Abstract

Diffuse optical correlation methods were adapted for three-dimensional (3D) tomography of cerebral blood flow (CBF) in small animal models. The image reconstruction was optimized using a noise model for diffuse correlation tomography which enabled better data selection and regularization. The tomographic approach was demonstrated with simulated data and during in-vivo cortical spreading depression (CSD) in rat brain. Three-dimensional images of CBF were obtained through intact skull in tissues deep (∼ 4 mm) below the skull surface.

© 2006 Optical Society of America

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2005 (5)

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

A. H. Hielscher, "Optical tomographic imaging of small animals," Curr. Opin. Biotechnol. 16, 79-88 (2005).
[CrossRef] [PubMed]

G. Q. Yu, T. Durduran, C. Zhou, H. W. Wang, M. E. Putt, H. M. Saunders, C. M. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
[CrossRef] [PubMed]

T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, "Diffuse Optical Measurement of Blood flow in Breast Tumors," Opt. Lett. 30, 2915-2917 (2005).
[CrossRef] [PubMed]

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, "Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy," J. Biomed. Opt. 10, 1-12 (2005).
[CrossRef]

2004 (6)

M. A. Franceschini and D. A. Boas, "Noninvasive measurement of neuronal activity with near-infrared optical imaging," Neuroimage 21, 372-386 (2004).
[CrossRef] [PubMed]

J. Choi, M. Wolf, V. Toronov, U. Wolf, C. Polzonetti, D. Hueber, L. P. Safonova, A. Gupta, R. Michalos,W. Mantulin, and E. Gratton, "Noninvasive determination of the optical properties of adult brain: near-infrared spectroscopy approach," J. Biomed. Opt. 9, 221-229 (2004).
[CrossRef] [PubMed]

T. Durduran, G. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, 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]

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, "Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

C. Ayata, H. K. Shin, S. Salomone, Y. Ozdemir-Gursoy, D. A. Boas, A. K. Dunn, and M. A. Moskowitz, "Pronounced hypoperfusion during spreading depression in mouse cortex," J. Cereb. Blood Flow Metab. 24, 1172-1182 (2004).
[CrossRef] [PubMed]

X. M. Song, B. W. Pogue, S. D. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, "Automated region detection based on the contrast-to-noise ratio in near-infrared tomography," Appl. Optics 43, 1053-1062 (2004).
[CrossRef]

2003 (4)

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003).
[CrossRef] [PubMed]

A. K. Dunn, A. Devor, H. Bolay, M. L. Andermann, M. A. Moskowitz, A. M. Dale, and D. A. Boas, "Simultaneous imaging of total cerebral hemoglobin concentration, oxygenation, and blood flow during functional activation," Opt. Lett. 28, 28-30 (2003).
[CrossRef] [PubMed]

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

J. P. Culver, T. Durduran, T. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, "Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia," J. Cereb. Blood Flow Metab. 23, 911-924 (2003).
[CrossRef] [PubMed]

2002 (1)

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, "Three-dimensional optical tomography of the premature infant brain," Phys. Med. Biol. 47, 4155-4166 (2002).
[CrossRef] [PubMed]

2001 (8)

T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).
[CrossRef] [PubMed]

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001).
[CrossRef]

D. M. Hueber,M. A. Franceschini, H. Y. Ma, Q. Zhang, J. R. Ballesteros, S. Fantini, D. Wallace, V. Ntziachristos, and B. Chance, "Non-invasive and quantitative near-infrared haemoglobin spectrometry in the piglet brain during hypoxic stress, using a frequency-domain multidistance instrument," Phys. Med. Biol. 46, 41-62. (2001).
[CrossRef] [PubMed]

A. Bluestone, G. Abdoulaev, C. Schmitz, R. Barbour, and A. Hielscher, "Three-dimensional optical tomography of hemodynamics in the human head," Opt. Express 9, 272-286 (2001).
[CrossRef] [PubMed]

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

A. Gorji, "Spreading depression: a review of the clinical relevance," Brain Res. Rev. 38, 33-60 (2001).
[CrossRef] [PubMed]

G. G. Somjen, "Mechanisms of spreading depression and hypoxic spreading depression-like depolarization," Physiol. Rev. 81, 1065-1096 (2001).
[PubMed]

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, "Dynamic imaging of cerebral blood flow using laser speckle," J. Cereb. Blood Flow Metab. 21, 195-201 (2001).
[CrossRef] [PubMed]

2000 (3)

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
[CrossRef] [PubMed]

A. N. Nielsen, M. Fabricius, and M. Lauritzen, "Scanning laser-Doppler flowmetry of rat cerebral circulation during cortical spreading depression," J. Vasc. Res. 37, 513-522 (2000).
[CrossRef]

J. Sonn and A. Mayevsky, "Effects of brain oxygenation on metabolic, hemodynamic, ionic and electrical responses to spreading depression in the rat," Brain Res. 882, 212-216 (2000).
[CrossRef] [PubMed]

1999 (6)

