Abstract

A Monte Carlo procedure has been developed to study photon migration through highly scattering nonhomogeneous media. When two scaling relationships are used, the temporal response when scattering or absorbing inhomogeneities are introduced can be evaluated in a short time from the results of only one simulation carried out for the homogeneous medium. Examples of applications to the imaging of defects embedded into a diffusing slab, a model usually used for optical mammography, are given. Comparisons with experimental results show the correctness of the results obtained.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  36. G. Zaccanti, J. Hebden, A. Sassaroli, C. Blumetti, M. Bassani, A. Ismaelli, “Imaging of scattering inhomogeneities within highly diffusing media,” in Photon Migration in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 462–470 (1997).
    [CrossRef]

1998 (1)

1997 (5)

F. Martelli, D. Contini, A. Taddeucci, G. Zaccanti, “Photon migration through a turbid slab described by a model based on the diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[CrossRef] [PubMed]

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–367 (1997).
[CrossRef] [PubMed]

D. Contini, F. Martelli, G. Zaccanti, “Photon migration through a turbid slab described by a model based on the diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[CrossRef] [PubMed]

D. J. Hall, J. Hebden, D. T. Delpy, “Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method,” Appl. Opt. 36, 7270–7276 (1997).
[CrossRef]

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

1996 (3)

1995 (5)

1994 (3)

1993 (6)

1992 (2)

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

J. C. Hebden, “Evaluating the spatial resolution performance of a time-resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

1991 (1)

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

1989 (1)

1987 (1)

1985 (1)

Aarnoudse, J. G.

Alcuffe, R. E.

A. H. Hielscher, R. E. Alcuffe, R. L. Barbour, “Transport and diffusion calculations on MRI-generated data,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 500–508 (1997).
[CrossRef]

Andersson-Engels, S.

Arridge, S. R.

Barbour, R. L.

A. H. Hielscher, R. E. Alcuffe, R. L. Barbour, “Transport and diffusion calculations on MRI-generated data,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 500–508 (1997).
[CrossRef]

Bassani, M.

G. Zaccanti, A. Sassaroli, D. Contini, F. Martelli, M. Bassani, C. Blumetti, A. Ismaelli, “Imaging of absorbing inhomogeneities within highly diffusing media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 724–732 (1997).
[CrossRef]

G. Zaccanti, J. Hebden, A. Sassaroli, C. Blumetti, M. Bassani, A. Ismaelli, “Imaging of scattering inhomogeneities within highly diffusing media,” in Photon Migration in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 462–470 (1997).
[CrossRef]

Battistelli, E.

G. Zaccanti, E. Battistelli, P. Bruscaglioni, Q. N. Wei, “Analytic relationships for the statistical moments of scattering point coordinates for photon migration in a scattering medium,” Pure Appl. Opt. 3, 897–905 (1994).
[CrossRef]

E. Battistelli, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Use of two scaling relations in the study of multiple scattering effects on the transmittance of light beams through a turbid atmosphere,” J. Opt. Soc. Am. A 2, 903–912 (1985).
[CrossRef]

Blumetti, C.

G. Zaccanti, J. Hebden, A. Sassaroli, C. Blumetti, M. Bassani, A. Ismaelli, “Imaging of scattering inhomogeneities within highly diffusing media,” in Photon Migration in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 462–470 (1997).
[CrossRef]

G. Zaccanti, A. Sassaroli, D. Contini, F. Martelli, M. Bassani, C. Blumetti, A. Ismaelli, “Imaging of absorbing inhomogeneities within highly diffusing media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 724–732 (1997).
[CrossRef]

Bonner, F. F.

A. H. Gandjbakhche, G. H. Weiss, F. F. Bonner, R. Nossal, “Random walk and diffusion-like models of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1995), pp. 333–401.
[CrossRef]

Bonner, R. F.

Bruscaglioni, P.

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

G. Zaccanti, E. Battistelli, P. Bruscaglioni, Q. N. Wei, “Analytic relationships for the statistical moments of scattering point coordinates for photon migration in a scattering medium,” Pure Appl. Opt. 3, 897–905 (1994).
[CrossRef]

E. Battistelli, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Use of two scaling relations in the study of multiple scattering effects on the transmittance of light beams through a turbid atmosphere,” J. Opt. Soc. Am. A 2, 903–912 (1985).
[CrossRef]

Chance, B.

