Electroencephalography and clinical Neurophysiology, 85 (1992) 253-264
253
© 1992 Elsevier Scientific Publishers Ireland, Ltd. 0924-980X/92/$05.00
ELMOCO 91167
D e t e r m i n i n g t h e site of s t i m u l a t i o n d u r i n g m a g n e t i c s t i m u l a t i o n of a p e r i p h e r a l n e r v e * Jan Nilsson a,**, Marcela Panizza a, Bradley J. Roth b Peter J. Basser b, Leonardo G. Cohen c Giuseppe Caruso d and Mark Hallett c a Laboratory of Clinical Neurophysiology, Fondazione Clinica del Lavoro, Castel Goffredo (MN) (Italy), b Biomedical Engineering and Instrumentation Program, National Center for Research Resources, National Institutes of Health, Bethesda, MD 20892 (U.S.A.), c Human Cortical Physiology Unit, Human Motor Control Section, Medical Neurology Branch, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892 (U.S.A.), and d EMG Laboratory, Fondazione Clinica del Lavoro, Campoli MT (BN) (Italy)
(Accepted for publication: 23 March 1992)
Summary Magnetic stimulation has not been routinely used for studies of peripheral nerve conduction primarily because of uncertainty about the location of the stimulation site. We performed several experiments to locate the site of nerve stimulation. Uniform latency shifts, similar to those that can be obtained during electrical stimulation, were observed when a magnetic coil was moved along the median nerve in the region of the elbow, thereby ensuring that the properties of the nerve and surrounding volume conductor were uniform. By evoking muscle responses both electrically and magnetically and matching their latencies, amplitudes and shapes, the site of stimulation was determined to be 3.0 + 0.5 cm from the center of an 8-shaped coil toward the coil handle. When the polarity of the current was reversed by rotating the coil, the latency of the evoked response shifted by 0.65+0.05 msec, which implies that the site of stimulation was displaced 4.1+0.5 cm. Additional evidence of cathode- and anode-like behavior during magnetic stimulation comes from observations of preferential activation of motor responses over H-reflexes with stimulation of a distal site, and of preferential activation of H-reflexes over motor responses with stimulation of a proximal site. Analogous behavior is observed with electrical stimulation. These experiments were motivated by, and are qualitatively consistent with, a mathematical model of magnetic stimulation of an axon.
Key words: Magnetic
stimulation; Mathematical modeling; Nerve conduction velocity studies; Virtual cathode
D u r i n g t h e last d e c a d e , m a g n e t i c s t i m u l a t i o n has b e e n used to activate cortical, spinal, a n d p e r i p h e r a l nerves for b o t h r e s e a r c h a n d clinical p u r p o s e s . In o r d e r to use m a g n e t i c s t i m u l a t i o n effectively, however, o n e m u s t k n o w w h e r e the nerve is d e p o l a r i z e d a n d h y p e r p o l a r i z e d , t h a t is, t h e l o c a t i o n s o f the virtual c a t h o d e and the virtual a n o d e . C o m m e r c i a l m a g n e t i c stimulators d o n o t identify t h e p o s i t i o n of the a n o d e and c a t h o d e , in p a r t b e c a u s e t h e m e c h a n i s m of nerve stimu l a t i o n is n o t w i d e l y u n d e r s t o o d , a n d in p a r t b e c a u s e t h e site of s t i m u l a t i o n c h a n g e s with t h e stimulus intensity a n d the p o s i t i o n a n d o r i e n t a t i o n of t h e coil relative to t h e nerve. T h e l o c a t i o n o f the virtual c a t h o d e d u r i n g m a g n e t i c s t i m u l a t i o n o f a p e r i p h e r a l nerve has b e e n i n f e r r e d f r o m c o m p a r i s o n s o f sensory a n d m o t o r r e s p o n s e s
e l i c i t e d by m a g n e t i c a n d electrical s t i m u l a t i o n ( D r e s s ler et al. 1988; E v a n s et al. 1988; M a c c a b e e et al. 1988, 1990a; C h o k r o v e r t y 1989; C h o k r o v e r t y et al. 1990; Claus et al. 1990; H a l l e t t et al. 1990; O l n e y et al. 1990; R a v n b o r g et al. 1990). T h e results, however, have b e e n inconsistent. M a t h e m a t i c a l m o d e l s of m a g n e t i c stimulation o f an axon have b e e n d e v e l o p e d ( D u r a n d et al. 1989; Reilly 1989; R o t h a n d B a s s e r 1990; B a s s e r a n d R o t h 1991), a n d o n e o f t h e s e ( B a s s e r a n d R o t h 1991) p r e d i c t s the site of s t i m u l a t i o n o f a p e r i p h e r a l axon in a limb. O u r goal is to d e t e r m i n e e x p e r i m e n t a l l y t h e site of activation d u r i n g m a g n e t i c s t i m u l a t i o n o f a p e r i p h eral nerve a n d to c o m p a r e it with t h e o r e t i c a l p r e d i c tions.
