Abstract

We have studied the spatial distributions of the sensitivity of time-resolved near-infrared diffuse reflectance measurement. Sensitivity factors representing a change of parameters of a measured optical signal induced by absorption perturbation in a certain voxel of the medium were simulated using the diffusion equation solution. The parameters were statistical moments of measured distributions of time of flight of photons (DTOFs) i.e., the total number of photons, mean time of flight and variance. The distributions of the sensitivity of statistical moments of DTOFs to a change in absorption were generated for various source-detector separations and various optical properties of the medium. Furthermore, differential sensitivity distributions for two different source-detector separations were calculated. A measurement geometry, in which two detection spots, separated by 5 mm, in combination with two sources was proposed. For this setup differences between the signals obtained for both detectors were calculated independently for both sources and afterward summed up for both source positions. Obtained differences in moments of DTOFs assessed at two source-detector separations and summed up for different positioning of the sources allowed to shape up the sensitivity profiles. Calculated sensitivity profiles show that positive sensitivities of the mean time of flight of photons and variance of the DTOF can be obtained. These positive sensitivity areas are located just between both detection spots and cover the compartment located deeply in the medium. The sensitivity in superficial compartments of the medium is negative and much smaller in amplitude. The proposed technique can be used for improved discrimination of optical signals related to the intracerebral change in absorption which remains a serious obstacle in the application of the NIRS technique in the assessment of brain oxygenation or perfusion.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

K. Tgavalekos, T. Pham, N. Krishnamurthy, A. Sassaroli, and S. Fantini, “Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects,” PLoS One 14(2), e0211710 (2019)..
[Crossref]

2016 (4)

2014 (2)

L. Gagnon, M. A. Yucel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” NeuroImage 85(Pt 1), 127–135 (2014).
[Crossref]

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

2013 (3)

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

A. Puszka, L. Herve, A. Planat-Chretien, A. Koenig, J. Derouard, and J. M. Dinten, “Time-domain reflectance diffuse optical tomography with Mellin-Laplace transform for experimental detection and depth localization of a single absorbing inclusion,” Biomed. Opt. Express 4(4), 569–583 (2013).
[Crossref]

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013).
[Crossref]

2012 (2)

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

S. N. Davie and H. P. Grocott, “Impact of extracranial contamination on regional cerebral oxygen saturation: a comparison of three cerebral oximetry technologies,” Anesthesiology 116(4), 834–840 (2012).
[Crossref]

2010 (2)

J. T. Elliott, M. Diop, K. M. Tichauer, T. Y. Lee, and K. St Lawrence, “Quantitative measurement of cerebral blood flow in a juvenile porcine model by depth-resolved near-infrared spectroscopy,” J. Biomed. Opt. 15(3), 037014 (2010).
[Crossref]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

2008 (1)

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

2007 (1)

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

2006 (3)

R. Pierrat, J. J. Greffet, and R. Carminati, “Photon diffusion coefficient in scattering and absorbing media,” J. Opt. Soc. Am. A 23(5), 1106–1110 (2006)..
[Crossref]

J. Selb, D. K. Joseph, and D. A. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11(4), 044008 (2006).
[Crossref]

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

2004 (2)

2002 (1)

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

2001 (2)

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, “Determining changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46(3), 879–896 (2001).
[Crossref]

V. Ntziachristos and B. Chance, “Accuracy limits in the determination of absolute optical properties using time-resolved NIR spectroscopy,” Med. Phys. 28(6), 1115–1124 (2001).
[Crossref]

1997 (1)

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

1995 (1)

1994 (2)

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]

K. Furutsu and Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 50(5), 3634–3640 (1994).
[Crossref]

1993 (1)

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

1989 (2)

Abdalmalak, A.

al-Rawi, P.

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

Andersson-Engels, S.

Arridge, S. R.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Auger, H.

Bherer, L.

Blaney, G.

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “New near-infrared spectroscopy method for local measurements of cerebral blood flow,” European Conferences on Biomedical Optics, Vol. 11074. (SPIE, 2019)

A. Sassaroli, G. Blaney, and S. Fantini, “Dual-slope method for enhanced depth sensitivity in diffuse optical spectroscopy,” J. Opt. Soc. Am. A (2009).

