Editor--Two recent papers (MoUCHAWAR et al., I992; YAUAGUCHt et aL, I992) evaluated stimulation of the heart with magnetic pulses. These papers are especially timely in view of the rapidly developing technology of magnetic resonance imaging. It is now accepted that future MRI technology will be constrained by the need to avoid stimulating excitable tissue in the patient through the action of the switched gradient fields. The possibility of cardiac excitation is especially worrisome. These commendable papers provide data and analyses that will be valuable for an understanding of the safety limits for timevarying magnetic exposure. The rheobasic electric field within the biological medium, defined as the minimum induced E-field threshold with an optimum stimulus, is of central concern for safety considerations. Yamaguchi et al. tested two dogs and reported that 30 V / m was the lowest peak E-field for inducing cardiac arrhythmias. Mouchawar et al. tested 11 dogs for the magnetic excitation threshold during concurrent electrical stimulation of the vagus nerve; the average peak threshold E-field was 213 V/m. These investigators adjusted their observed thresholds to infer that the mean threshold for an optimum squarewave E-field stimulus is 30 V/m, a value that is 2.4 times our estimate of 12-4 V / m for the medium threshold and 4.8 times our estimate of 6-2 V/m for the one-percentile rank (REILLY, 199l). There are a number of factors that might be responsible for the apparent discrepancy. Considering the importance of the minimum threshold in the consideration of safety standards, it is advisable to examine these factors in some detail. Dear

Factors p o t e n t i a l l y a f f e c t i n g e x p e r i m e n t a l thresholds Statistical distribution of sensitivity A variety of experiments on both humans and animals indicate the log-normal distribution for ventricular fibrillation (VF) thresholds among individual subjects (REILLY, 1992). Very little information is available about statistical variations of excitation thresholds. As the VF threshold is affected by more variables than the excitation threshold, it is likely that the statistical variance of VF thresholds provides a conservative model for excitation thresholds. For healthy animal hearts, a typical distribution of VF thresholds has a one-percentile rank that is approximately one-half of the median value. Compared with animal data, a much broader distribution of VF thresholds has been reported for human patients undergoing open-heart surgery for valve replacement (WATSONe t at., 1973). Expressing Watson's data in a Iog-normaI format (REILLu i992), the VF threshold at the ~) IFMBE: 1993 Medical & Biological Engineering & Computing

1 per cent rank is projected to lie below the median by the factor 0-2l. The factors responsible for the increased variance in Watson's patients are presendy unknown. Further investigations into the statistical distribution of thresholds for patients with pathological conditions or under drug treatment is needed to increase our confidence in the margin of safety in protective standards. Strength-duration considerations In Mouchawar's experiments, the stimulus duration to the first zero crossing was 0-571 ms, yielding an average E-field threshold of 124 V/m for an equivalent square-wave E-field. They extrapolated their average threshold to a presumed minimum rheobase, using the exponential form of the strength-duration (S-D) curve for monophasic squarewave stimuli: E 0 = E(1 -- e -t/*e)

(1)

where E o is the rheobasic E-field, E is the threshold E-field with a stimulus duration t and ze is the S-D time constant. Mouchawar et aL evaluated eqn. I with t = 0-571 ms and % = 2 - 1 4 m s , a value obtained from their earlier experiments in which dog hearts were stimulated with small contact electrodes (PEARCE et al., 1982). This procedure resulted in a multiplier of 0.234, which, when applied to the experimental threshold, yielded an estimated rheobase of about 30 V/m. This procedure depends critically of the accuracy of the estimate for %. Experimental values of % range from under l ms to over 7ms (REILLY, 1992). A significant part of the variability in % can often be traced to the size of the electrode contracting the heart in a particular experiment. Irnich (IRNICH, 1980) reports that % for cardiac excitation increases monotonically with electrode size. His data fit well to the relationship ze = 4A~ where A is electrode area in cm 2. This relationship is supported by the data of Smyth et al. (SMYTH et al., 1976) and is consistent with properties of nerve excitation, in which ~'e increases with the size of the stimulated area (JACK et al., 1983). As Pearce et al. used a small saline-filled pipette as the stimulating electrode, we might expect that ~'e derived from their experiments would be biased to small values. However, as the induced E-field with magnetic stimulation typically lacks focality when compared with the dimensions of the heart, we may think of the 'effective electrode size' as relatively large in magnetic stimulation of the heart. This would argue for a larger value of % than that assumed by Mouchawar et al. Although Yamaguchi et al. estimated ~ = 2 ms for their magnetic stimuli, their data appear to better support an interpretation of a larger %. If we evaluate eqn. 1 with % = 3 ms for example, we obtain the multiplier 0.173, resulting in an estimated rheobase of 21 V/m.

