Tramcnlllilll Alllgm•ri,· Stim11lllfio11 (EEG Suppl. 5/)
`Edi1m:-.: W. Pauhl',, M. Hallc11, P.M. Rossini, J.C. Ro1hwcll
`11', J'JlJ() El:-.cvicr Scicm:c 8.V. All righh rc~crvcd.
`
`3
`
`Chapter 1
`
`The history and basic principles of magnetic nerve stimulation*
`
`Anthony T. Barker*
`
`Department of Medical Physics and Clinical Engineering, Royal Hallamshire Hospital, Sheffield SJO 2JF (UK)
`
`Introduction
`
`Magnetic nerve stimulation has rapidly become
`established as a clinical tool following its develop(cid:173)
`ment at the Royal Hallamshire Hospital and the
`University of Sheffield, and the first demonstration
`of cortical magnetic stimulation in 1985. Over 3000
`stimulators are now in use world-wide, primarily
`for diagnostic and basic research purposes, but
`with rapidly increasing interest being shown in a
`variety of therapeutic applications. This chapter
`describes the development of magnetic stimulation
`as a clinical tool and its basic principles. It also
`introduces some of the technical issues surrounding
`the design of stimulators and how they affect the
`delivered stimulus.
`
`Basic principles of magnetic nerve stimulation
`
`Ever since the work of Galvani and Volta in the
`1790s, it has been known that nerves and muscles
`can be stimulated with externally applied electrical
`
`·:.- Reproduced by permission of Arnold, London (a
`member of the Hodder Headline Group): Barker, A.T. The
`history and basic principles of magnetic nerve stimulation.
`In: Pascual-Leony, Davey, Wassermann and Rothwell
`(Eds.), Handbook of Transcranial Magnetic Stimulation.
`Arnold, London, 1999.
`* Correspondence to: Dr. A.T. Barker, Degartment of
`Medical Physics and Clinical Engineering, Royal Hallam(cid:173)
`shire Hospital, Sheffield S 10 2JF (UK).
`
`currents. Electrical stimulation, in which current is
`injected into the body through surface, needle or
`implanted electrodes, has been in widespread clin(cid:173)
`ical use for many years. In electrical stimulation
`charge is carried by electrons flowing in the wires
`to the electrodes, and is transferred to a flow of ions
`at the electrode-tissue interface. A small fraction of
`the charge on these ions is transferred onto nearby
`excitable membranes and can result in depolarisa(cid:173)
`tion.
`Electrical stimulation is very effective when
`applied
`to superficial peripheral nerves using
`surface electrodes, or to deeper structures where
`needle electrodes can be placed close to the
`required site of stimulation. However it is difficult
`to stimulate deep nerves from the surface and,
`because bone has high electrical resistance, it is
`necessary to use high voltage stimuli to penetrate
`the skull in order to achieve cortical stimulation
`(Merton and Morton 1980).
`Magnetic stimulation differs from electrical
`stimulation in that it uses a pulse of magnetic
`field to cause current to flow in the tissue. The
`mechanism of stimulation, at the cellular level, is
`the same for both techniques. In both cases charge
`flows into an excitable cell membrane, causing a
`change in transmembrane potential. This can result
`in depolarisation of the membrane and the initiation
`of an action potential, which then propagates along
`the structure by the normal nerve conduction
`mechanisms.
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`Magnetic stimulation is based on the scientific
`principle of electromagnetic induction, discovered
`by Michael Faraday in 1831. In one of the most
`famous of scientific experiments he wound two
`coils of wire on opposite sides of an iron ring and
`observed that, when current was turned on or off to
`one coil (called the primary), a current flowed
`briefly in the secondary coil (Fig.
`la). A few
`weeks later he showed that the iron ring, whilst
`enhancing the induction by 'guiding' the magnetic
`field from primary to secondary, was not essential,
`and he demonstrated the same effect with two
`closely positioned air-cored coils (Fig. 1 b ).
