Abstract

In this study a new strategy that combines Granger causality mapping (GCM) and independent component analysis (ICA) is proposed to reveal complex neural network dynamics underlying cognitive processes using functional near infrared spectroscopy (fNIRS) measurements. The GCM-ICA algorithm implements the following two procedures: (i) extraction of the region of interests (ROIs) of cortical activations by ICA, and (ii) estimation of the direct causal influences in local brain networks using Granger causality among voxels of ROIs. Our results show that the use of GCM in conjunction with ICA is able to effectively identify the directional brain network dynamics in time-frequency domain based on fNIRS recordings.

© 2013 Optical Society of America

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  1. F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
    [CrossRef] [PubMed]
  2. B. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
    [CrossRef]
  3. J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
    [CrossRef] [PubMed]
  4. Z. Yuan, Q. Zhang, E. S. Sobel, H. Jiang, “Image-guided optical spectroscopy in diagnosis of osteoarthritis: A clinical study,” Biomed. Opt. Express 1(1), 74–86 (2010).
    [CrossRef] [PubMed]
  5. Z. Yuan, “Spatiotemporal and time-frequency analysis of functional near-infrared spectroscopy brain signals using independent component analysis,” J. Biomed. Opt. 18(10), 16011 (2013).
  6. I. Schelkanova, V. Toronov, “Independent component analysis of broadband near-infrared spectroscopy data acquired on adult human head,” Biomed. Opt. Express 3(1), 64–74 (2012).
    [CrossRef] [PubMed]
  7. R. C. Mesquita, M. A. Franceschini, D. A. Boas, “Resting state functional connectivity of the whole head with near-infrared spectroscopy,” Biomed. Opt. Express 1(1), 324–336 (2010).
    [CrossRef] [PubMed]
  8. T. J. Huppert, S. G. Diamond, M. A. Franceschini, D. A. Boas, “Homer: a review of time-series analysis methods for near-infrared spectroscopy of the brain,” Appl. Opt. 48(10), D280–D298 (2009).
    [CrossRef] [PubMed]
  9. C. B. Akgül, A. Akin, B. Sankur, “Extraction of cognitive activity-related waveforms from functional near-infrared spectroscopy signals,” Med. Biol. Eng. Comput. 44(11), 945–958 (2006).
    [CrossRef] [PubMed]
  10. J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
    [CrossRef] [PubMed]
  11. M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
    [CrossRef] [PubMed]
  12. O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
    [CrossRef] [PubMed]
  13. A. J. Bell, T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7(6), 1129–1159 (1995).
    [CrossRef] [PubMed]
  14. A. Delorme, S. Makeig, “EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis,” J. Neurosci. Methods 134(1), 9–21 (2004).
    [CrossRef] [PubMed]
  15. Z. Yuan, J. Ye, “Fusion of fNIRS and fMRI data: Identifying when and where hemodynamic signal are changing in human brains,” Front. Hum. Neurosci., doi: 10.3389/ fnhum.2013.00676(2013).
  16. A. K. Seth, “A MATLAB toolbox for Granger causal connectivity analysis,” J. Neurosci. Methods 186(2), 262–273 (2010).
    [CrossRef] [PubMed]
  17. W. Liu, L. Forrester, J. Whitall, “A note on time-frequency analysis of finger tapping,” J. Mot. Behav. 38(1), 18–28 (2006).
    [CrossRef] [PubMed]

2013

Z. Yuan, “Spatiotemporal and time-frequency analysis of functional near-infrared spectroscopy brain signals using independent component analysis,” J. Biomed. Opt. 18(10), 16011 (2013).

2012

2010

2009

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

T. J. Huppert, S. G. Diamond, M. A. Franceschini, D. A. Boas, “Homer: a review of time-series analysis methods for near-infrared spectroscopy of the brain,” Appl. Opt. 48(10), D280–D298 (2009).
[CrossRef] [PubMed]

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

2008

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

2006

C. B. Akgül, A. Akin, B. Sankur, “Extraction of cognitive activity-related waveforms from functional near-infrared spectroscopy signals,” Med. Biol. Eng. Comput. 44(11), 945–958 (2006).
[CrossRef] [PubMed]

W. Liu, L. Forrester, J. Whitall, “A note on time-frequency analysis of finger tapping,” J. Mot. Behav. 38(1), 18–28 (2006).
[CrossRef] [PubMed]

2004

A. Delorme, S. Makeig, “EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis,” J. Neurosci. Methods 134(1), 9–21 (2004).
[CrossRef] [PubMed]

2000

M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
[CrossRef] [PubMed]

1995

A. J. Bell, T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7(6), 1129–1159 (1995).
[CrossRef] [PubMed]

B. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

1977

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[CrossRef] [PubMed]

Akgül, C. B.

