IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 20, NO. 3, JUNE 2010 829

Circular Coil Array Model for Transcranial MagneticStimulation

Shuo Yang, Guizhi Xu, Lei Wang, Yaohua Geng, Hongli Yu, and Qingxin Yang

Abstract—Transcranial magnetic stimulation (TMS) is anintriguing technology for investigating functions in the brain.Magnetic coil in transcranial magnetic stimulation devices canproduce brief, strong magnetic pulses to induce electric fields inthe brain which modulate neural activity. Stimulation intensity,field attenuation in depth and focality are the keys of efficientfunctional magnetic stimulations. In this paper, three coil config-urations are analysed: circular coil, eight-figure coil and circularcoil array. The results show circular coil array has significantlylarger stimulation intensity compared to conventional circularcoil. The magnetic field attenuation in depth of circular coil arrayis the lowest one in the three kinds of coils.

Index Terms—Eddy current, finite element method, magneticfield, transcranial magnetic stimulation.

I. INTRODUCTION

T RANSCRANIAL magnetic stimulation (TMS) is a pow-erful, non-invasive tool for investigating functions in the

brain. TMS is produced by passing a brief, high current electricpulse through an insulated coil over the scalp. This pulse inducesa rapidly changing magnetic field which in turn induces an elec-tric field in the underlying brain tissue. If the amplitude, dura-tion and direction are appropriate, this electric field can depo-larize cortical neurons and generate action potentials [1]. Whenthe current is applied repetitively, repetitive transcranial mag-netic stimulation (rTMS), it can modulate cortical excitability,decreasing or increasing it, depending on the parameters of stim-ulation [2]. This technique is proved to have potential applica-tion as a diagnostic and therapeutic tool of neuropsychiatric dis-eases and provides a unique opportunity of studying brain be-havior relations in normal humans [3].

TMS has grown dramatically in popularity since its initialdemonstration by Barker, et al., in Sheffield, England, in 1985.

Manuscript received October 18, 2009. First published March 29, 2010; cur-rent version published May 28, 2010. This work was supported by the Nat-ural Science Foundation of China under Grant 50877023, the Natural ScienceFoundation of Hebei Province, China, under Grant E2009000049 and GrantE2008000053.

S. Yang, G. Xu, L. Wang, H. Yu, and Y. Geng are with Province-Ministry JointKey Laboratory of Electromagnetic Field and Electrical Apparatus Reliability,Hebei University of Technology, Tianjin 300130, China.

Q. Yang is with Province-Ministry Joint Key Laboratory of ElectromagneticField and Electrical Apparatus Reliability, Hebei University of Technology,Tianjin 300130, China and also with Tianjin Polytechnic University, Tianjin300160, China (e-mail: sureyang@126.com).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TASC.2010.2040379

Today TMS has been used in several applications in medicaland clinical research which include brain mapping, treatment ofmood disorder and schizophrenia, treatment of epilepsy, treat-ment of chronic pain and so on [4], [5]. TMS is combined withfunctional brain imaging techniques such as fMRI (functionalmagnetic resonance imaging), PET (positron emission tomog-raphy) and EEG to study the dynamics of human brain [6].RTMS with rapid trains of stimuli can produce long-lasting ther-apeutic effects in the treatment of depression, Parkinson’s dis-ease, and pain states. Recent work suggests [7] that efficacy maybe enhanced through optimization of rTMS dosing paradigms.For example, increased pulse intensity has been associated withimproved antidepressant efficacy [8].

In this study, a three-dimensional realistic head model duringTMS is built. Using Finite Element Method (FEM), magneticfield distributions and eddy currents induced by the coils in threeconfigurations (circular coil, eight-figure coil and circular coilarray) have been analysed. The performance of each model isassessed by comparing the distribution of magnetic field, stim-ulation intensity and decay with depth. This work may proveuseful in optimizing coil placement and orientation in order tostimulate a given target region in brain.

