Engineering, 2013, 5, 57-61
http://dx.doi.org/10.4236/eng.2013.510B012 Published Online October 2013 (http://www.scirp.org/journal/eng)
Information Transfer Index-A Promi sing Measure of the
Corticomusclar Interaction*
Ping Xie1, Peipei Ma1, Xiaoling Chen1, Xiaoli Li1, Yuping Su2
1Institute of Electrical Engineering, Yanshan Univer sity, Qinhuangdao, China
2Department of Rehabilitation, Qinhuangdao People’s Hospital, Qinhuangdao, China
Received October 2012
ABSTRACT
It is generally believed that a major cause of motor dysfunction is the impairment in neural network that controls
movement. But little is known about the underlying mechanisms of the impairment in cortical control or in the neural
connections between cortex and muscle that lead to the loss of motor ability. So understanding the functional connec-
tion between motor cortex and effector muscle is of utmost importance. Previous study mostly relied on cross-correla-
tion, coherence functions or model based approaches such as Granger causality or dynamic causal modeling. In this
work the information transfer index (ITI) was introduced to describe the information flows between motor cortex and
muscle. Based on the information entropy the ITI can detect both linear and nonlinear interaction between two signals
and thus represent a very comprehensive way to define the causality strength. The applicability of ITI is investigated
based on simulations and electroencephalogram (EEG), surface electromyography (sEMG) recordings in a simple mo-
tor task.
Keywords: Information Theory; Information Transfer Index; Corticomuscular Interaction
1. Introduction
The relationship and interdependence between simulta-
neously recorded neurophysiological signals, give in-
sights into the function of the systems that produce th em.
Since Conway discovered that oscillations at beta band
(15 - 30 HZ) in the magnetoencephalogram (MEG) in
humans are coherent with the surface electromyogram
(sEMG) in 1995 [1]. Many researches have been done
focusing on the functional relationship between neurons
in the sensorimotor cortex and motor units in the effector
muscle. To assess the interdependence between EEG and
EMG, cross-correlation or coherence functions have been
extensively used which can provide information on the
linear correlation between two signals [2]. Coherence has
been highly successful as a methodology for assessing
functional coupling in neurosciences. Previous study has
shown that increased corticomuscular coherence can im-
prove motor performance during steady-state motor out-
put [3] indicating that coherence may promote effective
corticomuscular interaction. Studies have also revealed
changes in coherence in some pathological conditions,
such as stroke [4]. The methods give useful information
in the study of corticomuscular interaction, but it has the
intrinsic limitation that the y are linear methods, althoug h
neural connectivity may be nonlinear. Thus linear me-
thods are insufficient for the study of complex neurophy-
siological data. Furthermore, they cannot give the direc-
tion of information flow. To better understand the un-
derlying mechanism and functional relevance of the sen-
sorimotor neural network, it is important to know the
direction of the information flow between EEG and
EMG [5]. In view of detecting coupling direction, di-
rected coherence was proposed based on Grang er causal-
ity methods [6]. But this is also a linear method. A po-
tential new method should be nonlinear naturally leading
to the application of information theoretic techniques.
Information theoretic tools, such as entropy, address the
issue of linearity and so far have numerous applications
in neuroscience. First attempts to measure the relation-
ship between two random variables were based on mu-
tual information (MI), which can be interpreted as the
amount of uncertainty about one signal that can be re-
duced by observation of another. MI is based on proba-
bility distributions and is sensitive to second and all
higher order correlations. But conventional MI can not
account for the direction of information flow, because it
is a symmetric measure. Seung-Hyun Jin addressed this
issue by defining the time-delayed mutual information
(TDMI), which adds a time delay in one of the variables
*
This work was supported by the National Natural Science Foundation
of China under Grants 61271142/F010802 and Postdoctoral Science
Foundation of China under Grants 2011M500539.

P. XIE ET AL.
58
[7]. Still it is based on static probability distribution thus
didn’t accounting for system dynamics. Transfer entropy
was proposed by Thomas Schreiber which is on the basis
of transition (dynamic) probabilities computation [8].
Many researches have found it a model-free measure of
effective connectivity for the neurosciences [9]. Goure-
vitch used transfer entropy to detect the information flow
between auditory c ortical neurons [10]. The main advan-
tage of this measure is that it is nonlinear and dynamic;
furthermore it has directional sense to define information
transfer.
The author has proposed the concept of information
transfer index (ITI) based on joint complexity entropy for
studies on mechanical fault diagnosis [11]. Taking ad-
vantages of transition (dynamic) probabilities in describ-
ing dynamic information interaction process, modifica-
tion is made to the original definition of ITI. In this paper
the modified ITI based on transition probabilities has
been introduced and used to describe the information
transfer of different coupling models and experimental
data.