Methods Correspondence to: Dr. Mark Hallett, Building 10, Room 5N226, NINDS, NIH, Bethesda, MD 20892 (U.S.A.). * Presented in part at the 43rd Annual Meeting of the American Academy of Neurology, Boston, MA, April 21-27, 1991. ** This work was supported in part by a grant to Jan Nilsson from the Gangstedfonden, Copenhagen, Denmark.
Six h e a l t h y v o l u n t e e r s , a g e d 2 8 - 3 9 y e a r s ( m e a n , 33 years), gave t h e i r w r i t t e n i n f o r m e d c o n s e n t for t h e study. W e r e c o r d e d m o t o r a n d sensory r e s p o n s e s a n d H - r e f l e x e s e v o k e d by m a g n e t i c a n d e l e c t r i c a l stimulation of t h e m e d i a n nerve, as well as m o t o r r e s p o n s e s a n d H - r e f l e x e s e v o k e d by s t i m u l a t i o n o f t h e tibial
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nerve. The elbow and knee regions were chosen for these experiments because the nerves are rather superficial there for 10-15 cm.
Stimulation We stimulated the nerves electrically using squarewave, constant-current pulses (Dantec 15E07, Dantec Electronics, Skovlunde, Denmark) of 0.1-1 msec duration. Current was delivered through surface electrodes (Dantec 13L22) mounted in a plastic mold (2.5 cm between anode and cathode) and placed at the cubital fossa for median nerve stimulation and at the popliteal fossa for tibial nerve stimulation. In 1 experiment, 6 stimulating electrodes were placed on the skin surface 2.5 cm apart along the median nerve at the elbow. Magnetic stimulation was delivered from a Dantec magnetic stimulator with two different stimulating coils: an 8-shaped coil and a circular coil. Each "wing" of the 8-shaped coil (Dantec B55) had a 3 cm inner diameter and a 5.5 cm outer diameter (Fig. 1A). The stimulus pulse induced with this coil had a duration of 160/.,sec, measured to the end of the first phase of the
biphasic wave form (Fig. 1B). The circular, tightly wound prototype coil had a 7 cm inner diameter and a 9.7 cm outer diameter, and the induced stimulus pulse had a duration of 105 /zsec. (The pulse durations differ, even when the same stimulator is used, because the coils have different inductances and resistances.) In some experiments, we used a Cadwell MES-10 magnetic stimulator (Cadwell Laboratories, Inc., Kennewick, WA, U.S.A.) with either a prototype 8-shaped coil (each wing, 4 cm in diameter) or a standard circular coil (4.6 cm inner diameter and 9.2 cm outer diameter). The stimulus wave form produced by the Cadwell stimulator oscillates with a duration of 80 tzsec measured to the end of the first phase (Fig. 1C). We used the Cadwell stimulator to demonstrate the similarities and differences between biphasic and oscillating stimulus wave forms. The stimulus intensity was approximately 2 - 3 times greater than threshold. The current in the center (intersection of the wings) of the Dantec 8-shaped coil is directed away from the coil handle. The coil was centered over the nerve with the handle parallel to the nerve (Figs. 1D and 2). The
Outer rim - center point
A
B
2 Gin
C
A
coil handle
m
Coil housing
! A
Windings of the 8-shaped coil
t
Current direction
[]
Center of the coil
1
D
] 5 KT/~ 0.2 ma
Motor recording
Sensory recording
Fig. 1. A: physicalcharacteristics of the Dantec 8-shaped coil. B: induced current wave form for Dantec stimulator. C: induced current wave form for Cadwell stimulator. D: positioning of the 8-shaped coil and recording electrodes on the arm and hand.
SITE OF MAGNETIC STIMULATION handle was oriented distally when muscle and sensory responses were evoked. When H-reflexes were evoked, the coil was rotated so that the handle was oriented proximally, which resulted in reversal of the current polarity. The initial direction of the current through the Cadwell 8-shaped coil is toward the handle (opposite that of the Dantec coil). The circular Dantec coil was held in a plane tangential to the axis of the arm or leg, with the handle perpendicular to the axis of the limb and with the inner edge of the coil over the position of the cathode having the lowest threshold during electrical stimulation. The polarity of the current was reversed by turning the circular coil over, or flipping it, so that the surface of the coil that had been facing up was then facing down.
