Abstract

A novel approach for time-domain diffuse correlation spectroscopy (TD-DCS) has been recently proposed, which has the unique advantage by simultaneous measurements of optical and dynamical properties in a scattering medium. In this study, analytical models for calculating the time-resolved electric-field autocorrelation function is presented for a multi-layer turbid sample, as well as a semi-infinite medium embedded with a small dynamic heterogeneity. To verify the analytical models, we used Monte Carlo simulations, which demonstrated that the theoretical prediction for the time-resolved autocorrelation function was highly consistent with the Monte Carlo simulation, validating the proposed analytical models. Using these analytical models, we also showed that TD-DCS has a higher sensitivity compared to conventional continuous-wave (CW) DCS for detecting the deeper dynamics. The presented analytical models and simulations can be utilized for quantification of optical and dynamical properties from future TD-DCS experimental data as well as for optimization of the experimental design to achieve maximum contrast for deep tissue dynamics.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2016 (2)

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, 31412 (2016).

J. Sutin, B. Zimmerman, D. Tyulmankov, D. Tamborini, K. C. Wu, J. Selb, A. Gulinatti, I. Rech, A. Tosi, D. A. Boas, and M. A. Franceschini, “Time-domain diffuse correlation spectroscopy,” Optica 3(9), 1006–1013 (2016).
[PubMed]

2015 (1)

2014 (2)

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).
[PubMed]

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

2011 (1)

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, 4390–4406 (2011).

2010 (3)

2008 (2)

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[PubMed]

2005 (2)

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(4), 44002 (2005).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

2003 (2)

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[PubMed]

F. Ferri and D. Magatti, “Hardware simulator for photon correlation spectroscopy,” Rev. Sci. Instrum. 74(10), 4273–4279 (2003).

1997 (1)

1995 (1)

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75(9), 1855–1858 (1995).
[PubMed]

1990 (2)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (France) 51, 2101–2127 (1990).

A. G. Yodh, P. D. Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B Condens. Matter 42(7), 4744–4747 (1990).
[PubMed]

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[PubMed]

1987 (1)

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65, 409–413 (1987).

Alerstam, E.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[PubMed]

Andersson-Engels, S.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[PubMed]

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).
[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, 31412 (2016).

J. Sutin, B. Zimmerman, D. Tyulmankov, D. Tamborini, K. C. Wu, J. Selb, A. Gulinatti, I. Rech, A. Tosi, D. A. Boas, and M. A. Franceschini, “Time-domain diffuse correlation spectroscopy,” Optica 3(9), 1006–1013 (2016).
[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).
[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).
[PubMed]

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[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 14, 192–215 (1997).

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75(9), 1855–1858 (1995).
[PubMed]

Buckley, E. M.

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).
[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, 4390–4406 (2011).

Campbell, L. E.

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75(9), 1855–1858 (1995).
[PubMed]

Carp, S. A.

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).
[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).
[PubMed]

Carp, S.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, 31412 (2016).

Chaikin, P. M.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[PubMed]

Chan, S.-T.

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).
[PubMed]

Choe, R.

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, 4390–4406 (2011).

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).
[PubMed]

Contini, D.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

Cova, S.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

Cubeddu, R.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

Dai, G. P.

Dalla Mora, A.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

Del Bianco, S.

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

Dietsche, G.

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(4), 44002 (2005).
[PubMed]

Diop, M.

Durduran, T.

T. Durduran and A. G. Yodh, “Diffuse correlation spectroscopy for non-invasive, micro-vascular cerebral blood flow measurement,” Neuroimage 85(Pt 1), 51–63 (2014).
[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, 4390–4406 (2011).

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).
[PubMed]

Elbert, T.

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(4), 44002 (2005).
[PubMed]

Evans, K. C.

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).
[PubMed]

Fang, Q.

Farzam, P.

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, 31412 (2016).

Ferri, F.

F. Ferri and D. Magatti, “Hardware simulator for photon correlation spectroscopy,” Rev. Sci. Instrum. 74(10), 4273–4279 (2003).

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, 31412 (2016).

J. Sutin, B. Zimmerman, D. Tyulmankov, D. Tamborini, K. C. Wu, J. Selb, A. Gulinatti, I. Rech, A. Tosi, D. A. Boas, and M. A. Franceschini, “Time-domain diffuse correlation spectroscopy,” Optica 3(9), 1006–1013 (2016).
[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).
[PubMed]

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[PubMed]

Gisler, T.

