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Importance of soft tissue inhomogeneity in magnetic peripheral nerve stimulation
ELSEVIER
Electroencephalography and clinical Neurophysiology 105 (1997) 406-413
Importance of soft tissue inhomogeneity in magnetic peripheral nerve stimulation Makoto
K o b a y a s h i a,b,*, S h o o g o U e n o a, T a k a h i d e K u r o k a w a b
alnstitute of Medical Electronics, Faculty of Medicine, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan bDepartment of Orthopedics, Faculty of Medicine, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan Accepted for publication: 23 May 1997
Abstract In magnetic peripheral nerve stimulation with a figure-of-eight coil, a 'tangential-edge' coil orientation (the nerve is beneath the coil intersection and perpendicular to the coil wings) is ideal theoretically. However, some experimental results show that strong muscle responses are elicited with a 'symmetrical-tangential' coil orientation (the nerve is beneath the coil intersection and parallel to the coil wings), which is inconsistent with the cable theory. We hypothesized that the 10:1 conductivity difference between muscle and fat would cause inconsistent results during magnetic median nerve stimulation in the elbow, which was verified using an inhomogeneous volume conductor model. The induced electric fields were measured in a model composed of saline solutions of different concentrations divided by a cellophane sheet. A nerve was imagined along the boundary between the two solutions, and the coil was held in a 'symmetricaltangential' position. Virtual cathodes, which were off the nerve in the homogeneous model, were on the nerve in the inhomogeneous model. The previous inconsistent results were explained by considering soft tissue inhomogeneity without any modification of the assumption in the cable theory that only the induced electric field component parallel to the nerve is responsible for nerve excitation. © 1997 Elsevier Science Ireland Ltd.
Keywords: Peripheral nerve; Magnetic stimulation; Figure-of-eight coil; Median nerve; Volume conductor model; Tissue inhomogeneity
1. Introduction Based on the experimental results (Rushton, 1927) that electric fields oriented parallel to nerve fibers are optimal for nerve excitation, mathematical models of magnetic stimulation of an axon have been developed (Durand et al., 1989; Reilly, 1989; Roth and Basser, 1990; Nagarajan et al., 1993). In those models, a long straight nerve excites at a virtual cathode where the negative spatial derivative of the electric field induced along the axon is large. Although this prediction is consistent with most experimental results (Evans et al., 1988; Chokroverty et al., 1990; Maccabee et al., 1990, 1991, 1993; Olney et al., 1990; Evans, 1991; Nilsson et al., 1992), some results are inconsistent with the theory (Cros et al., 1990; Hallett et al., 1990; Yunokuchi et al., 1995; Sun et al., 1995; Ruohonen et al., 1996). In the * Corresponding author. Tel.: +81 3 38122111; fax: +81 3 56897215; e-mail: rnakoto @medes.m.u-tokyo.ac.jp
latter, strong muscle responses were elicited despite coil orientations which theoretically generated no virtual cathode. Such a discrepancy between the theory and the experiments must come from invalid assumptions in the theory, including those regarding tissue inhomogeneity. In the past, tissue inhomogeneity was considered a problem only between bone and soft tissue (Maccabee et al., 1991, 1993). In this report, we discuss inhomogeneity between muscle and fat.
2. Methods and materials The median nerve in the elbow runs through subcutaneous fat tissue with the biceps brachii muscle at the radial side of the nerve (Fig. 1). The conductivity of muscle is about ten times higher than that of fat (Foster and Schwan, 1989). We hypothesized that magnetic median nerve stimu-
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lation might lead to inconsistent results because the median nerve runs near the boundary between muscle and fat; that is, the conductivity difference between muscle and fat might cause the electric field induced in the elbow to be different from that induced in homogeneous media. To verify this hypothesis, the results of two experiments were compared with each other. First, we investigated whether we could get inconsistent results by changing coil orientations during magnetic stimulation of the median nerve in the elbow. Second, the electric field induced in an inhomogeneous volume conductor model was measured to determine whether there was a virtual cathode on an imaginary nerve. In the model, the biceps brachii muscle and subcutaneous fat were represented simply by two troughs containing saline solutions of different concentrations. 2.1. Median nerve stimulation in a human subject 2.1.1. Subject
The subject was a 32 year old healthy male who gave informed consent. The median nerve in the left arm was stimulated both electrically and magnetically. 2.1.2. Electrical stimulation
Results of supramaximal electrical stimulation were used to estimate sites of excitation during magnetic stimulation. The median nerve was stimulated via surface electrodes with a cathode-anode distance of 25 mm. The duration of stimulating rectangular current was 0.2 ms. A monopolar needle electrode was inserted into the belly of the abductor pollicis brevis muscle (APB) and was referenced to a sura
Ulnar side
b
c
Radial side
Fig. 1. MRI cross-section of the left elbow (a 32 year old male who participated in the experiment as a subject). The level of the cross-section matched the reference point for electrical stimulation in the experiment, a, subcutaneous fat; b, median nerve; c, biceps brachii; d, brachialis; e, humerus; f, ulna (olecranon). The median nerve runs through subcutaneous tissue. The biceps brachii muscle is radial to the median nerve.
Orientation PROX DIST Coil current Proximal Distal Nerve and Perpend. Perpend. coil wings CRadial rv~e~~:~
f~jCoil
Ne
RAD Radial Parallel
ULN Ulnar Parallel
current
4 , . , , - - Proximal Fig. 2. Coil orientation.
face electrode placed on the distal tendon of the APB. Compound motor action potentials (CMAPs) were amplified by an electromyograph (Neuropack E, Nihon Kohden Co.) with a bandwidth of 2 H z - 3 kHz. A ground electrode was placed on the wrist. The course of the median nerve across the elbow was determined. The point where the nerve crosses the elbow flexion crease was marked as a common reference point for electric and magnetic stimulation. A cathode was kept exactly on the reference point during elbow stimulation. Each set of 5 C M A P recordings was averaged for 8 repetitions of elbow and wrist stimulation (40 stimuli at each site). The mean latency in each site, motor nerve conduction velocity (MCV) between the wrist and elbow and their standard deviations were calculated using 8 averaged values. 2.1.3. Magnetic stimulation
The relationship of coil orientation to muscle response during magnetic stimulation was investigated. The median nerve in the elbow was stimulated with a figure-of-eight coil (YM-111B, 10.0 cm o.d., 5.0 cm i.d.; Nihon Kohden Co.) held in 4 different orientations: PROX, DIST, RAD and ULN (Fig. 2). In each orientation, the midpoint of the intersection of the coil was placed on the same reference point as during electrical stimulation, and the coil plane was kept tangential to the skin surface. PROX and DIST correspond to a 'tangential-edge' orientation, and RAD and ULN to a 'symmetrical-tangential' position (Maccabee et al., 1990). The coil held in the latter position should generate no virtual cathode on the nerve, according to theoretical calculations for homogeneous media (Cohen et al., 1990; Roth and Basser, 1990; Nilsson et al., 1992; Ruohonen et al., 1996). Thus, large amplitudes of CMAPs in either RAD or ULN should be 'inconsistent' with the theory. The magnetic stimulator was a prototype (AAA-10687; Nihon-Kohden Co.). The wave form of the induced stimulus pulse was biphasic (Fig. 3a). The duration of its first phase was 65 ~s. The induced magnetic field increased linearly with the capacitor voltage; 70, 80 and 90% of maximal output were used for median nerve stimulation. The recording equipment was the same as that used during electrical stimulation. Each set of 5 CMAP recordings was averaged for 8 repe-
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"~"
a
Olney et al., 1990; Ravnborg et al., 1990; Nilsson et al., 1992; Ruohonen et al., 1996). 2.2. Electric field measurements in volume conductor models
I1
0.5 cm E a
b
Fig. 3. Induced stimulus pulse wave form and measuring probe. (a) Induced stimulus pulse wave form. As the stimulus current wave form was monophasic, the induced stimulus pulse (time derivative of current) wave form was biphasic. (b) Probe consisting of a coaxial cable bent at a right-angle 1 cm from the end. The cable was passed through an acrylic tube. The distal 10 ram of the outside insulation and shield of the cable were stripped to record the voltage drop between the cable shield and the bared distal tip.
