Radiation Protection Dosimetry (2014), Vol. 162, No. 3, pp. 268 – 279 Advance Access publication 8 December 2013
doi:10.1093/rpd/nct311
RADIOFREQUENCY CONTACT CURRENTS: SENSORY RESPONSES AND DOSIMETRY Robert Kavet1, R. A. Tell2 and R. G. Olsen3 1 Electric Power Research Institute, 3420 Hillview Avenue, Palo Alto, CA 94304, USA 2 Richard Tell Associates, Inc., 350 Falcon Ridge Parkway, Suite 103, Mesquite, NV 89027, USA 3 School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA *Corresponding author: [email protected]
The process of setting science-based exposure standards (or guidelines) for radiofrequency (RF) contact current exposure has been disadvantaged by a lack of relevant data. The authors first review the essential features and results of the available studies and illustrate the apparent discrepancies among them. Then, they examine the manner in which current was administered in these studies and suggest as to how the physical relationship of a contacting finger to the current electrode may play a role in affecting sensory thresholds specific to those configurations. A major factor in this analysis relates to whether current density is uniformly distributed across the contact area or whether an electrode’s ‘edge effects’ enhance currents with a net effect of decreasing apparent thresholds, when expressed as the bulk current entering a subject. For an exposure with a clear hazard potential, thresholds of human sensory response to RF currents require further investigation.
INTRODUCTION Exposure to radiofrequency (RF) contact current (about 100 kHz) may result from contact of part of the body, usually one or both hands or fingers with (a) a conductive object that is directly energised from a power source (e.g. an active antenna), or (b) a passive conductor indirectly energised by an RF field, which is referred to as ‘re-radiation’. These scenarios may also include exposure to an RF spark discharge—or an arc—that may bridge the gap between the conductor and the finger or hand just prior to the point at which actual physical contact with the conductor occurs, or upon breaking contact. Either continuous current via contact or an arc may inflict an adverse reaction (tissue heating to the point of pain or a burn). An important distinction is that the arc produces its effect immediately, whereas with a continuous current in the absence of an arc, an individual can often sense the temperature rise in tissue and withdraw contact before an injury occurs. An extensive amount of research has dealt with the potential biological effects associated with the direct coupling of RF fields with living bodies(1 – 3). Far less attention has been accorded to dose –effect characteristics of the sensory responses (e.g. perception, pain or aversion) to RF contact current, which presents a potentially hazardous condition that can precede a burn injury. This paper (a) reviews the studies that have addressed thresholds of sensory responses to continuous RF contact currents, (b) addresses the apparent discrepancies in reported thresholds for perception
and pain responses (c) and reflects on the adequacy of the available data for setting exposure standards for RF contact current.
SENSORY RESPONSES TO CONTACT CURRENT: EXPERIMENTAL STUDIES Experimental data on human reactions to contact current at 100 kHz or above have been reported by Chatterjee et al.,(4) Rogers(5) and Dalziel and Mansfield(6), with the key features of each study summarised in Table 1. As will be reported later, greater contact current thresholds are observed for grasp compared with touch contact. This is attributable to the relatively larger cross section of tissue exposed to a given level of current for grasp compared with touch contact, and thus lower current densities, which are responsible directly for local heating. Chatterjee et al.(4) published the only peer-reviewed paper to present data describing sensory responses of human subjects to RF currents of .200 kHz(4). Chatterjee noted that, ‘the sensation for frequencies below 100 kHz was one of tingling or pricking, localized in the area adjacent to the region of contact on the finger or hand. [For frequencies greater than 100 kHz] [t]he sensation was one of warmth or heat in the area below and around the plate electrode in the case of finger contact, and in the hand and wrist regions in the case of grasping contact’. The wrist, which has the smallest cross-sectional area (of soft tissue), in the current pathway for grasp is, thus, the site most prone to heating. Note that for testing touch thresholds,
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Received 14 June 2013; revised 31 October 2013; accepted 6 November 2013
Table 1. Comparison of RF contact current perception studies. Chatterjee 197 F and 170 C (18 –70 y old) 18–35: 70 F, 59 C 36–50: 66 F, 55 C 51–70: 61 F, 56 C 10-y-old thresholds inferred by body size scaling from males
Rogers
Touch: 28 F Hold (‘Grasp’): 28 F, 4 C; 72–76 % of males 30 y old
50 ‘persons’
10 and 30 kHz, 0.1, 0.3, 1 and 3 MHz
200 kHz
2, 5, 10, 15 and 20 MHz
Index Touch: fingertip Grasp: palm
Index Back of finger; fingertip, but no data presented
Contact with
Touch: square copper block Grasp: brass rod
Middle Touch: ‘fingertip’ but very possibly the finger pad Hold (‘Grasp’): palm (probably) Touch/tap: copper plate Hold (‘Grasp’): number 8-copper wire
Contact dimension
