Abstract

The development of diffuse optical tomography (DOT) instrumentation for neuroimaging of humans is challenging due to the large size and the geometry of the head and the desire to distinguish signals at different depths. One approach to this problem is to use dense imaging arrays that incorporate measurements at different source–detector distances. We previously developed a high-density DOT system that is able to obtain retinotopic measurements in agreement with functional magnetic resonance imaging and positron emission tomography. Further extension of high-density DOT neuroimaging necessitates a thorough study of the measurement and imaging sensitivity that incorporates the complex geometry of the head—including the head curvature and layered tissue structure. We present numerical simulations using a finite element model of the adult head to study the sensitivity of the measured signal as a function of the imaging array and data sampling strategy. Specifically, we quantify the imaging sensitivity available within the brain (including depths beyond superficial cortical gyri) as a function of increasing the maximum source–detector separation included in the data. Through the use of depth related sensitivity analysis, it is shown that for a rectangular grid [with 1.3cm first nearest neighbor (NN) spacing], second NN measurements are sufficient to record absorption changes along the surface of the brain’s cortical gyri (brain tissue depth <5mm). The use of fourth and fifth NN measurements would permit imaging down into the cortical sulci (brain tissue depth >15mm).

© 2009 Optical Society of America

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2008 (2)

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

2007 (1)

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (3)

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

2004 (2)

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

T. Durduran, G. Q. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, J. J. Wang, C. Zhou, and A. G. Yodh, “Diffuse optical measurement of blood flow, blood oxygenation, and metabolism in a human brain during sensorimotor cortex activation,” Opt. Lett. 29, 1766-1768 (2004).
[CrossRef] [PubMed]

2003 (5)

2002 (1)

G. Strangman, D. A. Boas, and J. P. Sutton, “Noninvasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679-693 (2002).
[CrossRef] [PubMed]

2001 (4)

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Appl. Opt. 26, 701-703(2001).

J. Ripoll, M. Nieto-Vesperinas, and S. R. Arridge, “Effect of roughness in nondiffusive regions within diffusive media,” J. Opt. Soc. Am. A 18, 940-947 (2001).
[CrossRef]

Y. L. Pei, H. L. Graber, and R. L. Barbour, “Normalized-constraint algorithm for minimizing interparameter crosstalk in DC optical tomography,” Opt. Express 9, 97-109(2001).
[CrossRef] [PubMed]

2000 (2)

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659-1670 (2000).
[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

1999 (1)

1995 (1)

1989 (1)

1955 (1)

R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc. 51, 406-413 (1955).
[CrossRef]

Arridge, S. R.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

A. Gibson, J. Riley, M. Schweiger, J. C. Hebden, S. R. Arridge, and D. T. Delpy, “A method for generating patient specific finite element meshes for head modelling,” Phys. Med. Biol. 48, 481-495 (2003).
[CrossRef] [PubMed]

J. Ripoll, M. Nieto-Vesperinas, and S. R. Arridge, “Effect of roughness in nondiffusive regions within diffusive media,” J. Opt. Soc. Am. A 18, 940-947 (2001).
[CrossRef]

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659-1670 (2000).
[CrossRef]

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

Austin, T.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

Bando, M.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Barbour, R. L.

Barnett, A. H.

Bayford, R. H.

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

Boas, D. A.

A. Custo, W. M. I. Wells, A. H. Barnett, E. M. C. Hillman, and D. A. Boas, “Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging,” Appl. Opt. 45, 4747-4755 (2006).
[CrossRef] [PubMed]

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett. 28, 2061-2063 (2003).
[CrossRef] [PubMed]

G. Strangman, D. A. Boas, and J. P. Sutton, “Noninvasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679-693 (2002).
[CrossRef] [PubMed]

Brooksby, B.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

Burnett, M. G.

Butler, J.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Cerussi, A.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Chance, B.

Chance, M. S.

Choe, R.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Cubeddu, R.

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

Culver, J. P.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (Jul 17 2007).
[CrossRef]

J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett. 28, 2061-2063 (2003).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Appl. Opt. 26, 701-703(2001).

Custo, A.

