Abstract

Diffuse optical tomography (DOT) is a non-invasive brain imaging technique that uses low-levels of near-infrared light to measure optical absorption changes due to regional blood flow and blood oxygen saturation in the brain. By arranging light sources and detectors in a grid over the surface of the scalp, DOT studies attempt to spatially localize changes in oxy- and deoxy-hemoglobin in the brain that result from evoked brain activity during functional experiments. However, the reconstruction of accurate spatial images of hemoglobin changes from DOT data is an ill-posed linearized inverse problem, which requires model regularization to yield appropriate solutions. In this work, we describe and demonstrate the application of a parametric restricted maximum likelihood method (ReML) to incorporate multiple statistical priors into the recovery of optical images. This work is based on similar methods that have been applied to the inverse problem for magnetoencephalography (MEG). Herein, we discuss the adaptation of this model to DOT and demonstrate that this approach provides a means to objectively incorporate reconstruction constraints and demonstrate this approach through a series of simulated numerical examples.

© 2010 OSA

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    [CrossRef] [PubMed]

2009 (2)

T. J. Huppert, M. S. Allen, S. G. Diamond, and D. A. Boas, “Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model,” Hum. Brain Mapp. 30(5), 1548–1567 (2009) (PMCID: 2670946.).
[CrossRef] [PubMed]

F. Abdelnour, B. Schmidt, and T. J. Huppert, “Topographic localization of brain activation in diffuse optical imaging using spherical wavelets,” Phys. Med. Biol. 54(20), 6383–6413 (2009) (PMCID: 2806654.).
[CrossRef] [PubMed]

2008 (2)

T. J. Huppert, S. G. Diamond, and D. A. Boas, “Direct estimation of evoked hemoglobin changes by multimodality fusion imaging,” J. Biomed. Opt. 13(5), 054031 (2008).
[CrossRef] [PubMed]

S. Perrey, “Non-invasive NIR spectroscopy of human brain function during exercise,” Methods 45(4), 289–299 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (4)

D. K. Joseph, T. J. Huppert, M. A. Franceschini, and D. A. Boas, “Diffuse optical tomography system to image brain activation with improved spatial resolution and validation with functional magnetic resonance imaging,” Appl. Opt. 45(31), 8142–8151 (2006).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

2005 (3)

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

D. A. Boas and A. M. Dale, “Simulation study of magnetic resonance imaging-guided cortically constrained diffuse optical tomography of human brain function,” Appl. Opt. 44(10), 1957–1968 (2005).
[CrossRef] [PubMed]

2004 (2)

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29(3), 256–258 (2004).
[CrossRef] [PubMed]

2002 (2)

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

2001 (1)

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 14–93 (1999).
[CrossRef]

1996 (1)

R. W. Cox, “AFNI: software for analysis and visualization of functional magnetic resonance neuroimages,” Comput. Biomed. Res. 29(3), 162–173 (1996).
[CrossRef] [PubMed]

1977 (2)

D. Harville, “Maximum likelihood approaches to variance component estimation and related problems,” J. Am. Stat. Assoc. 72(358), 320–338 (1977).
[CrossRef]

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39(1), 1–38 (1977).

Abdelnour, F.

F. Abdelnour, B. Schmidt, and T. J. Huppert, “Topographic localization of brain activation in diffuse optical imaging using spherical wavelets,” Phys. Med. Biol. 54(20), 6383–6413 (2009) (PMCID: 2806654.).
[CrossRef] [PubMed]

Allen, M. S.

T. J. Huppert, M. S. Allen, S. G. Diamond, and D. A. Boas, “Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model,” Hum. Brain Mapp. 30(5), 1548–1567 (2009) (PMCID: 2670946.).
[CrossRef] [PubMed]

Arridge, S. R.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 14–93 (1999).
[CrossRef]

Ashburner, J.

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

Boas, D. A.

