Lecture Notes in Computer Science

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2.2 Laguerre Polynomials

The Laguerre polynomials can be used for detecting experimental responses. This

family of polynomials can be specified as follows:

∑

=

L

i

a

i

i

t

g

f

t

h

)

(

)

(

(2)

where h(t) is the design coefficients to be input into X

i

in (1); L is the order of

Laguerre polynomial; ƒ

i

is the coefficient of the basis function, and g

i

a

(t) is the inverse

Z transform of the i-th Laguerre polynomial given by

)]

(

[

)

(

)

(

z

g

Z

az

a

z

az

z

Z

t

g

a

i

i

a

i

−

⎥

⎦

⎤

⎢

⎣

⎡

−

(3)

where a is a time constant. As an illustration, Fig. 1 gives the response coefficients

corresponding to L=2 and L =3.

(a) (b)

Fig. 1. The boxcar functions of experimental conditions in the Scott et al. study are depicted in

(a), and the Laguerre polynomials h(t) with L=2 and L =3 are depicted in (b)

3 Event-Related fMRI Experiments

We here introduce the experimental design behind the fMRI dataset used in the

empirical study, and select the design matrix suitable for the study.

h(t), L=2

h(t), L=3

Reproducibility Analysis of Event-Related fMRI Experiments

129

3.1 Experimental Design

In our empirical study, the dataset contains functional MR images of 10 subjects

who went through 10-12 experimental runs, with 10 stimulus trials in each run.

Experimental runs involved the change-detection task in which two images within a

pair differed in either the presence/absence of the position of a single object or the

color of the object. The two images were presented alternatively for 40 sec. In the first

30 sec, each image was presented for 300 msec followed by a 100 msec mask.

However, the mask was removed in the last 10 sec. Subjects pressed a button when

detecting something changing between the pair of images. The experimental images

and stimulus duration are shown in Fig. 2.

Fig. 2. The experimental images and stimulus duration in the Scott et al. study

3.2 Experimental Design Matrix

We used the Laguerre polynomials in Fig. 1 for specifying the design matrix in (1)

instead of the theoretical HRFs. According to the original experimental design, there

are two contrasts of interest in the Scott et al. study. The first is the response after the

task onset within the 40 secs trial, and the second is the difference between stimulus

presentations with and without the mask, that is, responses during the image

presentation with the mask (0 ~ 30 sec.) and without the mask (30 ~ 40 sec.) in Fig. 2.

The boxcar functions in Fig. 1 can also be specified in the design matrix as was

suggested in the study by Liou et al. (2006) for the on-and-off design. However, the

two boxcar functions are not orthogonal to each other and carry redundant

information on experimental effects. In the event-related fMRI experiment, the

duration of stimulus presentation is always longer than that in the on-and-off design.

The theoretical HRFs vanish during the stimulus presentation. There might be brain

regions continuously responding to the stimulus. The Laguerre polynomials are

orthogonal and offer possibilities for examining all kinds of experimental effects. We

130

H.-R. Su et al.

might also consider Laguerre polynomials in Fig. 1 as a smoothed version of the

boxcar functions.

4 Results

In the Scott et al. study, a response-contingent event-related analysis technique was used

in the data analyses, and the original results showed brain regions associated with different

processing components in the visual change-detection task. For instance, the lingual gyrus,

cuneus, precentral gyrus, and medial frontal gyrus showed activations associated with the

task onset. And the pattern of activation in dorsal and ventral visual pathways was

temporally associated with the duration of visual search. Finally parietal and frontal

regions showed systematic deactivations during task performance. In the reproducibility

analysis with Laguerre polynomials, we found the similar activation regions associated

with the task onset, visual search and deactivations. In addition, we found activation

regions in the parahippocampal, superior frontal gyrus, supramarginal gyrus and inferior

parietal lobule. Both positive and negative responses were also found in the lingual gyrus,

cuneus and precuneus which are also reproducible across all subjects; this finding is

consistent with our previous data analyses of fMRI studies involving object recognition

and word/pseudoword reading (Liou et al., 2006). Table 1 lists a few activation regions in

the change-detection task for the 10 subjects.

Table 1. The activation regions in the change-detection task. The plus sign indicates the positive

response and minus sign indicates the negative response.

