Abstract

The paper presents state space models of the hemodynamic response (HR) of fNIRS to an impulse stimulus in three brain regions: motor cortex (MC), somatosensory cortex (SC), and visual cortex (VC). Nineteen healthy subjects were examined. For each cortex, three impulse HRs experimentally obtained were averaged. The averaged signal was converted to a state space equation by using the subspace method. The activation peak and the undershoot peak of the oxy-hemoglobin (HbO) in MC are noticeably higher than those in SC and VC. The time-to-peaks of the HbO in three brain regions are almost the same (about 6.76 76 ± 0.2 s). The time to undershoot peak in VC is the largest among three. The HbO decreases in the early stage (~0.46 s) in MC and VC, but it is not so in SC. These findings were well described with the developed state space equations. Another advantage of the proposed method is its easy applicability in generating the expected HR to arbitrary stimuli in an online (or real-time) imaging. Experimental results are demonstrated.

© 2014 Optical Society of America

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  1. K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
    [CrossRef] [PubMed]
  2. M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
    [CrossRef] [PubMed]
  3. H. F. Chen, D. Z. Yao, and Z. X. Liu, “A comparison of Gamma and Gaussian dynamic convolution models of the fMRI BOLD response,” Magn. Reson. Imaging23(1), 83–88 (2005).
    [CrossRef] [PubMed]
  4. K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
    [CrossRef] [PubMed]
  5. X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
    [CrossRef] [PubMed]
  6. R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: the balloon model,” Magn. Reson. Med.39(6), 855–864 (1998).
    [CrossRef] [PubMed]
  7. K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
    [CrossRef] [PubMed]
  8. K. J. Friston, L. Harrison, and W. Penny, “Dynamic causal modelling,” Neuroimage19(4), 1273–1302 (2003).
    [CrossRef] [PubMed]
  9. K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
    [CrossRef] [PubMed]
  10. J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
    [CrossRef] [PubMed]
  11. M. A. Kamran and K. S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng.10(5), 056002 (2013).
    [CrossRef] [PubMed]
  12. N. Naseer, M. J. Hong, and K. S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res.232(2), 555–564 (2014).
    [CrossRef] [PubMed]
  13. X. S. Hu, K. S. Hong, and S. S. Ge, “Recognition of stimulus-evoked neuronal optical response by identifying chaos levels of near-infrared spectroscopy time series,” Neurosci. Lett.504(2), 115–120 (2011).
    [CrossRef] [PubMed]
  14. T. Shimokawa, T. Kosaka, O. Yamashita, N. Hiroe, T. Amita, Y. Inoue, and M. A. Sato, “Extended hierarchical Bayesian diffuse optical tomography for removing scalp artifact,” Biomed. Opt. Express4(11), 2411–2432 (2013).
    [CrossRef] [PubMed]
  15. R. Re, D. Contini, M. Turola, L. Spinelli, L. Zucchelli, M. Caffini, R. Cubeddu, and A. Torricelli, “Multi-channel medical device for time domain functional near infrared spectroscopy based on wavelength space multiplexing,” Biomed. Opt. Express4(10), 2231–2246 (2013).
    [CrossRef] [PubMed]
  16. M. Cope and D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput.26(3), 289–294 (1988).
    [CrossRef] [PubMed]
  17. R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector corrected near infrared spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage55(4), 1679–1685 (2011).
    [CrossRef] [PubMed]
  18. J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
    [CrossRef] [PubMed]
  19. M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
    [CrossRef] [PubMed]
  20. M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
    [CrossRef] [PubMed]
  21. X. S. Hu, K. S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng.9(2), 026012 (2012).
    [CrossRef] [PubMed]
  22. I. Schelkanova and V. Toronov, “Independent component analysis of broadband near-infrared spectroscopy data acquired on adult human head,” Biomed. Opt. Express3(1), 64–74 (2012).
    [CrossRef] [PubMed]
  23. Z. Yuan, “Combining independent component analysis and Granger causality to investigate brain network dynamics with fNIRS measurements,” Biomed. Opt. Express4(11), 2629–2643 (2013).
    [CrossRef] [PubMed]
  24. N. Naseer and K. S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett.553, 84–89 (2013).
    [CrossRef] [PubMed]
  25. H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
    [CrossRef] [PubMed]
  26. A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci.20(10), 435–442 (1997).
    [CrossRef] [PubMed]
  27. G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
    [CrossRef] [PubMed]
  28. Y. Hoshi, N. Kobayashi, and M. Tamura, “Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model,” J. Appl. Physiol.90(5), 1657–1662 (2001).
    [PubMed]
  29. S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
    [CrossRef] [PubMed]
  30. J. W. Barker, A. Aarabi, and T. J. Huppert, “Autoregressive model based algorithm for correcting motion and serially correlated errors in fNIRS,” Biomed. Opt. Express4(8), 1366–1379 (2013).
    [CrossRef] [PubMed]
  31. X. S. Hu, K. S. Hong, and S. S. Ge, “Reduction of trial-to-trial variability in functional near-infrared spectroscopy signals by accounting for resting-state functional connectivity,” J. Biomed. Opt.18(1), 017003 (2013).
    [CrossRef] [PubMed]
  32. M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
    [CrossRef] [PubMed]
  33. T. Katayama, Subspace methods for system identification, E. D. Sontag, M. Thoma, A. Isidori, J. H. vanSchuppen ed. (Springer-Verlag London Limited, 2005).
  34. F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
    [CrossRef] [PubMed]
  35. M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
    [CrossRef] [PubMed]
  36. M. J. Khan, M. J. Hong, and K. S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci.8, 244 (2014).
    [CrossRef]
  37. P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
    [CrossRef] [PubMed]
  38. E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
    [CrossRef] [PubMed]

