MODELING OF MOTOR NEURONAL STRUCTURES VIA

TRANSCRANIAL MAGNETIC STIMULATION

Giuseppe d’Aloja, Paolo Lino, Bruno Maione, Alessandro Rizzo

DEE-Dipartimento di Elettrotecnica ed Elettronica – Politecnico di Bari – Via Re David 200 – 70125 Bari Italy

Keywords: Neuronal Modeling, Spiking Neu

rons, Brain Waves, TMS.

Abstract: Transcranial Magnetic Stimulation (TMS) of human motor area can evoke different biological waves in the

epidural space of patients. These waves can evoke different muscle responses according to different types

and amplitudes of stimuli. In this paper we analyze the different types of epidural waves and we propose a

neuronal model for the biological structures involved in the experiments.

1 INTRODUCTION

Human nervous system is something much complex

and its operation is still rather obscure to scientists.

Nevertheless, more and more emerging techniques

are helping scientists in examining the human brain

in detail and making hypotheses on its operation. For

example, the use of transcranial cerebral

stimulations, such as the Transcranial Magnetic

Stimulation (TMS), allows us to understand some

cerebral mechanisms and identify several cerebral

areas. Pioneering studies on brain stimulation

through the intact scalp were carried out in the early

80s (Merton and Morton 1980) by stimulating the

brain through an electric field. This stimulation

technique is called Transcranial Electrical

Stimulation (TES). Unfortunately, it has been found

that TES is quite uncomfortable to the patient,

because only a small fraction of the applied current

flows through the resistance of the skull and scalp

into the brain, while the rest travels between the

electrodes on the surface, causing local pain and

contraction of scalp muscles. The development of

TMS (Barker et al., 1985) overcame these problems

of discomfort by using a magnetic field to carry the

electrical stimulus across the scalp and skull to the

brain. Opposite to the TES, TMS is painless and

lacking in harmful effects to the human nervous

system. TMS has also been exploited with success in

the treatment of mental illness and depression

(Wasserman, 1998). The first magnetic stimulators

were very heavy and they could reach low

stimulation frequencies. Recently, novel stimulators

with lower weight and smaller size have been

designed. The stimulator used in the experiments is

the Magstim 200

(Jalinous 1997). The magnetic

stimulation adopted in the experiment is provided by

a 70mm (internal diameter), eight-shaped coil,

placed above the cerebral motor area responsible of

the left hand movements. Different levels of

stimulation have been used, from 20% to 53% of the

maximum stimulator output, using a 3% increasing

step. The experimental data are collected from

patients who have spinal chord stimulators

implanted in the epidural space at C1-C2 vertebras

for the treatment of intractable dorsolumbar pain (V.

Di Lazzaro, 1998). Two different types of data are

available: the recordings from the patient’s epidural

space and the EMG recordings. The former is

important for the understanding of the nature of

brain waves; the latter is important for the

understanding of the effects of the voluntary muscle

contraction on the recorded muscle potentials. In

particular, the effects of voluntary contraction are

important at motoneuronal level, but they do not

influence the corticospinal volleys, as it will be

shown in the following. The paper is structured as

follows: in the next section we analyze the epidural

recordings of the biological waves, and the artifacts

due to the stimulus and the measurement method.

Moreover, we propose a first-attempt linear model.

In the third section we exploit the Izhikevich

nonlinear neuron model to build a model of the

neuronal structure under investigation. In the fourth

section we show the results. Finally, we draw our

conclusions in the fifth section.

d’Aloja G., Lino P., Maione B. and Rizzo A. (2005).

MODELING OF MOTOR NEURONAL STRUCTURES VIA TRANSCRANIAL MAGNETIC STIMULATION.

In Proceedings of the Second International Conference on Informatics in Control, Automation and Robotics - Signal Processing, Systems Modeling and

Control, pages 45-51

DOI: 10.5220/0001160500450051

 SciTePress

2 DATA ANALYSIS

The data analyzed in this paper have been collected

in experiments carried out by Prof. V. Di Lazzaro

and co-workers at the Neurological Institute at

Cattolica University in Rome, Italy. The recordings

have been collected from a patient with epidural

electrodes implanted at C1-C2 vertebras level. The

left hand motor area of the patient’s brain has been

stimulated by TMS. Consequently, brain potentials

have been evoked and recorded by a differential

amplifier from the epidural electrodes, and by an

EMG recorder from the First Dorsal Interosseus

muscle (FDI) of the left hand. Experimental data

have been recorded with different amplitudes of

magnetic stimulation and different levels of

voluntary muscle contractions.

Figure 1 shows a typical recording taken at the

epidural electrodes. Three different zones can be

clearly distinguished:

• Zone one: stimulus artifact;

• Zone two: actual biological waves;

• Zone three: noise.

