Abstract

We present a three-dimensional (3D) image reconstruction scheme for optical near-infrared imaging of highly scattering material. The algorithm reconstructs the spatial distribution of the optical parameters of a volume Ω from transillumination measurements on the boundary of Ω. We test the performance of the method for a cylindrical object with embedded absorbing perturbation for a number of different source and detector arrangements. Furthermore, we investigate the effect of a mismatched reconstruction, using a two-dimensional (2D) reconstruction model to image a single plane of the object from 3D tomographic data obtained in a single plane. The motivation for the application of 2D models is their advantage in speed and memory requirements. We found that the difference in the measurement data between 2D and 3D models depends greatly on the measurement type used, giving a much better agreement for mean time-of-flight data than for dc intensity data. Image artifacts that are due to data model mismatches can therefore be significantly reduced by use of mean time data.

© 1998 Optical Society of America

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1999 (1)

1998 (5)

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. R. Arridge, M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998); http://epubs.osa.org/oearchive/source/4014.htm .
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain near-infrared photo diffusion imaging: initial evaluation in multitarget tissuelike phantoms,” Med. Phys. 25, 183–193 (1998).
[CrossRef] [PubMed]

U. Hampel, R. Freyer, “Fast image reconstruction for optical absorption tomography in media with radially symmetric boundaries,” Med. Phys. 25, 92–101 (1998).
[CrossRef] [PubMed]

S. R. Arridge, W. R. B. Lionheart, “Non-uniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
[CrossRef]

1997 (4)

1995 (8)

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (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]

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, “Photon measurement density functions. Part 1: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

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

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

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

1993 (3)

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, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

1990 (2)

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: a time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

1988 (2)

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

M. Keijzer, W. M. Star, P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
[CrossRef] [PubMed]

’t Hooft, G. W.

Alfano, R. R.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

Aronson, R.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Arridge, S. R.

S. R. Arridge, M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998); http://epubs.osa.org/oearchive/source/4014.htm .
[CrossRef]

S. R. Arridge, W. R. B. Lionheart, “Non-uniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).
[CrossRef]

M. Schweiger, S. R. Arridge, “The finite element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef] [PubMed]

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

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]

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

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

S. R. Arridge, “Photon measurement density functions. Part 1: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[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, 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, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “The use of multiple data types in time-resolved optical absorption and scattering tomography (TOAST),” in Mathematical Methods in Medical Imaging II, J. N. Wilson, D. C. Wilson, eds., Proc. SPIE2035, 218–229 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natterer, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, New York, 1998), in press.

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97 Proceedings), Vol. 1230 of Lecture Notes in Computer Science (Springer, New York, 1997), pp. 71–84.
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, M. Firbank, D. T. Delpy, “Comparison of a finite element forward model with experimental phantom results: application to image reconstruction,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 179–190 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

Barbour, R. L.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Boas, D. A.

Bonner, R. F.

A. H. Gandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

Cai, W.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

Chance, B.

Chang, J.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Clark, N.

Colak, S. B.

Cope, M.

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Das, B. B.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

de Blasi, R. A.

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Delpy, D. T.

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]

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]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, M. Firbank, D. T. Delpy, “Comparison of a finite element forward model with experimental phantom results: application to image reconstruction,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 179–190 (1993).
[CrossRef]

Edwards, A. D.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Elwell, C. E.

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Fantini, S.

S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions of cylindrical inhomogeneities from frequency domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 137–141.

Fender, J. S.

Ferrari, M.

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Firbank, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, M. Firbank, D. T. Delpy, “Comparison of a finite element forward model with experimental phantom results: application to image reconstruction,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 179–190 (1993).
[CrossRef]

Freyer, R.

U. Hampel, R. Freyer, “Fast image reconstruction for optical absorption tomography in media with radially symmetric boundaries,” Med. Phys. 25, 92–101 (1998).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

A. H. Gandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

Graber, H. L.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Gratton, E.

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. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions of cylindrical inhomogeneities from frequency domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 137–141.

Greenough, C.

C. Greenough, K. Robinson, Finite Element Libarary (Numerical Algorithms Group, Rutherford Appelton Laboratory, Chilton, Oxfordshire, UK, 1981).

Hampel, U.

U. Hampel, R. Freyer, “Fast image reconstruction for optical absorption tomography in media with radially symmetric boundaries,” Med. Phys. 25, 92–101 (1998).
[CrossRef] [PubMed]

Hebden, J. C.