T. J. Huppert, M. S. Allen, S. G. Diamond, and D. A. Boas, “Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model,” Hum. Brain Mapp. 30(5), 1548–1567 (2009) (PMCID: 2670946.).
[CrossRef] [PubMed]

T. J. Huppert, S. G. Diamond, and D. A. Boas, “Direct estimation of evoked hemoglobin changes by multimodality fusion imaging,” J. Biomed. Opt. 13(5), 054031 (2008).
[CrossRef] [PubMed]

D. K. Joseph, T. J. Huppert, M. A. Franceschini, and D. A. Boas, “Diffuse optical tomography system to image brain activation with improved spatial resolution and validation with functional magnetic resonance imaging,” Appl. Opt. 45(31), 8142–8151 (2006).
[CrossRef] [PubMed]

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

D. A. Boas and A. M. Dale, “Simulation study of magnetic resonance imaging-guided cortically constrained diffuse optical tomography of human brain function,” Appl. Opt. 44(10), 1957–1968 (2005).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

A. Li, Q. Zhang, J. P. Culver, E. L. Miller, and D. A. Boas, “Reconstructing chromosphere concentration images directly by continuous-wave diffuse optical tomography,” Opt. Lett. 29(3), 256–258 (2004).
[CrossRef] [PubMed]

Bortfeld, H.

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

Brooksby, B. A.

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

Chance, B.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Choe, R.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Cox, R. W.

R. W. Cox, “AFNI: software for analysis and visualization of functional magnetic resonance neuroimages,” Comput. Biomed. Res. 29(3), 162–173 (1996).
[CrossRef] [PubMed]

Culver, J. P.

Dale, A. M.

D. A. Boas and A. M. Dale, “Simulation study of magnetic resonance imaging-guided cortically constrained diffuse optical tomography of human brain function,” Appl. Opt. 44(10), 1957–1968 (2005).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

Davis, S. C.

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

Dehghani, H.

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

Dempster, A. P.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39(1), 1–38 (1977).

Diamond, S. G.

T. J. Huppert, M. S. Allen, S. G. Diamond, and D. A. Boas, “Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model,” Hum. Brain Mapp. 30(5), 1548–1567 (2009) (PMCID: 2670946.).
[CrossRef] [PubMed]

T. J. Huppert, S. G. Diamond, and D. A. Boas, “Direct estimation of evoked hemoglobin changes by multimodality fusion imaging,” J. Biomed. Opt. 13(5), 054031 (2008).
[CrossRef] [PubMed]

Du, J.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Durduran, T.

U. Sunar, S. Makonnen, C. Zhou, T. Durduran, G. Yu, H. W. Wang, W. M. Lee, and A. G. Yodh, “Hemodynamic responses to antivascular therapy and ionizing radiation assessed by diffuse optical spectroscopies,” Opt. Express 15(23), 15507–15516 (2007).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Eda, H.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Franceschini, M. A.

D. K. Joseph, T. J. Huppert, M. A. Franceschini, and D. A. Boas, “Diffuse optical tomography system to image brain activation with improved spatial resolution and validation with functional magnetic resonance imaging,” Appl. Opt. 45(31), 8142–8151 (2006).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

Friston, K. J.

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

Gibson, A. P.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Glaser, D. E.

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

Harville, D.

D. Harville, “Maximum likelihood approaches to variance component estimation and related problems,” J. Am. Stat. Assoc. 72(358), 320–338 (1977).
[CrossRef]

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Henson, R. N.

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

Hinton, G.

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

Huppert, T. J.

T. J. Huppert, M. S. Allen, S. G. Diamond, and D. A. Boas, “Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model,” Hum. Brain Mapp. 30(5), 1548–1567 (2009) (PMCID: 2670946.).
[CrossRef] [PubMed]

F. Abdelnour, B. Schmidt, and T. J. Huppert, “Topographic localization of brain activation in diffuse optical imaging using spherical wavelets,” Phys. Med. Biol. 54(20), 6383–6413 (2009) (PMCID: 2806654.).
[CrossRef] [PubMed]

T. J. Huppert, S. G. Diamond, and D. A. Boas, “Direct estimation of evoked hemoglobin changes by multimodality fusion imaging,” J. Biomed. Opt. 13(5), 054031 (2008).
[CrossRef] [PubMed]

D. K. Joseph, T. J. Huppert, M. A. Franceschini, and D. A. Boas, “Diffuse optical tomography system to image brain activation with improved spatial resolution and validation with functional magnetic resonance imaging,” Appl. Opt. 45(31), 8142–8151 (2006).
[CrossRef] [PubMed]

Joseph, D. K.