2014 (5)

N. Naseer, M. J. Hong, and K. S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res.232(2), 555–564 (2014).
[CrossRef] [PubMed]

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

M. J. Khan, M. J. Hong, and K. S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci.8, 244 (2014).
[CrossRef]

2013 (8)

J. W. Barker, A. Aarabi, and T. J. Huppert, “Autoregressive model based algorithm for correcting motion and serially correlated errors in fNIRS,” Biomed. Opt. Express4(8), 1366–1379 (2013).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “Reduction of trial-to-trial variability in functional near-infrared spectroscopy signals by accounting for resting-state functional connectivity,” J. Biomed. Opt.18(1), 017003 (2013).
[CrossRef] [PubMed]

Z. Yuan, “Combining independent component analysis and Granger causality to investigate brain network dynamics with fNIRS measurements,” Biomed. Opt. Express4(11), 2629–2643 (2013).
[CrossRef] [PubMed]

N. Naseer and K. S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett.553, 84–89 (2013).
[CrossRef] [PubMed]

H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
[CrossRef] [PubMed]

T. Shimokawa, T. Kosaka, O. Yamashita, N. Hiroe, T. Amita, Y. Inoue, and M. A. Sato, “Extended hierarchical Bayesian diffuse optical tomography for removing scalp artifact,” Biomed. Opt. Express4(11), 2411–2432 (2013).
[CrossRef] [PubMed]

R. Re, D. Contini, M. Turola, L. Spinelli, L. Zucchelli, M. Caffini, R. Cubeddu, and A. Torricelli, “Multi-channel medical device for time domain functional near infrared spectroscopy based on wavelength space multiplexing,” Biomed. Opt. Express4(10), 2231–2246 (2013).
[CrossRef] [PubMed]

M. A. Kamran and K. S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng.10(5), 056002 (2013).
[CrossRef] [PubMed]

2012 (3)

M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng.9(2), 026012 (2012).
[CrossRef] [PubMed]

I. Schelkanova and V. Toronov, “Independent component analysis of broadband near-infrared spectroscopy data acquired on adult human head,” Biomed. Opt. Express3(1), 64–74 (2012).
[CrossRef] [PubMed]

2011 (2)

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector corrected near infrared spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage55(4), 1679–1685 (2011).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “Recognition of stimulus-evoked neuronal optical response by identifying chaos levels of near-infrared spectroscopy time series,” Neurosci. Lett.504(2), 115–120 (2011).
[CrossRef] [PubMed]

2010 (1)

X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
[CrossRef] [PubMed]

2009 (2)

M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
[CrossRef] [PubMed]

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

2008 (1)

K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
[CrossRef] [PubMed]

2007 (3)

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

2005 (1)

H. F. Chen, D. Z. Yao, and Z. X. Liu, “A comparison of Gamma and Gaussian dynamic convolution models of the fMRI BOLD response,” Magn. Reson. Imaging23(1), 83–88 (2005).
[CrossRef] [PubMed]

2003 (3)

K. J. Friston, L. Harrison, and W. Penny, “Dynamic causal modelling,” Neuroimage19(4), 1273–1302 (2003).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

2001 (2)

Y. Hoshi, N. Kobayashi, and M. Tamura, “Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model,” J. Appl. Physiol.90(5), 1657–1662 (2001).
[PubMed]

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

2000 (2)

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
[CrossRef] [PubMed]

1998 (2)

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: the balloon model,” Magn. Reson. Med.39(6), 855–864 (1998).
[CrossRef] [PubMed]

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

1997 (1)

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci.20(10), 435–442 (1997).
[CrossRef] [PubMed]

1988 (1)

M. Cope and D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput.26(3), 289–294 (1988).
[CrossRef] [PubMed]

Aarabi, A.

