Abstract

Diffuse correlation spectroscopy (DCS) has shown promise as a means to non-invasively measure cerebral blood flow in small animal models. Here, we characterize the validity of DCS at small source-detector reflectance separations needed for small animal measurements. Through Monte Carlo simulations and liquid phantom experiments, we show that DCS error increases as separation decreases, although error remains below 12% for separations > 0.2 cm. In mice, DCS measures of cerebral blood flow have excellent intra-user repeatability and strongly correlate with MRI measures of blood flow (R = 0.74, p<0.01). These results are generalizable to other DCS applications wherein short-separation reflectance geometries are desired.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

A. R. Proctor, G. A. Ramirez, S. Han, Z. Liu, T. M. Bubel, and R. Choe, “Validation of diffuse correlation spectroscopy sensitivity to nicotinamide-induced blood flow elevation in the murine hindlimb using the fluorescent microsphere technique,” J. Biomed. Opt. 23(3), 1–9 (2018).
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K. Vishwanath, R. Gurjar, D. Wolf, S. Riccardi, M. Duggan, and D. King, “Diffuse optical monitoring of peripheral tissues during uncontrolled internal hemorrhage in a porcine model,” Biomed. Opt. Express 9(2), 569–580 (2018).
[Crossref] [PubMed]

2017 (4)

W. Liu, J. Liu, X. Lou, D. Zheng, B. Wu, D. J. J. Wang, and L. Ma, “A longitudinal study of cerebral blood flow under hypoxia at high altitude using 3D pseudo-continuous arterial spin labeling,” Sci. Rep. 7(1), 43246 (2017).
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M. A. Carden, M. E. Fay, X. Lu, R. G. Mannino, Y. Sakurai, J. C. Ciciliano, C. E. Hansen, S. Chonat, C. H. Joiner, D. K. Wood, and W. A. Lam, “Extracellular fluid tonicity impacts sickle red blood cell deformability and adhesion,” Blood 130(24), 2654–2663 (2017).
[Crossref] [PubMed]

C. G. Favilla, A. B. Parthasarathy, J. A. Detre, A. G. Yodh, M. T. Mullen, S. E. Kasner, K. Gannon, and S. R. Messé, “Non-invasive respiratory impedance enhances cerebral perfusion in healthy adults,” Front. Neurol. 8(2), 45 (2017).
[Crossref] [PubMed]

S. Y. Lee, J. M. Pakela, M. C. Helton, K. Vishwanath, Y. G. Chung, N. J. Kolodziejski, C. J. Stapels, D. R. McAdams, D. E. Fernandez, J. F. Christian, J. O’Reilly, D. Farkas, B. B. Ward, S. E. Feinberg, and M. A. Mycek, “Compact dual-mode diffuse optical system for blood perfusion monitoring in a porcine model of microvascular tissue flaps,” J. Biomed. Opt. 22(12), 1–14 (2017).
[Crossref] [PubMed]

2016 (7)

T. Wood, E. Smit, E. Maes, D. Osredkar, M. Falck, M. Elstad, and M. Thoresen, “Monitoring of cerebral blood flow during hypoxia-ischemia and resuscitation in the neonatal rat using laser speckle imaging,” Physiol. Rep. 4(7), e12749 (2016).
[Crossref] [PubMed]

S. Fantini, A. Sassaroli, K. T. Tgavalekos, and J. Kornbluth, “Cerebral blood flow and autoregulation: current measurement techniques and prospects for noninvasive optical methods,” Neurophotonics 3(3), 031411 (2016).
[Crossref] [PubMed]

S. Han, A. R. Proctor, J. B. Vella, D. S. W. Benoit, and R. Choe, “Non-invasive diffuse correlation tomography reveals spatial and temporal blood flow differences in murine bone grafting approaches,” Biomed. Opt. Express 7(9), 3262–3279 (2016).
[Crossref] [PubMed]

G. Ramirez, A. R. Proctor, K. W. Jung, T. T. Wu, S. Han, R. R. Adams, J. Ren, D. K. Byun, K. S. Madden, E. B. Brown, T. H. Foster, P. Farzam, T. Durduran, and R. Choe, “Chemotherapeutic drug-specific alteration of microvascular blood flow in murine breast cancer as measured by diffuse correlation spectroscopy,” Biomed. Opt. Express 7(9), 3610–3630 (2016).
[Crossref] [PubMed]

T. K. Koo and M. Y. Li, “A guideline of selecting and reporting intraclass correlation coefficients for reliability research,” J. Chiropr. Med. 15(2), 155–163 (2016).
[Crossref] [PubMed]

K. Verdecchia, M. Diop, A. Lee, L. B. Morrison, T.-Y. Lee, and K. S. Lawrence, “Assessment of a multi-layered diffuse correlation spectroscopy method for monitoring cerebral blood flow in adults,” Biomed. Opt. Express 27(3659), 1951–1958 (2016).

D. A. Boas, S. Sakadžić, J. Selb, P. Farzam, M. A. Franceschini, and S. A. Carp, “Establishing the diffuse correlation spectroscopy signal relationship with blood flow,” Neurophotonics 3(3), 031412 (2016).
[Crossref] [PubMed]

2015 (5)

S. Han, J. Johansson, M. Mireles, A. R. Proctor, M. D. Hoffman, J. B. Vella, D. S. W. Benoit, T. Durduran, and R. Choe, “Non-contact scanning diffuse correlation tomography system for three-dimensional blood flow imaging in a murine bone graft model,” Biomed. Opt. Express 6(7), 2695–2712 (2015).
[Crossref] [PubMed]

V. S. Hedna, S. Ansari, S. Shahjouei, P. Y. Cai, A. S. Ahmad, J. Mocco, and A. I. Qureshi, “Validity of Laser Doppler flowmetry in predicting outcome in murine intraluminal middle cerebral artery occlusion stroke,” J. Vasc. Interv. Neurol. 8(3), 74–82 (2015).
[PubMed]

E. M. Buckley, S. D. Patel, B. F. Miller, M. A. Franceschini, and S. J. Vannucci, “In vivo Monitoring of Cerebral Hemodynamics in the Immature Rat: Effects of Hypoxia-Ischemia and Hypothermia,” Dev. Neurosci. 37(4-5), 407–416 (2015).
[Crossref] [PubMed]

E. M. Buckley, B. F. Miller, J. M. Golinski, H. Sadeghian, L. M. Mcallister, M. Vangel, C. Ayata, W. P. Meehan Iii, M. A. Franceschini, and M. J. Whalen, “Decreased microvascular cerebral blood flow assessed by diffuse correlation spectroscopy after repetitive concussions in mice,” J. Cereb. Blood Flow Metab.  35, 1995 (2015).