`Faraday's experiments showed that currents (and
`voltages) were only induced by a changing, or
`'time-varying' magnetic field, and not by a static
`field. In magnetic stimulation of the body, tissue
`forms the secondary circuit. The primary circuit is
`the stimulating coil, through which the stimulator
`drives current pulses, but which is not in electrical
`contact with the tissue. The magnetic field gener(cid:173)
`ated by the current flow in the coil is proportional to
`the current passing through it, and the electric field
`induced in the tissue is proportional to the rate of
`change of the magnetic field with respect to time.
`At the frequencies used in magnetic stimulation the
`magnetic field is not affected by the electrical prop(cid:173)
`erties of the body, and passes through both bone and
`soft tissue (and even clothing and air) without being
`affected by them. The magnetic field pulse induces
`
`a)
`
`b}
`
`Fig. 1. Schematic of the coil arrangements used by Michael
`Faraday (a, b) and in a modern magnetic stimulator (c).
`
`an electric field (a voltage difference between two
`points) in the tissue which causes an ionic current to
`flow (Fig. le). If the amplitude, spatial characteris(cid:173)
`tics and duration of this induced current are such
`that they cause depolarisation of a nerve membrane
`then stimulation, and the generation of an action
`potential, will occur.
`Thus the magnetic field does not itself directly
`stimulate the tissue and hence 'magnetic stimula(cid:173)
`tion'
`is a slight misnomer for the
`technique,
`although it is a convenient and well-established
`name.
`
`Development of magnetic stimulation as a
`clinical technique
`
`The first example of a physiological effect due to
`a time-varying magnetic field was reported by
`d' Arson val (1896) who observed that phosphenes
`(flicking lights 'seen' by a subject) and vertigo were
`produced when a volunteer's head was placed
`inside a coil driven at 42 Hz. This finding was
`subsequently confirmed by Silvanus P. Thompson
`(1910) and others (Fig. 2).
`The retina of the eye is the structure in man that
`is most sensitive to induced currents, and there has
`been much subsequent work on what are now
`known as magnetophosphenes. Threshold values
`for magnetophosphenes in normal subjects have
`been reported to be as low as 10 mT r.m.s. for a
`20 Hz sinusoidal magnetic field (Lovsund et al.
`1980).
`Kolin et al. (1959) demonstrated that exposed
`nerves could be stimulated by looping a frog sciatic
`nerve around the pole piece of an electromagnet
`and produced contractions in the gastrocnemius
`muscle with both 60 Hz and 1 kHz currents.
`Bickford and Freeming ( 1965) reported non(cid:173)
`invasive magnetic stimulation of human and animal
`peripheral nerves. They used a 500 Hz damped
`sinusoidal magnetic field with a peak amplitude
`of 4 Tesla decaying to zero over approximately
`40 ms, and a stimulating coil of mean diameter
`approximately 3 cm. Their choice of an oscillatory
`magnetic field waveform made it impossible to
`record nerve or muscle action potentials because
`of interference between the stimulating field and
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`the recording equipment, and their work was not
`pursued further.
`In 1974 Barker started to investigate the use of
`short duration pulsed magnetic fields as a possible
`method of achieving velocity selective stimulation
`of human peripheral nerves. He constructed an
`electromagnet from a closed 'C' core made of
`grain-orientated mild steel of cross section 30 X
`25 mm, with a 50 mm length removed from one
`of the long sides to form an airgap. Two capacitor
`banks, each of 800 µF charged to 200 V, were
`simultaneously discharged into separate windings
`on the core, each of ten turns. The resultant current
`pulse had a peak value of 2300 A with a risetime of
`approximately 120 µs and gave a peak magnetic
`field in the core of 2 T, Clear sensation could be
`felt, and
`slight muscular contractions were
`observed, when a wrist was placed in the airgap
`(Barker 1976).
`After these early experiments Barker and collea(cid:173)
`gues decided to pursue the goal of a practical clin-
`
`Fig. 2. Silvanus P. Thompson carrying out experiments to
`induce currents in his own head.
