Abstract

In recent years, studying the resting-state network (RSN) by using functional near-infrared spectroscopy (fNIRS) has received increased attention. The previous resting-state fNIRS studies mainly adopted the seed-based correlation and the independent component analysis to detect RSN. However, these methods have several inherent problems. For example, the seed-based correlation method relies on seed region selection and neglects the interactions among multiple regions. The ICA method usually relies on manual component selection, which requires rich experience from the experimenter. In the present study, we developed a new approach for fNIRS-RSN detection based on spectral clustering. It consists of two steps. First, it calculates the individual-level partition of the fNIRS measurement region by using spectral clustering with an automatically determined cluster number. Second, the individual-level partitioning results are further clustered. Those clusters with high group consistency are determined as RSN clusters. We validated the method by using simulated data and in vivo fNIRS data. The results showed that the proposed method was effective and robust for fNIRS-RSN detection.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  27. J. Shi and J. Malik, “Normalized cuts and image segmentation,” IEEE Trans. Pattern Anal. Machine Intell. 22(8), 888–905 (2000).
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  28. W. Kong, S. Hu, J. Zhang, and G. Dai, “Robust and smart spectral clustering from normalized cut,” Neural Comput. & Appl. 23(5), 1503–1512 (2013).
    [Crossref]
  29. X. Shen, X. Papademetris, and R. T. Constable, “Graph-theory based parcellation of functional subunits in the brain from resting-state fMRI data,” NeuroImage 50(3), 1027–1035 (2010).
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    [Crossref]
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    [Crossref]
  32. L. Duan, Z. Zhao, Y. Lin, X. Wu, Y. Luo, and P. Xu, “Wavelet-based method for removing global physiological noise in functional near-infrared spectroscopy,” Biomed. Opt. Express 9(8), 3805–3820 (2018).
    [Crossref]
  33. A. K. Singh, M. Okamoto, H. Dan, V. Jurcak, and I. Dan, “Spatial registration of multichannel multi-subject fNIRS data to MNI space without MRI,” NeuroImage 27(4), 842–851 (2005).
    [Crossref]
  34. J. C. Ye, S. Tak, K. E. Jang, J. Jung, and J. Jang, “NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy,” NeuroImage 44(2), 428–447 (2009).
    [Crossref]
  35. 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]
  36. M. Hiraoka, M. Firbank, M. Essenpreis, M. Cope, S. R. Arridge, D. Z. P. Van, and D. T. Delpy, “A Monte Carlo investigation of optical pathlength in inhomogeneous tissue and its application to near-infrared spectroscopy,” Phys. Med. Biol. 38(12), 1859–1876 (1993).
    [Crossref]
  37. B. Biswal, F. Zerrin Yetkin, V. M. Haughton, and J. S. Hyde, “Functional connectivity in the motor cortex of resting human brain using echo-planar MRI,” Magn. Reson. Med. 34(4), 537–541 (1995).
    [Crossref]
  38. V. D. Calhoun, T. Adali, G. D. Pearlson, and J. J. Pekar, “A method for making group inferences from functional MRI data using independent component analysis,” Hum. Brain Mapp. 14(3), 140–151 (2001).
    [Crossref]
  39. T. Wilcox and M. Biondi, “fNIRS in the developmental sciences,” WIREs Cogn. Sci. 6(3), 263–283 (2015).
    [Crossref]
  40. V. Bonomini, L. Zucchelli, R. Re, F. Ieva, L. Spinelli, D. Contini, A. Paganoni, and A. Torricelli, “Linear regression models and k-means clustering for statistical analysis of fNIRS data,” Biomed. Opt. Express 6(2), 615–630 (2015).
    [Crossref]
  41. X. Shen, F. Tokoglu, X. Papademetris, and R. T. Constable, “Groupwise whole-brain parcellation from resting-state fMRI data for network node identification,” NeuroImage 82, 403–415 (2013).
    [Crossref]

2020 (1)