Touch: 25 mm2, i.e. ,fingertip area for threshold study; 144 mm2 for impedance measurements Grasp: cylindrical brass rod 1.5 cm diameter, 14 cm long
Touch/tap: probably .fingertip area (i.e. finger pad) Grasp: number-8 copper wire (3.264 mm diameter)
18 mm diameter; length of tube . width of finger
Saline-moistened contact? Approach
Yes
Yes
Yes
Subthreshold
Subthreshold
Subthreshold
Perception
‘just felt a sensation’
‘mean value of current just causing sensation’
‘barely perceptible sensation’
Pain
‘the sensation was so uncomfortable that they would definitely not want to hold on to or touch the electrode’
NA
‘discomfort was felt’
Reporting
Perception versus current w/error bars
Probit plots
Histograms
Brass tube
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Frequency Finger for touch Part of finger/hand
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Subjects
Dalziel
R. KAVET ET AL. Table 2. Median response thresholds for males and females averaged (i.e. GM) for each from 100 kHz to 3 MHz, with male-to-female and pain-to-perception ratios (based on graphical data in Chatterjee et al.(4)). Response Touch perception (mA) Touch pain (mA) Pain:perception Grasp perception (mA) Grasp pain (mA)
F
C
F:C
39.8 49.2 1.24
36.3 45.3 1.25
1.10 1.09 —
290 360
229 286
1.27 —
Figure 1. Summary of sensory thresholds from Chatterjee et al.,(4) showing the geometric mean of male and female adult thresholds.
Chatterjee had the subjects contact a square 25-mm2 copper block with the saline-moistened tip of the index finger; the fingertip thus extended well beyond the electrode’s edge. To establish a more exact frequency at which the transition from electrostimulation to a warming sensation occurs, the investigators tested a subset of subjects who reported ‘tingling’ exclusively (i.e. electrostimulation) at 50 kHz. They state that, ‘at 70 kHz, some subjects felt tingling and some felt warmth. When the current was raised slightly for those subjects who reported tingling, the sensation changed to one of warmth’. The exposures in this and the two studies described later were continuous sinusoids, that is, they had a 100 % duty cycle; for lower duty cycles, the current threshold for warming would increase, and the initial response would be electrostimulation(7). The authors layered Chatterjee’s graphs for the three endpoints (touch perception, touch pain and grasp perception in Figures 4–6 in their paper) on an enlarged grid to enable us to derive a graphically based estimate of their data. The charted data points are treated as medians, that is, the estimated geometric mean (GM) for an assumed lognormal distribution. To provide a general comparison of the thresholds across the three endpoints, the authors averaged the male and female thresholds for each endpoint at each frequency to represent a mixed cohort of adults (Figure 1). As observed, the threshold profiles ‘flatten’ out to some degree between 100 kHz and 3 MHz. Accordingly, for male –female comparisons in this frequency range, gender-specific thresholds were calculated as the GM of the medians at each frequency. Thresholds representing the three endpoints for a mixed adult population were calculated as the GM of the values for each gender. The thresholds for male subjects were greater than those for females with a greater difference between
genders for grasp than for touch (Table 2). Apparent gender differences have been shown to be an artefact of an underlying body size relationship, rather than gender per se(8). The threshold for touch pain was 25 % greater than that for perception, and in a related observation, the investigators noted for a subset of subjects tested (N¼9) that, ‘when the current was adjusted to a value equal to the perception threshold, pain was reported typically within 10–20 s’. To determine the between-subjects range of adult sensory sensitivity to RF currents for touch perception and touch pain and for grasp, the authors estimated the geometric standard deviations (GSDs) from the published figures. For each gender/response combination (e.g. female/touch pain), the authors computed the GM of the GSDs for the four frequencies tested from 100 kHz to 3 MHz. Using the pooled value of male and female GSDs as the within-group GSD, and the differences between male and female GMs (each also averaged from 100 kHz to 3 MHz as noted earlier) as the between-group GSD, an overall ‘adult’ GSD was computed for each response type based on a standard ANOVA approach. This computation assumed equal sample sizes for male and female groups to represent an evenly mixed cohort of adults. Under the assumption of relatively constant thresholds for each sensory response from 100 kHz through 3 MHz, these computations allowed a view of the range of adult sensitivities in a single graphic (Figure 2). The authors project that for Chatterjee’s exposure scenario, roughly one in a hundred adult persons would have thresholds of 24.3 mA (or less) for touch perception, 31.0 mA for touch pain and 149 mA for grasp perception (i.e. 1st percentile thresholds). The value of 185 mA for grasp pain was derived by multiplying the grasp perception median threshold by the ratio of the median touch pain to median touch perception. The figure also indicates the 0.1th and 50th percentile values. In 1950, Dalziel and Mansfield reported on thresholds of current perception from 60 Hz to 200 kHz for
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Grasp pain ¼ grasp perception` pain:perception.
