Abstract

In this work, diffuse correlation spectroscopy (DCS) is explored in multi-layered geometries. A quantitative comparison of an homogeneous versus a two-layered model efficiencies to recover flow changes is presented. By simulating a realistic human head with MRI anatomical data, we show that the two-layered model allows distinction between changes in superficial layers and brain. We also show that the two-layered model provides a better estimate of the flow change than the homogeneous one. Experimental measurements with a two-layered dynamical phantom confirm the ability of the two-layered analytical model to distinguish flow increase in each layer.

© 2008 Optical Society of America

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2008 (1)

F. Lesage, L. Gagnon, and M. Dehaes, “Diffuse Optical-MRI fusion and applications,” Proc. SPIE 6850, C1–C11 (2008).

2006 (2)

G. Yu, T. Durduran, C. Zhou, T. C. Zhu, J. C. Finlay, T. M. Busch, S. B. Malkowicz, S. M. Hahn, and A. G. Yodh, “Real-time In Situ Monitoring of Human Prostate Photodynamic Therapy with Diffuse Light,” Photochem. Photobiol. 82, 1279–1284 (2006).
[CrossRef] [PubMed]

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

2005 (3)

G. Yu, T. Durduran, H. W. Wang, C. Zhou, E. M. Putt, H. M. Saunders, C. M. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Bush, “Noninvasive Monitoring of Murine Tumor Blood Flow During and After Photodynamic Therapy Provides Early Assessment of Therapeutic Efficacy,” Clin. Cancer Res. 11, 3543–3552 (2005).
[CrossRef] [PubMed]

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

T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, “Diffuse optical measurement of blood flow in breast tumors,” Opt. Lett. 30, 2915–2917 (2005).
[CrossRef] [PubMed]

2004 (3)

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

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

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

2003 (3)

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

F. Martelli, A. Sassaroli, S. Del-Bianco, Y. Yamada, and G. Zaccanti, “Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfucntion method.” Phys. Rev. E 67, 056,623 (2003).
[CrossRef]

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, 865–879 (2003).
[CrossRef] [PubMed]

2002 (1)

H. Obrig and A. Villringer, “Beyond the visible - imaging the human brain with light,” J. Cereb. Blood Flow Metab. 23, 1–18 (2002).
[PubMed]

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, 2053–2065 (2001).
[CrossRef] [PubMed]

1999 (3)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problem 15, R41–R93 (1999).
[CrossRef]

A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44, 2689–2702 (1999).
[CrossRef] [PubMed]

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

1998 (2)

1996 (1)

D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media : theory and biomedical applications,” Ph.D. thesis, University of Pennsylvania (1996).

1995 (3)

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

D. J. Durian, “Accuracy of diffusing-wave spectroscopy theories,” Phys. Rev. E 51, 3350–3358 (1995).
[CrossRef]

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Prog. Biomed. 47, 131–146 (1995).
[CrossRef]

1994 (4)

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, and J. G. Aarnoudse, “Laser Doppler blood flowmetry using two wavelengths: Monte Carlo simulations and measurements,” Appl. Opt. 33, 3549–3558 (1994).
[CrossRef] [PubMed]

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

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbman, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

D. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

1993 (5)

B. J. Tromberg, L. O. Svaasand, T. Tsay, and R. C. Haskell, “Properties of photon density waves in multiplesscattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

D. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47 (1993).
[CrossRef]

A. Villringer, C. Hock, L. Schleinkofer, and U. Dirnagl, “Near Infrared Spectroscopy (NIRS): A New Tool to Study Hemodynamic Changes During Activation of Brain Function in Human Adults,” Neurosci. Lett. 154, 101–104 (1993).
[CrossRef] [PubMed]

Y. Hoshi and M. Tamura, “Multichannel near-infrared optical imaging of human brain activity,” J. Appl. Physiol. 75, 1842–1846 (1993).
[PubMed]

R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, and J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–434 (1993).
[CrossRef] [PubMed]

1992 (1)

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, and U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

1991 (2)

A. A. Middleton and D. S. Fisher, “Discrete scatterers and autocorrelations of multiply scattered light,” Phys. Rev. B 43, 5934–5938 (1991).
[CrossRef]

T. Bellini, M. A. Glaser, N. A. Clark, and V. Degiorgio, “Effects of finite laser coherence in quasielastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herboltzheimer, “Diffusing-wave spectroscopy,” Phys. Rev. Lett. 60, 1134–1137 (1988).
[CrossRef] [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 65, 409–413 (1987).
[CrossRef]

1983 (1)

1969 (1)

G. H. Golub and J. H. Welsch, “Calculation of Gauss quadrature rules,” Math. Comput. 23, 221–230 (1969).
[CrossRef]

1941 (1)

L. G. Henyey and J. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).
[CrossRef]

Aarnoudse, J. G.