C. B. Akgül, A. Akin, B. Sankur, “Extraction of cognitive activity-related waveforms from functional near-infrared spectroscopy signals,” Med. Biol. Eng. Comput. 44(11), 945–958 (2006).
[CrossRef] [PubMed]

Akin, A.

C. B. Akgül, A. Akin, B. Sankur, “Extraction of cognitive activity-related waveforms from functional near-infrared spectroscopy signals,” Med. Biol. Eng. Comput. 44(11), 945–958 (2006).
[CrossRef] [PubMed]

Andreasen, N. C.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Bell, A. J.

A. J. Bell, T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7(6), 1129–1159 (1995).
[CrossRef] [PubMed]

Boas, D. A.

Bressler, S. L.

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
[CrossRef] [PubMed]

Calhoun, V. D.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Chance, B.

B. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Clark, V. P.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Cui, J.

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

Delorme, A.

A. Delorme, S. Makeig, “EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis,” J. Neurosci. Methods 134(1), 9–21 (2004).
[CrossRef] [PubMed]

Demirci, O.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Diamond, S. G.

Ding, M.

M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
[CrossRef] [PubMed]

Ding, M. Z.

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

Forrester, L.

W. Liu, L. Forrester, J. Whitall, “A note on time-frequency analysis of finger tapping,” J. Mot. Behav. 38(1), 18–28 (2006).
[CrossRef] [PubMed]

Franceschini, M. A.

Huppert, T. J.

Jang, J.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

Jang, K. E.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

Jiang, H.

Jöbsis, F. F.

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[CrossRef] [PubMed]

Jung, J.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

Liang, H.

M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
[CrossRef] [PubMed]

Liang, H. L.

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

Liu, J.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Liu, W.

W. Liu, L. Forrester, J. Whitall, “A note on time-frequency analysis of finger tapping,” J. Mot. Behav. 38(1), 18–28 (2006).
[CrossRef] [PubMed]

Makeig, S.

A. Delorme, S. Makeig, “EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis,” J. Neurosci. Methods 134(1), 9–21 (2004).
[CrossRef] [PubMed]

Mesquita, R. C.

Michael, A.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Pearlson, G. D.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Sankur, B.

C. B. Akgül, A. Akin, B. Sankur, “Extraction of cognitive activity-related waveforms from functional near-infrared spectroscopy signals,” Med. Biol. Eng. Comput. 44(11), 945–958 (2006).
[CrossRef] [PubMed]

Schelkanova, I.

Sejnowski, T. J.

A. J. Bell, T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7(6), 1129–1159 (1995).
[CrossRef] [PubMed]

Seth, A. K.

A. K. Seth, “A MATLAB toolbox for Granger causal connectivity analysis,” J. Neurosci. Methods 186(2), 262–273 (2010).
[CrossRef] [PubMed]

Sobel, E. S.

Stevens, M. C.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Tak, S.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

Toronov, V.

Whitall, J.

W. Liu, L. Forrester, J. Whitall, “A note on time-frequency analysis of finger tapping,” J. Mot. Behav. 38(1), 18–28 (2006).
[CrossRef] [PubMed]

White, T.

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Xu, L.

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

Yang, W.

M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
[CrossRef] [PubMed]

Ye, J. C.

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

Yodh, B.

B. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Yuan, Z.

Z. Yuan, “Spatiotemporal and time-frequency analysis of functional near-infrared spectroscopy brain signals using independent component analysis,” J. Biomed. Opt. 18(10), 16011 (2013).

Z. Yuan, Q. Zhang, E. S. Sobel, H. Jiang, “Image-guided optical spectroscopy in diagnosis of osteoarthritis: A clinical study,” Biomed. Opt. Express 1(1), 74–86 (2010).
[CrossRef] [PubMed]

Zhang, Q.

Appl. Opt.

Biol. Cybern.

