Pacemaker interference by 60-Hz contact currents ... - IEEE Xplore

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thresholds range from 63 to 340 A for bipolar pacemakers. Index Terms—Cardiac pacemaker, contact currents, electro- magnetic interference, modeling.
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Pacemaker Interference by 60-Hz Contact Currents Trevor W. Dawson*, Senior Member, IEEE, Krzysztof Caputa, Maria A. Stuchly, Fellow, IEEE, and Robert Kavet

Abstract—Contact currents occur when a person touches conductive surfaces at different potentials, thereby completing a path for current flow through the body. Such currents provide an additional coupling mechanism between the human body and external low-frequency fields. The resulting fields induced in the body can cause interference with implanted cardiac pacemakers. Modern computing resources used in conjunction with millimeter-scale human body conductivity models make numerical modeling a viable technique for examining any such interference. An existing well-verified scalar-potential finite-difference frequency-domain code has recently been modified to allow for combined current and voltage electrode sources, as well as to allow for implanted wires. Here, this code is used to evaluate the potential for cardiac pacemaker interference by contact currents in a variety of configurations. These include current injection into either hand, and extraction via: 1) the opposite hand; 2) the soles of both feet; or 3) the opposite hand and both feet. Pacemaker generator placement in both the left and right pectoral areas is considered in conjunction with atrial and ventricular electrodes. In addition, the effects of realistically implanted unipolar pacemaker leads with typical lumped resistance values of either 20 k and 100 k are investigated. It is found that the 60-Hz contact current interference thresholds for typical sensitivity settings of unipolar cardiac pacemaker range from 24 to 45 A. Voltage and electric field dosimetry are also used to provide crude threshold estimates for bipolar pacemaker interference. The estimated contact current thresholds range from 63 to 340 A for bipolar pacemakers.





Index Terms—Cardiac pacemaker, contact currents, electromagnetic interference, modeling.

I. INTRODUCTION

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UMAN exposure to external low-frequency electric or magnetic fields leads to the induction of secondary fields within the body. These induced fields can cause electromagnetic interference (EMI) with susceptible implanted medical devices, such as cardiac pacemakers. Such EMI at power line frequencies (50 or 60 Hz) has been observed in environmental and laboratory settings [1], [2]. Numerical modeling of EMI that was recently performed indicated that pacemakers with unipolar electrodes could be susceptible to EMI by 60-Hz electric fields of the order of 6 kV/m [3] and by 60-Hz magnetic fields of the order of 40 T (140 T) for atrial (ventricular) electrodes [4]. It was also confirmed that EMI for bipolar pacemaker electrodes was highly unlikely for typical electrode placements. Manuscript received July 18, 2001; revised March 26, 2002. This work was supported by the EPRI under Contract WO2966-14. Asterisk indicates corresponding author. *T. W. Dawson is with the Department of Electrical and Computer Engineering, University of Victoria, P.O. Box 3055 STN CSC, Victoria, B.C., V8W 3P6, Canada (e-mail: [email protected]). K. Caputa and M. A. Stuchly are with the Department of Electrical and Computer Engineering, University of Victoria, Victoria, B.C., V8W 3P6, Canada. R. Kavet is with EPRI, Palo Alto, CA 94304-1344 USA. Publisher Item Identifier 10.1109/TBME.2002.800771.