titions (40 stimuli were done) in each condition. The mean latency, mean amplitude and their standard deviations were calculated using 8 averaged values. 2.1.4. Statistical analysis First, the amplitudes in each coil orientation were compared among different stimulus intensities to determine whether the amplitudes were maximal. Then, the amplitudes at 90% intensity were compared among different coil orientations. All pairs were evaluated by the KruskalWallis method, and each pair was compared by the Scheffe F test (P < 0.05). 2.1.5. Sites of excitation As a nerve excites almost directly beneath the cathode in electrical stimulation (Wiederholt, 1970), sites of excitation at 90% intensity in magnetic stimulation were estimated from the latency difference between magnetic and electrical stimulation (Evans et al., 1988; Maccabee et al., 1988, 1990; Amassian et al., 1989; Claus et al., 1990; Hallett et al., 1990;
2.2.1. Volume conductor model A volume conductor model was composed of two troughs, a small one within a large one (Fig. 4a), The small and large troughs represented the biceps muscle and subcutaneous fat tissue, respectively. The large trough was made of acrylic boards. The frame of the small trough was made of acrylic rods, and its faces were made of cellophane sheets (Fig. 4b). As electrolytes can pass through cellophane sheets, the electric current flowed through the boundary between the small and large troughs. This 'double-lxough' model was used for both the homogeneous and inhomogeneous models. In accordance with the conductivity difference between muscle and fat as mentioned above (Foster and Schwan, 1989), the large and small troughs in the inhomogeneous model were filled with 0.1% and 0.9% saline, respectively. In the homogeneous model, both troughs were filled with 0.9% saline. 2.2.2. Magnetic coil and stimulator The figure-of-eight coil was held beneath the troughs by a wooden support. The coil and magnetic stimulator were the same as used in median nerve stimulation. The stimulus intensity was kept at 10% of its maximum. In the experiment with the homogeneous model, the coil current direction at the intersection was away from the small trough. With the inhomogeneous model, it was toward or away from the small trough. 2.2. 3. Electric field measurements A disc electrode was immersed in the saline solution as a ground electrode. The electric fields induced in the trough were measured with a probe made from a coaxial cable (Fig. 3b). The coaxial cable (3.0 nun o.d.) was passed through an
l} c m
cm
7c i...1
}il a
m
0.5 e m b
Fig. 4. Volume conductor model. (a) Double trough. The small trough was inside the large trough. In the inhomogeneous model, the small trough was filled with 0.9% saline solution, and the large one with 0.1% saline. In the homogeneous model, both troughs were filled with 0,9% saline solutions. A figure-ofeight coil was fixed beneath the trough by a wooden support. (b) The structure of the small trough. The small trough was constructed of an acrylic frame faced with cellophane sheets.
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E l b o w F l e x i o n Crease
(cmtlO
~
~
-
-
~
Proximal
Median Nerve
r----'---Coil Orientation Radial
Mean
-46 m m
~-~
-44 mm
Distal *
Ulnar Proximal
2.7 mm 21 m m
Error bar : + 1SD
-6o-so-4o- o-Ao-io o io 2o 3o 4o mm Fig. 5. The arrangement of two troughs. One of the edges of the small trough was on the line where Y= 0.5. Measurements were taken at 21 × 13 points in the X-Y plane parallel to the bottom of the trough. Only the X-component of the induced electric field (Ex) was measured.
acrylic tube (6.0 m m o.d.) and connected to an amplifier. The distal 10 mm of the outside insulation and shield of the cable were stripped to record the voltage drop between the cable shield and the bared distal tip. The distal end of the probe was bent at a right-angle and submerged in the saline solution. It was kept parallel to the X-axis 0.5 cm above the base of the trough and was moved in 10 mm increments in a given X - Y plane (Fig. 5). Thus, the voltage drop only in the X direction was recorded at 273 (21 x 13) different locations. By dividing the voltage drop by 10 mm, we calculated the X component of the induced electric field (Ex, mV/mm). As Maccabee et al. (1991), we also calculated the first spatial derivative of Ex (dEfldx). These values were normalized and illustrated as contour maps. 2.2.4. Decrease of the conductivity difference The conductivity of saline solution was controlled by its concentration. When two electrolyte solutions of different concentration are divided by a cellophane sheet, both the
181
Error bar : -4-1SD
20
16
,
60
~
1
-o- DIST -~- PROX NS -~- RAD
-¢- U I ~
, : p<0.005 NS : difference is not significant
70 80 90 Stimulus intensity (%)
Fig. 6. Relation of stimulus intensity to amplitudes. As the amplitudes in PROX reached their maximum at 70% intensity, 90% intensity might have been supramaximal. The amplitudes at 90% intensity in ULN were as large as those in PROX. Thus, 90% intensity in ULN might not have been supramaximal, but was at least maximal. In other coil orientations (DIST and RAD), the amplitudes did not reached their maximum.
Fig. 7. Estimated sites of excitation in magnetic stimulation. The distance between the site of excitation and the elbow flexion crease was assumed to be proportional to the latency difference between electrical and magnetic stimulation.
concentration and conductivity differences decrease with time. The electrical conductivity in the large and small trough were measured by a conductivity meter (YSI model 33 S-C-T Meter; Yellow Springs Co.) at the beginning, middle and end of the experiment with the inhomogeneous model where the coil current was toward the small trough to ensure the conductivity difference was maintained at a significant level.