Adriany, G.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Akin, A.

K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
[CrossRef] [PubMed]

Amita, T.

Aqil, M.

M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
[CrossRef] [PubMed]

Atlas, L. Y.

M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
[CrossRef] [PubMed]

Baraldi, P.

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

Barker, J. W.

Benali, H.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Berger, A. J.

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector corrected near infrared spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage55(4), 1679–1685 (2011).
[CrossRef] [PubMed]

Bhutta, M. R.

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

Boas, D. A.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

Brigadoi, S.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Buckner, R. L.

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

Buxton, R. B.

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: the balloon model,” Magn. Reson. Med.39(6), 855–864 (1998).
[CrossRef] [PubMed]

Caffini, M.

Ceccherini, L.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Chance, B.

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci.20(10), 435–442 (1997).
[CrossRef] [PubMed]

Chapuisat, S.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Chen, H. F.

H. F. Chen, D. Z. Yao, and Z. X. Liu, “A comparison of Gamma and Gaussian dynamic convolution models of the fMRI BOLD response,” Magn. Reson. Imaging23(1), 83–88 (2005).
[CrossRef] [PubMed]

Ciftçi, K.

K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
[CrossRef] [PubMed]

Cohen-Adad, J.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Contini, D.

Cooper, R. J.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Cope, M.

M. Cope and D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput.26(3), 289–294 (1988).
[CrossRef] [PubMed]

Cubeddu, R.

Culver, J. P.

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

Cutini, S.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Delpy, D. T.

M. Cope and D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput.26(3), 289–294 (1988).
[CrossRef] [PubMed]

Doyon, J.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Drysdale, P. M.

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

Eggebrecht, A. T.

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

Fantini, S.

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

Ferradal, S. L.

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

Fletcher, P.

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

Franceschini, M. A.

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

Frank, L. R.

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: the balloon model,” Magn. Reson. Med.39(6), 855–864 (1998).
[CrossRef] [PubMed]

Friston, K. J.

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

K. J. Friston, L. Harrison, and W. Penny, “Dynamic causal modelling,” Neuroimage19(4), 1273–1302 (2003).
[CrossRef] [PubMed]

K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
[CrossRef] [PubMed]

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

Gagnon, L.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Ge, S. S.

X. S. Hu, K. S. Hong, and S. S. Ge, “Reduction of trial-to-trial variability in functional near-infrared spectroscopy signals by accounting for resting-state functional connectivity,” J. Biomed. Opt.18(1), 017003 (2013).
[CrossRef] [PubMed]

M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng.9(2), 026012 (2012).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “Recognition of stimulus-evoked neuronal optical response by identifying chaos levels of near-infrared spectroscopy time series,” Neurosci. Lett.504(2), 115–120 (2011).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
[CrossRef] [PubMed]

Harrison, L.

K. J. Friston, L. Harrison, and W. Penny, “Dynamic causal modelling,” Neuroimage19(4), 1273–1302 (2003).
[CrossRef] [PubMed]

Hassanpour, M. S.

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

Hiroe, N.

Holmes, A.

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

Hong, K. S.

N. Naseer, M. J. Hong, and K. S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res.232(2), 555–564 (2014).
[CrossRef] [PubMed]

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

M. J. Khan, M. J. Hong, and K. S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci.8, 244 (2014).
[CrossRef]

X. S. Hu, K. S. Hong, and S. S. Ge, “Reduction of trial-to-trial variability in functional near-infrared spectroscopy signals by accounting for resting-state functional connectivity,” J. Biomed. Opt.18(1), 017003 (2013).
[CrossRef] [PubMed]

N. Naseer and K. S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett.553, 84–89 (2013).
[CrossRef] [PubMed]

H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
[CrossRef] [PubMed]

M. A. Kamran and K. S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng.10(5), 056002 (2013).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng.9(2), 026012 (2012).
[CrossRef] [PubMed]

M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “Recognition of stimulus-evoked neuronal optical response by identifying chaos levels of near-infrared spectroscopy time series,” Neurosci. Lett.504(2), 115–120 (2011).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
[CrossRef] [PubMed]

Hong, M. J.