Contact currents occur in a residence or workplace when a person touches conductive surfaces at different potentials and completes a path for current flow through the body. Typically, the current pathway is hand-to-hand and/or from a hand to one or both feet. Contact current sources may include appliance chassis that, because of typical residential wiring practices, carry a small potential above ground. Also, conductive objects situated in an electric field, such as a vehicle parked under a transmission line, serve as a sources of contact current. Contact currents provide an alternative coupling mechanism between the body and external fields than direct induction effects. ICNIRP and other organizations concerned with appliance safety (e.g., Underwriters Laboratories reviewed in [5]) have specified limits for contact or “leakage” currents. Contact current limits for frequencies less than 2.5 kHz are 1.0 mA for workers and 0.5 mA for the general public in guidelines [6], and they aim to avert hazardous startle and adverse perceptual effects. Values of 0.5 and 0.75 mA are listed as startle limits for portable and fixed appliances, respectively [5]. The National Electric Safety Code [7], which specifies safety practices for overhead transmission line construction and operation, limits steady-state whole body current from electric field induction under overhead high-voltage transmission lines to 5 mA. Recent developments in human electromagnetic models and computer resources make numerical modeling a viable resource for investigating EMI due to contact current sources. In this contribution, numerical methods and a realistic high-resolution model of the human body are used to compute the induced potential drop on unipolar pacemaker leads under a variety of contact current configurations, pacemaker placement and lead configurations. The modeling is based on an existing well-verified scalar-potential finite-difference frequency-domain code that has recently been modified to allow for combined current and voltage electrode sources [8], as well as to allow for implanted wires [4]. The methods used in this paper are not restricted to pacemaker interference. With appropriate adjustments for lead placement, etc., they could easily be applied to studying interference in other implanted devices or objects, such as implantable cardiac defibrillators. These can be as susceptible, or even more, to EMI than pacemakers. II. MODELING SCENARIOS A. Human Body Model The body model is derived from magnetic resonance imaging (MRI) and is described in detail elsewhere [9]. Briefly, the model of an average male (1.77 meters and 76 kg) has a realistic external shape, with over 30 organs and 80 major tissues identified. It comprises homogeneous cubic voxels with

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Fig. 1. Pacer on left.

3.6-mm sides. Each voxel is assigned the conductivity of the associated tissue. The conductivity values used in this work are from [10] and are tabulated in [11].

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Fig. 2.

Pacer on right. TABLE I SUMMARY OF THE VARIOUS SCENARIOS

B. Pacemaker Configurations The modeling additionally includes digital implantation of a metallic box representing the pacemaker generator in either the left or right pectoral subcutaneous fat layer of the model consistent with approximate clinical placements. To simulate the leads, one point on the pacemaker case is connected to a thin wire that follows a representative intravenous (i.v.) insertion path to a termination point within either the atrial or ventricular cardiac wall tissue. Only the total resistance between the pacemaker case and the cardiac electrode via the included electronics is important in modeling any effect due to the wire. The present modeling uses two representative values, 25 and 100 k , for lead plus amplifier bulk resistances (typically 10–100 ). Results taken from earlier work ignoring the presence of the wire [3] are also included for comparison. Fig. 1 shows a frontal view of the placement of the pacemaker generator on the left side of the body and the ventricular lead path within the body. The heart and associated major blood vessels are also indicated. Fig. 2 depicts the alternative scenario with the pacemaker case implanted on the right. C. Contact Electrode Configurations To simulate contact current sources, electrodes occupying 6 voxel faces (and, hence, having an area of squares of 6 4.67 cm ) were identified on the palm of each hand. When applicable, grounding at each foot was via the entire sole. The investigation covers six asymmetrical and one symmetrical current injection scenarios. The first three are based on 100 A [root mean square (RMS), at 60 Hz] injected into the left palm, and having (A) only the right palm grounded, (B) only the soles of both feet grounded, and (C) both the right palm and both feet grounded. The symmetric configuration (D) has 50 A injected into each palm, with the soles of both feet grounded. The final three asymmetric injection scenarios are analogous, but with the roles of right and left palms reversed. Thus each

has 100 A [at 60 Hz (RMS)] injected into the right palm, and having (E) only the left palm grounded, (F) only the soles of both feet grounded, and (G) both the left palm and both feet grounded. Table I summarizes the seven configurations. The chosen scenarios span the range of plausible situations, including the common cases of a person touching a charged object with one hand and a grounded object with the other, or with both feet grounded. Although all runs are normalized to 100 A (RMS) total current, the results can be linearly scaled to any desired source level. D. Computed Configurations The two pacemaker case locations, two pacing electrode locations and seven contact current scenarios combine to form 28 data values for each wire resistance and/or path. The cases presented below consist of no wire, and 20-k and 100-k i.v. wire paths for a total of 84 computations. III. COMPUTATIONAL METHODS A. Basic Computational Scheme The scalar potential finite difference method (SPFD), which applies under quasistatic approximation and is described in detail elsewhere [8], [12], is applied with modifications to handle the mixed boundary-value problem and the internal wires. All electromagnetic quantities are assumed to have a nonzero static limit. Hence, for example, the electric field would have the form ; the harmonic time factor will, henceforth, be