P. A. Lemieux and D. J. Durian, "Investigating non-Gaussian scattering processes by using nth-order intensity correlation functions," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 16, 1651-1664 (1999).
[CrossRef]

U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

R. D. Hoge, J. Atkinson, B. Gill, G. R. Crelier, S. Marrett, and G. B. Pike, "Investigation of BOLD signal dependence on cerebral blood flow and oxygen consumption: the deoxyhemoglobin dilution model," Magn. Reson. Med. 42, 849-63 (1999).
[CrossRef] [PubMed]

J. A. Detre and D. C. Alsop, "Perfusion magnetic resonance imaging with continuous arterial spin labeling: methods and clinical applications in the central nervous system," Eur. J. Radiol. 30, 115-124 (1999).
[CrossRef] [PubMed]

S. R. Arridge, "Optical Tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, "Spatially variant regularization improves diffuse optical tomography," Appl. Optics 38, 2950-2961 (1999).
[CrossRef]

1998 (3)

G. Zaharchuk, J. Bogdanov, A. A., J. J. Marota, M. Shimizu-Sasamata, R. M. Weisskoff, K. K. Kwong, B. G. Jenkins, R. Weissleder, and B. R. Rosen, "Continuous assessment of perfusion by tagging including volume and water extraction (CAPTIVE): a steady-state contrast agent technique for measuring blood flow, relative blood volume fraction, and the water extraction fraction," Magn. Reson. Med. 40, 666-678. (1998).
[CrossRef] [PubMed]

B. W. Pogue and K. D. Paulsen, "High-resolution near-infrared tomographic imaging simulations of the rat cranium by use of apriori magnetic resonance imaging structural information," Opt. Lett. 23, 1716-1718 (1998).
[CrossRef]

M. Kohl, U. Lindauer, U. Dirnagl, and A. Villringer, "Separation of changes in light scattering and chromophore concentrations during cortical spreading depression in rats," Opt. Lett. 23, 555-557 (1998).
[CrossRef]

1997 (4)

A. Villringer and B. Chance, "Non-invasive optical spectroscopy and imaging of human brain function," Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

G. Gratton, M. Fabiani, P. M. Corballis, D. C. Hood, M. R. Goodman-Wood, J. Hirsch, K. Kim, D. Friedman, and E. Gratton, "Fast and localized event-related optical signals (EROS) in the human occipital cortex: comparisons with the visual evoked potential and fMRI." Neuroimage 6, 168-180 (1997).
[CrossRef] [PubMed]

D. A. Boas and A. G. Yodh, "Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 14, 192-215 (1997).
[CrossRef]

M. Heckmeier, S. E. Skipetrov, G. Maret, and R. Maynard, "Imaging of dynamic heterogeneities in multiplescattering media," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 14, 185-191 (1997).
[CrossRef]

1995 (3)

D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and Imaging with Diffusing Temporal Field Correla-tions," Phys. Rev. Lett. 75, 1855-1858 (1995).
[CrossRef] [PubMed]

A. Yodh and B. Chance, "Spectroscopy and Imaging with Diffusing Light," Phys. Today 48, 34-40 (1995).
[CrossRef]

M. Lauritzen and M. Fabricius, "Real time laser-Doppler perfusion imaging of cortical spreading depression in rat neocortex," Neuroreport 6, 1271-1273 (1995).
[CrossRef] [PubMed]

1994 (2)

R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 11, 2727-2741 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media - analytic solution and applications," Proc. Natl. Acad. Sci. U. S. A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

1993 (1)

D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering and Wavelength Transduction of Diffuse Photon Density Waves," Phys. Rev. E 47, R2999-R3002 (1993).
[CrossRef]

1992 (3)

P. Hansen, "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Rev. 34, 561-580 (1992).
[CrossRef]

D. S. Williams, J. A. Detre, J. S. Leigh, and A. P. Koretsky, "Magnetic resonance imaging of perfusion using spin inversion of arterial water." Proc. Natl. Acad. Sci. U. S. A. 89, 212-216 (1992).
[CrossRef] [PubMed]

M. A. Oleary, D. A. Boas, B. Chance, and A. G. Yodh, "Refraction of diffuse photon density waves," Phys. Rev. Lett. 69, 2658-2661 (1992).
[CrossRef]

1991 (1)

A. Mayevsky and H. R. Weiss, "Cerebral Blood-Flow and Oxygen-Consumption in Cortical Spreading Depression," J. Cereb. Blood Flow Metab. 11, 829-836 (1991).
[CrossRef] [PubMed]

1988 (1)

K. Schatzel, M. Drewel, and S. Stimac, "Photon-Correlation Measurements at Large Lag Times - Improving Statistical Accuracy," J. Mod. Opt. 35, 711-718 (1988).
[CrossRef]

1987 (1)

G. Maret and P. Wolf, "Multiple light scattering from disordered media. The effect of brownian motion of scatterers," Z. Phys. B. 65, 409-413 (1987).
[CrossRef]

1983 (1)

