Abstract

There is a growing interest in the use of near-infrared spectroscopy for the noninvasive determination of the oxygenation level within biological tissue. Stemming from this application, there has been further research in the use of this technique for obtaining tomographic images of the neonatal head, with the view of determining the levels of oxygenated and deoxygenated blood within the brain. Owing to computational complexity, methods used for numerical modeling of photon transfer within tissue have usually been limited to the diffusion approximation of the Boltzmann transport equation. The diffusion approximation, however, is not valid in regions of low scatter, such as the cerebrospinal fluid. Methods have been proposed for dealing with nonscattering regions within diffusing materials through the use of a radiosity-diffusion model. Currently, this new model assumes prior knowledge of the void region location; therefore it is instructive to examine the errors introduced in applying a simple diffusion-based reconstruction scheme in cases in which there exists a nonscattering region. We present reconstructed images of objects that contain a nonscattering region within a diffusive material. Here the forward data is calculated with the radiosity-diffusion model, and the inverse problem is solved with either the radiosity-diffusion model or the diffusion-only model. The reconstructed images show that even in the presence of only a thin nonscattering layer, a diffusion-only reconstruction will fail. When a radiosity-diffusion model is used for image reconstruction, together with a priori information about the position of the nonscattering region, the quality of the reconstructed image is considerably improved. The accuracy of the reconstructed images depends largely on the position of the anomaly with respect to the nonscattering region as well as the thickness of the nonscattering region.

© 2000 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2000

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

J. Ripoll, S. R. Arridge, H. Dehghani, M. Nieto-Vesperinas, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17, 1671–1681 (2000).
[CrossRef]

1999

M. Schweiger, S. R. Arridge, “Application of temporal filters to time-resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
[CrossRef] [PubMed]

J. C. Ye, K. J. Webb, C. A. Bouman, R. P. Millane, “Optical diffusion tomography by iterative-coordinate-descent optimization in a Baysian framework,” J. Opt. Soc. Am. A 16, 2400–2412 (1999).
[CrossRef]

H. Dehghani, D. T. Delpy, S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

S. R. Arridge, “Topical review: optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

1998

1997

S. R. Arridge, M. Schweiger, “Direct calculation of the Laplace transform of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 36, 9042–9049 (1997).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
[CrossRef] [PubMed]

J. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997).
[CrossRef]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Ch. L. Matson, N. Clark, L. McMackin, J. S. Fender, “Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves,” Appl. Opt. 36, 214–220 (1997).
[CrossRef] [PubMed]

X. D. Li, T. Durduran, A. G. Yodh, B. Chance, D. N. Pattanayak, “Diffraction tomography for biochemical imaging with diffuse-photon density waves,” Opt. Lett. 22, 573–575 (1997).
[CrossRef] [PubMed]

S. A. Walker, S. Fantini, E. Gratton, “Image reconstruction by backprojection from frequency-domain optical measurements in highly scattering media,” Appl. Opt. 36, 170–179 (1997).
[CrossRef] [PubMed]

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

1996

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

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1996).
[CrossRef]

1995

1994

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

1993

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

P. N. den Outer, Th. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
[CrossRef]

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

1983

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogenous tissue,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Arridge, S. R.

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

J. Ripoll, S. R. Arridge, H. Dehghani, M. Nieto-Vesperinas, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17, 1671–1681 (2000).
[CrossRef]

M. Schweiger, S. R. Arridge, “Application of temporal filters to time-resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
[CrossRef] [PubMed]

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

S. R. Arridge, “Topical review: optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

H. Dehghani, D. T. Delpy, S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

S. R. Arridge, M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “Direct calculation of the Laplace transform of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 36, 9042–9049 (1997).
[CrossRef]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

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

S. R. Arridge, M. Schweiger, “Direct calculation of the moments of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 34, 2683–2687 (1995).
[CrossRef] [PubMed]

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

S. R. Arridge, M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

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

S. R. Arridge, M. Schweiger, M. Hiraoka, 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, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging, Lecture Notes in Computer Science, J. Duncan, G. Gindi, eds. (Springer-Verlag, Berlin, 1997), Vol. 1230, pp. 71–84.
[CrossRef]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for near infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

J. Ripoll, S. R. Arridge, M. Nieto-Vesperinas, “Effect of roughness in nondiffusive regions within diffusive media,” manuscript available from J. Ripoll: jripoll@icmm.csic.es.