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a sample of adults touching or tapping a copper plate with the middle finger, or holding (i.e. grasping) a number-8 wire (3.26 mm diameter) (Table 1)(6). They observed that, ‘[t]he touching and tapping contact tests using frequencies between 100,000 and 200,000 cycles [i.e. Hz] brought forth the opinion from all subjects that the sensation caused by the higher frequencies was one of heat rather than the muscle stimulation noted at the low frequencies’. They further observed that, ‘the change in sensation [heating] is a definite change, rather than the gradual changes experienced at frequencies below 100,000 cycles’. Finally, observing the clear difference in sensory experience above and below 100 kHz, Dalziel and Mansfield reported that ‘When currents of 100,000 or more cycles were adjusted to values slightly less than the perception values and maintained constant, perception was reported after an interval of several seconds. In contrast, for frequencies less than 100,000 cycles, currents of slightly less than the perception value were not perceived after an interval of several minutes’. Dalziel and Mansfield reported a median perception threshold at 70 kHz (based on 19 males) of 101.5 mA for holding the wire; the investigators extrapolated their plot to 100 kHz with a threshold the authors estimate from the graphic (not shown) to be 148 mA. For touching a copper plate (they use the term ‘copper block’ in their figures and ‘plate’ in text) with a finger, the median perception threshold was 43.8 mA at 100 kHz and 63.6 mA at 200 kHz (25 males). The thresholds for tapping contacts were lower than those for continuous touch. They attribute this to ‘accommodation’ wherein desensitisation occurs as exposure continues. The authors derived the 1st percentile thresholds from the graphs for touch and grasp in Dalziel and Mansfield (Figures 4 and 5 in the original publication), who provided the 0.5th percentile, in addition
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Figure 2. Summary of probits for touch and grasp estimated from the 100 kHz to 3 MHz data in the graphs in Chatterjee et al.(4).
to the 50th and 99.5th percentiles. For touch, which extended to 200 kHz, the plots did not appear to flatten above 100 kHz as Chatterjee et al.(4) had observed. From Figure 2, which presents the results from Chatterjee et al., the authors computed ratios of the 50th to 1st percentile of 1.56 and 1.73 for touch and grasp, respectively (some refer to this ratio as the ‘slope factor’(9)), representing males and females pooled from 100 kHz to 3 MHz. In Dalziel and Mansfield, and using log-transformed data for our calculations, this ratio for touch was 2.57 at 100 kHz and 1.48 at 200 kHz. For grasp, Dalziel and Mansfield’s ratio was 1.45 at 100 kHz, the highest frequency reported, whereas Figure 2 reflects a median to 1st percentile ratio of 1.73 for males and females pooled from 100 kHz to 3 MHz in Chatterjee et al. Despite these differences, the consistency between the two studies just discussed allows a generalisation that, for continuous sinusoidal currents, the transition from electrostimulation to warming sensations occurs at 100 kHz. In a workshop proceeding, Rogers reported on sensory thresholds for a group of 50 adult subjects contacting an 18-mm-diameter brass tube electrode with the back of their index finger(5). The distinction between the electrodes and mode of touch contact in the Chatterjee and Rogers studies (Figure 3) is critical to the discussion later, which addresses the discrepancies in their respective results. The endpoint identified by Rogers as ‘let-go’ appears to be functionally equivalent to that identified by Chatterjee as ‘pain’. Rogers explained that for each subject, he measured the threshold of perception, as well as another endpoint that he called discomfort in one paragraph, and let-go in another. In most literature on electric shock, the ‘let-go’ threshold refers to grip tetanus of a grasped conductor—a very painful condition. Equating ‘discomfort’ with ‘let-go’ at first seemed contradictory. With further reflection, it seems likely that Rogers’ subjects were responding to a condition in which they could not tolerate the stimulus, and consequently felt compelled to cease contact, that is, to let go of the energised conductor. Such terminology is said to have been common in the UK at the time of Rogers’ study. However, the authors cannot provide absolute certainty on this point. The authors were kindly provided numerical transcriptions of the histograms in Rogers’ report by Dr. B. J. Klauenberg and colleagues. The authors assigned the midpoint current value of each of Rogers’ histogram bars (e.g. 25, 35, 45 mA, etc.) to the number of individuals within the respective bar. To estimate the 1st percentile threshold for the perception and let-go responses, the authors first assumed that for each of these two responses, the probit distributions at each frequency maintain the same shape (are parallel to one another, the same assumption adopted for analysing Chatterjee et al.); analysing
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Figure 4. Probit distributions from Rogers data(5) for perception (triangles) and let-go (open squares). Also shown are the regression lines for each: linear for perception and quadratic for let-go.
