Estimation of Effective Fronto-Parietal

Connectivity during Motor Imagery using Partial

Granger Causality Analysis
Dheeraj Rathee, Hubert Cecotti, Girijesh Prasad
Intelligent Systems Research Centre
School of Computing and Intelligent Systems
Ulster University
Derry/Londonderry, Northern Ireland, UK
email: rathee-d@email.ulster.ac.uk

Abstract—Connectivity analysis has become an essential tool Stroke is a clinical condition wherein one or few sections
for the evaluation of functional brain dynamics. The functional of the brain lose their functionality possibly due to affected
connectivity between different parts of the brain, or between blood supply to these parts. It may lead to severe disabilities
different sensors, is assumed to provide key information for the
discrimination of brain responses. In this study, we propose and can affect the daily life of patients, thus degrading their
an estimation of effective cortical connectivity measures in quality of life. In the light of our elderly societies, the
frontal and parietal areas of human brain during four different encumbrance of stroke related issues is expected to grow in
Motor Imagery (MI) tasks. Feedback based brain-computer the future, and a crucial need to enrich our understanding of
interface (BCI) technology has been successfully implemented the MI related neurobiological factors emerges. Monitoring
for recovery of stroke patients as it can enhance the neural
plasticity in brain areas associated with motor execution. accurate neural correlates of motor activity and their dynam-
However, it is still challenging to obtain reliable information ics during various tasks could enhance the therapeutic effects
regarding improvement in neural functioning during rehabili- of rehabilitation procedures [3]. Functional neuroimaging
tation and its neuro-physiological dynamics. Brain connectivity techniques provide a reliable non-invasive method for deep
is a reliable biomarker associated with brain functionality. exploration of neural mechanisms underlying reorganisation
Here, we evaluate to what extent partial granger causality can
provide information in form of effective neural connectivity of brain networks and their effect on stroke patients recovery.
that can differentiate motor imagery tasks. Our results on BCI based rehabilitation of stroke patients has been success-
nine subjects using the EEG dataset (BCI competition 2008 fully achieved in several cases although it is still difficult
dataset 2A) show distinct connectivity patterns for all four to analyze the direct effects of MI based BCIs on neural
MI classes, and higher information flow in the fronto-parietal connectivity and recovery of the patient from stroke. Recent
network during task phase as compared to non-task phase.
The results support the conclusion that effective connectivity studies showed that brain connectivity analysis is a strong
analysis through partial granger causality can provide key measure of cortical variations and plasticity after stroke, and
information about neural interactions specific to different MI it can be a useful measure for monitoring recovery of stroke
tasks. Moreover these interactions can be utilized as reliable patients [4].
biomarkers for assessment of motor recovery during stroke The human brain has been divided into several areas
rehabilitation.
based on their anatomical and physiological characteristics.
These areas are connected to each other to form functional
I. I NTRODUCTION
brain networks which are dynamically employed to perform
Motor Imagery (MI), which involves imagination of a various sensorimotor and cognitive tasks. Analyzing these
particular motor action without its actual execution, has network connectivities and their dynamics during various
showed its promising effectiveness in various research fields brain states may provide a better understanding of pathophys-
including sport science, neuroscience and rehabilitation. MI iological mechanisms related to them. However, functional
based brain-computer interface (BCI) systems have been connectivity evaluations are unable to provide exact informa-
studied extensively, as specific patterns of brain activity in tion regarding the directionality of the interaction i.e. whether
electroencephalography (EEG) signals can be generated by information flow is from area A to area B or vice versa.
various imagery tasks. This approach has been used for a Effective connectivity analysis can derive better relationships
wide variety of communication and control purposes, such between two areas of interest by providing causality infor-
as controlling a cursor, wheelchair or prosthesis, BCI based mation. Effective connectivity is therefore a strong measure
spellers and navigation through the virtual environment. for better assessment of the induced physiological variations
However, recent studies have shown that MI-based BCIs can in the brain during MI tasks.
induce neural plasticity [1], and hence serve as important To estimate the causal interactions between distinct brain
tools to enhance motor rehabilitation for stoke patients [2]. areas, several imaging modalities can be exploited such

