Transcranial Magnetic Stimulation and Transcranial DirectCurrent Stimulation (Supplements to Clinical Neurophysiology. Vol. 56)Editors: W. Paulus, F. Tergau,M.A. Nitsche, J.e. Rothwell, U. Ziemann, M. Hallett© 2003 ElsevierScience B.V. All rights reserved

Chapter 1

Background physics for magnetic stimulation

Jarmo RuohonenNexstim Ltd.• Elimiienkatu 22B. FIN-0051O Helsinki (Finland)

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1. Introduction

With increasing use of magnetic stimulation inscience and clinics. it is most important to considerand revisit the basic phenomena behind the technique.This chapter includes a simplified introduction to thebasic physical principles. As examples. the chapteroutlines how coil positioning affects where magneticstimulation touches the brain. Moreover, advancedcomputation helps position the stimuli more accuratelyto desired spots. This chapter introduces startingpoints for engineering models that can be appliedto further develop brain stimulation devices intoadvanced navigated brain stimulation (NBS) scannersthat can produce important information complemen-tary to tMRI, MEG and PET.

2. Basic principles

Electrical current can excite excitable cells (neurons,muscles). The tingling sensation when short-circuiting

* Correspondence to: Dr. Janno Ruohonen, Ph.D.,Director, Research and Development, Nexstim Ltd.,Elimaenkatu 22B, FIN-00510 Helsinki, Finland.Tel: +358-9-2727 1711; Fax: +358-9-2727 1717;E-mail: janno.ruohonen@nexstim.comInternet: www.nexstim.com

a low-power battery with fingers is a good demonstra-tion of this. Even very strong electrical pulses can bebeneficially applied in medicine. for instance, in car-diac defibrillators.

Magnetic stimulation can "mimic" direct stimula-tion with electrical current: it generates. or induces,an electrical current in the tissue. This has beneficialconsequences. Unlike electrical stimulation, magneticstimulation can reach the tissue without need forphysical contact.

The mechanism of action is similar for bothelectrical and magnetic stimulation. In order tostimulate neuronal cells, an electric field E mustbe applied to the tissue; it forces coherent motion offree charges in intra- and extracellular spaces. Inother words, the electric field drives an intracranialelectrical current J=(JE, where (J is the electricalconductivity in the brain. Cell membranes thatinterrupt the current will depolarize or hyperpolarize.Eventually, the depolarization of the axon membranewill trigger a progressing depolarization front, oraction potential. Figure 1 illustrates the chain ofevents in magnetic stimulation.

2.1. Faraday's law of induction

The physical phenomenon behind magnetic stim-ulation is electromagnetic induction, and is governed

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- evokedneuronalactivity(EEG)

- changesin bloodflowand metabolism(PET. fMRI)

- muscletwitches(EMG)and changes in behavior

Fig. 1. Principles of TMS. Current pulse 1(1) in the coilgenerates a magnetic field B that induces an electric fieldE. The lines of B go through the coil; the lines of E followthe shape of the coil. The upper-right drawing illustratestwo pyramidal axons, together with a typical orientation ofthe intracranial E. The E-field affects the transmembranepotential, which may lead to local membrane depolariza-tion and firing of the neurons. Events following TMSinclude: (1) coherent activation of neurons; (2) metabolicand hemodynamic changes; and (3) behavioral changes.Reactions of the brain can be recorded with BEG(Ilmonierni et al., 1997), or with fMRI (Bohning et al.,1998), PET (Paus et al., 1997) or NIRS (Oliviero et al.,1999). Macroscopic responses are seen also with surface

EMG or as behavioral changes.

by a basic law of physics, namely, Faraday's law:

v x E =- iJB/iJt.

In practice, this relation states that an electric fieldE, and thereby electrical current J, is induced intissue by the time-varying magnetic field B fromthe coil. Solution to the equation above gives anestimate of the induced E that ignores the effects ofconductivity variations between and within the brain,skull and scalp.