Figure 5. Geometric means and lower 1st percentile values for perception and pain based on histograms in the Rogers report, and the analysis from Figure 4 and that described in the text (5).
each response separately was necessitated by the fact that the probit distributions for perception were different from those for let-go ( p , 0.0001), as discussed later. The authors then computed (using Excel), for each of the five frequencies—2, 5, 10, 15 and 20 MHz—the 2nd-through-98th percentile threshold current values in increments of two percentiles. For each frequency and percentile value, the current thresholds were normalised to the respective
frequency-specific GM threshold current (Ithresh/ IGM). For each percentile value, this normalised statistic was averaged across the five frequencies. For each response, these values were plotted with the vertical axis a probit of a normal distribution (distributed as the number of standard deviations from the GM), and the horizontal axis in terms of log10(Ithresh/IGM). On inspection, the distribution of the perception data points appeared linear (i.e. lognormal), and the let-go
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Figure 3. Difference between Chatterjee et al.(4) and Rogers(5) with respect to electrode contact. The bottom left (right) schematic is a simplified equivalent of the upper left (right) drawing.
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curve data appeared to have a quadratic component, and each was regressed accordingly (Figure 4). The regression equations were extrapolated to the 1st percentile level on the vertical axis, with the result that the 1st percentile threshold current was 50.5 % of the GM for perception, and 62.9 % of the GM for let-go (Figure 5). Rogers stated that his result: ‘indicates an approximate average hazard threshold current of 200 mA for the band 2–20 MHz. It was noted that perception and let-go currents for finger-tip contact were about twice those for back-of-finger contact and even higher for large area contact with the palm’. The plots in Figure 5 reflect that the distribution of let-go thresholds in the Rogers study were, for the most part, ,200 mA, with 1 % of the population projected to have a threshold of 89.4 mA at 2 MHz increasing to 133 mA at 20 MHz. For perception, the thresholds were largely ,100 mA, with 1 % of the
population projected to have a threshold of 25.3 mA at 2 MHz increasing to 53.8 mA at 20 MHz. For purposes of comparison, the median sensory threshold data from the three studies discussed earlier have been graphed together. For touch perception and grasp (Figure 6, left and right), the data from Chatterjee and Dalziel virtually overlap with relatively minor exceptions. With little overlap of the frequency ranges studied by Chatterjee and Rogers for touch perception and touch pain (let-go) (Figure 6, top left and right), the reasons for the differences between the two with respect to both thresholds and slope are not immediately apparent. The next section addresses a possible basis for these discrepancies, as well as for the doubling of threshold for fingertip contact relative to back-of-the-finger in the Rogers study.
FACTORS AFFECTING SENSORY THRESHOLDS The process of setting exposure standards for RF contact current has necessarily relied on the small set
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Figure 6. Comparison of median touch thresholds across the three studies reviewed (left); comparison of median pain thresholds from Chatterjee and Rogers (right); comparison of median grasp thresholds from Chatterjee and Dalziel & Mansfield (D&M) (middle)(4 – 6).
R. KAVET ET AL.
SAR ¼
2 Javg ; sr
Figure 7. Iso-effect thresholds for pain and burn in human skin. (Adapted from Dewhirst et al.(10)) (Data points from Dewhirst et al., and regressions performed for this paper.)
ð1Þ
where Javg represents the average current density through a tissue cross section with area, A; Javg ¼I/A (A m22); I is current (A); A is cross-sectional area (m2); s, tissue conductivity (S m21) and r, tissue density (kg m23). Under an adiabatic assumption, which is probably an acceptable assumption for brief finger contact, the rise in tissue temperature, DT (8C) over time, Dt (s), is calculated as follows: DT ¼
SAR Dt; c
ð2Þ
where c is the heat capacity of the affected tissue (Joules kg21 8C21). Dewhirst et al. published a comprehensive review of thermal thresholds in skin, reporting that a skin temperature of 44 to 488C for on the order of 6 s produces pain, and an increase to 53 to 598C for between 6 and 30 s will initiate the onset of blistering (i.e. a low grade burn)(10). An adaptation of the key curves from Dewhirst et al. describing pain and blistering skin temperature/time thresholds together with regressions of those curves performed for this paper are shown in Figure 7. As an example, using the properties of connective tissue [r ¼ 1500 kg m23; c ¼ 2400 (Joules kg21 8C21), and at 0.1 –30 MHz, s ffi 0.4 S m21](11) to represent the fingertip, one would calculate a temperature increase of 6.88C for a 140mA current distributed uniformly over a 1-cm2 contact area for 5 s. Thus, for perception or pain resulting from finger contact, the SAR and local increase in tissue temperature depends on the properties (s, r and c) of epidermal and subdermal tissue at the immediate site of electrode contact (for grasp contact, not dealt with in this discussion, the wrist is most likely the primary
Figure 8. SAR at the tissue interface with a 1-cm2 electrode as a function of tissue conductivity, s, and mass density, r.