Subjects

1

2

3

4

5

6

7

8

9

10

Lingual

gyrus

+/- +/- +/- +/- +/- +/- +/- +/- +/- +/-

Precuneus

+/-

Cuneus

+/- +/- +/- +/- +/- +/- +/- +/- +/- +/-

Posterior cingulate

+/-

Medial frontal gyrus

+/-

+/- + +/- +/-

+/-

Parahippocampal gyrus

+/-

Superior frontal gyrus

Supramarginal gyrus

In the table, there are 4 subjects showing activations in the superior frontal gyrus

and supramarginal gyrus in the change-detection task. The two regions have been

referred to in fMRI studies on language process (e.g., the study on word and

pseudoword reading). The 4 subjects, on average, had longer reaction time in the

change-detection task, that is, a delay of pressing the button until the image

presentation without the mask (30-40 sec.). Fig. 3 shows the brain activation regions

for Subjects 5 and 7 in the Scott et al. study. Subject 5 involved the superior frontal

gyrus and supramarginal gyrus and had the longest reaction time compared with other

subjects in the experiment. On the other hand, Subject 7 had relatively shorter

reaction time and showed no activations in the two regions.

Reproducibility Analysis of Event-Related fMRI Experiments

131

Fig. 3. Brain activation regions for Subjects 5 and 7 in the Scott et al. study

132

H.-R. Su et al.

Subject 5

Fig. 3. (continued)

Reproducibility Analysis of Event-Related fMRI Experiments

133

Subject 7

Fig. 3. (continued)

134

H.-R. Su et al.

5 Discussion

The reproducibility evidence suggests that the 10 subjects consistently show a pattern

of increased/decreased responses in the lingual gyrus, cuneus, and precuneus. Similar

observations were also found in our empirical studies on other datasets published by

the fMRIDC. In the fMRI literature, the precuneus, posterior cingulate and medial

prefrontal cortex are known to be the default network in a resting state and show

decreased activities in a variety of cognitive tasks. The physiological mechanisms

behind the decreased responses are still under investigation. However, discussions on

the network have given a focus on the decreased activities. We would suggest to

consider both positive and negative responses when interpreting the default network.

By the method of reproducibility analyses, we can clearly classify brain regions that

show consistent responses across subjects and those that show patterns and

inconsistencies across subjects (see results in Table 1). Higher mental functions are

individual and their localization in specific brain regions can be made only with some

probabilities. Accordingly, the higher mental functions are connected with speech,

that is, external or internal speech organizing personal behavior. Subjects differ from

each other as a result of using different speech designs when making decisions in

performing experimental tasks. Change of functional localization is an additional

characteristic of a subject’s psychological traits. The proposed methodology would

assist researchers in identifying those brain regions that are specific to individual

speech designs and those that are consistent across subjects.

Acknowledgments. The authors are indebted to the fMRIDC at Dartmouth College

for supporting the datasets analyzed in this study. This research was supported by the

grant NSC 94-2413-H-001-001 from the National Science Council (Taiwan).

References

1. Liou, M., Su, H.-R., Lee, J.-D., Aston, J.A.D., Tsai, A.C., Cheng, P.E.: A method for

generating reproducible evidence in fMRI studies. NeuroImage 29, 383–395 (2006)

2. Huettel, S.A., Guzeldere, G., McCarthy, G.: Dissociating neural mechanisms of visual

attention in change detection using functional MRI. Journal of Cognitive

Neuroscience 13(7), 1006–1018 (2001)

3. Liou, M., Su, H.-R., Lee, J.-D., Cheng, P.E., Huang, C.-C., Tsai, C.-H.: Bridging Functional

MR Images and Scientific Inference: Reproducibility Maps. Journal of cognitive

Neuroscience 15(7), 935–945 (2003)

4. Saha, S., Long, C.J., Brown, E., Aminoff, E., Bar, M., Solo, V.: Hemodynamic transfer

function estimation with Laguerre polynomials and confidence intervals construction from

functional magnetic resonance imaging (FMRI) data. IEEE ICASSP 3, 109–112 (2004)