255
A
Recording For sensory recordings from the median nerve, we placed two ring electrodes 1 cm apart near the tip of digit III. For recording from muscles innervated by the median nerve, we placed a surface electrode over the belly of the abductor pollicis brevis (APB) and referenced it to the 2nd phalanx of the thumb, or inserted a wire electrode into the flexor carpi radialis (FCR) and referenced it to a surface electrode placed 4 cm away from the muscle. For muscles innervated by the tibial nerve, we placed two surface electrodes over the soleus muscle 4 cm apart, with the active electrode proximal. Sensory and motor potentials were amplified by a low-noise amplifier (Dantec 15C01), using a bandwidth of 2-2000 Hz. A ground electrode was placed distal to the stimulating electrode.
I
I
0
5
I
II) cm
B
Fig. 2. X-ray films of the Dantec coils. A: the circular coil. B: the 8-shaped coil.
Mathematical modeling To mathematically model the depolarization of a nerve fiber, we calculated the electric field induced in the arm using the technique described by Roth et al. (1990a). The arm was assumed to be a homogeneous cylindrical volume conductor, and the nerve was assumed to be uniform along its length and to lie in a straight line parallel to the axis of the cylinder. X-ray films of the two Dantec coils are shown in Fig. 2. Line segments were used to approximate the path of the copper wire in each coil: 387 for the 8-shaped coil, and 286 for the circular coil. We computed the electric field induced by the changing magnetic field using an algorithm in which the contribution of each line segment is determined individually, and the results are added (Cohen et al. 1990; Roth et al. 1991). Because of the difference in conductivity between tissue and air, a charge distribution will exist on the surface of the limb. We calculated the electric field produced by this charge distribution by solving Laplace's equation in the cylindrical conductor (Roth et al. 1990a). The conductor was replaced by a grid of 140,000 nodes, separated by 0.22 cm in the axial and radial directions, and 5.6 ° in
the azimuthal direction. Laplace's equation was approximated as a finite difference equation, and the resulting equations were solved using the method of systematic overrelaxation. The total electric field, E, is the sum of the electric fields produced by induction and charge. The component of the total electric field parallel to the axon, Ex, was numerically differentiated to determine dEx/dx. The radius of the arm, 3.5 cm, was estimated from a magnetic resonance image (MRI) of a human forearm at the elbow. The depth of the nerve below the skin surface was estimated from the M R I and an anatomical atlas (Grant 1962) to be 0.9 cm. To account for the thickness of the coil housing and wires, we assumed the coil was 0.5 cm above the surface of the arm.
Results
Experiment 1 This experiment demonstrated a smooth shift in latency with stimulation of positions equally spaced
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J. NILSSON ET A U
Coil position "1
Oem
!
! I
Coil l~osition
q 2.5 cm
i
20 I.tV
0 crn
V
5 cm
I 7.5 e m
4 mV
5 cm
L !
i
L_ I !
I
2ms Fig. 3. Typical recording of the response from the right median nerve to magnetic stimulation at the elbow. Traces show the sensory response (digit Ili) elicited when the 8-shaped coil was moved in steps of 2.5 cm proximally. The recording distance from position "0 cm" was 36 cm. Output of the magnetic stimulator was at 100%.
along the path of the nerve. We chose the 8-shaped coil for this experiment because it has a well-defined, localized area where the current runs parallel to the nerve. The median nerve was stimulated at the cubital fossa. When the Dantec 8-shaped coil was moved in 2.5 cm steps along the nerve, the mean latency shift was 0.41 + 0.13 msec and 0.37 + 0.04 msec for sensory and motor responses, respectively (Figs. 3 and 4). With movement of the stimulating electrodes or the Cadwell 8-shaped coil in 2.5 cm steps along the nerve, the latency shifts were similar (0.37 + 0.10 msec for sensory responses and 0.40 + 0.14 msec for motor responses to
I
4ms Fig. 4. Magnetic stimulation of the right median nerve at the elbow. Traces show the motor responses (APB) elicited when the 8-shaped coil was at the coil positions of 0 and 5 cm. Output of the magnetic stimulator was at 100%.
electrical stimulation; 0.37 + 0.07 msec for sensory responses and 0.40 + 0.06 msec for motor responses to magnetic stimulation). We did not always observe a uniform latency shift when the circular coil was moved along the median nerve at the elbow. Often, we detected no latency shifts until the circular coil was moved approximately one coil radius, and then the latency would change suddenly by 1 - 2 msec.