Y. Zhang and C. Zhu, “Assessing Brain Networks by Resting-State Dynamic Functional Connectivity: An fNIRS-EEG Study,” Front. Neurosci. 13, 1430 (2020).
[Crossref]

2018 (2)

L. Cai, Q. Dong, and H. Niu, “The development of functional network organization in early childhood and early adolescence: A resting-state fNIRS study,” Dev. Cogn. Neurosci. 30, 223–235 (2018).
[Crossref]

L. Duan, Z. Zhao, Y. Lin, X. Wu, Y. Luo, and P. Xu, “Wavelet-based method for removing global physiological noise in functional near-infrared spectroscopy,” Biomed. Opt. Express 9(8), 3805–3820 (2018).
[Crossref]

2017 (4)

H. F.-H. Ieong and Z. Yuan, “Abnormal resting-state functional connectivity in the orbitofrontal cortex of heroin users and its relationship with anxiety: a pilot fNIRS study,” Sci. Rep. 7(1), 46522 (2017).
[Crossref]

H. Zhu, J. Xu, J. Li, H. Peng, T. Cai, X. Li, S. Wu, W. Cao, and S. He, “Decreased functional connectivity and disrupted neural network in the prefrontal cortex of affective disorders: A resting-state fNIRS study,” J. Affective Disord. 221, 132–144 (2017).
[Crossref]

D. S. Bassett and O. Sporns, “Network neuroscience,” Nat. Neurosci. 20(3), 353–364 (2017).
[Crossref]

G. S. Wig, “Segregated systems of human brain networks,” Trends Cognit. Sci. 21(12), 981–996 (2017).
[Crossref]

2016 (1)

J. Zhao, J. Liu, X. Jiang, G. Zhou, G. Chen, X. P. Ding, G. Fu, and K. Lee, “Linking resting-state networks in the prefrontal cortex to executive function: a functional near infrared spectroscopy study,” Front. Neurosci. 10, 452 (2016).
[Crossref]

2015 (3)

M. E. Raichle, “The brain's default mode network,” Annu. Rev. Neurosci. 38(1), 433–447 (2015).
[Crossref]

T. Wilcox and M. Biondi, “fNIRS in the developmental sciences,” WIREs Cogn. Sci. 6(3), 263–283 (2015).
[Crossref]

V. Bonomini, L. Zucchelli, R. Re, F. Ieva, L. Spinelli, D. Contini, A. Paganoni, and A. Torricelli, “Linear regression models and k-means clustering for statistical analysis of fNIRS data,” Biomed. Opt. Express 6(2), 615–630 (2015).
[Crossref]

2014 (1)

T. Fekete, F. D. Beacher, J. Cha, D. Rubin, and L. R. Mujica-Parodi, “Small-world network properties in prefrontal cortex correlate with predictors of psychopathology risk in young children: A NIRS study,” NeuroImage 85, 345–353 (2014).
[Crossref]

2013 (3)

W. Kong, S. Hu, J. Zhang, and G. Dai, “Robust and smart spectral clustering from normalized cut,” Neural Comput. & Appl. 23(5), 1503–1512 (2013).
[Crossref]

H. Niu, Z. Li, X. Liao, J. Wang, T. Zhao, N. Shu, X. Zhao, and Y. He, “Test-retest reliability of graph metrics in functional brain networks: a resting-state fNIRS study,” PLoS One 8(9), e72425 (2013).
[Crossref]

X. Shen, F. Tokoglu, X. Papademetris, and R. T. Constable, “Groupwise whole-brain parcellation from resting-state fMRI data for network node identification,” NeuroImage 82, 403–415 (2013).
[Crossref]

2012 (3)

S. Sasai, F. Homae, H. Watanabe, A. T. Sasaki, H. C. Tanabe, N. Sadato, and G. Taga, “A NIRS–fMRI study of resting state network,” NeuroImage 63(1), 179–193 (2012).
[Crossref]

L. Duan, Y. J. Zhang, and C. Z. Zhu, “Quantitative comparison of resting-state functional connectivity derived from fNIRS and fMRI: a simultaneous recording study,” NeuroImage 60(4), 2008–2018 (2012).
[Crossref]