5. Andrews, G.E., Askey, R., Roy, R.: Laguerre Polynomials. In: §6.2 in Special Functions,

pp. 282–293. Cambridge University Press, Cambridge (1999)

6. Arfken, G.: Laguerre Functions. In: §13.2 in Mathematical Methods for Physicists, 3rd ed.,

Orlando, FL, pp. 721–731. Academic Press, London (1985)

M. Ishikawa et al. (Eds.): ICONIP 2007, Part I, LNCS 4984, pp. 135–141, 2008.

The Effects of Theta Burst Transcranial Magnetic

Stimulation over the Human Primary Motor and Sensory

Cortices on Cortico-Muscular Coherence

Murat Saglam

, Kaoru Matsunaga

, Yuki Hayashida

, Nobuki Murayama

and Ryoji Nakanishi

Graduate School of Science and Technology, Kumamoto University, Japan

Department of Neurology, Kumamoto Kinoh Hospital, Japan

msaglam@brain.cs.kumamoto-u.ac.jp,

{yukih,murayama}@cs.kumamoto-u.ac.jp

Abstract. Recent studies proposed a new paradigm of repetitive transcranial

magnetic stimulation (rTMS), “theta burst stimulation” (TBS); to primary

motor cortex (M1) or sensory cortex (S1) can influence cortical excitability in

humans. Particularly it has been shown that TBS can induce the long-lasting

effects with the stimulation duration shorter than those of conventional rTMSs.

However, in those studies, effects of TBS over M1 or S1 were assessed only by

means of motor- and/or somatosensory-evoked-potentials. Here we asked how

the coherence between electromyographic (EMG) and electroencephalographic

(EEG) signals during isometric contraction of the first dorsal interosseous

muscle is modified by TBS. The coherence magnitude localizing for the C3

scalp site,

and at 13-30Hz band, significantly decreased 30-60 minutes after the

TBS on M1, but not that on S1, and recovered to the original level in 90-120

minutes. These findings indicate that TBS over M1 can suppress the cortico-

muscular synchronization.

Keywords: Theta Burst Transcranial Magnetic Stimulation, Coherence Electroen-

cephalogram, Electromyogram, Motor Cortex.

1 Introduction

Previous studies have demonstrated dense functional and anatomical projections

among motor cortex building a global network which realizes the communication

between the brain and peripheral muscles via the motor pathway [1, 2]. The quality of

the communication is thought to highly depend on the efficacy of the synaptic

transmission between cortical units. In the past few decades, repetitive transcranial

magnetic stimulation (rTMS) was considered to be a promising method to modify

cortical circuitry by leading the phenomena of long-term potentiation (LTP) and

depression (LTD) of synaptic connections in human subjects [3].

Furthermore, a recently developed rTMS paradigm, called “theta burst stimulation”

(TBS) requires less number of the stimulation pulses and even offers the longer after-

effects than conventional rTMS protocols do [4]. Previously, efficiency of TBS has

136

M. Saglam et al.

been assessed by means of signal transmission from cortex to muscle or from muscle to

cortex, by measuring motor-evoked-potential (MEP) or somatosensory-evoked-potential

(SEP), respectively. It was shown that TBS applied over the surface of sensory cortex

(S1) as well as primary motor cortex (M1) could modify the amplitude of SEP (recorded

from the S1 scalp site) lasting for tens of minutes after the TBS [5]. On the other hand,

the amplitude of MEP was not modified by the TBS applied over S1, while the

MEP amplitude was significantly decreased by the TBS applied over M1 [4, 5]. In the

present study, we examined the effects of TBS applied over either M1 or S1 on the

functional coupling between cortex and muscle by measuring the coherence between

electroencephalographic (EEG) and electromyographic (EMG) signals during voluntary

isometric contraction of the first dorsal interosseous (FDI) muscle.

2 Methods

2.1 Subjects

Seven subjects among whole set of recruited participants (approximately twenty)

showed significant coherence and only those subjects participated to TBS

experiments. Experiments on M1 and S1 performed on different days and subjects did

not report any side effects during or after the experiments.