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: a time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

Hiraoka, M.

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (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]

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, M. Firbank, D. T. Delpy, “Comparison of a finite element forward model with experimental phantom results: application to image reconstruction,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 179–190 (1993).
[CrossRef]

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1999).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain near-infrared photo diffusion imaging: initial evaluation in multitarget tissuelike phantoms,” Med. Phys. 25, 183–193 (1998).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Keijzer, M.

Kruger, R. A.

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: a time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

Lax, M.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

Lionheart, W. R. B.

Liu, F.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

Lubowsky, J.

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

Matson, C. L.

McMackin, L.

Melissen, J. B. M.

Nossal, R. J.

A. H. Gandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

O’Leary, M. A.

Osterberg, U. L.

Österberg, U. L.

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain near-infrared photo diffusion imaging: initial evaluation in multitarget tissuelike phantoms,” Med. Phys. 25, 183–193 (1998).
[CrossRef] [PubMed]

Paasschens, J. C. J.

Papaioannou, D. G.

Patterson, M. S.

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain near-infrared photo diffusion imaging: initial evaluation in multitarget tissuelike phantoms,” Med. Phys. 25, 183–193 (1998).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Paulsen, K. D.

H. Jiang, K. D. Paulsen, U. L. Osterberg, “Optical image reconstruction using frequency-domain data: simulations and experiments,” J. Opt. Soc. Am. A 13, 253–266 (1999).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain near-infrared photo diffusion imaging: initial evaluation in multitarget tissuelike phantoms,” Med. Phys. 25, 183–193 (1998).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

Pogue, B. W.

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Reynolds, E. O. R.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Richardson, C. E.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Robinson, K.

C. Greenough, K. Robinson, Finite Element Libarary (Numerical Algorithms Group, Rutherford Appelton Laboratory, Chilton, Oxfordshire, UK, 1981).

Safoue, F.

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Schomberg, H.

Schweiger, M.

S. R. Arridge, M. Schweiger, “A gradient-based optimisation scheme for optical tomography,” Opt. Express 2, 213–226 (1998); http://epubs.osa.org/oearchive/source/4014.htm .
[CrossRef]

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

M. Schweiger, S. R. Arridge, “The finite element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “Photon measurement density functions. Part 2: Finite element calculations,” Appl. Opt. 34, 8026–8037 (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]

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[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, 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, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, “The use of multiple data types in time-resolved optical absorption and scattering tomography (TOAST),” in Mathematical Methods in Medical Imaging II, J. N. Wilson, D. C. Wilson, eds., Proc. SPIE2035, 218–229 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natterer, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, New York, 1998), in press.

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97 Proceedings), Vol. 1230 of Lecture Notes in Computer Science (Springer, New York, 1997), pp. 71–84.
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, M. Firbank, D. T. Delpy, “Comparison of a finite element forward model with experimental phantom results: application to image reconstruction,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 179–190 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

Star, W. M.

Storchi, P. R. M.

Tamura, M.

M. Tamura, “Multichannel near-infrared optical imaging of human brain activity,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 8–10.

Taylor, R. L.

O. C. Zienkiewicz, R. L. Taylor, The Finite Element Method, 4th ed. (McGraw-Hill, London, 1987).

van Asten, N. A. A. J.

van der Mark, M. B.

Walker, S. A.

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. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions of cylindrical inhomogeneities from frequency domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 137–141.

Wray, S. C.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

Wyatt, J. S.

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Yodh, A. G.

Zeng, F. A.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

Zienkiewicz, O. C.

O. C. Zienkiewicz, R. L. Taylor, The Finite Element Method, 4th ed. (McGraw-Hill, London, 1987).

Appl. Opt. (8)

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, 180–213 (1997).
[CrossRef] [PubMed]

C. 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]

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

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, “Photon measurement density functions. Part 1: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995).
[CrossRef] [PubMed]

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

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]

M. Keijzer, W. M. Star, P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
[CrossRef] [PubMed]

J. Appl. Physiol. (2)

R. A. de Blasi, M. Cope, C. E. Elwell, F. Safoue, M. Ferrari, “Noninvasive measurement of human forearm oxygen consumption by near-infrared spectroscopy,” J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
[PubMed]

J. Math. Imag. Vision (1)

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 (1)