Experiment 2 We determined the site of stimulation by matching the latency, amplitude, and shape of the electrically evoked response to the magnetically evoked response. We adjusted the stimulating electrode position and
Coil center at position: Current
7"1 P'l
direction~ in coils ~
!
Magnetic stim
0 cm
[('f-~x~"~!"~ ~
Proximiltlr--~(
cath°de
]~D'is~al- - -
3 cm
For the electrical cathode
I
I
-2
0
:" .5
3 cra
2 ms
Fig. 5. Typical recordings of magnetic and electrical stimulation of the right median nerve at the elbow. Upper trace shows the sensory response (digit III) elicited by the 8-shaped magnetic coil (stimulator output, 100%). Lower trace shows the sensory response elicited by electrical stimulation, with the cathode position 3 cm closer to the recording electrodes than the center of the magnetic coil. The recording distance from position "0 cm" was 36 cm.
SITE OF MAGNETIC STIMULATION
257
Experiment 3
c u r r e n t until the two wave forms m o s t n e a r l y overl a p p e d . T h e o p t i m a l m a t c h was f o u n d w h e n t h e catho d e e l e c t r o d e was 3.0 + 0.5 cm f r o m t h e c e n t e r o f t h e coil in t h e d i r e c t i o n o f t h e h a n d l e (Fig. 5). This result did not c h a n g e w h e n the a n o d e e l e c t r o d e was m o v e d to 4 o t h e r p o s i t i o n s f a r t h e r f r o m t h e c a t h o d e .
In o r d e r to d e m o n s t r a t e l a t e n c y shifts, we elicited r e s p o n s e s f r o m t h e m e d i a n nerve with t h e D a n t e c 8 - s h a p e d a n d circular coils with a n d w i t h o u t reversal o f the c u r r e n t polarity. C a r e was t a k e n to e n s u r e that a f t e r moving t h e coil to r e v e r s e t h e p o l a r i t y it r e m a i n e d
Magnetic stimulation
A
Motor response
Sensory responses
Anode
2mV
diJtal z~ve e~d
I 101tV
i!' :I
Anode
dultel nervee n d 2 ms
4 ms "A" Side of coil with counter-clockwise current direction "B" Side of coil with clockwise current direction ref. Point of reference on the nerve
B
Electrical stimulation
Motor response
4 ms
Sensory responses
2
ms
Fig. 6. Magnetic and electrical stimulation of the right median nerve at the cubital fossa. A: latency changes recorded from APB (motor responses) and digit 1II (sensory responses) when the Dantec circular coil was flipped. B: shorter latency changes were recorded with electrical stimulation when the anode and cathode were interchanged.
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at the same distance from the nerve and in the same orientation (Fig. 6A). Rotating the Dantec 8-shaped coil resulted in latency shifts of 0.65 + 0.05 msee for both motor and sensory responses. The latency change caused by flipping the Dantec circular coil was 0.65 + 0.07 msec for both motor and sensory responses. With the Cadwell stimulator, we obtained latency shifts of 0.25 + 0.04 msec for the 8-shaped coil and 0.20 + 0.05 msec for the circular coil. During electrical stimulation, interchanging the cathode and anode caused a latency shift of 0.40 + 0.14 msec (Fig. 6B).
Experiment 4 During electrical stimulation, a proximal cathode and distal anode result in preferential stimulation of H-reflexes over motor responses; conversely a distal cathode and proximal anode result in preferential stimulation of motor nerves (Panizza et al. 1989, 1992). A similar effect was observed during magnetic stimulation of the tibial nerve with the Dantec circular coil. Motor responses were evoked preferentially with the coil oriented so that the coil current was directed proximally, and H-reflexes were evoked preferentially with the coil current directed distally (Fig. 7A), with the same stimulus intensity, 75%, used in both cases. We found no such differences when the Cadwell circular coil was flipped (Fig. 7B).
Model predictions We calculated the site of stimulation using the mathematical model of Basser and Roth (1991). Results from this model are illustrated in Fig. 8 for the simple case of coils positioned above, and oriented parallel to, a large volume conductor (for the moment we neglect the influence of charge on the arm surface). Fig. 8A shows the electric field lines induced 1 cm below the Dantec 8-shaped coil. The electric field follows the field lines and its strength is proportional to their density. Roth and Basser (1990) predicted that an axon is first depolarized where the negative derivative along the axon of the component of the electric field parallel to the axon, - d E x / d x , is large. For example, the electric field parallel to the nerve, Ex, is largest below the center of the Dantec 8-shaped coil (Fig. 8A), but Ex is uniform there, so the membrane is not depolarized (Fig. 8B). Proximal to the center of this coil, E~ is increasing along the path of the nerve, which implies hyperpolarization of the membrane. Distal to the coil E x is decreasing, which implies depolarization. A contour plot of dEx/dX (large negative values, in m V / c m 2, correspond to depolarization) is shown in Fig. 8B. Depolarization is maximum approximately 2.5 cm distal to the center of the coil, at the location marked "S," which represents the center of the virtual cathode.