Y. J. Zhang, L. Duan, H. Zhang, B. B. Biswal, C. M. Lu, and C. Z. Zhu, “Determination of dominant frequency of resting-state brain interaction within one functional system,” PLoS One 7(12), e51584 (2012).
[Crossref]

2011 (2)

H. Zhang, Y. J. Zhang, L. Duan, S. Y. Ma, C. M. Lu, and C. Z. Zhu, “Is resting-state functional connectivity revealed by functional near-infrared spectroscopy test-retest reliable?” J. Biomed. Opt. 16(6), 067008 (2011).
[Crossref]

H. Zhang, L. Duan, Y. J. Zhang, C. M. Lu, H. Liu, and C. Z. Zhu, “Test–retest assessment of independent component analysis-derived resting-state functional connectivity based on functional near-infrared spectroscopy,” NeuroImage 55(2), 607–615 (2011).
[Crossref]

2010 (8)

H. Zhang, Y. J. Zhang, S. Y. Ma, Y. F. Zang, and C. Z. Zhu, “Functional connectivity as revealed by independent component analysis of resting-state fNIRS measurements,” NeuroImage 51(3), 1150–1161 (2010).
[Crossref]

X. Shen, X. Papademetris, and R. T. Constable, “Graph-theory based parcellation of functional subunits in the brain from resting-state fMRI data,” NeuroImage 50(3), 1027–1035 (2010).
[Crossref]

R. C. Mesquita, M. A. Franceschini, and D. A. Boas, “Resting state functional connectivity of the whole head with near-infrared spectroscopy,” Biomed. Opt. Express 1(1), 324–336 (2010).
[Crossref]

M. D. Fox and M. Greicius, “Clinical applications of resting state functional connectivity,” Front. Syst. Neurosci. 4, 19 (2010).
[Crossref]

M. P. Van Den Heuvel and H. E. H. Pol, “Exploring the brain network: a review on resting-state fMRI functional connectivity,” Eur. Neuropsychopharmacol. 20(8), 519–534 (2010).
[Crossref]

Y. J. Zhang, C. M. Lu, B. B. Biswal, Y. F. Zang, D. L. Peng, and C. Z. Zhu, “Detecting resting-state functional connectivity in the language system using functional near-infrared spectroscopy,” J. Biomed. Opt. 15(4), 047003 (2010).
[Crossref]

F. Homae, H. Watanabe, T. Otobe, T. Nakano, T. Go, Y. Konishi, and G. Taga, “Development of global cortical networks in early infancy,” J. Neurosci. 30(14), 4877–4882 (2010).
[Crossref]

C. M. Lu, Y. J. Zhang, B. B. Biswal, Y. F. Zang, D. L. Peng, and C. Z. Zhu, “Use of fNIRS to assess resting state functional connectivity,” J. Neurosci. Methods 186(2), 242–249 (2010).
[Crossref]

2009 (2)

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

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

2008 (1)

M. Van Den Heuvel, R. Mandl, and H. H. Pol, “Normalized cut group clustering of resting-state FMRI data,” PLoS One 3(4), e2001 (2008).
[Crossref]

2007 (2)

U. Von Luxburg, “A tutorial on spectral clustering,” Stat. Comput. 17(4), 395–416 (2007).
[Crossref]

M. D. Fox and M. E. Raichle, “Spontaneous fluctuations in brain activity observed with functional magnetic resonance imaging,” Nat. Rev. Neurosci. 8(9), 700–711 (2007).
[Crossref]

2006 (1)

M. E. Raichle, “The brain's dark energy,” Science 314(5803), 1249–1250 (2006).
[Crossref]

2005 (1)

A. K. Singh, M. Okamoto, H. Dan, V. Jurcak, and I. Dan, “Spatial registration of multichannel multi-subject fNIRS data to MNI space without MRI,” NeuroImage 27(4), 842–851 (2005).
[Crossref]

2004 (1)

