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Sharp decrease in the Laplacian matrix rank of phase-space graphs: a potential biomarker in epilepsy

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Abstract

In this paper, phase space reconstruction from stereo-electroencephalography data of ten patients with focal epilepsy forms a series of graphs. Those obtained graphs reflect the transition characteristics of brain dynamical system from pre-seizure to seizure of epilepsy. Interestingly, it is found that the rank of Laplacian matrix of these graphs has a sharp decrease when a seizure is close to happen, which thus might be viewed as a new potential biomarker in epilepsy. In addition, the reliability of this method is numerically verified with a coupled mass neural model. In particular, our simulation suggests that this potential biomarker can play the roles of predictive effect or delayed awareness, depending on the bias current of the Gaussian noise. These results may give new insights into the seizure detection.

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Data availability

The Matlab code and data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We are grateful to Dr. Chuanzuo Yang for the pre-processing of data and constructive discussion. This research was supported by the National Science Foundation of China (Grant Nos. 12072021, 11772019 and 11932003), the Fundamental Research Funds for the Central Universities (FRF-TP-20-013A3), the Capital Health Research and Development of Special (2016-1-8012), Beijing Municipal Science & Technology Commission, China (Z161100000516230, Z161100002616016).

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Zecheng Yang & Denggui Fan

  2. Department of Dynamics and Control, Beihang University, Beijing, 100191, China

    Qingyun Wang

  3. Epilepsy Center, Sanbo Brain Hospital, Capital Medical University, Beijing, 100093, China

    Guoming Luan

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  1. Zecheng Yang
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  2. Denggui Fan
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  3. Qingyun Wang
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  4. Guoming Luan
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All authors designed, performed the research and analyzed the data as well as wrote the paper.

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Correspondence to Denggui Fan.

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The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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This study protocol was approved by the Ethics Committee of Sanbo Brain Hospital of Capital Medical University and all subjects were written informed consent.

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Yang, Z., Fan, D., Wang, Q. et al. Sharp decrease in the Laplacian matrix rank of phase-space graphs: a potential biomarker in epilepsy. Cogn Neurodyn 15, 649–659 (2021). https://doi.org/10.1007/s11571-020-09662-x

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