Journal of Medical Engineering & Technology

ISSN: 0309-1902 (Print) 1464-522X (Online) Journal homepage: http://www.tandfonline.com/loi/ijmt20

Computer modelling of brain cortex excitation by magnetic field pulses R. De Leo, G. Cerri, D. Balducci, F. Moglie, O. Scarpino & M. Guidi To cite this article: R. De Leo, G. Cerri, D. Balducci, F. Moglie, O. Scarpino & M. Guidi (1992) Computer modelling of brain cortex excitation by magnetic field pulses, Journal of Medical Engineering & Technology, 16:4, 149-156, DOI: 10.3109/03091909209030218 To link to this article: http://dx.doi.org/10.3109/03091909209030218

Published online: 09 Jul 2009.

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Date: 24 April 2016, At: 05:16

Journal of Medical Engineering & Technology, Volume 16, Number 4 (July/August 1992), pages 14S156

Computer modelling of brain cortex excitation by magnetic field pulses large part of the brain, normally not involved in the motor system, is excited.

R. De Leo, G. Cerri, D. Balducci, F. Moglie, 0. Scarpinot and M. Guidit

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Dipartimento di Elcttronica e Automatica, Universiti di Ancona and fINRCA, Unita di Neurologia, Ancona, Italy

In spite of many clinical and experimental applications, the technique of transcranial magnetic stimulation still presents obscure aspects. This especial& concerns safe& parameters and the exact characterization of the current induced by a single magnetic pulse. The model proposed consists of an equivalent electric network derived by Maxwell’s equations and applied to discretized magnetic resonance imaging of a normal subject. This model allows accurate prediction of current distribution, charge per phase and dissipated energy.

Introduction The excitation of the neural tissues by means of a time-varying magnetic field is becoming an accessible technique for clinical and experimental applications in many neurophysiological laboratories [ 1-31. The first attempt to stimulate the nervous tissue by a magneto-electrical stimulus was at the end of the 19th century when D’Arsonval [4] had experience of phosphenes when he exposed his head to a time-varying magnetic field. In 1910 Thompson [5] reported a sensation of ‘flickering illumination’ due to magnetic stimulation of the retina. Fifty years after these pioneering experiments Bickford and Fremming [6] had success in stimulating peripheral nerves using a magnetic stimulator which delivered a damped sinusoidal magnetic field ranging up to 4.0 Tesla. In 1985 a group of engineers from the University of Sheffield realized that a magnetic stimulator was capable of exciting the brain cortex [7]. The physical mechanism of neural excitation is based on the time-varying magnetic field which induces a current called ‘eddy current’ in a conducting medium. It is known that the magnetic field is not attenuated by biological tissues and the maximum value of the current is found on a plane orthogonal to the magnetic field. Its characteristics of being painless, activating deep structures and being easily applied, has encouraged attempts to stimulate the brain cortex and peripheral nerve, which techniques are now well established. This possibility is clinically very useful, since the central conduction time can be easily estimated [&lo]. Unfortunately, the magnetic pulse produced by the available commercial stimulators is relatively unfocused, thus a

A more selective excitation of the motor cortex can be realized electrically by superficial electrodes applied specifically in some areas of the skull. This technique, introduced some years ago, uses high-voltage discharge for a brief interval and is very unpleasant [11,12]; the discomfort is proportional to the intensity and duration of the electric shock. Knowledge of the biological modality and of the site of activation on the nervous tissues by pulsed magnetic fields remains very limited. It depends on a number of variables such as the dimension and shape of the coil, anatomical structures and their conductivities, intensity and time variation of the magnetic field. The distribution of induced currents has been analysed in a previous study assuming uniform isotropic frequencyindependent tissue conductivity [ 13,141. T o overcome the limitations resulting from the magnetic stimulation being unfocused, and to better understand the distribution of the induced current in a nonhomogeneous medium, a computer model of the head is proposed. The model was realized on the basis of discretized transverse head sections obtained by magnetic resonance imaging (MRI) of a normal subject (figure 1) on which it is possible to estimate the distribution and intensity of the current induced by a magnetic pulse, also taking into account the different conductivities corresponding to the tissues [ 15,161. The transverse section located 38 mm from the top of the head was chosen for our model. This is of particular interest in neurophysiology because it crosses the hand motor area, which is the target point of activation. Different positions, orientation and shape of the coil were successively tested and a three-dimensional model is proposed. The values of charge per phase and of energy dissipated in different parts of the brain are estimated and used as indexes to determine the exact value of current across an area able to activate the brain without any damage. These results have also been compared with those obtained by transcranial electric stimulation.