G. Blaney, A. Sassaoroli, T. Pham, C. Fernandez, and S. Fantini, “Phase dual-slopes in frequency-domain near-infrared spectroscopy for enhanced sensitivity to brain tissue: First applications to human subjects,” J. Biophotonics, Sep. 3 2019.

Boas, D. A.

L. Gagnon, M. A. Yucel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” NeuroImage 85(Pt 1), 127–135 (2014).
[Crossref]

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

J. Selb, D. K. Joseph, and D. A. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11(4), 044008 (2006).
[Crossref]

Borowska-Solonynko, A.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

Boucher, E.

Caffini, M.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

Caldwell, M.

M. Caldwell, F. Scholkmann, U. Wolf, M. Wolf, C. Elwell, and I. Tachtsidis, “Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy,” NeuroImage 143, 91–105 (2016).
[Crossref]

Carminati, R.

Chance, B.

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

V. Ntziachristos and B. Chance, “Accuracy limits in the determination of absolute optical properties using time-resolved NIR spectroscopy,” Med. Phys. 28(6), 1115–1124 (2001).
[Crossref]

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non/invasive measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989).
[Crossref]

Chen, Y.

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

Contini, D.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

Cooper, R. J.

L. Gagnon, M. A. Yucel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” NeuroImage 85(Pt 1), 127–135 (2014).
[Crossref]

Cope, M.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Davie, S. N.

S. N. Davie and H. P. Grocott, “Impact of extracranial contamination on regional cerebral oxygen saturation: a comparison of three cerebral oximetry technologies,” Anesthesiology 116(4), 834–840 (2012).
[Crossref]

Dehaes, M.

Delpy, D. T.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Derouard, J.

Dinten, J. M.

Diop, M.

Elliott, J. T.

J. T. Elliott, M. Diop, K. M. Tichauer, T. Y. Lee, and K. St Lawrence, “Quantitative measurement of cerebral blood flow in a juvenile porcine model by depth-resolved near-infrared spectroscopy,” J. Biomed. Opt. 15(3), 037014 (2010).
[Crossref]

Elwell, C.

M. Caldwell, F. Scholkmann, U. Wolf, M. Wolf, C. Elwell, and I. Tachtsidis, “Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy,” NeuroImage 143, 91–105 (2016).
[Crossref]

Essenpris, M.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Fabbri, F.

F. Fabbri, A. Sassaroli, M. E. Henry, and S. Fantini, “Optical measurements of absorption changes in two-layered diffusive media,” Phys. Med. Biol. 49(7), 1183–1201 (2004)..
[Crossref]

Fadel, P. J.

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

Fantini, S.

K. Tgavalekos, T. Pham, N. Krishnamurthy, A. Sassaroli, and S. Fantini, “Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects,” PLoS One 14(2), e0211710 (2019)..
[Crossref]

F. Fabbri, A. Sassaroli, M. E. Henry, and S. Fantini, “Optical measurements of absorption changes in two-layered diffusive media,” Phys. Med. Biol. 49(7), 1183–1201 (2004)..
[Crossref]

A. Sassaroli, G. Blaney, and S. Fantini, “Dual-slope method for enhanced depth sensitivity in diffuse optical spectroscopy,” J. Opt. Soc. Am. A (2009).

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “New near-infrared spectroscopy method for local measurements of cerebral blood flow,” European Conferences on Biomedical Optics, Vol. 11074. (SPIE, 2019)

G. Blaney, A. Sassaoroli, T. Pham, C. Fernandez, and S. Fantini, “Phase dual-slopes in frequency-domain near-infrared spectroscopy for enhanced sensitivity to brain tissue: First applications to human subjects,” J. Biophotonics, Sep. 3 2019.

Feng, T. C.

Fernandez, C.

G. Blaney, A. Sassaoroli, T. Pham, C. Fernandez, and S. Fantini, “Phase dual-slopes in frequency-domain near-infrared spectroscopy for enhanced sensitivity to brain tissue: First applications to human subjects,” J. Biophotonics, Sep. 3 2019.

Firbank, M.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Fischer, T.

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

Furutsu, K.

