Information Transfer Index-A Promising Measure of the Corticomusclar Interaction

doi:10.4236/eng.2013.510B012

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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

Email: pi [email protected] n, [email protected]

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.

[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

HX HYHXY

ITI HX

→

= ∈

(1)

where

( )

are the complexity entropy of

signal X and Y,

( )

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

( )

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

( )

tt tm

xxx

−+

=

( )

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

xxt xtxtxtd

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.

ti tit

xax u

−

= +

∑

(5)

ti tit

yay v

−

= +

∑

(6 )

where the coefficients

and

are drawn from a

normalized Gaussian distribution,

and

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.

added to the internal dynamics of Y a term related to the

past dynamics of X and

( )

ti titt

yby xv

γ γσ

−−

=− ++

∑

(7)

3) The third test case consisted in generating two qu-

adratically coupled processes.

( )

10 2

ti titt

ybyxv

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.

( )( )

4112

11 exp

ti tit

y byv

b bx

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

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

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

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

x (source)

y1 (independent)

y2 (linear)

y3 (qudratic)

y4 (threshold)

P. XIE ET AL.

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. 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. 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. 2

0. 4

0. 6

0. 8

c oupl i ng st rent h

t hreshold

y-x

x-y

05 10 15 2025 30 3540 45 50

0. 02

0. 04

0. 06

0. 08

Frequency/ Hz

Coherence

beta gamma

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.

addition in evaluating the integrity and functionality

neural circuits.

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