2.2 Determination of M1 and S1 Location

The optimal location of the stimulating coil was determined by searching the largest

MEP response(from the contralateral FDI-muscle) elicited by single pulse TMS while

Fig. 1. EEG-EMG signals recorded before and after the application of TBS as depicted in the

experiment time line. Subjects were asked to contract four times at each recording set. Location

and intensity for actual location were determined after pre30 session. Pre0 recording was done

to confirm searching does not make any conditioning. TBS paradigm is illustrated in the right-

above inset.

The Effects of Theta Burst Transcranial Magnetic Stimulation

137

moving the TMS coil in 1cm steps on the presumed position of M1. Stimulation was

applied by a with a High Power Magstim 200 machine and a figure-of-8 coil with

mean loop diameter of 70 mm (Magstim Co., Whitland, Dyfed, UK). The coil was

placed tangentially to the scalp with the handle pointing backwards and laterally at a

45˚ angle away from the midline. Based on previous reports S1 is assumed to be 2cm

posterior from M1 site [5].

2.3 Theta Burst Stimulation

Continuous TBS (cTBS) paradigm of 600 pulses was applied to the M1 and S1

location. cTBS consists of 50Hz triplets of pulses that are repeating themselves at

every 0.2s (5Hz) for 40s[4]. Intensity of each pulse was set to 80% active motor

threshold (AMT) which is defined as the minimum stimulation intensity that could

evoke an MEP of no less than 200μV during slight tonic contraction.

2.4 EEG and EMG Recording

EEG signals were recorded based on the international 10-20 scalp electrode

placement method (19 electrodes) with earlobe reference. EMG signal, during

isometric hand contraction at 15% level from the maximum, was recorded from the

FDI muscle of the right hand with reference to the metacarpal bone of the index

finger. EEG and EMG signals were recorded with 1000 Hz sampling frequency and

passbands of 0.5-200Hz and 5-300 Hz, respectively. Each recording set consists of 4

one-minute-long recordings with 30s-rest time intervals. To assess TBS effect with

respect to time, each set was performed 30 minutes before (pre30), just before (pre0),

0,30,60,90 and 120 minutes after the delivery of TBS. Stimulation location and

intensity were determined between pre30 and pre0 recordings (Fig. 1).

2.5 Data Analysis

Coherence function is the squared magnitude of the cross-spectra of the signal pair

divided by the product their power spectra. Therefore cross- and power-spectra

between EMG and 19 EEG channels were calculated. Fast Fourier transform, with an

epoch size of 1024, resulting in frequency resolution of 0.98 Hz was used to convert

the signals into frequency domain. The current source density (CSD) reference

method was utilized in order to achieve spatially sharpened EEG signals [6].

Coherency between EEG and EMG signals was obtained using the expression below:

)

(

)

(

)

(

)

(

≤

f

S

f

S

f

S

f

yy

xx

xy

xy

(1)

where S

(f) represents the cross-spectral density function. S

(f) and S

(f) stand for

the auto-spectral density of the signals x and y, respectively. Since coherence is a

normalized measure of the correlation between signal pairs, κ

xy

(f) =1 represents a

perfect linear dependence and κ

(f) =0 indicates a lack of linear dependence within

those signal pairs. Coherence values for κ

xy

(f) > 0 are assumed to be statistically

significant only if they are above 99% confidence limit that is estimated by:

138

M. Saglam et al.

)

1

(

(

100

−

⎟

⎠

⎞

⎜

⎝

⎛

−

=

n

(2)

where n is the number of epochs used for cross- and power- spectra calculations.

3 Results

First we have confirmed that EEG-EMG coherence values for all (n=7) subjects lie

above 99% significance level (coh ~= 0.02) and within beta (13-30 Hz) frequency

Table 1. Mean ± standard error of mean (SEM) of beta band EEG (C3)-EMG coherence values

and peak frequencies for TBS-over-M1 and S1 experiments (n=7)

Pre30

(min)

Pre0 (min)

0 (min)

30 (min)

60 (min)

90 (min)

120 (min)

Coherence

Magnitude

M1

0.061±0.008 0.051±0.014 0.053±0.014 0.03±0.007 0.031±0.009 0.057±0.015 0.067±0.016

0.059±0.021 0.068±0.026 0.058±0.027 0.061±0.023 0.052±0.014 0.034±0.006 0.040±0.016

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