Lancet (1)

A. D. Edwards, J. S. Wyatt, C. E. Richardson, D. T. Delpy, M. Cope, E. O. R. Reynolds, “Cotside measurement of cerebral blood flow in ill newborn infants by near infrared spectroscopy,” Lancet 2, 770–771 (1988).
[CrossRef] [PubMed]

Med. Phys. (7)

J. C. Hebden, R. A. Kruger, “Transillumination imaging performance: a time of flight imaging system,” Med. Phys. 17, 351–356 (1990).
[CrossRef] [PubMed]

K. D. Paulsen, H. Jiang, “Spatially-varying optical property reconstruction using a finite element diffusion equation approximation,” Med. Phys. 22, 691–701 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Österberg, M. S. Patterson, “Frequency-domain near-infrared photo diffusion imaging: initial evaluation in multitarget tissuelike phantoms,” Med. Phys. 25, 183–193 (1998).
[CrossRef] [PubMed]

U. Hampel, R. Freyer, “Fast image reconstruction for optical absorption tomography in media with radially symmetric boundaries,” Med. Phys. 25, 92–101 (1998).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, “The finite element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).
[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, 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]

Opt. Express (1)

Opt. Lett. (2)

Phys. Med. Biol. (2)

S. R. Arridge, M. Hiraoka, M. Schweiger, “Statistical basis for the determination of optical pathlength in tissue,” Phys. Med. Biol. 40, 1539–1558 (1995).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, H. Jiang, K. D. Paulsen, “Initial assessment of a simple system for frequency domain diffuse optical tomography,” Phys. Med. Biol. 40, 1709–1729 (1995).
[CrossRef] [PubMed]

Other (12)

M. Tamura, “Multichannel near-infrared optical imaging of human brain activity,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 8–10.

A. H. Gandjbakhche, R. J. Nossal, R. F. Bonner, “Theoretical study of resolution limits for time-resolved imaging of human breast,” in Advances in Laser and Light Spectroscopy to Diagnose Cancer and Other Diseases, R. R. Alfano, ed., Proc. SPIE2135, 176–185 (1994).
[CrossRef]

S. A. Walker, S. Fantini, E. Gratton, “Back-projection reconstructions of cylindrical inhomogeneities from frequency domain optical measurements in turbid media,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 137–141.

W. Cai, B. B. Das, F. Liu, F. A. Zeng, M. Lax, R. R. Alfano, “Three dimensional image reconstruction in highly scattering turbid media,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 241–244 (1997).
[CrossRef]

H. L. Graber, J. Chang, J. Lubowsky, R. Aronson, R. L. Barbour, “Near infrared absorption imaging of dense scattering media by steady-state diffusion tomography,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 372–386 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, D. T. Delpy, “Iterative reconstruction of near-infrared absorption images,” in Inverse Problems in Scattering and Imaging, M. A. Fiddy, ed., Proc. SPIE1767, 372–383 (1992).
[CrossRef]

S. R. Arridge, M. Schweiger, “The use of multiple data types in time-resolved optical absorption and scattering tomography (TOAST),” in Mathematical Methods in Medical Imaging II, J. N. Wilson, D. C. Wilson, eds., Proc. SPIE2035, 218–229 (1993).
[CrossRef]

M. Schweiger, S. R. Arridge, “Optimal data types in optical tomography,” in Information Processing in Medical Imaging (IPMI’97 Proceedings), Vol. 1230 of Lecture Notes in Computer Science (Springer, New York, 1997), pp. 71–84.
[CrossRef]

M. Schweiger, S. R. Arridge, M. Hiraoka, M. Firbank, D. T. Delpy, “Comparison of a finite element forward model with experimental phantom results: application to image reconstruction,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 179–190 (1993).
[CrossRef]

S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natterer, eds., Vol. 110 of IMA Volumes in Mathematics and Its Applications (Springer-Verlag, New York, 1998), in press.

C. Greenough, K. Robinson, Finite Element Libarary (Numerical Algorithms Group, Rutherford Appelton Laboratory, Chilton, Oxfordshire, UK, 1981).

O. C. Zienkiewicz, R. L. Taylor, The Finite Element Method, 4th ed. (McGraw-Hill, London, 1987).

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Figures (17)

Fig. 1
Fig. 1

Mesh structure of the cylindrical test object.