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogenous tissue,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Bassani, M.

Boas, D. A.

Bouman, C. A.

Chance, B.

Clark, N.

Cohen, M. F.

M. F. Cohen, J. R. Wallace, Radiosity and Realistic Image Synthesis (Academic, London, 1993).

Colak, S. B.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

Contini, D.

Cope, M.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for near infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

Dehghani, H.

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

J. Ripoll, S. R. Arridge, H. Dehghani, M. Nieto-Vesperinas, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17, 1671–1681 (2000).
[CrossRef]

H. Dehghani, D. T. Delpy, S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

Delpy, D. T.

H. Dehghani, D. T. Delpy, S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

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

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

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

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

S. R. Arridge, M. Schweiger, M. Hiraoka, 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, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for near infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

E. Okada, D. T. Delpy, “The effect of overlaying tissue on NIR light propagation in neonatal brain,” Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonic Series (Optical Society of America, Washington, D.C., 1996), pp. 338–343.

den Outer, P. N.

Durduran, T.

Fantini, S.

Fender, J. S.

Feng, S.

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 35, 3826–3836 (1995).
[CrossRef]

Ferwada, H. A.

Firbank, M.

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

Franceschini, M. A.

Fry, M. E.

Gonatas, C. P.

C. P. Gonatas, M. Ishii, J. S. Leigh, J. C. Schotland, “Optical diffusion imaging using a direct inversion method,” Phys. Rev. E 52, 4361–4365 (1995).
[CrossRef]

Gratton, E.

Groenhuis, R. A. J.

Hebden, J. C.

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogenous tissue,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Hillman, E. M. C.

Hiraoka, M.

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

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, 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, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

Ishii, M.

C. P. Gonatas, M. Ishii, J. S. Leigh, J. C. Schotland, “Optical diffusion imaging using a direct inversion method,” Phys. Rev. E 52, 4361–4365 (1995).
[CrossRef]

Jiang, H.

Kaipio, J. P.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Kaschke, M.

Kolehmainen, V.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Kolzer, J.

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

Lagendijk, A.

Leigh, J. S.

C. P. Gonatas, M. Ishii, J. S. Leigh, J. C. Schotland, “Optical diffusion imaging using a direct inversion method,” Phys. Rev. E 52, 4361–4365 (1995).
[CrossRef]

Li, X. D.

Lionheart, W. R. B.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Martelli, F.

Matson, Ch. L.

McMackin, L.

Melissen, J. B. M.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

Millane, R. P.

Mitic, G.

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

Moesta, K. T.

Nakai, T.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Nieto-Vesperinas, M.

J. Ripoll, S. R. Arridge, H. Dehghani, M. Nieto-Vesperinas, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17, 1671–1681 (2000).
[CrossRef]

J. Ripoll, S. R. Arridge, M. Nieto-Vesperinas, “Effect of roughness in nondiffusive regions within diffusive media,” manuscript available from J. Ripoll: jripoll@icmm.csic.es.

Nieuwenhuizen, Th. M.

Nishimura, G.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Norton, S. J.

O’Leary, M. A.

Okada, E.

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

E. Okada, D. T. Delpy, “The effect of overlaying tissue on NIR light propagation in neonatal brain,” Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonic Series (Optical Society of America, Washington, D.C., 1996), pp. 338–343.

Osterberg, U. L.

Otto, J.

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

Paasschens, J. C. J.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

Papaioannou, D. G.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

Pattanayak, D. N.

Patterson, M. S.

Paulsen, K. D.

Plies, E.

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

Pogue, B. W.

Ripoll, J.

J. Ripoll, S. R. Arridge, H. Dehghani, M. Nieto-Vesperinas, “Boundary conditions for light propagation in diffusive media with nonscattering regions,” J. Opt. Soc. Am. A 17, 1671–1681 (2000).
[CrossRef]

J. Ripoll, S. R. Arridge, M. Nieto-Vesperinas, “Effect of roughness in nondiffusive regions within diffusive media,” manuscript available from J. Ripoll: jripoll@icmm.csic.es.