978-1-5090-0620-5/16/$31.00 2016
c IEEE 2055
as positron emission tomography (PET), functional MRI (SMA) of brain. To cover SMA area, we included channel
(fMRI), Magnetoencephalography (MEG) and EEG. Due to C3, Cz and C4. Our results show that (1) there exist sig-
its high temporal resolution, ease of implementation and low nificant changes in the effective connectivity between these
cost, EEG has been most preferred among BCI researchers. areas during distinct MI tasks, and (2) it is possible to find a
Thus, the extraction of causality information from EEG difference of connectivity between different motor imagery
signals can be of high significance for the advancement of MI tasks. The remainder of the paper is organized as follows.
based BCI systems for rehabilitation. Several techniques have First, the methods and the evaluation procedure are described
been proposed for efficient assessment of directional inter- in Section II. Then, the results are presented in Section III,
actions from EEG/MEG signals [5]. Among these methods, and finally discussed in Section IV.
multivariate autoregressive (MVAR) model based methods
have been widely applied to human neurophysiological sig- II. M ETHODS
nals [6], [7], [8]. In general, an MVAR based process utilizes A. Multivariate Autoregressive Model
linear difference equations to model the causal interactions An MVAR model for a set of L observed time-sampled
between various EEG channels. It provides information about series x(t) ∈ RL , with 1 ≤ t ≤ N , N is the total number of
direct and indirect influences between channels representing samples, and model order r, can be defined as follows [23]:
the direction of information flow [9]. The notion of Granger ⎛ ⎞ ⎛ ⎞ ⎛ ⎞
x1 (n) r x1 (n − p) q1 (n)
causality (GC) [10] based on MVAR model, has been exten-
⎜ .. ⎟  ⎜ .. ⎟ ⎜ .. ⎟
sively employed to investigate directional influences within ⎝ . ⎠= Ap ⎝ . ⎠+⎝ . ⎠ (1)
coupled variables of dynamical systems in various areas, such p=1
xL (n) xL (n − p) qL (n)
as climate studies [11], [12], economics [13], [14] and neuro-
science [15], [16]. If prediction of any time-varying process where q = [q1 , . . . , qL ]T is a zero-mean white noise vector
X can be enhanced by considering the past information of with normally distributed real-values. The auto-regression
another time-varying process Y instead of the past informa- coefficient matrices Ap are given by:
⎛ p ⎞
tion of process X alone, then the process Y is said to granger a1,1 . . . ap1,L
cause process X. To describe the interactions between time- ⎜ .. ⎟
varying processes, three distinct frameworks of time-domain Ap = ⎝ ... ..
. . ⎠ (2)
GC (bivariate, conditional and partial) have been developed apL,1 . . . apL,L
in recent years [17], [18]. Fig. 1 depicts the schemes of these
where 1 ≤ p ≤ r. The matrix Ap ∈ RL×L reveals the linear
GC approaches wherein Bivariate-GC analysis is a basic
interactions between any two series at the time delay p. For a
technique to show causality between two concurrent coupled
reliable estimation using MVAR modeling, the total number
sources (e.g., X(t) and Y (t)), conditional-GC (CGC) deal
of available data points (LN ) must be significantly higher
with the bipolar interactions mediated by a third source
than the total number of estimated parameters (L2 r) [23].
Z(t) [19], and partial-GC (PGC), an extended form of CGC,
considers the confounding effects of exogenous input E B. Time-domain Partial Granger Causality Analysis
and latent variables L also [20]. PGC method enhances
Time-domain Partial Granger Causality (PGC) is a robust
the efficiency of standard GC measure by mitigating the
form of granger causality wherein causal interactions be-
effect of confounding factors using a concept similar to
tween multivariate data can be analyzed using MVAR mod-
partial correlation. It has been successfully implemented for
eling. Unlike bivariate GC and conditional GC, it provides
performing causal connectivity analysis during multi-trial
better estimation of the true interactions by mitigating the
ERPs [21], [22].
effect of confounding variables[20].
Let’s assume three time series data including X(t), Y (t)
and Z(t). Now to analyze the effective connectivity between
X(t) and Y (t) (conditioned on Z(t)) based on PGC rules,
the reduced model (inclusion of past values of the sink
variable conditioned on other variables) can be defined by:
k
 k

