Abstract

We propose a method to isolate absorption trends confined to the lower layer of a two-layer turbid medium, as is desired in near-infrared spectroscopy (NIRS) of cerebral hemodynamics. Several two-layer Monte Carlo simulations of NIRS time series were generated using a physiologically relevant range of optical properties and varying the absorption coefficients due to bottom-layer, top-layer, and/or global fluctuations. Initial results showed that by measuring absorption trends at two source–detector separations and performing a least-squares fit of one to the other, processed signals strongly resemble the simulated bottom-layer absorption properties. Through this approach, it was demonstrated that fitting coefficients can be estimated within less than ±2% of the ideal value without any a priori knowledge of the optical properties present in the model. An analytical approximation for the least-squares coefficient provides physical insight into the nature of errors and suggests ways to reduce them.

© 2005 Optical Society of America

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  1. J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
    [CrossRef] [PubMed]
  2. A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
    [CrossRef] [PubMed]
  3. M. Franceschini, D. Boas, “Noninvasive measurement if neuronal activity with near infrared optical imaging,” Neuroimage 21, 372–386 (2004).
    [CrossRef] [PubMed]
  4. K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
    [CrossRef] [PubMed]
  5. G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
    [CrossRef] [PubMed]
  6. D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
    [CrossRef] [PubMed]
  7. H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
    [CrossRef] [PubMed]
  8. Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
    [CrossRef]
  9. T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
    [CrossRef]
  10. P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
    [CrossRef] [PubMed]
  11. F. Fabbri, A. Sassaroli, M. Henry, S. Fantini, “Optical measurements of absorption changes in two-layered diffusive media,” Phys. Med. Biol. 49, 1183–1201 (2004).
    [CrossRef] [PubMed]
  12. M. Hiraoka, M. Firbank, M. Essenpries, M. Cope, S. R. Arridge, P. van der Zee, D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38, 1859–1876 (1993).
    [CrossRef] [PubMed]
  13. D. Boas, A. Dale, M. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004).
    [CrossRef] [PubMed]
  14. M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
    [CrossRef] [PubMed]
  15. J. Steinbrink, H. Wabnitz, H. Obrig, A. Villringer, H. Rinneberg, “Determination of changes in NIR absorption using a layered model of the human head,” Phys. Med. Biol. 46, 879–896 (2001).
    [CrossRef] [PubMed]
  16. J. Choi, M. Wolf, V. Toronov, U. Wolf, C. Polzonetti, D. Hueber, L. Safonova, R. Gupta, A. Michalos, W. Mantulin, E. Gratton, “Noninvasive determination of optical properties of adult brain: near-infrared spectroscopy approach,” J. Biomed. Opt. 9, 221–229 (2004).
    [CrossRef] [PubMed]
  17. S. Matcher, M. Cope, D. Delpy, “Use of the water absorption spectrum to quantify tissue chromophore changes in near-infrared spectroscopy,” Phys. Med. Biol. 38, 177–196 (1993).
  18. A. Pifferi, R. Berg, P. Taroni, S. Andersson-Engels, “Fitting of time-resolved reflectance curves with a Monte Carlo model,” in Advances in Optical Imaging and Photon Migration, R. R. Alfono and J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 311–314.
  19. A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
    [CrossRef] [PubMed]
  20. E. Okada, D. Delpy, “Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer,” Appl. Opt. 42, 2906–2914 (2003).
    [CrossRef] [PubMed]
  21. E. Okada, D. Delpy, “Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal,” Appl. Opt. 42, 2915–2922 (2003).
    [CrossRef] [PubMed]

2005

Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
[CrossRef]

2004

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

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

D. Boas, A. Dale, M. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004).
[CrossRef] [PubMed]

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

2003

E. Okada, D. Delpy, “Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer,” Appl. Opt. 42, 2906–2914 (2003).
[CrossRef] [PubMed]

E. Okada, D. Delpy, “Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal,” Appl. Opt. 42, 2915–2922 (2003).
[CrossRef] [PubMed]

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

2002

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

2001

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

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

2000

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

1998

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

1996

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

1993

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

S. Matcher, M. Cope, D. Delpy, “Use of the water absorption spectrum to quantify tissue chromophore changes in near-infrared spectroscopy,” Phys. Med. Biol. 38, 177–196 (1993).

