Abstract

Finite-difference time-domain (FDTD) analysis has been used to predict the time-resolved reflectance from multilayered slabs with a nonscattering layer. Light propagation across the nonscattering layer was calculated based on the light intensity characteristics along a ray in free space. Additional equivalent source functions due to light from scattering regions across the nonscattering region were introduced into the diffusion equation and an additional set of the diffusion equation was solved by FDTD analysis by employing new boundary conditions. The formulation was used to calculate time-resolved reflectances of three- and four-layered slabs containing a nonscattering layer. The received light intensity and the mean time of flight estimated from the time-resolved reflectance are in reasonable agreement with previously reported experimental data and Monte Carlo simulations.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Fabiani, D. D. Schmorrow, and G. Gratton, “Optical imaging of the intact human brain (guest editorial),” IEEE Eng. Med Biol. Mag. 26, 14–16 (2007).
    [CrossRef]
  2. A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997), Chap. 9.
  3. F. G. Gao, H. Z. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 779–791 (2002).
  4. R. D. Frostig, In Vivo Optical Imaging of Brain Function (CRC, 2002), Chap. 8.
  5. A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient based iterative image reconstruction schema for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
    [CrossRef]
  6. J. Selb, A. M. Dale, and D. A. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).
    [CrossRef]
  7. Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
    [CrossRef]
  8. A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
    [CrossRef]
  9. 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 (March, 1993).
    [CrossRef]
  10. T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21, 181–184 (2002).
    [CrossRef]
  11. S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
    [CrossRef]
  12. J. B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” J. Opt. Soc. Am. A 10, 127–140 (1993).
    [CrossRef]
  13. T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
    [CrossRef]
  14. M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
    [CrossRef]
  15. L. Dombrovsky, J. Randrianalisoa, and D. Baillis, “Modified two-flux approximation for identification of radiative properties of absorbing and scattering media from directional-hemispherical measurements,” J. Opt. Soc. Am. A 23, 91–98 (2006).
    [CrossRef]
  16. S. A. Prahl, M. J. C. van Gemert, and A. J. Welch, “Determining the optical properties of turbid mediaby using the adding—doubling method,” Appl. Opt. 32, 559–568 (1993).
    [CrossRef]
  17. W. A. Fiveland, “Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method,” J. Thermophys. 2, 309–316 (1988).
    [CrossRef]
  18. A. D. Klose and A. H. Hielscher, “Iterative reconstruction schema for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
    [CrossRef]
  19. Z. Guo and K. Kim, “Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates methods,” Appl. Opt. 42, 2897–2905 (2003).
    [CrossRef]
  20. S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
    [CrossRef]
  21. E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of adult head,” Appl. Opt. 36, 21–31 (1997).
    [CrossRef]
  22. T. Hayashi, Y. Kashio, and E. Okada, “Hybrid MonteCarlo-diffusion method for light propagation in tissue with a low-scattering region,” Appl. Opt. 42, 2888–2896 (2003).
    [CrossRef]
  23. T. Tanifuji, S. Tabata, K. Okimatsu, and N. Nishio, “Finite difference time domain and steady-state analysis with novel boundary conditions of optical pulse transport in a three-dimensional scattering medium illuminated by an isotropic point source,” Appl. Opt. 50, 1697–1706 (2011).
    [CrossRef]
  24. M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: Boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995).
    [CrossRef]
  25. T. Tanifuji, T. Ohtomo, D. Ohmori, and T. Ishikawa, “Time resolved reflectance of an optical pulse from scattering bodies with nonscattering regions utilizing the finite difference time domain analysis,” in Proceedings of 25th Annual International Conference of the IEEE EMBS (IEEE,2003), pp. 1094–1097.
  26. E. Okada and D. Delpy, “Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer,” Appl. Opt. 42, 2906–2914 (2003).
    [CrossRef]

2011 (2)

2008 (1)

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

2007 (2)