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dropped. The electric field within the body can then be represented in terms of a scalar potential field as (1) The current density is conserved to lowest order in frequency, , leading to the requirement that the scalar potential satisfy the differential equation (2) at any interior point in the body. At any point on a surface contact electrode having specified current density, this is replaced by the boundary condition (3) is the static limit of the local external current denwhere is the local outward unit normal, both evaluated sity, and at the body surface. If the potential is not specified at any point, the result is a pure Neumann boundary-value problem, and the potential is indeterminate to within an additive constant. In the present case, however, the problem of interest also has electrodes of specified potential (typically a ground value of zero), leading to a mixed Dirichlet–Neumann problem, in which the solution is determinate. In the present problem, the body surface is assumed to have , at each of which a a set of surface “current electrodes,” specified current is injected and a set of “voltage electrodes,” , at each of which a known voltage is specified. At a current electrode, the appropriate boundary condition is (4) is the total conduction current flowing into the body Here through an infinitesimal open surface lying within the conductor is the static limit and surrounding the surface point , and of the injected current at this point. In the present work, any total current injected at a given current electrode is assumed to be uniformly distributed over its associated nodes. At a each point on a voltage electrode, the boundary condition is simply (5) is the constant static limit of the specified potential Here, on the patch, and is zero for the grounded patches used in this work. In the finite difference implementation, voltage values are specified at voxel vertices (nodes). These may be viewed as connected by a lattice of conductors associated with the voxel edges. Application of (2) at an interior node “ ” in some global numbering scheme gives rise to an equation of the form (6) is the total body current leaving the node along its 6 where associated edge conductors. Application of (4) at a surface node “ ” on a current electrode gives rise to an equation of the form (7) is the total current entering the surface current node where is the specified current enalong less than 6 edges, and tering the body at the node. Finally, application of (5) at a surface node “ ” on a voltage electrode gives rise to an equation of the form (8)

where is the body potential at the node, and is the specified electrode potential. The assemblage of all such equations leads to a global matrix system of the form (9) Here, is a column vector consisting of all unknown potentials, while is a column vector containing any sources (involving specified potentials or currents at the surface source electrodes). Further, is diagonal matrix whose elements are the sum of all body edge conductances terminating at the corresponding node. Finally, is a symmetric matrix with at most 6 off-diagonal elements per row or column, whose elements consists of the various edge conductances linking pairs of adjacent nodes. If all boundary conditions are of the form (7) (pure Neumann case), this system of equations is also singular since any row or column of the matrix sums to zero. However, the right-hand side also then sums to zero, and the system can be regularized in a global symmetric manner by adding an equation that the solution have zero mean. Each equation of the form (8) (mixed problem) reduces the order of the matrix system by one and renders it nonsingular. For the model used in this work the matrix dimension is approximately 1.6 10 . Additional relevant discussion is given in [4]. B. Incorporation of Pacemaker Lead joining body nodes The effects of a wire of conductance and can be incorporated simply as follows. The current flowing in the wire is given by (10) wire) current is conserved at the joining Since total (body nodes, the net effect of the wire is, thus, to modify the two associated body potential equations (6) to and It is then readily seen that a wire of conductance SPFD matrix system (9) to

(11) alters the (12)

is diagonal and all zero apart from a value in the Matrix ) and ( ) diagonal entries. Matrix is a symmetric ( in the ( ) matrix whose only two nonzero values are ) off-diagonal slots. This modification is analogous to and ( that occurring in the case of magnetic induction [4], except the right-hand side is here unchanged in the absence of any applied emf. Additional wires contribute additional sparse matrices in an obvious manner. The wire modifications preserve all of the properties of the original system, apart from the heptadiagonal nature. The wire effects are easily incorporated into an iterative solution scheme by using minor modifications to the matrix-vector multiplication procedure. The wire current can be computed at the post-processing stage from (10). The solver used for this work is a standard Conjugate Gradient Method [13] written in-house. For the present computations, the residual error typically are reduced by 10–11 decades in approximately 3000 iterations.