N. Naseer, M. J. Hong, and K. S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res.232(2), 555–564 (2014).
[CrossRef] [PubMed]

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

M. J. Khan, M. J. Hong, and K. S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci.8, 244 (2014).
[CrossRef]

H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
[CrossRef] [PubMed]

Hoshi, Y.

Y. Hoshi, N. Kobayashi, and M. Tamura, “Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model,” J. Appl. Physiol.90(5), 1657–1662 (2001).
[PubMed]

Hu, X. P.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Hu, X. S.

X. S. Hu, K. S. Hong, and S. S. Ge, “Reduction of trial-to-trial variability in functional near-infrared spectroscopy signals by accounting for resting-state functional connectivity,” J. Biomed. Opt.18(1), 017003 (2013).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng.9(2), 026012 (2012).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “Recognition of stimulus-evoked neuronal optical response by identifying chaos levels of near-infrared spectroscopy time series,” Neurosci. Lett.504(2), 115–120 (2011).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
[CrossRef] [PubMed]

Huppert, T. J.

Inoue, Y.

Jang, J.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

Jang, K. E.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

Jasdzewski, G.

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

Jeong, M. Y.

M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
[CrossRef] [PubMed]

Josephs, O.

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

Jung, J.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

Kahya, Y. P.

K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
[CrossRef] [PubMed]

Kamran, M. A.

M. A. Kamran and K. S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng.10(5), 056002 (2013).
[CrossRef] [PubMed]

Khan, M. J.

M. J. Khan, M. J. Hong, and K. S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci.8, 244 (2014).
[CrossRef]

Kim, B. M.

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

Kim, S. P.

H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
[CrossRef] [PubMed]

Kim, Y. H.

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

Kobayashi, N.

Y. Hoshi, N. Kobayashi, and M. Tamura, “Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model,” J. Appl. Physiol.90(5), 1657–1662 (2001).
[PubMed]

Kosaka, T.

Kwong, K. K.

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

Lee, S. H.

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

Lesage, F.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Liberati, D.

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

Lina, J. M.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Lindquist, M. A.

M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
[CrossRef] [PubMed]

Liu, Z. X.

H. F. Chen, D. Z. Yao, and Z. X. Liu, “A comparison of Gamma and Gaussian dynamic convolution models of the fMRI BOLD response,” Magn. Reson. Imaging23(1), 83–88 (2005).
[CrossRef] [PubMed]

Maccotta, L.

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

Maieron, M.

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

Manginelli, A. A.

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

Mechelli, A.

K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
[CrossRef] [PubMed]

Meng Loh, J.

M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
[CrossRef] [PubMed]

Miezin, F. M.

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

Naseer, N.

N. Naseer, M. J. Hong, and K. S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res.232(2), 555–564 (2014).
[CrossRef] [PubMed]

N. Naseer and K. S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett.553, 84–89 (2013).
[CrossRef] [PubMed]

Ollinger, J. M.

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

Penny, W.

K. J. Friston, L. Harrison, and W. Penny, “Dynamic causal modelling,” Neuroimage19(4), 1273–1302 (2003).
[CrossRef] [PubMed]

Petersen, S. E.

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

Pfeuffer, J.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Poldrack, R. A.

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

Porro, C. A.

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

Price, C. J.

K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
[CrossRef] [PubMed]

Re, R.

Robinson, P. A.

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

Rossignol, S.

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Rugg, M. D.

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

Saager, R. B.

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector corrected near infrared spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage55(4), 1679–1685 (2011).
[CrossRef] [PubMed]

Sankur, B.

K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
[CrossRef] [PubMed]

Santosa, H.

H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
[CrossRef] [PubMed]

Sato, M. A.

Scarpa, F.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Scatturin, P.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Schelkanova, I.

Selb, J.

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

Shimokawa, T.

Shmuel, A.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Snyder, A. Z.

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

Spinelli, L.

Stephan, K. E.

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

Strangman, G.

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

Tak, S.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

Tamura, M.

Y. Hoshi, N. Kobayashi, and M. Tamura, “Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model,” J. Appl. Physiol.90(5), 1657–1662 (2001).
[PubMed]

Telleri, N. L.

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector corrected near infrared spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage55(4), 1679–1685 (2011).
[CrossRef] [PubMed]

Thompson, J. H.