B
A
[i
253
© 1992 Elsevier Scientific Publishers Ireland, Ltd. 0924-980X/92/$05.00
ELMOCO 91167
D e t e r m i n i n g t h e site of s t i m u l a t i o n d u r i n g m a g n e t i c s t i m u l a t i o n of a p e r i p h e r a l n e r v e * Jan Nilsson a,**, Marcela Panizza a, Bradley J. Roth b Peter J. Basser b, Leonardo G. Cohen c Giuseppe Caruso d and Mark Hallett c a Laboratory of Clinical Neurophysiology, Fondazione Clinica del Lavoro, Castel Goffredo (MN) (Italy), b Biomedical Engineering and Instrumentation Program, National Center for Research Resources, National Institutes of Health, Bethesda, MD 20892 (U.S.A.), c Human Cortical Physiology Unit, Human Motor Control Section, Medical Neurology Branch, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, MD 20892 (U.S.A.), and d EMG Laboratory, Fondazione Clinica del Lavoro, Campoli MT (BN) (Italy)
(Accepted for publication: 23 March 1992)
Summary Magnetic stimulation has not been routinely used for studies of peripheral nerve conduction primarily because of uncertainty about the location of the stimulation site. We performed several experiments to locate the site of nerve stimulation. Uniform latency shifts, similar to those that can be obtained during electrical stimulation, were observed when a magnetic coil was moved along the median nerve in the region of the elbow, thereby ensuring that the properties of the nerve and surrounding volume conductor were uniform. By evoking muscle responses both electrically and magnetically and matching their latencies, amplitudes and shapes, the site of stimulation was determined to be 3.0 + 0.5 cm from the center of an 8-shaped coil toward the coil handle. When the polarity of the current was reversed by rotating the coil, the latency of the evoked response shifted by 0.65+0.05 msec, which implies that the site of stimulation was displaced 4.1+0.5 cm. Additional evidence of cathode- and anode-like behavior during magnetic stimulation comes from observations of preferential activation of motor responses over H-reflexes with stimulation of a distal site, and of preferential activation of H-reflexes over motor responses with stimulation of a proximal site. Analogous behavior is observed with electrical stimulation. These experiments were motivated by, and are qualitatively consistent with, a mathematical model of magnetic stimulation of an axon.
Key words: Magnetic
stimulation; Mathematical modeling; Nerve conduction velocity studies; Virtual cathode
D u r i n g t h e last d e c a d e , m a g n e t i c s t i m u l a t i o n has b e e n used to activate cortical, spinal, a n d p e r i p h e r a l nerves for b o t h r e s e a r c h a n d clinical p u r p o s e s . In o r d e r to use m a g n e t i c s t i m u l a t i o n effectively, however, o n e m u s t k n o w w h e r e the nerve is d e p o l a r i z e d a n d h y p e r p o l a r i z e d , t h a t is, t h e l o c a t i o n s o f the virtual c a t h o d e and the virtual a n o d e . C o m m e r c i a l m a g n e t i c stimulators d o n o t identify t h e p o s i t i o n of the a n o d e and c a t h o d e , in p a r t b e c a u s e t h e m e c h a n i s m of nerve stimu l a t i o n is n o t w i d e l y u n d e r s t o o d , a n d in p a r t b e c a u s e t h e site of s t i m u l a t i o n c h a n g e s with t h e stimulus intensity a n d the p o s i t i o n a n d o r i e n t a t i o n of t h e coil relative to t h e nerve. T h e l o c a t i o n o f the virtual c a t h o d e d u r i n g m a g n e t i c s t i m u l a t i o n o f a p e r i p h e r a l nerve has b e e n i n f e r r e d f r o m c o m p a r i s o n s o f sensory a n d m o t o r r e s p o n s e s
e l i c i t e d by m a g n e t i c a n d electrical s t i m u l a t i o n ( D r e s s ler et al. 1988; E v a n s et al. 1988; M a c c a b e e et al. 1988, 1990a; C h o k r o v e r t y 1989; C h o k r o v e r t y et al. 1990; Claus et al. 1990; H a l l e t t et al. 1990; O l n e y et al. 1990; R a v n b o r g et al. 1990). T h e results, however, have b e e n inconsistent. M a t h e m a t i c a l m o d e l s of m a g n e t i c stimulation o f an axon have b e e n d e v e l o p e d ( D u r a n d et al. 1989; Reilly 1989; R o t h a n d B a s s e r 1990; B a s s e r a n d R o t h 1991), a n d o n e o f t h e s e ( B a s s e r a n d R o t h 1991) p r e d i c t s the site of s t i m u l a t i o n o f a p e r i p h e r a l axon in a limb. O u r goal is to d e t e r m i n e e x p e r i m e n t a l l y t h e site of activation d u r i n g m a g n e t i c s t i m u l a t i o n o f a p e r i p h eral nerve a n d to c o m p a r e it with t h e o r e t i c a l p r e d i c tions.