3. Results
3.1. Median nerve stimulation on a human subject 3.1.1. Electrical stimulation The latency in elbow stimulation was 7.12 ms (SD 0.0214). The MCV between the elbow and wrist was 76.0 m/s (SD 1.10). 3.1.2. Magnetic stimulation Fig. 6 shows the relation between the stimulus intensities and the amplitudes of CMAPs in each coil orientation. DIST, PROX, RAD and ULN in Fig. 6 refer to current directions in the coil (see Fig. 2). The amplitudes at 90% intensity in ULN, theoretically with no virtual cathode, were as large as those in PROX. Although the coils were 'symmetrical-tangential' in both RAD and ULN, the amplitudes were significantly smaller in RAD than in ULN. These results suggest that the coil current direction determines whether the 'symmetrical-tangential' orientation leads to 'inconsistent' results. When the coils were held in the 'tangential-edge' orientation, the amplitudes of CMAPs were significantly larger in PROX than in DIST. 3.1.3. Sites of excitation Estimated sites of excitation in magnetic stimulation are shown in Fig. 7. As 90% intensity in RAD and DIST was
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submaximal, estimated values in these two orientations are not as reliable as those in ULN and PROX. The site of excitation in ULN was 2.7 (SD 1.9) mm distal to the reference point directly beneath the coil intersection.
were symmetric with respect to the imaginary nerve, shown by a broken line (Fig. 8a). PNB in the inhomogeneous models were off the imaginary nerve toward the small trough containing 0.9% saline solution (Fig. 8c and 8e). There was no large negative peak of dEJdx on the imaginary nerve in the homogeneous model (Fig. 8b). In contrast, there were two (Fig. 8d) and one (Fig. 8f) large negative peaks in the inhomogeneous models. It is likely that imaginary nerves would excite at these virtual cathodes.
3.2. Electric field measurements in volume conductor models 3.2.1. Electric fields and their first spatial derivatives Fig. 8 shows the X-components of electric fields (Ex) and their derivatives (dEJdx). In Fig. 8, the coil current directions and imaginary nerves are shown by arrow heads and broken lines, respectively. The positive-negative boundaries (PNB, shown by white lines) in the homogeneous model
3.2.2. Comparison between estimated sites of excitation and negative peaks of dEJdx Estimated sites of excitation in magnetic median nerve stimulation are indicated with circles on Fig. 8d and 8f. As
a: Homogeneous, Ex
-6 -10
6
5 0 x (cm)
+10
-10
0 x (cm)
+10
+6
0H -6 -10
+6
-6 0
-10
0
x (cm)
x (cm)
e : Inhomogeneous, Ex
f: Inhomogeneous, dEx/dx
+10
÷6
g0 -6 -10
0H -6 0 x (cm)
+10
-10
0 x (cm)
+10
Fig. 8. Contour graphs of the X-component of induced electric fields (E~) and their gradient (dEJdx). All values were normalized. Areas of positive Y correspond to the small trough which represents the biceps brachii muscle. Areas of positive X correspond to the distal side of the elbow. The coil current directions and imaginary nerves are shown by arrow heads and broken lines, respectively. The contours of the figure-of-eight coil are projected with gray lines. Boundary lines between positive and negative values (shown by white lines) in the inhomogeneous models are off the imaginary nerve toward the small trough (c and e) compared to those in the homogeneous model (a). There are large negative peaks of dE~/dx only in the inhomogeneous models (d and f). The estimated sites of excitation in median nerve stimulation are projected with circles (d and f). The relationship between the circle and negative peaks is consistent in (f).
M. Kobayashi et al. /Electroencephalography and clinical Neurophysiology 105 (1997) 406-413
the biceps brachii muscle was represented by the small trough, RAD and ULN orientations correspond to Fig. 8d and Fig. 8f, respectively. The site of excitation in ULN was estimated very close to the virtual cathode in Fig. 8f. 3.2.3. Decrease o f the conductivity difference
The ratio of the inner to outer conductivity in the inhomogeneous model was 8:1 in the beginning and 3:1 at the end of the measurement shown in Fig. 8c which took 106 min (Table 1). We judged that the conductivity difference was maintained at a significant level during measurements.
4. Discussion Most studies note that round coils in 'tangential-edge' orientation elicit the highest amplitudes (Evans et al., 1988; Maccabee et al., 1988, 1991; Chokroverty et al., 1990; Olney et al., 1990; Evans, 1991), which is consistent with the cable theory for magnetic nerve stimulation (Durand et al., 1989; Reilly, 1989; Roth and Basser, 1990; Nagarajan et al., 1993). The figure-of-eight coil in PROX and DIST orientations corresponds to a round coil in the 'tangential-edge' orientation on each side of a nerve. Similarly, RAD and ULN orientations correspond to the 'symmetrical-tangential' orientation. The figure-of-eight coil, originally proposed for hyperthermia therapy (Ueno et al., 1987) and applied to nerve stimulation (Ueno et al., 1988), is preferred for its good focality (Cohen et al., 1990; Maccabee et al., 1990; Olney et al., 1990). It is consistent with the theory to use the figure-of-eight coil in the 'tangentialedge' orientation (Evans, 1991; Ueno et al., 1991; Maccabee et al., 1993), but some authors argue that figure-of-eight coils in the 'symmetrical-tangential' orientation elicited high amplitudes (Sun et al., 1995; Yunokuchi et al., 1995; Ruohonen et al., 1996), which is inconsistent with the theory but consistent with our result. Sites of excitation estimated in PROX agree with findings from other authors (Maccabee et al., 1990; Olney et al., 1990; Evans, 1991; Nilsson et al., 1992; Ruohonen et al., 1996). Nilsson et al. (1992) concluded that the amplitudes recorded with distal coil current would be smaller than those with proximal coil current because of action potential propagation beyond the hyperpolarized area, or a virtual anode. Table 1 Conductivity (in m~3/cm)of saline solution Time (min)
Trough Outside (0.1% NaCI) Inside (0.9% NaC1) Inside:outside ratio
0
54
106
1.78 14.5
2.95 15.2
4.45 15.0
8.1
5.2
3.4
411