K. Schatzel, "Noise in photon-correlation and photon structure functions," Optica ACTA 30, 155-166 (1983).
[CrossRef]

1980 (1)

R. S. J. Frackowiak, G. L. Lenzi, T. Jones, and J. D. Heather, "Quantitative Measurement of Regional Cerebral Blood-Flow and Oxygen-Metabolism in Man Using O-15 and Positron Emission Tomography - Theory, Procedure, and Normal Values," J. Comput. Assist. Tomogr. 4, 727-736 (1980).
[CrossRef] [PubMed]

1974 (2)

D. E. Koppel, "Statistical accuracy in fluorescence correlation spectroscopy," Phys. Rev. A 10, 1938-1945 (1974).
[CrossRef]

A. Mayevsky and B. Chance, "Repetitive Patterns of Metabolic Changes During Cortical Spreading Depression of Awake Rat," Brain Res. 65, 529-533 (1974).
[CrossRef] [PubMed]

1970 (1)

C. D. Cantrell, "N-Fold Photonelectric counting statistics of gaussian light," Phys. Rev. A 1, 672-685 (1970).
[CrossRef]

1967 (1)

L. D. Lukyanov and J. Bures, "Changes in PO2 Due to Spreading Depression in Cortex and Nucleus Caudatus of Rat," Physiologia Bohemoslovaca 16, 449-455 (1967).

1944 (1)

A. A. P. Leao, "Spreading depression of activity in cerebral cortex," J. Neurophysiol. 7, 359-390 (1944).

Abdoulaev, G.

Alsop, D. C.

J. A. Detre and D. C. Alsop, "Perfusion magnetic resonance imaging with continuous arterial spin labeling: methods and clinical applications in the central nervous system," Eur. J. Radiol. 30, 115-124 (1999).
[CrossRef] [PubMed]

Andermann, M. L.

Arridge, S. R.

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

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, "Three-dimensional optical tomography of the premature infant brain," Phys. Med. Biol. 47, 4155-4166 (2002).
[CrossRef] [PubMed]

S. R. Arridge, "Optical Tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

Atkinson, J.

R. D. Hoge, J. Atkinson, B. Gill, G. R. Crelier, S. Marrett, and G. B. Pike, "Investigation of BOLD signal dependence on cerebral blood flow and oxygen consumption: the deoxyhemoglobin dilution model," Magn. Reson. Med. 42, 849-63 (1999).
[CrossRef] [PubMed]

Austin, T.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, "Three-dimensional optical tomography of the premature infant brain," Phys. Med. Biol. 47, 4155-4166 (2002).
[CrossRef] [PubMed]

Ayata, C.

C. Ayata, H. K. Shin, S. Salomone, Y. Ozdemir-Gursoy, D. A. Boas, A. K. Dunn, and M. A. Moskowitz, "Pronounced hypoperfusion during spreading depression in mouse cortex," J. Cereb. Blood Flow Metab. 24, 1172-1182 (2004).
[CrossRef] [PubMed]

Ballesteros, J. R.

D. M. Hueber,M. A. Franceschini, H. Y. Ma, Q. Zhang, J. R. Ballesteros, S. Fantini, D. Wallace, V. Ntziachristos, and B. Chance, "Non-invasive and quantitative near-infrared haemoglobin spectrometry in the piglet brain during hypoxic stress, using a frequency-domain multidistance instrument," Phys. Med. Biol. 46, 41-62. (2001).
[CrossRef] [PubMed]

Barbour, R.

Benaron, D. A.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
[CrossRef] [PubMed]

Bluestone, A.

Boas, D.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
[CrossRef] [PubMed]

Boas, D. A.

C. Ayata, H. K. Shin, S. Salomone, Y. Ozdemir-Gursoy, D. A. Boas, A. K. Dunn, and M. A. Moskowitz, "Pronounced hypoperfusion during spreading depression in mouse cortex," J. Cereb. Blood Flow Metab. 24, 1172-1182 (2004).
[CrossRef] [PubMed]

M. A. Franceschini and D. A. Boas, "Noninvasive measurement of neuronal activity with near-infrared optical imaging," Neuroimage 21, 372-386 (2004).
[CrossRef] [PubMed]

A. K. Dunn, A. Devor, H. Bolay, M. L. Andermann, M. A. Moskowitz, A. M. Dale, and D. A. Boas, "Simultaneous imaging of total cerebral hemoglobin concentration, oxygenation, and blood flow during functional activation," Opt. Lett. 28, 28-30 (2003).
[CrossRef] [PubMed]

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, "Dynamic imaging of cerebral blood flow using laser speckle," J. Cereb. Blood Flow Metab. 21, 195-201 (2001).
[CrossRef] [PubMed]

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001).
[CrossRef]

D. A. Boas and A. G. Yodh, "Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 14, 192-215 (1997).
[CrossRef]

D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and Imaging with Diffusing Temporal Field Correla-tions," Phys. Rev. Lett. 75, 1855-1858 (1995).
[CrossRef] [PubMed]

D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media - analytic solution and applications," Proc. Natl. Acad. Sci. U. S. A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering and Wavelength Transduction of Diffuse Photon Density Waves," Phys. Rev. E 47, R2999-R3002 (1993).
[CrossRef]

M. A. Oleary, D. A. Boas, B. Chance, and A. G. Yodh, "Refraction of diffuse photon density waves," Phys. Rev. Lett. 69, 2658-2661 (1992).
[CrossRef]

Bogdanov, J.