`
`5
`
`ical magnetic nerve stimulator that used field pulses
`short enough to allow evoked nerve and muscle
`action potentials to be recorded. They changed
`their coil to an air-cored design to avoid magnetic
`saturation (most ferromagnetic materials saturate at
`fields of approximately 2 T), and to give a relatively
`small and light structure which could be moved
`readily around the body. In 1982 they reported the
`stimulation of superficial nerves at the wrist and the
`recording of supramaximal evoked potentials over
`the thenar eminence using a 500 V, 6000 µF capa(cid:173)
`citor discharge system with a risetime of 180 µs
`(Polson et al. 1982). Supramaximal responses
`were achieved with the capacitor bank discharged
`from 340 V, giving a peak coil current of 6800 A and
`peak field in the centre of the coil of 2.2 T. (Fig. 3).
`Using a new high voltage design of stimulator
`which was more efficient at transferring energy
`from the storage capacitor to the coil (transfer effi(cid:173)
`ciency having been improved from -20% to -80%),
`the Sheffield group achieved the first magnetic
`stimulation of the human motor cortex (Barker et
`al. 1985a). Placing a coil of 100 mm outside
`diameter centrally over the vertex of a normal
`subject they demonstrated clear hand movements
`and recorded evoked muscle action potentials
`from Abductor Digiti Minimi using surface elec(cid:173)
`trodes (Figs. 4 and 5).
`There was no pain or discomfort associated with
`this first cortical magnetic stimulation, a consider(cid:173)
`able contrast to the sensations felt with electrical
`stimulation using electrodes placed on the scalp.
`Public demonstrations of cortical magnetic stimula(cid:173)
`tion using the prototype stimulator on volunteers at
`the 11th International Congress of Electroencepha(cid:173)
`lography and Clinical Neurophysiology in London
`and at the Physiological Society in Oxford (Barker
`et al. 1985b,c) caused considerable interest. In
`response to a number of requests, the first stimula(cid:173)
`tors specifically for routine clinical use were
`designed and built in the department of Medical
`Physics and Clinical Engineering at the Royal
`Hallamshire Hospital, Sheffield, for five groups in
`the U.K. and the U.S.A., who wished to evaluate the
`technique (Fig. 6).
`Early clinical studies using magnetic stimulation
`were presented in 1985 and 1986 (Barker et al.
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`6
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`Fig. 3. Dr. M.J.R. Polson with the stimulator used to produce supramaximal peripheral responses in 1982.
`
`1985d, 1986). Interest in magnetic stimulation grew
`quickly and, to expedite its adoption as a clinical
`tool, the Sheffield group introduced a number of
`manufacturers
`to
`the
`technique during 1985.
`Commercial stimulators from at least three manu(cid:173)
`facturers are in widespread use at present. The basic
`theory, advantages and safety considerations of
`magnetic stimulation, along with the first detailed
`clinical evaluation of the technique in the study of
`multiple sclerosis and motor neurone disease, were
`described in 1987 (Barker et al. 1987).
`
`Characteristics of the output field pulses from a
`magnetic nerve stimulator
`
`A magnetic field pulse of peak amplitude in the
`range 1-4 T is usually require to stimulate nerves,
`the exact value depending on a number of para(cid:173)
`meters such as the stimulating coil geometry, the
`depth and path of the nerve, and the local anatomy.
`The
`first generation of magnetic stimulators
`produced these pulses at relatively low maximum
`repetition rates, typically one pulse every few
`seconds
`('standard
`rate'
`stimulators). Their
`magnetic field pulses were monophasic, with rise(cid:173)
`times of order 100 µs, decaying back to zero over
`about 800 µs. This was achieved by discharging a
`
`capacitor, previously charged to a high voltage, into
`a stimulating coil via an electronic switch called a
`thyristor (Fig. 7).
`The coil current reaches its peak after a time
`determined by the value of the storage capacitor
`and by the inductance of the stimulating coil. The
`current then decays back to zero, at a rate deter(cid:173)
`mined by the coil inductance and value of resistor,
`
`Smsec
`..........,..r--,t
`
`Fig. 4. Upper trace: response due to a single magnetic
`stimulus applied to the motor cortex. Lower trace: response
`due to a single magnetic stimulus applied to the ulnar nerve
`at the elbow (from Barker et al., 1985a).