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

Toronov, V.

Torricelli, A.

Turner, R.

K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
[CrossRef] [PubMed]

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

Turola, M.

Ugurbil, K.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Van De Moortele, P. F.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Villringer, A.

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci.20(10), 435–442 (1997).
[CrossRef] [PubMed]

Wager, T. D.

M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
[CrossRef] [PubMed]

Wagner, J.

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

Weiskopf, N.

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

White, B. R.

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

Wong, E. C.

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: the balloon model,” Magn. Reson. Med.39(6), 855–864 (1998).
[CrossRef] [PubMed]

Yacoub, E.

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Yamashita, O.

Yao, D. Z.

H. F. Chen, D. Z. Yao, and Z. X. Liu, “A comparison of Gamma and Gaussian dynamic convolution models of the fMRI BOLD response,” Magn. Reson. Imaging23(1), 83–88 (2005).
[CrossRef] [PubMed]

Ye, J. C.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

Yuan, Z.

Zucchelli, L.

Biomed. Eng. Online (1)

X. S. Hu, K. S. Hong, S. S. Ge, and M. Y. Jeong, “Kalman estimator- and general linear model-based on-line brain activation mapping by near-infrared spectroscopy,” Biomed. Eng. Online9(1), 82 (2010).
[CrossRef] [PubMed]

Biomed. Opt. Express (5)

Exp. Brain Res. (1)

N. Naseer, M. J. Hong, and K. S. Hong, “Online binary decision decoding using functional near-infrared spectroscopy for the development of brain-computer interface,” Exp. Brain Res.232(2), 555–564 (2014).
[CrossRef] [PubMed]

Front. Hum. Neurosci. (1)

M. J. Khan, M. J. Hong, and K. S. Hong, “Decoding of four movement directions using hybrid NIRS-EEG brain-computer interface,” Front. Hum. Neurosci.8, 244 (2014).
[CrossRef]

J. Appl. Physiol. (1)

Y. Hoshi, N. Kobayashi, and M. Tamura, “Interpretation of near-infrared spectroscopy signals: a study with a newly developed perfused rat brain model,” J. Appl. Physiol.90(5), 1657–1662 (2001).
[PubMed]

J. Biomed. Opt. (1)

X. S. Hu, K. S. Hong, and S. S. Ge, “Reduction of trial-to-trial variability in functional near-infrared spectroscopy signals by accounting for resting-state functional connectivity,” J. Biomed. Opt.18(1), 017003 (2013).
[CrossRef] [PubMed]

J. Neural Eng. (2)

X. S. Hu, K. S. Hong, and S. S. Ge, “fNIRS-based online deception decoding,” J. Neural Eng.9(2), 026012 (2012).
[CrossRef] [PubMed]

M. A. Kamran and K. S. Hong, “Linear parameter-varying model and adaptive filtering technique for detecting neuronal activities: an fNIRS study,” J. Neural Eng.10(5), 056002 (2013).
[CrossRef] [PubMed]

Magn. Reson. Imaging (1)

H. F. Chen, D. Z. Yao, and Z. X. Liu, “A comparison of Gamma and Gaussian dynamic convolution models of the fMRI BOLD response,” Magn. Reson. Imaging23(1), 83–88 (2005).
[CrossRef] [PubMed]

Magn. Reson. Med. (1)

R. B. Buxton, E. C. Wong, and L. R. Frank, “Dynamics of blood flow and oxygenation changes during brain activation: the balloon model,” Magn. Reson. Med.39(6), 855–864 (1998).
[CrossRef] [PubMed]

Med. Biol. Eng. Comput. (2)

K. Ciftçi, B. Sankur, Y. P. Kahya, and A. Akin, “Constraining the general linear model for sensible hemodynamic response function waveforms,” Med. Biol. Eng. Comput.46(8), 779–787 (2008).
[CrossRef] [PubMed]

M. Cope and D. T. Delpy, “System for long-term measurement of cerebral blood and tissue oxygenation on newborn infants by near infra-red transillumination,” Med. Biol. Eng. Comput.26(3), 289–294 (1988).
[CrossRef] [PubMed]

Med. Image Anal. (1)

J. Cohen-Adad, S. Chapuisat, J. Doyon, S. Rossignol, J. M. Lina, H. Benali, and F. Lesage, “Activation detection in diffuse optical imaging by means of the general linear model,” Med. Image Anal.11(6), 616–629 (2007).
[CrossRef] [PubMed]