M. Fabiani, D. D. Schmorrow, and G. Gratton, “Optical imaging of the intact human brain (guest editorial),” IEEE Eng. Med Biol. Mag. 26, 14–16 (2007).
[CrossRef]

J. Selb, A. M. Dale, and D. A. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).
[CrossRef]

2006 (1)

2003 (3)

2002 (2)

F. G. Gao, H. Z. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 779–791 (2002).

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21, 181–184 (2002).
[CrossRef]

2000 (1)

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

1999 (2)

A. D. Klose and A. H. Hielscher, “Iterative reconstruction schema for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient based iterative image reconstruction schema for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

1997 (1)

1996 (1)

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
[CrossRef]

1995 (1)

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

1993 (3)

1992 (1)

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef]

1988 (1)

W. A. Fiveland, “Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method,” J. Thermophys. 2, 309–316 (1988).
[CrossRef]

Arridge, S. R.

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 (March, 1993).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
[CrossRef]

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

Baillis, D.

Bassi, A.

Boas, D. A.

Contini, D.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Cope, M.

Cova, S.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Cubeddu, R.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Dale, A. M.

Dehghani, H.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

Delpy, D.

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 (March, 1993).
[CrossRef]

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
[CrossRef]

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

Dombrovsky, L.

Fabiani, M.

M. Fabiani, D. D. Schmorrow, and G. Gratton, “Optical imaging of the intact human brain (guest editorial),” IEEE Eng. Med Biol. Mag. 26, 14–16 (2007).
[CrossRef]

Farrell, T. J.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef]

Firbank, M.

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
[CrossRef]

Fishkin, J. B.

Fiveland, W. A.

W. A. Fiveland, “Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method,” J. Thermophys. 2, 309–316 (1988).
[CrossRef]

Frostig, R. D.

R. D. Frostig, In Vivo Optical Imaging of Brain Function (CRC, 2002), Chap. 8.

Gao, F. G.

F. G. Gao, H. Z. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 779–791 (2002).

Gratton, E.

Gratton, G.

M. Fabiani, D. D. Schmorrow, and G. Gratton, “Optical imaging of the intact human brain (guest editorial),” IEEE Eng. Med Biol. Mag. 26, 14–16 (2007).
[CrossRef]

Guo, Z.

Hanson, K. M.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient based iterative image reconstruction schema for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

Hayashi, T.

Hielscher, A. H.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient based iterative image reconstruction schema for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction schema for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef]

Hijikata, M.

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21, 181–184 (2002).
[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 (March, 1993).
[CrossRef]

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

Ishikawa, T.

T. Tanifuji, T. Ohtomo, D. Ohmori, and T. Ishikawa, “Time resolved reflectance of an optical pulse from scattering bodies with nonscattering regions utilizing the finite difference time domain analysis,” in Proceedings of 25th Annual International Conference of the IEEE EMBS (IEEE,2003), pp. 1094–1097.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997), Chap. 9.

Jaywant, S. M.

S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
[CrossRef]

Kashio, Y.

Kim, K.

Klose, A. D.

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient based iterative image reconstruction schema for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction schema for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef]

Madsen, S. J.

S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
[CrossRef]

Martelli, F.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Mora, A. D.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Nishio, N.

Ohmori, D.

T. Tanifuji, T. Ohtomo, D. Ohmori, and T. Ishikawa, “Time resolved reflectance of an optical pulse from scattering bodies with nonscattering regions utilizing the finite difference time domain analysis,” in Proceedings of 25th Annual International Conference of the IEEE EMBS (IEEE,2003), pp. 1094–1097.

Ohtomo, T.

T. Tanifuji, T. Ohtomo, D. Ohmori, and T. Ishikawa, “Time resolved reflectance of an optical pulse from scattering bodies with nonscattering regions utilizing the finite difference time domain analysis,” in Proceedings of 25th Annual International Conference of the IEEE EMBS (IEEE,2003), pp. 1094–1097.

Okada, E.

Okimatsu, K.

Othonos, A.

S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
[CrossRef]

Patterson, M. S.