G. Zaharchuk, J. Bogdanov, A. A., J. J. Marota, M. Shimizu-Sasamata, R. M. Weisskoff, K. K. Kwong, B. G. Jenkins, R. Weissleder, and B. R. Rosen, "Continuous assessment of perfusion by tagging including volume and water extraction (CAPTIVE): a steady-state contrast agent technique for measuring blood flow, relative blood volume fraction, and the water extraction fraction," Magn. Reson. Med. 40, 666-678. (1998).
[CrossRef] [PubMed]

Bolay, H.

Brooks, D. H.

D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001).
[CrossRef]

Buerk, D. G.

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

Bures, J.

L. D. Lukyanov and J. Bures, "Changes in PO2 Due to Spreading Depression in Cortex and Nucleus Caudatus of Rat," Physiologia Bohemoslovaca 16, 449-455 (1967).

Burnett, M. G.

T. Durduran, G. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, 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]

T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, "Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
[CrossRef] [PubMed]

Busch, T. M.

G. Q. Yu, T. Durduran, C. Zhou, H. W. Wang, M. E. Putt, H. M. Saunders, C. M. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
[CrossRef] [PubMed]

Campbell, L. E.

D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and Imaging with Diffusing Temporal Field Correla-tions," Phys. Rev. Lett. 75, 1855-1858 (1995).
[CrossRef] [PubMed]

Cantrell, C. D.

C. D. Cantrell, "N-Fold Photonelectric counting statistics of gaussian light," Phys. Rev. A 1, 672-685 (1970).
[CrossRef]

Chance, B.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003).
[CrossRef] [PubMed]

D. M. Hueber,M. A. Franceschini, H. Y. Ma, Q. Zhang, J. R. Ballesteros, S. Fantini, D. Wallace, V. Ntziachristos, and B. Chance, "Non-invasive and quantitative near-infrared haemoglobin spectrometry in the piglet brain during hypoxic stress, using a frequency-domain multidistance instrument," Phys. Med. Biol. 46, 41-62. (2001).
[CrossRef] [PubMed]

A. Villringer and B. Chance, "Non-invasive optical spectroscopy and imaging of human brain function," Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

A. Yodh and B. Chance, "Spectroscopy and Imaging with Diffusing Light," Phys. Today 48, 34-40 (1995).
[CrossRef]

D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media - analytic solution and applications," Proc. Natl. Acad. Sci. U. S. A. 91, 4887-4891 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering and Wavelength Transduction of Diffuse Photon Density Waves," Phys. Rev. E 47, R2999-R3002 (1993).
[CrossRef]

M. A. Oleary, D. A. Boas, B. Chance, and A. G. Yodh, "Refraction of diffuse photon density waves," Phys. Rev. Lett. 69, 2658-2661 (1992).
[CrossRef]

A. Mayevsky and B. Chance, "Repetitive Patterns of Metabolic Changes During Cortical Spreading Depression of Awake Rat," Brain Res. 65, 529-533 (1974).
[CrossRef] [PubMed]

Cheong, W. F.

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
[CrossRef] [PubMed]

Cheung, C.

J. P. Culver, T. Durduran, T. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, "Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia," J. Cereb. Blood Flow Metab. 23, 911-924 (2003).
[CrossRef] [PubMed]

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Choe, R.

T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, "Diffuse Optical Measurement of Blood flow in Breast Tumors," Opt. Lett. 30, 2915-2917 (2005).
[CrossRef] [PubMed]

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003).
[CrossRef] [PubMed]

Choi, J.

J. Choi, M. Wolf, V. Toronov, U. Wolf, C. Polzonetti, D. Hueber, L. P. Safonova, A. Gupta, R. Michalos,W. Mantulin, and E. Gratton, "Noninvasive determination of the optical properties of adult brain: near-infrared spectroscopy approach," J. Biomed. Opt. 9, 221-229 (2004).
[CrossRef] [PubMed]

Corballis, P. M.

G. Gratton, M. Fabiani, P. M. Corballis, D. C. Hood, M. R. Goodman-Wood, J. Hirsch, K. Kim, D. Friedman, and E. Gratton, "Fast and localized event-related optical signals (EROS) in the human occipital cortex: comparisons with the visual evoked potential and fMRI." Neuroimage 6, 168-180 (1997).
[CrossRef] [PubMed]

Crelier, G. R.

R. D. Hoge, J. Atkinson, B. Gill, G. R. Crelier, S. Marrett, and G. B. Pike, "Investigation of BOLD signal dependence on cerebral blood flow and oxygen consumption: the deoxyhemoglobin dilution model," Magn. Reson. Med. 42, 849-63 (1999).
[CrossRef] [PubMed]

Culver, J. P.