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Monophasic versus biphasic thresholds Eqn. 1 applies to a monophasic (i.e. unidirectional) square-wave E-field stimulus. However, S-D curves for biphasic stimuli can differ substantially from eqn. 1 (REILLY, 1992). Both Mouchawar and Yamaguchi used charge-balanced biphasic waveforms, as all magnetically induced E-fields must be biphasic. If the collapse of a stimulating magnetic field is gradual in comparison with its rise, or if the collapse is sufficiently delayed with respect to the rising phase, the induced E-field can often be treated as if it is a monophasic pulse. However, judging by the waveform of Mouchawar and Yamaguchi, such treatment does not appear justified in these particular cases. As the phase reversal of a biphasic waveform tends to nullify the stimulating action of the initial phase, a biphasic waveform requires a larger thresholds than a monophasic wave of the same phase duration. This principle was demonstrated by Roy et al. (RoY et al., 1985), who measured the thresholds of cardiac excitation in isolated rabbit hearts. They showed that cardiac excitation with a biphasic current of 1 ms duration requires nearly five times the amplitude of a monophasic wave of the same duration. The lack of waveform efficacy for biphasic stimuli was not accounted for in either experiment considered here; consequently, the inferred rheobase may be too large. Direction of the stimulating E-field A nerve fibre is most easily excited when the stimulating E-field is aligned with its longitudinal axis; it is difficult to excite when the field is oriented in the orthogonal sense. Cardiac stimulation also appears to be directionally sensitive to the applied field. Various experiments with animals (REILLY, 1992) establish that, when a stimulating current is applied across the fore limbs of an animal, the ventricular fibrillation threshold is about twice that of when current is applied from one fore limb to one hind limb. Although the current distribution in the thorax differs in the two cases, these findings are consistent with the hypothesis that the heart is more easily excited when the E-field is aligned with its long axis, as compared with alignment in the orthogonal direction. Judging from Fig. 4 of Mouchawar, the peak E-field appears to be aligned at about 45 ~ with respect to the heart's long axis, thus reducing the efficacy of their stimulus. Note that simply turning the coils by 45 ~ in their experiment would not necessarily exhibit a lower threshold, because the contours of the animal body might reduce the mgnetic coupling between coil and thorax (see below). Another important consideration is the polarity of the applied field. With pulsed DC stimulation along a handto-foot path, the VF threshold is substantially lower when the feet are at a positive potential relative to a hand electrode as compared with the opposite polarity (FERRlS et al., 1936; BIEGELMEIER, 1987). Consequently, it may be surmised that the optimum magnetic stimulus not only requires an induced E-field vector that is aligned with the long axis of the heart, but it also requires the initial phase to be anodal with respect to the apex of the heart. Shape of thorax and its conductive paths Both Mouchawar and Yamaguchi determined the induced E-field using a theoretical model of magnetic coupling to a semi-infinite volume of uniform conductivity. In the experimental context, boundary conditions imposed by the shape of the thorax of the experimental animal will result in an in situ E-field that is less than the predictions from the idealised theoretical model. Deviations from the 652

idealised model can become particularly significant if the experimental coil extends beyond the thorax, as in Mouchawar's tests with coils oriented for the optimum E-field direction with respect to the heart. It is also important to account for the conductive paths in the thorax in an experimental context and to compare the animal model with the human. We could better define the in situ E-field by using small probes in an experimental animal or phantom model.