S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
[CrossRef]

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef]

Pifferi, A.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Prahl, S. A.

Randrianalisoa, J.

Schmorrow, D. D.

M. Fabiani, D. D. Schmorrow, and G. Gratton, “Optical imaging of the intact human brain (guest editorial),” IEEE Eng. Med Biol. Mag. 26, 14–16 (2007).
[CrossRef]

Schweiger, 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 (March, 1993).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

E. Okada, M. Firbank, M. Schweiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of adult head,” Appl. Opt. 36, 21–31 (1997).
[CrossRef]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
[CrossRef]

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

Selb, J.

Spinelli, L.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Tabata, S.

Tanifuji, T.

T. Tanifuji, S. Tabata, K. Okimatsu, and N. Nishio, “Finite difference time domain and steady-state analysis with novel boundary conditions of optical pulse transport in a three-dimensional scattering medium illuminated by an isotropic point source,” Appl. Opt. 50, 1697–1706 (2011).
[CrossRef]

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21, 181–184 (2002).
[CrossRef]

T. Tanifuji, T. Ohtomo, D. Ohmori, and T. Ishikawa, “Time resolved reflectance of an optical pulse from scattering bodies with nonscattering regions utilizing the finite difference time domain analysis,” in Proceedings of 25th Annual International Conference of the IEEE EMBS (IEEE,2003), pp. 1094–1097.

Torricelli, A.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Tosi, A.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Valentini, G.

van Gemert, M. J. C.

Welch, A. J.

Wilson, B.

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef]

Wilson, B. C.

S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
[CrossRef]

Yamada, Y.

F. G. Gao, H. Z. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 779–791 (2002).

Zaccanti, G.

Q. Zhao, L. Spinelli, A. Bassi, G. Valentini, D. Contini, A. Torricelli, R. Cubeddu, G. Zaccanti, F. Martelli, and A. Pifferi, “Functional tomography using time-gated ICCD Camera,” Biomed. Opt. Express 2, 705–716 (2011).
[CrossRef]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Zappa, F.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Zhao, H. Z.

F. G. Gao, H. Z. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 779–791 (2002).

Zhao, Q.

Appl. Opt. (1)

F. G. Gao, H. Z. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 779–791 (2002).

Appl. Opt. (6)

Biomed. Opt. Express (1)

IEEE Eng. Med Biol. Mag. (1)

M. Fabiani, D. D. Schmorrow, and G. Gratton, “Optical imaging of the intact human brain (guest editorial),” IEEE Eng. Med Biol. Mag. 26, 14–16 (2007).
[CrossRef]

IEEE Trans. Med. Imaging (2)

A. H. Hielscher, A. D. Klose, and K. M. Hanson, “Gradient based iterative image reconstruction schema for time-resolved optical tomography,” IEEE Trans. Med. Imaging 18, 262–271 (1999).
[CrossRef]

T. Tanifuji and M. Hijikata, “Finite difference time domain (FDTD) analysis of optical pulse responses in biological tissues for spectroscopic diffused optical tomography,” IEEE Trans. Med. Imaging 21, 181–184 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Thermophys. (1)

W. A. Fiveland, “Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method,” J. Thermophys. 2, 309–316 (1988).
[CrossRef]

Med. Phys. (5)

A. D. Klose and A. H. Hielscher, “Iterative reconstruction schema for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).
[CrossRef]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, “The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000).
[CrossRef]

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

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 (March, 1993).
[CrossRef]

T. J. Farrell, M. S. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef]

Opt. Express (1)

Phys. Med. Biol. (1)

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering body with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. D. Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100, 138101 (2008).
[CrossRef]

Proc. SPIE (1)

S. J. Madsen, M. S. Patterson, B. C. Wilson, S. M. Jaywant, and A. Othonos, “Numerical model and experimental studies of light propagation in inhomogeneous random media,” Proc. SPIE 1888, 90–102 (1993).
[CrossRef]

Other (3)

A. Ishimaru, Wave Propagation and Scattering in Random Media (IEEE, 1997), Chap. 9.

R. D. Frostig, In Vivo Optical Imaging of Brain Function (CRC, 2002), Chap. 8.

T. Tanifuji, T. Ohtomo, D. Ohmori, and T. Ishikawa, “Time resolved reflectance of an optical pulse from scattering bodies with nonscattering regions utilizing the finite difference time domain analysis,” in Proceedings of 25th Annual International Conference of the IEEE EMBS (IEEE,2003), pp. 1094–1097.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Position of field parameters in Yee grid.