Magnetic fields encountered in magnetic stimula-tion travel freely in air and can easily penetratethrough tissue. Therefore, magnetic stimulation can

Fig. 2. Accurate localization of the stimulating coil andreal-time calculation of the electric field induced in thebrain offer interactive targeting and mapping. The imageshows the electric fieldon 3-D MR images while navigationis used to guide the coil optimally for motor cortex stimu-

lation. (Courtesy of Nexstim Ltd., Helsinki, Finland.)

readily reach brain cells even through the highlyresistive skull.

Several references include detailed information onthe physical formulas governing magnetic stimulation(Barker, 1991; Grandori and Ravazzani, 1991;llmoniemi et al., 1999; Ruohonen and Ilmoniemi,2002).

3. ''Hot spot" modeling

Modeling of magnetic stimulation can be divided intotwo main parts:

(I) computation of the macroscopic electric field Ein the brain, and

(2) cellular mechanisms.

3.1. Hot spots of activation

Figure 2 illustrates results from straightforwardmodeling. The figure shows a 3-D reconstruction ofthe MR images of a subject's head together with thecomputed induced field E that touches the cortex.

The coil has been positioned optimally to obtainmuscle twitches in the right hand fingers with helpof eXimia NBS navigation system (Nexstim Ltd.•Finland). The "hot spot" of the electric field coin-cides nicely with the location of the hand motor area,identified from structural MRIs in the precentralomega-shaped knob.

The calculation of the electric field E induced inthe tissue has several benefits. Most importantly,together with accurate localization of the coil withrespect to anatomical landmarks, the induced E canbe used to determine the cortical areas influenced bystimulation. This can significantly help interpret theexperimental findings and enables new paradigms, forinstance, based on functional information acquiredwith other brain scanning modalities.

3.2. E-field computation

Generally, the electric field induced in the tissuedepends on

(1) coil shape;(2) coil location and orientation; and(3) electrical conductivity structure of the head.

The computation of the electromagnetic fieldsinduced in the brain is well understood. The totalfield is the sum of the directly induced field fromFaraday's law and the secondary field arisingfrom surfaces of different conductivity (Fig. 3) (Rothet al., 1991; Durand et al., 1992; Ruohonen andIlmoniemi, 2002). Accurate calculation would requireknowledge of the exact electrical conductivity and itspreferential direction in the subject's head (Wanget aI., 1994; Cerci et al., 1995; D'Inzeo et al., 1995).However, computational algorithms that can makeuse of such information are extremely complicatedand time consuming, and hence cannot be used inpractical investigations.

Although dedicated MR imaging sequences can beused to estimate the conductivity profile of the head.the actually achievable resolution is poor, and thevalues determined are questionable - at least untilotherwise proven. And, the procedure should berepeated for every patient examined. For these

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Total induced electric field =

+

Fig. 3. The total induced electric field is the sum ofprimary and secondary fields: E = E( +E2• The primaryfield is induced by the coil according to Faraday's law(left). The secondary field arises from charges that accu-

mulate on surfaces where conductivity changes (right).

reasons, conductivity profiles such as the sphericalmodel have been developed that approximate theshape of the head and brain (Eaton, 1992; Heller andVan Hulsteyn, 1992). Such models are still compli-cated, but modem computers allow for fast andreproducible computation.

The spherical head model has relatively good accu-racy for biomagnetic studies of the brain (Hamalainenet al., 1993). There is little information regarding thespherical model's usefulness in special circumstancessuch as a stroke.

4. Cellular mechanisms

There is considerable theoretical and physiologicalevidence that the cerebral cortex is activated predom-inantly at the location of the maximum of the inducedelectric field. Of course, the strength and focus of themagnetic field are irrelevant.

The complex shape of the neurons makes it diffi-cult to predict precisely the effects of stimulation.Modeling studies suggest that TMS predominantlycauses excitation at bends of corticocortical or ofcorticospinal fibers or at nerve endings near thesurface of the cortex (Basser and Roth, 1990;Nagarajan et al., 1993; Abdeen and Stuchly, 1994).Experimental data seem to support these conclusions(Maccabee et al., 1993; Nagarajan et al., 1997;

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+ + + + + + +

0-+-+-+-+0+ + + + + + +

(a) Axon membrane ....!..