Biol ic TMS are of two kinds

re is always a saturated peak

particular case of this patient it has been

og al waves evoked by

(Di Lazzaro, 2004). The first one, called D wave

(Direct wave) is supposed to be produced by direct

stimulation of the pyramidal tract axons. The second

one is called I wave (Indirect wave), and is supposed

to be produced by synaptic activation of the

pyramidal neurons of the same tract. With TMS, a D

wave is present only if the stimulus amplitude is

greater than a threshold, whereas I waves are always

present. If a D wave is present, it precedes the I

waves. In the recorded data, I waves are numbered

according to their temporal sequence. The

recordings have been collected using a differential

method; therefore, for each volley recorded, two

peaks (a positive and a negative one) are present .

Figure 2 shows the amplitude of the I1 wa

(computed on the experimental data as the half-

peak-to-peak amplitude) for different voluntary

muscle contraction at different stimulation levels. As

it is seen from Figure 2 the amplitude of the I1 wave

increases linearly with the stimulation level and it is

independent from the voluntary contraction level. In

fact, muscle contraction increases motoneuronal

excitability and has no effect at the corticospinal

level. On the other hand, voluntary contraction

makes the recordings more noisy and lowers the

signal to noise ratio.

In our recordings the

which occurs at the same instant (0.02s) of

application of the magnetic stimulus. This saturated

peak is biologically implausible, and systematically

occurs in every experimental recording. Thus, we

can conclude that this is a stimulus artifact due to

both the electromagnetic coupling and the

displacement current (O’Keffe et al., 2001),

(McLean et al., 1996). To analyze the actual

biological waves we have reconstructed the stimulus

artifact for different stimulation amplitudes. In

particular we have developed 4 different stimulus

artifact models according to the stimulus amplitude.

Figure 3 shows, in clockwise direction from top-left,

the stimulus artifacts from low to high stimulation

intensity. In our modeling, the reconstructed

stimulus artifact is subtracted from the experimental

data to obtain the experimental biological waves to

be modeled. Subsequently, the artifact is added

again to the modeled waves to rebuild the modeled

signal.

For the

found that the amplitudes of subsequent I waves are

well modeled by an exponential decreasing law. As

stated before, the amplitude of I1 wave increases

almost linearly with the stimulus amplitude.

Therefore, a first-attempt model has been carried out

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055

0.06

-15

-10

-5

amplitude (uV)

time (s)

zone 1

zone 2

zone 3

Figure 1: Typical recording taken at the epidural

electrodes

20 25 30 35 40 45 50 55

stimulation level %

amplitude

rest

20% activity

max activity

Figure 2: Amplitude of the first I wave evoked by TMS

for different muscle contractions levels.

ICINCO 2005 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

0.015 0.02 0.025 0.03 0.035 0.04 0.045

-25

-20

-15

-10

-5

Model output and data at 20 % stimulation level

model

data

0 0.01 0.02 0.03 0.04 0. 05 0.06 0.07 0.08 0.09 0.1

-20

-15

-10

-5

time (s)

amplitude (uV)

artifact

data

0 0.01 0.02 0.03 0.04 0. 05 0.06 0.07 0.08 0.09 0.1

-30

-20

-10

time (s)

amplitude (uV)

artifact

data

0 0.01 0.02 0.03 0.04 0. 05 0.06 0.07 0.08 0.09 0.1

-10

-5

time(s)

amplitude (uV)

artifact

data

0 0.01 0.02 0.03 0.04 0. 05 0.06 0.07 0.08 0.09 0.1

-15

-10

-5

time (s)

amplitude (uV)

artifact

data

-10

-5

by considering a second order linear system,

described by the following transfer function:

he Laplace transform of the input stimulus, as the

he K parameter changes linearly with the

as biologically plausible, and useful, data.

The facts

monophasic current produced by the eight-shaped

coil (Kammer et al., 2001), is:

stimulation amplitude and simulates the stimulus

increase. In Figures 3 and 4 we show some results

achieved with the linear model described above.

This model gave good results for this experiment bu

is not suitable for experimental data collected in

other patients, nor for other similar experiments

reported in literature (Houlden,1999). In fact, the use

of a linear model implies the periodicity of I waves.