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`7
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`Fig. 5. From left to right: Dr. R. Jalinous, Prof. I.L. Freeston and Dr. A.T. Barker with the magnetic stimulator used to achieve
`the first cortical responses in February 1985.
`
`R, The stored energy, which starts in the capacitor
`as electrical energy, is transfeITed to the coil as
`magnetic energy as the coil cuITent increases, and
`then returns to be dissipated as heat in resistor R as
`the magnetic field collapses The electric field and
`cuITent induced in the body is proportional to the
`rate of change of magnetic field (Fig. 8), which in
`turn is propo1tional to the coil cuITent, just as it was
`in the secondary coil of Faraday's classic experi(cid:173)
`ments on electromagnetic induction.
`The first stimulators were designed to produce
`the waveforms of Fig. 8 because the resultant
`signals induced in tissue were similar in time course
`to those from charge-balanced electrical stimula(cid:173)
`tors, whose effectiveness was well proven. They
`have the. technical advantage that the reverse
`voltage, which appears on the storage capacitor
`during the decay of the coil cuJTent, is limited to
`about 20% of the discharge voltage, thus length(cid:173)
`ening the life of the capacitor. Typical maximum
`values found in such stimulators are: capacitor
`discharge voltage 3 kV, stored energy 500 J, peak
`coil CUJTent 8 kA and maximum stimulusrepetition
`rate 0.3 Hz at full output. Some standard rate stimu-
`
`lators have been designed to produce an oscillatory
`output similar to that of the rapid rate devices
`described below. Standard rate stimulators continue
`to be widely used, and are ideally suited to diag(cid:173)
`nostic and research applications where responses to
`single stimuli are to be studied.
`
`Rapid rate stimulators
`Widespread interest has recently been shown in
`the use of rapid rate stimulators, capable of produ(cid:173)
`cing tens of pulses per second in bursts lasting up to
`about one minute, primarily for therapeutic appli(cid:173)
`cations. They are usually based on a variation of the
`circuit shown in Fig. 7, with the resistor omitted and
`the diode repositioned across the thyristor switch.
`This produces an oscillatory magnetic field output,
`as opposed to the monophasic one of the standard
`rate stimulator (Fig. 9).
`Oscillatory output stimulators have two main
`advantages, both relating to their energy require(cid:173)
`ments. Firstly, at the end of the stimulating pulse
`(the complete waveform shown in Fig. 9), approxi(cid:173)
`mately 40% of the original energy stored on the
`capacitor has returned to it. Thus only 60% of the
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`8
`
`Fig. 6. The first clinical magnetic stimulator in use, Shef(cid:173)
`field, November, 1985.
`
`original stored energy needs to be supplied to the
`capacitor in order to recharge it in readiness for the
`next stimulus. A variety of configurations which
`can be used to achieve such energy saving have
`been described by Jalinous (1988).
`Secondly, oscillatory waveforms achieve stimu(cid:173)
`lation at lower levels of peak magnetic field than
`monophasic ones, and hence less energy is required
`to be stored in the stimulator. McRobbie and Foster
`( 1984) investigated the effects of different magnetic
`stimulator waveforms on the stimulation threshold
`of the median nerve in the forearm. They found
`that, using an oscillatory waveform of period 280
`µs (approximately the same as that in Fig. 9), only
`59% of the peak rate of change of magnetic field of
`a monophasic waveform was required to achieve
`the same level of stimulation. This would suggest
`that only about 35% of the stored energy of a mono(cid:173)
`phasic waveform stimulator is required for an oscil(cid:173)
`latory stimulator.
`
`Wada et al. (1996) investigated the effect of
`stimulator waveform both analytically, using the
`Frankenhaeuser-Huxley membrane model, and
`experimentally using
`the
`frog
`sciatic nerve.