+ + -~- + + +~+ + -+O~::+- ~-~O (c)

+ + 0 + + +i!l+ +(b)

Fig. 4. Schematic illustration of activation mechanismsfor magnetic stimulation of a long straight axon. Themembrane polarization is sketched for different externallyapplied electric field patterns (arrows): (a) uniform E alongthe axon, no change from the resting state; (b) gradientactivation, with iJEJiJx"# 0; (c) gradient activation for abent axon in uniform E. Regions of depolarization andhyperpolarization are indicated by D and H, respectively.

Amassian et al., 1998). The major implications frommodels are (see also Fig. 4):

(1) straight long axons are most easily stimulatedwhere the gradient of the electric field along theaxon is the strongest (dE/dx for axons along xaxis);

(2) short axons are most easily stimulated at theirends; and

(3) curved axons are most easily stimulated at thebends, where the effective electric field gradientalong the axon is the strongest

In summary, TMS most likely stimulates short andcurved cortical neurons near bends. and where theinduced electric field is the strongest. The orientationof the electric field affects it as well. The practicalstrength to elicit hand muscle twitches is on the orderof 100 mY/mm.

The basic mechanisms and effects of TMS havebeen recently reviewed by Terao and Ugawa (2002).

4.1. Transcranial electrical vs. magneticstimulation

In their fundamental works, Day et al. (1989) andAmassian et al. (1989) reported that the CMAPs with

TMS are about 2 ms longer than with transcranialelectrical stimulation (TCES), which most likelystimulates pyramidal axons in the white matter. Thismeans that TMS probably stimulates more superficialstructures than TCES. The site of excitation in TMSis possibly in the grey matter and in TCES in thewhite matter. By appropriately orienting the TMScoil, the CMAPs match, leaving the possibility thatTMS can activate the pyramidal axons also directly.

Distribution and orientation of the electric fields inTCES and TMS are significantly different. In TMS,the field is always in the direction along the scalp;there is no radial electric field. This probably explainsthe observed differences in the CMAP latencies. InTCES, there are both field directions: the relativestrengths of the field components parallel and perpen-dicular to the scalp depend on the electrodeconfiguration.

4.2. Comparison withfMRl, MEG and PET findings

Comparative results from localization of thesomatosensory cortex indicate that the activationoccurs near, or at the site of, the strongest externallyapplied E. Krings et al. (1997) compared stereotacticmagnetic stimulation maps with direct corticalstimulation results, finding agreement to within lessthan 5-10 rom. The site of the strongest E has beenfound to agree with the localization results fromMEG (Morioka et al., 1995a, b; Ruohonen et al.,1996), PET (Wassermann et al., 1996) and tMRI(Terao et al., 1998a; Herwig et al., 2002) to within5-20 rom. Similarly, tMRI, PET and TMS havelocalized the frontal eye field to the precentral gyrus(Carter and Zee, 1997; Paus et aI., 1997; Terao et aI.,1998b).

5. TMS devices

A circuit containing a discharge capacitor connected inseries with the coil by a thyristor, generates the currentpulses in a TMS coil (Cadwell, 1990; Barker, 1991).With the capacitor first charged to 2-3 kY, the gatingof the thyristor into the conducting state will cause thedischarging of the capacitor through the coil. The

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150

Iii'

0 ~....~'C

-150500 t [j.lS] 1000

(C)

150

100~(fJ

50 ~-"C0

::::"C

-50500 t [j.ls] 1000

(d)

o

150

-150300

Currentdirection

Capacitance

Resistance

100 t [j.l5] 200

(b)

G

(a)

IThyristor conductingll Diode conducting5

-5o

Fig. 5. (a) Schematic illustration of the stimulator circuit. The current I(t) and its rate of change dUdt for (b) biphasic,(c) polyphasic, and (d) monophasic current pulses. Inserts to (b) depict the conducting periods of the thyristor T and diodeD and the direction of the current in the coil. Parameters used: coil inductance L = 15 f.LH. capacitance 100 f.LF, resistance

50 mO, initial capacitor voltage 2,000 V.

resulting current waveform is typically a dampedsinusoidal pulse that has a peak value of 5-10 kA.Typically, the power consumption is 2-3 kW atmaximum stimulus intensity and I-Hz repetition rate.