S. Han, M. D. Hoffman, A. R. Proctor, J. B. Vella, E. A. Mannoh, N. E. Barber, H. J. Kim, K. W. Jung, D. S. W. Benoit, and R. Choe, “Non-invasive monitoring of temporal and spatial blood flow during bone graft healing using diffuse correlation spectroscopy,” PLoS One 10(12), e0143891 (2015).
[Crossref] [PubMed]

2014 (7)

T. Durduran and A. G. Yodh, “Diffuse correlation spectroscopy for non-invasive, micro-vascular cerebral blood flow measurement,” Neuroimage 85(1), 51–63 (2014).
[Crossref] [PubMed]

E. M. Buckley, A. B. Parthasarathy, P. E. Grant, A. G. Yodh, and M. A. Franceschini, “Diffuse correlation spectroscopy for measurement of cerebral blood flow: future prospects,” Neurophotonics 1(1), 011009 (2014).
[Crossref] [PubMed]

Y. Tajima, H. Takuwa, H. Kawaguchi, K. Masamoto, Y. Ikoma, C. Seki, J. Taniguchi, I. Kanno, N. Saeki, and H. Ito, “Reproducibility of measuring cerebral blood flow by laser-Doppler flowmetry in mice,” Front. Biosci. 6(11), 62–68 (2014).
[PubMed]

C. C. Giza and D. A. Hovda, “The new neurometabolic cascade of concussion,” Neurosurgery 75(04), S24–S33 (2014).
[Crossref] [PubMed]

J. Selb, D. A. Boas, S.-T. Chan, K. C. Evans, E. M. Buckley, and S. A. Carp, “Sensitivity of near-infrared spectroscopy and diffuse correlation spectroscopy to brain hemodynamics: simulations and experimental findings during hypercapnia,” Neurophotonics 1(1), 015005 (2014).
[Crossref] [PubMed]

G. Hong, S. Diao, J. Chang, A. L. Antaris, C. Chen, B. Zhang, S. Zhao, D. N. Atochin, P. L. Huang, K. I. Andreasson, C. J. Kuo, and H. Dai, “Through-skull fluorescence imaging of the brain in a new near-infrared window,” Nat. Photonics 8(9), 723–730 (2014).
[Crossref] [PubMed]

V. Jain, E. M. Buckley, D. J. D. Licht, J. M. Lynch, P. J. Schwab, M. Y. Naim, N. A. Lavin, S. C. Nicolson, L. M. Montenegro, A. G. Yodh, and F. W. Wehrli, “Cerebral oxygen metabolism in neonates with congenital heart disease quantified by MRI and optics,” J. Cereb. Blood Flow Metab. 34(3), 380–388 (2014).
[Crossref] [PubMed]

2013 (1)

2012 (5)

M. Diop, K. Verdecchia, T.-Y. Lee, and K. St Lawrence, “Erratum: Calibration of diffuse correlation spectroscopy with a time-resolved near-infrared technique to yield absolute cerebral blood flow measurements: errata,” Biomed. Opt. Express 3(6), 1476–1477 (2012).
[Crossref] [PubMed]

E. M. Buckley, D. Hance, T. Pawlowski, J. Lynch, F. B. Wilson, R. C. Mesquita, T. Durduran, L. K. Diaz, M. E. Putt, D. J. Licht, M. A. Fogel, and A. G. Yodh, “Validation of diffuse correlation spectroscopic measurement of cerebral blood flow using phase-encoded velocity mapping magnetic resonance imaging,” J. Biomed. Opt. 17(3), 037007 (2012).
[Crossref] [PubMed]

M. Muller, Y. van der Graaf, F. L. Visseren, W. P. T. M. Mali, M. I. Geerlings, and SMART Study Group, “Hypertension and longitudinal changes in cerebral blood flow: the SMART-MR study,” Ann. Neurol. 71(6), 825–833 (2012).
[Crossref] [PubMed]

S. Purkayastha and F. Sorond, “Transcranial Doppler ultrasound: technique and application,” Semin. Neurol. 32(4), 411–420 (2012).
[Crossref] [PubMed]

A. K. Dunn, “Laser speckle contrast imaging of cerebral blood flow,” Ann. Biomed. Eng. 40(2), 367–377 (2012).
[Crossref] [PubMed]

2011 (8)

F. S. Foster, J. Hossack, and S. L. Adamson, “Micro-ultrasound for preclinical imaging,” Interface Focus 1(4), 576–601 (2011).
[Crossref] [PubMed]

Y. Shang, L. Chen, M. Toborek, and G. Yu, “Diffuse optical monitoring of repeated cerebral ischemia in mice,” Opt. Express 19(21), 20301–20315 (2011).
[Crossref] [PubMed]

R. C. Mesquita, T. Durduran, G. Yu, E. M. Buckley, M. N. Kim, C. Zhou, R. Choe, U. Sunar, and A. G. Yodh, “Direct measurement of tissue blood flow and metabolism with diffuse optics,” Philos Trans A Math Phys Eng Sci 369(1955), 4390–4406 (2011).
[Crossref]

S. J. E. Lucas, K. R. Burgess, K. N. Thomas, J. Donnelly, K. C. Peebles, R. A. I. Lucas, J. L. Fan, J. D. Cotter, R. Basnyat, and P. N. Ainslie, “Alterations in cerebral blood flow and cerebrovascular reactivity during 14 days at 5050 m,” J. Physiol. 589(3), 741–753 (2011).
[Crossref] [PubMed]

N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates’ brains in the first six weeks of life,” Hum. Brain Mapp. 32(7), 1179 (2011).
[Crossref]

M. Kaiser, A. Yafi, M. Cinat, B. Choi, and A. J. Durkin, “Noninvasive assessment of burn wound severity using optical technology: a review of current and future modalities,” Burns 37(3), 377–386 (2011).
[Crossref] [PubMed]

D. Irwin, L. Dong, Y. Shang, R. Cheng, M. Kudrimoti, S. D. Stevens, and G. Yu, “Influences of tissue absorption and scattering on diffuse correlation spectroscopy blood flow measurements,” Biomed. Opt. Express 2(7), 1969–1985 (2011).
[Crossref] [PubMed]

B. Hallacoglu, A. Sassaroli, S. Fantini, and A. M. Troen, “Cerebral perfusion and oxygenation are impaired by folate deficiency in rat: absolute measurements with noninvasive near-infrared spectroscopy,” J. Cereb. Blood Flow Metab. 31(6), 1482–1492 (2011).
[Crossref] [PubMed]

2010 (6)

M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocrit. Care 12(2), 173–180 (2010).
[Crossref] [PubMed]

P. Zirak, R. Delgado-Mederos, J. Martí-Fàbregas, and T. Durduran, “Effects of acetazolamide on the micro- and macro-vascular cerebral hemodynamics: a diffuse optical and transcranial Doppler ultrasound study,” Biomed. Opt. Express 1(5), 1443–1459 (2010).
[Crossref] [PubMed]

T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
[Crossref] [PubMed]

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
[Crossref] [PubMed]

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[Crossref] [PubMed]

S. A. Carp, G. P. Dai, D. A. Boas, M. A. Franceschini, and Y. R. Kim, “Validation of diffuse correlation spectroscopy measurements of rodent cerebral blood flow with simultaneous arterial spin labeling MRI; towards MRI-optical continuous cerebral metabolic monitoring,” Biomed. Opt. Express 1(2), 553–565 (2010).
[Crossref] [PubMed]

2009 (6)

H. Piilgaard and M. Lauritzen, “Persistent increase in oxygen consumption and impaired neurovascular coupling after spreading depression in rat neocortex,” J. Cereb. Blood Flow Metab. 29(9), 1517–1527 (2009).
[Crossref] [PubMed]