K. Furutsu and Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 50(5), 3634–3640 (1994).
[Crossref]

Gagnon, L.

L. Gagnon, M. A. Yucel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” NeuroImage 85(Pt 1), 127–135 (2014).
[Crossref]

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

Gauthier, C.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

Greffet, J. J.

Griffiths, P.

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

Grocott, H. P.

S. N. Davie and H. P. Grocott, “Impact of extracranial contamination on regional cerebral oxygen saturation: a comparison of three cerebral oximetry technologies,” Anesthesiology 116(4), 834–840 (2012).
[Crossref]

Haskell, R. C.

Henry, M. E.

F. Fabbri, A. Sassaroli, M. E. Henry, and S. Fantini, “Optical measurements of absorption changes in two-layered diffusive media,” Phys. Med. Biol. 49(7), 1183–1201 (2004)..
[Crossref]

Herve, L.

Hetzer, R.

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

Hiraoka, M.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Hoge, R.

Hoge, R. D.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

Horiuchi, M.

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

Intes, X.

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

Ishimaru, A.

Jacques, S. L.

S. L. Jacques, “Optical properties of biological tissues: a review,” Phys. Med. Biol. 58(11), R37–R61 (2013).
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Janusek, D.

Jelzow, A.

A. Jelzow, In vivo quantification of absorption changes in the human brain by time-domain diffuse near-infrared spectroscopy (Technischen Universität Berlin, 2013).

Joseph, D. K.

J. Selb, D. K. Joseph, and D. A. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11(4), 044008 (2006).
[Crossref]

Kacprzak, M.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

Kirkpatrick, P. J.

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

Koenig, A.

Komine, H.

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

Krajewski, P.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

Krishnamurthy, N.

K. Tgavalekos, T. Pham, N. Krishnamurthy, A. Sassaroli, and S. Fantini, “Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects,” PLoS One 14(2), e0211710 (2019)..
[Crossref]

Kuebler, W. M.

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

Kuppe, H.

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

Lam, J. M.

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

Lee, T. Y.

J. T. Elliott, M. Diop, K. M. Tichauer, T. Y. Lee, and K. St Lawrence, “Quantitative measurement of cerebral blood flow in a juvenile porcine model by depth-resolved near-infrared spectroscopy,” J. Biomed. Opt. 15(3), 037014 (2010).
[Crossref]

Lesage, F.

H. Auger, L. Bherer, E. Boucher, R. Hoge, F. Lesage, and M. Dehaes, “Quantification of extra-cerebral and cerebral hemoglobin concentrations during physical exercise using time-domain near infrared spectroscopy,” Biomed. Opt. Express 7(10), 3826–3842 (2016).
[Crossref]

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

Liebert, A.

D. Milej, A. Abdalmalak, D. Janusek, M. Diop, A. Liebert, and K. St Lawrence, “Time-resolved subtraction method for measuring optical properties of turbid media,” Appl. Opt. 55(7), 1507–1513 (2016).
[Crossref]

D. Milej, A. Abdalmalak, P. McLachlan, M. Diop, A. Liebert, and K. St Lawrence, “Subtraction-based approach for enhancing the depth sensitivity of time-resolved NIRS,” Biomed. Opt. Express 7(11), 4514–4526 (2016).
[Crossref]

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
[Crossref]

S. Wojtkiewicz, A. Liebert, H. Rix, P. Sawosz, and R. Maniewski, A novel method for measurement of dynamic light scattering phase function of particles utilizing laser-Doppler power density spectra (Optical Society of America, 2012).

Macdonald, R.

Maniewski, R.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

S. Wojtkiewicz, A. Liebert, H. Rix, P. Sawosz, and R. Maniewski, A novel method for measurement of dynamic light scattering phase function of particles utilizing laser-Doppler power density spectra (Optical Society of America, 2012).

McAdams, M. S.

McLachlan, P.

Milej, D.

Miyazawa, T.

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

Moeller, M.

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

Moller, M.

Ntziachristos, V.

V. Ntziachristos and B. Chance, “Accuracy limits in the determination of absolute optical properties using time-resolved NIR spectroscopy,” Med. Phys. 28(6), 1115–1124 (2001).
[Crossref]

Obrig, H.