`Comparing a monophasic waveform with a one(cid:173)
`cycle oscillatory waveform of period 280 µs they
`found the latter required 67% of the storage capa(cid:173)
`citor voltage (equivalent to 44% of the stored
`energy) to achieve the same response in their
`analytic model. With their sciatic nerve experiment
`they obtained similar results when using a stimu(cid:173)
`lating waveform of period 0.8 ms.
`The physical mechanism which causes nerves to
`be more sensitive to oscillatory waveforms has yet
`to be explored in detail, but may be related to
`membrane time constant (Wada et al. 1996) and
`membrane non-linearity (Reilly 1992).
`
`The effect of magnetic field risetime
`For a given stimulating coil in a fixed position
`relative to the nerve of interest, and assuming that
`the nerve membrane is regarded as a lossless capa(cid:173)
`citor, it can be shown that the charge transferred to
`that membrane is proportional to both the peak
`magnetic field and the square root of the magnetic
`energy in the coil, irrespective of the risetime of the
`magnetic field (Barker et al. 1987). In practice,
`nerve membranes do not behave like lossless capa(cid:173)
`citors. Leakage resistance within the membrane
`causes any applied charge to decay with time,
`resulting in the familiar stimulus 'strength-duration
`curve' seen with electrical stimulation. The effects
`of pulse duration are well known in the context of
`electrical
`stimulation, but apply equally
`to
`magnetic stimulation. A magnetic field pulse that
`
`S1
`
`energy
`storage
`capacitor
`
`D
`
`R
`
`Fig. 7. Simplified schematic diagram of a standard rate
`magnetic nerve stimulator.
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`9
`
`KT : : ; ; , · · :
`
`• . ...... ; ................ : .......... j .......... ; ................ , ................ ; ................ ; ................ ; .......... ..!. ............. .
`jl r
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`4
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`3
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`1
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`l'G
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`0.4
`0.6
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`0.1
`0.2
`0.3
`0.5
`0.7
`0.8
`0.9
`1
`0
`time msec
`
`Fig. 8. The time course of the magnetic field measured at the centre of a stimulating coil driven by a standard rate magnetic
`stimulator (Magstim 200), and the resultant induced electric field waveform.
`
`rises rapidly to its peak allows less time for charge
`to leak away, and hence achieves depolarisation at
`lower peak fields and magnetic energies. This has
`practical advantages because it decreases
`the
`energy storage requirements of the stimulator, the
`
`heat dissipated in the coil and the stimulator energy
`consumption, the latter being primarily a problem
`for fast repetition rate stimulators.
`The effect of field risetime on the efficiency of
`stimulation has been experimentally quantified
`
`5
`
`4
`
`'iii 3 -·c ::, 2
`~ e 1
`l'G --:E
`~ -e 0
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`al
`"ti
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`-0.1
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`0.1
`0.2
`0.3
`0.4
`0.5
`0.6
`0.7
`0.8
`0.9
`1
`time msec
`
`Fig. 9. The time course of the magnetic field measured at the centre of a stimulating coil driven by a rapid rate magnetic
`stimulator (Magstim Rapid), and the resultant induced electric field waveform.
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`10
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`using a stimulator with an output waveform having
`the same shape as that of Fig. 8 but whose timescale
`could be varied. Shorter rise time (-60 µs) pulses
`were shown to need approximately half the stored
`energy of those with longer risetimes (- 180 µs)
`(Fig. 10).
`The use of a stimulator with two or more
`magnetic field risetimes enables membrane time(cid:173)
`constant to be measured and the first measurements
`of this type have shown values of approximately
`150 µs for both peripheral and cortical stimulation
`(Barker et al. 1991 ). Non-invasive determination of
`membrane timeconstant has yet to be systemati(cid:173)
`cally studied in man, using either magnetic or elec(cid:173)
`trical stimulation, but such measurements may
`contain useful clinical information relating to the
`condition of the nerve membrane.
`
`The mechanism of stimulation - the 'activating
`function'
`
`The site of stimulation of a nerve fibre is that
`point along its length at which sufficient current
`to cause depolarisation passes out of the axon and
`through its membrane. When using electrical stimu(cid:173)
`lation with surface electrodes, stimulation
`is
`normally assumed to occur under the cathode elec(cid:173)
`trode, and this is a reasonable approximation in the
`case of a long, relatively straight, superficial nerve.