site of thermal sensations even though the proximal site of contact is the palm). Tissue conductivity, s, is a function of frequency that varies among tissue types. s is thus an important factor in quantifying SAR (equation 1) across a frequency spectrum. Tissue density, r, and heat capacity, c, also vary across tissue types, but do not exhibit a frequency dependency. Because most anatomical sites consist of a mix of tissue types, a single type is unlikely to completely determine the time rate of thermal energy deposition. Various investigators have selected default values for these quantities to illustrate a general principle about tissue heating(12), whereas others have categorised tissues as having high, medium or low water content, selecting conductivity, and tissue density values to represent each(13, 14). Figure 8 shows how SAR from a current of 200 mA uniformly distributed over a 1-cm2 cross section of skin varies across a realistic joint range of tissue conductivity and tissue density, with a likelihood that the actual value would fall in this
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of studies reviewed in the previous section. Given the differences among the three studies with respect to study design and procedures (reviewed in Table 1), in addition to discrepancies in their results, standard setting is disadvantaged by an absence of a larger pool of information on thresholds of sensory responses to RF contact current. Nonetheless, it is instructive to examine possible reasons for apparently divergent results, especially between the Chatterjee and Rogers studies. The fundamental biophysical interaction between RF current and tissue may be expressed by the formula for specific absorption rate (SAR) (W kg21), the same quantity used to express dose rate in tissue (or whole body) from exposure to RF fields. For RF contact current,
SENSORY RESPONSES TO RF CURRENT
parameter space. Using these SAR values and a range of realistic heat capacities, the skin temperature could rise between 2.5 and 16.78C with a 2-s exposure (Figure 9). As a relatively simple example, one can propose how site-specific s could explain the doubling of thresholds for fingertip compared with the back of the finger in the Rogers study. Assuming uniform current flow across the contact cross section (more on this below), one could expect relatively higher conductivity in the fingertip, because it is padded with soft tissue, compared with the back of the index finger with a relatively thinner epithelia and bone immediately below the point of contact. With similar tissue densities and heat capacities assumed for the two sites, together with the same physical contact area assigned to both sites (equations 1 and 2), the higher conductivity in the fingertip would lead to a higher perception threshold for the fingertip, as was the case reported by Rogers; this analytical approach is expanded upon in the ensuing discussion. In addition to the part of a finger in contact with the electrode and its tissue properties just discussed, the factors that can affect experimental results may include: the size of the physical contact area, the subjective response criteria specific to each study and the manner in which subcutaneous heat and pain receptors are distributed and process and integrate sensory input from RF current. However, the greatest potential source of uncertainty relevant to the differences between Chatterjee’s and Rogers’ results may be related to the physical relationship of the skin to the electrode (see Figure 3). In the Chatterjee study, a moistened index fingertip was applied to a square 25-mm2 electrode. Thus, the fingertip entirely covered the area of the contact electrode. Studies concerned with electrosurgery and defibrillation have described the edge effects associated with skin burns from these procedures. When the
Figure 10. Modelled current density 0.5 mm under a square defibrillating electrode as a function of the relative distance from the electrode centre to the edge along horizontal and diagonal axes (see inset). The electrode modelled was 8.86 cm on each side with a resistivity of the interface of 20 V-m, and total interface resistance of ,2.5 V. The curves represent the current densities along the ‘Across’ and ‘Diagonal’ trajectories in one quadrant of the figure. Adapted from Krasteva et al.(17)
skin area extends beyond the outer bound of the contacting electrode, current density maxima—and thus greater burn risks—are concentrated at the edge of the electrode. For example, Kim et al. developed a computer model of current associated with a rectangular dispersive electrode (10` 12 cm) applied to the thigh, reporting that 45 % of the total current passed through the outer 26 % of the electrode’s area(15). Similarly, Wiley and Webster calculated that 50 % of the current from a circular electrosurgical electrode contacting skin is concentrated in the outer ring that accounts for 25 % of the electrode’s crosssectional area(16). Krasteva and Papzov calculated the current density in tissue directly beneath a square defibrillation electrode located on a single layer of tissue with resistivity 20 V-m and total resistance of ,2.5 V(17). Although the electrode was 8.86 cm on each side placed over the thorax, it is instructive to relate their results to Chatterjee’s experimental configuration (Figure 3). As illustrated in Figure 10, these investigators reported that the current density in the tissue below the centre of an edge and a corner reached, respectively, about three and six times the current density in the centre of the electrode (and in both cases, the current in tissue spread beyond the outer border of the electrode). In a subsequent paper, Kim et al. reported an inverse relationship between the extent of an edge effect and the resistivity of a gel layer introduced between an electrode and the skin (with the skin extending beyond the gel layer’s periphery)(18). In other words, a gel layer of relatively greater resistivity produced a more uniform current density across the
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Figure 9. Temperature increase in tissue after 2 s as a function of SAR for three values of tissue heat capacity.