J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003).
[CrossRef] [PubMed]

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

J. P. Culver, T. Durduran, T. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, "Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia," J. Cereb. Blood Flow Metab. 23, 911-924 (2003).
[CrossRef] [PubMed]

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Czerniecki, B. J.

Dale, A. M.

Dehghani, H.

X. M. Song, B. W. Pogue, S. D. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, "Automated region detection based on the contrast-to-noise ratio in near-infrared tomography," Appl. Optics 43, 1053-1062 (2004).
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T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, "Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
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A. P. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50, R1-R43 (2005).
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D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
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G. Gratton, M. Fabiani, P. M. Corballis, D. C. Hood, M. R. Goodman-Wood, J. Hirsch, K. Kim, D. Friedman, and E. Gratton, "Fast and localized event-related optical signals (EROS) in the human occipital cortex: comparisons with the visual evoked potential and fMRI." Neuroimage 6, 168-180 (1997).
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D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
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R. D. Hoge, J. Atkinson, B. Gill, G. R. Crelier, S. Marrett, and G. B. Pike, "Investigation of BOLD signal dependence on cerebral blood flow and oxygen consumption: the deoxyhemoglobin dilution model," Magn. Reson. Med. 42, 849-63 (1999).
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J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003).
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G. Gratton, M. Fabiani, P. M. Corballis, D. C. Hood, M. R. Goodman-Wood, J. Hirsch, K. Kim, D. Friedman, and E. Gratton, "Fast and localized event-related optical signals (EROS) in the human occipital cortex: comparisons with the visual evoked potential and fMRI." Neuroimage 6, 168-180 (1997).
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C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
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J. Choi, M. Wolf, V. Toronov, U. Wolf, C. Polzonetti, D. Hueber, L. P. Safonova, A. Gupta, R. Michalos,W. Mantulin, and E. Gratton, "Noninvasive determination of the optical properties of adult brain: near-infrared spectroscopy approach," J. Biomed. Opt. 9, 221-229 (2004).
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D. M. Hueber,M. A. Franceschini, H. Y. Ma, Q. Zhang, J. R. Ballesteros, S. Fantini, D. Wallace, V. Ntziachristos, and B. Chance, "Non-invasive and quantitative near-infrared haemoglobin spectrometry in the piglet brain during hypoxic stress, using a frequency-domain multidistance instrument," Phys. Med. Biol. 46, 41-62. (2001).
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J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, "Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy," J. Biomed. Opt. 10, 1-12 (2005).
[CrossRef]

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X. M. Song, B. W. Pogue, S. D. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, "Automated region detection based on the contrast-to-noise ratio in near-infrared tomography," Appl. Optics 43, 1053-1062 (2004).
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R. S. J. Frackowiak, G. L. Lenzi, T. Jones, and J. D. Heather, "Quantitative Measurement of Regional Cerebral Blood-Flow and Oxygen-Metabolism in Man Using O-15 and Positron Emission Tomography - Theory, Procedure, and Normal Values," J. Comput. Assist. Tomogr. 4, 727-736 (1980).
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D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
[CrossRef] [PubMed]

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D. A. Boas, D. H. Brooks, E. L. Miller, C. A. DiMarzio, M. Kilmer, R. J. Gaudette, and Q. Zhang, "Imaging the body with diffuse optical tomography," IEEE Signal Process. Mag. 18, 57-75 (2001).
[CrossRef]

Kim, K.

G. Gratton, M. Fabiani, P. M. Corballis, D. C. Hood, M. R. Goodman-Wood, J. Hirsch, K. Kim, D. Friedman, and E. Gratton, "Fast and localized event-related optical signals (EROS) in the human occipital cortex: comparisons with the visual evoked potential and fMRI." Neuroimage 6, 168-180 (1997).
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J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, "Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy," J. Biomed. Opt. 10, 1-12 (2005).
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D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong, and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-477 (2000).
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X. M. Song, B. W. Pogue, S. D. Jiang, M. M. Doyley, H. Dehghani, T. D. Tosteson, and K. D. Paulsen, "Automated region detection based on the contrast-to-noise ratio in near-infrared tomography," Appl. Optics 43, 1053-1062 (2004).
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R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, and B. J. Tromberg, "Boundary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 11, 2727-2741 (1994).
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U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

Wallace, D.

D. M. Hueber,M. A. Franceschini, H. Y. Ma, Q. Zhang, J. R. Ballesteros, S. Fantini, D. Wallace, V. Ntziachristos, and B. Chance, "Non-invasive and quantitative near-infrared haemoglobin spectrometry in the piglet brain during hypoxic stress, using a frequency-domain multidistance instrument," Phys. Med. Biol. 46, 41-62. (2001).
[CrossRef] [PubMed]

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G. Q. Yu, T. Durduran, C. Zhou, H. W. Wang, M. E. Putt, H. M. Saunders, C. M. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
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Weiss, H. R.