Kiebel, S.

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

Kilger, A.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Konishi, I.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Kubota, K.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Laird, N. M.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39(1), 1–38 (1977).

Lee, W. M.

Li, A.

Loevner, L.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Lustig, R.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Makonnen, S.

Mattout, J.

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

Miller, E. L.

Miyai, I.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Nioka, S.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Oda, I.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Paulsen, K. D.

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

Penny, W.

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

Penny, W. D.

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

Perrey, S.

S. Perrey, “Non-invasive NIR spectroscopy of human brain function during exercise,” Methods 45(4), 289–299 (2008).
[CrossRef] [PubMed]

Phillips, C.

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

Pogue, B. W.

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

Quon, H.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Rubin, D. B.

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39(1), 1–38 (1977).

Rugg, M. D.

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

Sase, I.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Schmidt, B.

F. Abdelnour, B. Schmidt, and T. J. Huppert, “Topographic localization of brain activation in diffuse optical imaging using spherical wavelets,” Phys. Med. Biol. 54(20), 6383–6413 (2009) (PMCID: 2806654.).
[CrossRef] [PubMed]

Song, X.

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

Sunar, U.

U. Sunar, S. Makonnen, C. Zhou, T. Durduran, G. Yu, H. W. Wang, W. M. Lee, and A. G. Yodh, “Hemodynamic responses to antivascular therapy and ionizing radiation assessed by diffuse optical spectroscopies,” Opt. Express 15(23), 15507–15516 (2007).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Suzuki, T.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Tanabe, H. C.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Tsunazawa, Y.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Wang, H. W.

Wilcox, T.

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

Woods, R.

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

Wruck, E.

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

Yanagida, T.

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

Yodh, A. G.

U. Sunar, S. Makonnen, C. Zhou, T. Durduran, G. Yu, H. W. Wang, W. M. Lee, and A. G. Yodh, “Hemodynamic responses to antivascular therapy and ionizing radiation assessed by diffuse optical spectroscopies,” Opt. Express 15(23), 15507–15516 (2007).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Yu, G.

U. Sunar, S. Makonnen, C. Zhou, T. Durduran, G. Yu, H. W. Wang, W. M. Lee, and A. G. Yodh, “Hemodynamic responses to antivascular therapy and ionizing radiation assessed by diffuse optical spectroscopies,” Opt. Express 15(23), 15507–15516 (2007).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Zhang, J.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Zhang, Q.

Zhou, C.

U. Sunar, S. Makonnen, C. Zhou, T. Durduran, G. Yu, H. W. Wang, W. M. Lee, and A. G. Yodh, “Hemodynamic responses to antivascular therapy and ionizing radiation assessed by diffuse optical spectroscopies,” Opt. Express 15(23), 15507–15516 (2007).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

Appl. Opt. (2)

Comput. Biomed. Res. (1)

R. W. Cox, “AFNI: software for analysis and visualization of functional magnetic resonance neuroimages,” Comput. Biomed. Res. 29(3), 162–173 (1996).
[CrossRef] [PubMed]

Hum. Brain Mapp. (1)

T. J. Huppert, M. S. Allen, S. G. Diamond, and D. A. Boas, “Estimating cerebral oxygen metabolism from fMRI with a dynamic multicompartment Windkessel model,” Hum. Brain Mapp. 30(5), 1548–1567 (2009) (PMCID: 2670946.).
[CrossRef] [PubMed]

Inverse Probl. (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), 14–93 (1999).
[CrossRef]