Methods Correspondence to: Dr. Mark Hallett, Building 10, Room 5N226, NINDS, NIH, Bethesda, MD 20892 (U.S.A.). * Presented in part at the 43rd Annual Meeting of the American Academy of Neurology, Boston, MA, April 21-27, 1991. ** This work was supported in part by a grant to Jan Nilsson from the Gangstedfonden, Copenhagen, Denmark.
Six h e a l t h y v o l u n t e e r s , a g e d 2 8 - 3 9 y e a r s ( m e a n , 33 years), gave t h e i r w r i t t e n i n f o r m e d c o n s e n t for t h e study. W e r e c o r d e d m o t o r a n d sensory r e s p o n s e s a n d H - r e f l e x e s e v o k e d by m a g n e t i c a n d e l e c t r i c a l stimulation of t h e m e d i a n nerve, as well as m o t o r r e s p o n s e s a n d H - r e f l e x e s e v o k e d by s t i m u l a t i o n o f t h e tibial
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nerve. The elbow and knee regions were chosen for these experiments because the nerves are rather superficial there for 10-15 cm.
Stimulation We stimulated the nerves electrically using squarewave, constant-current pulses (Dantec 15E07, Dantec Electronics, Skovlunde, Denmark) of 0.1-1 msec duration. Current was delivered through surface electrodes (Dantec 13L22) mounted in a plastic mold (2.5 cm between anode and cathode) and placed at the cubital fossa for median nerve stimulation and at the popliteal fossa for tibial nerve stimulation. In 1 experiment, 6 stimulating electrodes were placed on the skin surface 2.5 cm apart along the median nerve at the elbow. Magnetic stimulation was delivered from a Dantec magnetic stimulator with two different stimulating coils: an 8-shaped coil and a circular coil. Each "wing" of the 8-shaped coil (Dantec B55) had a 3 cm inner diameter and a 5.5 cm outer diameter (Fig. 1A). The stimulus pulse induced with this coil had a duration of 160/.,sec, measured to the end of the first phase of the
biphasic wave form (Fig. 1B). The circular, tightly wound prototype coil had a 7 cm inner diameter and a 9.7 cm outer diameter, and the induced stimulus pulse had a duration of 105 /zsec. (The pulse durations differ, even when the same stimulator is used, because the coils have different inductances and resistances.) In some experiments, we used a Cadwell MES-10 magnetic stimulator (Cadwell Laboratories, Inc., Kennewick, WA, U.S.A.) with either a prototype 8-shaped coil (each wing, 4 cm in diameter) or a standard circular coil (4.6 cm inner diameter and 9.2 cm outer diameter). The stimulus wave form produced by the Cadwell stimulator oscillates with a duration of 80 tzsec measured to the end of the first phase (Fig. 1C). We used the Cadwell stimulator to demonstrate the similarities and differences between biphasic and oscillating stimulus wave forms. The stimulus intensity was approximately 2 - 3 times greater than threshold. The current in the center (intersection of the wings) of the Dantec 8-shaped coil is directed away from the coil handle. The coil was centered over the nerve with the handle parallel to the nerve (Figs. 1D and 2). The
Outer rim - center point
A
B
2 Gin
C
A
coil handle
m
Coil housing
! A
Windings of the 8-shaped coil
t
Current direction
[]
Center of the coil
1
D
] 5 KT/~ 0.2 ma
Motor recording
Sensory recording
Fig. 1. A: physicalcharacteristics of the Dantec 8-shaped coil. B: induced current wave form for Dantec stimulator. C: induced current wave form for Cadwell stimulator. D: positioning of the 8-shaped coil and recording electrodes on the arm and hand.