M. Ding, S. L. Bressler, W. Yang, H. Liang, “Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment,” Biol. Cybern. 83(1), 35–45 (2000).
[CrossRef] [PubMed]

Biomed. Opt. Express

J. Biomed. Opt.

Z. Yuan, “Spatiotemporal and time-frequency analysis of functional near-infrared spectroscopy brain signals using independent component analysis,” J. Biomed. Opt. 18(10), 16011 (2013).

J. Mot. Behav.

W. Liu, L. Forrester, J. Whitall, “A note on time-frequency analysis of finger tapping,” J. Mot. Behav. 38(1), 18–28 (2006).
[CrossRef] [PubMed]

J. Neurosci. Methods

A. K. Seth, “A MATLAB toolbox for Granger causal connectivity analysis,” J. Neurosci. Methods 186(2), 262–273 (2010).
[CrossRef] [PubMed]

A. Delorme, S. Makeig, “EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis,” J. Neurosci. Methods 134(1), 9–21 (2004).
[CrossRef] [PubMed]

Med. Biol. Eng. Comput.

C. B. Akgül, A. Akin, B. Sankur, “Extraction of cognitive activity-related waveforms from functional near-infrared spectroscopy signals,” Med. Biol. Eng. Comput. 44(11), 945–958 (2006).
[CrossRef] [PubMed]

Neural Comput.

A. J. Bell, T. J. Sejnowski, “An information-maximization approach to blind separation and blind deconvolution,” Neural Comput. 7(6), 1129–1159 (1995).
[CrossRef] [PubMed]

Neural Netw.

J. Cui, L. Xu, S. L. Bressler, M. Z. Ding, H. L. Liang, “BSMART: A MATLAB/C toolbox for analysis of multichannel neural time series,” Neural Netw. 21(8), 1094–1104 (2008).
[CrossRef] [PubMed]

Neuroimage

J. C. Ye, S. Tak, K. E. Jang, J. Jung, J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” Neuroimage 44(2), 428–447 (2009).
[CrossRef] [PubMed]

O. Demirci, M. C. Stevens, N. C. Andreasen, A. Michael, J. Liu, T. White, G. D. Pearlson, V. P. Clark, V. D. Calhoun, “Investigation of relationships between fMRI brain networks in the spectral domain using ICA and Granger causality reveals distinct differences between schizophrenia patients and healthy controls,” Neuroimage 46(2), 419–431 (2009).
[CrossRef] [PubMed]

Phys. Today

B. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Science

F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198(4323), 1264–1267 (1977).
[CrossRef] [PubMed]

Other

Z. Yuan, J. Ye, “Fusion of fNIRS and fMRI data: Identifying when and where hemodynamic signal are changing in human brains,” Front. Hum. Neurosci., doi: 10.3389/ fnhum.2013.00676(2013).

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Figures (11)

Fig. 1
Fig. 1

Channel configurations of the Shimadzu’s FOIRE 3000 systems (Red circles: sources; blue circles: detectors).

Fig. 2
Fig. 2

Channel configurations along the cerebral cortex for 2D and 3D analysis of fNIRS signals.

Fig. 3
Fig. 3

Run by run visualization in temporal domain for the raw HbO2 (a), HbR (b) and HbT measurements (c) from an arbitrary selected channel 36. The bottom curve plots the run average for each chromophore. Runs were imaged in (bottom-to-top) order of their occurrence during the experiment.

Fig. 4
Fig. 4

The spatiotemporal analysis of independent components that contribute the most to the original HbO2 measurements (a), HbR measurements(b), and HbT measurements (c). Brain activation maps in 2D are also provided and the cortical activations were mostly seen in the left primary motor cortex and supplementary motor area. (The black thick lines indicate the data envelope (i.e. minimum and maximum of all channels at every time point) and the colored ones show the components of different chromophores).

Fig. 5
Fig. 5

The most important independent components (ICs) calculated from HbO2 measurements (a), HbR measurements (b), and HbT measurements (c). The combinations of these ICs for each specific chromophore will generate its ROIs for right finger tapping tasks and the ROIs are shown in the fourth column of Fig. 5. The cortical activations were mostly seen in the left primary motor cortex and supplementary motor area.

Fig. 6
Fig. 6

Directional influences measured as Granger causality among channels G1-G5 for HbO2 measurements. Time-frequency causality influences are shown in the left column and the single spectra are given in the right column with the spectrum in the time window centered at 25s (time points: 200). Stimuli onset time: 25s (time point 200); stimulus processing time: 25s-45s (time points 200-360). Only significant influences are provided due to limited space.

