computation of electric and magnetic stimulation in human head using the 3-d impedance method

900 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 50, NO. 7, JULY 2003

Computation of Electric and Magnetic Stimulation inHuman Head Using the 3-D Impedance Method

Mohammad Nadeem*, Thorleif Thorlin, Om P. Gandhi, Life Fellow, IEEE, and Mikael Persson

Abstract—A comparative, computational study of the modelingof transcranial magnetic stimulation (TMS) and electroconvulsivetherapy (ECT) is presented using a human head model. The mag-netic fields from a typical TMS coil of figure-eight type is modeledusing the Biot–Savart law. The TMS coil is placed in a position usedclinically for treatment of depression. Induced current densitiesand electric field distributions are calculated in the model using theimpedance method. The calculations are made using driving cur-rents and wave forms typical in the clinical setting. The obtainedresults are compared and contrasted with the corresponding ECTresults. In the ECT case, a uniform current density is injected onone side of the head and extracted from the equal area on the op-posite side of the head. The area of the injected currents corre-sponds to the electrode placement used in the clinic. The currentsand electric fields, thus, produced within the model are computedusing the same three-dimensional impedance method as used forthe TMS case. The ECT calculations are made using currents andwave forms typical in the clinic. The electrical tissue propertiesare obtained from a 4-Cole-Cole model. The numerical results ob-tained are shown on a two-dimenaional cross section of the model.In this study, we find that the current densities and electric fieldsin the ECT case are stronger and deeper penetrating than the cor-responding TMS quantities but both methods show biologically in-teresting current levels deep inside the brain.

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I. INTRODUCTION

UNTIL a few years ago the prevailing dogma in neuro-science stated that no neurons could be created in the brain

after the developmental period. We now know that this is nottrue, and the birth of new neurons from neuronal stem cells, aprocess called neurogenesis, have been seen in adult brains fromboth rodents and humans [1], [2]. The search for ways to con-trol and stimulate this inherent ability of the brain to producenew nerve cells is intense, as a stimulated neurogenesis has thepotential to become a very useful therapeutic tool in the future.In sight are possibilities to create therapies where new neuronal

Manuscript received August 19, 2002; revised January 11, 2002. The work ofT. Thorlin was supported in part by the Swedish Society for Medical Research.Asterisk indicates corresponding author.

*M. Nadeem is with the Department of Electromagnetics, Chalmers Univer-sity of Technology, 65 Merkuriusgatan, Bersjon, S-41296 Gothenburg, Sweden(e-mail: [email protected]).

T. Thorlin is with the Institute of Clinical Neuroscience, Gothenburg Univer-sity, S-41345 Gothenburg, Sweden.

O. P. Gandhi is with the Department of Electrical Engineering, University ofUtah, Salt Lake City, UT 84112-9206 USA.

M. Persson is with the Department of Electromagnetics, Chalmers Universityof Technology, Bersjon, S-41296 Gothenburg, Sweden.

Digital Object Identifier 10.1109/TBME.2003.813548

cells can replace cells that have succumbed during injury or dis-ease. The problem now is how to achieve this goal in a way thatis efficient but without the risk of producing severe side effects.The main motivation for the present project is a new hypothesisthat endogenous neurogenesis can be stimulated by externallyinduced currents. Recently, it has been shown that one of themost powerful ways to stimulate neurogenesis in the rat brainis by electro convulsive therapy (ECT) [5]–[7]. In addition, arecent model for the development of depression in humans hasbeen formed over the last years, which includes neurogenesis asa factor of importance in the depressive disease [8]. This lattertheory is based in part on findings that specific brain regionshave decreased volumes during depression, and that antidepres-sive treatments such as ECT increase neurogenesis in these sameareas. During the last five years an alternative to ECT as an-tidepressive therapy has been developed. It is called transcra-nial magnetic stimulation (TMS). It uses the physical principleof induced electrical currents in the brain by applied externalmagnetic fields, and the method has been proven to have sim-ilar antidepressive effects as classical ECT [9], [10]. However,TMS has substantial advantages over ECT; it is painless and canbe given to an awake patient, eliminating the need for anesthesianecessary in ECT treatment, and TMS is not afflicted with thebad reputation ECT unjustly has amongs the public, making theuse of ECT sometimes difficult. In a broader perspective, thisnewly discovered ability of electric currents to induce neuroge-nesis in the brain is interesting since these methods can be usedin the treatment of the different neurological disorders whereincreased neurogenesis is considered to be beneficial, such asParkinson’s and Alzheimer’s diseases, stroke and depression.Also, the method might have relevance in improving the sur-vival and differentiation of transplanted stem cells in the brain.The cost of neurological diseases to society is staggering, andthe overall goal of this paper is to improve treatment for severedepressions and degenerative neurological diseases. The cost toSwedish society for depression alone was in 1996 estimated tobe about 9.3% of the total health budget [3].