The current pulse properties vary among manufac-turers. Three pulse waveforms are available (Fig. 5):

(I) monophasic, i.e. rapid rise from zero to peak andslower decrease to zero;

(2) biphasic, i.e. one damped cycle of sinusoid; and(3) polyphasic, i.e. multiple-cycle damped sinusoid.

The duration of the pulse is typically 200-300 f.LS forbiphasic and about 600 f.LS for monophasic pulses.Unlike in electrical stimulation. it is difficult tomodify the pulse shape in magnetic stimulation.

rTMS devices operate at 10-60 Hz at 40-100% ofthe maximum intensity of single pulses. The durationof sustained operation is limited by coil heating to100-1000 pulses at maximum power. With proper

coil cooling, the duration of the stimulus train is notlimited by heating.

6. Coils

The size of the stimulated area, and the direction ofthe induced current flow, depend greatly on the coil'sshape. Successful targeting of stimulation requiresthat the field pattern from the coil is taken intoaccount. Likewise, significant improvements in stim-ulator design can be achieved only through goodunderstanding of the electromagnetic fields aroundthe coil.

Effective coil design is challenged by the highamount of energy that must be driven throughthe coil in a very short time. In brain stimulation.this energy is about 500 J, which would suffice tothrow a weight of I kg to a height of 50 m. Thissection describes some available coil types with theirexcitation fields.

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Fig. 6. The strength of E below circular and figure-of-eight coil.

6.1. Circular coil

The region activated by the circular coil is roughlyunder the circumference of the coil, not under itscenter (see Fig. 6a). Figure 7a shows the inducedfield for two coil orientations: the coil centered over

the vertex (Fig. 6a) and shifted with one edge overthe vertex (edge-tangential coil, Fig. 7b). The field isstronger with the coil over the vertex, but it is distrib-uted in a large area below the windings of the coil.The field distribution is more confined when the coilis edge-tangential.

200 200 200

E E (e) E (f)~ ~ ~

:5!~ 100

:5!: 100.!i100 u

u i ~.~

" iiiiii UJ

0 0 0-90 --45 0 45 90 -90 -45 0 4S 90 -90 -45 0 45 90

Angle a (dog] Angle [dog] Angle a [dog]

Fig. 7. Pattern of the electric field induced by: (a) circular coil over the vertex; (b) circular coil edge-tangential over thevertex; (c) figure-of-eight coil. The illustrations show the field strength on a spherical surface, 20 rom below the coils asgray level maps. The plots in (d, e, f) show the field in points of a circular arc going from the left ear to the right ear,when the arc is at different distances from the coil (d =, 20, 30, 40, 50, 60, 70 rom). The coils consisted of 16 concentricturns (2 x 8, 8-shaped coil) 60 rom in diameter and were driven with dI/dt =lOS Als. The spherical head model was used.

Figures 7d and 7e show the field strengths for thevertex and edge-tangential coils along a semicircleat different depths below the coil (20 to 70 mm).The field strength decreases quickly with distancefrom the coil. Notably, the strength of the secondarypeak at a = 35° produced by the edge-tangentialcoil orientation is 73% of the primary peale Thissecondary peak should be taken into account whenpositioning the coil since it may stimulate undesiredcortical areas.

6.2. Figure-of-eight coil

The region activated by the figure-of-eight coil isunder its center (Fig. 6b). The total induced field isthe sum of the fields from the two wings of thecoil. The resulting field is much more focused thanthe field produced by a single coil of the same size.Also, the figure-of-eight coil produces a stronger fieldthan single coils, provided that the coils are drivenwith the same energy. The field strength from thefigure-of-eight coil decreases about as quickly withdistance (Fig. 7t) as the field from the single coils.The field strength exceeds its half-maximum valueover an arc of about 25°. The secondary peak strengthfrom the figure-of-eight coil is about 25% of theprimary peak.