Discussion Mouchawar et al. infer a rheobasic E-field of 30 V/m for magnetic excitation of the heart by a monophasic squarewave pulse. Yamaguchi et al. report a peak E-field of 30V/m as the minimum threshold for an oscillating Efield. In this discussion, we have attempted to identify several factors that would suggest that the minimum E-field for safety applications might be well below 30 V/m. The factors developed here are (a) Mouchawar and Yamaguchi did not allow for the statistical distribution of excitation thresholds among exposed patients. (b) the value of the S-D time constant re assumed by the investigators might be too small. (c) the biphasic E-field waveforms used by Mouchawar and Yamaguchi might have reduced the efficacy of their stimuli. (d) the direction of the experimentally applied E-field might have been less than optimum. (e) the shape of the thorax and its conductive paths in the experimental animal might have resulted in induced E-fields below the values calculated by the investigators. Any of these factors could result in an overestimate of the minimum rheobasic threshold. Together, the effects could be very significant. Our past studies (REILLY, 1989, 1991) have assumed a minimum safety threshold of 6.2V/m for both nerves and heart. Based on currently available evidence, we do not feel it is justified to raise that standard for safety applications. We encourage further studies of the sort conducted by Mouchawar and Yamaguchi, with particular attention to the factors identified in this discussion, in order to determine if the standard should be raised or lowered. References BIEGELMEIER,G. (1987): Effects of current passing through the human body and the electrical impedance of the human body. Guide to IEC-Report 469, ETZ Report 20, VDE-Verlag, Berlin EERRIS, L. P., KING, B. G., SPENCE, P. W., and WILLIAMS,H. B. (1936): Effect of electric shock on the heart, AIEE Trans., 55, pp. 498-515 IRNICH, W. (1980): The chronaxie time and its practical importance, PACE, 3, pp. 29~301 JACK, J. J., NOBLE,D., and TSIEN, R. W. (1983): Electric current flow in excitable cells. Clarendon Press, Oxford MOUCHAWAR, G. A., BOURLAND,J. D., NYENHUIS,J. A., GEDDES, L. A., FOSTER,K. S. JONES,J. Z., and GRABER,G. P. (1992): Closed-chest cardiac stimulation with a pulsed magnetic field, Med. & Biol. Eng. & Comput., 30, pp. 162-168 PEARCE, J. A., BOURLANO,J. D., NEILSEN,W., GEDDES,L. A., and VOELZ, M. (1982): Myocardial stimulation with ultrashort duration current pulses, Pace, 5, pp. 52-58 REILLV, J. P. (1989): Peripheral nerve stimulation by induced electric currents: Exposure to time-varying magnetic fields, Med. & Biol. Eng.& Comput., 27, pp. 101 110 REILLY, J. P. (1991): Magnetic field excitation of peripheral nerves and the heart: a comparison of thresholds, Med. & Biol. Eng. & Comput., 29, pp. 571-579

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REILLY,J. P. (1992): Electrical stimulation and electropathology. Cambridge University Press, New York RoY, O. Z. (1980): Summary of cardiac fibrillation thresholds for 60 Hz currents and voltages applied directly to the heart, IEEE Trans., BME-24 (5), pp. 430-435 RoY, O. Z., MORTIMER, A. J., TROLLOPE,B. J., and VILLENEUVE, E. J. (1985): Electrical stimulation of the isolated rabbit heart by short duration transients, in BRIDGES,J. E., FORD, G. L., SHERMAN, I. A., and VAINBERG, M. (Eds.): Electrical shock safety criteria. Pergamon Press, New York, pp. 77-86 SMYTH,P. D., TARJAN,P. P., CHERNOF,E., and BAKER,N. (1976): The significance of electrode surface area and stimulating thresholds in permanent cardiac pacing, J. Thorac. Card. Surg., 71, (4), pp. 559-565 SUGIMOTO,T., SCHAAL,F., and WALLACE, A. G. (1967): Factors