Contini, D.

Cope, M.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Cubeddu, R.

Dassel, A. C. M.

Davies, E. R.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

de Mul, F. F. M.

Delpy, D. T.

D. J. Hall, J. Hebden, D. T. Delpy, “Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method,” Appl. Opt. 36, 7270–7276 (1997).
[CrossRef]

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–367 (1997).
[CrossRef] [PubMed]

J. C. Hebden, D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311–313 (1994).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

den Outer, P. N.

Fantini, S.

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

Feng, S.

Franceschini, M. A.

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

Gaida, G.

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

Gandjbakhche, A. H.

A. H. Gandjbakhche, G. H. Weiss, F. F. Bonner, R. Nossal, “Random walk and diffusion-like models of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1995), pp. 333–401.
[CrossRef]

Graaff, R.

Gratton, E.

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

Hall, D. J.

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–367 (1997).
[CrossRef] [PubMed]

D. J. Hall, J. Hebden, D. T. Delpy, “Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method,” Appl. Opt. 36, 7270–7276 (1997).
[CrossRef]

Hasegawa, Y.

Y. Yamada, Y. Hasegawa, Y. Yamashita, “Simulation of fan-beam-type optical computed-tomography imaging of strongly scattering and weakly absorbing media,” Appl. Opt. 32, 4808–4814 (1993).
[CrossRef] [PubMed]

Y. Yamada, Y. Hasegawa, “Time-dependent FEM analysis of photon migration in random media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. Alfano, eds., Proc. SPIE1888, 167–178 (1993).
[CrossRef]

Haselgrove, J. C.

Havlin, S.

Hebden, J.

D. J. Hall, J. Hebden, D. T. Delpy, “Imaging very-low-contrast objects in breastlike scattering media with a time-resolved method,” Appl. Opt. 36, 7270–7276 (1997).
[CrossRef]

G. Zaccanti, J. Hebden, A. Sassaroli, C. Blumetti, M. Bassani, A. Ismaelli, “Imaging of scattering inhomogeneities within highly diffusing media,” in Photon Migration in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 462–470 (1997).
[CrossRef]

Hebden, J. C.

D. J. Hall, J. C. Hebden, D. T. Delpy, “Evaluation of spatial resolution as a function of thickness for time-resolved optical imaging of highly scattering media,” Med. Phys. 24, 361–367 (1997).
[CrossRef] [PubMed]

J. C. Hebden, “Imaging through scattering media using characteristics of the temporal distribution of transmitted laser pulses,” Opt. Laser Technol. 27, 263–268 (1995).
[CrossRef]

J. C. Hebden, D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311–313 (1994).
[CrossRef] [PubMed]

J. C. Hebden, “Evaluating the spatial resolution performance of a time-resolved optical imaging system,” Med. Phys. 19, 1081–1087 (1992).
[CrossRef] [PubMed]

Hibst, R.

A. Kienle, R. Hibst, R. Steiner, “The use of a neural network and Monte Carlo simulations to determine the optical coefficients with spatially resolved transmittance measurements,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134, 364–371 (1994).

Hielscher, A. H.

A. H. Hielscher, R. E. Alcuffe, R. L. Barbour, “Transport and diffusion calculations on MRI-generated data,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 500–508 (1997).
[CrossRef]

Ismaelli, A.

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

E. Battistelli, P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Use of two scaling relations in the study of multiple scattering effects on the transmittance of light beams through a turbid atmosphere,” J. Opt. Soc. Am. A 2, 903–912 (1985).
[CrossRef]

G. Zaccanti, J. Hebden, A. Sassaroli, C. Blumetti, M. Bassani, A. Ismaelli, “Imaging of scattering inhomogeneities within highly diffusing media,” in Photon Migration in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 462–470 (1997).
[CrossRef]

G. Zaccanti, A. Sassaroli, D. Contini, F. Martelli, M. Bassani, C. Blumetti, A. Ismaelli, “Imaging of absorbing inhomogeneities within highly diffusing media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 724–732 (1997).
[CrossRef]

Jackson, P. C.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Jacques, S. L.