2. Method
2.1. Calculation of Information Transfer Index
Let X and Y be two signals recorded from two associated
systems, the original ITI is defined as:
()( )()
( )
+ -,
[0,1]
c cc
xy
c
HX HYHXY
ITI HX
→
= ∈
(1)
where
( )
c
HX
,
( )
c
HY
are the complexity entropy of
signal X and Y,
( )
,
c
H XY
is their joint complexity
entropy. This calculation can describe the amount of in-
formation in X that shared by Y. Though it isn’t ac-
counting for system dynamics and it cannot discriminate
against common history and input signals. Taking ad-
vantages of transition probabilities, the new definition is
based on the concept that if the future of a signal Y is
better predicted with the observation of the past and
present of a signal X, then it is believed that there is in-
formation transmitted from X to Y. To quantify the in-
fluence of X on the system Y, the modified ITI is calcu-
lated as:
() ()
( )
+
||, [0,1]
|
n mn
tuttu tt
xy n
tu t
HyyHyx y
ITI Hy y
++
→
−
= ∈
(2)
where
( )
|
n
tu t
Hy y
+
is the entropy of the process Y con-
ditional on its past. The ITI indicates the directed infor-
mation interactions by measuring the uncertainty reduc-
tion via conditional entropy. It quantifies how much the
past of a process X influence the transition probabilities
of another process Y. We are interested in the deviation
from the following generalized Markov condition.
() ()
| |,
n mn
tuttu tt
HyyHyx y
++
=
(3)
where
( )
1
,,
m
tt tm
xxx
−+
=
,
( )
1
,,
m
tt tm
yyy
−+
=
. When
the transition probabilities or dynamics of Y are inde-
pendent of the past of X, (3) is fully satisfied, and we
infer an absence of directed interaction from X to Y. Oth-
er way there is information flow from X to Y. ITI natu-
rally incorporates direc tional and dynamical information,
because it is inherently asymmetric and based on transi-
tion probabilities.
Sensible causality hypotheses are formulated in terms
of the underlying systems rather than on the signals being
actually measured. To overcome this problem recon-
structing the full state space of a dynamical system from
the observed signals is needed. In this work, we use de-
lay-coordinates to create a set of vectors in a higher di-
mensional space according to (4) to map our scalar time
series into trajectories in a state space of high dimension.
() () ()() ( )
( )
,,2,...,1
d
xxt xtxtxtd
t
ττ τ =− −−−
(4)
2.2. Parameter Selection
This procedure depends on two parameters, the dimen-
sion d and the delay τ of the embedding. The two para-
meters considerably affect the outcome of the ITI esti-
mates. For instance, a low value of d can not sufficiently
unfold the state space of a system. On the other hand, a
too large dimensionality may lower the estimation accu-
racy and significantly enlarges the computing time. A
popular option is to take the delay embedding τ as the
auto-correlation decay time of the signal. To determine
the embedding dimension, the Cao criterion offers an
algorithm based on false neig hb ors com putation [12].
3. Simulation and EEG Experiment
3.1. Simulation Data
To test the ability of ITI to detect the direction of infor-
mation flow and identify the relationship between two
time series. We used four different models, i.e. indepen-
dent, linear, quadratic and threshold models.
1) The first test case we used two independent time se-
ries X and Y generated by t he followin g process e s.
10
1
ti tit
i
xax u σ
−
=
= +
∑
(5)
10
11 ti tit
i
yay v σ
−
=
= +
∑
(6 )
where the coefficients
i
a
and
i
b
are drawn from a
normalized Gaussian distribution,
t
u
and
t
v
are inde-
pendent Gaussian noise of unit variance.
2) The second test case consisted in simulating a li-
near causal interaction between the two systems. We

P. XIE ET AL.
59
added to the internal dynamics of Y a term related to the
past dynamics of X and
γ
( )
10
21
1
ti titt
i
yby xv
δ
γ γσ
−−
=
=− ++
∑
(7)
3) The third test case consisted in generating two qu-
adratically coupled processes.
( )
10 2
31
1
ti titt
i
ybyxv
δ
γ γσ
−−
=
=− ++
∑
(8)
4) The last pair of time series is mediated by the thre-
shold function reflecting the effective connectivity of
special relevance in neuroscience applications.
( )( )
10
4112
1
11 exp
ti tit
it
y byv
b bx
δ
γγ σ
−
=−
=−+ +
++
∑
(9)
3.2. EEG Experiment
Our experiments were preformed on 12 volunteers (mean
age 22 years ± 3 years). During the experiments the sub-
ject performed knee flexion and extension. Scalp EEG
and sEMG were recorded. Bipolar sEMG was recorded
from quadriceps femoris and gastrocnemius (Figure 1).
