Proceedings, APSIPA Annual Summit and Conference 201812-15 November 2018, Hawaii

Analysis of VNS Effect on EEG Connectivity withGranger Causality and Graph Theory
Tsuyoshi Uchida∗ , Koichi Fujiwara∗ , Takao Inoue† , Yuichi Maruta† , Manabu Kano∗ , Michiyasu Suzuki†∗ Kyoto University, Kyoto, Japan

E-mail: fujiwara.koichi@i.kyoto-u.ac.jp Tel/Fax: +81-75-753-3369† Yamaguchi University, Yamaguchi, Japan

Abstract—Vagus Nerve Stimulation (VNS) is treatment ofrefractory epilepsy; however, its physiological mechanism has notbeen fully understood. The effectiveness of VNS for each patientcannot be predicted preoperatively. Thus, the mechanism of VNS
needs to be investigated in order to avoid ineffective operations.
Because an epileptic seizure is caused by the spread of excessive
discharge from neurons in the cerebrum, analyzing effects ofVNS on electroencephalogram (EEG) would be useful for VNS
mechanism investigation. In the present work, the EEG dataof epileptic patients with VNS were analyzed by using Granger
Causality (GC) and the graph theory. Since GC is an index
which expresses the intensity of a causal relation between twotime series, it may illustrate information interactions between
EEG channels. In addition, a directed graph constructed fromthose GC values would express neural connection. The analysis
was carried out with the EEG data of two patients with frontal
lobe epilepsy receiving the VNS therapy. The result supported
the existing hypothesis indicating the bilateral asymmetry of theVNS effect on the brain, and furthermore, it suggested that VNS
would increase neural connection between the frontal lobe andother brain regions, and that should control epileptic seizures bykeeping patients awake.

I. I NTRODUCTION
Epilepsy is a neurological disorder caused by abnormal
discharge on the cerebrum, and it causes various types ofseizures like spasm and disturbance of consciousness. 1%of population worldwide has epilepsy regardless of age andsex [1]. Epileptic seizures are categorized into some groups
depending on the epileptic focus. For example, the frontal lobe
epilepsy causes various symptoms like the spasm of the arms
or the spasms in the whole body. The generalized epilepsy
whose epileptic focus is not localized will cause the patientsvarious symptoms like disturbance of consciousness.
A brain region from which abnormal discharge emerges iscalled an epileptic focus, and electroencephalogram (EEG) isused for epileptic focus identification.
Although epileptic seizures are controlled with anti-epilepticdrugs, about 30% of epileptic patients cannot control their
seizures even if they select the best drug, which is calledrefractory epilepsy [2]. The resection of an epileptic focus is acandidate of refractory epilepsy treatment; however, it is difficult to identify the epileptic focus precisely. In addition, thereis the risk that resection damages important brain functions.
This work was partially supported in part by AMED SENTAN # 171122,
the SECOM science and technology foundation, and JSPS KAKENHI #JP15H05719.

978-988-14768-5-2 ©2018 APSIPAFig. 1. schematic diagram of VNS [3]The vagus nerve stimulation (VNS) therapy is another option for refractory seizure treatment; however, the effectivenessof VNS on each patient is unpredictable prior to its operation
because physiological mechanisms of VNS have not been fully
understood. This may lead to ineffective implants.
This work analyzes the EEG data recorded from epileptic
patients with VNS in order to clarify the mechanisms of VNS,
in which Granger Causality (GC) and the graph theory are used
for EEG analysis to investigate the differences of functional
neural network before and during the VNS therapy.
II. VAGUS N ERVE S TIMULATION
Vagus Nerve Stimulation (VNS) is palliative treatment forrefractory epilepsy, in which a device implanted in the left
breast gives stimuli to the vagus nerve. The schematic diagramof VNS is shown in Fig. 1. VNS implant operations weretreated for over 80,000 patients worldwide by the end of2014 [4]. Although the VNS stimuli may reduce the frequency
and the intensity of seizures, about 50% of patients with
VNS do not get seizure frequency reduction [5]. Since themechanisms of VNS have remained to be unknown, it should
be investigated for avoiding ineffective VNS operations.
III. M ETHODThis section explains EEG analysis methods used for VNS
mechanism investigation in this work.
A. EEGThe 10 - 20 electrode system shown in Fig. 2 is a typical electrode allocation for EEG recording. Since the EEG
voltage is in the order of microvolts, the EEG recording is
intolerable to artifacts caused by various sources like motion
and blinks [6]. Thus, appropriate filters are needed before EEG
analysis. EEG is classified into the five frequency bands listed
in Table I: the δ wave, the θ wave, the α wave, the β wave, and861