N. Toda, K. Ayajiki, and T. Okamura, “Cerebral blood flow regulation by nitric oxide: recent advances,” Pharmacol. Rev. 61(1), 62–97 (2009).
[Crossref] [PubMed]

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
[Crossref] [PubMed]

C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. 14(3), 034015 (2009).
[Crossref] [PubMed]

E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express 17(15), 12571–12581 (2009).
[Crossref] [PubMed]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[Crossref] [PubMed]

2008 (1)

E. R. Muir, Q. Shen, and T. Q. Duong, “Cerebral blood flow MRI in mice using the cardiac-spin-labeling technique,” Magn. Reson. Med. 60(3), 744–748 (2008).
[Crossref] [PubMed]

2007 (3)

C. Werner and K. Engelhard, “Pathophysiology of traumatic brain injury,” Br. J. Anaesth. 99(1), 4–9 (2007).
[Crossref] [PubMed]

A. Durukan and T. Tatlisumak, “Acute ischemic stroke: overview of major experimental rodent models, pathophysiology, and therapy of focal cerebral ischemia,” Pharmacol. Biochem. Behav. 87(1), 179–197 (2007).
[Crossref] [PubMed]

G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, “Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI,” Opt. Express 15(3), 1064–1075 (2007).
[Crossref] [PubMed]

2006 (1)

2005 (1)

G. 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(9), 3543–3552 (2005).
[Crossref] [PubMed]

2004 (3)

2001 (1)

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(8), 2053–2065 (2001).
[Crossref] [PubMed]

1999 (2)

1997 (3)

A. Kienle and M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to the source,” Phys. Med. Biol. 42(9), 1801–1819 (1997).
[Crossref] [PubMed]

S.-G. Kim and N. V. Tsekos, “Perfusion imaging by a flow-sensitive alternating inversion recovery (FAIR) technique: application to functional brain imaging,” Magn. Reson. Med. 37(3), 425–435 (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. 14(1), 192 (1997).
[Crossref]

1995 (1)

S.-G. Kim, “Quantification of relative cerebral blood flow change by flow-sensitive alternating inversion recovery (FAIR) technique: application to functional mapping,” Magn. Reson. Med. 34(3), 293–301 (1995).
[Crossref] [PubMed]

1994 (2)

D. V. Cicchetti, “Guidelines, criteria, and rules of thumb for evaluating normed and standardized assessment instruments in psychology,” Psychol. Assess. 6(4), 284–290 (1994).
[Crossref]

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11(10), 2727–2741 (1994).
[Crossref] [PubMed]

1993 (1)

1992 (2)

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(1), 212–216 (1992).
[Crossref] [PubMed]

D. Heimbach, L. Engrav, B. Grube, and J. Marvin, “Burn depth: a review,” World J. Surg. 16(1), 10–15 (1992).
[Crossref] [PubMed]

1989 (2)

L. I.-K. Lin, “A concordance correlation coefficient to evaluate reproducibility,” Biometrics 45(1), 255–268 (1989).
[Crossref] [PubMed]

S. Strandgaard and O. B. Paulson, “Cerebral blood flow and its pathophysiology in hypertension,” Am. J. Hypertens. 2(6), 486–492 (1989).
[Crossref] [PubMed]

1988 (1)

T. M. Jay, G. Lucignani, A. M. Crane, J. Jehle, and L. Sokoloff, “Measurement of local cerebral blood flow with [14C]iodoantipyrine in the mouse,” J. Cereb. Blood Flow Metab. 8(1), 121–129 (1988).
[Crossref] [PubMed]

1985 (1)

P. Herscovitch and M. E. Raichle, “What is the correct value for the brain-blood partition coefficient for water?” J. Cereb. Blood Flow Metab. 5(1), 65–69 (1985).
[Crossref] [PubMed]

Adams, R. R.

Adamson, S. L.

F. S. Foster, J. Hossack, and S. L. Adamson, “Micro-ultrasound for preclinical imaging,” Interface Focus 1(4), 576–601 (2011).
[Crossref] [PubMed]

Ahmad, A. S.

V. S. Hedna, S. Ansari, S. Shahjouei, P. Y. Cai, A. S. Ahmad, J. Mocco, and A. I. Qureshi, “Validity of Laser Doppler flowmetry in predicting outcome in murine intraluminal middle cerebral artery occlusion stroke,” J. Vasc. Interv. Neurol. 8(3), 74–82 (2015).
[PubMed]

Ainslie, P. N.

S. J. E. Lucas, K. R. Burgess, K. N. Thomas, J. Donnelly, K. C. Peebles, R. A. I. Lucas, J. L. Fan, J. D. Cotter, R. Basnyat, and P. N. Ainslie, “Alterations in cerebral blood flow and cerebrovascular reactivity during 14 days at 5050 m,” J. Physiol. 589(3), 741–753 (2011).
[Crossref] [PubMed]

Altman, D. G.

J. M. Bland and D. G. Altman, “Measuring agreement in method comparison studies,” Stat. Methods Med. Res. 8(2), 135–160 (1999).
[Crossref] [PubMed]

Andreasson, K. I.

G. Hong, S. Diao, J. Chang, A. L. Antaris, C. Chen, B. Zhang, S. Zhao, D. N. Atochin, P. L. Huang, K. I. Andreasson, C. J. Kuo, and H. Dai, “Through-skull fluorescence imaging of the brain in a new near-infrared window,” Nat. Photonics 8(9), 723–730 (2014).
[Crossref] [PubMed]

Ansari, S.

V. S. Hedna, S. Ansari, S. Shahjouei, P. Y. Cai, A. S. Ahmad, J. Mocco, and A. I. Qureshi, “Validity of Laser Doppler flowmetry in predicting outcome in murine intraluminal middle cerebral artery occlusion stroke,” J. Vasc. Interv. Neurol. 8(3), 74–82 (2015).
[PubMed]

Antaris, A. L.

G. Hong, S. Diao, J. Chang, A. L. Antaris, C. Chen, B. Zhang, S. Zhao, D. N. Atochin, P. L. Huang, K. I. Andreasson, C. J. Kuo, and H. Dai, “Through-skull fluorescence imaging of the brain in a new near-infrared window,” Nat. Photonics 8(9), 723–730 (2014).
[Crossref] [PubMed]

Arger, P. H.

Atochin, D. N.

G. Hong, S. Diao, J. Chang, A. L. Antaris, C. Chen, B. Zhang, S. Zhao, D. N. Atochin, P. L. Huang, K. I. Andreasson, C. J. Kuo, and H. Dai, “Through-skull fluorescence imaging of the brain in a new near-infrared window,” Nat. Photonics 8(9), 723–730 (2014).
[Crossref] [PubMed]

Ayajiki, K.

N. Toda, K. Ayajiki, and T. Okamura, “Cerebral blood flow regulation by nitric oxide: recent advances,” Pharmacol. Rev. 61(1), 62–97 (2009).
[Crossref] [PubMed]

Ayata, C.

E. M. Buckley, B. F. Miller, J. M. Golinski, H. Sadeghian, L. M. Mcallister, M. Vangel, C. Ayata, W. P. Meehan Iii, M. A. Franceschini, and M. J. Whalen, “Decreased microvascular cerebral blood flow assessed by diffuse correlation spectroscopy after repetitive concussions in mice,” J. Cereb. Blood Flow Metab.  35, 1995 (2015).