Thus, what causes the differences of muscle responses between RAD and ULN in our results? Sun et al. (1995) also mentioned these differences. They could be explained mainly by the asymmetry of the tissues surrounding the median nerve because the figure-of-eight coil was placed symmetrically with respect to the nerve. Ruohonen et al. (1996) did not mention these differences, which is probably because they used an oscillating current pulse. The effect of tissue asymmetry is hidden by oscillating current pulse because virtual cathodes and anodes replace each other at very short intervals (Maccabee et al., 1993). The absence of a virtual cathode on the imaginary nerve in the homogeneous model with the 'symmetrical-tangential' figure-of-eight coil (Fig. 8b) agrees with theoretical calculations (Cohen et al., 1990; Roth and Basser, 1990; Nilsson et al., 1992; Ruohonen et al., 1996). Moreover, there were two (Fig. 8d) and one (Fig. 8f) virtual cathodes on the imaginary nerve in the inhomogeneous models. This result explains the previous inconsistent results during magnetic median nerve stimulation. In the cable theory, it is assumed for simplicity that a nerve is surrounded by a homogeneous medium (Roth and Basser, 1990); the 'inconsistent' results compels us to consider tissue inhomogeneity. It is also assumed in the cable theory that only the induced electric field component parallel to the nerve is responsible for nerve excitation (Roth and Basser, 1990). Ruohonen et al. (1996) proposed that the electric field component perpendicular to the nerve should be included in the theory. Concerning 'bone to soft tissue' inhomogeneity, some models were proposed in the past (Maccabee et al., 1991, 1993). Such a 'bone to soft tissue' model consisting of a non-conducting medium and an electrolyte solution may be appropriate for the human anatomy where the nerve lies close to bone, as, for example, the spinal nerve roots (Maccabee et al., 1991) and the ulnar nerve in the osseous ulnar groove (Amassian et al., 1989). But the median nerve in the elbow is separated from bone by the brachialis muscle (Fig. 1). Thus, we proposed a 'soft tissue' model to explain inconsistent results in median nerve stimulation. In Fig. 8d, although there was one virtual cathode on each side of the virtual anode, the site of excitation was projected near the left cathode. If the nerve excites at both virtual cathodes, the action potentials collide and vanish between two cathodes, and the site of excitation is estimated near the right cathode. This discrepancy suggests that the nerve did not excite at the right cathode in vivo. The biceps brachii muscle, though represented by a rectangular trough in our model, tapers off and becomes tendinous at its distal end. Such longitudinal asymmetry may cause the right cathode in Fig. 8d to be ineffective, or weak, for nerve excitation in vivo. If true, the differences of muscle responses between RAD and ULN can be explained as follows. In Fig. 8d, as the right virtual cathode is not 'strong' enough, action potentials are generated only at the left virtual cathode and attenuated through the 'strong' virtual anode on their
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M. Kobayashi et al. /Electroencephalography and clinical Neurophysiology 105 (1997) 406-413
w a y to the muscle. In Fig. 8f, on the other hand, action potentials g e n e r a t e d at the ' s t r o n g ' virtual cathode are not attenuated through the right virtual anode as m u c h as in Fig. 8d. This hypothesis should be verified by an e x p e r i m e n t with a longitudinally a s y m m e t r i c trough (e.g. a t r a p e z o i d or conical trough). T h e figure-of-eight coil w e used had greater d i m e n s i o n s than the d i a m e t e r o f the arm at the elbow. Thus, R A D and U L N coil orientations c o u l d c o n f e r greater degrees o f m a g netic flux into the arm than P R O X and D I S T . But there w e r e differences in amplitudes and latencies b e t w e e n R A D and U L N (Figs. 6 and 7) despite the s a m e degree o f m a g n e t i c flux. Furthermore, Y u n o k u c h i et al. (1995) argued that the amplitude in U L N was significantly larger than in P R O X , e v e n though they used a small coil w h i c h m i g h t not cause significant differences o f m a g n e t i c flux in different coil orientation. Thus, we c o n s i d e r soft tissue i n h o m o g e n e i t y m o r e significant for the ' i n c o n s i s t e n t ' results than different degrees o f m a g n e t i c flux. T h e c o n d u c t i v i t y o f m u s c l e is h i g h e r in the direction parallel to m u s c l e fibers (Foster and Schwan, 1989). Our m o d e l does not represent this anisotropy. M o r e o v e r , the decrease o f the c o n d u c t i v i t y difference (Table 1) m a k e s our m o d e l inappropriate for lengthy m e a s u r e m e n t s . A l t h o u g h there is still r o o m for i m p r o v e m e n t , our simple 'soft tissue' m o d e l e x p l a i n e d the p r e v i o u s inconsistent results. T h e cable theory for m a g n e t i c stimulation must take account o f tissue i n h o m o g e n e i t y in a c c o r d a n c e with the local a n a t o m y o f the stimulated site.
Acknowledgements T h e authors gratefully thank A k i r a H y o d o , Sunao Iwaki, K e n i c h i U e n o , Seiji N a k a g a w a , M a s a k a t s u H o r i and Dr. Yasuto Tajiri for their technical assistance, and T a k a f u m i Ito f r o m N i h o n K o h d e n Co. for his helpful collaboration. This w o r k was supported in part by a grant to M . K . f r o m the M a g n e t i c Health S c i e n c e Foundation.
References Amassian, V.E., Maccabee, P.J. and Cracco, R.Q. Focal stimulation of human peripheral nerve with the magnetic coil: a comparison with electrical stimulation. Exp. Neurol., 1989, 103: 282-289. Chokroverty, S., Spire, J.P., DiLullo, J., Moody, E. and Maselli, R. magnetic stimulation of the human peripheral nerves. In: S. Chokroverty (Ed.), Magnetic Stimulation in Clinical Neurophysiology. Butterworth, Stoneham, MA, 1990, pp. 249-273. Claus, D., Murray, N.M., Spitzer, A. and Flugel, D, The influence of stimulus type on the magnetic excitation of nerve structures. Electroenceph, clin. Neurophysiol., 1990, 75: 342-349. Cohen, L.G., Roth, B.J., Nilsson, J., Dang, N., Panizza, M., Bandinelli, S., Friauf, W. and Hallett, M. Effects of coil design on delivery of focal magnetic stimulation. Technical considerations. Electroenceph. clin. Neurophysiol., 1990, 75: 350-357. Cros, D., Day, T.J. and Shahani, B.T. Spatial dispersion of magnetic
stimulation in peripheral nerves. Muscle Nerve, 1990, 13: 10761082. Durand, D., Ferguson, A.S. and Dalbasti, T. Induced electric fields by magnetic stimulation in non-homogeneous conducting media. In: Proceedings 1lth Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Seattle, WA, 1989, pp. 1252-1253. Evans, B.A., Litchy, W.J. and Danbe, J.R. The utility of magnetic stimulation for routine peripheral nerve conduction studies. Muscle Nerve, 1988, 11: 1074-1078. Evans, B.A. Magnetic stimulation of the peripheral nervous system. J. Clin. Neurophysiol., 1991, 8: 77-84. Foster, K.R. and Schwan, H.P. Dielectric properties of tissues and biological materials: a critical review. Crit. Rev. Biomed. Eng., 1989, 17: 25-104. Hallett, M., Cohen, L.G., Nilsson, J. and Panizza, M. Differences between electrical and magnetic stimulation of human peripheral nerve and motor cortex. In: S. Chokroverty (Ed.), Magnetic Stimulation in Clinical Neurophysiology. Butterworth, Stoneham, MA, 1990, pp. 275-287. Maccabee, P.J., Amassian, V.E., Cracco, R.Q. and Cadwell, J.A. An analysis of peripheral motor nerve stimulation