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Dehghani, H.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (Jul 17 2007).
[CrossRef]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42, 135-145 (2003).
[CrossRef] [PubMed]

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659-1670 (2000).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Delpy, D. T.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

A. Gibson, J. Riley, M. Schweiger, J. C. Hebden, S. R. Arridge, and D. T. Delpy, “A method for generating patient specific finite element meshes for head modelling,” Phys. Med. Biol. 48, 481-495 (2003).
[CrossRef] [PubMed]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659-1670 (2000).
[CrossRef]

Detre, J. A.

Durduran, T.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

T. Durduran, G. Q. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, J. J. Wang, C. Zhou, and A. G. Yodh, “Diffuse optical measurement of blood flow, blood oxygenation, and metabolism in a human brain during sensorimotor cortex activation,” Opt. Lett. 29, 1766-1768 (2004).
[CrossRef] [PubMed]

Durkin, A.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Everdell, N.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

Franceschini, M. A.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

Fry, M. E.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

Fuchino, Y.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Giambattistelli, E.

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

Gibson, A.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

A. Gibson, J. Riley, M. Schweiger, J. C. Hebden, S. R. Arridge, and D. T. Delpy, “A method for generating patient specific finite element meshes for head modelling,” Phys. Med. Biol. 48, 481-495 (2003).
[CrossRef] [PubMed]

Graber, H. L.

Greenberg, J. H.

Hayashi, T.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Hebden, J. C.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

A. Gibson, J. Riley, M. Schweiger, J. C. Hebden, S. R. Arridge, and D. T. Delpy, “A method for generating patient specific finite element meshes for head modelling,” Phys. Med. Biol. 48, 481-495 (2003).
[CrossRef] [PubMed]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

Hillman, E. M. C.

A. Custo, W. M. I. Wells, A. H. Barnett, E. M. C. Hillman, and D. A. Boas, “Effective scattering coefficient of the cerebral spinal fluid in adult head models for diffuse optical imaging,” Appl. Opt. 45, 4747-4755 (2006).
[CrossRef] [PubMed]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

Holboke, M. J.

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Appl. Opt. 26, 701-703(2001).

Holder, D. S.

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

Horesh, L.

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

Hsiang, D.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Ichikawa, N.

Jiang, S.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

Katura, T.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Kawaguchi, H.

Kogel, C.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

Koizumi, H.

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

H. Koizumi, T. Yamamoto, A. Maki, Y. Yamashita, H. Sato, H. Kawaguchi, and N. Ichikawa, “Optical topography: practical problems and new applications,” Appl. Opt. 42, 3054-3062 (2003).
[CrossRef] [PubMed]

Maki, A.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

H. Koizumi, T. Yamamoto, A. Maki, Y. Yamashita, H. Sato, H. Kawaguchi, and N. Ichikawa, “Optical topography: practical problems and new applications,” Appl. Opt. 42, 3054-3062 (2003).
[CrossRef] [PubMed]

McBride, T.

Meek, J. H.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

Mehta, R.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Morimoto, K.

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

Nagao, M.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Naito, M.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Nakamura, K.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Nieto-Vesperinas, M.

Ntziachristos, V.

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Appl. Opt. 26, 701-703(2001).

Obata, A.

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

Obrig, H.

H. Obrig and A. Villringer, “Beyond the visible--imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1-18 (2003).
[CrossRef]

Osterberg, U.

Patterson, M. S.

Paulsen, K.

Paulsen, K. D.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42, 135-145 (2003).
[CrossRef] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Pei, Y. L.

Penrose, R.

R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc. 51, 406-413 (1955).
[CrossRef]

Pifferi, A.

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

Pogue, B. W.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42, 135-145 (2003).
[CrossRef] [PubMed]

B. W. Pogue, T. McBride, U. Osterberg, and K. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270-286 (1999).
[CrossRef] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Poplack, S. P.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

H. Dehghani, B. W. Pogue, S. P. Poplack, and K. D. Paulsen, “Multiwavelength three-dimensional near-infrared tomography of the breast: initial simulation, phantom, and clinical results,” Appl. Opt. 42, 135-145 (2003).
[CrossRef] [PubMed]

Riley, J.

A. Gibson, J. Riley, M. Schweiger, J. C. Hebden, S. R. Arridge, and D. T. Delpy, “A method for generating patient specific finite element meshes for head modelling,” Phys. Med. Biol. 48, 481-495 (2003).
[CrossRef] [PubMed]

Ripoll, J.

