Application of the finite-element method for the forward and inverse models in optical tomography," J. Mathematical Imaging and Vision 3, 263-283 (1993).
[CrossRef]

S. R. Arridge and M. Schweiger, "Inverse Methods for Optical Tomography," in Information Processing in Medical Imaging (IPMI'93 Proceedings), Lecture Notes in Computer Science, (Springer-Verlag, 1993).

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]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego 1978).

M. S. Patterson, B. Chance and B. C. Wilson, "Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef] [PubMed]

R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams and B. J. Tromberg,"Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 11, 2727-2741 (1994).
[CrossRef]

K. Furutsu and Y. Yamada, "Diffusion approximation for a dissipative random medium and the applications," Phys. Rev. E 50, 3634 (1994).
[CrossRef]

T. Durduran, B. Chance, A. G. Yodh and D. A. Boas, "Does the photon diffusion coefficient depend on absorption?," J. Opt. Soc. Am. A 14, 3358-3365 (1997).
[CrossRef]

D. J. Durian, "The diffusion coefficient depends on absorption," Opt. Lett. 23, 1502-1504 (1998).
[CrossRef]

R. Aronson and N. Corngold, "Photon diffusion coefficient in an absorbing medium," J. Opt. Soc. Am. A 16, 1066-1071 (1999).
[CrossRef]

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York 1988).

S. R. Arridge, M. Cope and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-60 (1992).
[CrossRef] [PubMed]

H. Dehghani, D. C. Barber and I. Basarab-Horwath, "Incorporating a priori anatomical information into image reconstruction in electrical impedance tomography," Physiol. Meas. 20, 87-102 (1999).
[CrossRef] [PubMed]

V. Kolehmainen, M. Vauhkonen, P. A. Karjalainen and J. P. Kaipio,"Assessment of errors in static electrical impedance tomography with adjacent and trigonometric current patterns," Physiol Meas 18, 289-303 (1997).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1.
Fig. 1.

Illustration of experimental geometry with the absorbing object.

Fig. 2.
Fig. 2.

Absorption image reconstructions from simulated data with uncertainty in the source and detector strengths of 0%, 40%, and 80% in a/d, b/e, and c/f respectively. The images span X and Y from -3 to 3 cm and Z-slices are indicated from 0.5 to 5.5 cm. Reconstructions without consideration for the uncertainty in the optode coupling strengths are shown in a-c. d-f show the results when simultaneously reconstructing the optode strengths.

Equations (10)

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

· ( D ( r ) Φ ( r , t ) ) + v μ a ( r ) Φ ( r , t ) + Φ ( r , t ) t = vS ( r , t ) .
Φ = Φ ο + Φ pert
Φ = Φ o exp ( Φ pert ) .
Φ pert ( r s , r d ) = 1 Φ o ( r s , r d ) Φ o ( r s , r ) v δ μ a ( r ) D o G ( r , r d ) d r .
Φ o ( r s , r d ) = sd G ( r s , r d ) .
F ( x ) = i = 1 N meas [ ln Φ Theory, i ( x ) ln Φ Meas, i ] 2
x ̂ = A T ( AA T + λI ) 1 y ,
y i = ln [ Φ ( r s , i , r d , i ) Φ o ( r s , i , r d , i ) ] = ln [ s k ( i ) ] + ln [ d l ( i ) ] + j A i , j δμ a , j .
ξ = [ δμ a , 1 μ ao δμ a , N v μ ao ln s 1 ln s N s ln d 1 ln d N d ] .
[ S D ] = [ 1 0 1 0 1 0 0 1 0 1 1 0 0 1 0 1 ] .

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