Ackerson, B. J.

R. L. Dougherty, B. J. Ackerson, N. M. Reguigui, F. Dorri-Nowkoorani, and U. Nobbman, “Correlation transfer: development and application,” J. Quant. Spectrosc. Radiat. Transfer 52, 713–727 (1994).
[CrossRef]

B. J. Ackerson, R. L. Dougherty, N. M. Reguigui, and U. Nobbman, “Correlation transfer: application of radiative transfer solution methods to photon correlation problems,” J. Thermophys. Heat Transfer 6, 577–588 (1992).
[CrossRef]

Arridge, S.

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

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problem 15, R41–R93 (1999).
[CrossRef]

Bassi, A.

F. Martelli, S. D. Bianco, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Phantom validation and in vivo application of an inversion procedure for retrieving the optical properties of diffusive layered media from time-resolved reflectance measurements.” Opt. Lett.29 (2004).
[CrossRef] [PubMed]

Bays, R.

Bellini, T.

T. Bellini, M. A. Glaser, N. A. Clark, and V. Degiorgio, “Effects of finite laser coherence in quasielastic multiple scattering,” Phys. Rev. A 44, 5215–5223 (1991).
[CrossRef] [PubMed]

Bianco, S. D.

F. Martelli, S. D. Bianco, G. Zaccanti, A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, and R. Cubeddu, “Phantom validation and in vivo application of an inversion procedure for retrieving the optical properties of diffusive layered media from time-resolved reflectance measurements.” Opt. Lett.29 (2004).
[CrossRef] [PubMed]

Boas, D.

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

D. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

D. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47 (1993).
[CrossRef]

D. Boas, L. E. Campbell, and A. G. Yodh, “Scattering and Imaging with Diffusing Temporal Field Correlations,” Phys. Rev. Lett.75 (1995).
[CrossRef] [PubMed]

D. Boas and A. G. Yodh, “Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation,” J. Opt. Soc. Am. A14 (1997).

T. Huppert, R. Hoge, A. M. Dale, M. Franceschini, and D. Boas, “Quantitative spatial comparison of diffuse optical imaging with blood oxygen level-dependent and arterial spin labeling-based functional magnetic resonance imaging,” J. Biomed. Opt.11 (2006).
[CrossRef] [PubMed]

D. Boas, J. Culver, J. Stott, and A. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogenous media including the adult human head,” Opt. Express10 (2002).
[PubMed]

Boas, D. A.

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, 865–879 (2003).
[CrossRef] [PubMed]

D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media : theory and biomedical applications,” Ph.D. thesis, University of Pennsylvania (1996).

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C. Zhou, G. Q. Yu, D. Furuya, J. H. Greenberg, A. G. Yodh, and T. Durduran, “Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain,” Opt. Express 14, 1125–1144 (2006).
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Figures (9)

Fig. 1.
Fig. 1.

Localisation of the optical probe on the MRI anatomical data. The human head was segmented in skin, skull, CSF, white matter and gray matter. Source and detectors are illustrated by red and green arrows respectively.

Fig. 2.
Fig. 2.

Schematic view of the dynamical phantom. The division which separates the two compartments is mobile allowing different thicknesses for the first layer. The two compartments are filled with a 1 % Liposin solution. The optical fibers are fixed to the phantom by a rubber band glued to its side.

Fig. 3.
Fig. 3.

Comparison of MC simulations with the analytical model of Eqs. (5) and (7) on a two-layered medium. The simulations are represented by points while the analytical model by solid lines. The thickness of the first layer was 10 mm and the source-detector (S-D) distances varied from 10 to 30 mm. The optical properties (µa =0.0074 mm-1 and µ s =1.28 mm-1) were constant for the two layers while the Brownian diffusion coefficient DB was 10-8 mm2/s and 10-6 mm2/s for the first and second layer respectively.

Fig. 4.
Fig. 4.

Changes in DB recovered from MC simulations both with the two-layered and the homogeneous model. These changes were estimated by recovering the DB of two simulations. In the first one (baseline), we set the Brownian diffusion coefficient to 10-8 in the 10 mm thick first layer and to 10-7 in the second one. In the second simulation (increased flow) we kept the DB to 10-8 in the first layer but increased it to 1.5×10-7 in the second layer which corresponds to an increase of 50 %. The source-detector (S-D) distances varied from 10 to 30 mm and the optical properties (µa =0.01 mm-1 and µ s =1.28 mm-1) were constant for the two layers in both simulations (baseline and increased flow).

