Abstract

Light propagation in highly scattering media as a result of the injection of short laser pulses is described by the diffusion model, with absorption and scattering being considered as parameter functions. Different boundary conditions are discussed. The resulting parabolic differential equation with boundary conditions of the third kind has been integrated by the finite-element method, which allows different geometries and various embedded objects to be taken into account. For image reconstruction we introduce an iterative method based on the finite-element method forward model and on an optimization strategy that uses the full information contained in the time-resolved measurements. The algorithm includes a regularization strategy so that it is specifically fit for solving the ill-posed problem. Furthermore, it is shown that considerable improvements in reconstruction results can be achieved by adaptation of the detector–source arrangement.

© 1997 Optical Society of America

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  1. B. W. Pogue, M. S. Patterson, and T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 328–339 (1995).
    [CrossRef]
  2. R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
    [CrossRef]
  3. R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
    [CrossRef]
  4. R. Model and R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).
  5. M. Orlt, M. Walzel, and R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 346–357 (1995).
    [CrossRef]
  6. 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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
    [CrossRef]
  7. S. R. Arridge and M. Schweiger, “Sensitivity to prior knowledge in optical tomographic reconstruction,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 378–388 (1995).
    [CrossRef]
  8. S. C. Feng and F.-A. Zeng, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 54–63 (1995).
    [CrossRef]
  9. Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
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  15. M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
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  16. F. Liu, K. M. Yoo, and R. R. Alfano, “How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 103–106 (1993).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 297–305 (1993).
    [CrossRef]
  20. A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
    [CrossRef] [PubMed]
  21. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
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1996 (1)

R. Model and R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

1995 (10)

M. Orlt, M. Walzel, and R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 346–357 (1995).
[CrossRef]

B. W. Pogue, M. S. Patterson, and T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 328–339 (1995).
[CrossRef]

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
[CrossRef]

S. R. Arridge and M. Schweiger, “Sensitivity to prior knowledge in optical tomographic reconstruction,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 378–388 (1995).
[CrossRef]

S. C. Feng and F.-A. Zeng, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 54–63 (1995).
[CrossRef]

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

R. Model and R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 56–65 (1995).
[CrossRef]

A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

1993 (4)

R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 297–305 (1993).
[CrossRef]

F. Liu, K. M. Yoo, and R. R. Alfano, “How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 103–106 (1993).
[CrossRef]

L. O. Svaasand, R. C. Haskell, B. J. Tromberg, and M. McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 214–226 (1993).
[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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

1992 (1)

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

1989 (2)

W. M. Star, “Comparing the P3 approximation with the diffusion theory and with Monte Carlo calculations of light propagation in a slab geometry,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller and D. Sliney, eds., Proc. SPIE 1035, 146–154 (1989).

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

Alfano, R. R.

F. Liu, K. M. Yoo, and R. R. Alfano, “How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 103–106 (1993).
[CrossRef]

Aronson, R.

R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 297–305 (1993).
[CrossRef]

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Arridge, S. R.

S. R. Arridge and M. Schweiger, “Sensitivity to prior knowledge in optical tomographic reconstruction,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 378–388 (1995).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

Barbour, R. L.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Boas, D. A.

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

Chance, B.

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

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

Chang, J.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

Farrell, T. J.

B. W. Pogue, M. S. Patterson, and T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 328–339 (1995).
[CrossRef]

Feng, S. C.

S. C. Feng and F.-A. Zeng, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 54–63 (1995).
[CrossRef]

Graber, H. L.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Haskell, R. C.

L. O. Svaasand, R. C. Haskell, B. J. Tromberg, and M. McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 214–226 (1993).
[CrossRef]

Hielscher, A. H.

A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

Hünlich, R.

R. Model and R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
[CrossRef]

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

R. Model and R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 56–65 (1995).
[CrossRef]

Jacques, S. L.

A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Liu, F.

F. Liu, K. M. Yoo, and R. R. Alfano, “How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 103–106 (1993).
[CrossRef]

Liu, H.

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

Lubowski, J.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

McAdams, M.

L. O. Svaasand, R. C. Haskell, B. J. Tromberg, and M. McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 214–226 (1993).
[CrossRef]

Model, R.