1992

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Andersson-Engels, S.

A. Pifferi, R. Berg, P. Taroni, S. Andersson-Engels, “Fitting of time-resolved reflectance curves with a Monte Carlo model,” in Advances in Optical Imaging and Photon Migration, R. R. Alfono and J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 311–314.

Arridge, S. R.

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

Atkinson, J.

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

Ausman, J.

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Barnett, N.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

Berg, R.

A. Pifferi, R. Berg, P. Taroni, S. Andersson-Engels, “Fitting of time-resolved reflectance curves with a Monte Carlo model,” in Advances in Optical Imaging and Photon Migration, R. R. Alfono and J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 311–314.

Boas, D.

Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
[CrossRef]

D. Boas, A. Dale, M. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004).
[CrossRef] [PubMed]

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

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

Braddick, O.

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

Brooks, D.

Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
[CrossRef]

Cannestra, A.

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

Cheng, X.

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

Choi, J.

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

Cope, M.

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

S. Matcher, M. Cope, D. Delpy, “Use of the water absorption spectrum to quantify tissue chromophore changes in near-infrared spectroscopy,” Phys. Med. Biol. 38, 177–196 (1993).

Dale, A.

D. Boas, A. Dale, M. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004).
[CrossRef] [PubMed]

Delpy, D.

Delpy, D. T.

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

Dujovny, M.

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Elwell, C. E.

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

Essenpries, M.

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

Evans, P.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

Fabbri, F.

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

Fantini, S.

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

Firbank, M.

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

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

Franceschini, M.

Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
[CrossRef]

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

D. Boas, A. Dale, M. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004).
[CrossRef] [PubMed]

Gaudette, T.

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

Germon, T.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

Gratton, E.

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

Gupta, R.

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

Henry, M.

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

Hiraoka, M.

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

Horst, S.

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Hueber, D.

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

Isobe, K.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Itoh, S.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Jasdzewski, G.

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

Kienle, A.

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

Kohl, M.

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Kohl-Bareis, M.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

Kondo, M.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Kusaka, T.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Kwong, K.

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

Lewis, G.

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Malak, J.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

Manara, A.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

Mandeville, J.

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

Mantulin, W.

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

Marota, J.

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

Matcher, S.

S. Matcher, M. Cope, D. Delpy, “Use of the water absorption spectrum to quantify tissue chromophore changes in near-infrared spectroscopy,” Phys. Med. Biol. 38, 177–196 (1993).

McCormick, P.

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Meek, J. H.

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

Michalos, A.

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

Nagano, K.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Nelson, R.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

Obrig, H.

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

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

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Okada, E.

Okubo, K.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Onishi, S.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Patterson, M. S.

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

Pifferi, A.

A. Pifferi, R. Berg, P. Taroni, S. Andersson-Engels, “Fitting of time-resolved reflectance curves with a Monte Carlo model,” in Advances in Optical Imaging and Photon Migration, R. R. Alfono and J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 311–314.

Poldrack, R.

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

Polzonetti, C.

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

Rinneberg, H.

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

Safonova, L.

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

Sassaroli, A.

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

Steinbrink, J.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

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

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Stewart, M.

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Strangman, G.

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

Taroni, P.

A. Pifferi, R. Berg, P. Taroni, S. Andersson-Engels, “Fitting of time-resolved reflectance curves with a Monte Carlo model,” in Advances in Optical Imaging and Photon Migration, R. R. Alfono and J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 311–314.

Thomas, F.

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Toga, A.

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

Toronov, V.