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(4), 44002 (2005).
[PubMed]

Gulinatti, A.

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (France) 51, 2101–2127 (1990).

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[PubMed]

Iftime, D.

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(4), 44002 (2005).
[PubMed]

Kaplan, P. D.

A. G. Yodh, P. D. Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B Condens. Matter 42(7), 4744–4747 (1990).
[PubMed]

Kim, M. N.

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, 4390–4406 (2011).

Kim, Y. R.

Lee, T. Y.

Li, J.

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(4), 44002 (2005).
[PubMed]

Magatti, D.

F. Ferri and D. Magatti, “Hardware simulator for photon correlation spectroscopy,” Rev. Sci. Instrum. 74(10), 4273–4279 (2003).

Maret, G.

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(4), 44002 (2005).
[PubMed]

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65, 409–413 (1987).

Martelli, F.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

Mesquita, R. C.

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, 4390–4406 (2011).

Morrison, L. B.

Pifferi, A.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

Pine, D. J.

A. G. Yodh, P. D. Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B Condens. Matter 42(7), 4744–4747 (1990).
[PubMed]

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (France) 51, 2101–2127 (1990).

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[PubMed]

Rech, I.

Rockstroh, B.

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(4), 44002 (2005).
[PubMed]

Sakadžic, S.

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, 31412 (2016).

Selb, J.

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, 31412 (2016).

J. Sutin, B. Zimmerman, D. Tyulmankov, D. Tamborini, K. C. Wu, J. Selb, A. Gulinatti, I. Rech, A. Tosi, D. A. Boas, and M. A. Franceschini, “Time-domain diffuse correlation spectroscopy,” Optica 3(9), 1006–1013 (2016).
[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).
[PubMed]

Skipetrov, S. E.

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(4), 44002 (2005).
[PubMed]

Spinelli, L.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

St Lawrence, K.

Strangman, G.

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[PubMed]

Sunar, U.

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, 4390–4406 (2011).

Sutin, J.

Svensson, T.

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[PubMed]

Tamborini, D.

Torricelli, A.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

Tosi, A.

J. Sutin, B. Zimmerman, D. Tyulmankov, D. Tamborini, K. C. Wu, J. Selb, A. Gulinatti, I. Rech, A. Tosi, D. A. Boas, and M. A. Franceschini, “Time-domain diffuse correlation spectroscopy,” Optica 3(9), 1006–1013 (2016).
[PubMed]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

Tyulmankov, D.

Verdecchia, K.

Weitz, D. A.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (France) 51, 2101–2127 (1990).

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[PubMed]

Wolf, P. E.

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65, 409–413 (1987).

Wu, K. C.

Yodh, A. G.

T. Durduran and A. G. Yodh, “Diffuse correlation spectroscopy for non-invasive, micro-vascular cerebral blood flow measurement,” Neuroimage 85(Pt 1), 51–63 (2014).
[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, 4390–4406 (2011).

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).
[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 14, 192–215 (1997).

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75(9), 1855–1858 (1995).
[PubMed]

A. G. Yodh, P. D. Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B Condens. Matter 42(7), 4744–4747 (1990).
[PubMed]

Yu, G.

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, 4390–4406 (2011).

Zaccanti, G.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

Zappa, F.

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

Zhou, C.

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, 4390–4406 (2011).

Zhu, J. X.

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (France) 51, 2101–2127 (1990).

Zimmerman, B.

Biomed. Opt. Express (3)

J. Biomed. Opt. (2)

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(4), 44002 (2005).
[PubMed]

E. Alerstam, T. Svensson, and S. Andersson-Engels, “Parallel computing with graphics processing units for high-speed Monte Carlo simulation of photon migration,” J. Biomed. Opt. 13(6), 060504 (2008).
[PubMed]

J. Opt. Soc. Am. A (1)

J. Phys. (France) (1)

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, “Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit,” J. Phys. (France) 51, 2101–2127 (1990).

Neuroimage (2)

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

G. Strangman, M. A. Franceschini, and D. A. Boas, “Factors affecting the accuracy of near-infrared spectroscopy concentration calculations for focal changes in oxygenation parameters,” Neuroimage 18(4), 865–879 (2003).
[PubMed]

Neurophotonics (2)

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, 31412 (2016).

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).
[PubMed]

Optica (1)

Philos Trans A Math Phys. Eng. Sci. (1)

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, 4390–4406 (2011).