The author's reply--The authors applaud Reilly's critical review of our paper 'Closed-chest cardiac stimulation with a pulsed magnetic field', appreciate his identification of factors which may have contributed to the discrepancy in cardiac rheobase between our results and those predicted by his computer models, and thank the Editor of M B E C for an opportunity to respond. We share Reilly's concern for carefully establishing safety standards for medical devices employing timevarying magnetic fields. We are particularly concerned that if too conservative standards are adopted for MRI, then the advantages afforded by fast-scan techniques may be unduly limited. On the other hand, if too liberal standards are used, then patients may be subjected to unacceptable risks. We address the factors identified by Reilly in the same order. Statistical distribution of sensitivity We observed a mean threshold electrical field strength of 213 V/m for the damped sinusoidal waveform with damping of 0-105 and duration of 571 #s. When adjusted for waveform and duration, this yields a mean rheobase of approximately 30V/m for a rectangular pulse induced in the heart (which would be produced by a linear ramp of current in the coil). Reilly's model predicts a median rheobase of 12.4V/m. The median threshold electrical field strength observed in our study is 213V/m, yielding a median rheobase of 30 V/m, i.e. the data do not suggest a skewed distribution. Therefore, we cannot agree that the statistical distribution of thresholds is a significant factor in this study of the healthy mongrel dog for resolving the discrepancy. We share Reilly's desire for additional data on human subjects and from subjects with pathological conditions and under medical therapy. Strength-duration considerations We agree with Reilly that there is considerable variation with reported values for the cardiac muscle time constant %, and that an estimate for the rheobase depends quite strongly on the value selected. We selected the value reported by Pearce et al. (PEARCEet al., 1982) because we knew from personal experience that the study was carefully conducted, and because % falls within the range reported by others. The issue is further complicated by the facts that the value for % extracted from experimental data depends on the statistical technique used for fitting the data to the S-D curve, and that different investigators use different techMedical & Biological Engineering & Computing

determining vulnerability to ventricular fibrillation induced by 60-cps alternating current, Circ. Res., 21, pp. 601-608 WATSON, A. B., WRmHT, J. S., and LOUGrn~AN,J. (1973): Electrical thresholds for ventricular fibrillation in man, Med. J. Austral., 1, pp. 1179-1182 YAMAGUCHI,M., ANDOH,T., GOTO, T., HOSONO,A., KAWAKAMI, T., OKtr~tmA, F., TAKENAKA,T., and YAMAMOTO, I. (1992): Heart stimulation by time-varying magnetic fields, Jpn. J. Appl. Phys., 31, (7), pp. 2310-2316 J. P. Reilly, The John Hopkins University, Applied Physics Laboratory, Laurel MD 20723, USA. Received 25 January 1993

niques. We wish that we could provide more help on this important issue. The 'effective electrode size' corresponding to magnetically determined threshold is a perplexing issue. The papers cited by Reilly, in which z e is reported to increase with electrode size, address smaU-area electrodes. Stimulation of the cardiac ventricles requires excitation of only a single cell, and hence a small-area analogue may be appropriate. On the other hand, the electric field induced in the heart by the coils used in our study does not change rapidly with distance from the site of maximal field intensity, in a plane parallel to that of the coils, arguing for a large-area-electrode analogue. Definitive resolution of this issue awaits results from studies in which the duration of magnetic pulses is varied over a sufficient time period to permit calculation of strength-duration curve parameters. Monophasic versus biphasic thresholds The thresholds observed in our study are indeed probably greater than thresholds for a monophasic stimulus waveform, but care should be exercised in using the results from Roy to estimate the increase in threshold. The waveforms investigated by Roy (RoY et al., 1985) are not the same as those used in our study, and the experiment required to measure the effect of the decaying magnetic field is different from that performed by Roy et al., which compared thresholds for a sine wave with and without an offset. The magnetic stimulator used in our study produces an exponentially decaying, sinusoidal current in the coil; the induced electric field is the first time derivative of the coil current, appropriately scaled for geometry. The waveform of the induced electric field includes a first phase that resembles a 90 ~ cosine, followed by an exponentially decaying sinusoidal waveform with opposite polarity and much smaller amplitude and longer period. (The magnetic stimulator contains a resistor-diode network to reduce the amplitude and prolong the duraction of the second phase, the 'tail', of the induced electric field.) The 5 : 1 change in theshold observed by Roy was for an offset sine wave (only one phase) compared to a sine wave (equal-amplitude phases), and stimulus intensity is reported in terms of the peak-to-peak current. Consequently, the amplitude of the first phase was reduced by one-half for the charge-balanced waveform, relative to the 'monophasic' waveform. An experiment more relevant to the elevation in threshold by the 'tail', due to a collapsing magnetic field, is one in which the threshold for a 180~ sine wave is compared to

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that for a 360 ~ sine wave, i.e. a monophasic waveform with and without an equal amplitude tail. However, that is not the experiment conducted by Roy. We expect the elevation in threshold due to the tail to be small, but we have no experimental data to quantify the change. We agree with Reilly that including the effect of the 'tail' would reduce the discrepancy between his calculations and our results; the degree of reduction is debatable.