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
[Crossref]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, “Determining changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46(3), 879–896 (2001).
[Crossref]

Ogoh, S.

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

Osei, E. K.

Patterson, M. S.

Pham, T.

K. Tgavalekos, T. Pham, N. Krishnamurthy, A. Sassaroli, and S. Fantini, “Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects,” PLoS One 14(2), e0211710 (2019)..
[Crossref]

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “New near-infrared spectroscopy method for local measurements of cerebral blood flow,” European Conferences on Biomedical Optics, Vol. 11074. (SPIE, 2019)

G. Blaney, A. Sassaoroli, T. Pham, C. Fernandez, and S. Fantini, “Phase dual-slopes in frequency-domain near-infrared spectroscopy for enhanced sensitivity to brain tissue: First applications to human subjects,” J. Biophotonics, Sep. 3 2019.

Pickard, J. D.

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

Pierrat, R.

Pifferi, A.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

Planat-Chretien, A.

Puszka, A.

Re, R.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

Rinneberg, H.

Rix, H.

S. Wojtkiewicz, A. Liebert, H. Rix, P. Sawosz, and R. Maniewski, A novel method for measurement of dynamic light scattering phase function of particles utilizing laser-Doppler power density spectra (Optical Society of America, 2012).

Sassaoroli, A.

G. Blaney, A. Sassaoroli, T. Pham, C. Fernandez, and S. Fantini, “Phase dual-slopes in frequency-domain near-infrared spectroscopy for enhanced sensitivity to brain tissue: First applications to human subjects,” J. Biophotonics, Sep. 3 2019.

Sassaroli, A.

K. Tgavalekos, T. Pham, N. Krishnamurthy, A. Sassaroli, and S. Fantini, “Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects,” PLoS One 14(2), e0211710 (2019)..
[Crossref]

F. Fabbri, A. Sassaroli, M. E. Henry, and S. Fantini, “Optical measurements of absorption changes in two-layered diffusive media,” Phys. Med. Biol. 49(7), 1183–1201 (2004)..
[Crossref]

T. Pham, A. Sassaroli, G. Blaney, and S. Fantini, “New near-infrared spectroscopy method for local measurements of cerebral blood flow,” European Conferences on Biomedical Optics, Vol. 11074. (SPIE, 2019)

A. Sassaroli, G. Blaney, and S. Fantini, “Dual-slope method for enhanced depth sensitivity in diffuse optical spectroscopy,” J. Opt. Soc. Am. A (2009).

Sawosz, P.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

S. Wojtkiewicz, A. Liebert, H. Rix, P. Sawosz, and R. Maniewski, A novel method for measurement of dynamic light scattering phase function of particles utilizing laser-Doppler power density spectra (Optical Society of America, 2012).

Scholkmann, F.

M. Caldwell, F. Scholkmann, U. Wolf, M. Wolf, C. Elwell, and I. Tachtsidis, “Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy,” NeuroImage 143, 91–105 (2016).
[Crossref]

Selb, J.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

J. Selb, D. K. Joseph, and D. A. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11(4), 044008 (2006).
[Crossref]

Smielewski, P.

J. M. Lam, P. Smielewski, P. al-Rawi, P. Griffiths, J. D. Pickard, and P. J. Kirkpatrick, “Internal and external carotid contributions to near-infrared spectroscopy during carotid endarterectomy,” Stroke 28(5), 906–911 (1997).
[Crossref]

Spinelli, L.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

St Lawrence, K.

Steinbrink, J.

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
[Crossref]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, “Determining changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46(3), 879–896 (2001).
[Crossref]

Sugawara, J.

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

Svaasand, L. O.

Tachtsidis, I.

M. Caldwell, F. Scholkmann, U. Wolf, M. Wolf, C. Elwell, and I. Tachtsidis, “Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy,” NeuroImage 143, 91–105 (2016).
[Crossref]

Tgavalekos, K.

K. Tgavalekos, T. Pham, N. Krishnamurthy, A. Sassaroli, and S. Fantini, “Frequency-resolved analysis of coherent oscillations of local cerebral blood volume, measured with near-infrared spectroscopy, and systemic arterial pressure in healthy human subjects,” PLoS One 14(2), e0211710 (2019)..
[Crossref]

Tichauer, K. M.