L. Wang, S. L. Jacques, “Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10, 1746–1752 (1993).
[CrossRef]

M. R. Ostermeyer, S. L. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE.2389, 98–102 (1995).
[CrossRef]

Jess, H.

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

Kaschke, M.

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

Key, H.

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

Kiefer, J. E.

Kienle, A.

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

A. Kienle, R. Hibst, R. Steiner, “The use of a neural network and Monte Carlo simulations to determine the optical coefficients with spatially resolved transmittance measurements,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134, 364–371 (1994).

Koelink, M. H.

Kolzer, J.

Lagendijk, Ad.

Leigh, J. S.

Liszka, H.

Mantulin, W. W.

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

Martelli, F.

D. Contini, F. Martelli, G. Zaccanti, “Photon migration through a turbid slab described by a model based on the diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[CrossRef] [PubMed]

F. Martelli, D. Contini, A. Taddeucci, G. Zaccanti, “Photon migration through a turbid slab described by a model based on the diffusion approximation. II. Comparison with Monte Carlo results,” Appl. Opt. 36, 4600–4612 (1997).
[CrossRef] [PubMed]

G. Zaccanti, A. Sassaroli, D. Contini, F. Martelli, M. Bassani, C. Blumetti, A. Ismaelli, “Imaging of absorbing inhomogeneities within highly diffusing media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 724–732 (1997).
[CrossRef]

Mitic, G.

Moesta, K. T.

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

Nieuwenhuizen, Th. M.

Nossal, R.

Ostermeyer, M. R.

M. R. Ostermeyer, S. L. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE.2389, 98–102 (1995).
[CrossRef]

Otto, J.

Patterson, M. S.

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M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: Initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
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Y. Yamada, Y. Hasegawa, “Time-dependent FEM analysis of photon migration in random media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. Alfano, eds., Proc. SPIE1888, 167–178 (1993).
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Zeng, F.-A.

Zijlstra, W. G.

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Appl. Opt. (15)

M. S. Patterson, B. Chance, 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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D. Contini, F. Martelli, G. Zaccanti, “Photon migration through a turbid slab described by a model based on the diffusion approximation. I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
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S. Havlin, J. E. Kiefer, B. Trus, G. H. Weiss, R. Nossal, “Numerical method for studying the detectability of inclusions hidden in optically turbid tissue,” Appl. Opt. 32, 617–627 (1993).
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S. R. Arridge, M. Schweiger, “Photon-measurement density functions. Part 2: Finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
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R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, G. Valentini, “Time-resolved imaging on a realistic tissue phantom: μs′ and μa images versus time-integrated images,” Appl. Opt. 35, 4533–4540 (1996).

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Appl. Phys. B (1)

P. Bruscaglioni, A. Ismaelli, G. Zaccanti, “Monte-Carlo calculations of LIDAR returns: procedure and results,” Appl. Phys. B 60, 325–329 (1995).
[CrossRef]

J. Opt. Soc. Am. A (4)

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Opt. Laser Technol. (1)

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Phys. Med. Biol. (3)

H. Key, E. R. Davies, P. C. Jackson, P. N. T. Wells, “Monte Carlo modeling of light propagation in breast tissue,” Phys. Med. Biol. 36, 591–602 (1991).
[CrossRef] [PubMed]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
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Proc. Natl. Acad. Sci. USA (1)

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G. Zaccanti, E. Battistelli, P. Bruscaglioni, Q. N. Wei, “Analytic relationships for the statistical moments of scattering point coordinates for photon migration in a scattering medium,” Pure Appl. Opt. 3, 897–905 (1994).
[CrossRef]

Other (7)

G. Zaccanti, A. Sassaroli, D. Contini, F. Martelli, M. Bassani, C. Blumetti, A. Ismaelli, “Imaging of absorbing inhomogeneities within highly diffusing media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 724–732 (1997).
[CrossRef]