H. Sato, M. Kiguchi, F. Kawaguchi, and A. Maki, “Practicality of wavelength selection to improve signal-to-noise ratio in near-infrared spectroscopy,” NeuroImage 21(4), 1554–1562 (2004).
[Crossref]

2001 (1)

V. D. Calhoun, T. Adali, G. D. Pearlson, and J. J. Pekar, “A method for making group inferences from functional MRI data using independent component analysis,” Hum. Brain Mapp. 14(3), 140–151 (2001).
[Crossref]

2000 (1)

J. Shi and J. Malik, “Normalized cuts and image segmentation,” IEEE Trans. Pattern Anal. Machine Intell. 22(8), 888–905 (2000).
[Crossref]

1995 (1)

B. Biswal, F. Zerrin Yetkin, V. M. Haughton, and J. S. Hyde, “Functional connectivity in the motor cortex of resting human brain using echo-planar MRI,” Magn. Reson. Med. 34(4), 537–541 (1995).
[Crossref]

1993 (1)

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

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]

Adali, T.

V. D. Calhoun, T. Adali, G. D. Pearlson, and J. J. Pekar, “A method for making group inferences from functional MRI data using independent component analysis,” Hum. Brain Mapp. 14(3), 140–151 (2001).
[Crossref]

Arridge, S. R.

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

Bassett, D. S.

D. S. Bassett and O. Sporns, “Network neuroscience,” Nat. Neurosci. 20(3), 353–364 (2017).
[Crossref]

Beacher, F. D.

T. Fekete, F. D. Beacher, J. Cha, D. Rubin, and L. R. Mujica-Parodi, “Small-world network properties in prefrontal cortex correlate with predictors of psychopathology risk in young children: A NIRS study,” NeuroImage 85, 345–353 (2014).
[Crossref]

Biondi, M.

T. Wilcox and M. Biondi, “fNIRS in the developmental sciences,” WIREs Cogn. Sci. 6(3), 263–283 (2015).
[Crossref]

Biswal, B.

B. Biswal, F. Zerrin Yetkin, V. M. Haughton, and J. S. Hyde, “Functional connectivity in the motor cortex of resting human brain using echo-planar MRI,” Magn. Reson. Med. 34(4), 537–541 (1995).
[Crossref]

Biswal, B. B.

Y. J. Zhang, L. Duan, H. Zhang, B. B. Biswal, C. M. Lu, and C. Z. Zhu, “Determination of dominant frequency of resting-state brain interaction within one functional system,” PLoS One 7(12), e51584 (2012).
[Crossref]

Y. J. Zhang, C. M. Lu, B. B. Biswal, Y. F. Zang, D. L. Peng, and C. Z. Zhu, “Detecting resting-state functional connectivity in the language system using functional near-infrared spectroscopy,” J. Biomed. Opt. 15(4), 047003 (2010).
[Crossref]

C. M. Lu, Y. J. Zhang, B. B. Biswal, Y. F. Zang, D. L. Peng, and C. Z. Zhu, “Use of fNIRS to assess resting state functional connectivity,” J. Neurosci. Methods 186(2), 242–249 (2010).
[Crossref]

Boas, D. A.

Bonomini, V.

Cai, L.

L. Cai, Q. Dong, and H. Niu, “The development of functional network organization in early childhood and early adolescence: A resting-state fNIRS study,” Dev. Cogn. Neurosci. 30, 223–235 (2018).
[Crossref]

Cai, T.

H. Zhu, J. Xu, J. Li, H. Peng, T. Cai, X. Li, S. Wu, W. Cao, and S. He, “Decreased functional connectivity and disrupted neural network in the prefrontal cortex of affective disorders: A resting-state fNIRS study,” J. Affective Disord. 221, 132–144 (2017).
[Crossref]

Calhoun, V. D.

V. D. Calhoun, T. Adali, G. D. Pearlson, and J. J. Pekar, “A method for making group inferences from functional MRI data using independent component analysis,” Hum. Brain Mapp. 14(3), 140–151 (2001).
[Crossref]

Cao, W.