II. MATHEMATIC MODEL IN TMS

In TMS, excitation is achieved by driving intense pulses ofcurrent through a coil located above the head. The typ-ical pulse lasting time is about hundreds of microseconds, so thefrequency used in TMS is 1–10 kHz. The biological tissue per-mittivity is about . The biological tissue resistivity isabout 1 S/m. In this condition, displacement current can be ne-glected and Ampere circuital theorem can be written as:

(1)

where is current density. The activation source is the electricfield induced in the tissues, obtained from Faraday’s law:

(2)

The tissue material properties are:

(3)

where is reluctivity. According to:

(4)

and

(5)

1051-8223/$26.00 © 2010 IEEE

830 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 20, NO. 3, JUNE 2010

where is magnetic vector potential, there is

(6)

Using electric scalar potential , (6) can also be expressed as:

(7)

Current density,

(8)

is current density applied outside. The induced currentdensity satisfies the Ohm’s Law:

(9)

The total is:

(10)

or

(11)

For

(12)

we have

(13)

The boundary condition satisfies:

(14)

(15)

III. STIMULATION MODEL USED IN FEM

Both the geometries and the tissue properties of human headare complex. Analytical modeling of such a problem is verydifficult. Therefore, this problem is often solved numericallyrather than analytically using finite-element approximations,which necessitate a finite-element model of geometrical andstructural characteristics similar to realistic human head [9].Therefore, we developed a 3D realistic head model from MRIpictures using image process and reconstruction technique. Themodel consists of scalp, skull, cerebrospinal fluid (CSF) andbrain. Tetrahedron element is used to mesh the head model. Andwe get 315190 tetrahedron elements. The electrical propertiesof encephalic tissues used in this calculation are provided byStok in 1986 [10]. The relative permeability of the four kindsof tissues all are 1. The conductivity of scalp, skull, CSF andbrain are 0.33 S/m, 0.0042 S/m, 1 S/m, 0.33 S/m, respectively.

The traditional coils used in transcranial magnetic stimulatorare circular coil and eight-figure coil. In this paper, the circularcoil model is a coil with a loop diameter of 4.50 cm and six

Fig. 1. Circular coil model.

Fig. 2. Eight-figure coil model.

Fig. 3. Circular coil array model.

turns, which is shown in Fig. 1. The eight-figure coil consists ofdouble circular coils, which is shown in Fig. 2.

The induced magnetic field of a circular coil reaches max-imum approximately under the mean diameter. The field atten-uation in depth of circular coil is lower than that of eight-figurecoil [11]. But the stimulation intensity of circular coil is smallerthan that of eight-figure coil. So a circular coil array is proposed.Circular coil array is composed of seven circular coils, each ofwhich is six turns and 4.50 cm wide (shown in Fig. 3).

The coil of transcranial magnetic stimulator is powered bythe transient current (Fig. 4.) produced by the RLC circuit. Inthis simulation, the transient current is applied by the method ofload step which is a configuration of loads for which a solutionis obtained. The transient current is specified ramped, that is,excitation amplitude is gradually increased with each substep.In this paper, the excitation current from zero to the first max-imum is divided into ten substeps. The results given below iscalculated when the third substep is applied.

IV. RESULTS

The coordinate systems of three kinds of coils are shown inFig. 5.

The excitation current applied in circular coil is supposed an-ticlockwise. The excitation current applied in eight-figure coilis supposed that the current in one coil is anticlockwise and thecurrent in the other coil is clockwise. The excitation current ap-plied in circular coil array is that the current in the center coil

YANG et al.: CIRCULAR COIL ARRAY MODEL FOR TRANSCRANIAL MAGNETIC STIMULATION 831

Fig. 4. Coil input current in the RLC circuit.

Fig. 5. Coordinate system. (a) Circular coil (b) Eight-figure coil (c) Circularcoil array.

Fig. 6. Magnetic flux density radial distribution during magnetic stimulation.

is clockwise and the current in the other coils are all anticlock-wise. The current intensity applied in each coil in eight-figurecoil and circular coil array is the same to the circular coil.

The radial magnetic flux density distribution in the circularcoil, eight-figure coil and circular coil array are shown in Fig. 6.Fig. 6 shows that the shape of magnetic field distribution pro-duced by the circular coil array is very similar to that producedby circular coil. But the magnitude of the magnetic flux densityproduced by the circular coil array is obviously higher than thatproduced by the circular coil.