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compared with back-of-finger contact, but no data were provided. For fingertip contact with the brass tube in the Rogers study, the authors will assume that the physical contact area was greater than Chatterjee’s, the current was uniform across the contact area and the conductivities of the underlying fingertip tissues were comparable to Chatterjee’s. The authors sought to understand the Rogers –Chatterjee discrepancy by determining which combinations of (1) the ratio of the respective physical contact areas, (2) Jeff, associated with enhancement of current density at an electrode’s edge (in Chatterjee’s case), with Jeff ¼1 signifying no edge effect (uniform current density) and (3) the relative tissue conductivities (sRog/sChat, the authors explained earlier why they believe this ratio is 1.0), could result in the identical local SAR in each study, and therefore ideally the same sensory threshold, even though the absolute values of their respective contact current exposures differed. Thus, IRog/IChat yielding the same SARs was plotted against combinations of Jeff and sRog/sChat for scenarios in which the physical contact area in the Rogers study was 2, 4 and 6 times the area in the Chatterjee study (the ‘Area Ratio’). The results plotted in 3D surface charts (Figure 11) reflect that IRog/IChat is directly proportional to both the area ratio and Jeff and to (sRog/sChat)0.5. The results indicate clearly that, with the authors’ stated assumptions, Rogers and Chatterjee could achieve the same sensory thresholds with very different current magnitudes. Except for one case, IRog/IChat was greater than unity, with a maximum value of 24 (the exception was when ‘Area Ratio’ ¼ 2, Jeff ¼ 1 and sRog/sChat ¼ 0.10). For the brass tube electrode used in the Rogers study, the authors have shown using electrostatic theory, which is appropriate in this case, that no edge enhancement effects occur for either back-of-thefinger or fingertip contacts (see Appendix). Rogers’ observation of a doubling of the current threshold for fingertip relative to back-of-the-finger contact would thus occur, according to this simple model, when the ratio of the fingertip (ft) to back-of-finger (bf ) physical contact areas, Aft/Abf, multiplied by the square root of the fingertip to back-of-finger conductivities, (sft/sbf )0.5, equals 2.0. Given in all likelihood that Aft/Abf is not vastly different than 1.0, the conductivity ratio would be a key factor with a doubling of current threshold occurring when the fingertip’s conductivity was 4-fold greater than the conductivity of the back of the finger. A factor suggested earlier as partially responsible for discrepant study results (i.e. Chatterjee versus Rogers), but not dealt with at a quantitative level, concerns the possible differential sensitivity of heat and pain receptors in the tissue proximally exposed to RF current. Thus, if the net effect of the concentration of temperature and pain receptor free nerve
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gel –skin boundary, compared with a layer of lesser resistivity. This observation was consistent with an earlier result reported by Caruso et al.(19) Thus, given these results, and the much lower resistivities of the electrode in the Chatterjee study and saline relative to the skin, moistening the fingertip with saline in that study should have had a negligible effect on the edge effect produced by the electrode. A different result, however, would be expected in the Rogers study, in which the moistened back of the index finger was applied to an 18-mm-diameter brass tube (Figure 3). In this scenario, the tube extends beyond the boundary of the contact in the vertical direction, whereas in the direction transverse to the tube, the finger separates from the tube due to the latter’s curvature with a small air gap in between (Figure 3). At the frequencies of interest here ( ,25 MHz), the air gap can be considered to be an insulator since its reactance is high compared with the conductance of the finger. Hence, the conductor is larger than the contact area between conductor and finger. Given that all dimensions are small compared with a wavelength, the electric field (and hence current) in the finger can be found using electrostatic theory. The Appendix describes how the current in this case is uniformly distributed across a homogeneous finger (it is assumed that the conductor and the far end of the finger are at a constant potential). The point of this exercise is to show that the edge effects (that is, highly non-uniform currents) characteristic of the case for which the finger is larger than the contact area between conductor and finger do not occur in this case. A similar result has been demonstrated theoretically and empirically by Olsen et al.(20) for a conducting post positioned across the narrow dimension of a waveguide exposed to a uniform electric field parallel to the post. Given this background, the current into the back of the finger in the Rogers scenario would be regarded as relatively uniform, a view also supported by Lewis and Wasserstrom(21). Thus, when the skin extends beyond an electrode’s edge, as would be in the case of the Chatterjee study, the total current through the electrode does not appear to represent a perception or pain stimulus as an absolute quantity, but is equivalent to a greater current were it ideally distributed uniformly over the contact area. To this end, the authors established a dimensionless parameter, Jeff, to represent the current density linked to sensory response as a multiple of Javg (see Equation 1). For perception and pain (‘let-go’), the authors estimate from their analysis of the published graphs that Rogers’ thresholds at 2 MHz were, respectively, 1.33 and 3.26 times greater than Chatterjee’s thresholds at 3 MHz (see Figure 6); this ratio of thresholds is referred to here as IRogers/IChatterjee. Also, according to Rogers, the threshold values in his experiment roughly doubled when fingertip contact was
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CONCLUSION
endings, their proximity to the skin surface and the efficiency with which they are recruited to transmit sensory input to the central nervous system is enhanced at tissue site 1 compared with tissue site 2, with all else equal (e.g. contact area, s, etc.), then one would expect lower RF current sensory thresholds at tissue site 1. Whether or not these factors would be dominant or subordinate to the factors discussed earlier in quantitative terms remains uncertain.