Fig. 7
Fig. 7

Directional influences measured as Granger causality among channels G1-G6 for HbR measurements. Time-frequency causality influences are shown in the left column and the single spectra are given in the right column with the spectrum in the time window centered at 25s. Stimuli onset time: 25s (time point 200); stimulus processing time: 25s-45 (time points 200-360). Only significant influences are provided due to limited space.

Fig. 8
Fig. 8

Directional influences measured as Granger causality among channels G1-G5 for HbT measurements. Time-frequency causality influences are shown in the left column and the single spectra are given in the right column with the spectrum in the time window centered at 25s. Stimuli onset time: 25s (time point 200); stimulus processing time: 25s-45s(time points 200-360). Only significant influences are provided due to limited space.

Fig. 9
Fig. 9

Granger causality networks constructed for the time window centered at 25 s (a), and centered at 35s (b). 25s is the stimuli onset time and 35s is the stimulus processing time. The first column is for HbO2 measurement, the second column is for HbR measurement while the third column is for HbT measurement. The arrow represents the direction of Granger causality influences while the width of the blue lines shows the strength of the influences.

Fig. 10
Fig. 10

Motor cortex areas of human brain (open access website: http://neuroscience.uth.tmc.edu/s3/chapter03.html).

Fig. 11
Fig. 11

The typical ICs that identify the body movement and boundary noise.

Equations (16)

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

[ Δ O D ( r , t ) | λ 1 Δ O D ( r , t ) | λ 2 ] = D P F ( r ) l ( r ) [ ε 1 ( λ 1 ) ε 2 ( λ 1 ) ε 1 ( λ 2 ) ε 2 ( λ 2 ) ] [ Δ H b O 2 ( r , t ) Δ H b R ( r , t ) ]
[ Δ H b O 2 ( r , t ) Δ H b R ( r , t ) ] = [ Q H b O 2 ( r , t ) Q H b R ( r , t ) ] / ( D P F ( r ) l ( r ) )
[ Δ H b O 2 Δ H b R ] = ( E T R 1 E ) 1 E T R 1 [ Δ O D | λ 1 Δ O D | λ 2 ... Δ O D | λ n ] / ( D P F × l ) ; E = [ ε 1 ( λ 1 ) ε 2 ( λ 1 ) ... ... ε 1 ( λ n ) ε 2 ( λ n ) ]
Δ H b O 2 = [ Δ H b O 2 ( r 1 , t 1 ) Δ H b O 2 ( r 1 , t 2 ) ... Δ H b O 2 ( r 1 , t M ) Δ H b O 2 ( r 2 , t 1 ) Δ H b O 2 ( r 2 , t 2 ) ... Δ H b O 2 ( r 2 , t M ) Δ H b O 2 ( r K , t 1 ) Δ H b O 2 ( r K , t 2 ) ... Δ H b O 2 ( r K , t M ) ]
Δ H b O 2 = A S
X = W ( Δ H b O 2 ( r ) )
X 1 ( t ) = j = 1 p A 11 , j X 1 ( t j ) + j = 1 p A 12 , j X 2 ( t j ) + E 1 ( t )
X 2 ( t ) = j = 1 p A 21 , j X 1 ( t j ) + j = 1 p A 22 , j X 2 ( t j ) + E 2 ( t )
G 2 1 = ln var ( E 1 R ( 12 ) ) var ( E 1 U )
Σ = [ var ( E 1 U ) cov ( E 1 U , E 2 U ) cov ( E 1 U , E 3 U ) cov ( E 2 U , E 1 U ) var ( E 2 U ) cov ( E 2 U , E 3 U ) cov ( E 3 U , E 1 U ) cov ( E 3 U , E 2 U ) var ( E 3 U ) ]
ρ = [ var ( E 1 R ) cov ( E 1 R , E 3 R ) cov ( E 3 R , E 1 R ) var ( E 3 R ) ]
G 2 1 | 3 = ln var ( E 1 R ) var ( E 1 U )
E ( t ) = m = 0 p A m X ( t m )
H ( f ) = m = 0 p ( A m e i m 2 π f ) 1
S ( f ) = H ( f ) V H * ( f )
I j i ( f ) = log ( 1 ( V j , j V i , j 2 V j , j | H i , j ( f ) | 2 S i , i ( f ) )

Metrics