6.3. Cap-shaped and cone coils

Cap-shaped or cone coils are constructed with a pairof circular windings at such an angle with respectto each other that they fit the curvature of the head.The cone coils are somewhat more effective than thenormal planar coils, but at the cost of focality.The secondary peaks from the cone figure-of-eightcoil are about 40% of the primary peaks. The primarypeak is slightly wider for the cone coil than for theplanar figure-of-eight coil.

6.4. Sham/placebo coils

Sham stimulation is required in many TMS studiesto control any side-effects due to the coil click orsomatosensory scalp stimulation. The aim of sham

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TMS is to apply pulses without stimulating the brainbut still causing the perception of real TMS. Shamstimulation can be obtained, for instance, by tiltingor lifting the coil so that the electric field inducedin the brain will decrease. Generally the disadvantageof these solutions is that the auditory and/or somato-sensory sensations may be significantly different fromthose in real TMS.

An advanced approach is to use a special figure-of-eight coil that is suitable for both real and shamTMS. This can be realized by switching the direc-tion of the current in one of the wings of the coil(Ruohonen et al., 2000). As compared to the normalfigure-of-eight coil, the sham coil induces no primarypeak below the coil's center. This type of shamstimulation requires a two-channel computerizedstimulator device and allows interleaved and random-ized trains of real and sham stimuli.

7. Navigated brain stimulation systems

TMS responses are often highly variable. Animportant source of variability is the variation in thepositioning of the coil. Shifts of a few millimetersor small angling of the coil may change the electro-magnetic fields in the brain significantly, and therebycause the response to change or even disappear.Accurate coil positioning, preferably framelessimage guidance, is clearly needed (Ruohonen et al..1996; Miranda et aI., 1997; Paus and Wolforth,1998; Ilmoniemi et al., 1999; Krings et al., 200 I).Visualization of the electric field on individual MRimages of the subject greatly enhances targeting topredefined cortical loci.

Navigated brain stimulation (NBS) systems havebeen developed that record automatically the locationand orientation of the coil (Fig. 8). The motorresponse strengths, and other responses, can be linkedwith individual stimulation pulses to produce imme-diate colored maps of the stimulation effects. Thedata reviewing possibilities include browsing of the"hot spots" and comparison of the response mapswith the realized strength and direction of the elec-tric field at different locations of the brain. And when

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Fig. 8. Navigated brain stimulation (NBS) system.(Courtesy of Nexstim Ltd., Helsinki, Finland.)

stimuli are delivered in sequence, navigation canproduce "dose" distributions that are the cumulativesum of the electromagnetic exposure everywhere inthe brain. Figure 9 shows an example from motorcortex mapping with Navigated Brain Stimulation(NBS).

8. Conclusions

Transcranial magnetic stimulation is based on thewell-understood phenomenon of electromagneticinduction. The electric field induced in the neuronaltissue drives ionic currents, which charge the capac-itances of neuronal membranes and thereby triggerthe firing of neurons. The most likely location ofneuronal stimulation in the cerebral cortex is thelocation of the strongest electric field induced by thestimulation coil.

Frameless stereotaxy combined with MR imagesis gradually becoming the preferred way of doing

Fig. 9. Motor cortex localization experiment with navi-gated brain stimulation. The colored dots represent coilpositioning; the color indicates the corresponding motorresponse strength. The induced electric field is shown in

the 3-D MRIs is for the selected coil placement.

TMS. Such Navigated Brain Stimulation equipment,or NBS scanners, comprise a "hot spot" localizationsystem with 3-D visualization of the stimulating fieldlocations within the brain and automatic generationof reaction maps. This allows new clinical conceptssuch as reporting of the dose of stimulation forimproved reliability of clinical examinations.

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