R. Model and R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
[CrossRef]

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

M. Orlt, M. Walzel, and R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 346–357 (1995).
[CrossRef]

R. Model and R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 56–65 (1995).
[CrossRef]

O’Leary, M. A.

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

Orlt, M.

R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
[CrossRef]

M. Orlt, M. Walzel, and R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 346–357 (1995).
[CrossRef]

Patterson, M. S.

B. W. Pogue, M. S. Patterson, and T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 328–339 (1995).
[CrossRef]

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

Pogue, B. W.

B. W. Pogue, M. S. Patterson, and T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 328–339 (1995).
[CrossRef]

Richter, D.

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

Rinneberg, H.

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

Schweiger, M.

S. R. Arridge and M. Schweiger, “Sensitivity to prior knowledge in optical tomographic reconstruction,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 378–388 (1995).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

Star, W. M.

W. M. Star, “Comparing the P3 approximation with the diffusion theory and with Monte Carlo calculations of light propagation in a slab geometry,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller and D. Sliney, eds., Proc. SPIE 1035, 146–154 (1989).

Svaasand, L. O.

L. O. Svaasand, R. C. Haskell, B. J. Tromberg, and M. McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 214–226 (1993).
[CrossRef]

Tittel, F. K.

A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Tromberg, B. J.

L. O. Svaasand, R. C. Haskell, B. J. Tromberg, and M. McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 214–226 (1993).
[CrossRef]

Wabnitz, H.

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

Walzel, M.

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

M. Orlt, M. Walzel, and R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 346–357 (1995).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
[CrossRef]

Wang, L.

A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Wilson, B. C.

Yodh, A. G.

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

Yoo, K. M.

F. Liu, K. M. Yoo, and R. R. Alfano, “How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 103–106 (1993).
[CrossRef]

Zeng, F.-A.

S. C. Feng and F.-A. Zeng, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 54–63 (1995).
[CrossRef]

Appl. Opt. (1)

Med. Phys. (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light scattering media: boundary and source condition,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

A. H. Hielscher, S. L. Jacques, L. Wang, and F. K. Tittel, “The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissue,” Phys. Med. Biol. 40, 1957–1975 (1995).
[CrossRef] [PubMed]

Proc. SPIE (14)

D. A. Boas, H. Liu, M. A. O’Leary, B. Chance, and A. G. Yodh, “Photon migration within the P3 approximation,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 240–247 (1995).
[CrossRef]

W. M. Star, “Comparing the P3 approximation with the diffusion theory and with Monte Carlo calculations of light propagation in a slab geometry,” in Dosimetry of Laser Radiation in Medicine and Biology, G. Mueller and D. Sliney, eds., Proc. SPIE 1035, 146–154 (1989).

F. Liu, K. M. Yoo, and R. R. Alfano, “How to describe the scattered ultrashort laser pulse profiles measured inside and at the surface of a random medium using the diffusion theory,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 103–106 (1993).
[CrossRef]

L. O. Svaasand, R. C. Haskell, B. J. Tromberg, and M. McAdams, “Properties of photon density waves at boundaries,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 214–226 (1993).
[CrossRef]

R. Model and R. Hünlich, “Parameter sensitivity in near infrared imaging,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 56–65 (1995).
[CrossRef]

R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 297–305 (1993).
[CrossRef]

B. W. Pogue, M. S. Patterson, and T. J. Farrell, “Forward and inverse calculations for 3-D frequency-domain diffuse optical tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 328–339 (1995).
[CrossRef]

R. Model, R. Hünlich, D. Richter, H. Rinneberg, H. Wabnitz, and M. Walzel, “Imaging in random media: simulating light transport by numerical integration of the diffusion equation,” in Photon Transport in Highly Scattering Tissue, S. Avrillier, B. Chance, G. Mueller, A. Priezzhev, and V. Tuchin, eds., Proc. SPIE 2326, 11–22 (1995).
[CrossRef]

R. Model, R. Hünlich, M. Orlt, and M. Walzel, “Image reconstruction for random media by diffusion tomography,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 400–410 (1995).
[CrossRef]

M. Orlt, M. Walzel, and R. Model, “Transillumination imaging performance using time domain data,” in Photon Propagation in Tissues, B. Chance, D. Delpy, and G. Mueller, eds., Proc. SPIE 2626, 346–357 (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, R. Alfano and B. Chance, eds., Proc. SPIE 1888, 360–371 (1993).
[CrossRef]