Methods Discretized model Sequential transverse sections of the head derived from MRI of a normal subject were performed. I49

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0 199” Taylor & Francis Lid

R. De Leo

et al. Computer modelling of brain cortex excitation

resenting the transverse head section 38 mm from the scalp, is shown. By discretizing equations ( 1 ) and ( 2 ) and considering a constant electric field for each cell side, the following equations are obtained:

aHz Ei = - pot

at

for all meshes

(4)

i

oiEi = 0

for all independent nodes ( 5 )

I

e is the dimension of a cell.

where

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In equation (4) the magnetic field component H, is the only component considered, because in the coordinate system adopted the section of the head lies in a plane parallel to the x-- plane. In this way the integro-differential equations ( 1 ) and (2) are converted into a linear system of order N ( N + 1 being equal to the sum of meshes and nodes) where the unknowns are represented by the electric field in each side of the cells and the known terms are represented by the electromotive force induced in each cell by the external magnetic field (right-hand side of equation (4)). Magnetic Jield

In equation (4) H, is the magnetic field produced by a coil along the z-axis and it has been evaluated in a standard way by the magnetic vector potential A: p$=VXA (6) is due to the current I flowing along the coil:

Figure 1. Discretized model of the transverse head section 38 mm from the scalp derived from MRI of a normal subject. The same section is considered in the following simulations.

where

The images were discretized in squared cells of 4 mm and the value of conductivity of the relevant tissue (table 1) [ 171 was assigned to each cell. The following equations were applied:

where F' indicates a source point and 7 a field point; the line integral (7) is performed along the coil perimeter

A

0

CI.

The expressions of Hp and He for a circular coil of radius a and lying in the 8 = l ~ I 2plane, in a spherical coordinate system centred at the centre of the coil, are respectively: where E, H a n d 3 are electric field, magnetic field and current density respectively; p is the volume charge density; t is the time and po is magnetic permeability of free space, C, is the line contour of the surface S and V is a volume enclosed by the surface Sv. Time-dependence of electric charge is neglected because of the low maximum frequency (10 kHz) of the pulse spectrum, thus equation ( 2 ) simplifies to: r

fsJ;i;=O

KYr,%+)

0

+ cos + d+

la 4lTr

He(r,8) = - -

(9)

2m

I 0

J?(r,O,+)-r(r-asin

8 cos +)

K%,%+)

cos

+ d+

where:

Moreover

j= u ( ~ E

(3)

where a(:) is the appropriate conductivity of tissue. In figure 1 our discretized bidimensional model, rep150

i

J?(r,O,+)cos B+ra sin 8 cos 8 cos

q r , e , + )= d/12+a2-2ra

sin e cos

+

(10)

In equations (8) and (9) the current I has been considered constant along the coil. Therefore, H, = H,, cos 8 He sin 8

+

R. De Leo et id. Computer modelling of brain cortex excitation Table I . Condtutivio values (mho/m) of the different head tissues

Figure 3 shows the current distribution in the chosen section as described in figure 1 produced by a single magnetic pulse delivered at 70% of maximum intensity by the coil positioned flat on the vertex area. This intensity was adequate in a clinical application, to evoke clear compound muscle action potentials in the upper limbs of the subject. The current shows a diffuse distribution and its higher values occur on a circle approximately with the same mean diameter as the stimulating coil.

00 1 0133 0.4 0.778

Skull

White matter Grey matter Skin

Cerebrospinal 1.538

fluid

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Computer code

The computer code is written in Fortran 77 and implemented for use on a pVax 3600. The sparse matrix system has been solved by using NAG subroutines (NAG FOlBRF-NAG F04AXF). I n this way the time for a linear system solution is a function of the nonzero elements ( n ) of the coefficient matrix: 5 CPUti,, = - k n2 2kn (1 1) N

The maximum value of the current density, 26.3 mA/cm' (black regions in figure 3) is found mostly in the motor cortex. This current value for this area has been used as a reference value in the following simulated configurations, where it is always obtained indepen-

+

where k is a constant depending on the used computer. The magnetic field has been evaluated by approximate analytical solutions when possible, or numerical integration by means of NAG DOlANF subroutine. The whole simulation requires a CPU time of about 10 min.

Results The magnetic stimulator considered in this simulation is a Novametrix Mag-Stim 200 model, with a coil of 19 turns, inner diameter 5.6 cm and outer diameter of 12 cm; it can deliver a peak current of 5500 A as a maximum for each pulse. The magnetic field intensity can be selected in percentage. Results reported in the present paper are referred to an external magnetic flux density, whose intensity as a function of time has been experimentally determined. The pulse is characterized by a rise time of about 100 ps and life time of about 2 ms as shown in figure 2. 1.5

I

i

0 0

1

msec Figure 2. Magnetic Jrux density pulse.

2

Figure 3. Current distribution obtained by magnetic stimulation with the coil disposed jkzt over the vertex area; J,,, = 26.3 m A / m 2 obtained b~ a magnetic pulse intensity of 70%. This value evoked compound muscle action potentials in the upper limbs.