Neuroimage (13)

R. B. Saager, N. L. Telleri, and A. J. Berger, “Two-detector corrected near infrared spectroscopy (C-NIRS) detects hemodynamic activation responses more robustly than single-detector NIRS,” Neuroimage55(4), 1679–1685 (2011).
[CrossRef] [PubMed]

J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage44(2), 428–447 (2009).
[CrossRef] [PubMed]

M. S. Hassanpour, B. R. White, A. T. Eggebrecht, S. L. Ferradal, A. Z. Snyder, and J. P. Culver, “Statistical analysis of high density diffuse optical tomography,” Neuroimage85(Pt 1), 104–116 (2014).
[CrossRef] [PubMed]

M. Aqil, K. S. Hong, M. Y. Jeong, and S. S. Ge, “Detection of event-related hemodynamic response to neuroactivation by dynamic modeling of brain activity,” Neuroimage63(1), 553–568 (2012).
[CrossRef] [PubMed]

K. J. Friston, P. Fletcher, O. Josephs, A. Holmes, M. D. Rugg, and R. Turner, “Event-related fMRI: characterizing differential responses,” Neuroimage7(1), 30–40 (1998).
[CrossRef] [PubMed]

M. A. Lindquist, J. Meng Loh, L. Y. Atlas, and T. D. Wager, “Modeling the hemodynamic response function in fMRI: efficiency, bias and mis-modeling,” Neuroimage45(1Suppl), S187–S198 (2009).
[CrossRef] [PubMed]

K. J. Friston, A. Mechelli, R. Turner, and C. J. Price, “Nonlinear responses in fMRI: the balloon model, volterra kernels, and other hemodynamics,” Neuroimage12(4), 466–477 (2000).
[CrossRef] [PubMed]

K. J. Friston, L. Harrison, and W. Penny, “Dynamic causal modelling,” Neuroimage19(4), 1273–1302 (2003).
[CrossRef] [PubMed]

K. E. Stephan, N. Weiskopf, P. M. Drysdale, P. A. Robinson, and K. J. Friston, “Comparing hemodynamic models with DCM,” Neuroimage38(3), 387–401 (2007).
[CrossRef] [PubMed]

G. Jasdzewski, G. Strangman, J. Wagner, K. K. Kwong, R. A. Poldrack, and D. A. Boas, “Differences in the hemodynamic response to event-related motor and visual paradigms as measured by near-infrared spectroscopy,” Neuroimage20(1), 479–488 (2003).
[CrossRef] [PubMed]

S. Brigadoi, L. Ceccherini, S. Cutini, F. Scarpa, P. Scatturin, J. Selb, L. Gagnon, D. A. Boas, and R. J. Cooper, “Motion artifacts in functional near-infrared spectroscopy: a comparison of motion correction techniques applied to real cognitive data,” Neuroimage85(Pt 1), 181–191 (2014).
[CrossRef] [PubMed]

F. M. Miezin, L. Maccotta, J. M. Ollinger, S. E. Petersen, and R. L. Buckner, “Characterizing the hemodynamic response: effects of presentation rate, sampling procedure, and the possibility of ordering brain activity based on relative timing,” Neuroimage11(6), 735–759 (2000).
[CrossRef] [PubMed]

P. Baraldi, A. A. Manginelli, M. Maieron, D. Liberati, and C. A. Porro, “An ARX model-based approach to trial by trial identification of fMRI-BOLD responses,” Neuroimage37(1), 189–201 (2007).
[CrossRef] [PubMed]

Neurosci. Lett. (2)

N. Naseer and K. S. Hong, “Classification of functional near-infrared spectroscopy signals corresponding to the right- and left-wrist motor imagery for development of a brain-computer interface,” Neurosci. Lett.553, 84–89 (2013).
[CrossRef] [PubMed]

X. S. Hu, K. S. Hong, and S. S. Ge, “Recognition of stimulus-evoked neuronal optical response by identifying chaos levels of near-infrared spectroscopy time series,” Neurosci. Lett.504(2), 115–120 (2011).
[CrossRef] [PubMed]

NMR Biomed. (1)

E. Yacoub, A. Shmuel, J. Pfeuffer, P. F. Van De Moortele, G. Adriany, K. Ugurbil, and X. P. Hu, “Investigation of the initial dip in fMRI at 7 Tesla,” NMR Biomed.14(7-8), 408–412 (2001).
[CrossRef] [PubMed]

Psychophysiology (1)