The specific goal of our study is, therefore, to compareand contrast induced currents in ECT and TMS in order todevelop methods and tools to clinically control the magneticallyinduced currents to specific regions of the brain. Saypolet al.[4] investigated theoretically the characteristics of the electricfield produced during electric and magnetic stimulation of thebrain using a three-layer spherical head model. In this paper,we present results of a computational study carried out onTMS and ECT stimulation in a three-dimensional (3-D) humanhead model. Numerical results of the distribution of electricfields and current densities are presented. We have modeled a

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NADEEM et al.: COMPUTATION OF ELECTRIC AND MAGNETIC STIMULATION IN HUMAN HEAD USING THE 3-D IMPEDANCE METHOD 901

Fig. 1. The human head model used.

typical TMS coil of figure-eight type. The magnetic field ofthe coil is calculated using the Biot–Savart’s law with the coilplaced at the clinically relevant position on the head. Usingpatient-related currents in the coils, pulse forms, and pulsewidths, induced current densities and electric field distributionsare calculated using the 3-D impedance method [11], [15],[16]. These results are then compared and contrasted with thecorresponding ECT calculation. Here, a uniform current densityis injected at one side of the head model and extracted from theopposite side, again using typically used values for amplitude,wave form, and pulse widths. The numerical results obtainedboth in TMS and ECT cases are shown on a cross section ofthe 3-D model. We find that for the conditions studied, inducedcurrent and electric field in TMS is considerably weakerand less penetrating than the corresponding results for ECT.However, the TMS electric fields deeper in the brain are still inthe range of biologic effects on the cellular level. The detailedspatial resolution of the model enables mapping of fields andcurrents in different brain regions of interest, and can be usedfor future modeling of TMS coils and stimulating parameters.

The remainder of the paper is organized as follows: In Sec-tion II, the virtual model used in the present study and the cal-culation of electrical tissue properties is discussed. The numer-ical method used to calculate the current and electric field inthe model is described in Section III. Sections IV and V are de-voted to the TMS and ECT calculations and presentation of thenumerical results. The paper is concluded in Section VI.

II. THE MODEL

In this paper, we have used a fully 3-D human head modelobtained from Brooks Air Force Laboratory, (Brooks Air Force,TX)1 shown in Fig. 1. The model is based on anatomical slices

1[Online]. Available: www.brooks.af.mil/AFRL/HED/hedr/reports/dielec-tric/Report/Report.html

TABLE ITHE TISSUE PROPERTIESUSED FOR THE

CALCULATION

from a male cadaver and were originally obtained from the vi-sual Human Project2

The head model consists of 24 tissues which are listed inTable I. The brain consist of eight tissues: CSF, gray matter,blood, cerebellum, ligament, white matter, nerve/spine, andglands.

The electrical properties, obtained from the Brooks AirForce Laboratory database3 [12]–[14], are modeled usingthe 4-Cole-Cole model [17]. The tissue conductivities, thusobtained and used in this paper, are as given in Table I.

III. T HE NUMERICAL METHOD

For the calculations of induced current and electric field in thehuman head model, we used a 3-D impedance method [11], [15],[16]. The model is described using a uniform 3-D Cartesian gridand is composed of small cubical cells or voxels. Assuming that,in each cell, the electric conductivities are isotropic and constantin all direction, the model is considered as a 3-D resistance net-work of impedances. Kirchoff voltage law around each loop inthis network generates a system of equations for the loop cur-rents. In the case of magnetic stimulation, these loop currentsare driven by Faraday induction from the magnetic field of theapplicator. In the ECT case, the currents are injected at the elec-trodes and then distributed according to the Kirchoff laws. Thissystem of equations is solved numerically using the standard it-erative method of successive-over-relaxation. The net inducedcurrents within the body are then calculated from these known

2[Online]. Available: www.nlm.nih.gov/research/visible/visible\_human.html

3[Online]. Available: www.brooks.af.mil/AFRL/HED/hedr/reports/dielec-tric/Report/Report.html



loop currents. The induced electric field is in turn calculatedfrom the net induced currents using Ohm’s law.

It can be noted that the skin-air interface is naturally resolvedusing the impedance method which inherently imposed theboundary condition that the current flow across this boundaryis zero as air conductivity is zero.