Fig. 2.
Fig. 2.

Optical coupling between scattering regions through a nonscattering region. r s and r s is located at the interface between scattering and nonscattering region. A pencil beam is assumed as a source for illuminating the multilayered slab, which is approximated by a point source given by Eq. (5).

Fig. 3.
Fig. 3.

Irradiance at the clear layer interface r s , due to radiated photons at r b

Fig. 4.
Fig. 4.

Geometry and optical parameters of a three-layered slab with a clear layer.

Fig. 5.
Fig. 5.

Examples of steady-state reflectance.

Fig. 6.
Fig. 6.

Time-resolved reflectances as a function of time for a three-layered slab. The intensity is normalized by its maximum value.

Fig. 7.
Fig. 7.

Steady-state reflectance and mean delay dependences on d for three-layered slab with a 10 mm thick clear layer.

Fig. 8.
Fig. 8.

Steady-state reflectance and mean delay dependences on d for a three-layered slab with a 1 mm thick clear layer.

Fig. 9.
Fig. 9.

Geometry and optical parameters of a three-layered slab with a clear layer.

Fig. 10.
Fig. 10.

Diffuse-reflected optical pulses in a four-layered slab.

Fig. 11.
Fig. 11.

Steady-state reflectance and mean delay dependences on d for the four-layered slab shown in Fig. 9.

Fig. 12.
Fig. 12.

Steady-state reflectance and mean delay dependences on d for the four-layered slab shown in Fig. 9 for index matching ( n 1 = n 2 ) and mismatching ( n 1 n 2 ) at the clear layer boundary.

Equations (24)