X(t) = (a1,p X(t − p)) + (c1,p Z(t − p)) + (3)
p=1 p=1

1 (t) + E L
1 (t) + β1 (L)1 (t)
Fig. 1. Schematic diagram of (a) BGC, (b) CGC and (c) PGC. k k
 
Y (t) = (b1,p Y (t − p)) + (d1,p Z(t − p)) + (4)
In the present study, we estimate the effective connectivity p=1 p=1
in the fronto-parietal sensors by performing a time-domain 2 (t) + E L
2 (t) + β2 (L)2 (t)
PGC analysis of scalp EEG data involving MI tasks. In
our investigation, we utilize data from five scalp electrodes where p is the model order, (t) is the prediction error,
including frontal (Fz), parietal (Pz) and sensorimotor area E (t) and β(L)L (t) are the residual errors corresponding to

2056 2016 International Joint Conference on Neural Networks (IJCNN)

exogenous (E) and latent (L) inputs, respectively. Similarly, D. Data Processing and Analysis
the full model (inclusion of past values of the sink variable Multi-trial PGC analysis involves a high computational
along with past values of source variable conditioned on rest cost. To reduce the processing time, the EEG data were
of variables) can also be defined as: downsampled from 250 Hz to 125 Hz, hence reducing the
k
 k
 trial length by half. Data belonging to MI task phase (300
X(t) = (a2,p X(t − p)) + (b2,p Y (t − p)) + (5) to 600 ms) for all trials were extracted and concatenated (all
p=1 p=1
four classes separately) for session-wise inter-class analysis.
k
 For MI versus Non-MI analysis, class-wise data from MI
(c2,p Z(t − p)) + 3 (t) + E L
3 (t) + β3 (L)3 (t) task phase (300 to 600 ms) and non-MI task phase (0 to 300
p=1
ms) were considered. To counter the issues related to inter-
k
 k
 trial variations and non-stationarity, processes of detrending
Y (t) = (d2,p X(t − p)) + (e2,p Y (t − p)) + (6) and demeaning of the data were performed wherein the
p=1 p=1
ensemble average was subtracted from each trial separately
k
 along with division of each trial by ensemble standard
(f2,p Z(t − p)) + 4 (t) + E L
4 (t) + β4 (L)4 (t) deviation [25]. The coefficients of MVAR model for multi-
p=1
trial data were estimated using the LWR algorithm [26].
The collective prediction errors can be taken from the Akaike information criterion (AIC) [27] and the Bayesian
previous equations, and are represented as: information criterion (BIC) [28] techniques were used for
μi = i (t) + E L
i (t) + βi (L)i (t) (7) estimating the optimal value of the model order p (i.e. the
number of time-lags). The expressions for these two methods
with 1 ≤ i ≤ 4.
are given as follows:
The covariance matrix for the reduced model can be
generated as: 2pL2
AIC(p) = log[det(Σ)] + (12)
var(μ1 (t)) cov(μ1 (t), μ2 (t)) N
R = (8) 2
cov(μ2 (t), μ1 (t)) var(μ2 (t)) pL
BIC(p) = log[det(Σ)] + log(N ) (13)
Likewise, the covariance matrix for the full model as: N
var(μ3 (t)) cov(μ3 (t), μ4 (t)) where Σ is the estimated noise covariance matrix, L is
L = (9) the number of EEG channels, and N is the number of