An in-depth analysis on the latency of the I waves

shows that in fact they are not periodic and each

wave has a fixed latency for all the stimulation

levels. We remind that the recordings are the results

of different mechanisms: the stimulus artifact, the

artifact due to the propagation of the nervous

potentials through the fibers and the artifact due to

the differential measurement method. Therefore, the

aspect of the recordings is not entirely due to the

action potentials generating in the fiber, and only

amplitude and latency of I waves can be considered

Therefore, we have developed another model based

on a neuronal network of spiking neurons.

on which we base our hypotheses is that the

potential recorded at the electrodes comes from the

output of a huge number of spinal fibers, and the

)(

⋅=

0.015 0.02 0.025 0.03 0.035 0.04 0.045

-25

-20

-15

Model output and data at 29 % stimulation level

model

data

Figure 3: Reconstructed stimulus artifacts versus

experimental data for different stimulation levels.

bsas

ebsG

rits

+⋅+

⋅⋅=

⋅−

)(

0.015 0.02 0.025 0.03 0.035 0.04 0.045

-25

-20

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-10

-5

Model output and data at 41% s timulat ion level

model

data

0.015 0.02 0.025 0.03 0.035 0.04 0.045

-25

-20

-15

-10

-5

Model output and data at 50% s timulat ion level

model

data

Figure 4: model output and data for different

stimulation level

MODELING OF MOTOR NEURONAL STRUCTURES VIA TRANSCRANIAL MAGNETIC STIMULATION

greater the stimulation amplitude is, the higher the

number of stimulated fibers is. This hypothesis is

supported by the biological law of “nothing or all”

which states that neurons produce a fixed voltage

level when they are excited above a threshold. If the

stimulation is under the threshold the action

potential is not generated and, correspondently, a

descending wave at the electrodes is not revealed.

3 NEURONAL MODELS

is section

consists of Izhikevich spiking neurons (Izhikevich,

With th

u← u+d

al, u is a recovery

ory period and

slower

•

to the fluctuations of the

•

The

to: a=0.4 -65, d=6. This choice makes the

)(' ubvau −=

The neuronal network developed in th

2003). It is described by the equation system:

140504.0'

Iuvvv +−++=

e reset condition:

If v≥30 mV then v← c

where v is the membrane potenti

variable which considers the refract

the K

current activation after the action potential.

The mechanism of iperpolarization is considered by

the c parameter which has the -64 mV value. We can

now analyze the meaning of the parameters.

• a describes the time scale of the recovery

variable u. Smaller values result in

recovery;

b describes the sensitivity of the recovery

variable u

membrane potential v;

c describes the after-spike reset value of the

membrane potential v;

• d describes after-spike reset of the recovery

variable u.

parameters of the neuron model have been fixed

, b=0.26, c=

neuron spiking and with a latency comparable to that

of the experimental recordings.

The experimental recordings cannot reveal the

action potentials of the single neuron activated by

the stimulation, so we have studied the global

behavior of the network, by simulating an

appropriate inducted current at different neuronal

areas, produced by the eight-shaped coil.

The amplitude of each I wave is proportional to the

number of corticospinal neurons transinaptically

activated by the stimulation. The generation of a D

wave is due to the direct stimulation of the

corticospinal neurons for high stimulation levels, as

the inducted current activates the deep brainstem and

activates cortical neurons directly. Nevertheless, for

the generation of the simulated I waves, the number

of neurons actually involved is unknown. We

assumed that each stimulated neuron contributes to

the formation of the I wave with a 1µV spike and

consequently we estimated the number of neurons

involved in the stimulation process.

Based on these considerations, we have simulated a

500 cortical neurons network connected to a 100

corticospinal neurons network. Both networks are

considered within a regular topology. Each

corticospinal neuron is synaptically connected to

five cortical neurons. As it is illustrated in Figure 5,

an eight-shaped coil induces an electric field with

the highest peaks located in three main areas: one

located immediately below the coil with the

maximum intensity, the other two on the two sides

of the coil, with a peak of intensity which is about a

half of the highest one. The hypothesis made in this

paper is that the electric field mainly stimulates

groups of neurons located under the highest field

peaks (Rosler, 2001 – Sakay). Therefore, an I wave

consists of the sum of the outputs of many neurons

which fires at the same time, because they are

essentially stimulated by the same field. This

hypotesis is supported by the following facts, which

can be observed in the experimental data:

Figure 5: Electric field shape for circular and eight-

shaped stimulation coils

• In these experiments a maximum of three

waves is generated, and there are three

main areas in which a peak of electric field

exists.

• For high intensities, the field peaks are

higher and more spread in space.

Consequently, more neurons are activated

and the correspondent I wave is larger.

• For low intensities, the electric field has

only one peak located under the coil.

Correspondently, only one I wave is

generated for low intensity field.

ICINCO 2005 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

Therefore, the cortical network (and consequently

the corticospinal one) has been partitioned in three

areas, each responsible for the generation of one of

the three I waves. When the stimulation intensity

increases, the number of activated neurons increases

and larger waves are produced. This simulates the

spatial spreading of the stimulus at higher intensity

of stimulation. Therefore, different I waves are

generated because a different current for each

neuronal area is inducted by the magnetic field.