M. A. Franceschini, S. Fantini, J. H. Thompson, J. P. Culver, and D. A. Boas, “Hemodynamic evoked response of the sensorimotor cortex measured noninvasively with near-infrared optical imaging,” Psychophysiology40(4), 548–560 (2003).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

M. R. Bhutta, K. S. Hong, B. M. Kim, M. J. Hong, Y. H. Kim, and S. H. Lee, “Note: three wavelengths near-infrared spectroscopy system for compensating the light absorbance by water,” Rev. Sci. Instrum.85(2), 026111 (2014).
[CrossRef] [PubMed]

H. Santosa, M. J. Hong, S. P. Kim, and K. S. Hong, “Noise reduction in functional near-infrared spectroscopy signals by independent component analysis,” Rev. Sci. Instrum.84(7), 073106 (2013).
[CrossRef] [PubMed]

Trends Neurosci. (1)

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci.20(10), 435–442 (1997).
[CrossRef] [PubMed]

Other (1)

T. Katayama, Subspace methods for system identification, E. D. Sontag, M. Thoma, A. Isidori, J. H. vanSchuppen ed. (Springer-Verlag London Limited, 2005).

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Figures (17)

Fig. 1
Fig. 1

Experimental paradigm for obtaining impulse HR functions: For the motor cortex (MC), a right middle-finger tapping (RMFT) was repeated three times; for the somatosensory cortex (SC), the right index-finger poking using a nail was used, and for the visual cortex (VC), a 3-sec checkerboard display was employed.

Fig. 2
Fig. 2

Optodes configuration for MC (black box) and SC (dotted red box): 1 emitter and 10 detectors → 10 channels.

Fig. 3
Fig. 3

Optodes configuration for VC: 1 emitter and 7 detectors → 7 channels.

Fig. 4
Fig. 4

Characteristics of the canonical HR: a1 stands for the peak amplitude of the main response, a2 is the magnitude of undershoot, t1 is the time-to-peak, t2 is the time-to-undershoot, T1 denotes the activation period, T2 denotes the deactivation period, m1 is the mean in T1, and m2 is the mean in T2.

Fig. 5
Fig. 5

Experiment for demonstrating the MC and SC models: (a) Optodes configuration (MC - black box; SC - dotted red box) and (b) the experimental paradigm including 5 taps/pokes at 30 and 90 s (1 tap/poke for 2 s); 10 taps/pokes at 60 and 120 s (1 tap/poke per s); and 1 tap (or poke) at 150, 170, and 190 s.

Fig. 6
Fig. 6

Experiment for demonstrating the VC model: (a) Optodes configuration and (b) experimental paradigm with 10 s checkerboard displays after the initial 30 s rest period.

Fig. 7
Fig. 7

Examples of HRs (blue solid curves) upon middle-finger taps (thick red impulses) in MC (Subject 10): (a) active channel (Ch. 7); (b) de-active channel (Ch. 8); (c) the averaged HR from (a); (d) the averaged HR from (b).

Fig. 8
Fig. 8

HRs in MC (Ch. 7): (a) The averaged HR over three stimuli in Fig. 1, (b) the averaged HR over 15 subjects in (a) and its standard deviation.

Fig. 9
Fig. 9

HRs in SC (Ch. 4): (a) The averaged HR over three stimuli in Fig. 1, (b) the averaged HR over 14 subjects in (a) and its standard deviation.

Fig. 10
Fig. 10

HRs in VC (Ch. 7): (a) The averaged HR over three stimuli in Fig. 1, (b) the averaged HR over 16 subjects in (a) and its standard deviation.

Fig. 11
Fig. 11

Comparison of the impulse HbO (solid line), HbR (dotted line), and HbT (dashed line): (a) MC (Ch. 7), (b) SC (Ch. 4), and (c) VC (Ch. 7).

Fig. 12
Fig. 12

Comparison of the impulse HbOs in three brain regions.

Fig. 13
Fig. 13

Comparison between the experimental HbOs (blue dashed curves) and the reconstructed ones (red solid curves): (a) MC, (b) SC, and (c) VC.

Fig. 14
Fig. 14

Comparison of the predicted HRs (the red dashed curves are through Eq. (3) and the black solid curves are through the state space method): (a) MC, (b) SC, and (c) VC.

Fig. 15
Fig. 15

Identified HRs in MC (Subject 2): (a) Active channel (Ch. 12), (b) de-active channel (Ch. 11).

Fig. 16
Fig. 16

Identified HRs in SC (Subject 1): (a) Active channel (Ch. 13), (b) de-active channel (Ch. 23).