Schlag, P. M.

Schmidt, F. E. W.

Schomberg, H.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

Schotland, J. C.

J. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997).
[CrossRef]

C. P. Gonatas, M. Ishii, J. S. Leigh, J. C. Schotland, “Optical diffusion imaging using a direct inversion method,” Phys. Rev. E 52, 4361–4365 (1995).
[CrossRef]

Schweiger, M.

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

M. Schweiger, S. R. Arridge, “Application of temporal filters to time-resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
[CrossRef] [PubMed]

J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999).
[CrossRef]

S. R. Arridge, M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “Direct calculation of the Laplace transform of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 36, 9042–9049 (1997).
[CrossRef]

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

S. R. Arridge, M. Schweiger, “Direct calculation of the moments of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 34, 2683–2687 (1995).
[CrossRef] [PubMed]

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

S. R. Arridge, M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

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

S. R. Arridge, M. Schweiger, M. Hiraoka, 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, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging, Lecture Notes in Computer Science, J. Duncan, G. Gindi, eds. (Springer-Verlag, Berlin, 1997), Vol. 1230, pp. 71–84.
[CrossRef]

Solkner, G.

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

t’Hooft, G. W.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

Tamura, M.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Ten Bosch, J. J.

van Asten, N. A. A. J.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

van der Mark, M. B.

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

van der Zee, P.

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for near infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

P. van der Zee, “Measurement and modelling of the optical properties of human tissue in the near infrared,” Ph.D. dissertation (University College London, London, 1993).

Vauhkonen, M.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

Vo-Dinh, T.

Walker, S. A.

Wallace, J. R.

M. F. Cohen, J. R. Wallace, Radiosity and Realistic Image Synthesis (Academic, London, 1993).

Webb, K. J.

Yamamoto, K.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

Ye, J. C.

Yodh, A. G.

Zaccanti, G.

Zeng, F.

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 35, 3826–3836 (1995).
[CrossRef]

Zinth, W.

G. Mitic, J. Kolzer, J. Otto, E. Plies, G. Solkner, W. Zinth, “Time-gated transillumination of biological tissue and tissuelike phantoms,” Opt. Lett. 33, 6699–6710 (1994).

Appl. Opt.

Ch. L. Matson, N. Clark, L. McMackin, J. S. Fender, “Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves,” Appl. Opt. 36, 214–220 (1997).
[CrossRef] [PubMed]

S. A. Walker, S. Fantini, E. Gratton, “Image reconstruction by backprojection from frequency-domain optical measurements in highly scattering media,” Appl. Opt. 36, 170–179 (1997).
[CrossRef] [PubMed]

S. B. Colak, D. G. Papaioannou, G. W. t’Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997).
[CrossRef]

S. A. Walker, D. A. Boas, E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998).
[CrossRef]

S. Fantini, S. A. Walker, M. A. Franceschini, M. Kaschke, P. M. Schlag, K. T. Moesta, “Assessment of the size, position, and optical properties of breast tumor in vivo by noninvasive optical methods,” Appl. Opt. 37, 1982–1989 (1998).
[CrossRef]

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 35, 3826–3836 (1995).
[CrossRef]

R. A. J. Groenhuis, H. A. Ferwada, J. J. Ten Bosch, “Scattering and absorption of turbid materials determined from reflection measurements” (parts 1 and 2), Appl. Opt. 22, 2456–2467 (1983).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “Direct calculation of the moments of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 34, 2683–2687 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “Direct calculation of the Laplace transform of the distribution of photon time of flight in tissue with a finite-element method,” Appl. Opt. 36, 9042–9049 (1997).
[CrossRef]

S. R. Arridge, M. Schweiger, “Photon-measurement density functions. Part 2: finite-element-method calculations,” Appl. Opt. 34, 8026–8037 (1995).
[CrossRef] [PubMed]

Inverse Probl.

V. Kolehmainen, S. R. Arridge, W. R. B. Lionheart, M. Vauhkonen, J. P. Kaipio, “Recovery of region boundaries of piecewise constant coefficients of an elliptic PDE from boundary data,” Inverse Probl. 15, 1375–1391 (1999).
[CrossRef]

S. R. Arridge, “Topical review: optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

J. Math. Imag. Vision

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

J. Opt. Soc. Am. A

Med. Phys.