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

( 1 c t + s ^ · + μ t ) I ( r , s ^ , t ) = μ t 4 π 4 π p ( s ^ , s ^ ) I ( r , s ^ , t ) d ω + ε ( r , s ^ , t ) .
I ( r , s ^ , t ) = ϕ ( r , t ) 4 π + 3 4 π J ( r , t ) s ^ .
1 c J ( r , t ) t + 1 3 ϕ ( r , t ) + μ tr J ( r , t ) = 4 π ε ( r , s ^ , t ) s ^ d ω ,
1 c ϕ ( r , t ) t + · J ( r , t ) + μ a ϕ ( r , t ) = 4 π ε ( r , s ^ , t ) d ω .
ε ( r , s ^ , t ) = 1 4 π μ s μ a + μ s f ( t z 0 c ) δ ( r r 0 ) , r 0 = ( x 0 , y 0 , z 0 ) ,
4 π ε ( r , s ^ , t ) d ω = μ s ' μ a + μ s ' f ( t z 0 c ) δ ( r r 0 ) ,
4 π ε ( r , s ^ , t ) ( s ^ · x ^ ) d ω = 4 π ε ( r , s ^ , t ) ( s ^ · y ^ ) d ω = 4 π ε ( r , s ^ , t ) ( s ^ · z ^ ) d ω = 0.
ϕ ( r , t ) + 2 A J n ( r , t ) = 0 ,
I ( r b , s ^ , t ) = ϕ ( r b , t ) 4 π + 3 4 π [ J n ( r b , t ) n ^ + J t ( r b , t ) t ^ ] · s ^ ,
I t ( r s , s ^ θ 2 , t ) = n 2 3 n 1 3 cos θ 2 cos θ 1 | T | 2 I i ( r s , s ^ θ 1 , t ) ,
| T | 2 = [ | 2 n 1 cos θ 1 n 2 cos θ 1 + n 1 cos θ 2 | 2 + | 2 n 1 cos θ 1 n 1 cos θ 1 + n 2 cos θ 2 | 2 ] / 2.
I t ( r s , s ^ θ 2 , t ) d ω 2 ( r s ) = n 2 3 n 1 3 cos θ 2 cos θ 1 | T | 2 I ( r b , s ^ θ 1 , t ) e μ a | r s r b | d ω 1 ( r s ) d ω 2 ( r s ) d ω 1 ( r s ) .
d ω 2 ( r s ) d ω 1 ( r s ) = cos θ 1 cos θ 2 n 1 2 n 2 2 ,
I t ( r s , s ^ θ 2 , t ) d ω 2 ( r s ) = n 2 n 1 | T | 2 I ( r b , s ^ θ 1 , t ) e μ a | r s r b | d ω 1 ( r s ) .
P t ( r s , t ) = cos θ 2 I t ( r s , s ^ θ 2 , t ) ( s ^ θ 2 · n ^ ) d ω 2 ( r s ) = n 2 n 1 | T | 2 e μ a | r s r b | cos θ 2 I ( r b , s ^ θ 1 , t ) ( s ^ θ 1 · n ^ ) d ω 1 ( r s ) .
P t ( r s , t ) = { n 2 n 1 r b S 1 | T | 2 [ ϕ ( r b , t ) 4 π + J n ( r b , t ) 2 π ] e μ a | r s r b | Δ z 2 | r s r b | 2 ( θ 1 = 0 ) n 2 n 1 r b S 1 | T | 2 I ( r b , s ^ θ 1 , t ) e μ a | r s r b | cos θ 1 cos θ 2 Δ z 2 | r s r b | 2 ( else ) ,
ε ( r s , s ^ θ 2 , t ) = 1 4 π μ s ' P t ( r s , t ) μ a + μ s ' δ ( r r s ) .
| R | 2 = [ | n 1 cos θ 2 n 2 cos θ 1 n 1 cos θ 2 + n 2 cos θ 1 | 2 + | n 1 cos θ 1 n 2 cos θ 2 n 1 cos θ 1 + n 2 cos θ 2 | 2 ] / 2.
Γ ( r s ) = A 1 I ( r b , s ^ θ i ) e μ a | r s r b | cos 2 θ 1 | r s r b | 2 d A 1 ,
I ( r b , s ^ ) ϕ ( r b ) 4 π ( 1 + cos θ 1 0.71 ) = ϕ ( r b ) 4 π ( 1 + 1.41 × cos θ 1 ) .
I ( r b , s ^ , t ) = ϕ ( r b , t ) 4 π ( 1 + 1.5 × cos θ 1 ) + 3 4 π J t ( r b , t ) t ^ · s ^ .
I ( r b , s ^ θ 1 , t ) ( s ^ θ 1 · n ^ ) d ω 1 = 2 π d φ 0 Δ θ 1 [ ϕ ( r b , t ) 4 π + 3 4 π ( J n ( r b , t ) n ^ + J t ( r b , t ) t ^ ) · s ^ ] cos θ sin θ d θ = 2 π d φ 0 Δ θ 1 [ ϕ ( r b , t ) 4 π + 3 4 π ( J n ( r b , t ) cos θ + J t ( r b , t ) sin θ · cos φ ) ] cos θ sin θ d θ .
I ( r b , s ^ θ 1 , t ) ( s ^ θ 1 · n ^ ) d ω 1 = [ ϕ ( r b , t ) 4 + J n ( r b , t ) 2 ] sin 2 ( Δ θ 1 ) [ ϕ ( r b , t ) 4 + J n ( r b , t ) 2 ] a 2 | r s r b | 2 .
I ( r b , s ^ θ 1 , t ) ( s ^ θ 1 · n ^ ) d ω 1 = J n ( r b , t ) sin 2 ( Δ θ 1 ) J n ( r b , t ) a 2 | r s r b | 2 .

Metrics