IV. TRANSCRANIAL MAGNETIC STIMULATION (TMS)

One of the applicators commonly used for TMS is a figure-eight-shaped coil that is manually moved above the target untilthe desired response is achieved. We have modeled the appli-cator coil MC-B70 manufactured by Medtronic NeuroMuscular(Skovlunde, Denmark). The coil is placed in 3-D space at thepoint and oriented along the– plane withwings along the axis, and that the centers of the wings are atpoints , where cm is thedistance of the wing center from the center of the coil .The wings are at angle downward around the lines

, where cm is the inner radiusof the circular wings. The outer radii of the wings arecm and the number of wire turns in each wing is . Thecoil wings are then given by

Here, is the coil wire parameter, is theinitial phase, and is the wire position vector at point. Dividing this parameter domain in to small subintervals

defined by , the coil wire is divided into small length elements whose position vectorsare calculated using the above equation. This set of vectorsdescribes the coil geometry in the– plane. The part of thisset of geometry points that lies beyond the coil wing bendinglines is transformed for eachwing into a plane obtained by rotating the– plane about therespective lines through angle using the following3-D rotation matrix:

The connecting wire geometry points are then added manuallyinto the set of coil geometry points . The total wirelength of the coil is m. The coil, thus, obtained isas shown in Fig. 2.

Note that the coil is constructed in such a way that the endpoint of one wing is connected to the starting point of the otherso that both wings are connected in series and form one contin-uous current path.

The amplitude of the current in the TMS coil is kAwhich is in the range of typical values used in clinical settings.

(a)

(b)

Fig. 2. (a) Simulated figure-eight coil (MC-B70) in 3-D space and (b) itsmagnetic fieldjBj versusx (lower/upper solid curve: 2 mm above/below thesurface of the coil, lower/upper dashed curve: 20 mm above/10 mm below,dashed-dotted curve: 5 mm below).

The magnetic field is then calculated using the Biot–Savart’slaw



(a)

(b)

Fig. 3. (a) Normalized currentI versus timet in the TMS coil and (b) itsFourier spectrumF [I(t)].

Fig. 4. The TMS applicator placed on the human head.

where , ,, and .

The magnetic field of the simulated figure-eight coil, calculatednumerically, is shown in Fig. 2.

A. Wave Form

Following a typical clinical procedure we use the current am-plitude kA in the TMS coil. The time variation of the

(a)

(b)

Fig. 5. (a) The variation ofjJj and (b)jEj on cross sectiony = 0:075 of thehuman head in the TMS case.

normalized coil current is one period of 3.6-kHz sine wavewith repetition frequency of 20 Hz as shown in Fig. 3.

B. Numerical Results

The TMS applicator is placed on the surface of the humanhead model as shown in Fig. 4.

The induced current density and electric field is calcu-lated using the impedance method as described in Section III.The numerical results, thus, obtained are shown in Fig. 5.

The magnitude of the induced current densityis propor-tional to the frequency, the amplitude of the magnetic field, and



Fig. 6. The ECT electrodes indicated on the human head.

the tissue conductivity. It is also expected to increase with in-creasing model size since larger structures can confine largermagnetic flux.

The maximum induced current densityin the head is inthe range 30–130 A/m, and is produced in tissues cerebralspinal fluid, muscle, and ligament, which have considerablyhigher conductivities than other tissues except blood. The in-duced current magnitude decreases rapidly away from the coilsurface due to decay in magnitude of the magnetic field. Thecorresponding induced electric fieldshave maximum values0.25–50.70 kV/m produced in bone marrow near the coil sur-face.

V. ELECTROCONVULSIVETHERAPY (ECT)

During ECT treatment in the clinic electric currents arepassed between two electrodes on the head of an anesthetizedpatient. In this study, two 13 ECT electrodes are placed onthe head model in the most commonly used bilateral position,as indicated in Fig. 6.

In Fig. 6, the horizontal and vertical parts of the cross indi-cates the width and height of the electrode plates, respectively.We injected a total current 0.9 from right in the direction ofthe blue arrow uniformly distributed over a square area of 13

, and extracted similarly the same current on the oppositeside.

A. Wave Form

The time variation of the normalized current in the ECTapplicator is a square pulse of width 0.25 with repetitionfrequency 70 as shown in Fig. 7

B. Numerical Results

Employing the same method as used for the TMS calcula-tions, the current density and electric field distributions in the

(a)

(b)

Fig. 7. (a) Normalized currentI versus timet in the ECT applicator and (b)its Fourier spectrumF [I(t)].

head model were calculated in a simulation of ECT. The calcu-lated current density and electric field distributions are shownin Fig. 8.