S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

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

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

Opt. Express

Opt. Lett.

Phys. Med. Biol.

J. C. Hebden, S. R. Arridge, D. T. Delpy, “Optical imaging in medicine. I. experimental techniques,” Phys. Med. Biol. 42, 825–840 (1997).
[CrossRef] [PubMed]

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogenous tissue,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[CrossRef]

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

M. Schweiger, S. R. Arridge, “Application of temporal filters to time-resolved data in optical tomography,” Phys. Med. Biol. 44, 1699–1717 (1999).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “Optical tomographic reconstruction in a complex head model using a priori region boundary information,” Phys. Med. Biol. 44, 2703–2721 (1999).
[CrossRef] [PubMed]

H. Dehghani, D. T. Delpy, S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol. 44, 2897–2906 (1999).
[CrossRef]

Phys. Rev. E

C. P. Gonatas, M. Ishii, J. S. Leigh, J. C. Schotland, “Optical diffusion imaging using a direct inversion method,” Phys. Rev. E 52, 4361–4365 (1995).
[CrossRef]

Other

P. van der Zee, “Measurement and modelling of the optical properties of human tissue in the near infrared,” Ph.D. dissertation (University College London, London, 1993).

M. F. Cohen, J. R. Wallace, Radiosity and Realistic Image Synthesis (Academic, London, 1993).

S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for near infrared absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991).
[CrossRef]

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging, Lecture Notes in Computer Science, J. Duncan, G. Gindi, eds. (Springer-Verlag, Berlin, 1997), Vol. 1230, pp. 71–84.
[CrossRef]

S. R. Arridge, M. Schweiger, M. Hiraoka, 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, R. R. Alfano, eds., Proc. SPIE1888, 360–371 (1993).
[CrossRef]

E. Okada, D. T. Delpy, “The effect of overlaying tissue on NIR light propagation in neonatal brain,” Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonic Series (Optical Society of America, Washington, D.C., 1996), pp. 338–343.

J. Ripoll, S. R. Arridge, M. Nieto-Vesperinas, “Effect of roughness in nondiffusive regions within diffusive media,” manuscript available from J. Ripoll: jripoll@icmm.csic.es.

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Figures (11)

Fig. 1
Fig. 1

(a) Outline of the model (radius=35 mm) used for the co-centrally placed circular nonscattering region (radius=10 mm). The optical properties of the diffusion region are μs=2 mm-1,μa=0.01 mm-1, and refractive index=1.4. For the nonscattering region, μa=0.005 mm-1 and refractive index=1.4. A circular anomaly (blob of radius=3 mm) was modeled within the diffusing region with μs=2 mm-1 and μa=0.02 mm-1. (b) Reconstructed image with a diffusion-only model. (c) Reconstructed image with a radiosity-diffusion model.

Fig. 2
Fig. 2

(a) Outline of the model (radius=35 mm) used. The nonscattering annular region is 2-mm thick at a radius extending from 10 to 12 mm. The optical properties of the diffusion region are μs=2 mm-1,μa=0.01 mm-1, and refractive index=1.4. For the nonscattering region, μa=0.005 mm-1 and refractive index=1.4. A circular anomaly (blob of radius=3 mm) was modeled within the diffusing region with μs=2 mm-1 and μa=0.02 mm-1. (b) Reconstructed image with a diffusion-only model. (c) Reconstructed image with a radiosity-diffusion model.

Fig. 3
Fig. 3

(a) Outline of the model (radius=35 mm) used. The nonscattering annular region has a thickness of 1–4 mm, at a radius of 28–32 mm. The optical properties of the diffusion region are μs=2 mm-1,μa=0.01 mm-1, and refractive index=1.4. For the nonscattering region, μa=0.005 mm-1 and refractive index=1.4. A circular anomaly (blob of radius=3 mm) was modeled within the diffusing region with μs=2 mm-1 and μa=0.04 mm-1. (b)–(e) Reconstructed images with a diffusion-only model for the 1–4 mm nonscattering region. (f)–(i) Reconstructed images with a radiosity-diffusion model for the 1–4 mm nonscattering region.