SITE OF MAGNETIC STIMULATION handle was oriented distally when muscle and sensory responses were evoked. When H-reflexes were evoked, the coil was rotated so that the handle was oriented proximally, which resulted in reversal of the current polarity. The initial direction of the current through the Cadwell 8-shaped coil is toward the handle (opposite that of the Dantec coil). The circular Dantec coil was held in a plane tangential to the axis of the arm or leg, with the handle perpendicular to the axis of the limb and with the inner edge of the coil over the position of the cathode having the lowest threshold during electrical stimulation. The polarity of the current was reversed by turning the circular coil over, or flipping it, so that the surface of the coil that had been facing up was then facing down.
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A
Recording For sensory recordings from the median nerve, we placed two ring electrodes 1 cm apart near the tip of digit III. For recording from muscles innervated by the median nerve, we placed a surface electrode over the belly of the abductor pollicis brevis (APB) and referenced it to the 2nd phalanx of the thumb, or inserted a wire electrode into the flexor carpi radialis (FCR) and referenced it to a surface electrode placed 4 cm away from the muscle. For muscles innervated by the tibial nerve, we placed two surface electrodes over the soleus muscle 4 cm apart, with the active electrode proximal. Sensory and motor potentials were amplified by a low-noise amplifier (Dantec 15C01), using a bandwidth of 2-2000 Hz. A ground electrode was placed distal to the stimulating electrode.
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Fig. 2. X-ray films of the Dantec coils. A: the circular coil. B: the 8-shaped coil.
Mathematical modeling To mathematically model the depolarization of a nerve fiber, we calculated the electric field induced in the arm using the technique described by Roth et al. (1990a). The arm was assumed to be a homogeneous cylindrical volume conductor, and the nerve was assumed to be uniform along its length and to lie in a straight line parallel to the axis of the cylinder. X-ray films of the two Dantec coils are shown in Fig. 2. Line segments were used to approximate the path of the copper wire in each coil: 387 for the 8-shaped coil, and 286 for the circular coil. We computed the electric field induced by the changing magnetic field using an algorithm in which the contribution of each line segment is determined individually, and the results are added (Cohen et al. 1990; Roth et al. 1991). Because of the difference in conductivity between tissue and air, a charge distribution will exist on the surface of the limb. We calculated the electric field produced by this charge distribution by solving Laplace's equation in the cylindrical conductor (Roth et al. 1990a). The conductor was replaced by a grid of 140,000 nodes, separated by 0.22 cm in the axial and radial directions, and 5.6 ° in
the azimuthal direction. Laplace's equation was approximated as a finite difference equation, and the resulting equations were solved using the method of systematic overrelaxation. The total electric field, E, is the sum of the electric fields produced by induction and charge. The component of the total electric field parallel to the axon, Ex, was numerically differentiated to determine dEx/dx. The radius of the arm, 3.5 cm, was estimated from a magnetic resonance image (MRI) of a human forearm at the elbow. The depth of the nerve below the skin surface was estimated from the M R I and an anatomical atlas (Grant 1962) to be 0.9 cm. To account for the thickness of the coil housing and wires, we assumed the coil was 0.5 cm above the surface of the arm.
Results
Experiment 1 This experiment demonstrated a smooth shift in latency with stimulation of positions equally spaced
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2ms Fig. 3. Typical recording of the response from the right median nerve to magnetic stimulation at the elbow. Traces show the sensory response (digit Ili) elicited when the 8-shaped coil was moved in steps of 2.5 cm proximally. The recording distance from position "0 cm" was 36 cm. Output of the magnetic stimulator was at 100%.
along the path of the nerve. We chose the 8-shaped coil for this experiment because it has a well-defined, localized area where the current runs parallel to the nerve. The median nerve was stimulated at the cubital fossa. When the Dantec 8-shaped coil was moved in 2.5 cm steps along the nerve, the mean latency shift was 0.41 + 0.13 msec and 0.37 + 0.04 msec for sensory and motor responses, respectively (Figs. 3 and 4). With movement of the stimulating electrodes or the Cadwell 8-shaped coil in 2.5 cm steps along the nerve, the latency shifts were similar (0.37 + 0.10 msec for sensory responses and 0.40 + 0.14 msec for motor responses to
I
4ms Fig. 4. Magnetic stimulation of the right median nerve at the elbow. Traces show the motor responses (APB) elicited when the 8-shaped coil was at the coil positions of 0 and 5 cm. Output of the magnetic stimulator was at 100%.
electrical stimulation; 0.37 + 0.07 msec for sensory responses and 0.40 + 0.06 msec for motor responses to magnetic stimulation). We did not always observe a uniform latency shift when the circular coil was moved along the median nerve at the elbow. Often, we detected no latency shifts until the circular coil was moved approximately one coil radius, and then the latency would change suddenly by 1 - 2 msec.