`In the case of magnetic stimulation the situation is
`less well defined and depends on a number of
`factors.
`For both electrical and magnetic stimulation the
`'activating function', which causes transmembrane
`current to flow and hence stimulation to occur, can
`be described mathematically as 'the spatial deriva(cid:173)
`tive of the electric field along the nerve' (see for
`example Reilly 1992; Abdeen and Stuchly 1994;
`Garnham et al. 1995). This can best be visualised
`by considering a long straight nerve in a homoge(cid:173)
`neous volume. Magnetic stimulation induces an
`electric field in tissue. If this electric field is
`uniform, and parallel to the nerve, it will cause
`current to flow both inside and outside the fibre
`but not across its membrane (Fig. I la). However,
`electric current is a continuous function, in other
`words the current entering any volume has to be
`
`1.8
`
`1.6
`
`1.4
`
`1.2 -
`
`0.8
`
`0.6
`
`0.4
`
`0.2 -
`
`I Data from 10 normal subjects ± 1 S.D.
`
`>, QI
`0111
`._ C
`QI 0
`CC.
`QI Ill
`
`,:, ! e,:, o-.. 0
`
`Ill .C
`QI Ill
`> QI
`.:;~
`ca ..
`a, 0
`a::-
`
`0 W ~ ~ M 1001W1~1~1MW0
`Risetime to Speak 1,1sec
`
`Fig. 10. The relative stored energy required to achieve
`threshold cortical stimulation versus magnetic field risetime.
`(from Barker, 1991 ).
`
`the same as that leaving it. Thus if the current
`within the axon changes along its length, that
`change must pass through the membrane and can
`cause stimulation (Fig. 11 b ).
`
`a)
`
`- - - -
`- - - -
`- - - -
`- - - -
`- - - -
`
`b)
`
`- -
`-!J
`- -
`- - 7
`- - -:)
`- -
`
`4
`4
`
`Fig. 11. Diagrammatic representation of (a) the cun-ent flow
`due to a uniform electric field parallel to a nerve fibre,
`causing no transmembrane cun-ent, (b) the cun-ent flow
`due to an electric field varying along the length of a nerve
`fibre nerve, resulting in transmembrane cun-ent, (c) a
`uniform electric field and a bent nerve also resulting in a
`transmembrane cun-ent.
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`ll
`
`V/m
`
`0 06
`
`0 04
`
`0 02
`
`0
`
`-0 02
`
`-0 04
`
`.o 06
`
`.Q 08
`
`.o 08
`
`.o 06
`
`.o 04
`
`.o 02
`
`o o 02 o 04
`
`0.06 o os o 1 m
`
`Fig. 12. The distribution of induced electric field, 20 mm below a 66.5 mm mean diameter circular coil.
`
`A change of electric field along the axon is
`required to change the current flowing within it,
`and hence the activating function is proportional
`to the rate of change of electric field, otherwise
`known as its spatial derivative, along the nerve.
`The situation becomes more complex in the case
`of a bent nerve. In this case a spatially uniform
`electric field can cause stimulation. Current flow
`will again be approximately parallel to the electric
`field. Where the axon bends across the field, the
`current will tend to continue in a straight line and
`pass out of the fibre across the membrane. Again
`the relevant parameter is the spatial derivative of
`electric field along the nerve, but in this case the
`bend in the nerve causes it to be non-zero, as shown
`in Fig. I le (Maccabee et al. 1993; Abdeen and
`Stuchly 1994).
`
`Coil geometry and the site of stimulation
`
`focused at a point. The physics of magnetic fields
`causes them to diverge after they leave their source
`and hence it is not possible to focus magnetic fields
`at a distance using only a single coil.