Fig. 4
Fig. 4

Cross-section plot (from bottom left to top right of the model) of the calculated μa distribution. μa is shown for a purely diffusing model (b) as well as for the models shown in Figs. 3(c)3(f). The actual distribution is also shown as the target (a).

Fig. 5
Fig. 5

(a) Outline of the model (radius=35 mm) used. The nonscattering annular region has a thickness of 2 mm and is moved from a radius of 20 to a radius of 24 mm. The optical properties of the diffusion region are μs=2 mm-1,μa=0.01 mm-1, and refractive index=1.4. For the nonscattering region, μa=0.005 mm-1 and refractive index=1.4. A circular anomaly (blob of radius=3 mm) was modeled within the diffusing region with μs=2 mm-1 and μa=0.04 mm-1. (b)–(f) Reconstructed images with a radiosity-diffusion model for the 2-mm nonscattering regions, moving from a radius of 20 to a radius of 24 mm.

Fig. 6
Fig. 6

Cross-section plot (from bottom left to top right of the model) of the calculated μa distribution. μa is shown for a purely diffusing model as well as the model shown in Fig. 5. The actual distribution is also shown as the target.

Fig. 7
Fig. 7

Reconstructed images of a diffusion-only model where the anomaly is displaced radially from the center of the model (a) to a radius of 28 mm (k) in 11 equal steps.

Fig. 8
Fig. 8

Reconstructed images of the radiosity-diffusion model in the presence of a 2-mm clear ring extending from a radius of 26 to a radius of 28 mm. The anomaly is again as in Fig. 7, displaced radially from the center of the model (i) to a radius of 28 mm (xi) in 11 equal steps.

Fig. 9
Fig. 9

(a) Radial position of the peak value of the calculated μa versus the true radial position for the two different models in Figs. 7 and 8. (b) FWHM of the μa cross section of each model in Figs. 7 and 8, as the anomaly is radially moved outward. The FWHM of the actual forward model is also shown. In both graphs, the solid vertical lines present the boundaries of the clear nonscattering ring.

Fig. 10
Fig. 10

(a) Outline of the model (radius=35 mm) used. The nonscattering region has a maximum thickness of 2.5 mm and a minimum thickness of 0.5 mm, at a radius of 32 mm. The optical properties of the diffusion region are μs=2 mm-1,μa=0.01 mm-1, and refractive index=1.4. For the nonscattering region, μa=0.005 mm-1 and refractive index=1.4. A circular anomaly (blob of radius=3 mm) was modeled within the diffusing region with μs=2 mm-1 and μa=0.04 mm-1. (b) Reconstructed image with a radiosity-diffusion model.

Fig. 11
Fig. 11

Cross-section plot (from bottom left to top right of the model) of the calculated μa distribution of the image shown in Fig. 10(b). μa is shown for a purely diffusing model as well as for the models shown in Figs. 3(h) and 3(i) (curves b, d, and c, respectively). The actual distribution is also shown as the target (a).

Tables (1)

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Table 1 Definition of Parameters in Models

Equations (14)

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-κ(r)Φ(r, ω)+μa+iωcΦ(r, ω)=q0(r, ω),
κ=13(μa+μs).
Γ2i(r2)=I1(r1)cos(θ1)cos(θ2)|r1-r2|2×exp[-|r1-r2|(μa+iω/c)],
yM=FM[μa, κ],
(μ^a, κˆ)=argminμa,κ[yM-FM(μa, κ)R+Ψ(μa, κ)],
[K(κ)+C(μ)+ζA+iωB]Φ(ω)=q0(ω),
Kij=Ωκ(r)ui(r)uj(r)dnr,
Cij=Ωμa(r)ui(r)uj(r)dnr,
Bij=1cΩui(r)uj(r)dnr,
Aij=Ωui(r)uj(r)dn-1r,
yM=M[Φ].
[K(κ)+C(μ)+ζA+iωB-E(ω)]Φ(ω)=q0(ω),
Eij=ζAiui(r1)Ajuj(r2)h(r1, r2) cos(θ1)cos(θ2)|r1-r2|2×exp-[|r1-r2|(μa+iω/c)]dn-1r2dn-1r1,
Ψ(p)=i=1Dj=1nn(i)λ(p)|pi-pn(i, j)|α

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