A. Mayevsky and H. R. Weiss, "Cerebral Blood-Flow and Oxygen-Consumption in Cortical Spreading Depression," J. Cereb. Blood Flow Metab. 11, 829-836 (1991).
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D. S. Williams, J. A. Detre, J. S. Leigh, and A. P. Koretsky, "Magnetic resonance imaging of perfusion using spin inversion of arterial water." Proc. Natl. Acad. Sci. U. S. A. 89, 212-216 (1992).
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T. Wohland, R. Rigler, and H. Vogel, "The standard deviation in fluorescence correlation spectroscopy," Biophys. J. 80, 2987-2999 (2001).
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U. Meseth, T. Wohland, R. Rigler, and H. Vogel, "Resolution of fluorescence correlation measurements," Biophys. J. 76, 1619-1631 (1999).

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J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, "Three-dimensional optical tomography of the premature infant brain," Phys. Med. Biol. 47, 4155-4166 (2002).
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A. Yodh and B. Chance, "Spectroscopy and Imaging with Diffusing Light," Phys. Today 48, 34-40 (1995).
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G. Q. Yu, T. Durduran, C. Zhou, H. W. Wang, M. E. Putt, H. M. Saunders, C. M. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
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T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, "Diffuse Optical Measurement of Blood flow in Breast Tumors," Opt. Lett. 30, 2915-2917 (2005).
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T. Durduran, G. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, 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).
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T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, "Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
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J. P. Culver, T. Durduran, T. Furuya, C. Cheung, J. H. Greenberg, and A. G. Yodh, "Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia," J. Cereb. Blood Flow Metab. 23, 911-924 (2003).
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C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
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D. A. Boas and A. G. Yodh, "Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation," J. Opt. Soc. Am. A-Opt. Image Sci. Vis. 14, 192-215 (1997).
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D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and Imaging with Diffusing Temporal Field Correla-tions," Phys. Rev. Lett. 75, 1855-1858 (1995).
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D. A. Boas, M. A. Oleary, B. Chance, and A. G. Yodh, "Scattering and Wavelength Transduction of Diffuse Photon Density Waves," Phys. Rev. E 47, R2999-R3002 (1993).
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M. A. Oleary, D. A. Boas, B. Chance, and A. G. Yodh, "Refraction of diffuse photon density waves," Phys. Rev. Lett. 69, 2658-2661 (1992).
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Yu, G.

Yu, G. Q.

G. Q. Yu, T. Durduran, C. Zhou, H. W. Wang, M. E. Putt, H. M. Saunders, C. M. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
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J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, "Three-dimensional optical tomography of the premature infant brain," Phys. Med. Biol. 47, 4155-4166 (2002).
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T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, "Diffuse Optical Measurement of Blood flow in Breast Tumors," Opt. Lett. 30, 2915-2917 (2005).
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T. Durduran, G. Yu, M. G. Burnett, J. A. Detre, J. H. Greenberg, 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).
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T. Durduran, M. G. Burnett, G. Yu, C. Zhou, D. Furuya, A. G. Yodh, J. A. Detre, and J. H. Greenberg, "Spatiotemporal Quantification of Cerebral Blood Flow During Functional Activation in Rat Somatosensory Cortex Using Laser-Speckle Flowmetry," J. Cereb. Blood Flow Metab. 24, 518-525 (2004).
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J. P. Culver, R. Choe, M. J. Holboke, L. Zubkov, T. Durduran, A. Slemp, V. Ntziachristos, B. Chance, and A. G. Yodh, "Three-dimensional diffuse optical tomography in the parallel plane transmission geometry: Evaluation of a hybrid frequency domain/continuous wave clinical system for breast imaging," Med. Phys. 30, 235-247 (2003).
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Supplementary Material (1)

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Figures (12)

Fig. 1.
Fig. 1.

Experimental setup used to test the accuracy of the noise model. One source-detector pair, with a 1 cm separation, is placed into an Intralipid phantom. A long coherence length laser (∼ 50 m) is provides light to the phantom. In order to test the noise-model under different signal-to-noise ratio conditions, the input power is adjusted manually using an optical attenuator connected to the input fiber. The light is detected by a photon counting APD the output of which is fed into a correlator board to calculate the normalized intensity auto-correlation function g 2(τ). g 2(τ) is then collected and saved in a desktop computer. A hundred g 2(τ) curves are measured under the same conditions. The measurement noise, plotted in Fig. 2(a), is calculated as the standard deviation of the fluctuation at each delay time τ.

Fig. 2.
Fig. 2.

(a) Comparison of measured noise (dots) and calculated noises using the model (solid lines). All input parameters for the noise model are obtained from experiments. Measurement noise decreases as the delay time τ increases. The “steps” are due to the multi-tau arrangement of our correlator. (b) Signal-to-Noise Ratio (SNR) comparison of the measured correlation curves and the model predictions. Although the measurement noise decreases as the delay time τ increases, the SNR of the DCS measurements also decreases because the “signal” drops even faster as τ increases. (kcps = kilo-counts per second)

Fig. 3.
Fig. 3.