J. Am. Stat. Assoc. (1)

D. Harville, “Maximum likelihood approaches to variance component estimation and related problems,” J. Am. Stat. Assoc. 72(358), 320–338 (1977).
[CrossRef]

J. Biomed. Opt. (4)

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, “Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study,” J. Biomed. Opt. 11(6), 064021 (2006).
[CrossRef] [PubMed]

T. Wilcox, H. Bortfeld, R. Woods, E. Wruck, and D. A. Boas, “Using near-infrared spectroscopy to assess neural activation during object processing in infants,” J. Biomed. Opt. 10(1), 011010 (2005).
[CrossRef] [PubMed]

T. J. Huppert, S. G. Diamond, and D. A. Boas, “Direct estimation of evoked hemoglobin changes by multimodality fusion imaging,” J. Biomed. Opt. 13(5), 054031 (2008).
[CrossRef] [PubMed]

B. W. Pogue, S. C. Davis, X. Song, B. A. Brooksby, H. Dehghani, and K. D. Paulsen, “Image analysis methods for diffuse optical tomography,” J. Biomed. Opt. 11(3), 033001 (2006).
[CrossRef] [PubMed]

J. R. Stat. Soc., B (1)

A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,” J. R. Stat. Soc., B 39(1), 1–38 (1977).

Methods (1)

S. Perrey, “Non-invasive NIR spectroscopy of human brain function during exercise,” Methods 45(4), 289–299 (2008).
[CrossRef] [PubMed]

Neuroimage (5)

I. Miyai, H. C. Tanabe, I. Sase, H. Eda, I. Oda, I. Konishi, Y. Tsunazawa, T. Suzuki, T. Yanagida, and K. Kubota, “Cortical mapping of gait in humans: a near-infrared spectroscopic topography study,” Neuroimage 14(5), 1186–1192 (2001).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

J. Mattout, C. Phillips, W. D. Penny, M. D. Rugg, and K. J. Friston, “MEG source localization under multiple constraints: an extended Bayesian framework,” Neuroimage 30(3), 753–767 (2006).
[CrossRef] [PubMed]

K. J. Friston, W. Penny, C. Phillips, S. Kiebel, G. Hinton, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: theory,” Neuroimage 16(2), 465–483 (2002).
[CrossRef] [PubMed]

K. J. Friston, D. E. Glaser, R. N. Henson, S. Kiebel, C. Phillips, and J. Ashburner, “Classical and Bayesian inference in neuroimaging: applications,” Neuroimage 16(2), 484–512 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (2)

F. Abdelnour, B. Schmidt, and T. J. Huppert, “Topographic localization of brain activation in diffuse optical imaging using spherical wavelets,” Phys. Med. Biol. 54(20), 6383–6413 (2009) (PMCID: 2806654.).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50(4), R1–R43 (2005).
[CrossRef] [PubMed]

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I. Daubechies, Ten Lectures On Wavelets. SIAM, 1992.

K. J. Friston, Statistical parametric mapping: the analysis of functional brain images. 2007, London: Academic. vii, 647.

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Figures (13)

Fig. 1
Fig. 1

Diffuse optical imaging uses fiber optic based light sources and detectors to record changes in the optical absorption of underlying tissue. A grid of sensors is placed non-invasively on the head of a participant and used to measure changes in oxy- and deoxy-hemoglobin in the brain during task-evoked activation. The source-detector arrangement in the probe above is shown in Fig. 2.

Fig. 2
Fig. 2

Simulation (A) and optical probe geometry (B) used in the construction of sample problems in this work. This probe was based on a tomography (over-lapping measurement) design described in [18] consisting of eight source positions (circles) and fifteen detector postions (squares).

Fig. 3
Fig. 3

The optical inverse model was reparameterized in terms of wavelet coefficients. In the wavelet representation, the original image is described as a linear combination of low-pass, band-pass, and high-pass filter banks (left; for 1-dimensional case). The wavelet transform can be implemented in matrix form, which has the same filter structure (right) and will be used to apply a frequency bias to the superficial and deeper layers of the reconstruction.