Baker, W. B.

T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[Crossref] [PubMed]

Barber, N. E.

S. Han, M. D. Hoffman, A. R. Proctor, J. B. Vella, E. A. Mannoh, N. E. Barber, H. J. Kim, K. W. Jung, D. S. W. Benoit, and R. Choe, “Non-invasive monitoring of temporal and spatial blood flow during bone graft healing using diffuse correlation spectroscopy,” PLoS One 10(12), e0143891 (2015).
[Crossref] [PubMed]

Basnyat, R.

S. J. E. Lucas, K. R. Burgess, K. N. Thomas, J. Donnelly, K. C. Peebles, R. A. I. Lucas, J. L. Fan, J. D. Cotter, R. Basnyat, and P. N. Ainslie, “Alterations in cerebral blood flow and cerebrovascular reactivity during 14 days at 5050 m,” J. Physiol. 589(3), 741–753 (2011).
[Crossref] [PubMed]

Benoit, D. S. W.

Bland, J. M.

J. M. Bland and D. G. Altman, “Measuring agreement in method comparison studies,” Stat. Methods Med. Res. 8(2), 135–160 (1999).
[Crossref] [PubMed]

Boas, D. A.

D. A. Boas, S. Sakadžić, J. Selb, P. Farzam, M. A. Franceschini, and S. A. Carp, “Establishing the diffuse correlation spectroscopy signal relationship with blood flow,” Neurophotonics 3(3), 031412 (2016).
[Crossref] [PubMed]

J. Selb, D. A. Boas, S.-T. Chan, K. C. Evans, E. M. Buckley, and S. A. Carp, “Sensitivity of near-infrared spectroscopy and diffuse correlation spectroscopy to brain hemodynamics: simulations and experimental findings during hypercapnia,” Neurophotonics 1(1), 015005 (2014).
[Crossref] [PubMed]

N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates’ brains in the first six weeks of life,” Hum. Brain Mapp. 32(7), 1179 (2011).
[Crossref]

D. A. Boas and A. K. Dunn, “Laser speckle contrast imaging in biomedical optics,” J. Biomed. Opt. 15(1), 011109 (2010).
[Crossref] [PubMed]

S. A. Carp, G. P. Dai, D. A. Boas, M. A. Franceschini, and Y. R. Kim, “Validation of diffuse correlation spectroscopy measurements of rodent cerebral blood flow with simultaneous arterial spin labeling MRI; towards MRI-optical continuous cerebral metabolic monitoring,” Biomed. Opt. Express 1(2), 553–565 (2010).
[Crossref] [PubMed]

Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
[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. 14(1), 192 (1997).
[Crossref]

Brown, E. B.

Bubel, T. M.

A. R. Proctor, G. A. Ramirez, S. Han, Z. Liu, T. M. Bubel, and R. Choe, “Validation of diffuse correlation spectroscopy sensitivity to nicotinamide-induced blood flow elevation in the murine hindlimb using the fluorescent microsphere technique,” J. Biomed. Opt. 23(3), 1–9 (2018).
[Crossref] [PubMed]

Buckley, E.

S. Y. Lee, C. Zheng, and E. Buckley, “Monte-Carlo lookup table-based inverse model for non-invasive quantification of cerebral optical properties in small animal using frequency-domain near-infrared spectroscopy,” in Biophotonics Congress: Biomedical Optics Congress (2018).

Buckley, E. M.

E. M. Buckley, B. F. Miller, J. M. Golinski, H. Sadeghian, L. M. Mcallister, M. Vangel, C. Ayata, W. P. Meehan Iii, M. A. Franceschini, and M. J. Whalen, “Decreased microvascular cerebral blood flow assessed by diffuse correlation spectroscopy after repetitive concussions in mice,” J. Cereb. Blood Flow Metab.  35, 1995 (2015).

E. M. Buckley, S. D. Patel, B. F. Miller, M. A. Franceschini, and S. J. Vannucci, “In vivo Monitoring of Cerebral Hemodynamics in the Immature Rat: Effects of Hypoxia-Ischemia and Hypothermia,” Dev. Neurosci. 37(4-5), 407–416 (2015).
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T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
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M. Kaiser, A. Yafi, M. Cinat, B. Choi, and A. J. Durkin, “Noninvasive assessment of burn wound severity using optical technology: a review of current and future modalities,” Burns 37(3), 377–386 (2011).
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S. Han, J. Johansson, M. Mireles, A. R. Proctor, M. D. Hoffman, J. B. Vella, D. S. W. Benoit, T. Durduran, and R. Choe, “Non-contact scanning diffuse correlation tomography system for three-dimensional blood flow imaging in a murine bone graft model,” Biomed. Opt. Express 6(7), 2695–2712 (2015).
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T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys. 73(7), 076701 (2010).
[Crossref] [PubMed]

M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocrit. Care 12(2), 173–180 (2010).
[Crossref] [PubMed]

T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
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T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
[Crossref] [PubMed]

E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express 17(15), 12571–12581 (2009).
[Crossref] [PubMed]

C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. 14(3), 034015 (2009).
[Crossref] [PubMed]

G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, “Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI,” Opt. Express 15(3), 1064–1075 (2007).
[Crossref] [PubMed]

C. Zhou, G. Yu, D. Furuya, J. Greenberg, A. Yodh, and T. Durduran, “Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain,” Opt. Express 14(3), 1125–1144 (2006).
[Crossref] [PubMed]

G. 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(9), 3543–3552 (2005).
[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(15), 1766–1768 (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(15), 1766–1768 (2004).

Durian, D. J.

Durkin, A. J.

M. Kaiser, A. Yafi, M. Cinat, B. Choi, and A. J. Durkin, “Noninvasive assessment of burn wound severity using optical technology: a review of current and future modalities,” Burns 37(3), 377–386 (2011).
[Crossref] [PubMed]

Durning, S. M.

T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
[Crossref] [PubMed]

Durukan, A.

A. Durukan and T. Tatlisumak, “Acute ischemic stroke: overview of major experimental rodent models, pathophysiology, and therapy of focal cerebral ischemia,” Pharmacol. Biochem. Behav. 87(1), 179–197 (2007).
[Crossref] [PubMed]

Edlow, B. L.

M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocrit. Care 12(2), 173–180 (2010).
[Crossref] [PubMed]

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
[Crossref] [PubMed]

Elstad, M.

T. Wood, E. Smit, E. Maes, D. Osredkar, M. Falck, M. Elstad, and M. Thoresen, “Monitoring of cerebral blood flow during hypoxia-ischemia and resuscitation in the neonatal rat using laser speckle imaging,” Physiol. Rep. 4(7), e12749 (2016).
[Crossref] [PubMed]

Engelhard, K.

C. Werner and K. Engelhard, “Pathophysiology of traumatic brain injury,” Br. J. Anaesth. 99(1), 4–9 (2007).
[Crossref] [PubMed]

Engrav, L.

D. Heimbach, L. Engrav, B. Grube, and J. Marvin, “Burn depth: a review,” World J. Surg. 16(1), 10–15 (1992).
[Crossref] [PubMed]

Eucker, S. A.