The axial direction is axis-z which is at right angles to xoylevel ground. Zero point of axis-z is at the surface of parietallobe scalp. The axial magnetic flux density distribution in thecircular coil, eight-figure coil and circular coil array are shownin Fig. 7.

The attenuation rate of magnetic field in depth (axial distance)is calculated by:

Fig. 7. Magnetic flux density axial distribution (z) during magnetic stimulation.

Fig. 8. Eddy current density induced by circular coil on the scalp during mag-netic stimulation.

Fig. 9. Eddy current density induced by eight-figure coil on the scalp duringmagnetic stimulation.

(16)

where is the magnetic flux density at the point thataxial distance is 0.085 m. is the magnetic flux densityat the point that axial distance is zero. The attenuation rate ofcircular coil, eight-figure coil and circular coil array is1.88%,0.72% and 2.68%, respectively. The magnetic field attenuationin depth of the circular coil array is lowest. The magnetic fieldattenuation in depth of the eight-figure coil is highest.

The eddy current density induced by circular coil, eight-figurecoil and circular coil array on the scalp are gotten which areillustrated in Figs. 8, 9, and 10, respectively. The coil positionsare shown in Figs. 1, 2, and 3.

The maximum of the eddy current density induced by circularcoil is approximately under the coil boundary. And the eddy cur-rent density induced by circular coil array reaches the maximumapproximately under the center circular coil boundary. On the

832 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 20, NO. 3, JUNE 2010

Fig. 10. Eddy current density induced by circular coil array on the scalp duringmagnetic stimulation.

Fig. 11. Eddy current density induced by circular coil on the brain during mag-netic stimulation.

Fig. 12. Eddy current density induced by eight-figure coil on the brain duringmagnetic stimulation.

Fig. 13. Eddy current density induced by circular coil array on the brain duringmagnetic stimulation.

scalp, as against the circular coil, the maximal eddy current den-sity of circular coil array increases by 7.967 . The increaseis about 60.39% of the eddy current density induced by circularcoil.

The eddy current density induced by circular coil and cir-cular coil array on the brain are gotten which are illustrated inFigs. 11, 12, and 13.

On the brain surface, as against the circular coil, the maximaleddy current density of circular coil array increases by 1.146

. The increase is about 19.89% of the eddy current densityinduced by circular coil.

V. CONCLUSIONS AND DISCUSSION

This paper performs a study about magnetic field and eddycurrent distribution produced by three types of coils (circularcoil, eight-figure coil and circular coil array) on the head duringTMS. In order to get precise simulation results, the three-dimen-sional realistic head model from MRI is created. The magneticfield and eddy current distribution is solved by FEM.

The stimulation intensity of circular coil is smaller than thatof eight-figure coil. But the field attenuation in depth of eight-figure coil is higher than that of circular coil. The magnetic fielddistribution tendency of circular coil array is similar to the cir-cular coil. The stimulation intensity of the circular coil arrayis bigger than that of circular coil. And the field attenuation indepth of circular coil array is the lowest in the three kinds ofcoils.

Recent work suggests that TMS efficacy may be enhancedthrough optimization of TMS dosing paradigms. Big stimula-tion intensity at target tissues is what the clinical trials need.In deep-brain stimulation, the low field attenuation in depth isalso needed in order to get good stimulation intensity at deeptarget tissues [7]. But neuronal stimulation in the motor cortexis estimated to occur at a depth of approximately 2 cm from thesurface of the scalp [12], [13]. Fig. 7 shows the magnetic fluxdensity produced by the circular coil array is bigger than by thecircular coil within 2.5 cm below the array (axial distance inFig. 7. is from 0 to 0.025 m). These suggest that the circularcoil can be used in deep-brain stimulation. But the focality ofcircular coil is not as good as that of eight-figure coil. In orderto improve the focality, a conductive shield plate [14] can beused under the circular coil array, which will be explored in ourfuture work.

In our next optimization design of TMS coils, the heat gen-eration of coils would be taken into account. During TMS, thecoils generate a lot of heat which could affect the duration andfrequency of repetitive stimulation. Superconducting coil wouldbe helpful to reduce the heat generation.