`The geometry of the stimulating coil is just one
`of the factors, along with others such as nerve
`geometry and local variations in tissue conduc(cid:173)
`tivity, which determines the amplitude and spatial
`distribution of the activating function. This in turn
`will determine the site of stimulation. The effect of
`coil geometry can be illustrated by considering the
`induced fields from the two most commonly used
`coil shapes, circular and figure-of-eight. In the
`following analysis it has been assumed, for simpli(cid:173)
`city, that nerve is situated within a homogeneous
`semi-infinite volume conductor, and parallel to the
`surface on which
`the coil rests. The results
`presented below can be extrapolated to coils having
`the same geometry but different dimensions by
`appropriate scaling of the spatial axes.
`
`Magnetic stimulation does not, in general, give a
`small and predicable site of stimulation._Ihe term
`'focal' stimulation is sometimes used, but this is
`misleading because it implies that the stimulus is
`
`The circular coil
`The first magnetic stimulator coils to be used
`were circular, and this is still the most widely
`used shape. Circular coils have the advantage that
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`12
`
`m
`
`0.08
`
`0.06
`
`004
`
`002
`
`0
`
`-002
`
`-0 04
`
`-006
`
`-0 08
`
`V/m2
`2500
`
`2000
`
`1500
`
`1000
`
`500
`
`0
`
`-500
`
`-1000
`
`-1500
`
`-2000
`
`-2500
`
`-0.1
`
`-0 08
`
`-0 06
`
`-0.04
`
`-0 02
`
`o o 02 o 04 o 06 o 08
`
`o 1 m
`
`Fig. 13. The rate of change of electric field, calculated in the direction of the shown nerve, 20 mm below a 66.5 mm mean
`diameter circular coil.
`
`they are relatively easy to construct and may conve(cid:173)
`niently be positioned over many parts of the body.
`Their primary disadvantage is the relative uncer(cid:173)
`tainty as to the exact site of stimulation.
`In a semi-infinite homogeneous medium the
`induced electric field and current loops will be
`circular and concentric. Fig. 12 shows this circular
`distribution of the amplitude of induced electric
`field, calculated in a plane at a depth of 20 mm
`below a realistic model of a commercial coil
`(d//dt = 108 Ns, inside tum diameter 41.5 mm,
`outside
`tum diameter 91.5 mm, number of
`turns= 15).
`As previously discussed, the activating function
`is the rate of change of electric field along the
`nerve. Fig. 13 shows this function calculated
`along a straight nerve positioned in the direction
`shown.
`A nerve positioned as shown relative to the coil
`will experience an induced transmembrane current
`which will tend to depolarise it in region A and
`hyperpolarise it in region B. These regions can be
`thought of, by analogy with electrical stimulation,
`as a 'virtual cathode' and a 'virtual anode' respec-
`
`tively. If the nerve of Fig. 13 had a sharp bend
`somewhere between these regions, the rate of
`change of electric field along the nerve would be
`increased at the bend and the site of stimulation
`would tend to shift to it.
`It should also be borne in mind that, because of
`circular symmetry, all structures which have the
`same stimulation threshold and which lie tangential
`
`Approximate
`-site of
`stimulation
`
`--Coil
`
`Fig. 14. Schematic representation of the site of stimulation
`for three nerves lying at different angles to a circular stimu(cid:173)
`lating coil.
`
`Allergan EX1098
`
`

`

`m
`
`0.15 .-------------......i.---""-----'-----1-
`
`0.1
`
`0.05
`
`0
`
`-005
`
`-0.1
`
`13
`
`Vim
`
`160
`
`140
`
`120
`
`100
`
`20
`
`-0.1
`
`-0.05
`
`0
`
`0.05
`
`0.1
`
`o.1sm
`
`Fig. 15. The electric field amplitude calculated in a plane 20 mm below a 73 mm mean diameter figure-of-eight coil.
`
`to a loop of given radius will be equally likely to be
`stimulated. This can be seen in Fig. 13 by the
`presence of an inverted virtual anode-cathode pair
`on the other side of the coil, and schematically in
`Fig. 14 which shows the approximate site of stimu(cid:173)
`lation of three nerves lying at different angles to the
`coil. Additionally, as
`the stimulus strength is
`increased, the site of stimulation will move further
`along the nerve, away from the coil, due to the
`shape of the 'activating function' (Garnham et al.