C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. 14(3), 034015 (2009).
[Crossref] [PubMed]

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J. Selb, D. A. Boas, S.-T. Chan, K. C. Evans, E. M. Buckley, and S. A. Carp, “Sensitivity of near-infrared spectroscopy and diffuse correlation spectroscopy to brain hemodynamics: simulations and experimental findings during hypercapnia,” Neurophotonics 1(1), 015005 (2014).
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Falck, M.

T. Wood, E. Smit, E. Maes, D. Osredkar, M. Falck, M. Elstad, and M. Thoresen, “Monitoring of cerebral blood flow during hypoxia-ischemia and resuscitation in the neonatal rat using laser speckle imaging,” Physiol. Rep. 4(7), e12749 (2016).
[Crossref] [PubMed]

Fan, J. L.

S. J. E. Lucas, K. R. Burgess, K. N. Thomas, J. Donnelly, K. C. Peebles, R. A. I. Lucas, J. L. Fan, J. D. Cotter, R. Basnyat, and P. N. Ainslie, “Alterations in cerebral blood flow and cerebrovascular reactivity during 14 days at 5050 m,” J. Physiol. 589(3), 741–753 (2011).
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Fang, Q.

Fantini, S.

S. Fantini, A. Sassaroli, K. T. Tgavalekos, and J. Kornbluth, “Cerebral blood flow and autoregulation: current measurement techniques and prospects for noninvasive optical methods,” Neurophotonics 3(3), 031411 (2016).
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B. Hallacoglu, A. Sassaroli, S. Fantini, and A. M. Troen, “Cerebral perfusion and oxygenation are impaired by folate deficiency in rat: absolute measurements with noninvasive near-infrared spectroscopy,” J. Cereb. Blood Flow Metab. 31(6), 1482–1492 (2011).
[Crossref] [PubMed]

Farkas, D.

S. Y. Lee, J. M. Pakela, M. C. Helton, K. Vishwanath, Y. G. Chung, N. J. Kolodziejski, C. J. Stapels, D. R. McAdams, D. E. Fernandez, J. F. Christian, J. O’Reilly, D. Farkas, B. B. Ward, S. E. Feinberg, and M. A. Mycek, “Compact dual-mode diffuse optical system for blood perfusion monitoring in a porcine model of microvascular tissue flaps,” J. Biomed. Opt. 22(12), 1–14 (2017).
[Crossref] [PubMed]

Farzam, P.

Favilla, C. G.

C. G. Favilla, A. B. Parthasarathy, J. A. Detre, A. G. Yodh, M. T. Mullen, S. E. Kasner, K. Gannon, and S. R. Messé, “Non-invasive respiratory impedance enhances cerebral perfusion in healthy adults,” Front. Neurol. 8(2), 45 (2017).
[Crossref] [PubMed]

R. C. Mesquita, S. S. Schenkel, D. L. Minkoff, X. Lu, C. G. Favilla, P. M. Vora, D. R. Busch, M. Chandra, J. H. Greenberg, J. A. Detre, and A. G. Yodh, “Influence of probe pressure on the diffuse correlation spectroscopy blood flow signal: extra-cerebral contributions,” Biomed. Opt. Express 4(7), 978–994 (2013).
[Crossref] [PubMed]

Fay, M. E.

M. A. Carden, M. E. Fay, X. Lu, R. G. Mannino, Y. Sakurai, J. C. Ciciliano, C. E. Hansen, S. Chonat, C. H. Joiner, D. K. Wood, and W. A. Lam, “Extracellular fluid tonicity impacts sickle red blood cell deformability and adhesion,” Blood 130(24), 2654–2663 (2017).
[Crossref] [PubMed]

Feinberg, S. E.

S. Y. Lee, J. M. Pakela, M. C. Helton, K. Vishwanath, Y. G. Chung, N. J. Kolodziejski, C. J. Stapels, D. R. McAdams, D. E. Fernandez, J. F. Christian, J. O’Reilly, D. Farkas, B. B. Ward, S. E. Feinberg, and M. A. Mycek, “Compact dual-mode diffuse optical system for blood perfusion monitoring in a porcine model of microvascular tissue flaps,” J. Biomed. Opt. 22(12), 1–14 (2017).
[Crossref] [PubMed]

Feng, T.-C.

Fernandez, D. E.

S. Y. Lee, J. M. Pakela, M. C. Helton, K. Vishwanath, Y. G. Chung, N. J. Kolodziejski, C. J. Stapels, D. R. McAdams, D. E. Fernandez, J. F. Christian, J. O’Reilly, D. Farkas, B. B. Ward, S. E. Feinberg, and M. A. Mycek, “Compact dual-mode diffuse optical system for blood perfusion monitoring in a porcine model of microvascular tissue flaps,” J. Biomed. Opt. 22(12), 1–14 (2017).
[Crossref] [PubMed]

Floyd, T. F.

Fogel, M. A.

E. M. Buckley, D. Hance, T. Pawlowski, J. Lynch, F. B. Wilson, R. C. Mesquita, T. Durduran, L. K. Diaz, M. E. Putt, D. J. Licht, M. A. Fogel, and A. G. Yodh, “Validation of diffuse correlation spectroscopic measurement of cerebral blood flow using phase-encoded velocity mapping magnetic resonance imaging,” J. Biomed. Opt. 17(3), 037007 (2012).
[Crossref] [PubMed]

Foster, F. S.

F. S. Foster, J. Hossack, and S. L. Adamson, “Micro-ultrasound for preclinical imaging,” Interface Focus 1(4), 576–601 (2011).
[Crossref] [PubMed]

Foster, T. H.

Franceschini, M. A.

D. A. Boas, S. Sakadžić, J. Selb, P. Farzam, M. A. Franceschini, and S. A. Carp, “Establishing the diffuse correlation spectroscopy signal relationship with blood flow,” Neurophotonics 3(3), 031412 (2016).
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E. M. Buckley, S. D. Patel, B. F. Miller, M. A. Franceschini, and S. J. Vannucci, “In vivo Monitoring of Cerebral Hemodynamics in the Immature Rat: Effects of Hypoxia-Ischemia and Hypothermia,” Dev. Neurosci. 37(4-5), 407–416 (2015).
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E. M. Buckley, B. F. Miller, J. M. Golinski, H. Sadeghian, L. M. Mcallister, M. Vangel, C. Ayata, W. P. Meehan Iii, M. A. Franceschini, and M. J. Whalen, “Decreased microvascular cerebral blood flow assessed by diffuse correlation spectroscopy after repetitive concussions in mice,” J. Cereb. Blood Flow Metab.  35, 1995 (2015).

E. M. Buckley, A. B. Parthasarathy, P. E. Grant, A. G. Yodh, and M. A. Franceschini, “Diffuse correlation spectroscopy for measurement of cerebral blood flow: future prospects,” Neurophotonics 1(1), 011009 (2014).
[Crossref] [PubMed]

N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates’ brains in the first six weeks of life,” Hum. Brain Mapp. 32(7), 1179 (2011).
[Crossref]

S. A. Carp, G. P. Dai, D. A. Boas, M. A. Franceschini, and Y. R. Kim, “Validation of diffuse correlation spectroscopy measurements of rodent cerebral blood flow with simultaneous arterial spin labeling MRI; towards MRI-optical continuous cerebral metabolic monitoring,” Biomed. Opt. Express 1(2), 553–565 (2010).
[Crossref] [PubMed]

Frangos, S.