Direction of the stimulating E-field Care should be exercised in extrapolating results from experiments with electrodes on a subject's limbs to results from magnetic stimuli, because the current pathways are vastly different. Probably the most important consideration is the orientation of cardiac cells with respect to the direction of the induced electric field. Orientation of cells varies greatly near the left ventricular apex, which is most likely the region of the heart stimulated by the magnetic pulses used in our study, and it is likely that some cells were near optimal alignment with respect to the induced electric field. Consequently, we suspect that the increase in measured threshold caused by suboptimal cell orientation is small, but we have no experimental data to support the notion. We suspected that the polarity of the applied field could affect the threshold; however, our results do not support this hypothesis. As is shown in Table 1 of our paper (MouCHAWAR et al., 1992), the mean coil current at threshold intensity for one direction of current flow was 9273 A, whereas the coil current for the oposite direction was 9209 A, and the means were not significantly different (p = 0.05). Comparing the thresholds for each direction of the induced electric field in each animal, 5/11 subjects exhibited the lowest threshold for one direction of the induced field, 3/11 subjects exhibited the lowest threshold for the opposite direction, and the threshold was the same in the other three subjects. The greatest difference in the observed threshold with the direction of the induced field was 11.3 per cent; resolution of the threshold was limited to 10 per cent by the procedure of the experiment. The reported data do not support the hypothesis that threshold depends on the polarity of the induced electric field.

Shape of thorax and its conductive paths We agree that a semi-infinite volume of uniform conductivity represents a gross oversimplification of the complex thoracic structure. Results from a finite-element model of

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the dog thorax show that, for the coplanar coils used in this study, the calculated current density induced in the heart is approximately 6 per cent greater using a homogeneous model than under a finite-element model, which accounts for the inhomogeneous structure of the thorax (MouCHAWAR et al., 1991). However, the finite-element model also predicts that, for a z-axis MRI gradient field, the calculated current density induced in the heart is approximately 5 per cent less using a homogeneous model than under the finite-element model. It appears that the inhomogeneous structure of the thorax does not greatly alter cardiac safety in the MRI environment, for the fields considered. Discussion We agree that all five factors identified by ReiUy could contribute to a reduction of the rheobasic electric field strength required for cardiac stimulation. We reported population statistics for the normal mongrel dog. Similar data for a large sample of human subjects are needed. We also agree with Reilly on the need for additional studies to quantify the importance of the other factors he identified, and we would add that refined computer models would be helpful in interpreting results. We conclude, however, that the risk of inducing cardiac arrhythmias via direct stimulation of the myocardium by any MR imaging system known to us is very small. References ROY, O. Z., MORTIMER,A. J., TROLLOPE,B. J. and VILLENEUVE,E. J. (1985): Electrical stimulation of the isolated rabbit heart by short duration transients, in BRIDGES, J. E., FORD, G. L., SHERMAN, I. A., and VAINBERG, M. (Eds.): Electrical shock safety criteria. Pergamon Press, New York, pp. 77-86. MOUCHAWAR, G. A. (1991): Magnetic stimulation of excitable tissue: prediction of the eddy-current pathway via a threedimensional finite-element model. PhD Thesis, Purdue University, West Lafayette, Indiana MOUCHAWAR, G. A., BOURLAND,J. D., NYENHUIS,J. A., GEDDES, L. A., FOSTER, K. S., JONES, J. T., and GRABER, G. P. (1992): Closed-chest cardiac stimulation with a pulsed magnetic field, Med. & Biol. Eng. & Comput., 30, pp. 162-168 PEARCE, J. A., BOURLAND,J. D., NEILSEN,W., GEDDES,L. A., and VOELZ, M. (1982): Myocardial stimulation with ultrashort duration current pulses, Pace, 5, pp. 52-58

Gabriel A. Mouchawar, Siemens Pacesetter, Inc., 15900 Valley View Court, PO Box 9221, Sylmar CA 91392-9221, USA. Received 19 April 1993

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