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

Uludag, K.

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

van der Zee, P.

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

Villringer, A.

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

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

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Wabnitz, H.

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

Wagner, J.

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

Wall, P.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

Wartenburger, I.

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

Wenzel, R.

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Wobst, P.

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

Wolf, M.

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

Wolf, U.

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

Wyatt, J. S.

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

Yasuda, S.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Zhang, Y.

Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
[CrossRef]

Appl. Opt.

Int. J. Psychophysiol.

H. Obrig, R. Wenzel, M. Kohl, S. Horst, P. Wobst, J. Steinbrink, F. Thomas, A. Villringer, “Near-infrared spectroscopy: does it function in functional activation studies in the adult brain?” Int. J. Psychophysiol. 35, 125–142 (2000).
[CrossRef] [PubMed]

J. Biomed. Opt.

Y. Zhang, D. Brooks, M. Franceschini, D. Boas, “Eigenvector-based spatial filtering for reduction of physiological interference in diffuse optical imaging,” J. Biomed. Opt. 10, 011014 (2005).
[CrossRef]

M. Kohl-Bareis, H. Obrig, J. Steinbrink, J. Malak, K. Uludag, A. Villringer, “Noninvasive monitoring of cerebral blood flow by a dye bolus method: Separation of brain from skin and skull signals,” J. Biomed. Opt. 7, 464–470 (2002).
[CrossRef] [PubMed]

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

J. Clin. Monit. Comput.

T. Germon, P. Evans, A. Manara, N. Barnett, P. Wall, R. Nelson, “Sensitivity of near infrared spectroscopy to cerebral and extra-cerebral oxygenation changes is determined by emitter-detector separation,” J. Clin. Monit. Comput. 14, 353–360 (1998).
[CrossRef]

J. Neurosurg.

P. McCormick, M. Stewart, G. Lewis, M. Dujovny, J. Ausman, “Intracerebral penetration of infrared light,” J. Neurosurg. 76, 315–318 (1992).
[CrossRef] [PubMed]

Neuroimage

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

D. Boas, A. Dale, M. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23, S275–S288 (2004).
[CrossRef] [PubMed]

G. Jasdzewski, G. Strangman, J. Wagner, K. Kwong, R. Poldrack, D. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage 20, 479–488 (2003).
[CrossRef] [PubMed]

D. Boas, T. Gaudette, G. Strangman, X. Cheng, J. Marota, J. Mandeville, “The accuracy of near infrared spectroscopy and imaging during focal changes in cerebral hemodynamics,” Neuroimage 13, 76–90 (2001).
[CrossRef] [PubMed]

NeuroReport

A. Cannestra, I. Wartenburger, H. Obrig, A. Villringer, A. Toga, “Functional assessment of Broca’s area using near infrared spectroscopy in humans,” NeuroReport 14, 1961–1965 (2003).
[CrossRef] [PubMed]

Neurosci. Lett.

K. Isobe, T. Kusaka, K. Nagano, K. Okubo, S. Yasuda, M. Kondo, S. Itoh, S. Onishi, “Functional imaging of the brain in sedated newborn infants using near infrared topography during passive knee movement,” Neurosci. Lett. 299, 221–224 (2001).
[CrossRef] [PubMed]

Pediatr. Res

J. H. Meek, M. Firbank, C. E. Elwell, J. Atkinson, O. Braddick, J. S. Wyatt, “Regional hemodynamic responses to visual stimulation in awake infants,” Pediatr. Res. 43, 840–843 (1998).
[CrossRef] [PubMed]

Phys. Med. Biol.

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

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

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

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[CrossRef] [PubMed]

S. Matcher, M. Cope, D. Delpy, “Use of the water absorption spectrum to quantify tissue chromophore changes in near-infrared spectroscopy,” Phys. Med. Biol. 38, 177–196 (1993).