M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocrit. Care 12(2), 173–180 (2010).
[Crossref] [PubMed]

Friess, S. H.

C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. 14(3), 034015 (2009).
[Crossref] [PubMed]

Furuya, D.

Gannon, K.

C. G. Favilla, A. B. Parthasarathy, J. A. Detre, A. G. Yodh, M. T. Mullen, S. E. Kasner, K. Gannon, and S. R. Messé, “Non-invasive respiratory impedance enhances cerebral perfusion in healthy adults,” Front. Neurol. 8(2), 45 (2017).
[Crossref] [PubMed]

Gaynor, J. W.

T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
[Crossref] [PubMed]

Geerlings, M. I.

M. Muller, Y. van der Graaf, F. L. Visseren, W. P. T. M. Mali, M. I. Geerlings, and SMART Study Group, “Hypertension and longitudinal changes in cerebral blood flow: the SMART-MR study,” Ann. Neurol. 71(6), 825–833 (2012).
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Giza, C. C.

C. C. Giza and D. A. Hovda, “The new neurometabolic cascade of concussion,” Neurosurgery 75(04), S24–S33 (2014).
[Crossref] [PubMed]

Glatstein, E.

G. 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(9), 3543–3552 (2005).
[Crossref] [PubMed]

Golinski, J. M.

E. M. Buckley, B. F. Miller, J. M. Golinski, H. Sadeghian, L. M. Mcallister, M. Vangel, C. Ayata, W. P. Meehan Iii, M. A. Franceschini, and M. J. Whalen, “Decreased microvascular cerebral blood flow assessed by diffuse correlation spectroscopy after repetitive concussions in mice,” J. Cereb. Blood Flow Metab.  35, 1995 (2015).

Grady, M. S.

M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocrit. Care 12(2), 173–180 (2010).
[Crossref] [PubMed]

Grant, P. E.

E. M. Buckley, A. B. Parthasarathy, P. E. Grant, A. G. Yodh, and M. A. Franceschini, “Diffuse correlation spectroscopy for measurement of cerebral blood flow: future prospects,” Neurophotonics 1(1), 011009 (2014).
[Crossref] [PubMed]

N. Roche-Labarbe, S. A. Carp, A. Surova, M. Patel, D. A. Boas, P. E. Grant, and M. A. Franceschini, “Noninvasive optical measures of CBV, StO2, CBF index, and rCMRO2 in human premature neonates’ brains in the first six weeks of life,” Hum. Brain Mapp. 32(7), 1179 (2011).
[Crossref]

Greenberg, J.

Greenberg, J. H.

R. C. Mesquita, S. S. Schenkel, D. L. Minkoff, X. Lu, C. G. Favilla, P. M. Vora, D. R. Busch, M. Chandra, J. H. Greenberg, J. A. Detre, and A. G. Yodh, “Influence of probe pressure on the diffuse correlation spectroscopy blood flow signal: extra-cerebral contributions,” Biomed. Opt. Express 4(7), 978–994 (2013).
[Crossref] [PubMed]

M. N. Kim, T. Durduran, S. Frangos, B. L. Edlow, E. M. Buckley, H. E. Moss, C. Zhou, G. Yu, R. Choe, E. Maloney-Wilensky, R. L. Wolf, M. S. Grady, J. H. Greenberg, J. M. Levine, A. G. Yodh, J. A. Detre, and W. A. Kofke, “Noninvasive measurement of cerebral blood flow and blood oxygenation using near-infrared and diffuse correlation spectroscopies in critically brain-injured adults,” Neurocrit. Care 12(2), 173–180 (2010).
[Crossref] [PubMed]

T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
[Crossref] [PubMed]

T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
[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(15), 1766–1768 (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(15), 1766–1768 (2004).

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(8), 2053–2065 (2001).
[Crossref] [PubMed]

Grube, B.

D. Heimbach, L. Engrav, B. Grube, and J. Marvin, “Burn depth: a review,” World J. Surg. 16(1), 10–15 (1992).
[Crossref] [PubMed]

Gurjar, R.

Hallacoglu, B.

B. Hallacoglu, A. Sassaroli, S. Fantini, and A. M. Troen, “Cerebral perfusion and oxygenation are impaired by folate deficiency in rat: absolute measurements with noninvasive near-infrared spectroscopy,” J. Cereb. Blood Flow Metab. 31(6), 1482–1492 (2011).
[Crossref] [PubMed]

Han, S.

A. R. Proctor, G. A. Ramirez, S. Han, Z. Liu, T. M. Bubel, and R. Choe, “Validation of diffuse correlation spectroscopy sensitivity to nicotinamide-induced blood flow elevation in the murine hindlimb using the fluorescent microsphere technique,” J. Biomed. Opt. 23(3), 1–9 (2018).
[Crossref] [PubMed]

G. Ramirez, A. R. Proctor, K. W. Jung, T. T. Wu, S. Han, R. R. Adams, J. Ren, D. K. Byun, K. S. Madden, E. B. Brown, T. H. Foster, P. Farzam, T. Durduran, and R. Choe, “Chemotherapeutic drug-specific alteration of microvascular blood flow in murine breast cancer as measured by diffuse correlation spectroscopy,” Biomed. Opt. Express 7(9), 3610–3630 (2016).
[Crossref] [PubMed]

S. Han, A. R. Proctor, J. B. Vella, D. S. W. Benoit, and R. Choe, “Non-invasive diffuse correlation tomography reveals spatial and temporal blood flow differences in murine bone grafting approaches,” Biomed. Opt. Express 7(9), 3262–3279 (2016).
[Crossref] [PubMed]

S. Han, M. D. Hoffman, A. R. Proctor, J. B. Vella, E. A. Mannoh, N. E. Barber, H. J. Kim, K. W. Jung, D. S. W. Benoit, and R. Choe, “Non-invasive monitoring of temporal and spatial blood flow during bone graft healing using diffuse correlation spectroscopy,” PLoS One 10(12), e0143891 (2015).
[Crossref] [PubMed]

S. Han, J. Johansson, M. Mireles, A. R. Proctor, M. D. Hoffman, J. B. Vella, D. S. W. Benoit, T. Durduran, and R. Choe, “Non-contact scanning diffuse correlation tomography system for three-dimensional blood flow imaging in a murine bone graft model,” Biomed. Opt. Express 6(7), 2695–2712 (2015).
[Crossref] [PubMed]

Hance, D.

E. M. Buckley, D. Hance, T. Pawlowski, J. Lynch, F. B. Wilson, R. C. Mesquita, T. Durduran, L. K. Diaz, M. E. Putt, D. J. Licht, M. A. Fogel, and A. G. Yodh, “Validation of diffuse correlation spectroscopic measurement of cerebral blood flow using phase-encoded velocity mapping magnetic resonance imaging,” J. Biomed. Opt. 17(3), 037007 (2012).
[Crossref] [PubMed]

Hansen, C. E.