FUNDING Much of this work was supported by the Electric Power Research Institute. R. G. Olsen and R. A. Tell also contributed personal resources to this effort. The authors thank J. Patrick Reilly for helpful insights at the inception of this paper. REFERENCES
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1. AGNIR. Health effects from radiofrequency electromagnetic fields. Report of the independent Advisory Group on Non-ionising Radiation. RCE-20, Health Protection Agency (2012).
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Figure 11. The ratio of current in the Rogers configuration to the current in the Chatterjee configuration that would produce the same SAR as a function of the ratio of conductivities (sRog/sChat), the effective current density in the Chatterjee configuration given edge effects (Jeff ) (no edge effect assumed for Rogers) over a range of Rogers:Chatterjee ‘Area Ratios’ of 2 (top), 4 (middle) and 6 (bottom).
IEEE’s Standard 95.1 for exposure to fields from 3 kHz to 300 GHz(22) proposed a hierarchy of RF effects from the ‘practical perspective of managing RF safety issues within industrial environments’. Out of six possible effects, RF shocks and burn ranked first as ‘the most harmful RF exposure hazard’. It was followed in order of priority by: localised RF heating effects, surface heating effects, whole body heating effects, microwave hearing effects and low-level effects (i.e. effects at exposure levels that do not cause thermal effects). The amount of research invested into potential effects on health and safety from RF field and current exposures appears to have been roughly related to this hierarchical order in an inverse manner. Although RF currents have been examined from the perspective of harnessing them for electrosurgical cutting, tissue coagulation(23) and defibrillation(17), little attention has been accorded to potential effects of RF contact currents from environmental sources. The hierarchical order of hazard from RF exposures described earlier is based more on anecdotal incidents of RF current-induced injury than on a well-developed body of research literature. This paper has reviewed the studies upon which standard setting has had to rely and has attempted to reconcile apparent discrepancies in the results from experiments in human subjects. The organisations that have published RF exposure limits to date (ICNIRP and IEEE) have made an effort to apply the data from this limited literature in as responsible a manner as possible in the authors’ opinion(22, 24). However, the studies the authors reviewed employed different methodologies, and there were no experimental observations of .20 MHz, even though current versions of both the ICNIRP Guideline for RF and the IEEE Standard for RF extend the frequency range for RF current limits to 110 MHz. Future well-designed and well-controlled studies with human subjects would contribute valuably to assuring that RF contact current exposure limits are specified at levels that provide for a safe environment.
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20.
21. 22.
23. 24.
dispersive electrodes. J. Biomech. Eng. 104, 324–329 (1982). Olsen, R. G., Geithman, G. A. and Schrader, D. H. A microwave irradiation chamber for scientific studies on agricultural products. IEEE Trans. Microwave Theory Tech. 25, 428– 433 (1977). Lewis, J. A. and Wasserstrom, E. The field singularity at the edge of an electrode on a semiconductor surface. Bell Syst. Tech. J. 1183– 1194 (July –Aug 1970). IEEE. IEEE standard for safety levels with respect to human exposure to radio frequency electromagnetic fields, 3 kHz to 300 GHz. Institute of Electrical and Electronic Engineers, IEEE Std. C95.1 (2005). Bussiere, R. L. Principles of Electrosurgery, Tektran Incorporated (1997). ICNIRP. International commission on non-ionizing radiation protection. Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz). Health Phys. 74, 494– 522 (1998).