in humans using the magnetic coil. Electroenceph. clin. Neurophysiol., 1988, 70: 524-533. Maccabec, P.J., Ebede, L., Amassian, V.E., Cracco, R.Q., Rudell, A. and Jayachandra, M. Spatial distribution of the electric field induced in volume by round and figure '8' magnetic coils: relevance to activation of sensory nerve fibers. Electroenceph. clin. Neurophysiol., 1990, 76: 131-141. Maccabee, P.J., Amassian, V.E., Ebede, L.P., Rudell, A.P., Cracco, R.Q., Lai, K.S. and Somasundarum, M. Measurement of the electric field induced into inhomogeneous volume conductors by magnetic coils: application to human spinal neurogeometry. Electroenceph. clin. Neurophysiol., 1991, 81: 224-237. Maccabee, P.J., Amassian, V.E., Ebede, L.P. and Cracco, R.Q. Magnetic coil stimulation of straight and bent amphibian and mammalian peripheral nerve in vitro: locus of excitation. J. Physiol., 1993, 460: 201-219. Nagarajan, S.S., Durand, D.M. and Warman, E.N. Effects of induced electric fields on finite neuronal structures: a simulation study. IEEE Trans. Biomed. Eng., 1993, 40: 1175-1188. Nilsson, J., Panizza, M., Roth, B.J., Basser, P.J., Cohen, L.G., Caruso, G. and Hailett, M. Determining the site of stimulation during magnetic stimulation of a peripheral nerve. Electroenceph. clin. Neurophysiol., 1992, 85: 253-264. Olney, R.K., So, Y.T., Goodin, D.S. and Aminoff, M.J. A comparison of magnetic and electrical stimulation of peripheral nerves. Muscle Nerve, 1990, 13: 957-963. Ravnborg, M., Blinkenberg, M. and Dahl, K. Significance of magnetic coil position in peripheral motor nerve stimulation. Muscle Nerve, 1990, 13: 681-686. Reilly, J.P. Peripheral nerve stimulation by induced electric currents: exposure to time-varying magnetic fields. Med. Biol. Eng. Comput., 1989, 27: 101-110. Roth, B.J. and Basset, P.J. A model of the stimulation of a nerve fiber by electromagnetic induction. IEEE Trans. Biomed. Eng., 1990, BME-37: 588-597. Ruohonen, J., Panizza, M., Nilsson, J., Ravazzani, P., Grandori, F. and Tognola, G. Transverse-field activation mechanism in magnetic stimulation of peripheral nerves. Electroenceph. clin. Neurophysiol., 1996, 101: 167-174. Rushton, W.A.H. Effect upon the threshold for nervous excitation of the length of the nerve exposed and the angle between current and nerve. J. Physiol., 1927, 63: 357-377. Sun, S., Tobimatsu, S. and Kato, M. The effect of magnetic coil orientation on excitation of human median nerve. Electroenceph. clin. Neurophysiol., 1995, 97: $200. Ueno, S, Tashiro, T., Kamise, S. and Harada, K. Localized hyperthermia by means of a paired-coil configuration: calculation of current distributions in cubital model. IEEE Trans. Magn., 1987, MAG-23: 24372439.
M. Kobayashi et al. /Electroencephalography and clinical Neurophysiology 105 (1997) 406-413 Ueno, S., Tashiro, T. and Harada, K. Localized stimulation of neural tissues in the brain by means of a paired configuration of time-varying magnetic fields. J. Appl. Phys., 1988, 64: 5862-5864. Ueno, S., Matsuda, T. and Hiwaki, O. Estimation of structures of neural fibers in the human brain by vectorial magnetic stimulation. IEEE Trans. Magn., 1991, 27: 5387-5389.
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Wiederholt W.C. Threshold and conduction velocity in isolated mixed mammalian nerves. Neurology, 1970, 20: 347-352. Yunokuchi, K., Mamitsuka, K. and Asakusa, T. Estimation of focal magnetic stimulation in the peripheral nerve model. Electroenceph. clin. Neurophysiol., 1995, 97: $200.
Electroencephalography and clinical Neurophysiology 105 (1997) 406-413
Importance of soft tissue inhomogeneity in magnetic peripheral nerve stimulation Makoto
K o b a y a s h i a,b,*, S h o o g o U e n o a, T a k a h i d e K u r o k a w a b
alnstitute of Medical Electronics, Faculty of Medicine, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan bDepartment of Orthopedics, Faculty of Medicine, the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan Accepted for publication: 23 May 1997
Abstract In magnetic peripheral nerve stimulation with a figure-of-eight coil, a 'tangential-edge' coil orientation (the nerve is beneath the coil intersection and perpendicular to the coil wings) is ideal theoretically. However, some experimental results show that strong muscle responses are elicited with a 'symmetrical-tangential' coil orientation (the nerve is beneath the coil intersection and parallel to the coil wings), which is inconsistent with the cable theory. We hypothesized that the 10:1 conductivity difference between muscle and fat would cause inconsistent results during magnetic median nerve stimulation in the elbow, which was verified using an inhomogeneous volume conductor model. The induced electric fields were measured in a model composed of saline solutions of different concentrations divided by a cellophane sheet. A nerve was imagined along the boundary between the two solutions, and the coil was held in a 'symmetricaltangential' position. Virtual cathodes, which were off the nerve in the homogeneous model, were on the nerve in the inhomogeneous model. The previous inconsistent results were explained by considering soft tissue inhomogeneity without any modification of the assumption in the cable theory that only the induced electric field component parallel to the nerve is responsible for nerve excitation. © 1997 Elsevier Science Ireland Ltd.
Keywords: Peripheral nerve; Magnetic stimulation; Figure-of-eight coil; Median nerve; Volume conductor model; Tissue inhomogeneity
1. Introduction Based on the experimental results (Rushton, 1927) that electric fields oriented parallel to nerve fibers are optimal for nerve excitation, mathematical models of magnetic stimulation of an axon have been developed (Durand et al., 1989; Reilly, 1989; Roth and Basser, 1990; Nagarajan et al., 1993). In those models, a long straight nerve excites at a virtual cathode where the negative spatial derivative of the electric field induced along the axon is large. Although this prediction is consistent with most experimental results (Evans et al., 1988; Chokroverty et al., 1990; Maccabee et al., 1990, 1991, 1993; Olney et al., 1990; Evans, 1991; Nilsson et al., 1992), some results are inconsistent with the theory (Cros et al., 1990; Hallett et al., 1990; Yunokuchi et al., 1995; Sun et al., 1995; Ruohonen et al., 1996). In the * Corresponding author. Tel.: +81 3 38122111; fax: +81 3 56897215; e-mail: rnakoto @medes.m.u-tokyo.ac.jp
latter, strong muscle responses were elicited despite coil orientations which theoretically generated no virtual cathode. Such a discrepancy between the theory and the experiments must come from invalid assumptions in the theory, including those regarding tissue inhomogeneity. In the past, tissue inhomogeneity was considered a problem only between bone and soft tissue (Maccabee et al., 1991, 1993). In this report, we discuss inhomogeneity between muscle and fat.