APSIPA-ASC 2018

Proceedings, APSIPA Annual Summit and Conference 2018

Fp1
F7A1

T3

C3

T5

P30010

Fp2Fz

F312-15 November 2018, Hawaii

F4Cz

C4Pz

P4O1F8T4A2

10
1000010000

T6O2Fig. 3. directed graph D and its adjacency matrix AFig. 2. 10 - 20 international electrode system

the γ wave. It is assumed that each frequency bands containdifferent types of information, for example, the α wave isuseful for sleep stage scoring.
B. Laplacian filter
Because an EEG electrode records the potential emerged bynerve cells surrounding the electrode, applying a spatial filter
to the recorded data would improve signal-to-noise ratio of thedata. The Laplacian filter is a kind of spatial filters, which isexpressed as follows [7]:ViLAP = ViER −∑gij VjER

(1)j∈SiViLAP

whereis the filtered potential of the i-th electrode,
ViER is the potential between the i-th electrode and the earreference, and Si is the set of electrodes located around thei-th electrode. gij is a weighting coefficient depending on thedistance between the electrodes, and it is defined as follows:
1/dijj∈Si 1/dij

gij = ∑(2)where dij is the distance between the i-th and j-th electrodes.
C. Connectivity
The connectivity is a concept of physical or functional
connection between brain regions. In this work, the functional
connectivity based on the Granger Causality (GC) and thegraph theory are adopted.
D. Granger Causality
GC is an index that illustrates the causal relation between
two time series [8]. The present value of a time series xj (t)would be represented by the linear combination of its pastvalues:q∑xj (t) =aj (k)xj (t − k) + ej (t).
(3)
k=1

TABLE IEEG BANDWIDTHSClassδ wave
θ waveα waveβ waveγ waveFrequency [Hz]
0.5 –
4
4–
88–
1313–
40
40
–
80

In addition, xj (t) can be represented by the linear combinationof its past values and another time series xi (t) as
xj (t) =q∑
k=1

aj (k)xj (t − k) +q∑

ai (k)xi (t − k) + eij (t) (4)k=1

where aj (k) and ai (k) are the regression coefficients, and q is
the model order. ej (t) and eij (t) are the errors, respectively.
Using these errors, GC from xi (t) to xj (t) is defined asfollows:)(var[ej (t)]GCi→j = ln(5)var[eij (t)]where var[·] denotes variance.
When the GC between the two time series is large, there
may be a strong causal relation between them. The modelorder can be determined by the Akaike Information Criterion(AIC) [9].
E. Directed Graph and Adjacency Matrix
A directed graph D consists of a set of vertices V and a setof directed edges connecting vertex pairs E. To express theconnection in a graph, an adjacency matrix A is used. In anunweighted directed graph, A(i, j) is defined as follows:{1 if there is an edge from vertex i to vertex j,A(i, j) =0 otherwise.
In a directed graph, the in- and out-degrees can be definedat each vertex, which are the numbers of edges comingfrom other vertices and edges going out from the vertex,
respectively. Fig. 3 shows an example of a directed graph Dand its corresponding adjacency matrix A. Since there is anedge from vertex 1 to vertex 2 in D, A(1, 2) has 1. The indegree of vertex 2 is 2 because there are two edges fromvertices 1 and 3.
In EEG connectivity analysis, the graph vertices denote theEEG electrodes, and directed edges illustrate their functional
connection. When a vertex has a large in-degree, there would
be a large information flow coming from other brain regions.
For example, Fallani et al. analyzed the functional connectivity during moving the feet and lips simultaneously [10].
They generated directed graphs with GC from the β waveof EEG and analyzed the functional connectivities. Large outdegree values were observed around the vertices corresponding
to the cingulate motor area, which indicated that the cingulatemotor area works as a hub of the functional neural network
during the task.
IV. R ESULTThis section reports an analysis procedure of the EEG data
recorded from patients with VNS and its result.

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Proceedings, APSIPA Annual Summit and Conference 201812-15 November 2018, Hawaii

TABLE IIPATIENT PROFILE
Sub142M
Frontal lobe
512138Sub1, VNS ON
Sub1, VNS OFF
Sub2, VNS ON
Sub2, VNS OFF-32Sub227F
Frontal lobe
512
330

AIC

SubjectAgeSex
Epileptic focus
EEG sampling rate [Hz]VNS period [s]wave-30-34-36

15101540302010120 240 360 480 600 720 0Time [s]120 240 360 480 600 720

35

AIC

-28-29-30-311510152025

Fig. 4. original EEG spectrogram (left) and EEG spectrogram after filtering (right)