Recording diameter of each electrode was 8 mm and
center-to-center interelectrode distance was 2 cm. A ref-
erence electrode was placed on the skin overlying the
tibial tuberosity. Th e EMG s ign als were amp lified ( 1000);
band-pass filtered (1 Hz - 500 Hz). Scalp EEG signals
referenced to the common linked electrodes at the ear-
lobes were recorded simultaneously during the task and
were amplified (1000); band-pass filtered (0.3 Hz - 75
Hz).
We cut the trials into 10 s segments and manually dis-
carded the segments trials contaminated with eye-blinks
and sensor jumps. Signals from C3 and C4, which
represents the sensorimotor cortex were selected for fur-
ther investigation. Then functional relationship between
motor cortex and muscle was analyzed from EEG, sE MG
electrode pairs using the algorithm to compute informa-
tion transfer index as described above.
4. Result
4.1. Simulation Studies
1) Detection of information interactions for different
coupling models (Figure 2). ITI correctly detected effec-
tive connectivity (X→Y) for all three simulated coupling
types (linear, threshold, quadratic) 30 trials were used to
compute statistics. No false positives, i.e. significant re-
sults for the direction Y→X, were observed. For these
analysis we used a coupling constant
γ
of 0.5 a delay
time u of 20 samples prediction time u of 21 samples.
2) ITI calculated as a function of coupling strength.
The statistical evaluation shows that the ITI calculated
via a range of coupling strength
γ
from 0 - 1 reliably
reflect the different coupling strength (Figure 3) for all
three investigated coupling models (linear, threshold,
quadratic). For these analyses, we used a delay time u of
20 samples prediction time u of 21 samples.
3) Detection of interaction delay. 30 trials from the
quadratically coupled model, the coupling strength
γ
was chosen as 0.5, the interaction delay δ was set to 25
samples and prediction time u was scanned from 1 to 50
samples (Figure 4).
Figure 1. EEG recorded together with EMG during the
task.
Figure 2. Averaged ITI calculated from different test models. Coupling strength γ = 0.5; delay time δ = 20; prediction time u
= 21.
100 150 200
100 150 200
100 150 200
100 150 200
100 150 200
x (source)
y1 (independent)
y2 (linear)
y3 (qudratic)
y4 (threshold)

P. XIE ET AL.
60
Figure 3. Averaged ITI calculated as a function of coupling strength from the three different coupling models. Coupling
strength was set from 0 to1.
Figure 4. ITI calculated as a function of prediction time
from a quadratically coupled model, the coupling strength γ
was chosen as 0.5, the interaction delay δ was set to 25 samples
and prediction time was scanned u from 1 to 50 samples.
4.2. ITI between EEG and EMG
As expected, ITI during the movement was significantly
higher than the non-moved period (Figure 5). Figure 6
shows the ITIs calculated in different frequency bands
(beta band and gamma band). The information is not
only travels from cortex to muscle but also back from
muscle to cortex. The descending flow is expected as the
motor command and the other way contains the sensory
feedback which may allow the cortex to measure the
states of the limb.
5. Conclusions
In this study, we introduced the information transfer in-
dex as a model-free and nonlinear method to detect in-
formation flow between two time series. The ability to
detect linear and nonlinear information flow was tested
on simulated data generated from different models, that
is, independent, linear, threshold and quadratic models.
The result shows that our method reliably detects the
causal relationship between two time series correctly.
And the ITI shows the ability of reflecting the coupling
delay and strength. In conclusion, information transfer
index or ITI has promising features that should make it
useful fo r studies on corticomusclar interaction.
The next step of this work is to investigate information
transmission mechanism in sensorimotor system in pa-
Figure 5. A segment of simultaneously recorded EEG
sEMG pair and ITI calculated between them.
Figure 6. The upper graph presents the coherence between
the EEG and sEMG, and the below are the ITIs calculated
in different f requency.
tients with various neurological disorders such as stroke,
peripheral nerve injury. This method will be a helpful
00.2 0.4 0.6 0.8 1
0
0. 2
0. 4
0. 6
0. 8
1li near
ITI
c oupl i ng st rent h00.2 0.4 0.6 0.8 1
0
0. 2
0. 4
0. 6
0. 8
1quadrat i c
c oupl i ng st rent h00.2 0.4 0.6 0.8 1
0
0. 2
0. 4
0. 6
0. 8
1
c oupl i ng st rent h
t hreshold
y-x
x-y
05 10 15 2025 30 3540 45 50
0
0. 02
0. 04
0. 06
0. 08
Frequency/ Hz
Coherence
beta gamma
0
0. 02
0. 04
0. 06
0. 08
0. 1
I nf orm ati on trans f er i ndex
EEG-EMG
EMG-EEG
Beta Gamma

P. XIE ET AL.
61
addition in evaluating the integrity and functionality
neural circuits.
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