H. Zhu, J. Xu, J. Li, H. Peng, T. Cai, X. Li, S. Wu, W. Cao, and S. He, “Decreased functional connectivity and disrupted neural network in the prefrontal cortex of affective disorders: A resting-state fNIRS study,” J. Affective Disord. 221, 132–144 (2017).
[Crossref]

Cha, J.

T. Fekete, F. D. Beacher, J. Cha, D. Rubin, and L. R. Mujica-Parodi, “Small-world network properties in prefrontal cortex correlate with predictors of psychopathology risk in young children: A NIRS study,” NeuroImage 85, 345–353 (2014).
[Crossref]

Chen, G.

J. Zhao, J. Liu, X. Jiang, G. Zhou, G. Chen, X. P. Ding, G. Fu, and K. Lee, “Linking resting-state networks in the prefrontal cortex to executive function: a functional near infrared spectroscopy study,” Front. Neurosci. 10, 452 (2016).
[Crossref]

Cohen, A. L.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

Constable, R. T.

X. Shen, F. Tokoglu, X. Papademetris, and R. T. Constable, “Groupwise whole-brain parcellation from resting-state fMRI data for network node identification,” NeuroImage 82, 403–415 (2013).
[Crossref]

X. Shen, X. Papademetris, and R. T. Constable, “Graph-theory based parcellation of functional subunits in the brain from resting-state fMRI data,” NeuroImage 50(3), 1027–1035 (2010).
[Crossref]

Contini, D.

Cope, M.

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

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]

Culver, J. P.

B. R. White, A. Z. Snyder, A. L. Cohen, S. E. Petersen, M. E. Raichle, B. L. Schlaggar, and J. P. Culver, “Resting-state functional connectivity in the human brain revealed with diffuse optical tomography,” NeuroImage 47(1), 148–156 (2009).
[Crossref]

Dai, G.

W. Kong, S. Hu, J. Zhang, and G. Dai, “Robust and smart spectral clustering from normalized cut,” Neural Comput. & Appl. 23(5), 1503–1512 (2013).
[Crossref]

Dan, H.

A. K. Singh, M. Okamoto, H. Dan, V. Jurcak, and I. Dan, “Spatial registration of multichannel multi-subject fNIRS data to MNI space without MRI,” NeuroImage 27(4), 842–851 (2005).
[Crossref]

Dan, I.

A. K. Singh, M. Okamoto, H. Dan, V. Jurcak, and I. Dan, “Spatial registration of multichannel multi-subject fNIRS data to MNI space without MRI,” NeuroImage 27(4), 842–851 (2005).
[Crossref]

Delpy, D. T.

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

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]

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[Crossref]

Zerrin Yetkin, F.

B. Biswal, F. Zerrin Yetkin, V. M. Haughton, and J. S. Hyde, “Functional connectivity in the motor cortex of resting human brain using echo-planar MRI,” Magn. Reson. Med. 34(4), 537–541 (1995).
[Crossref]

Zhang, H.

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[Crossref]

H. Zhang, Y. J. Zhang, L. Duan, S. Y. Ma, C. M. Lu, and C. Z. Zhu, “Is resting-state functional connectivity revealed by functional near-infrared spectroscopy test-retest reliable?” J. Biomed. Opt. 16(6), 067008 (2011).
[Crossref]

H. Zhang, L. Duan, Y. J. Zhang, C. M. Lu, H. Liu, and C. Z. Zhu, “Test–retest assessment of independent component analysis-derived resting-state functional connectivity based on functional near-infrared spectroscopy,” NeuroImage 55(2), 607–615 (2011).
[Crossref]

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[Crossref]

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W. Kong, S. Hu, J. Zhang, and G. Dai, “Robust and smart spectral clustering from normalized cut,” Neural Comput. & Appl. 23(5), 1503–1512 (2013).
[Crossref]

Zhang, Y.