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Fig. 3.

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Sample electric field distributions for the seven contact current (all 100-A at 60-Hz RMS) scenarios.

IV. RESULTS AND DISCUSSION A. Overview and Validation Fig. 3 provides an overview of the computations. The panels depict the induced electric field magnitude in fixed median body cross sections and on a common scale (in V/m). It may be noted from Table I that cases (A) and (E) should in fact be identical for harmonic sources. Confirmation of this result provides a check on the computer implementation of the boundary conditions. In fact, the equivalence of scenarios A and E (current flow from

hand to hand) is evident in Fig. 3, as is the relative symmetry of scenario D. The asymmetry of scenarios B and F (current flow from arm to feet) and of C and G (current flow from one hand to opposite hand and both feet) are also clearly evident. These views are taken from the runs with no leads, but as will be seen, the effect of the leads is small. One useful subset of data from the modeling is the potential and current at each active electrode. Table II summarizes the appropriate current data. Missing entries are associated with passive electrodes (those at which no external boundary condition

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TABLE II PEAK CONTACT ELECTRODE CURRENTS (MICROAMPERES FROM THE NUMERICAL MODELING FOR A 60-Hz, 100-A (RMS) TOTAL CONTACT CURRENT

TABLE III PEAK CONTACT ELECTRODE POTENTIALS (MILLIVOLTS) FROM THE NUMERICAL MODELING FOR A 60-Hz, 100-A (RMS) TOTAL CONTACT CURRENT

TABLE IV BODY RESISTANCES TO GROUND (KILOHMS) FROM THE NUMERICAL MODELING

is specified). Since the total source currents are all 100 A, a check on the computations is provided by the fact that all exit currents sum to 100 A. The corresponding contact electrode potentials are indicated in Table III. The zero values indicate the proper application of the grounded boundary condition where appropriate. The inclusion of the extravenous lead paths as considered in [4] would lead to an additional 56 computations. However, given the conservative nature of the field under purely electric excitation, and the identical lead resistances, the i.v. and extravenous paths should give identical results. This was confirmed by several trial computations, and provided an additional check on the coding.

C. Whole-Body Potential Distributions Table V provides further information on the induced whole-body potential distributions, in the absence of the leads. All values are in mV. These value are located at voxel centers, and are obtained by 8-point averages of the computed potential values at the voxel vertices. The upper (lower) half of the table pertains to implantation of the pacemaker generator on the left (right). It is evident from comparison of the two halves that the generator placement has only minor effects on the whole-body potential distributions. The rows labeled “Min,” “Avg” and “Max” respectively give the whole-body voxel minimum, mean and maximum values. Despite the grounded electrodes, the indicated minima differ slightly from zero due to the averaging used to evaluate the voxel-center potentials. For reference, the final row of each half indicates the (uniform) potential of the pacemaker case. To model the metallic case, a conductivity value of 1 kS/m was assigned. This value is considerably greater than all tissue values, and rendered the case equipotential to within 0.01%. It is interesting to note that the pacemaker case potential is close to the whole-body average in all cases.

B. Whole-Body Resistances The whole-body potential information allows computation of the effective resistance of the body between the source electrode(s) and ground using Ohm’s law. The relevant information is presented in Table IV. The values follow a predictable patterns. Among the single source electrode cases, the hand-to-hand resistance is highest, while the hand-to-hand and both feet resistances are the lowest. The hand-to-feet case is intermediate. The lowest overall resistance is provided by the symmetric both hands to both feet case. That these are sensible can be seen using simple arguments based on resistors in series and in parallel.