cov(μ4 (t), μ3 (t)) var(μ4 (t))
data samples. The model orders p were calculated for each
The PGC indices can be calculated by taking the log
estimation in the range of 1 ≤ p ≤ 40. The final model order
ratio of partial variance of prediction error of reduced model
was selected by comparing and choosing the highest model
and partial variance of prediction error of full model. The
order value provided by AIC and BIC. We implemented two
following two equations provide the PGC indices for Y (t)
different techniques to confirm the legitimacy of applied re-
causing X(t) and vice-versa, respectively:
gression models. Durbin-Watson whiteness test [29] has been
−1
R1,1 − R1,2 R2,2 R2,1 used for approximating whiteness of uncorrelated residuals.
GY →X|Z = ln( ) (10)
L1,1 − L1,2 L−1
2,2 L2,1
The test returns a significant value of d≈1.8, a confirmatory
−1 indication for rejection of null hypothesis. Further validation
R2,2 − R2,1 R1,1 R1,2
GX→Y |Z = ln( ) (11) of the model was confirmed using the Ding method [25]
L2,2 − L2,1 L−1
1,1 L1,2 by checking the consistency of the correlation structure.
C. Dataset Overview The Ding consistency test provided a higher value (nearly
The BCI Competition IV dataset 2A [24] has been an- equal to 1), which shows that the selected MVAR model
alyzed for investigating causal interactions between various has effectively predicted the time series. Finally, to eliminate
brain areas of interest. The dataset comprised of EEG signals the statistical biasness the permutation resampling test was
acquired from nine subjects that were recorded using a cue- used with the values of bwin (window size of samples) and
based paradigm during two sessions on different days [24]. nperm (the number of permutation) as 75 and 5, respectively.
The MI tasks include four different classes: left hand MI The computational work has been performed on a Intel Core
(class 1), right hand MI (class 2), both feet MI (class 3), and i7-4790 with 16 gb of memory, using MATLAB (V8.1) and
tongue MI (class 4). Each data acquisition session consists the GCCA (V2.9) toolbox [30] for the estimation of causal
of 6 runs where each run comprised of 48 trials (12 trials for effects.
each class). Thus the complete study involved 288 trials from
III. R ESULTS
each session of the dataset. The data were acquired from 25
channels (22 EEG channels along with three monopolar EOG The estimation of effective connectivity between the se-
channels) with sampling frequency of 250 Hz and bandpass lected five channels has been conducted over two types of
filtered between 0.5 Hz to 100 Hz. Out of 22 EEG channels, comparisons: pair-wise Inter-class analysis, and MI versus
5 channels (Fz, Cz, Pz, C3 and C4) are selected to study the non-MI (n-MI) analysis. This study provides information
fronto-parietal network during MI activities. about the cortical networks during MI state and resting