M. A. Carden, M. E. Fay, X. Lu, R. G. Mannino, Y. Sakurai, J. C. Ciciliano, C. E. Hansen, S. Chonat, C. H. Joiner, D. K. Wood, and W. A. Lam, “Extracellular fluid tonicity impacts sickle red blood cell deformability and adhesion,” Blood 130(24), 2654–2663 (2017).
[Crossref] [PubMed]

Haskell, R. C.

Hedna, V. S.

V. S. Hedna, S. Ansari, S. Shahjouei, P. Y. Cai, A. S. Ahmad, J. Mocco, and A. I. Qureshi, “Validity of Laser Doppler flowmetry in predicting outcome in murine intraluminal middle cerebral artery occlusion stroke,” J. Vasc. Interv. Neurol. 8(3), 74–82 (2015).
[PubMed]

Heimbach, D.

D. Heimbach, L. Engrav, B. Grube, and J. Marvin, “Burn depth: a review,” World J. Surg. 16(1), 10–15 (1992).
[Crossref] [PubMed]

Helton, M. C.

S. Y. Lee, J. M. Pakela, M. C. Helton, K. Vishwanath, Y. G. Chung, N. J. Kolodziejski, C. J. Stapels, D. R. McAdams, D. E. Fernandez, J. F. Christian, J. O’Reilly, D. Farkas, B. B. Ward, S. E. Feinberg, and M. A. Mycek, “Compact dual-mode diffuse optical system for blood perfusion monitoring in a porcine model of microvascular tissue flaps,” J. Biomed. Opt. 22(12), 1–14 (2017).
[Crossref] [PubMed]

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P. Herscovitch and M. E. Raichle, “What is the correct value for the brain-blood partition coefficient for water?” J. Cereb. Blood Flow Metab. 5(1), 65–69 (1985).
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Hoffman, M. D.

S. Han, M. D. Hoffman, A. R. Proctor, J. B. Vella, E. A. Mannoh, N. E. Barber, H. J. Kim, K. W. Jung, D. S. W. Benoit, and R. Choe, “Non-invasive monitoring of temporal and spatial blood flow during bone graft healing using diffuse correlation spectroscopy,” PLoS One 10(12), e0143891 (2015).
[Crossref] [PubMed]

S. Han, J. Johansson, M. Mireles, A. R. Proctor, M. D. Hoffman, J. B. Vella, D. S. W. Benoit, T. Durduran, and R. Choe, “Non-contact scanning diffuse correlation tomography system for three-dimensional blood flow imaging in a murine bone graft model,” Biomed. Opt. Express 6(7), 2695–2712 (2015).
[Crossref] [PubMed]

Hong, G.

G. Hong, S. Diao, J. Chang, A. L. Antaris, C. Chen, B. Zhang, S. Zhao, D. N. Atochin, P. L. Huang, K. I. Andreasson, C. J. Kuo, and H. Dai, “Through-skull fluorescence imaging of the brain in a new near-infrared window,” Nat. Photonics 8(9), 723–730 (2014).
[Crossref] [PubMed]

Hossack, J.

F. S. Foster, J. Hossack, and S. L. Adamson, “Micro-ultrasound for preclinical imaging,” Interface Focus 1(4), 576–601 (2011).
[Crossref] [PubMed]

Hovda, D. A.

C. C. Giza and D. A. Hovda, “The new neurometabolic cascade of concussion,” Neurosurgery 75(04), S24–S33 (2014).
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V. S. Hedna, S. Ansari, S. Shahjouei, P. Y. Cai, A. S. Ahmad, J. Mocco, and A. I. Qureshi, “Validity of Laser Doppler flowmetry in predicting outcome in murine intraluminal middle cerebral artery occlusion stroke,” J. Vasc. Interv. Neurol. 8(3), 74–82 (2015).
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Riccardi, S.

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Schenkel, S. S.

Schultz, S.

Schwab, P. J.

V. Jain, E. M. Buckley, D. J. D. Licht, J. M. Lynch, P. J. Schwab, M. Y. Naim, N. A. Lavin, S. C. Nicolson, L. M. Montenegro, A. G. Yodh, and F. W. Wehrli, “Cerebral oxygen metabolism in neonates with congenital heart disease quantified by MRI and optics,” J. Cereb. Blood Flow Metab. 34(3), 380–388 (2014).
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E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express 17(15), 12571–12581 (2009).
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D. A. Boas, S. Sakadžić, J. Selb, P. Farzam, M. A. Franceschini, and S. A. Carp, “Establishing the diffuse correlation spectroscopy signal relationship with blood flow,” Neurophotonics 3(3), 031412 (2016).
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Shahjouei, S.

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Shen, Q.

E. R. Muir, Q. Shen, and T. Q. Duong, “Cerebral blood flow MRI in mice using the cardiac-spin-labeling technique,” Magn. Reson. Med. 60(3), 744–748 (2008).
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T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
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W. Liu, J. Liu, X. Lou, D. Zheng, B. Wu, D. J. J. Wang, and L. Ma, “A longitudinal study of cerebral blood flow under hypoxia at high altitude using 3D pseudo-continuous arterial spin labeling,” Sci. Rep. 7(1), 43246 (2017).
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[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

C. Zhou, S. A. Eucker, T. Durduran, G. Yu, J. Ralston, S. H. Friess, R. N. Ichord, S. S. Margulies, and A. G. Yodh, “Diffuse optical monitoring of hemodynamic changes in piglet brain with closed head injury,” J. Biomed. Opt. 14(3), 034015 (2009).
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E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express 17(15), 12571–12581 (2009).
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T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
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G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, “Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI,” Opt. Express 15(3), 1064–1075 (2007).
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C. Zhou, G. Yu, D. Furuya, J. Greenberg, A. Yodh, and T. Durduran, “Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain,” Opt. Express 14(3), 1125–1144 (2006).
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G. 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(9), 3543–3552 (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(15), 1766–1768 (2004).
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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(15), 1766–1768 (2004).

Zimmerman, R. A.

T. Durduran, C. Zhou, E. M. Buckley, M. N. Kim, G. Yu, R. Choe, J. W. Gaynor, T. L. Spray, S. M. Durning, S. E. Mason, L. M. Montenegro, S. C. Nicolson, R. A. Zimmerman, M. E. Putt, J. Wang, J. H. Greenberg, J. A. Detre, A. G. Yodh, and D. J. Licht, “Optical measurement of cerebral hemodynamics and oxygen metabolism in neonates with congenital heart defects,” J. Biomed. Opt. 15(3), 037004 (2010).
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K. Verdecchia, M. Diop, A. Lee, L. B. Morrison, T.-Y. Lee, and K. S. Lawrence, “Assessment of a multi-layered diffuse correlation spectroscopy method for monitoring cerebral blood flow in adults,” Biomed. Opt. Express 27(3659), 1951–1958 (2016).