S. R. Arridge and M. Schweiger, “Sensitivity to prior knowledge in optical tomographic reconstruction,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 378–388 (1995).
[CrossRef]

S. C. Feng and F.-A. Zeng, “Analytical perturbation theory of photon migration in the presence of a single absorbing or scattering defect sphere,” in Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance and R. Alfano, eds., Proc. SPIE 2389, 54–63 (1995).
[CrossRef]

Y. Wang, J. Chang, R. Aronson, R. L. Barbour, H. L. Graber, and J. Lubowski, “Imaging of scattering media by diffusion tomography: an iterative perturbation approach,” in Physiological Monitoring and Early Detection Diagnostic Methods, T. Mang, ed., Proc. SPIE 1641, 58–71 (1992).
[CrossRef]

Z. Angew. Math. Mech. (1)

R. Model and R. Hünlich, “Optical imaging of highly scattering media,” Z. Angew. Math. Mech. 76, 483–484 (1996).

Other (4)

C. W. Groetsch, Inverse Problems in the Mathematical Science (Braunschweig, Wiesbaden, Germany, 1993).

A. Ishimaru, Wave Propagation in Random Scattering Media (Academic, New York, 1978).

J.-M. Kaltenbach and M. Kaschke, “Frequency- and time-domain modelling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, in Vol. IS11 of Institute Series of SPIE Optical Engineering, G. Mueller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 61–82.

J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstraint Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, N.J., 1983).

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Figures (10)

Fig. 1
Fig. 1

Initial triangle FEM grid.

Fig. 2
Fig. 2

Isolines of the photon density (DENS) under different boundary conditions.

Fig. 3
Fig. 3

(a) Photon flux in detector position opposite the source, (b) photon flux in detector position on the same side as the source.

Fig. 4
Fig. 4

Test object with three absorbers and reconstruction results for different detector arrangements.

Fig. 5
Fig. 5

Top left: object with three absorbers, top right: reconstruction results without regularization, bottom left: with regularization βa=10-6, bottom right: βa=10-7.

Fig. 6
Fig. 6

Surface plot of the absorption coefficient for a test object. Absorbers have a 1.25-fold absorption.

Fig. 7
Fig. 7

Surface plot of the absorption coefficient for the reconstructed object with three absorbers with a 1.25-fold absorption.

Fig. 8
Fig. 8

Top: object with two scatterers, middle: reconstruction result without regularization, bottom: result with regularization.

Fig. 9
Fig. 9

Left: object with one (fourfold) absorber and a smaller (threefold) scatterer, middle: reconstructed absorption, right: reconstructed reduced scattering.

Fig. 10
Fig. 10

Left: object with one (fourfold) absorber and one (threefold) scatterer of the same size, middle: reconstructed absorption, right: reconstructed reduced scattering.

Equations (12)

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tΦ(x, t)=div[D grad Φ(x, t)]-cμa(x)Φ(x, t)+s(x, t)xΩ,0tT.
D=c3[μa(x)+μs(x)],
J(x, t)=-D(x)Φn(x, t)Ω
-D(x)Φn(x, t)=chΦ(x, t)(x, t)Ω×(0, T).
1.Choose an initial approximationμaand/orμs2.Solve the forward problem,i.e.,computeJsim(μa,μs)3.CompareJsim(μa, μs) with Jmes; ifJsim(μa,μs)Jsim <, then go to step 5.4.Correct μa and/or μs; go to step 2.5.End.
Jsim(μa, μs)-Jmes2=i=1lj=1mik=1nij|Jisim(xij, tijk, μaμs)-Jimes(xij, tijk)|2=i=1pFi2p=i=1lj=1minij.
E(μa, μs)=Jsim(μ)-Jmes2+βaμa2+βsμs2=i=1p+2Fi2=min!,
μa2=Ωμa2dx=j=1naμaj2Aj,Fp+12=βaμa2,
μs2=Ωμs2dx=j=1nsμsj2Sj,Fp+22=βsμs2,
βaμa2Jsim(μ)-Jmes2,
βsμs2Jsim(μ)-Jmes2.
μk+1=μk-{[(F)TF](μk)+λkI}-1[(F)TF](μk).

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