2016 International Joint Conference on Neural Networks (IJCNN) 2057

state along with further analysis, and comparative evalua- cluding (Cz→Fz), (Pz→Fz), (Pz→C3), (Fz→Cz), (C3→Cz),
tions of connectivity during distinct MI tasks (four classes). (C4→Cz), (Pz→Cz), (Fz→C4), (Pz→C4), (Fz→Pz), and
Fig. 2 includes a montage of examined scalp electrodes, (Cz→Pz) do not vary significantly during these tasks.
showing strong effective connectivity (PGC value greater Effective connectivity values during both feet and tongue
than 0.13) between them. For the pairwise comparisons, we imagery tasks infer stronger directional causality from C3
consider Wilcoxon signed rank test with a false discovery rate to Fz, C3 to Pz, Cz to Pz and C4 to Pz during both
correction for multiple comparisons across the 20 possible feet MI, while these effective connectivity measures remain
connectivity measures (p<0.025). at lower values during tongue MI. All other connectivity
measures stay almost similar during both feet and tongue
MI. Thus, the results show that the sensorimotor area has
been strongly connected to the parietal region during feet
MI task as compared to tongue MI task. There are signif-
icant variations in the connectivity measures for (C4→Fz),
(Cz→C3), (C4→C3), (Cz→Pz) and (C4→Pz) during Left-
Feet MI comparative analysis. Likewise, during Left-tongue
analysis, differences in effective connectivity for (C3→Fz),
(Cz→C3), and (C3→Pz) are statistically significant. The
study estimated high variations can be observed in effective
connectivity measures for (C3→C4), (Cz→C4), (C4→Pz),
and (C3→Fz), (C3→C4), (Cz→C4), (C3→Pz), (Cz→Fz)
during Right-Tongue and Right-Feet MI analysis, respec-
tively.
B. MI versus Non-MI Analysis
In this analysis, causality interactions between five elec-
trodes were estimated from EEG data belonging to MI task
and EEG data belonging to the non-MI phase, separately.
The analysis was done over multi-trial EEG data for each
Fig. 2. Causal interactions on the EEG scalp topographical placements of subject separately to get 20 non-zero effective connectivity
electrodes corresponding to PGC values greater than 0.13 of (a) Left MI,
(b) Right MI, (c) Feet MI and (d) Tongue MI.
measures. Moreover, the difference between MI based PGC
measure and its corresponding non-MI based PGC measure
has been calculated for all 20 non-zero pairs and for all
A. Inter-class Analysis subjects separately. Finally, the mean values and standard
In this part of analysis, the effective connectivity in the deviations of 20 difference of connectivity features (Δ-PGC)
frontal and parietal areas of the brain with special emphasis across 9 subjects have been calculated for each class and
on sensorimotor area has been estimated for each class by comparative bar plots has been provided in Fig. 5.
analyzing the EEG data related to various MI tasks. For Results from Fig. 5 and Table II show that there has been
each class and each subject, a PGC index matrix has been a significant increase in almost all connectivity values across
estimated wherein we get 20 non-zero connectivity measures. the fronto-parietal network during performance of Left, Right
Fig. 3 shows PGC matrices for each subject during left, right, tasks as compared to rest state (non-MI). Statistically signif-
feet and tongue imagery tasks. icant variations in connectivity values including (C4→Fz),
Furthermore, the mean values and standard deviations (Cz→C3), (C4→C3), (Fz→Cz), (C3→Cz), (Cz→Pz) and
of 20 connectivity features across 9 subjects have been (C4→Pz) are observed during Feet MI analysis. Although
calculated for each class and a comparative plot for inter- there are not much variations in the connectivity values dur-
class analysis has been provided in Fig. 4. Connectivity ing tongue MI task when compared to non-MI connectivity
measures which rejected the null hypothesis (p<0.05, FDR values. The strongest differences (p<0.01, FDR corrected) of
corrected) during pair-wise inter-class comparative analysis connectivity measures during MI versus non-MI comparative
are provided in Table I. The information from the plot analysis for each class are provided in Table II.
and table illustrates that during right MI, there is a higher
amount of information flow from C3 to Fz, Cz to C4, IV. D ISCUSSION
C3 to C4 and C4 to Pz whereas during left MI strong Conventionally, patient care and recovery from stroke
directional connectivity measures are observed from C4 to often rely on behavioral assessments for making crucial de-
Fz and C3, and from C3 to Pz. Thus the contralateral cisions related to therapeutic procedures. Recently the whole
sensorimotor area of the brain is strongly connected to the paradigm has started shifting to biomarkers as they involve
frontal area and central area while ipsilateral sensorimotor objective monitoring. Evidences suggest that variations of
area is strongly connected to the parietal area during left- effective cortical connectivity can be utilized as biomarkers
right MI tasks. The rest of the connectivity measures in- for stroke patient rehabilitation. MI based BCI technology

2058 2016 International Joint Conference on Neural Networks (IJCNN)

 S1 S2 S3 S4 S5 S6 S7 S8 S9
Fig. 3. Individual connectivity matrices for each subject and each MI task.

Fig. 4. PGC measures during MI tasks with pairwise comparisons. The error bar represents the standard error across subjects.