Fig. 4
Fig. 4

This figure shows a comparison the ReML and L-curve tuned Tikhonov regularized reconstructions for simulations at low noise (signal-to-noise ratio of 100:1). In the top row (row-A), the original target (A1), the EM-reconstructed image (A2) and the L-curve reconstructed image (A3) of oxy-hemoglobin ( + 1μM simulated) is shown. In the bottom row (row-B) the original and reconstructed images of deoxy-hemoglobin (−0.25μM simulated). Notably, the ReML and L-curve techniques are nearly identical for this trivial case of only a single regularization hyper-parameter (λ = Λ12).

Fig. 5
Fig. 5

This figure shows a comparison the EM and L-curve tuned Tikhonov regularized reconstructions for simulations at high noise (signal-to-noise ratio of 5:1). The definitions of the subplots are identical to Fig. 4.

Fig. 6
Fig. 6

In this figure, we compare the value of the hyperparameter (λ) determined by the L-curve and ReML technique (REML λ = Λ12) for simulations with a contrast-to-noise ranging from 1:10 to 100,000:1 (half decade intervals). The L-curve and ReML techniques agree closely over this range implying that the ReML technique performs as well as the L-curve method for the trivial example of a single covariance component.

Fig. 7
Fig. 7

In this figure, a perturbation in oxy-hemoglobin only (row A) was simulated. No deoxy-hemogobin changes were simulated (row B). In the Tikhonov regularized inverse [Eq. (19)], which applies the same regularization factor to both the oxy- and deoxy-hemoglobin parameters, the L-curve technique (A3 and B3) gave a reliable estimate for oxy-hemoglobin, but this same level of regularization resulted in a very noisy deoxy-hemoglobin image. The ReML approach (A2 and B2) used separate hyperparameters to regularize the two hemoglobin species and resulted in close estimation of both images. Row B shows the deoxy-hemoglobin results.

Fig. 8
Fig. 8

In this figure, measurements were simulated to have a signal-to-noise ratio of 2:1 at the 830nm wavelength and only 1:2 at the 690nm wavelength. The resulting image reconstructions obtained via the ReML regularization using separate covariance components for oxy- and deoxy-hemoglon (A3 and B3) was very noisy (as expected at this very low SNR). The noise in the images was reduced when a third covariance component modeling the negative-covariance between oxy- and deoxy-hemoglobin was also included (A2 and B2). Row A and B show the oxy- and deoxy-hemoglobin images respectively. Subplot A1 and B1 are the simulated (truth) images.

Fig. 9
Fig. 9

In this figure, we compare reconstructions of the two-layered model. In rows A and B the superficial and deeper layers are shown. Only the oxy-hemoglobin results are shown. A perturbation was simulated only in deeper layer (B1). In A2 and B2, we show the reconstruction using a covariance component that spans both layers (akin to conventional Tikhonov regularization). Here, the same regularization is applied to both layers and the reconstructed image is heavily biased to the upper layer and underestimated. In A3 and B3, we show reconstructions using separate covariance components for the upper and lower level, which allows a total of four (2 layers x oxy- and deoxy-hemoglobin) hyperparameters to be estimated via the ReML method. This allows an empirically determined spatially distributed regularization of the model that results in correct placement of the reconstructed object in the bottom layer. This result is nearly identical to a cortically constrained reconstruction (B4) where the top layer is masked and only the bottom layer reconstructed.

Fig. 10
Fig. 10

In this figure, we compare image reconstructions in the case of a two-layered model with non-zero noise structure ( + 1μM) in the superficial layer (A1). Row A shows the top layer and row B shows the deeper (“brain”) layer. Only oxy-hemoglobin results are shown. In A2 and B2, we show the results using the reconstruction using the ReML approach with covariance components for the two layers but without any frequency bias (e.g. σ1 = σ2 = 1 voxel). In A3 and B3, the reconstruction using a low-frequency bias in the top layer is shown (σ1 = 2.2 voxels and σ2 = 1 voxel). In B4, the reconstruction with a cortical-constraint is shown, which artificially pulls the superficial noise into the bottom layer and results in a grossly overestimated signal.