`1995).
`A practical example of the effect of the inverted
`virtual anode-cathode pair shown in Fig. 13 can be
`observed by stimulating using a 40 mm mean
`diameter coil placed centrally over the wrist. Both
`the ulnar and median nerve will be stimulated
`simultaneously, but at different positions along
`their lengths. Uncertainty as to the site of stimula(cid:173)
`tion can be decreased by using smaller coils, but
`there are considerable
`technical problems
`in
`making coils below approximately 25 mm mean
`diameter that can withstand the energies required,
`and that do not rapidly overheat. Depth or-penetra(cid:173)
`tion and lack of discomfort, which are two of the
`
`main advantages of magnetic stimulation when
`compared to conventional electrical stimulation,
`also decrease with smaller coils.
`In order to maximise the electric field induced in
`the tissue, stimulating coils are usually placed with
`one of their flat surfaces parallel to the skin as shown
`in Fig. le. It is also possible to achieve stimulation
`by placing a circular coil with its surface perpendi(cid:173)
`cular to the skin and parallel to the nerve of interest.
`This has the advantage of improving selectivity but
`has the disadvantage of very poor coupling of the
`magnetic field to the tissue. As a result the depth of
`penetration is greatly decreased and much higher
`stimulating energies are required. For these reasons
`this orientation is rarely used.
`Finally, perhaps the most common misconcep(cid:173)
`tion about magnetic stimulation is that the site of
`stimulation is underneath the centre of a circular
`coil. Figs. 12 and 13 show that both the electric
`field, and its spatial derivative, are zero under the
`centre of the coil. Hence, unless major tissue inho(cid:173)
`mogeneities causing gross distortion of the electric
`field patterns are nearby, this is the position where
`stimulation is least likely to occur.
`
`Allergan EX1098
`
`

`

`14
`
`The jigure-o_feight coil
`
`The only other coil geometry that is widely used
`at present is the figure-of-eight configuration first
`proposed by Ueno et al. (I 988). Two circular coils
`are placed side by side, and connected such that the
`current from the stimulator in one coil rotates in the
`opposite direction to that in the other. The advan(cid:173)
`tage of this geometry is that it can, under some
`conditions, decrease the uncertainty as to the site
`of stimulation. Fig. 15 shows the distribution of
`electric field loops calculated beneath a realistic
`model of a commercial
`figure-of-eight coil
`(d//dt = 108 Als, inside tum diameter 56 mm,
`outside tum diameter 90 mm, number of turns per
`winding = 9).
`The electric field (and current) loops induced in
`the tissue can be seen to add below the position
`where the two coils approach each other, but not
`elsewhere. This results in electric fields under the
`centre of the figure-of-eight coil typically twice
`those elsewhere under the coil. Fig. 16 shows the
`rate of change of electric field in a direction parallel
`
`to the mid-line between the two coils, calculated for
`the same plane.
`In contrast to the circular geometry of Fig. 13, the
`virtual cathode and anode regions (A and B, respec(cid:173)
`tively), where the rate of change of electric field are
`a maximum and minimum, occur only on the
`midline between the two coils for a nerve in this
`direction. Thus stimulation is more likely to occur
`on the centreline of this configuration than else(cid:173)
`where. The secondary peaks (C and D) which
`occur at the sides of the figure-of-eight coil are
`typically about half the amplitude of the central
`peaks. As is the case with circular coils, the site
`of stimulation of a nerve on the midline of this
`configuration and having a sharp bend near the
`centre of the coil, will tend to be at that bend
`(Abdeen and Stuchly 1994 ). Other examples of
`electric field distributions from both circular and
`figure-of-eight coils have been presented by Jali(cid:173)
`nous (1991 ).
`Figure-of-eight coils have been used to map
`cortical representation (see for example Levy et
`al. 1991) and are effective in stimulating structures
`
`m
`
`0.1
`
`0.05
`
`0
`
`-0.05
`
`-0.1
`
`V/m2
`3000
`
`2000
`
`1000
`
`0
`
`-0.1
`
`-0.