Phys. Rev. B Condens. Matter (1)

A. G. Yodh, P. D. Kaplan, and D. J. Pine, “Pulsed diffusing-wave spectroscopy: High resolution through nonlinear optical gating,” Phys. Rev. B Condens. Matter 42(7), 4744–4747 (1990).
[PubMed]

Phys. Rev. Lett. (4)

A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: Improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005).
[PubMed]

A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008).
[PubMed]

D. A. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and imaging with diffusing temporal field correlations,” Phys. Rev. Lett. 75(9), 1855–1858 (1995).
[PubMed]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988).
[PubMed]

Rep. Prog. Phys. (1)

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).
[PubMed]

Rev. Sci. Instrum. (1)

F. Ferri and D. Magatti, “Hardware simulator for photon correlation spectroscopy,” Rev. Sci. Instrum. 74(10), 4273–4279 (2003).

Z. Phys. B Condens. Matter (1)

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media: The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65, 409–413 (1987).

Other (2)

D. A. Boas, C. Pitris, and N. Ramanujam, Handbook of Biomedical Optics, (CRC Press, 2011), Chap. 10.

F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media: Theory. Solutions, and Software (SPIE Press, Bellingham, 2009).

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Figures (9)

Fig. 1
Fig. 1

Scheme of the N-layer scattering medium including the position of the source and detector.

Fig. 2
Fig. 2

Geometric scheme for the perturbation model including the position of the source, detector and heterogeneity inclusion.

Fig. 3
Fig. 3

Simulation result of the 3-layer head-like model for the source-detector separation = 3.0 cm: the normalized electric-field autocorrelation function g1 from the analytical model and Monte Carlo simulation for the three selected pathlengths s = 10 (red), 20 (blue), and 25 cm (black), respectively.

Fig. 4
Fig. 4

Simulation result of the 3-layer head-like model for the source-detector separation = 0.0 cm: the normalized electric-field autocorrelation function g1 from the analytical model and Monte Carlo simulation for the three selected pathlengths s = 10 (red), 20 (blue), and 25 cm (black), respectively.

Fig. 5
Fig. 5

Simulation result for a semi-infinite medium embedded with a small spherical dynamic heterogeneity: The source-detector separation = 0 cm. The normalized electric-field autocorrelation function g1 obtained by the analytical model and Monte Carlo (MC) simulations for the four selected pathlengths s = 5 (red), 10 (pink), 20 (blue) and 40 cm (black), respectively.

Fig. 6
Fig. 6

(a) The normalized intensity autocorrelation function g2-1 of CW-DCS. (b) The change in g2 between baseline and stimulation for CW-DCS. (c) The normalized intensity autocorrelation function g2-1 of TD-DCS with a selected pathlength s = 20 cm for the baseline and stimulation. (d) The change in g2 between baseline and stimulation for TD-DCS.

Fig. 7
Fig. 7

(a) The change in g2 between the baseline and stimulation in the 3-layer model (source-detector separation = 3.0 cm) for different pathlengths. (b) The diffuse reflectance, R (photons/cm2ps) with respect to the photon pathlength.

Fig. 8
Fig. 8

The autocorrelation function g2 in (a) CW-DCS and TD-DCS for selected pathlength (b) s = 20 cm and (c) s = 30 cm. In each case, the theoretical prediction from the 3-layer model and simulation on g2 are presented for the baseline and stimulation.

Fig. 9
Fig. 9

The pathlength-resolved normalized electric field autocorrelation function g1 for the 3-layer head-like model with a source-detector separation of 0 cm for the baseline and stimulation with pathlengths of s = 10, 15, and 20 cm. The parameters used for the stimulation were the same as those used in Figs. 7 and 8, except for the source-detector separation.