Fig. 11
Fig. 11

In this figure, a two layer model with two perturbations placed either 6 voxels (40mm; row A) or 2 voxels (1.3 mm; row B) apart. Only the deeper layer and only the oxy-hemoglobin results are shown. In A2 and B2, we show the reconstructions using the ReML model without any specific region-of-interest priors. In A3 and B3, we show the reconstructions using a statistical region-of-interest prior. The arrows indicate the magnitude of the simulated values.

Fig. 12
Fig. 12

Here, we show cross-sections of the reconstructions shown in Fig. 11.

Fig. 13
Fig. 13

In this figure, we demonstrate the effects of using an incorrect region-of-interest prior. The simulated true image (A1; SNR = 10:1) had a single perturbation in the second layer. The top layer and deoxy-hemoglobin results are not shown. In A2, we show the reconstructed image without any region-of-interest priors. In B1, we show the reconstructed image using the correct region-of-interest as a prior (prior is outlined in black). Finally in B2, we show the reconstruction using an incorrectly placed region-of-interest prior (outlined in black). Using the incorrect prior produced nearly identical results to the case in which no prior was used demonstrating that the ReML method correctly assigned a near-zero weight to the incorrect prior.

Equations (22)

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

O D λ i , j = L λ i , j ( μ λ A , μ S λ ) + G λ i , j + υ λ i , j
O D λ i , j = L o g ( I λ i , j I λ 0 )
Δ O D λ i , j = A λ i , j ( μ λ A , μ S λ ) Δ μ λ A + υ λ i , j
Δ μ λ A λ , = ε H b O 2 λ ( Δ [ H b O 2 ] + ω H b O 2 ) + ε H b λ ( Δ [ H b ] + ω H b ) ,
Δ O D λ i , j = A λ i , j ( ε H b O 2 λ ( Δ [ H b O 2 ] + ω H b O 2 ) + ε H b λ ( Δ [ H b ] + ω H b ) ) + υ λ i , j
[ Δ O D λ 1 i , j Δ O D λ 2 i , j Δ O D λ N i , j ] = [ A λ 1 i , j ε H b O 2 λ 1 A λ i , j ε H b λ 1 A λ 2 i , j ε H b O 2 λ 2 A λ i , j ε H b λ 2 A λ N i , j ε H b O 2 λ N A λ i , j ε H b λ N ] ( [ Δ [ H b O 2 ] Δ [ H b ] ] + [ ω H b O 2 ω H b ] ) + [ υ λ 1 i , j υ λ 2 i , j υ λ N i , j ]
Y = H ( β + ω ) + υ
β = [ Δ [ H b O 2 ] Δ [ H b ] ]
arg min    β Y H β N 2
arg min    β Y H β N 2 + λ β β 0 P 2
arg min    β Y H β I 2 + λ 1 M β I 2 + λ 2 ( 1 M ) β I 2
M = | 1 if in region-of-interest 0 else
β = β 0 + ( H T N H + λ P ) 1 H T N ( Y H β 0 )
arg max    { β , C N , C P } 1 2 Y H β 2 C N 1 2 β β 0 2 C P 1 2 L o g | C N | 1 2 L o g | C P |
C N = i Λ i Q N , i C P = j Λ j Q P , j
β = β 0 + ( H T C 1 N H + C P 1 ) 1 H T C 1 N ( Y H β 0 )
β W = W β β = W T β W
Y = H W T ( β W + ω W ) + υ
β = ( H T H + λ I ) 1 H T Y
Q H b O 2 / H b = [ 0 I H b O 2 / H b I H b O 2 / H b 0 ]
Q L o w p a s s = [ I L o w p a s s 1 σ 2 I B a n d p a s s 1 σ 4 I H i g h p a s s ]
Q R O I { i , j } = | 1 if {i,j} in region-of-interest 0 else

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