G. Zaccanti, J. Hebden, A. Sassaroli, C. Blumetti, M. Bassani, A. Ismaelli, “Imaging of scattering inhomogeneities within highly diffusing media,” in Photon Migration in Tissues III, D. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 462–470 (1997).
[CrossRef]

A. H. Gandjbakhche, G. H. Weiss, F. F. Bonner, R. Nossal, “Random walk and diffusion-like models of photon migration in turbid media,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1995), pp. 333–401.
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M. R. Ostermeyer, S. L. Jacques, “Perturbation theory for optical diffusion theory: a general approach for absorbing and scattering objects in tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media, Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE.2389, 98–102 (1995).
[CrossRef]

A. Kienle, R. Hibst, R. Steiner, “The use of a neural network and Monte Carlo simulations to determine the optical coefficients with spatially resolved transmittance measurements,” in Laser–Tissue Interaction V, S. L. Jacques, ed., Proc. SPIE2134, 364–371 (1994).

A. H. Hielscher, R. E. Alcuffe, R. L. Barbour, “Transport and diffusion calculations on MRI-generated data,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE.2979, 500–508 (1997).
[CrossRef]

Y. Yamada, Y. Hasegawa, “Time-dependent FEM analysis of photon migration in random media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. Alfano, eds., Proc. SPIE1888, 167–178 (1993).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Geometric scheme assumed for numerical simulations.

Fig. 2
Fig. 2

Probability that received photons have to pass through different regions of the slab: numerical (top row) and experimental (bottom row) results. Left column, infinitely extended homogeneous slab; middle column, a totally absorbing plane boundary 8 mm from the light beam; right column, a totally absorbing spherical inhomogeneity with radius r = 4 mm at x = -10 and z = 20 mm. The slab is 40 mm thick with μ ao = 0.0003 mm-1 and μ so ′ = 0.5 mm-1.

Fig. 3
Fig. 3

Effect of a plane absorbing boundary: The values of the three parameters that best fit the temporal response are shown versus the distance of the light beam from the boundary. The results are given for μ so ′ = 0.5 and 1 mm-1 for a slab 40 mm thick with μ ao = 0.

Fig. 4
Fig. 4

Examples of the ERF: numerical and experimental results. The different curves refer to MC results and show the energy received within different gating times: 70, 100, 200, 500, 1000 ps and cw attenuation (upper to lower curve). The symbols with the error marks refer to cw experimental results. Data refer to s = 40 mm, μ so ′ = 0.5 mm, and μ ao = 0.0003 mm-1. The opaque surface was in the center of the slab.

Fig. 5
Fig. 5

Images of two totally absorbing spheres: comparison among experimental (first row) and numerical (second row) results. The images have been generated by the cw attenuation (left panel) and the mean path length (right panel). The sphere on the right is in the center of the slab; the other is at z = 10 mm. s = 40 mm, μ so ′ = 1 mm-1, and μ ao = 0.0025 mm-1.

Fig. 6
Fig. 6

Images of two spheres (radius, r = 5 mm) in the center of a slab with s = 40 mm, μ so ′ = 0.5 mm-1, and μ ao = 0.005 mm-1. The sphere with its center at C 1 ≡ (-16, 0, and 20 mm) has μ si ′ = 0.4 mm-1 and μ ai = μ ao ; the one in C 2 ≡ (0, 0, and 20 mm) has μ si ′ = μ so ′ and μ ai = 0.01 mm-1. From left to right, the images have been obtained with the following: cw attenuation, mean path length, and phase delay for a modulation frequency of 100 MHz (top row); μ sf ′ and amplitude factor μ af obtained from the least-squares fit (middle row); and attenuation for three different gating times, 20, 100, and 400 ps (bottom row).

Fig. 7
Fig. 7

For the same conditions of Fig. 6: the parameters μ sf ′ and μ af for y = 0 are shown together with the standard deviation obtained from the fitting procedure.

Equations (3)

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

0 θ w   2 π p θ sin   θ d θ = w ,
w = exp - μ ai l i - μ ao l o ,
w = μ si μ so K i   exp - μ si - μ so l i ,

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