J. T. Elliott, M. Diop, K. M. Tichauer, T. Y. Lee, and K. St Lawrence, “Quantitative measurement of cerebral blood flow in a juvenile porcine model by depth-resolved near-infrared spectroscopy,” J. Biomed. Opt. 15(3), 037014 (2010).
[Crossref]

Torricelli, A.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

Tromberg, B. J.

Tsay, T. T.

Tu, T.

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

Uludag, K.

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
[Crossref]

vanderZee, P.

M. Hiraoka, M. Firbank, M. Essenpris, M. Cope, S. R. Arridge, P. vanderZee, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
[Crossref]

Villringer, A.

Wabnitz, H.

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43(15), 3037–3047 (2004).
[Crossref]

J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, and H. Rinneberg, “Determining changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46(3), 879–896 (2001).
[Crossref]

Weigl, W.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

Wilson, B. C.

Wojtkiewicz, S.

S. Wojtkiewicz, A. Liebert, H. Rix, P. Sawosz, and R. Maniewski, A novel method for measurement of dynamic light scattering phase function of particles utilizing laser-Doppler power density spectra (Optical Society of America, 2012).

Wolf, M.

M. Caldwell, F. Scholkmann, U. Wolf, M. Wolf, C. Elwell, and I. Tachtsidis, “Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy,” NeuroImage 143, 91–105 (2016).
[Crossref]

Wolf, U.

M. Caldwell, F. Scholkmann, U. Wolf, M. Wolf, C. Elwell, and I. Tachtsidis, “Modelling confounding effects from extracerebral contamination and systemic factors on functional near-infrared spectroscopy,” NeuroImage 143, 91–105 (2016).
[Crossref]

Yamada, Y.

K. Furutsu and Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 50(5), 3634–3640 (1994).
[Crossref]

Yucel, M. A.

L. Gagnon, M. A. Yucel, D. A. Boas, and R. J. Cooper, “Further improvement in reducing superficial contamination in NIRS using double short separation measurements,” NeuroImage 85(Pt 1), 127–135 (2014).
[Crossref]

Zhang, J.

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

Zolek, N.

P. Sawosz, M. Kacprzak, W. Weigl, A. Borowska-Solonynko, P. Krajewski, N. Zolek, R. Maniewski, and A. Liebert, “Experimental estimation of the sensitivity profiles of time-resolved reflectance measurement: phantom and cadaver studies,” Phys. Med. Biol. 57(23), 7973–7981 (2012).
[Crossref]

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

Zucchelli, L.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” NeuroImage 85(Pt 1), 28–50 (2014).
[Crossref]

Adv. Exp. Med. Biol. (1)

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” Adv. Exp. Med. Biol. 662, 143–148 (2010).
[Crossref]

Anesthesiology (1)

S. N. Davie and H. P. Grocott, “Impact of extracranial contamination on regional cerebral oxygen saturation: a comparison of three cerebral oximetry technologies,” Anesthesiology 116(4), 834–840 (2012).
[Crossref]

Appl. Opt. (5)

Biomed. Opt. Express (3)

Eur. J. Appl. Physiol. (1)

T. Miyazawa, M. Horiuchi, H. Komine, J. Sugawara, P. J. Fadel, and S. Ogoh, “Skin blood flow influences cerebral oxygenation measured by near-infrared spectroscopy during dynamic exercise,” Eur. J. Appl. Physiol. 113(11), 2841–2848 (2013).
[Crossref]

J. Biomed. Opt. (5)

J. T. Elliott, M. Diop, K. M. Tichauer, T. Y. Lee, and K. St Lawrence, “Quantitative measurement of cerebral blood flow in a juvenile porcine model by depth-resolved near-infrared spectroscopy,” J. Biomed. Opt. 15(3), 037014 (2010).
[Crossref]

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008).
[Crossref]

J. Selb, D. K. Joseph, and D. A. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11(4), 044008 (2006).
[Crossref]

M. Kacprzak, A. Liebert, P. Sawosz, N. Zolek, and R. Maniewski, “Time-resolved optical imager for assessment of cerebral oxygenation,” J. Biomed. Opt. 12(3), 034019 (2007).
[Crossref]