Example of the field auto-correlation function g 1(τ). Points corresponding to different values of n are notated n is defined as the point where g 1(τ) decreases to exp(-n) of its initial value (i.e. we write g 1(τ) = exp(-n)g 1(0)).

Fig. 4.
Fig. 4.

Simulation geometry: (a) A spherical object with a radius of 0.2 cm is placed in a homogeneous background at three distances from the source/detector plane (0.4 cm, 0.2 cm, 0.4 cm). The dynamic property of the object is 10% lower than the background (αDb , = 0.9 × 10-8 cm2/s, αDb0 = 1 × 10-8 cm2/s). The static optical properties of the sphere and background are the same (μa = 0.1 cm-1, μs ́ = 8 cm-1). (b) 25 sources and 16 detectors are placed at the z = 0 cm plane and cover a region ranging from -0.6 cm to 0.6 cm in both the x and y dimensions. An analytical solution is used for the simulation. Measurement noise is calculated and added to the simulated data with a normal distribution.

Fig. 5.
Fig. 5.

Choice of the optimal data set and optimal regularization parameter: (a) The normalzed image noise σ ϕ s ϕ s N c plotted as a function of n. The optimal data set is obtained at n = 1, where the upper limit of the normalized image noise is a minimum. (b) L-Curves with noisy data at different n are plotted to identify the optimal regularization parameter λ. The n = 1 curve is the closest to the origin, which also indicates the advantage of using a data set with n = 1 for image reconstruction.

Fig. 6.
Fig. 6.

Reconstructed images using data with n = 1. Reconstructed 3D images cover the region (x: -0.8 cm - 0.8 cm, y: -0.8 cm - 0.8 cm, z: 0 cm - 0.8 cm) with 1 mm3 voxels. Images at every 2 mm along the z direction are shown (from left to right). The depth for each layer is marked for each column. (a) Simulation (Sim) geometry. (b) Reconstructed images using data directly from the noisy raw data (Direct Raw-data Reconstruction, DRR). The object is found at a displaced layer (z=0.6 cm). (c) Images using data from the fitted curve (by minimizing ∥g 2m (τ) - g 2c (τ)∥) to reconstruct the images (Smoothed Fitting Reconstruction, SFR). Image artifacts are greatly reduced. (d) Using noise information in the fitting process (by minimizing g 2 m ( τ ) g 2 c ( τ ) σ ( τ ) ) can further improve the image quality (Noise Fitting Reconstruction, NFR).

Fig. 7.
Fig. 7.

Quantitative comparison of different image reconstruction schemes: (a) Volume weighted rCBF for the reconstructed object normalized to the simulation (Sim). Noise Fitting Reconstruction (NFR) gives the most accurate value compared to the simulation. (b) Distance from the center of the simulation to the center of the reconstructed object. NFR provides the best location accuracy (∼ 1 mm). (c) Contrast to noise ratio (CNR) of the reconstructed images. NFR gives the highest CNR over the three reconstruction schemes.

Fig. 8.
Fig. 8.

System setup for the in-vivo rat brain CSD study. A grid-like pattern of source/detector fibers (3 sources, 8 detectors) was mounted on the back of a 35 mm camera body. The light was sent to and detected from the tissues through a relay lens avoiding contact with the tissue. Light from a CW, long coherence length laser operating at 800 nm was connected to the non-contact probe through optical switches in order to time-share the source positions. The output of the APDs was fed into a custom built correlator board which calculated the intensity auto-correlation function g 2(τ). The whole system was automated and controlled by a desktop computer and a full frame was acquired every ∼ 6.5 seconds.

Fig. 9.
Fig. 9.

Cortical Spreading Depresstion (CSD); During experiments, a rat was fixed on a stereotaxic frame with the scalp retracted and the skull intact. CSD was induced by placing KCl solution on the rat brain through a small hole drilled on the skull. Periodic activations and deactivations of the neurons then spread out radially on the cortex as shown on the sketch.

Fig. 10.
Fig. 10.

Reconstructed 3D rCBF images at different layers (from top to bottom) of the rat brain during CSD. CSD is induced at the top, slightly to the left of the midline (∼ x = 0 mm). Images (from left to right) are shown about every 20 seconds from immediately before KCl was applied until the end of the first CSD peak. rCBF responses are mainly localized to the cortex and spread across the cortex tangentially from the point where KCl was applied. No significant activity is visible in the top panel, which corresponds to the skull, and in the bottom panel, which penetrates below the cortex, indicating that the activity is localized in the cortex. Images are oriented as shown in Fig. 8(b).

Fig. 11.
Fig. 11.

rCBF changes on the cortex of the rat brain during CSD. Images (from left to right, from top to bottom) are shown roughly every 20 seconds from immediately before KCl was applied until the end of the second CSD peak. The panel titles indicate the corresponding time point. A strong increase in blood flow appears from the top and proceeds to the bottom of the image. After the peak, there is a sustained decrease in blood flow which covers most of the image area. Three regions of interest (ROI) were selected and the time series of rCBF changes from these ROIs are plotted in Fig. 12(a). A movie showing the rCBF changes at different brain layers during CSD is also provided as supporting media (1.5MB). [Media 1]

Fig. 12.
Fig. 12.