M. Diop, K. Verdecchia, T.-Y. Lee, and K. St Lawrence, “Erratum: Calibration of diffuse correlation spectroscopy with a time-resolved near-infrared technique to yield absolute cerebral blood flow measurements: errata,” Biomed. Opt. Express 3(6), 1476–1477 (2012).
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P. Zirak, R. Delgado-Mederos, J. Martí-Fàbregas, and T. Durduran, “Effects of acetazolamide on the micro- and macro-vascular cerebral hemodynamics: a diffuse optical and transcranial Doppler ultrasound study,” Biomed. Opt. Express 1(5), 1443–1459 (2010).
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R. C. Mesquita, S. S. Schenkel, D. L. Minkoff, X. Lu, C. G. Favilla, P. M. Vora, D. R. Busch, M. Chandra, J. H. Greenberg, J. A. Detre, and A. G. Yodh, “Influence of probe pressure on the diffuse correlation spectroscopy blood flow signal: extra-cerebral contributions,” Biomed. Opt. Express 4(7), 978–994 (2013).
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G. Ramirez, A. R. Proctor, K. W. Jung, T. T. Wu, S. Han, R. R. Adams, J. Ren, D. K. Byun, K. S. Madden, E. B. Brown, T. H. Foster, P. Farzam, T. Durduran, and R. Choe, “Chemotherapeutic drug-specific alteration of microvascular blood flow in murine breast cancer as measured by diffuse correlation spectroscopy,” Biomed. Opt. Express 7(9), 3610–3630 (2016).
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S. Han, J. Johansson, M. Mireles, A. R. Proctor, M. D. Hoffman, J. B. Vella, D. S. W. Benoit, T. Durduran, and R. Choe, “Non-contact scanning diffuse correlation tomography system for three-dimensional blood flow imaging in a murine bone graft model,” Biomed. Opt. Express 6(7), 2695–2712 (2015).
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S. Han, A. R. Proctor, J. B. Vella, D. S. W. Benoit, and R. Choe, “Non-invasive diffuse correlation tomography reveals spatial and temporal blood flow differences in murine bone grafting approaches,” Biomed. Opt. Express 7(9), 3262–3279 (2016).
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S. A. Carp, G. P. Dai, D. A. Boas, M. A. Franceschini, and Y. R. Kim, “Validation of diffuse correlation spectroscopy measurements of rodent cerebral blood flow with simultaneous arterial spin labeling MRI; towards MRI-optical continuous cerebral metabolic monitoring,” Biomed. Opt. Express 1(2), 553–565 (2010).
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K. Vishwanath, R. Gurjar, D. Wolf, S. Riccardi, M. Duggan, and D. King, “Diffuse optical monitoring of peripheral tissues during uncontrolled internal hemorrhage in a porcine model,” Biomed. Opt. Express 9(2), 569–580 (2018).
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D. Irwin, L. Dong, Y. Shang, R. Cheng, M. Kudrimoti, S. D. Stevens, and G. Yu, “Influences of tissue absorption and scattering on diffuse correlation spectroscopy blood flow measurements,” Biomed. Opt. Express 2(7), 1969–1985 (2011).
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C. Zhou, G. Yu, D. Furuya, J. Greenberg, A. Yodh, and T. Durduran, “Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain,” Opt. Express 14(3), 1125–1144 (2006).
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Y. Shang, L. Chen, M. Toborek, and G. Yu, “Diffuse optical monitoring of repeated cerebral ischemia in mice,” Opt. Express 19(21), 20301–20315 (2011).
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E. M. Buckley, N. M. Cook, T. Durduran, M. N. Kim, C. Zhou, R. Choe, G. Yu, S. Schultz, C. M. Sehgal, D. J. Licht, P. H. Arger, M. E. Putt, H. H. Hurt, and A. G. Yodh, “Cerebral hemodynamics in preterm infants during positional intervention measured with diffuse correlation spectroscopy and transcranial Doppler ultrasound,” Opt. Express 17(15), 12571–12581 (2009).
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Q. Fang and D. A. Boas, “Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units,” Opt. Express 17(22), 20178–20190 (2009).
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T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, “Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients,” Opt. Express 17(5), 3884–3902 (2009).
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G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, “Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI,” Opt. Express 15(3), 1064–1075 (2007).
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Figures (4)

Fig. 1
Fig. 1 DCS accuracy when simulated g1(ρ,τ) data is fit with the constraint of g1(��)> 0.01 (left column) or g1(��)>0.4 (right column) (a,b) Representative Monte Carlo simulated g1(ρ,τ) data (solid line) at 2 and 0.6 cm with μs’ = 4.6 cm−1 and μa = 0.12 cm−1, along with the best fit using the semi-infinite solution to the correlation diffusion equation (dotted line). (c,d) Percent error in DB as a function of source detector separation and known DB at a fixed μs’ = 10 cm−1 and μa = 0.2 cm−1. (e,f) Percent error in DB as a function of absorption and reduced scattering coefficients at a 0.6cm source-detector separation and a known DB of 1x10−8 cm2/s. (g,h) Percent error in the relative change in DB as a function of the baseline DB and the known relative change in DB. Data was generated using a 0.6 cm source-detector separation with μa = 0.2 cm−1 and μs’ = 10 cm−1.
Fig. 2
Fig. 2 (a) Representative measured (solid) and fitted (dashed) g2(ρ,τ) curves at 1.5cm (left) and 0.6cm (middle: used g2(ρ,τ) > 1.005, right: used g2(ρ,τ) > 1.2) on the same liquid phantom (μs’ = 4.6 cm−1 and μa = 0.12 cm−1) at 38°C. (b,c) Comparison between DB,0.6cm and DB,1.5cm for two sets of phantoms (b: μs’ = 10 cm−1, μa = 0.12 cm−1 and c: μs’ = 4.6 cm−1, μa = 0.12 cm−1) using different g2(ρ,τ) thresholds to fit data (blue: g2(ρ,τ) > 1.005, red: g2(ρ,τ) >1.2). Error bar represents the standard deviation; CCC denotes Lin’s concordance correlation coefficient; dotted line denotes a line of identity. (d,e) Bland-Altman plots for b and c, respectively, of the percent difference between DB,0.6cm and DB,1.5cm versus the mean of these parameters. The solid horizontal line represents the mean percent difference and dashed horizontal lines represent the 95% limits of agreement.
Fig. 3
Fig. 3 (a) Anatomical image of ASL-MRI mouse with one ROI (red) used to obtain a perfusion value of CBF concurrent with the region that DCS measures. (b) Cerebral blood flow index measured by DCS versus cerebral blood flow measured by ASL-MRI in both healthy (n = 4, 7 hemispheric data points, red) and concussed mice (n = 2, 4 hemispheric data points, cyan). Data from left and right hemisphere were treated as independent samples. Black line denotes line of best fit and grey shaded region denotes 95% confidence interval. Error bars represent the standard deviation.
Fig. 4
Fig. 4 Intraclass correlation coefficient (ICC) for intra- and inter- user repeatability measured on a mouse and for inter-user repeatability measured on a liquid phantom.

Equations (5)

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g 1 (ρ,τ)= i=1 N p e 1 3 Y i k 0 2 Δ r 2 (τ) e μ a L i i=1 N p e 1 3 Y i k 0 2 Δ r 2 (0) e μ a L i .
g 1 (ρ,τ)= [ e K(τ) r 1 r 1 e K(τ) r 2 r 2 ] [ e K(0) r 1 r 1 e K(0) r 2 r 2 ]
M ns = M 0 (12 e TI T 1 )
M ss = M 0 (12 e TI T 1 * )
1 T 1 * = 1 T 1 + f δ

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