Y. Zhang and C. Zhu, “Assessing Brain Networks by Resting-State Dynamic Functional Connectivity: An fNIRS-EEG Study,” Front. Neurosci. 13, 1430 (2020).
[Crossref]

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L. Duan, Y. J. Zhang, and C. Z. Zhu, “Quantitative comparison of resting-state functional connectivity derived from fNIRS and fMRI: a simultaneous recording study,” NeuroImage 60(4), 2008–2018 (2012).
[Crossref]

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[Crossref]

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H. Zhang, Y. J. Zhang, S. Y. Ma, Y. F. Zang, and C. Z. Zhu, “Functional connectivity as revealed by independent component analysis of resting-state fNIRS measurements,” NeuroImage 51(3), 1150–1161 (2010).
[Crossref]

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[Crossref]

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[Crossref]

Zhao, J.

J. Zhao, J. Liu, X. Jiang, G. Zhou, G. Chen, X. P. Ding, G. Fu, and K. Lee, “Linking resting-state networks in the prefrontal cortex to executive function: a functional near infrared spectroscopy study,” Front. Neurosci. 10, 452 (2016).
[Crossref]

Zhao, T.

H. Niu, Z. Li, X. Liao, J. Wang, T. Zhao, N. Shu, X. Zhao, and Y. He, “Test-retest reliability of graph metrics in functional brain networks: a resting-state fNIRS study,” PLoS One 8(9), e72425 (2013).
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Zhao, X.

H. Niu, Z. Li, X. Liao, J. Wang, T. Zhao, N. Shu, X. Zhao, and Y. He, “Test-retest reliability of graph metrics in functional brain networks: a resting-state fNIRS study,” PLoS One 8(9), e72425 (2013).
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Zhou, G.

J. Zhao, J. Liu, X. Jiang, G. Zhou, G. Chen, X. P. Ding, G. Fu, and K. Lee, “Linking resting-state networks in the prefrontal cortex to executive function: a functional near infrared spectroscopy study,” Front. Neurosci. 10, 452 (2016).
[Crossref]

Zhu, C.

Y. Zhang and C. Zhu, “Assessing Brain Networks by Resting-State Dynamic Functional Connectivity: An fNIRS-EEG Study,” Front. Neurosci. 13, 1430 (2020).
[Crossref]

Zhu, C. Z.

L. Duan, Y. J. Zhang, and C. Z. Zhu, “Quantitative comparison of resting-state functional connectivity derived from fNIRS and fMRI: a simultaneous recording study,” NeuroImage 60(4), 2008–2018 (2012).
[Crossref]

Y. J. Zhang, L. Duan, H. Zhang, B. B. Biswal, C. M. Lu, and C. Z. Zhu, “Determination of dominant frequency of resting-state brain interaction within one functional system,” PLoS One 7(12), e51584 (2012).
[Crossref]

H. Zhang, Y. J. Zhang, L. Duan, S. Y. Ma, C. M. Lu, and C. Z. Zhu, “Is resting-state functional connectivity revealed by functional near-infrared spectroscopy test-retest reliable?” J. Biomed. Opt. 16(6), 067008 (2011).
[Crossref]

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[Crossref]