D. Unipolar Pacemaker Interference Table VI summarizes the induced voltage drops on the leads as obtained from the 84 numerical modeling scenarios. The indicated wire resistances are in kilohms. The expected identical values for contact current scenarios A and E also provide a validation of the code. One point to note from this table is that inclusion of the wire conductivity has only a small effect (up to about 3%) on the induced voltages. This provides a confirmation of the assumptions used in an earlier investigation of pacemaker EMI by external electric fields [3], in which the presence of the wires was not accounted for. The voltage information in

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TABLE V WHOLE BODY VOLTAGE (MILLIVOLTS) DISTRIBUTION INFORMATION FROM THE NUMERICAL MODELING FOR A 60-Hz (RMS), 100-A TOTAL CONTACT CURRENT

TABLE VI PEAK INDUCED VOLTAGES (MILLIVOLTS) BETWEEN THE PACEMAKER CASE AND PACING ELECTRODE FROM THE NUMERICAL MODELING FOR A 60-Hz, 100-A (RMS) TOTAL CONTACT CURRENT

TABLE VII CONTACT CURRENTS (MICROAMPERES, 60 Hz, RMS) REQUIRED TO PRODUCE A PEAK VOLTAGE DIFFERENCE OF 0.25 (0.75) mV FOR THE UNIPOLAR ATRIAL (VENTRICULAR) PACEMAKER CONFIGURATIONS

Table VI can be used to show that the induced over-currents on the pacemaker leads ranges from 2.7–81 nA for the 20-k resistance and from 0.55–17 nA for the 100-k resistance. These values are extremely small compared to the 100- A total current flow, again underlining the small effect of including the effects of the leads. Typical sensitivity settings for atrial pacemakers range from 0.25 to 1.6 mV, while the corresponding values for ventricular pacemakers range from 0.75 to 4.0 mV [14], [15]. Using the lower value in each case as a threshold, Table VI can be recast to yield the contact current required to produce the appropriate unipolar threshold potential difference. Table VII presents the resulting data. For unipolar atrial electrodes with the pacemaker case on the left, the contact currents required to achieve the in-

terference threshold range from a low of about 24 A for scenarios A and E (current flow from hand to hand) to a high of about 150 A for scenario F (current flow from right hand to both feet). The observed values ( 30 A) for scenarios B and C (current flow from left hand to feet or feet plus arm) are also close to the minimum. The lower values (scenarios A, B, C, E) and higher values (scenario F) are consistent with the location of both the pacemaker and the heart on the left side of the body. The values for the symmetric scenario D ( 72 A) and for scenario G ( 60 A, for current flow from right hand to the other three extremities) are intermediate. For unipolar atrial electrodes with the pacemaker case on the right, the threshold currents are slightly higher, in a sensible pattern. The lowest values ( 30 A) are again associated with the

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TABLE VIII HEART VOLTAGE DISTRIBUTIONS (MILLIVOLTS) RELATIVE TO THE PACEMAKER GENERATOR CASE FROM THE NUMERICAL MODELING FOR A 60-Hz, 100-A (RMS) TOTAL CONTACT CURRENT

TABLE IX HEART ELECTRIC FIELD (MILLIVOLTS/METER) DOSIMETRY FROM THE NUMERICAL MODELING FOR A 60-Hz, 100-A (RMS) TOTAL CONTACT CURRENT

arm-to-arm current flow scenarios A and E. The observed values ( 30 A) for scenarios F and G (current flow from right hand to feet or feet plus arm) are again close to the minimum. Scenarios C ( 84 A for right hand to the remaining three extremities) and the symmetric scenario D ( 66 A) are again intermediate. The highest levels ( 450 A) are associated with scenario B (current flow from right hand to both feet), and are presumably associated with the dominant effective current flowing furthest from the heart. For unipolar ventricular electrodes with the pacemaker case on the left, the threshold currents range from a minimum of about 56 A for scenario B and about 66 A for scenario C, to a maximum of about 300 A for Scenario G. The symmetric scenario D also has a relatively low threshold of about 78 A. Thresholds for the remaining three scenarios A, E and F are intermediate at about 114 A. For unipolar ventricular electrodes with the pacemaker case on the right, the minimum threshold currents are slightly lower, being approximately 48 A for scenarios F and G. Scenarios A and E also have relatively low thresholds ( 60 A) as does the symmetric scenario D ( 72 A). The threshold for scenario B (current flow from left hand to feet) jumps by a factor of three to approximately 198 A. Scenario C (current flow from left hand to the remaining three extremities) has the highest threshold ( 600 A) of all cases considered. In practice, pacemaker and defibrillator manufacturers design 60 Hz filters into their device input circuits. These filters are constrained by the fact that excessive filtering will decrease the sensitivity of the devices to the natural and electrical frequencies of the heart. Thus the same “sensitivity setting” may give different behaviors in units from different manufacturers, and even in different models from the same manufacturer. The results reported here are, therefore, also device-dependent. The