Other

A. Pifferi, R. Berg, P. Taroni, S. Andersson-Engels, “Fitting of time-resolved reflectance curves with a Monte Carlo model,” in Advances in Optical Imaging and Photon Migration, R. R. Alfono and J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics (Optical Society of America, 1996), pp. 311–314.

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Figures (5)

Fig. 1
Fig. 1

Graphical representation of the model described in the Monte Carlo simulation.(a) d N , d F are the source–detector separations for the near and far detector, respectively, and S N , S F are the detected signals at those locations. Note that this is merely a cartoon of the system; items are not drawn to scale. (b) Typical plots of the fluctuations in absorption properties specific to each layer. (c) Plots of the detected absorption changes at each detector.

Fig. 2
Fig. 2

Results for simulations with no interfering effects in the bottom layer ( γ = 0 ) . (a) From top to bottom, these plots show the individual Δ μ a 2 in the bottom layer, the detected signal at the far detector alone ( α = 0 , i.e., a SDO configuration), the extracted signal from the least-squares approach, and the ideal extraction calculated from average photon pathlengths. (b) Plots of the block average of 12 individual events under the same conditions.

Fig. 3
Fig. 3

Characterization of error sources in the least-squares estimate. (a) Mean and distribution of error values described by δ α ̂ 1 (stars) and δ α ̂ 2 (circles) as a function of epochs recorded (i.e., measurement time); while δ α ̂ 1 is independent of d N , δ α ̂ 2 is shown here for d N = 1 mm . (b) Mean and distribution of error values as a function of d N ; all data shown were calculated from a 12-epoch measurement.

Fig. 4
Fig. 4

Results for simulations with equal contributions of interference and activation in the bottom layer ( γ = 0.5 ) . (a) From top to bottom, these plots show the individual Δ μ a 2 in the bottom layer, the detected signal at the far detector alone ( α = 0 , i.e., a SDO configuration), the extracted signal from the least-squares approach, and the ideal extraction calculated from average photon path lengths. (b) Plots of the block average of 12 individual events under the same conditions.

Fig. 5
Fig. 5

Results for simulations with both top layer and global interference terms ( γ = 0.3 ) . (a) From top to bottom, these plots show the individual Δ μ a 2 in the bottom layer, the detected signal at the far detector alone ( α = 0 , i.e., a SDO configuration), the extracted signal from the least-squares approach, and the ideal extraction calculated from average photon path lengths. (b) Plots of the block average of 12 individual events under the same conditions.

Tables (1)

Tables Icon

Table 1 Parameter Space of Optical and Physiologic Properties Examined in Simulations

Equations (31)