Sato, H.

Schlaggar, B. L.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (Jul 17 2007).
[CrossRef]

Schmidt, F. E. W.

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

Schweiger, M.

Selb, J.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

Shah, N.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Siegel, A. M.

Sorensen, A. G.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

Srinivasan, S.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Stott, J. J.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

J. P. Culver, A. M. Siegel, J. J. Stott, and D. A. Boas, “Volumetric diffuse optical tomography of brain activity,” Opt. Lett. 28, 2061-2063 (2003).
[CrossRef] [PubMed]

Strangman, G.

G. Strangman, D. A. Boas, and J. P. Sutton, “Noninvasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679-693 (2002).
[CrossRef] [PubMed]

Suda, M.

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

Sutton, J. P.

G. Strangman, D. A. Boas, and J. P. Sutton, “Noninvasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679-693 (2002).
[CrossRef] [PubMed]

Taroni, A.

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

Tizzard, A.

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

Torricelli, A.

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

Tromberg, B. J.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

Villringer, A.

H. Obrig and A. Villringer, “Beyond the visible--imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1-18 (2003).
[CrossRef]

Wang, J. J.

Wells, W. M. I.

White, B. R.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (Jul 17 2007).
[CrossRef]

Wilson, B. C.

Wyatt, J. S.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

Yalavarthy, P. K.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

Yamamoto, T.

Yamashita, Y.

Yerworth, R. J.

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

Yodh, A. G.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

T. Durduran, G. Q. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, J. J. Wang, C. Zhou, and A. G. Yodh, “Diffuse optical measurement of blood flow, blood oxygenation, and metabolism in a human brain during sensorimotor cortex activation,” Opt. Lett. 29, 1766-1768 (2004).
[CrossRef] [PubMed]

J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: a singular-value analysis,” Appl. Opt. 26, 701-703(2001).

Yoro, T.

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Yu, G. Q.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

T. Durduran, G. Q. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, J. J. Wang, C. Zhou, and A. G. Yodh, “Diffuse optical measurement of blood flow, blood oxygenation, and metabolism in a human brain during sensorimotor cortex activation,” Opt. Lett. 29, 1766-1768 (2004).
[CrossRef] [PubMed]

Yusof, R.

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

Zeff, B. W.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (Jul 17 2007).
[CrossRef]

Zhou, C.

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

T. Durduran, G. Q. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, J. J. Wang, C. Zhou, and A. G. Yodh, “Diffuse optical measurement of blood flow, blood oxygenation, and metabolism in a human brain during sensorimotor cortex activation,” Opt. Lett. 29, 1766-1768 (2004).
[CrossRef] [PubMed]

Appl. Opt. (6)

Biol. Psychiat. (1)

G. Strangman, D. A. Boas, and J. P. Sutton, “Noninvasive neuroimaging using near-infrared light,” Biol. Psychiat. 52, 679-693 (2002).
[CrossRef] [PubMed]

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction algorithms,” Commun. Numer. Methods Eng. , doi: 10.1002/cnm.1162.
[PubMed]

J. Biomed. Opt. (2)

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10, 011013 (2005).
[CrossRef]

C. Zhou, R. Choe, N. Shah, T. Durduran, G. Q. Yu, A. Durkin, D. Hsiang, R. Mehta, J. Butler, A. Cerussi, B. J. Tromberg, and A. G. Yodh, “Diffuse optical monitoring of blood flow and oxygenation in human breast cancer during early stages of neoadjuvant chemotherapy,” J. Biomed. Opt. 12, 051903 (2007).
[CrossRef] [PubMed]

J. Cereb. Blood Flow Metab. (1)

H. Obrig and A. Villringer, “Beyond the visible--imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1-18 (2003).
[CrossRef]

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

NeuroReport (1)

M. Suda, K. Morimoto, A. Obata, H. Koizumi, and A. Maki, “Emotional responses to music: towards scientific perspectives on music therapy,” NeuroReport 19, 75-78 (2008).
[CrossRef] [PubMed]

Neurosci. Lett. Suppl. (1)