151

R. De Leo et al. Computer modelling of brain cortex excitation

dently from the changing intensity and characteristics of the sources. The disadvantage of a diffuse current distribution as described in the previous example is avoided by a different coil orientation. Figure 4 shows the current distribution in the case of a coil disposed perpendicularly over the lateral frontal area and lying in the same plane of the head section. In this case only a small area of brain cortex corresponding to the frontal lobe is affected by the current flow.

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In figure 5 the current distribution produced by an electric stimulation is shown. The cathode and anode are disposed respectively on the middle front and the

Figure 5. Current distribution obtained by electric transcranial stimulation; black arrows indicate the position of the electrodes: cathode on the middle front and anode on the lateral frontal area. A voltage of 600 V is needed to obtain approximately the same value of current in the motor cortex. lateral frontal area. A high voltage (-6OOV) must be applied in order to achieve in the motor cortex the same values of current obtained by magnetic stimulation. This value must be adopted because of the high resistance of the skull, and it generally produces great discomfort for the patient because cutaneous pain receptors are strongly activated by the high current flowing in the skin.

Figure 4. Current distribution obtained by magnetic stimulation with the coil placed perpendicularly on the lateral frontal area and lying in the same plane of the considered section. I n this case the percentage of magneticjkld intensity must be 3.1 times higher than in the previous example to produce the same current in the motor cortex. 152

Following a successful clinical attempt [ 181 a combined electric and magnetic stimulation was simulated (figure 6). This technique overcomes the limitations resulting from the magnetic stimulation being unfocused and the electric stimulation being painful. In this example the combined magneto-electric stimulation, inducing the

R. De Leo et al. Computer modelling

of brain cortex excitation

same current in the motor area, is produced by electric and magnetic stimuli, each of half the amplitude that is required when used separately.

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Furthermore, the model proposed is capable of estimating the induced current by whatever coil configuration. An example of the current induced by a coil composed of two loops where the current flows in opposite directions is shown in figure 7. This condition provides a doubling of the current focused in the space where the two loops are closer. In clinical application a similar design has shown better focusing of the stimulus with better selectivity of the response [2].

Figure 7. Current distribution obtained by an ‘eight-shaped’ coil.

Safety aspects

[fly1 Figure 6. Current distribution obtained by combined magnetoelectric stimulation; the coil is disposed on the vertex and the electrodes are placed as in jigure 5. The value adopted f o r each modalig is approximately halfof the in/ensip applied f o r single magnetic or electric stimulation.

In the literature only theoretical models and a few animal studies are available to assist in establishing the stimulus parameters capable of inducing excitation of the motor cortex and the threshold for brain damage [ 19,201. These data cannot be transferred automatically to humans because they are often obtained using different procedures and without considering the morphological head. and physiological characteristics of the human The present model, which reproduces a real anatomical structure of the head, enables one to establish the maximum values of induced electrical field, current density, charge per phase (charge displaced by the current during a pulse) and energy dissipated per pulse for each discretized cell. 153

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The data obtained by a magnetic pulse as simulated in the model of figure 3 and corresponding to the highest values in the considered brain section (figure 8), are compared in table 2 with the values calculated in a simple model by Barker [l]. These results, especially for current density and charge per phase, are much lower in respect of those considered dangerous in previous animal studies [21]. If it is assumed that all cells dissipate as the most conductive cell, a maximum value of power dissipation of 3 mW is obtained. This value is considerably below the 13 W of cerebral metabolic power [22].

Extension to three-dimensional models

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This methodology can be extended to a three-dimensional model. In particular, equation (4) becomes:

while node equations are the same as in equation (5). It is noteworthy that the number of independent equations in the three-dimensional system is given by the sum of

1. node number minus one; 2. number of all independent meshes in two orthogonal directions; 3. number of mesh equations in only one plane in the third direction. However, the memory requirement and the computer

Current density (mNcm2)

Charge density per phase (pC/cm*)

Energy dissipation per pulse (pJkm3)

Figure 8. Selected area corresponding approximately to the motor cortex and relative values of the electric parameters used f o r saf e p considerations. I54

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Table .?a. Homogeneous brain model (Barker et al. [I])

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Stimulator characteristic

25

Value

Mean stimulating coil diameter Stimulator figure of merit Pulse rise time

90 mm F = 195"' 140 ps

Quantity

Maximum value

Electric field Current density Charge density per phase Energy dissipation per pulse Maximum temperature rise

2.6 V/cm 9.1 mA/cm' 0.8 pC/cm' 1.8 pJ/cm3

Computer modelling of brain cortex excitation by magnetic field pulses.

In spite of many clinical and experimental applications, the technique of transcranial magnetic stimulation still presents obscure aspects. This espec...
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