2016 International Joint Conference on Neural Networks (IJCNN) 2059

 Fig. 5. Difference of PGC measures (ΔPGC) during MI tasks with pairwise comparisons. The error bar represents the standard error across subjects.

TABLE I
S IGNIFICANT CONNECTIVITIES FOR INTER - CLASS COMPARISONS ( P<0.05, FDR CORRECTED ).

Condition Relevant connectivities

Left-Right (C3→Fz), (C4→Fz), (Cz→C3), (C4→C3), (C3→C4), (Cz→C4), (C3→Pz), (C4→Pz)
Left-Feet (C4→Fz), (Cz→C3), (C4→C3), (Fz→Cz), (Cz→Pz), (C4→Pz)
Left-Tongue (C3→Fz), (Cz→C3), (C4→C3), (Pz→C3), (C3→Pz)
Right-Feet (C3→Fz), (C3→C4), (Cz→C4), (C3→Pz), (Cz→Pz)
Right-Tongue (C4→Fz), (C3→C4), (Cz→C4), (C4→Pz)
Feet-Tongue (C3→Fz), (C4→Fz), (C3→Pz), (Cz→Pz), (C4→Pz)

TABLE II
S IGNIFICANT CONNECTIVITIES FOR MI VERSUS NON -MI COMPARISONS ( P<0.01, FDR CORRECTED ).

Condition Relevant connectivities

Left (C4→Fz), (Fz→C3), (Cz→C3), (C4→C3), (Pz→C3), (Fz→Cz), (C3→Cz), (Fz→C4), (Pz→C4), (Fz→Pz), (C3→Pz),
Right (C3→Fz), (C4→Fz), (Fz→C3), (Cz→C3), (C4→C3), (Pz→C3), (Fz→Cz), (C3→CZ), (C4→Cz), (Fz→C4), (C3→C4),
(Cz→C4), (Pz→C4), (Fz→Pz), (C3→Pz), (C4→Pz)
Feet (C4→Fz), (Cz→C3), (C4→C3), (Fz→Cz), (C3→Cz), (Cz→Pz), (C4→Pz)
Tongue ∅

has been used for rehabilitation after stroke by involving activities within the frontal and parietal brain cortices [31].
patients in BCI-feedback training. To improve this BCI- Furthermore, during left and right MI tasks, the strong
feedback training therapy, brain connectivity measures can forward connection between contralateral SMA and frontal
be utilized for objective assessment of patient recovery. It area, and backward connection between ipsilateral SMA
is therefore important to study these variations in healthy and parietal cortex provide significant information about
patients during various motor imagery tasks, so as to provide the variations within fronto-parietal network. Similar results
a reliable standard for comparative diagnosis of the cortical were reported during motor imagery and motor execution
connectivity measures of stroke patients. However, in general tasks in recent study [32]. In addition, we also successfully
brain connectivity has been determined on the source and/or estimated the effective connectivity during feet and tongue
sensor level using fMRI, PET and MEG but these methods imagery tasks. These connectivity maps provide a crucial
have restrictions in clinical applications. Moreover, high information regarding neurophysiology during MI which can
computational load and less cost-effectiveness hinder their be implemented as standard features for assessment of motor
prospective use in continuous monitoring. The current study recovery during BCI based rehabilitation of stroke patients.
focused on estimation of effective connectivity in frontal and
parietal cortex of brain using scalp EEG. V. C ONCLUSION
Our results displayed a strong forward and backward ef- In this paper, we have used PGC analysis on scalp EEG
fective connectivity loop between the parietal and the frontal data from a set of five electrode (Fz, Cz, Pz, C3 and
area of brain during execution of motor imagery tasks. This C4) covering the important regions of frontal, parietal and
concurrence is consistent with earlier neurophysiological sensorimotor area of brain. The results showed significant
fMRI studies, which reported correlated patterns of neural variations in the effective connectivity during various MI

2060 2016 International Joint Conference on Neural Networks (IJCNN)

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