millivolt sensitivity amplitudes presented to the pulse generator are dependent, for their subsequent effect, on the pulse generator and on the manufacturer’s filter circuits in the input circuit portions of the pulse generator. E. Interference Estimates for Other Scenarios The data presented above are based on the particular choices of location of the single pacing electrode in either the atrial or ventricular walls. Detailed results for other unipolar electrode insertion points, or for bipolar pacemakers would require considerable further computations. However, estimates for both problems can be obtained from either the voltage or electric field distributions over the whole heart, which are available from the computed whole-body data sets. The relevant estimates based on the voltage distributions are presented in Table VIII. This table contains information pertaining to voxel center potentials (in mV) in the heart muscle, relative to the pacemaker generator case. The segmentation used in the present modeling is unable to distinguish between atrial and ventricular muscle, and so the data are representative but crude estimates. The values are the minimum, mean and maximum potential differences between any heart muscle voxel and the pacemaker generator. Also included in the table for reference are the particular potential differences from Table VI pertaining to the chosen atrial “(Atr)” and ventricular “(Ven)” electrode locations used earlier, but with the effect of the leads ignored. From the table, it is evident that in cases where the current flow is predominantly vertical (current injection via one or both hands with only the feet grounded, i.e., scenarios B, D, and F) that the induced voltages at the ventricular electrode are both greater than those at the atrial electrode and are close to the whole-heart maxima. With the pacemaker implanted on the left,

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TABLE X CONTACT CURRENT ESTIMATES FOR BIPOLAR PACEMAKER INTERFERENCE (A)

the voltages at the atrial electrode are greater than at the ventricular electrode for scenarios A, E, and G. With the pacemaker implanted on the right, this situation holds only for Scenario C. All cases involve transverse current flow (arm-to-arm) in the chest. The asymmetry of the heart and pacemaker locations combine to yield the observed results. This table could also be used to derive upper and lower bounds for induced voltages on unipolar leads with differing placements of the pacing electrode. Similar data for the heart electric field distributions are presented in Table IX. Tables VIII and IX can each be used to estimate the contact currents required to produce interference with bipolar pacemaker leads, with the resulting approximations presented in Table X. The first estimate (“Voltage”) is based on Table VIII. Assuming a characteristic dimension of 10 cm for the heart, the induced voltage range (“Max”–“Min”) can be used to estimate a voltage gradient. Assuming an interference threshold of 0.25 mV (0.75 mV) and a bipolar pacing electrode spacing of 1.5 cm (2.5 cm) for atrial (ventricular) pacing, the associated contact current are computed by a linear interpolation and scaling. An alternative estimate (“Electric”) is provided by the electric field (i.e., voltage gradient) dosimetry of Table IX. Here, the maximum electric field is multiplied by the electrode spacing to get an upper estimate for the induced voltage, which can then be used to compute the contact current associated with the appropriate threshold. The resulting current estimates range from a minimum of 63 A (electric field estimate for atrial pacing with generator implanted on the left for Scenarios A and E) to a maximum of 340 A (voltage field estimate for ventricular pacing with generator implanted on the left for Scenario D). The voltage-based estimated are always greater than the electric field-based estimates, generally by a factor of 2–3. It should be emphasized that these estimates are crude, and more realistic values could be obtained by performing calculations for specific bipolar pacing electrode locations.