Fig. 2
Fig. 2

Placement of μ a perturbations in the cylinder. Image planes indicate the locations of the 11 cross sections representing the 3D image in Figs. 3 7 and Fig. 9. Measurement planes indicate the locations of the planes at which measurement sites are located on the circumference of the cylinder. For the measurement configurations used, see Table 1.

Fig. 3
Fig. 3

Target μ a image for 3D reconstructions: 11 horizontal slices through a cylindrical object containing three absorbers in different planes.

Fig. 4
Fig. 4

3D reconstruction from 16 × 16 × 1 (single-plane) intensity data.

Fig. 5
Fig. 5

3D reconstruction from 16 × 16 × 2 (two-plane) intensity data.

Fig. 6
Fig. 6

3D reconstruction from 16 × 16 × 3 (three-plane) intensity data.

Fig. 7
Fig. 7

3D reconstruction from 16 × 16 × 5 (five-plane) intensity data.

Fig. 8
Fig. 8

Image norms for 3D reconstructions from one-, two-, three-, and five-layer intensity data as a function of CG iteration.

Fig. 9
Fig. 9

3D reconstruction from 16 × 16 × 1 (single-plane) 〈t〉 data.

Fig. 10
Fig. 10

Comparison of image norms for single-plane reconstructions from intensity (E) and mean time-of-flight (〈t〉) data.

Fig. 11
Fig. 11

Comparison of (a) data norm and (b) solution norm of 16 × 16 × 1 reconstruction from noiseless data and data with added noise, assuming 104 photons received at each measurement site.

Fig. 12
Fig. 12

Comparison of (a) E and (b) 〈t〉 data for the homogeneous case, generated in the central plane of the cylinder with the 3D forward model and data generated from a circular object with the 2D forward model.

Fig. 13
Fig. 13

Ratio of 2D/3D (a) intensity and (b) mean time data as a function of source–detector separation.

Fig. 14
Fig. 14

Reconstruction of the central plane of the cylinder from single-plane data with the 2D reconstruction method. Data types: (a) E and (b) 〈t〉. The bottom row contains reconstructions from data modified with polynomial fit to 2D/3D homogeneous data to account for model mismatch: (c) fitted E and (d) fitted 〈t〉.

Fig. 15
Fig. 15

Cross sections along the vertical diameter of images in Fig. 14: (a) E and (b) 〈t〉.

Fig. 16
Fig. 16

As Fig. 14 but using homogeneous reference data and reconstructing for parameter differences only. These images were scaled individually because of their different dynamic ranges. Data types: (a) E and (b) 〈t〉.

Fig. 17
Fig. 17

Cross sections along the vertical diameter of images in Fig. 16.

Tables (2)

Tables Icon

Table 1 Measurement Geometries for 3D Cylinder Reconstructionsa

Tables Icon

Table 2 Solution Norms for 2D Reconstructions from 3D Data after 50 Iterationsa

Equations (8)

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

Φ r ,   t t - · c r κ r Φ r ,   t + c r μ a r Φ r ,   t = q 0 r ,   t ,   r Ω ,
Φ ξ + 2 κ A n Φ ξ = 0 ,   ξ Ω ,
q 0 r ,   t = δ r - ζ δ t - t 0 ,   ζ Ω .
Γ ξ ,   t = - c ξ κ ξ n Φ ξ ,   t .
Ω = x ,   y ,   z | x 2 + y 2 a 2 - h / 2 z h / 2 .
N 1 = 1 ,   0 ,   - 1 ,   N 2 = - 1 2 ,   - 3 2 ,   - 1 , N 3 = - 1 2 ,   3 2 ,   - 1 , N 4 = 1 ,   0 ,   1 ,   N 5 = - 1 2 ,   - 3 2 ,   1 , N 6 = 1 2 ,   3 2 ,     1 ,
u 1 x ,   y ,   z = 1 6 1 + 2 x 1 - z , u 2 x ,   y ,   z = 1 6 1 - x - 3 y 1 - z , u 3 x ,   y ,   z = 1 6 1 - x + 3 y 1 - z , u 4 x ,   y ,   z = 1 6 1 + 2 x 1 + z , u 5 x ,   y ,   z = 1 6 1 - x - 3 y 1 + z , u 6 x ,   y ,   z = 1 6 1 - x + 3 y 1 + z .
ε = Ω   | μ a target r - μ a recon r | 2 d r 1 / 2 ,

Metrics