Experiment 2 We determined the site of stimulation by matching the latency, amplitude, and shape of the electrically evoked response to the magnetically evoked response. We adjusted the stimulating electrode position and
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Fig. 5. Typical recordings of magnetic and electrical stimulation of the right median nerve at the elbow. Upper trace shows the sensory response (digit III) elicited by the 8-shaped magnetic coil (stimulator output, 100%). Lower trace shows the sensory response elicited by electrical stimulation, with the cathode position 3 cm closer to the recording electrodes than the center of the magnetic coil. The recording distance from position "0 cm" was 36 cm.
SITE OF MAGNETIC STIMULATION
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Experiment 3
c u r r e n t until the two wave forms m o s t n e a r l y overl a p p e d . T h e o p t i m a l m a t c h was f o u n d w h e n t h e catho d e e l e c t r o d e was 3.0 + 0.5 cm f r o m t h e c e n t e r o f t h e coil in t h e d i r e c t i o n o f t h e h a n d l e (Fig. 5). This result did not c h a n g e w h e n the a n o d e e l e c t r o d e was m o v e d to 4 o t h e r p o s i t i o n s f a r t h e r f r o m t h e c a t h o d e .
In o r d e r to d e m o n s t r a t e l a t e n c y shifts, we elicited r e s p o n s e s f r o m t h e m e d i a n nerve with t h e D a n t e c 8 - s h a p e d a n d circular coils with a n d w i t h o u t reversal o f the c u r r e n t polarity. C a r e was t a k e n to e n s u r e that a f t e r moving t h e coil to r e v e r s e t h e p o l a r i t y it r e m a i n e d
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Sensory responses
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Fig. 6. Magnetic and electrical stimulation of the right median nerve at the cubital fossa. A: latency changes recorded from APB (motor responses) and digit 1II (sensory responses) when the Dantec circular coil was flipped. B: shorter latency changes were recorded with electrical stimulation when the anode and cathode were interchanged.
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at the same distance from the nerve and in the same orientation (Fig. 6A). Rotating the Dantec 8-shaped coil resulted in latency shifts of 0.65 + 0.05 msee for both motor and sensory responses. The latency change caused by flipping the Dantec circular coil was 0.65 + 0.07 msec for both motor and sensory responses. With the Cadwell stimulator, we obtained latency shifts of 0.25 + 0.04 msec for the 8-shaped coil and 0.20 + 0.05 msec for the circular coil. During electrical stimulation, interchanging the cathode and anode caused a latency shift of 0.40 + 0.14 msec (Fig. 6B).
Experiment 4 During electrical stimulation, a proximal cathode and distal anode result in preferential stimulation of H-reflexes over motor responses; conversely a distal cathode and proximal anode result in preferential stimulation of motor nerves (Panizza et al. 1989, 1992). A similar effect was observed during magnetic stimulation of the tibial nerve with the Dantec circular coil. Motor responses were evoked preferentially with the coil oriented so that the coil current was directed proximally, and H-reflexes were evoked preferentially with the coil current directed distally (Fig. 7A), with the same stimulus intensity, 75%, used in both cases. We found no such differences when the Cadwell circular coil was flipped (Fig. 7B).
Model predictions We calculated the site of stimulation using the mathematical model of Basser and Roth (1991). Results from this model are illustrated in Fig. 8 for the simple case of coils positioned above, and oriented parallel to, a large volume conductor (for the moment we neglect the influence of charge on the arm surface). Fig. 8A shows the electric field lines induced 1 cm below the Dantec 8-shaped coil. The electric field follows the field lines and its strength is proportional to their density. Roth and Basser (1990) predicted that an axon is first depolarized where the negative derivative along the axon of the component of the electric field parallel to the axon, - d E x / d x , is large. For example, the electric field parallel to the nerve, Ex, is largest below the center of the Dantec 8-shaped coil (Fig. 8A), but Ex is uniform there, so the membrane is not depolarized (Fig. 8B). Proximal to the center of this coil, E~ is increasing along the path of the nerve, which implies hyperpolarization of the membrane. Distal to the coil E x is decreasing, which implies depolarization. A contour plot of dEx/dX (large negative values, in m V / c m 2, correspond to depolarization) is shown in Fig. 8B. Depolarization is maximum approximately 2.5 cm distal to the center of the coil, at the location marked "S," which represents the center of the virtual cathode.
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