Numerical estimates indicate EMI thresholds under the worst case scenario as about 24 A for arm-to-arm current flow for a unipolar atrial pacemaker with generator implanted on the left side of the body and a 0.25-mV sensitivity setting. The corresponding value for a unipolar ventricular electrode is about 45 A for the generator on the right, and current injected via the right hand with both feet grounded. Depending on the scenario and estimation method, the lower bound estimates for bipolar EMI range from 63 to 340 A. These estimates support the sensible conclusion that bipolar pacemakers are less sensitive to contact-current-induced EMI than unipolar ones. Although all evaluations have been made for a model with the hands close to the sides, our previous experience with other postures, combined with simple circuit arguments viewing the arm and leg segments as resistors in series with the torso, indicates that evaluations with similar electrode placements under differing postures would lead to similar computed voltage differences. Other possible factors to address in future work are the consequences of the large contact area provide by whole soles of the feet, as well as differences that would arise if hand contact involved a single fingertip, as opposed to an area of the palm. Finally, it should be emphasized that the values presented here pertain specifically to the indicated body, electrode and pacemaker models used, and so are indicative only. The values in general will depend on lead placement, body size and shape, chosen conductivity values, and a variety of other relevant factors. One simple comment that can be made is the obvious one that if a) all body and wire conductivities are scaled by a con, b) any voltage contact electrodes are at stant , i.e., zero (ground) potential, and c) the injected current at all current is a solution of contact electrodes are unchanged, then the resulting modified boundary value problem. Thus doubling all conductivities would halve all voltage differences and electric fields. Similar arguments could be applied to homogeneous scaling of body dimensions. Information for more complicated variations in the problem would require detailed computations.

V. CONCLUSION Numerical simulations using a millimeter-resolution heterogeneous human body model have been performed to evaluate EMI with implanted cardiac pacemakers due to 60-Hz contact currents. Detailed evaluations have been made only for unipolar pacemakers. Heart muscle induced field dosimetry has also been used to provide lower bounds for contact currents associated with bipolar pacemaker EMI.

REFERENCES [1] P. S. Astridge, G. C. Kay, S. Whitworth, P. Kelly, A. J. Camm, and E. J. Perrins, “The response of implanted dual chamber pacemakers to 50 Hz extraneous electrical interference,” P.A.C.E., vol. 16, pp. 1966–1974, Oct. 1993. [2] G. C. Kaye, G. S. Butrous, A. Allen, S. J. Meldrum, J. C. Male, and A. J. Camm, “The effect of 50 hz external electrical interference on implanted cardiac pacemakers,” P.A.C.E., vol. 11, pp. 999–1008, Jul. 1988.

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[3] T. W. Dawson, M. A. Stuchly, K. Caputa, A. Sastre, R. B. Shepard, and R. Kavet, “Pacemaker interference and low frequency electric induction in humans by external fields and electrodes,” IEEE Trans. Biomed. Eng., vol. 47, pp. 1211–1218, Sept. 2000. [4] T. W. Dawson, K. Caputa, M. A. Stuchly, R. B. Shepard, R. Kavet, and A. Sastre, “Pacemaker interference by magnetic fields at power line frequencies,” IEEE Trans. Biomed. Eng., vol. 49, pp. 254–262, Mar. 2002. [5] J. P. Reilly, Applied Bioelectricity: From Electrical Stimulation to Electropathology. New York: Springer-Verlag, 1998. [6] International Commission on Non-Ionizing Radiation Protection (ICNIRP), “Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz),” Health Phys., vol. 74, pp. 494–522, 1998. [7] National Electric Safety Code (NESC), 1993 National Electric Safety Code. Piscataway, NJ: IEEE Press, 1993. [8] T. W. Dawson, K. Caputa, M. A. Stuchly, and R. Kavet, “Electric fields in the human body from 60-Hz contact currents,” IEEE Trans. Biomed. Eng., vol. 48, pp. 1020–1026, Sept. 2001. [9] T. W. Dawson and M. A. Stuchly, “High-resolution organ dosimetry for human exposure to low-frequency magnetic fields,” IEEE Trans. Magn., vol. 34, pp. 708–718, May 1998. [10] S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues: III parametric models of the dielectric spectrum of tissues,” Phys. Med. Biol., vol. 41, pp. 2271–2293, 1996. [11] T. W. Dawson, K. Caputa, and M. A. Stuchly, “A comparison of 60-Hz uniform magnetic and electric induction in the human body,” Phys. Med. Biol., vol. 42, pp. 2319–2329, 1997. [12] M. A. Stuchly and T. W. Dawson, “Interaction of low frequency electric and magnetic fields with the human body,” Proc. IEEE, vol. 85, pp. 643–664, May 2000. [13] R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadelphia, PA: SIAM, 1994. [14] A. Sastre, “Susceptibility of implanted pacemakers and defibrillators to interference by power-frequency electric and magnetic fields,” A.S. Consulting & Research, Inc., Tech. Rep., EPRI, 1997. [15] B. Nowak, T. Voiglander, and E. Himmrich, et al., “Cardiac output in single lead VDD pacing versus rate-matched VVIR pacing,” Amer. J. Cardiology, vol. 75, pp. 904–907, 1995.