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Δ A ( t ) = ln ( S ( t ) S 0 ) = Δ μ a ( t ) L ,
Δ A N ( t ) = Δ μ a 1 ( t ) L 1 N + Δ μ a 2 ( t ) L 2 N ,
Δ A F ( t ) = Δ μ a 1 ( t ) L 1 F + Δ μ a 2 ( t ) L 2 F ,
R ( t ) Δ A F ( t ) K Δ A N ( t ) = Δ μ a 1 ( t ) ( L 1 F K L 1 N ) + Δ μ a 2 ( t ) ( L 2 F K L 2 N ) .
K = L 1 F L 1 N ,
Δ μ a 1 = G ,
Δ μ a 2 = γ G + B ,
lim t B G G G = 0 .
α I = L 1 F + γ L 2 F L 1 N + γ L 2 N ,
R = [ L 2 F ( 1 L 2 N L 2 F L 1 F + γ L 2 F L 1 N + γ L 2 N ) ] 1 B ,
ϵ = L 2 N L 1 N ,
α L S = Δ A N Δ A F Δ A N Δ A N .
α L S α I + L 2 F L 1 N B G G G + ϵ { [ ( B + γ G ) ( B + γ G ) G G 2 { G ( B + γ G ) G G } 2 ] L 2 F L 1 N G ( B + γ G ) G G L 1 F L 1 N } α ̂ L S .
α I L 1 F + γ L 2 F L 1 N .
δ α ̂ = α ̂ L S α I α I = δ α ̂ 1 + δ α ̂ 2 ,
δ α ̂ 1 = B G G G ( L 2 F L 1 F + γ L 2 F )
δ α ̂ 2 = ϵ { [ B G G G + γ ] + [ γ B G G G + 2 ( B G G G ) 2 B B G G ] [ L 2 F L 1 F + γ L 2 F ] } .
α L S = Δ A N Δ A F Δ A N Δ A N .
α L S = [ Δ μ a 1 ( t ) L 1 F + Δ μ a 2 ( t ) L 2 F ] [ Δ μ a 1 ( t ) L 1 N + Δ μ a 2 ( t ) L 2 N ] [ Δ μ a 1 ( t ) L 1 N + Δ μ a 2 ( t ) L 2 N ] [ Δ μ a 1 ( t ) L 1 N + Δ μ a 2 ( t ) L 2 N ] .
μ 11 Δ μ α 1 ( t ) Δ μ α 1 ( t ) ,
μ 12 Δ μ α 1 ( t ) Δ μ α 2 ( t ) ,
μ 22 Δ μ α 2 ( t ) Δ μ α 2 ( t ) .
α L S = μ 11 L 1 F L 1 N + μ 12 [ L 1 F L 2 N L 1 N L 1 N + L 2 F L 1 N ] + μ 22 L 2 F L 2 N L 1 N L 1 N μ 11 + 2 μ 12 L 2 N L 1 N + μ 22 L 2 N L 2 N L 1 N L 1 N .
= μ 11 L 1 F L 1 N + μ 12 [ L 1 F L 1 N ϵ + L 2 F L 1 N ] + μ 22 L 2 F L 1 N ϵ μ 11 + 2 μ 12 ϵ + μ 22 ϵ 2 .
α L S μ 11 L 1 F L 1 N + μ 12 [ L 1 F L 1 N ϵ + L 2 F L 1 N ] + μ 22 L 2 F L 1 N ϵ μ 11 + 2 μ 12 ϵ
{ μ 11 L 1 F L 1 N + μ 12 [ L 1 F L 1 N ϵ + L 2 F L 1 N ] + μ 22 L 2 F L 1 N ϵ } 1 μ 11 [ 1 2 ϵ μ 12 μ 11 ]
{ L 1 F L 1 N + μ 12 μ 11 [ L 1 F L 1 N ϵ + L 2 F L 1 N ] + μ 22 μ 11 L 2 F L 1 N ϵ } [ 1 2 ϵ μ 12 μ 11 ]
L 1 F L 1 N + μ 12 μ 11 L 2 F L 1 N + ϵ { μ 22 μ 11 L 2 F L 1 N μ 12 μ 11 L 1 F L 1 N 2 [ μ 12 μ 11 ] 2 L 2 F L 1 N } + O ( ϵ 2 ) .
α L S L 1 F L 1 N + G ( B + γ G ) G G L 2 F L 1 N + ϵ { ( B + γ G ) ( B + γ G ) G G L 2 F L 1 N G ( B + γ G ) G G L 1 F L 1 N 2 [ G ( B + γ G ) G G ] 2 L 2 F L 1 N }
( L 1 F L 1 N + γ L 2 F L 1 N ) + G B G G L 2 F L 1 N + ϵ { ( B + γ G ) ( B + γ G ) G G L 2 F L 1 N G ( B + γ G ) G G L 1 F L 1 N 2 [ G ( B + γ G ) G G ] 2 L 2 F L 1 N } .
α L S α I + L 2 F L 1 N B G G G + ϵ { [ ( B + γ G ) ( B + γ G ) G G 2 { G ( B + γ G ) G G } 2 ] L 2 F L 1 F G ( B + γ G ) G G L 1 F L 1 N } α ̂ L S ,

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