2. Methods and materials The median nerve in the elbow runs through subcutaneous fat tissue with the biceps brachii muscle at the radial side of the nerve (Fig. 1). The conductivity of muscle is about ten times higher than that of fat (Foster and Schwan, 1989). We hypothesized that magnetic median nerve stimu-
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lation might lead to inconsistent results because the median nerve runs near the boundary between muscle and fat; that is, the conductivity difference between muscle and fat might cause the electric field induced in the elbow to be different from that induced in homogeneous media. To verify this hypothesis, the results of two experiments were compared with each other. First, we investigated whether we could get inconsistent results by changing coil orientations during magnetic stimulation of the median nerve in the elbow. Second, the electric field induced in an inhomogeneous volume conductor model was measured to determine whether there was a virtual cathode on an imaginary nerve. In the model, the biceps brachii muscle and subcutaneous fat were represented simply by two troughs containing saline solutions of different concentrations. 2.1. Median nerve stimulation in a human subject 2.1.1. Subject
The subject was a 32 year old healthy male who gave informed consent. The median nerve in the left arm was stimulated both electrically and magnetically. 2.1.2. Electrical stimulation
Results of supramaximal electrical stimulation were used to estimate sites of excitation during magnetic stimulation. The median nerve was stimulated via surface electrodes with a cathode-anode distance of 25 mm. The duration of stimulating rectangular current was 0.2 ms. A monopolar needle electrode was inserted into the belly of the abductor pollicis brevis muscle (APB) and was referenced to a sura
Ulnar side
b
c
Radial side
Fig. 1. MRI cross-section of the left elbow (a 32 year old male who participated in the experiment as a subject). The level of the cross-section matched the reference point for electrical stimulation in the experiment, a, subcutaneous fat; b, median nerve; c, biceps brachii; d, brachialis; e, humerus; f, ulna (olecranon). The median nerve runs through subcutaneous tissue. The biceps brachii muscle is radial to the median nerve.
Orientation PROX DIST Coil current Proximal Distal Nerve and Perpend. Perpend. coil wings CRadial rv~e~~:~
f~jCoil
Ne
RAD Radial Parallel
ULN Ulnar Parallel
current
4 , . , , - - Proximal Fig. 2. Coil orientation.
face electrode placed on the distal tendon of the APB. Compound motor action potentials (CMAPs) were amplified by an electromyograph (Neuropack E, Nihon Kohden Co.) with a bandwidth of 2 H z - 3 kHz. A ground electrode was placed on the wrist. The course of the median nerve across the elbow was determined. The point where the nerve crosses the elbow flexion crease was marked as a common reference point for electric and magnetic stimulation. A cathode was kept exactly on the reference point during elbow stimulation. Each set of 5 C M A P recordings was averaged for 8 repetitions of elbow and wrist stimulation (40 stimuli at each site). The mean latency in each site, motor nerve conduction velocity (MCV) between the wrist and elbow and their standard deviations were calculated using 8 averaged values. 2.1.3. Magnetic stimulation
The relationship of coil orientation to muscle response during magnetic stimulation was investigated. The median nerve in the elbow was stimulated with a figure-of-eight coil (YM-111B, 10.0 cm o.d., 5.0 cm i.d.; Nihon Kohden Co.) held in 4 different orientations: PROX, DIST, RAD and ULN (Fig. 2). In each orientation, the midpoint of the intersection of the coil was placed on the same reference point as during electrical stimulation, and the coil plane was kept tangential to the skin surface. PROX and DIST correspond to a 'tangential-edge' orientation, and RAD and ULN to a 'symmetrical-tangential' position (Maccabee et al., 1990). The coil held in the latter position should generate no virtual cathode on the nerve, according to theoretical calculations for homogeneous media (Cohen et al., 1990; Roth and Basser, 1990; Nilsson et al., 1992; Ruohonen et al., 1996). Thus, large amplitudes of CMAPs in either RAD or ULN should be 'inconsistent' with the theory. The magnetic stimulator was a prototype (AAA-10687; Nihon-Kohden Co.). The wave form of the induced stimulus pulse was biphasic (Fig. 3a). The duration of its first phase was 65 ~s. The induced magnetic field increased linearly with the capacitor voltage; 70, 80 and 90% of maximal output were used for median nerve stimulation. The recording equipment was the same as that used during electrical stimulation. Each set of 5 CMAP recordings was averaged for 8 repe-
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"~"
a
Olney et al., 1990; Ravnborg et al., 1990; Nilsson et al., 1992; Ruohonen et al., 1996). 2.2. Electric field measurements in volume conductor models
I1
0.5 cm E a
b
Fig. 3. Induced stimulus pulse wave form and measuring probe. (a) Induced stimulus pulse wave form. As the stimulus current wave form was monophasic, the induced stimulus pulse (time derivative of current) wave form was biphasic. (b) Probe consisting of a coaxial cable bent at a right-angle 1 cm from the end. The cable was passed through an acrylic tube. The distal 10 ram of the outside insulation and shield of the cable were stripped to record the voltage drop between the cable shield and the bared distal tip.
titions (40 stimuli were done) in each condition. The mean latency, mean amplitude and their standard deviations were calculated using 8 averaged values. 2.1.4. Statistical analysis First, the amplitudes in each coil orientation were compared among different stimulus intensities to determine whether the amplitudes were maximal. Then, the amplitudes at 90% intensity were compared among different coil orientations. All pairs were evaluated by the KruskalWallis method, and each pair was compared by the Scheffe F test (P < 0.05). 2.1.5. Sites of excitation As a nerve excites almost directly beneath the cathode in electrical stimulation (Wiederholt, 1970), sites of excitation at 90% intensity in magnetic stimulation were estimated from the latency difference between magnetic and electrical stimulation (Evans et al., 1988; Maccabee et al., 1988, 1990; Amassian et al., 1989; Claus et al., 1990; Hallett et al., 1990;
2.2.1. Volume conductor model A volume conductor model was composed of two troughs, a small one within a large one (Fig. 4a), The small and large troughs represented the biceps muscle and subcutaneous fat tissue, respectively. The large trough was made of acrylic boards. The frame of the small trough was made of acrylic rods, and its faces were made of cellophane sheets (Fig. 4b). As electrolytes can pass through cellophane sheets, the electric current flowed through the boundary between the small and large troughs. This 'double-lxough' model was used for both the homogeneous and inhomogeneous models. In accordance with the conductivity difference between muscle and fat as mentioned above (Foster and Schwan, 1989), the large and small troughs in the inhomogeneous model were filled with 0.1% and 0.9% saline, respectively. In the homogeneous model, both troughs were filled with 0.9% saline. 2.2.2. Magnetic coil and stimulator The figure-of-eight coil was held beneath the troughs by a wooden support. The coil and magnetic stimulator were the same as used in median nerve stimulation. The stimulus intensity was kept at 10% of its maximum. In the experiment with the homogeneous model, the coil current direction at the intersection was away from the small trough. With the inhomogeneous model, it was toward or away from the small trough. 2.2. 3. Electric field measurements A disc electrode was immersed in the saline solution as a ground electrode. The electric fields induced in the trough were measured with a probe made from a coaxial cable (Fig. 3b). The coaxial cable (3.0 nun o.d.) was passed through an
l} c m
cm
7c i...1
}il a
m
0.5 e m b
Fig. 4. Volume conductor model. (a) Double trough. The small trough was inside the large trough. In the inhomogeneous model, the small trough was filled with 0.9% saline solution, and the large one with 0.1% saline. In the homogeneous model, both troughs were filled with 0,9% saline solutions. A figure-ofeight coil was fixed beneath the trough by a wooden support. (b) The structure of the small trough. The small trough was constructed of an acrylic frame faced with cellophane sheets.