Y. Fuchino, M. Nagao, T. Katura, M. Bando, M. Naito, A. Maki, K. Nakamura, T. Hayashi, H. Koizumi, and T. Yoro, “High cognitive function of an ALS patient in the totally locked-in state,” Neurosci. Lett. Suppl. 435, 85-89 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Meas. (1)

A. Tizzard, L. Horesh, R. J. Yerworth, D. S. Holder, and R. H. Bayford, “Generating accurate finite element meshes for the forward model of the human head in EIT,” Phys. Meas. 26, S251-S261 (2005).
[CrossRef]

Phys. Med. Biol. (3)

A. Torricelli, A. Pifferi, A. Taroni, E. Giambattistelli, and R. Cubeddu, “In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy,” Phys. Med. Biol. 46, 2227-2237 (2001).
[CrossRef] [PubMed]

A. Gibson, J. Riley, M. Schweiger, J. C. Hebden, S. R. Arridge, and D. T. Delpy, “A method for generating patient specific finite element meshes for head modelling,” Phys. Med. Biol. 48, 481-495 (2003).
[CrossRef] [PubMed]

J. C. Hebden, A. Gibson, T. Austin, R. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys. Med. Biol. 49, 1117-1130 (2004).
[CrossRef] [PubMed]

Proc. Cambridge Philos. Soc. (1)

R. Penrose, “A generalized inverse for matrices,” Proc. Cambridge Philos. Soc. 51, 406-413 (1955).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. USA 104, 12169-12174 (Jul 17 2007).
[CrossRef]

Rev. Sci. Instrum. (1)

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delpy, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256-265(2000).
[CrossRef]

Technol. Cancer Res. Treat. (1)

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, “Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction,” Technol. Cancer Res. Treat. 5, 513-526 (2005).

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Figures (6)

Fig. 1
Fig. 1

Hypothetical DOT imaging systems and measurement configurations. (a) Definitions of first through fifth nearest neighbor measurements within the context of our imaging pad. (b) Measurement designs and noise floors necessary for 2NN and 5NN DOT systems. Red dots are simulated light level measurements in the absence of noise. Altering the instrument noise floor changes the amount of measurements that can be included with an SNR > 100 .

Fig. 2
Fig. 2

Three dimensional (3D) model of the adult brain. (a) View of the FEM mesh. (b)–(d) Cross-sectional maps of absorption at 849 nm .

Fig. 3
Fig. 3

(a) Back view and (b) side view schematic showing the placement of the imaging grid over the visual cortex of the adult head model with 24 sources (red squares) and 28 detectors (blue circles).

Fig. 4
Fig. 4

Total normalized forward model sensitivity shown as contour lines on the back portion of the axial view of the 3D adult head model for each nearest neighbor (NN) set. The shades in each image represent the optical absorption properties at 849 nm , as shown in Fig. 2. Each contour line represents 10% of the total sensitivity with the dashed black line at 10% and dashed white line at 1% sensitivity.

Fig. 5
Fig. 5

Cross section (along the region depicted by the dashed line in Fig. 4e) of the flat-field image test for each nearest neighbor as a function of distance from surface of the head. The solid vertical line represents the surface of the brain.

Fig. 6
Fig. 6

Reconstructed baseline tomographic images of hemodynamic activation at different depths within the brain, using 1 NN through 5 NN measurement strategies. Images shown are absorption changes measured at 849 nm , with each pane scaled to its maximum value. Each row corresponds to an activation depth, and each column is a different measurement combination. Only the back portion of the axial view of the 3D adult head model is shown, with solid cyan lines representing the skull outline. The activation corresponds to a 3.8 μM rise in total hemoglobin and 3.76% change in oxygen saturation.

Tables (2)

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Table 1 Physiological Parameters Used for Each Region of the 3D Model [14] and the Absorption and Reduced Scattering Coefficients at 849 nm

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Table 2 Total Number for Measurements for 24 Sources and 28 Detectors Using Either 1st, 2nd 3rd, 4th, or 5th Nearest Neighbor Combinations, Together with the Maximum Distance of These Source–Detector Pairs

Equations (4)

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J T ( J J T + λ L ) 1 Φ = μ a ,
L = 1 diag ( J J T + β ) 1 / 2 ,
J j total = i = 1 NM J i , j max ( abs ( i = 1 NM J i , j ) ) ,
Φ = J μ .

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