Tables (1)

Tables Icon

Table 1 Parameters for the 3-layer model (head-like model)

Equations (14)

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

[ 2 (3 μ a μ + s ' 6 μ s ' 2 k 2 D B τ) 3 μ s ' v t ]G(r,t,τ)=3 μ s ' δ(rr ) s δ(t)
G (q,z,ω,τ)= t dtexp(iωt) ρ d 2 ρG(ρ,z,t,τ)exp(iq ρ )
[ z 2 3 μ s ' ( μ a +2 μ s ' k 2 D B τ iω c ) q 2 ] G (q,z,ω,τ)=3 μ s ' δ(z z s )
G n (q,z,ω,τ)= A n exp( β n z)+ B n exp( β n z)
G 0 (q,z,ω,τ) z 0 z G 0 (q,z,ω,τ)=0, z=0 G 0 (q,z,ω,τ)= G 1 (q,z,ω,τ), z= z s z G 0 (q,z,ω,τ)= z G 1 (q,z,ω,τ)+3 μ s ' (1) , z= z s G n (q,z,ω,τ)= G n+1 (q,z,ω,τ), z= L n ,n=1...N1 D n z G n (q,z,ω,τ)= D n+1 z G n+1 (q,z,ω,τ), z= L n ,n=1...N1 G N (q,z,ω,τ)+ z N z G N (q,z,ω,τ)=0, z= L N
G 0 (q,z=0,ω,τ)= Numerator Denominator
Numerator=3 μ s ' (1) z 0 exp( β 1 z s ) Denominator=1+ β 1 z 0
Numerator=3 μ s ' (1) z 0 { β 1 D 1 cosh[ β 1 ( Δ 1 z ) s ]+ β 2 D 2 sinh[ β 1 ( Δ 1 z ) s ] } Denominator= β 1 (D + 1 β 2 D 2 z 0 )cosh( β 1 Δ 1 )+( β 2 D 2 + β 1 2 D 1 z 0 )sinh(β Δ 1 1 )
Numerator=3 μ s ' (1) z 0 ( β 1 D 1 cosh( β 1 ( Δ 1 z ) s )( β 2 D 2 cosh( β 2 Δ 2 )+ β 3 D 3 sinh( β 2 Δ 2 )) + β 2 D 2 (β D 3 3 cosh( β 2 Δ 2 )+ β 2 D 2 sinh( β 2 Δ 2 ))sinh( β 1 ( Δ 1 z ) s )) Denominator= β 2 D 2 cosh( β 2 Δ 2 )( β 1 (D + 1 β 3 D 3 z 0 )cosh( β 1 Δ 1 )+( β 3 D 3 + β 1 2 D 1 z 0 )sinh( β 1 Δ 1 )) +(β ( β 3 D 1 D 3 + β 2 2 D 2 2 z 0 ) 1 cosh( β 1 Δ 1 )+(β 2 2 D 2 2 + β 1 2 β 3 D 1 D 3 z 0 )sinh( β 1 Δ 1 ))×sinh( β 2 Δ 2 )
G(ρ,z=0,t,τ)= 1 2π ω dω 1 (2π) 2 q d 2 q G 0 (q,z=0,ω,τ)exp(iqρ)exp(iωt) = 1 (2π) 2 ω dω q dq G 0 (q,z=0,ω,τ)q J 0 (ρq)exp(iωt)
G 0 (ρ,t,τ)= v (4πDt) 3/2 exp( ρ 2 4Dt ( μ a +2 μ s ' D B k 2 τ)vt)× { exp( z s 2 4Dt )exp[ (z + s 2 z 0 ) 2 4Dt ] }
δG( r 1 , r 2 , r 3 ,t,τ)= v 2 (4πD) 5/2 t 3/2 exp[ ( μ a +2 μ s ' D k B 2 τ)vt ]× v d 3 r 2 (2 μ s ' δ D B k 2 τ)× { ( 1 ρ 12 + + 1 ρ + 23 )exp[ ( ρ 12 + +ρ + 23 ) 2 4Dt ]( 1 ρ 12 + + 1 ρ 23 )exp[ ( ρ 12 + +ρ 23 ) 2 4Dt ] ( 1 ρ 12 + 1 ρ + 23 )exp[ ( ρ 12 +ρ + 23 ) 2 4Dt ]+( 1 ρ 12 + 1 ρ 23 )exp[ ( ρ 12 +ρ 23 ) 2 4Dt ] }
ρ 12 + = [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 + ( z 2 ) 2 ] 1 2 ρ 12 = [ ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 + ( z 2 +2 z 0 ) 2 ] 1 2 ρ 23 + = [ ( x 3 x 21 ) 2 + ( y 3 y 2 ) 2 + ( z 2 ) 2 ] 1 2 ρ 23 =[ ( x 3 x 2 ) 2 + ( y 3 y 2 ) 2 + ( 2 z 0 +z 2 ) 2 ]
g 1 (τ,s)= i=1 M W(s ) i exp(2 k 2 τ j N μ s ,(j) s ij D B (j) )