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E l b o w F l e x i o n Crease
(cmtlO
~
~
-
-
~
Proximal
Median Nerve
r----'---Coil Orientation Radial
Mean
-46 m m
~-~
-44 mm
Distal *
Ulnar Proximal
2.7 mm 21 m m
Error bar : + 1SD
-6o-so-4o- o-Ao-io o io 2o 3o 4o mm Fig. 5. The arrangement of two troughs. One of the edges of the small trough was on the line where Y= 0.5. Measurements were taken at 21 × 13 points in the X-Y plane parallel to the bottom of the trough. Only the X-component of the induced electric field (Ex) was measured.
acrylic tube (6.0 m m o.d.) and connected to an amplifier. The distal 10 mm of the outside insulation and shield of the cable were stripped to record the voltage drop between the cable shield and the bared distal tip. The distal end of the probe was bent at a right-angle and submerged in the saline solution. It was kept parallel to the X-axis 0.5 cm above the base of the trough and was moved in 10 mm increments in a given X - Y plane (Fig. 5). Thus, the voltage drop only in the X direction was recorded at 273 (21 x 13) different locations. By dividing the voltage drop by 10 mm, we calculated the X component of the induced electric field (Ex, mV/mm). As Maccabee et al. (1991), we also calculated the first spatial derivative of Ex (dEfldx). These values were normalized and illustrated as contour maps. 2.2.4. Decrease of the conductivity difference The conductivity of saline solution was controlled by its concentration. When two electrolyte solutions of different concentration are divided by a cellophane sheet, both the
181
Error bar : -4-1SD
20
16
,
60
~
1
-o- DIST -~- PROX NS -~- RAD
-¢- U I ~
, : p<0.005 NS : difference is not significant
70 80 90 Stimulus intensity (%)
Fig. 6. Relation of stimulus intensity to amplitudes. As the amplitudes in PROX reached their maximum at 70% intensity, 90% intensity might have been supramaximal. The amplitudes at 90% intensity in ULN were as large as those in PROX. Thus, 90% intensity in ULN might not have been supramaximal, but was at least maximal. In other coil orientations (DIST and RAD), the amplitudes did not reached their maximum.
Fig. 7. Estimated sites of excitation in magnetic stimulation. The distance between the site of excitation and the elbow flexion crease was assumed to be proportional to the latency difference between electrical and magnetic stimulation.
concentration and conductivity differences decrease with time. The electrical conductivity in the large and small trough were measured by a conductivity meter (YSI model 33 S-C-T Meter; Yellow Springs Co.) at the beginning, middle and end of the experiment with the inhomogeneous model where the coil current was toward the small trough to ensure the conductivity difference was maintained at a significant level.
3. Results
3.1. Median nerve stimulation on a human subject 3.1.1. Electrical stimulation The latency in elbow stimulation was 7.12 ms (SD 0.0214). The MCV between the elbow and wrist was 76.0 m/s (SD 1.10). 3.1.2. Magnetic stimulation Fig. 6 shows the relation between the stimulus intensities and the amplitudes of CMAPs in each coil orientation. DIST, PROX, RAD and ULN in Fig. 6 refer to current directions in the coil (see Fig. 2). The amplitudes at 90% intensity in ULN, theoretically with no virtual cathode, were as large as those in PROX. Although the coils were 'symmetrical-tangential' in both RAD and ULN, the amplitudes were significantly smaller in RAD than in ULN. These results suggest that the coil current direction determines whether the 'symmetrical-tangential' orientation leads to 'inconsistent' results. When the coils were held in the 'tangential-edge' orientation, the amplitudes of CMAPs were significantly larger in PROX than in DIST. 3.1.3. Sites of excitation Estimated sites of excitation in magnetic stimulation are shown in Fig. 7. As 90% intensity in RAD and DIST was
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submaximal, estimated values in these two orientations are not as reliable as those in ULN and PROX. The site of excitation in ULN was 2.7 (SD 1.9) mm distal to the reference point directly beneath the coil intersection.
were symmetric with respect to the imaginary nerve, shown by a broken line (Fig. 8a). PNB in the inhomogeneous models were off the imaginary nerve toward the small trough containing 0.9% saline solution (Fig. 8c and 8e). There was no large negative peak of dEJdx on the imaginary nerve in the homogeneous model (Fig. 8b). In contrast, there were two (Fig. 8d) and one (Fig. 8f) large negative peaks in the inhomogeneous models. It is likely that imaginary nerves would excite at these virtual cathodes.
3.2. Electric field measurements in volume conductor models 3.2.1. Electric fields and their first spatial derivatives Fig. 8 shows the X-components of electric fields (Ex) and their derivatives (dEJdx). In Fig. 8, the coil current directions and imaginary nerves are shown by arrow heads and broken lines, respectively. The positive-negative boundaries (PNB, shown by white lines) in the homogeneous model
3.2.2. Comparison between estimated sites of excitation and negative peaks of dEJdx Estimated sites of excitation in magnetic median nerve stimulation are indicated with circles on Fig. 8d and 8f. As
a: Homogeneous, Ex
-6 -10
6
5 0 x (cm)
+10
-10
0 x (cm)
+10
+6
0H -6 -10
+6
-6 0
-10
0
x (cm)
x (cm)
e : Inhomogeneous, Ex
f: Inhomogeneous, dEx/dx
+10
÷6
g0 -6 -10
0H -6 0 x (cm)
+10
-10
0 x (cm)
+10
Fig. 8. Contour graphs of the X-component of induced electric fields (E~) and their gradient (dEJdx). All values were normalized. Areas of positive Y correspond to the small trough which represents the biceps brachii muscle. Areas of positive X correspond to the distal side of the elbow. The coil current directions and imaginary nerves are shown by arrow heads and broken lines, respectively. The contours of the figure-of-eight coil are projected with gray lines. Boundary lines between positive and negative values (shown by white lines) in the inhomogeneous models are off the imaginary nerve toward the small trough (c and e) compared to those in the homogeneous model (a). There are large negative peaks of dE~/dx only in the inhomogeneous models (d and f). The estimated sites of excitation in median nerve stimulation are projected with circles (d and f). The relationship between the circle and negative peaks is consistent in (f).
M. Kobayashi et al. /Electroencephalography and clinical Neurophysiology 105 (1997) 406-413
the biceps brachii muscle was represented by the small trough, RAD and ULN orientations correspond to Fig. 8d and Fig. 8f, respectively. The site of excitation in ULN was estimated very close to the virtual cathode in Fig. 8f. 3.2.3. Decrease o f the conductivity difference
The ratio of the inner to outer conductivity in the inhomogeneous model was 8:1 in the beginning and 3:1 at the end of the measurement shown in Fig. 8c which took 106 min (Table 1). We judged that the conductivity difference was maintained at a significant level during measurements.