T. Tu, Y. Chen, J. Zhang, X. Intes, and B. Chance, “Analysis on performance and optimization of frequency-domain near-infrared instruments,” J. Biomed. Opt. 7(4), 643 (2002).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Thorac. Cardiovasc. Surg. (1)

J. Steinbrink, T. Fischer, H. Kuppe, R. Hetzer, K. Uludag, H. Obrig, and W. M. Kuebler, “Relevance of depth resolution for cerebral blood flow monitoring by near-infrared spectroscopic bolus tracking during cardiopulmonary bypass,” J. Thorac. Cardiovasc. Surg. 132(5), 1172–1178 (2006).
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Med. Phys. (1)

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Figures (9)

Fig. 1.
Fig. 1. Geometry used for sensitivity distributions simulations. Red arrows mark positions of source and detector located at interoptode distance on the surface of the medium (plane XZ).
Fig. 2.
Fig. 2. Spatial distributions of sensitivity factors (for attenuation – MPP, for mean time of flight – MTSF and for variance of the DTOF – VSF) obtained for source-detector separation of ρ=3cm i.e. for the source located at x = 0, y = 0,z = 0 and the detection spot located at x = 3cm, y = 0, z = 0 (geometry presented in Fig. 1).
Fig. 3.
Fig. 3. Distributions of sensitivity factors (for attenuation – MPP, for mean time of flight – MTSF and for variance of the DTOF – VSF) in XZ projection for different source-detector separations ρ.
Fig. 4.
Fig. 4. Sensitivities of differences between statistical moments ΔSF = SFρ1-SFρ2 acquired at two source-detector separations ρ1=3 cm and ρ2=2.5 cm presented in XZ projection.
Fig. 5.
Fig. 5. Distrubutions of sensitivity differences between statistical moments ΔSF = SFρ1-SFρ2 acquired for ρ1=3 cm and three different ρ2 (2 cm, 2.5 cm and 2.75 cm), presented in XZ projection.
Fig. 6.
Fig. 6. The geometry of measurement scenario in which two sources were used and for each of them two detection spots were applied.
Fig. 7.
Fig. 7. Distributions of sums of the sensitivities ΔSF obtained for two sources and two detectors Σs1s2ΔSF presented in XZ projection for ρ1=3 cm and ρ2=2.5 cm and for different positions of the set of sources and detectors as shown in left column.
Fig. 8.
Fig. 8. Distributions of sums of the sensitivities Σs1s2ΔSF obtained for two sources and two detectors (at the same location for both sources) presented in XZ projection for ρ1=3 cm and three different ρ2 values (2 cm, 2.5 cm and 2.75 cm).
Fig. 9.
Fig. 9. Distributions of sums of the sensitivities Σs1s2ΔSF obtained for two sources and two detectors (at the same location for both sources) presented in XZ projection for ρ1=3cm and ρ2 = 2.5 cm, obtained for three different values of reduced scattering coefficient µs’=20 cm-1, 10 cm-1 and 5 cm-1.

Equations (14)

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1 c t Φ ( r , t ) D 2 Φ ( r , t ) + μ a Φ ( r , t ) = S ( r , t )
R h ( ρ , t ) = ( μ s ) 1 ( 4 π D c ) 3 / 2 t 5 / 2 exp ( ρ 2 4 D c t μ a c t )
Δ R ( r , ρ , t ) = Δ μ a d V S [ Φ ( r , t ) E ( r , ρ , t ) ]
R ( r , ρ , t ) = R h ( ρ , t ) + Δ R ( r , ρ , t )
m k ( r , ρ ) = 0 t k R ( r , ρ , t ) d t / 0 R ( r , ρ , t ) d t
Δ A = log ( N t o t N t o t h )
Δ t = t t h
Δ V = V V h
M P P i = Δ A Δ μ a , i
M T S F i = Δ t Δ μ a , i
V S F i = Δ V Δ μ a , i
Δ A = c t Δ μ a i M P P i = c t
Δ t = c V Δ μ a i M T S F i = c V
Δ V = c m 3 Δ μ a i V S F i = c m 4