REFERENCES

[1] M. De Lucia, G. J. M. Parker, K. Embleton, J. M. Newton, and V.Walsh, “Diffusion tensor MRI-based estimation of the influence ofbrain tissue anisotropy on the effects of transcranial magnetic stimula-tion,” NeuroImage, vol. 36, pp. 1159–1170, 2007.

[2] T. Wagner, U. Eden, F. Fregni, A. Valero-Cabre, C. Ramos-Estebanez,V. Pronio-Stelluto, A. Grodzinsky, M. Zahn, and A. Pascual-Leone,“Transcranial magnetic stimulation and brain atrophy: A computer-based human brain model study,” Exp Brain Res, vol. 186, pp. 539–550,2008.

[3] Y. F. Low, K. Schwerdtfeger, A. R. Harris, and D. J. Strauss, “An in-vestigation on the effects of single pulse transcranial magnetic stimula-tion in a modified maximum entropy auditory stimulation paradigm,” inProc. 31st Annual International Conference of the IEEE EMBS, Min-neapolis, 2009, pp. 678–681.

[4] S. Luquet, V. Barra, and J. J. Lemaire, “Transcranial magnetic stim-ulation: Magnetic field computation in empty free space,” in Proc. ofthe 2005 IEEE Engineering in Medicine and Biology 27th Annu. Conf.,Shang Hai, 2005.

[5] J. Ruohonen, P. Ravazzani, J. Nilsson, M. Panizza, F. Grandori, andG. Tognola, “A volume-conduction analysis of magnetic stimulationof peripheral nerves,” IEEE Trans. Biomedical Engineering, vol. 43,pp. 669–678, 1996.

[6] M. Iwahashi, Y. Katayama, S. Ueno, and K. Iramina, “Effect of tran-scranial magnetic stimulation on P300 of event-related potential,” inProc. 31st Annual International Conference of the IEEE EMBS, Min-neapolis, 2009, pp. 1359–1362.

YANG et al.: CIRCULAR COIL ARRAY MODEL FOR TRANSCRANIAL MAGNETIC STIMULATION 833

[7] Z.-D. Deng, A. V. Peterchev, and S. H. Lisanby, “Coil design consider-ations for Deep-Brain Transcranial Magnetic Stimulation (dTMS),” inProc. 30th Annual International IEEE EMBS Conference, Vancouver,2008, pp. 5675–5679.

[8] M. Gross, L. Nakamura, A. Pascual-Leone, and F. Fregni, “Has repeti-tive transcranial magnetic stimulation (rTMS) treatment for depressionimproved? A systematic review and meta-analysis comparing the re-cent vs. the earlier rTMS studies,” Acta Psychiatr Scand, vol. 116, pp.165–173, 2007.

[9] G. Xu, Q. Yang, S. Yang, F. Liu, and W. Yan, “Electrical characteristicsof real head model based on electrical impedance tomography,” IEEETrans. Applied Superconductivity, vol. 14, pp. 1617–1620, 2004.

[10] C. J. Stok, “The Inverse Problem in EEG and MEG With Applica-tion to the Visual Evoked Responses,” Ph.D. dissertation, Universityof Twente, , Netherlands, 1986.

[11] S. Yang, G. Xu, L. Wang, D. Geng, and Q. Yang, “Electromagnetic fieldsimulation of 3D realistic head model during transcranial magneticstimulation,” in Proc. of the 1st International Conference on Bioinfor-matics and Biomedical Engineering, Wuhan, 2007, pp. 668–671.

[12] C. M. Epstein, D. G. Schwartzberg, K. R. Davey, and D. B. Sudderth,“Localizing the site of magnetic brain stimulation in humans,” Neu-rology, vol. 40, pp. 666–670, 1990.

[13] D. Rudiak and E. Marg, “Finding the depth of magnetic brain stim-ulation: A re-evaluation,” Electroenceph Clin Neurophys, vol. 93, pp.358–371, 1994.

[14] D.-H. Kim, G. E. Georghiou, and C. Won, “Improved field localizationin transcranial magnetic stimulation of the brain with the utilization ofa conductive shield plate in the stimulator,” IEEE Trans. BiomedicalEngineering, vol. 53, pp. 720–725, 2006.