Trevor W. Dawson (M’95–SM’98) received the B.Sc. degree in physics and applied mathematics (Honors) in 1976 and the Ph.D. degree in geophysics (EM induction) in 1979, both from the University of Victoria, Victoria, BC, Canada. From 1979-1994, he worked at Defence Research Establishment Pacific. There, his research varied from the modeling of remote sensing and propagation of internal waves, to the modeling of coupled seismo-acoustic propagation in the Artic Ocean, its basement, and ice canopy. In 1994, he started work at the University of Victoria as a Research Scientist under the NSERC/BC Hydro/TransAlta Industrial Research Chair. His current research interests include the application of numerical methods to the modeling of induced electromagnetic fields in biological systems, and in related applications of analytical methods.

Krzysztof Caputa received the M.Sc. degree in experimental physics from Nicolaus Copernicus University,Torun, Poland, in 1975. After immigration to Canada in 1981, he worked in the field of marine electronics while continuing his studies at the University of Victoria, Victoria, BC, Canada. He received the MASc. degree in control engineering in 1993. He is currently working as a Research Engineer at the University of Victoria. His professional interests include the design of data acquisition and control systems, computational electrodynamics and biophysics.

Maria A. Stuchly (S’71–SM’76–F’91) received the M.Sc. degree in electrical engineering from the Warsaw Technical University, Warsaw, Poland, in 1962, and the Ph.D. degree in electrical engineering from the Polish Academy of Sciences, Warsaw, Poland, in 1970. From 1962 to 1970, she was with the Warsaw Technical University and the Polish Academy of Sciences. In 1970, she joined the University of Manitoba. In 1975, she joined the Bureau of Radiation and Medical Devices in Health and Welfare, Ottawa, ON, Canada, as a Research Scientist. In 1978, she was associated with the Electrical Engineering Department, University of Ottawa, as an Adjunct Professor. From 1990 to 1991, she was a Funding Director of the Institute of Medical Engineering. In 1992, she joined the University of Victoria, Victoria, BC, Canada, as a Visiting Professor with the Department of Electrical and Computer Engineering. Since January 1994, she has been a Professor and Industrial Research Chairholder funded by the Natural Sciences and Engineering Research Council of Canada, BC, Hydro and Trans Alta Utilities. Her current research interests are in numerical modeling of interactions of electromagnetic fields with the human body and wireless communication antennas.

Robert Kavet received the B.S. degree in 1966 and M.E. degree in 1967, both from Cornell University, Ithaca, NY. He received the M.S. degree in environmental health sciences in 1972 and the D.Sc. degree in respiratory physiology in 1977, both from Harvard University, Cambridge, MA. He is currently EMF Business Area Manager, which includes programs in EMF health assessment, electromagnetic compatibility, and radiofrequency safety, at EPRI, Palo Alto, CA, He is also currently a Visiting Lecturer on Environmental Health Sciences, Harvard University. He was a Senior Staff Scientist with the Health Effects Institute (HEI), Cambridge, MA, joining HEI in 1984. From 1986 until 1992, he was a consultant focused largely on potential health effects from exposure to electric and magnetic fields (EMF). He has published extensively in the area of EMF health effects, and has directed short courses and seminars on this subject.