35

Sub1, VNS ON
Sub1, VNS OFF
Sub2, VNS ON
Sub2, VNS OFF-27

Time [s]30degree
wave

-26

AIC

0200-20-40-60-80-100-120-140

Power [dB]5030

Sub1, VNS ON
Sub1, VNS OFFSub2, VNS ON
Sub2, VNS OFF-2760

Frequency [Hz]25wave-26020degree-28-2915101520253035

degreewave-16

Sub1, VNS ON
Sub1, VNS OFF
Sub2, VNS ON
Sub2, VNS OFF-17-18-19-20-21

1

510

15

20253035

degreewave-10

Sub1, VNS ON
Sub1, VNS OFF
Sub2, VNS ON
Sub2, VNS OFF

-11

AIC

The present work collected the EEG data from two epileptic
patients with VNS Sub1 and Sub2, whose profiles are shownin Table II. The data collection and the analysis were approvedby the ethics committee of the faculty of Medicine and HealthSciences, Yamaguchi University.
The Laplacian filter was applied to the EEG data. In thisresearch, Si was determined as a set of electrodes locatedwithin 0.98 times the scalp radius from the i-th electrode.
Fig. 4 shows examples of spectrograms of the EEG data collected from Sub1. In this figure, the horizontal axis represents
time and the vertical axis represents frequency, and the color
represents the magnitude of the power. The left figure shows
spectrogram calculated from the original EEG data, in which
the power around 30Hz increased for 30 seconds periodicallyin every 138 seconds due to the stimuli of the VNS therapy.
Thus, notch filters were applied to the EEG data in order toreduce artifacts of the VNS stimuli. A spectrogram of thefiltered EEG is shown in the right figure, in which the stimuliof the VNS therapy were not observed.
After the filtering with the Laplacian filter and notch filters,
the EEG data were decomposed into the five frequency bands
listed in Table I by applying bandpass filters. Then, the GCs
among the EEG electrodes were calculated while VNS wason and off, respectively.
The degrees of the regression models were determined byAIC. Fig. 5 shows changes in mean AIC values of all electrodepairs by model degrees. Based on Fig. 5, the model orders
were determined to be 25 for all patients and frequency bands.
A matrix M was generated so that M (i, j) stores GC fromthe i-th to the j-th electrodes. The elements in M whose
values were ranked in the top some proportions among all M
elements were replaced by 1, and the other components werereplaced by 0. Although the computation was executed withthreshold proportions of 30%, 50%, and 70%, only the results

AICA. Analysis Process-12-13-14-15

15101520253035degree

Fig. 5. changes in mean AIC values of all electrode pairs by model degrees

with the 30% threshold were shown here. This manipulation
formed a binary matrix A, and a directed graph D wasconstructed by A. The in-degree and the out-degree of allvertices of D were displayed on a scalp map that is a headshaped figure which contains electrode positions. An exampleof a scalp map is shown in Fig. 6. Red and blue represents
high and low values, respectively. Because the number of theelectrodes used in this analysis was 19, the highest value andthe lowest value in scalp maps were 18 and 0, respectively.
B. Analysis ResultFigs. 7 and 8 are scalp maps which show characteristic patterns of in-degree distribution. Fig. 7 shows the indegree of Sub1. While VNS was on, some vertices on theleft hemisphere had particularly large in-degree especially inthe δ bandwidth. The previous research indicated that theEEG power between 20Hz and 50Hz increased on the righthemisphere during the VNS stimuli [11]. The present result
agrees with the existing hypothesis in terms of the bilateralasymmetry of the VNS effect on the brain.

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Proceedings, APSIPA Annual Summit and Conference 201812-15 November 2018, Hawaii

0.5

concluded that the VNS treatment at low stimulus would
improve daytime sleepiness.

0V. C ONCLUSION AND F UTURE W ORK
In this work, the effect of the VNS therapy on the EEG
connectivity was analyzed in order to clarify the mechanismsof VNS. GCs among the EEG electrodes were computed, andthe functional connectivity was expressed as a directed graphconstructed from GC, whose in-degrees and out-degrees werevisualized with scalp maps.
The analysis results supported the existing hypothesis of thebilateral asymmetric effect of the VNS therapy on the brain.
In addition, the result suggested that the VNS therapy would
increase the functional neural connection from the frontal
lobe into other brain regions. This may contribute to epileptic
seizure control through keeping patients awake.
In the future work, additional EEG data will be collectedfrom patients with VNS in order to discuss the effectivenesschange of the VNS therapy depending on the epileptic foci.

-0.5Fig. 6. scalp map

VNSOFFVNS ON
18129degree

15R EFERENCES

630Fig. 7. in-degree of Sub1VNS
OFFVNS ON
18129degree

15630Fig. 8. in-degree of Sub2Fig. 8 shows the in-degree of Sub2. During the VNS stimuli,
high values were observed around the frontal lobe in the δwave and the α wave. It was reported that the VNS therapy
enhanced the recognition memory [12]. In addition, it wasalso reported that the EEG power of the δ wave increased
during the working memory task [13]. In consequence, it wassuggested that the VNS therapy would increase the functional
connection from the frontal lobe to other brain regions, andwould keep a patient awake. Therefore, VNS may control
absence seizures which occur accompanied by the lack ofconsciousness. Malow et al. performed polysomnography andmultiple sleep latency tests (MSLT) on refractory epileptic
patients with VNS [14]. They compared mean sleep latency(MSL) recorded before and after 3 months of VNS, and[1] M. J. England, C. T. Liverman, A. M. Schultz, and L. M. Strawbridge,“Epilepsy across the spectrum: Promoting health and understanding,”
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