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Journal of Integrative Neuroscience  2019, Vol. 18 Issue (2): 133-139    DOI: 10.31083/j.jin.2019.02.102
Original Research Previous articles | Next articles
Model for cascading failures in functional networks: application to epileptic patients with generalized tonic-clonic seizures
Ming Ke1, *(), Li Cao1, Guangyao Liu2
1 College of Computer and Communication, Lanzhou University of Technology, Lanzhou, Gansu, 730050, P. R. China
2 Department of Nuclear Magnetic Resonance, The Second Hospital of Lanzhou University, Lanzhou, Gansu, 733000, P. R. China
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The dynamic process of epilepsy is modeled as a cascading failure model in functional networks derived from graph theory. The aim is to test whether cascading failure identified from functional magnetic resonance imaging data could simulate epileptic discharges in 18 subjects with generalized tonic-clonic seizure and 17 demographically matched healthy controls. A cascading failure model was used to simulate the neural networks underlying generalized tonic-clonic seizure and healthy controls by stimulation of the node with the greatest number of connections. Results showed that the efficiency of generalized tonic-clonic seizure dropped significantly when compared to controls. Particular nodes whose efficiency altered significantly showed a correlation with the symptoms of generalized tonic-clonic seizure. Results also indicated that the left middle frontal lobe may be a potential focal area in the initiation of generalized tonic-clonic seizure.

Key words:  Cascading failure      functional magnetic resonance imaging      shortest path      generalized tonic-clonic seizure      graph theory     
Submitted:  17 January 2019      Accepted:  15 April 2019      Published:  30 June 2019     
  • 61263047/National Science Foundation of China
*Corresponding Author(s):  Ming Ke     E-mail:

Cite this article: 

Ming Ke, Li Cao, Guangyao Liu. Model for cascading failures in functional networks: application to epileptic patients with generalized tonic-clonic seizures. Journal of Integrative Neuroscience, 2019, 18(2): 133-139.

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Table 1  Clinical data for GTCS subjects and healthy controls (HC)
Male Female
Average age
Duration (year) Average duration
7 ~ 46
15 ~ 37
26.4 ± 6.9
25.8 ± 6.2
1 ~ 30
Figure 1.  Decreased efficiency of nodes after overload among GTCS subjects and controls. The horizontal axis label refers to the rest nodes after overload, the vertical axis label refers to the decreased efficiency among two groups, controls (green line) and GTCS (blue line).

Table 2  Compared with controls, the regions of GTCS decreased significantly within functional connectivity (p < 0.001 without correction).
Brain regions Voxels MNI coordinate
x y z
Right lingual 19 12 -39 -9
Left middle occipital 58 -36 -81 24
Left inferior triangle frontal 17 -51 30 33
Left middle occipital 15 -24 -66 42
Figure 2.  Relationship between threshold (t) and network density (m). Red and blue lines indicate GTCS and control subjects, respectively.

Figure 3.  Relationship between the global efficiency, local efficiency and the tolerance parameter among GTCS and controls. The ordinate (E) gives the efficiency (global and local) among GTCS and control groups and the abscissa (a) represents the tolerance parameter, the red line indicates controls, and the blue line gives the response under GTCS.

Table 3  Encephalic regions with greater alteration in GTCS
Encephalic regions Value of alteration
Right rolandic operculum 0.4702
Right anterior cingulum 0.4323
Left pallidum 0.3874
Right lingual 0.3821
Right posterior cingulum 0.3801
Right insula 0.3762
Right inferior occipital 0.3757
Right superior occipital 0.3756
Right supramarginal 0.3618
Left putamen 0.3491
Right precuneus 0.3436
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