Figures. 6, 7 and 8 show a comparison between the

amplitude of simulated I1, I2 and I3 waves and the

experimental ones, versus the stimulus intensity.

Once amplitudes and latencies have been modeled,

the signal shape must be reconstructed. We already

dealt with the fact that the differential measurement

configuration introduces an artifact in the

measurements, producing a sequence of one positive

and one negative volley for each cerebral I wave.

20 25 30 35 40 45 50 55

stimulation level (%)

amplit ude (uV)

data

model

The propagation velocity of the impulse has been

calculated in about 50 m/s. The propagation delay

for the I1 wave is about 2.2 ms. For I waves, due to

their synaptic nature, an approximately 1 ms delay

due to the synaptic mechanism must be added.

Therefore, a total latency for the I1 wave equal to

3.6 ms has been reckoned, which is coherent with

the distance of 12 cm between stimulation and

recording site.

Figure 6: amplitude of the I1 waves for different

stimulation levels.

Therefore, taking into account the propagation

velocity of the waves and the distance between the

electrodes, the artifact can be reconstructed.

4 RESULTS

A good fitting of the experimental data for all the

stimulation levels has been obtained with the

neuronal structure explained above.

To fit the experimental data we have reproduced the

stimulus artifact, the measure setup and the

propagation artifacts.

Figures 9, 10 and 11 illustrate a comparison between

the output of the model and the experimental data. It

can be clearly noticed that the neuronal network

gives better results than the linear model. It respects

Figure 7: Amplitude of the I2 waves for different

stimulation levels.

20 25 30 35 40 45 50 55

stimulation level (%)

amplitude (uV )

data

model

Figure 8: Amplitude of the I3 waves for different

stimulation levels.

20 25 30 35 40 45 50 55

0.5

1.5

2.5

3.5

4.5

stimulation level %

amplitude (uV)

data

model

0.015 0.02 0.025 0.03 0.035 0.04 0.045

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data

model output

Figure 9: Model output and data for a 20% stimulation

level.

MODELING OF MOTOR NEURONAL STRUCTURES VIA TRANSCRANIAL MAGNETIC STIMULATION

the aperiodicity of the response, taking into account

the different latencies of I waves, and provides a

better fitting for wave amplitudes.

0.015 0.02 0.025 0.03 0.035 0.04 0.045

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data

model output

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data

model output

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data

model output

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data

model output

0.015 0.02 0.025 0.03 0.035 0.04 0.045

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data

model output

Figure 11: Model output and data for 47%, 53%

stimulation level.

5 CONCLUSIONS

In this paper a model of motor neuronal structures

has been built and validated on the basis of

experimental recordings obtained via Transcranial

Magnetic Stimulation (TMS). With this technique,

the brain of the patient is stimulated by a suitable

magnetic field placed above the cerebral motor area

responsible of the left hand movements. The

stimulation evokes different biological waves in the

brain which are transmitted from the motor cortex,

through the pyramidal neurons via synaptic

connection, to the spinal chord, where signals are

collected by a couple of electrodes implanted in the

epidural space at C1-C2 vertebras level.

0.015 0.02 0.025 0.03 0.035 0.04 0.045

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data

model output

After a thorough data analysis phase, the motor

neuronal structure has been modeled by a neural

network based on Izhikevich neurons, for both the

motor cortex and the pyramidal neuron areas.

Moreover, stimulus and measurement artifacts have

been reconstructed and considered in the modeling

phase. The results are fully satisfactory, model

Figure 10: Model output and data for 23%, 32%, 35%,

44% stimulation level.

ICINCO 2005 - SIGNAL PROCESSING, SYSTEMS MODELING AND CONTROL

output and experimental recordings match for each

available experiment.

Further research will involve a more accurate

modeling of the motor cortex and its connections

with the pyramidal tracts. At present, an hypothesis

of a five-to-one local connection between cortex and

pyramidal neurons has been made. In the future,

optimization strategies will be considered to find an

adequate connection scheme between cortex and

pyramidal tracts, and with different topologies,

involving also the plasticity mechanism (i.e. time-

variant connections). Moreover, the model is being

validated on several recordings coming from

different patients, with different stimulation

protocols.

ACKNOWLEDGEMENTS

This work is supported by the national research

project MIUR "Innovative Bio-Inspired Strategies

for the Control of Motion Systems", No.:

2003090328, 2003. The authors acknowledge Prof.

Di Lazzaro (Institute of Neurology, Università

Cattolica, Rome, Italy), Prof. Mazzone

(Neurochirurgia CTO, Rome, Italy), Dr. Ghirlanda

(Department of Psychology, University of Bologna,

Italy) and their research groups for having provided

the experimental data and the prior knowledge for an

in-depth data analysis.

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