Fig. 5.
Fig. 5.

Error on the recovered flow change due to the estimation of the absorption µa and reduced scattering µ s coefficient for each layer. The thickness of the first layer was 10 mm and the S-D distance was 15 mm. Top) Error on the assumed absorption. Bottom) Error on the assumed scattering.

Fig. 6.
Fig. 6.

Error on the recovered flow changes due to a wrong estimation of the thickness of the first layer. For this simulation, the real absorption coefficient was 0.01 mm-1 and the effective scattering coefficient µ s was 1.28 mm-1 for both layers. The thickness of the first layer was 10 mm and the S-D distance was 15 mm.

Fig. 7.
Fig. 7.

Recovered CBF changes in each layer with the two-layered model following an increase of 50 % of the Brownian diffusion coefficient in the brain tissue (white and gray matter). Again, the source and the detectors were located over the motor region (Fig. (1)).

Fig. 8.
Fig. 8.

Experimental DCS measurements done on a two-layered dynamical phantom. The set up consisted in two detectors located at 10 mm from the source and two others at 20 mm. The blue curves were obtained while the liquid was at rest in the phantom and the red ones when agitation was induced in the second layer by the magnetic agitator. The thickness of the first layer of the phantom was 10 mm while the S-D distances were 10 and 20 mm.

Fig. 9.
Fig. 9.

Decreases in recovered DB measured on the phantom after the introduction of the Liposin solution containing 6 % of glycerol in the second compartment. The data was analyzed both with the homogeneous and the two layered model. The thickness of the first layer of the phantom was 10 mm while the S-D distances were 10 and 20 mm. The real DB decrease of 37 % has been measured experimentally on an homogeneous phantom using the homogeneous model to analyze the data.

Tables (2)

Tables Icon

Table 1. Optical properties used in the MC simulations of the segmented human head. [57]

Tables Icon

Table 2. Brownian diffusion coefficients recovered using the two-layered analytical model in the fitting procedure. In these fits, the thickness of the first layer and the optical properties was assumed to be known. In these simulations, µ s =1.28 mm-1 for both layers and µa was respectively 0.008 and 0.0176 mm-1 for the first and second layers. The thickness of the first layer was 10 mm. Results obtained using a homogeneous model are also shown for comparison.

Equations (15)

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G 1 ( r , τ ) = E ( r , t ) E * ( r , t + τ ) .
[ D 2 μ a 1 3 μ s k 0 2 Δ r 2 ( τ ) ] G 1 ( x , y , z , τ ) = S ( x , y , z )
[ D 1 2 μ a 1 2 μ s 1 k 0 2 D B 1 τ ] G 1 1 ( x , y , z , τ ) = δ ( x , y , z z 0 ) 0 z l ,
[ D 2 2 μ a 2 2 μ s 2 k 0 2 D B 2 τ ] G 1 2 ( x , y , z , τ ) = 0 l z
G ˜ 1 1 ( s , z , τ ) = sinh [ α 1 ( z b + z 0 ) ] D 1 α 1 × D 1 α 1 cosh [ α 1 ( z ) ] + D 2 α 2 sinh [ α 1 ( z ) ] D 1 α 1 cosh [ α 1 ( + z b ) ] + D 2 α 2 sinh [ α 1 ( + z b ) ]
sinh [ α 1 ( z 0 z ) ] D 1 α 1
z b = 1 + R eff 1 R eff 2 D 1 .
G 1 1 ( ρ , z , τ ) = 1 2 π 0 G ˜ 1 1 ( s , z , τ ) 1 s J 0 ( s ρ ) d s
g 1 s ( τ ) = exp [ 1 6 q 2 Δ r 2 ( τ ) ]
g 1 γ ( τ ) = Σ j = 1 n exp [ 2 k 0 2 ( 1 cos θ j ) D B j τ ] .
g 1 γ ( τ ) = Σ i = 1 m Σ j = 1 n exp [ 2 k 0 2 ( 1 cos θ j ) D B j τ μ a i L i ]
G 2 ( τ ) = I ( t ) I ( t + τ ) .
G 2 ( τ ) = I 2 + β G 1 ( τ ) 2
g 2 ( τ ) = 1 + β g 1 ( τ ) 2
g 1 ( τ ) = G 1 ( τ ) I .

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