In the human head cross-section, , shown in Fig. 8,the maximum current density is in the range 140–570 A/mand is obtained inmuscleand CSF. The maximum electric field

is in the range 1.6–80 and is produced mainly inbonemarrowand in the tissues very near the applicator plates. Bothcurrent density and electric field decay rapidly with distance tothe applicator plates regardless of the variation in tissue prop-erties and structure. It can be noted that the current density isaround four times larger in the ECT than that for TMS in thehead.

Note that in Fig. 8 the results are shown on the cross sectionwhich is not directly under the electrode but approximately 1cm behind the electrodes. The choice of displaying this specificcut is medically motivated, as we want to display certain part ofthe brain. Furthermore, in Figs. 5 and 8 due to limitations in thenumbers of colors that can be resolved, in particular after repro-duction, and due to the large variations in the current density andelectric field data we have chosen a pallet which is not linear. Infact, the palette is linear up to a chosen value and then constant(dark red) above this value. This is a compromise in order tokeep the dynamic range in the picture while still being able todiscuss the region of large field values. For example, in Fig. 5,the electric field in the bone marrow region shown as dark redis not 50 kV/m, the maximum value on the legend, but it mustbe read as that it is somewhere between 0.25 and 50 kV/m, andactually it is around 0.3 kV/m.

While the numerical resolution of the model is 1 mm, theanatomical resolution is somewhat lower. The results shown inFigs. 5 and 8 are, therefore, averaged over 2 mmarea at eachpoint in the model.

The experimental study of [18] concluded that interpretationof the measurements in terms of an isotropic spherical humanhead model suggest that most of the current injected by ECT



(a)

(b)

Fig. 8. (a) The variation ofjJj and (b)jEj on the cross sectiony = 0:075 ofthe human head in the ECT case.

applicator is shunted through the scalp. Our results indicate thatin the central vertical plane of the current is passingthrough the brain. This is because conductivities of the scalptissues (skin, fat, and muscle) in our case (0.002, 0.002, and 0.33S/m) are much lower than what was found in [18], where thisregion was modeled by a single tissue of conductivity 0.44 S/m.

As a test case, we set the tissues making up the scalp equal tothe above mentioned measured value of conductivity and com-puted the currents densities and corresponding electric fields in

Fig. 9. Ratio of the total current passing through the brain. solid curve:scalp tissue conductivities are as in our calculation; dashed curve: these are asmeasured in [18].

the same human head model. With this increased conductivity ofscalp tissues (skin, fat, and muscle), the current is now shuntedthrough the scalp as can be seen in Fig. 9.

In general, conductivities of biological tissues exposed totime varying electric fields vary with the frequency. For lowfrequencies this variation is almost negligible.Since in both TMS and ECT the frequencies in the spectra arein the kHz range as can be seen in Figs. 3 and 7, our results donot depend on frequencies of the applied current wave forms.

VI. CONCLUSION

We have presented comparative results on modeling of TMSand ECT indicating similarities and differences for clinicallyused applicator parameters. Using typical currents, pulse formsand pulse widths in the TMS coil, induced current densities andelectric field distributions from TMS were computed using the3-D impedance method. These results are compared and con-trasted with the corresponding ECT calculations for the samehead model. Here a uniform current density was injected at oneside of the models and extracted from the opposite side againusing typical values for amplitude, wave form, and pulse widths.The numerical results obtained both in TMS and ECT caseswere visualized on a cross section of the models. We foundthat under the conditions studied induced currents and electricfields for TMS is considerably weaker and less penetrating thanthe corresponding results for ECT. However, currents are pen-etrating to the inner part of the brain for both methods and thelocalization of TMS is of interest in a situation where one wouldlike to stimulate a specific region of the brain. Interestingly, thelevels of electric fields in deeper, not cortical, areas of the brainis found to be in the 100-500 mV/m range for TMS and ECT.The effective fields for electrically induced effects in living cellsare around 100 mV/m [19]. For example, the cellular movementtoward an electrode, so called galvanotaxis, is seen in astrocytesexposed to 50-500 mV/m [20]. It is speculated based on thepresent findings that effects from electric brain therapy in part



is resulting from electric field interactions with neuronal cellsdeeper in the brain, rather than from excitation of superficialcortical neurons. The somewhat higher electric fields in deepbrain regions seen for ECT might in the TMS case be compen-sated for on the biologic response level by the longer stimulationtimes used in TMS treatment. The presented model with a ratherhigh resolution description of brain electric fields and currentsduring ECT and TMS is aimed to help in the search for a betterunderstanding of the mechanisms involved in the electric ther-apies, in which neurogenesis is seen to be induced. This willenable us to refine and design new instruments for noninvasiveinduction of neurogenesis in the brain, mainly by the use of fo-cused high-intensity magnetic fields.