Fig. 17
Fig. 17

Identified HRs in VC (Subject 1): (a) Active channel (Ch. 1), (b) de-active channel (Ch. 3).

Tables (5)

Tables Icon

Table 1 Examples of t-values in MC (Ch. 7, Ch. 8)

Tables Icon

Table 2 Mean value during the activation period (m1): MC

Tables Icon

Table 3 Mean value during the deactivation period (m2): MC

Tables Icon

Table 4 p-value between m1 and m2 for MC

Tables Icon

Table 5 Comparison of HR parameters between experiment and reconstruction: MC, SC, and VC

Equations (13)

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

Δ A i ( k; λ j )=[ a HbO ( λ j )Δ c HbO i ( k )+ a HbR ( λ j )Δ c HbR i ( k ) ]× l i × d i ,j=1,2
[ Δ c HbO i ( k ) Δ c HbR i ( k ) ]= [ a HbO ( λ 1 ) a HbR ( λ 1 ) a HbO ( λ 2 ) a HbR ( λ 2 ) ] 1 [ Δ A i ( k; λ 1 ) Δ A i ( k; λ 2 ) ]× 1 l i d i .
y M ( k )=s( k )*h( k ),
y H i ( k )= x 1 ( k ) β 1 i ( k )+ x 2 ( k ) β 2 i ( k )+ x 3 ( k ) β 3 i ( k )+ x 4 ( k ) β 4 i ( k )+ v i ( k ), = X T ( k ) β i ( k )+ v i ( k )
e i ( k )= y H i ( k ) y ^ H i ( k ), y ^ H i ( k )= X T ( k ) β ^ i ( k1 ), β ^ i ( k )= β ^ i ( k1 )+L( k ) e i ( k ), L( k )=P( k1 )X( k ) ( 1+ X T ( k )P( k1 )X( k ) ) 1 , P( k )=P( k1 )L( k ) X T ( k )P( k1 ),
t i ( k )= c T β ^ i ( k ) σ ^ i2 ( k ) c T [ j=1 k X T ( j )X( j ) ] 1 c ,
σ ^ i2 ( k )= 1 kr j=1 k [ y H i ( j ) X T ( j ) β ^ i ( j ) ] 2 ,
z( k+1 )=Az( k )+Bu( k )+w( k ), y( k )=Cz( k )+Du( k )+v( k ),
U=[ u(0) u(1) u(N1) u(1) u(2) u(N) u(q1) u(q) u(q+N2) ] q×N ,
Y=[ y(0) y(1) y(N1) y(1) y(2) y(N) y(q1) y(q) y(q+N2) ] q×N ,
A=[ a 11 a 12 a 16 a 21 a 22 a 26 a 61 a 62 a 66 ]=[ 100 0.84 0.02 0.17 0 0.04 0.18 99.98 1.41 0.03 0.34 0.01 0.01 0.28 99.63 2.45 0.05 0.52 0 0.02 0.31 100.18 3.72 0.09 0 0 0 0.79 99.98 3.77 0 0 0.02 0.01 0.52 98.53 ], B= [ b 11 b 12 b 16 ] T = [ 0.08 0.18 0.17 0.01 0.01 0.01 ] T , C=[ c 11 c 12 c 16 ]=[ 0.80 0.66 0.32 0.14 0.07 0.03 ], D=4.0565× 10 8 .
A=[ 100 1.05 0.01 0.18 0.01 0.02 0.16 99.89 1.84 0 0.35 0.01 0.01 0.25 99.97 3.88 0.07 0.36 0 0.03 0.44 99.83 4.61 0.04 0 0.01 0.07 0.47 99.77 6.20 0 0 0 0.05 3.60 81.96 ], B= [ 0.09 0.16 0.07 0.01 0.01 0 ] T , C=[ 0.81 0.52 0.19 0.09 0.03 0.01 ], D=3.422× 10 8 .
A=[ 99.94 0.39 0.03 0.04 0.12 0.02 0.39 99.76 0.15 0.15 0.39 0.07 0.08 0.21 100.04 0.93 0.86 0.05 0.04 0.19 1.29 99.95 0.46 0.17 0.09 0.31 0.33 0.84 99.62 0.59 0.02 0.02 0.06 0.14 0.18 100.05 ], B= [ 0.48 0.65 0.24 0.21 0.35 0.07 ] T , C=[ 0.48 0.66 0.17 0.14 0.42 0.11 ], D=2.3951× 10 6 .

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