(a) Time series of rCBF changes from three ROIs illustrated in Fig. 11. From these curves, the propagation of the CSD waves can be clearly identified. (b) Dependence of maximum rCBF on depth in the second region of interest. The maximal change is localized at a depth of 1 mm below the skull This corresponds to the surface of the cortex. The peak spreads ∼ 0.5 mm above and below the cortical surface as expected from the broadening due to the diffuse nature of photons (see text). There is no significant change at the surface (skull) or in deeper regions.

Equations (29)

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( D G 1 ( r , τ ) ) ( v μ a + 1 3 v μ s k 0 2 α Δ r 2 ( τ ) ) G 1 ( r , τ ) = v S δ 3 ( r r s ) .
G 1 ( r , τ ) = v S e K ( τ ) r 1 4 π D r 1 v S e K ( τ ) r 2 4 π D r 2 ,
g 2 ( r , τ ) = 1 + β g 1 ( r , τ ) 2 .
ϕ s ( r si , r di , τ ) = ln g 1 ( r si , r di , τ ) g 1,0 ( r si , r di , τ ) = j = 1 N W ij ( r si , r di , r j , τ ) Δ ( α D b ( r j ) ) .
W ij ( r si , r di , r j , τ ) = 2 v μ s k 0 2 τ G 1 ( r si , r j , τ ) H ( r j , r di , τ ) DG 1 ( r si , r di , τ ) ,
Δ ( α D b ( r ) ) = W T ( W W T + λ I ) 1 ϕ s ,
λ ( z ) = λ c + λ e ( e ( z z max ) z max 1 ) ,
σ ( τ ) = T t [ β 2 ( 1 + e 2 Γ T ) ( 1 + e 2 Γ T ) + 2 m ( 1 e 2 Γ T ) e 2 Γ T ( 1 e 2 Γ T )
+ 2 n 1 β ( 1 + e 2 Γ T ) + n 2 ( 1 + e 2 Γ τ ) ] 1 2 .
σ ϕ s ( r si , r di , r j , τ ) = 1 2 σ ( r si , r j , τ ) ( g 2 ( r si , r di , τ ) 1 ) = 1 2 1 SNR .
τ = 1 μ s k 0 2 α D b ( n 2 r s r d 2 2 n 3 μ a μ s r s r d ) .
σ Δ ( α D b ) Δ ( α D b ) σ ϕ s ϕ s N c ,
CNR = rCBF ROI ¯ rCBF bg ¯ ( ω ROI σ ROI 2 + ω bg σ bg 2 ) 1 2 .
G ̂ 2 ( τ ) = 1 N i = 1 N n ( iT ) n ( iT + τ ) ,
S ̂ ( τ ) G ̂ 2 ( τ ) n ̂ 2 ,
n ̂ 2 = [ n ( n n ̂ ) ] 2
n 2 ( 1 2 n n ̂ n )
= 2 n n ̂ n 2 .
σ ( τ ) = var ( S ̂ ( τ ) ) n 4 .
var ( S ̂ ( τ ) ) = var ( G ̂ 2 ( τ ) 2 n n ̂ )
= var ( 1 N i = 1 N n ( iT ) [ n ( iT + τ ) 2 n ] ) .
x ( iT ) n ( iT ) [ n ( iT + τ ) 2 n ] ,
var ( S ̂ ( τ ) ) = N 1 var ( x ) + 2 N 1 k = 1 N 1 [ x ( 0 ) x ( kT ) x 2 ] × ( 1 kN 1 ) .
n ( iT ) ! ( n ( iT ) l ) ! = I ( iT ) l ,
var ( S ̂ ( τ ) ) = 1 N [ n 4 β 2 ( 1 + e 2 Γ T ) ( 1 + e 2 Γ τ ) + 2 m ( 1 e 2 Γ T ) e 2 Γ τ ( 1 e 2 Γ τ )
+ 2 n 3 β ( 1 + e 2 Γ τ ) + n 2 ( 1 + β e Γ τ ) ] .
σ ( τ ) = T t [ β 2 ( 1 + e 2 Γ T ) ( 1 + e 2 Γ τ ) + 2 m ( 1 e 2 Γ T ) e 2 Γ τ ( 1 e 2 Γ T )
+ 2 n 1 β ( 1 + e 2 Γ τ ) + n 2 ( 1 + β e Γ τ ) ] 1 2 ,
σ ( τ ) = 1 Γ t [ β 2 ( 1 + e 2 Γ τ + 2 m Γ T e 2 Γ τ ) + 2 n 1 β Γ T ( 1 + e 2 Γ τ ) + n 2 Γ T ( 1 + β e Γ τ ) ] 1 2 .

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