Comparing the results presented in this paper with the corre-sponding results of Saypolet al. [4] we find a qualitative agree-ment in the structure of the electric field produced in the headduring ECT and TMS. The electric field from TMS is more lo-calized and decays faster with distance from the skull. We alsofound that the ECT results are sensitive to the skull tissue con-ductivities, as was seen in Fig. 9 where higher skull conductiv-ities gave higher currents and electric field in the skull.

In this paper, the tissues conductivities are treated asisotropic. The question of anisotropy in the tissue conductivityis one of great interest. However, to include this in the modelingin a proper way would require an association with each tissuea space-dependent anisotropic conductivity varying fromone voxel to the next. This would be very complicated andis outside the scope of this paper. However, to some extentanisotropy is included in the modeling as the brain is treated asa heterogeneous tissue with varying conductivity.

ACKNOWLEDGMENT

The authors would like to thank Brooks Air Force Laboratoryand the Visual Human project for providing the models.

REFERENCES

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Mohammad Nadeemreceived the M.Sc. degree inapplied mathematics and the M.Phil. degree in fu-sion plasma from Quaid-e-Azam University, Islam-abad, Pakistan, and the Ph.D. degree in fusion plasmaphysics from University of Manchester Institute ofScience and Technology (UMIST), Manchester, U.K.

He is an Assistant Professor of bioelectromag-netics at the Chalmers University of Technology,Gothenburg, Sweden. He is an author or coauthor ofmore than ten journal articles on fusion plasmas andelectromagnetic dosimetry.

Thorleif Thorlin received the M.D. degree fromGothenburg University, Gothenburg, Sweden, in1992 and the Ph.D. degree in neurobiology from thesame university in 1998.

He is an Assistant Professor at the Instituteof Clinical Neuroscience, Sahlgrens UniversityHospital, Gothenburg, Sweden. He is author orcoauthor of more than 20 scientific papers in thefield of neurobiology. His research is focused onastrocytes and neuronal stem cells in the brain.



Om P. Gandhi (S’57–M’58–SM’65–F’79–LF’99),received the M.S. and Ph.D. degrees in electrical en-gineering from University of Michigan, Ann Arbor,in 1957 and 1961, respectively.

He is a Professor of Electrical Engineering at theUniversity of Utah, Salt Lake City. He was electeda Fellow of the American Institute for Medicaland Biological Engineering in 1997. He has beenChairman of the Department of Electrical Engi-neering, University of Utah (1992–1999), Presidentof the Bioelectromagnetics Society (1992–1993),

Co-chairman of IEEE SCC 28.IV Subcommittee on the RF Safety Standards(1988–1997), and Chairman of the IEEE Committee on Man and Radiation(COMAR) 1980–1982. He is the author or coauthor of several book chapters,and over 200 journal articles on electromagnetic dosimetry, microwave tubes,and solid-state devices. He also edited the book,Biological Effects and MedicalApplications of Electromagnetic Energy(Englewood Cliffs, NJ: Prentice-Hall,1990), and coedited the bookElectromagnetic Biointeraction(New York:Plenum, 1989).

Dr. Gandhi received the d’Arsonval Medal of the Bioelectromagnetics So-ciety for pioneering contributions to the field of bioelectromagnetics in 1995and the Microwave Pioneer Award of the IEEE Microwave Theory and Tech-niques Society in 2001, and the State of Utah Governor’s Medal for Scienceand Technology in 2002. He is listed inWho’s Who in the World, Who’s Whoin America, Who’s Who in Engineering, andWho’s Who in Technology Today.

Mikael Persson received the M.Sc. and Ph.D.degrees from Chalmers University of Technology,Gothenburg, Sweden, in 1982 and 1987, respectively.

He is Professor of Electromagnetics at ChalmersUniversity of Technology. He is the author or coau-thor of over 100 journal and conference papers in fu-sion and computational electromagnetics.

Dr. Persson has served on the European fusionPhysics committee (2001–2002) and is a presentmember of the Swedish fusion Physics committee.


computation of electric and magnetic stimulation in human head using the 3-d impedance method

Documents

ect case

human head model

ect calculations

tms quantities

colecole model

typical tms coil of

used forthe tms case

electroconvulsivetherapy