4. Discussion Most studies note that round coils in 'tangential-edge' orientation elicit the highest amplitudes (Evans et al., 1988; Maccabee et al., 1988, 1991; Chokroverty et al., 1990; Olney et al., 1990; Evans, 1991), which is consistent with the cable theory for magnetic nerve stimulation (Durand et al., 1989; Reilly, 1989; Roth and Basser, 1990; Nagarajan et al., 1993). The figure-of-eight coil in PROX and DIST orientations corresponds to a round coil in the 'tangential-edge' orientation on each side of a nerve. Similarly, RAD and ULN orientations correspond to the 'symmetrical-tangential' orientation. The figure-of-eight coil, originally proposed for hyperthermia therapy (Ueno et al., 1987) and applied to nerve stimulation (Ueno et al., 1988), is preferred for its good focality (Cohen et al., 1990; Maccabee et al., 1990; Olney et al., 1990). It is consistent with the theory to use the figure-of-eight coil in the 'tangentialedge' orientation (Evans, 1991; Ueno et al., 1991; Maccabee et al., 1993), but some authors argue that figure-of-eight coils in the 'symmetrical-tangential' orientation elicited high amplitudes (Sun et al., 1995; Yunokuchi et al., 1995; Ruohonen et al., 1996), which is inconsistent with the theory but consistent with our result. Sites of excitation estimated in PROX agree with findings from other authors (Maccabee et al., 1990; Olney et al., 1990; Evans, 1991; Nilsson et al., 1992; Ruohonen et al., 1996). Nilsson et al. (1992) concluded that the amplitudes recorded with distal coil current would be smaller than those with proximal coil current because of action potential propagation beyond the hyperpolarized area, or a virtual anode. Table 1 Conductivity (in m~3/cm)of saline solution Time (min)
Trough Outside (0.1% NaCI) Inside (0.9% NaC1) Inside:outside ratio
0
54
106
1.78 14.5
2.95 15.2
4.45 15.0
8.1
5.2
3.4
411
Thus, what causes the differences of muscle responses between RAD and ULN in our results? Sun et al. (1995) also mentioned these differences. They could be explained mainly by the asymmetry of the tissues surrounding the median nerve because the figure-of-eight coil was placed symmetrically with respect to the nerve. Ruohonen et al. (1996) did not mention these differences, which is probably because they used an oscillating current pulse. The effect of tissue asymmetry is hidden by oscillating current pulse because virtual cathodes and anodes replace each other at very short intervals (Maccabee et al., 1993). The absence of a virtual cathode on the imaginary nerve in the homogeneous model with the 'symmetrical-tangential' figure-of-eight coil (Fig. 8b) agrees with theoretical calculations (Cohen et al., 1990; Roth and Basser, 1990; Nilsson et al., 1992; Ruohonen et al., 1996). Moreover, there were two (Fig. 8d) and one (Fig. 8f) virtual cathodes on the imaginary nerve in the inhomogeneous models. This result explains the previous inconsistent results during magnetic median nerve stimulation. In the cable theory, it is assumed for simplicity that a nerve is surrounded by a homogeneous medium (Roth and Basser, 1990); the 'inconsistent' results compels us to consider tissue inhomogeneity. It is also assumed in the cable theory that only the induced electric field component parallel to the nerve is responsible for nerve excitation (Roth and Basser, 1990). Ruohonen et al. (1996) proposed that the electric field component perpendicular to the nerve should be included in the theory. Concerning 'bone to soft tissue' inhomogeneity, some models were proposed in the past (Maccabee et al., 1991, 1993). Such a 'bone to soft tissue' model consisting of a non-conducting medium and an electrolyte solution may be appropriate for the human anatomy where the nerve lies close to bone, as, for example, the spinal nerve roots (Maccabee et al., 1991) and the ulnar nerve in the osseous ulnar groove (Amassian et al., 1989). But the median nerve in the elbow is separated from bone by the brachialis muscle (Fig. 1). Thus, we proposed a 'soft tissue' model to explain inconsistent results in median nerve stimulation. In Fig. 8d, although there was one virtual cathode on each side of the virtual anode, the site of excitation was projected near the left cathode. If the nerve excites at both virtual cathodes, the action potentials collide and vanish between two cathodes, and the site of excitation is estimated near the right cathode. This discrepancy suggests that the nerve did not excite at the right cathode in vivo. The biceps brachii muscle, though represented by a rectangular trough in our model, tapers off and becomes tendinous at its distal end. Such longitudinal asymmetry may cause the right cathode in Fig. 8d to be ineffective, or weak, for nerve excitation in vivo. If true, the differences of muscle responses between RAD and ULN can be explained as follows. In Fig. 8d, as the right virtual cathode is not 'strong' enough, action potentials are generated only at the left virtual cathode and attenuated through the 'strong' virtual anode on their
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w a y to the muscle. In Fig. 8f, on the other hand, action potentials g e n e r a t e d at the ' s t r o n g ' virtual cathode are not attenuated through the right virtual anode as m u c h as in Fig. 8d. This hypothesis should be verified by an e x p e r i m e n t with a longitudinally a s y m m e t r i c trough (e.g. a t r a p e z o i d or conical trough). T h e figure-of-eight coil w e used had greater d i m e n s i o n s than the d i a m e t e r o f the arm at the elbow. Thus, R A D and U L N coil orientations c o u l d c o n f e r greater degrees o f m a g netic flux into the arm than P R O X and D I S T . But there w e r e differences in amplitudes and latencies b e t w e e n R A D and U L N (Figs. 6 and 7) despite the s a m e degree o f m a g n e t i c flux. Furthermore, Y u n o k u c h i et al. (1995) argued that the amplitude in U L N was significantly larger than in P R O X , e v e n though they used a small coil w h i c h m i g h t not cause significant differences o f m a g n e t i c flux in different coil orientation. Thus, we c o n s i d e r soft tissue i n h o m o g e n e i t y m o r e significant for the ' i n c o n s i s t e n t ' results than different degrees o f m a g n e t i c flux. T h e c o n d u c t i v i t y o f m u s c l e is h i g h e r in the direction parallel to m u s c l e fibers (Foster and Schwan, 1989). Our m o d e l does not represent this anisotropy. M o r e o v e r , the decrease o f the c o n d u c t i v i t y difference (Table 1) m a k e s our m o d e l inappropriate for lengthy m e a s u r e m e n t s . A l t h o u g h there is still r o o m for i m p r o v e m e n t , our simple 'soft tissue' m o d e l e x p l a i n e d the p r e v i o u s inconsistent results. T h e cable theory for m a g n e t i c stimulation must take account o f tissue i n h o m o g e n e i t y in a c c o r d a n c e with the local a n a t o m y o f the stimulated site.
Acknowledgements T h e authors gratefully thank A k i r a H y o d o , Sunao Iwaki, K e n i c h i U e n o , Seiji N a k a g a w a , M a s a k a t s u H o r i and Dr. Yasuto Tajiri for their technical assistance, and T a k a f u m i Ito f r o m N i h o n K o h d e n Co. for his helpful collaboration. This w o r k was supported in part by a grant to M . K . f r o m the M a g n e t i c Health S c i e n c e Foundation.
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