H. Zhang, Y. J. Zhang, S. Y. Ma, Y. F. Zang, and C. Z. Zhu, “Functional connectivity as revealed by independent component analysis of resting-state fNIRS measurements,” NeuroImage 51(3), 1150–1161 (2010).
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1. The flow chart of the spectral clustering-based fNIRS-RSN detection approach.
Fig. 2.
Fig. 2. The results of the simulation experiment. The four rows correspond to the four conditions of RSN number. The first column shows the spatial configuration. The second column shows the histogram of the automatically estimated cluster number for 100 times of simulation. The third and after columns show the group consistency maps of all the group-level clusters. The color in the group consistency map indicates the group consistency value (as defined in Eq. (11).
Fig. 3.
Fig. 3. Results derived from the real HbO data. (A) The group-level consistency maps of the four group-level components. Color indicates the group consistency value (as defined in Eq. (11). The green line in component ${\xi _1}$ marks the significant channels. (B) The sensorimotor template. (C) Distribution of the automatic estimated individual cluster numbers. (D) A representative individual cluster map in ${\xi _1}$ (GOF = 0.39). (E) Distribution of the GOF indices for the individual-level cluster maps in ${\xi _1}$.
Fig. 4.
Fig. 4. comparison between the spectral clustering method and the seed-based correlation method. (A) The group-level RSN maps derived from the spectral clustering-based method (the first row) and the seed-based correlation method (the second row), respectively. The third row shows the sensorimotor template. (B) The receiver operating characteristic (ROC) curve. The red line corresponds to the ROC curve of the spectral clustering-based method, and the blue line corresponds to the ROC curve of the seed-based correlation method.
Fig. 5.
Fig. 5. Validation results of different signal-to-noise ratio (SNR). (A) The spatial configuration of the simulation experiment. Two different 5${\times} $5 RSN clusters (the white regions) were simulated. (B) The goodness-of-fit indices derived from different SNR data. When SNR was below 0.02, the method cannot detect any RSN. When SNR was between 0.02 and 0.04, the goodness-of-fit index increased rapidly. When SNR was larger than or equal to 0.04, the method can detect all the RSNs perfectly.
Fig. 6.
Fig. 6. The results of the RSN volume validation. The three rows correspond to the three conditions of small, middle and large RSN volume, respectively. The first column shows the spatial configuration. The second column shows the histogram of the automatically estimated cluster number for 100 times of simulation. The third and after columns show the group consistency maps of all the group-level clusters. For each of the three volume sizes (3${\times} $3, 5${\times} $5 and 7${\times} $7), the method detected all the RSN components. The GOF was 0.67, 1 and 1, respectively.
Fig. 7.
Fig. 7. The results of the unbalanced RSN volume ratio validation. Two RSNs clusters with volume size ratio of 3:1 were simulated, and were detected by our method (GOF = 1).
Fig. 8.
Fig. 8. Results derived from the in vivo HbR data. (A) The group-level consistency maps of the four group-level components. Color indicates the group consistency value (as defined in Eq. (11). The green circles in component ${\xi _1}$ mark the significant channels (Channel 9, 13, 17 in the left hemisphere and Channel 30, 36, 34, 46 in the right hemisphere. p < 0.05, Bonferroni-corrected. GOF = 0.36). (B) The sensorimotor template. (C) Distribution of the automatic estimated individual cluster numbers. (D) A representative individual cluster map in ${\xi _1}$ (GOF = 0.33). (E) Distribution of the GOF indices for the individual-level cluster maps in ${\xi _1}$. The mean GOF was 0.25, with the standard deviation of 0.10.
Fig. 9.
Fig. 9. comparison between the spectral clustering method and the seed-based correlation method for HbR data. (A) The group-level RSN maps derived from the spectral clustering-based method (the first row) and the seed-based correlation method (the second row), respectively. The third row shows the sensorimotor template. (B) The receiver operating characteristic (ROC) curve. The red line corresponds to the ROC curve of the spectral clustering-based method, and the blue line corresponds to the ROC curve of the seed-based correlation method.

Equations (11)

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

Ncut ( α , β ) = cut ( α , β ) Vol ( α ) + cut ( α , β ) Vol ( β ) ,
cut ( α , β ) = v i α , v j β w i j .
x i = { 1 , if v i α 0 , if v i β ,
Ncut ( α , β ) = x T L x x T d + x T L x ( 1 x ) T d .
Q ( y ) = y T L y y T D y ,
L ~ x = λ x ,
cos ( z i , z j ) = | z i T z j | z i z j = { 1 , v i and v j belong to the same cluster , 0 , v i and v j belong to different clusters .
b i j = { 1 , if ε c i j 1 ε 0 , if c i j < ε o r c i j > 1 ε .
s = i , j b i j .
m a p k i ( c h a n n e l ) = { 1 , if c h a n n e l α k i , 0 , else .
c o n s i s t e n c y _ m a p ξ i = m a p j ξ i m a p j M .