APPENDIX: CURRENT DENSITY IN A FINGER CONTACTING A LARGE-AREA ELECTRODE The object of this exercise is to determine whether it is fair to assume that the current density through a finger at the interface between it and a large metallic electrode is uniform across that interface. Consider a cylinder of tissue representing a finger in good electrical contact with a large metallic plate (see Figure A1), where it is assumed that all dimensions are small compared with a wavelength so that electrostatic theory can be applied. The solution is required to satisfy the Laplace equation: r2 c ¼
1@ @c 1 @2c @2c r þ 2 2þ 2 ¼0; r @r r @w @r @z
ðA:1Þ
where c ¼ c(z, r, f ), the potential at a given location within the finger (volts). First assume that conduction currents in the finger are much larger than displacement currents ði.e. s 2pfe0 Þ where f represents frequency (Hz) and 10 represents permittivity of free space (8.854` 10 –12 F m21). For typical bulk tissue conductivities (0.2 to 0.6 S m21), this inequality is satisfied at the frequencies of interest. For example, if s ¼ 0.4 S m21, s/(2pf10) ¼ 288 at 25 MHz. Given the dominance of conduction currents, virtually no current passes through the cylinder’s sides, i.e. @ c/@r ¼ 0 at r ¼ a. Since the finger is thin, it will be assumed (to be validated later) that @ c/@r ¼ 0 for 0 , r , a and the first term drops from equation A.1.
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2. EFHRAN. European health risk assessment network on electromagnetic fields exposure, risk analysis of human exposure to electromagnetic fields (revised). European Commission, Report D2 (2012). 3. SCENIHR. Scientific committee on emerging and newly identified health risks, health effects of exposure to EMF. European Commission (2009). 4. Chatterjee, I., Wu, D. and Gandhi, O. P. Human body impedance and threshold currents for perception and pain for contact hazard analysis in the VLF-MF band. IEEE Trans. Biomed. Eng. 33, 486 –494 (1986). 5. Rogers, S. J. Radiofrequency burn hazards in the MF/HF band. In: Proceedings of a Workshop on the Protection of Personnel Against Radiofrequency Electromagnetic Radiation, Mitchell, J.C., ed. Brooks Air Force Base, Texas, U.S. Air Force School of Aerospace Medicine, Aerospace Medical Division, 1981, pp. 76–89. 6. Dalziel, C. F. and Mansfield, T. H. Effect of frequency on perception currents. AIEE Trans. 69, 1162–1168 (1950). 7. Reilly, J. P. and Diamant, A. M. Electrostimulation. Artech House (2011). 8. Reilly, J. P. Applied Bioelectricity: From Electrical Stimulation to Electropathology. Springer (1998). 9. IEEE. IEEE standard for safety levels with respect to human exposure to electromagnetic fields, 0 –3 kHz. Institute of Electrical and Electronic Engineers, IEEE Std. C95.6 (2002). 10. Dewhirst, M. W., Viglianti, B. L., Lora-Michiels, M., Hanson, M. and Hoopes, P. J. Basic principles of thermal dosimetry and thermal thresholds for tissue damage from hyperthermia. Int. J. Hyperthermia. 19, 267– 294 (2003). 11. Hasgall, P. A., Neufeld, E., Gosselin, M. C., Klingenbo¨ck, A. and Kuster, N. IT’IS database for thermal and electromagnetic parameters of biological tissues, Version 2.2. www.itis.ethz.ch/database 11 July 2012. 12. Olsen, R. G., Schneider, J. B. and Tell, R. A. Radio frequency burns in the power system workplace. IEEE Trans. Power. Deliv. 26, 352 –359 (2011). 13. Chen, J. Y. and Gandhi, O. P. Thermal implications of high SAR’s in the body extremities at the ANSI-recommended MF-VHF safety levels. IEEE Trans. Biomed. Eng. 35, 435– 441 (1988). 14. Gandhi, O. P., Chen, J. Y. and Riazi, A. Currents induced in a human being for plane-wave exposure conditions 0– 50 MHz and for RF sealers. IEEE Trans. Biomed. Eng. 33, 757 –767 (1986). 15. Kim, Y., Webster, J. G. and Tompkins, W. J. Simulated and experimental studies of temperature elevation around electrosurgical dispersive electrodes. IEEE Trans. Biomed. Eng. 31, 681 –692 (1984). 16. Wiley, J. D. and Webster, J. G. Analysis and control of the current distribution under circular dispersive electrodes. IEEE Trans. Biomed. Eng. 29, 381–385 (1982). 17. Krasteva, V. T. and Papazov, S. P. Estimation of current density distribution under electrodes for external defibrillation. Biomed. Eng. Online. 1, 7 (2002). 18. Kim, Y., Fahy, J. B. and Tupper, B. J. Optimal electrode designs for electrosurgery, defibrillation, and external cardiac pacing. IEEE Trans. Biomed. Eng. 33, 845– 853 (1986). 19. Caruso, P. M., Pearce, J. A. and DeWitt, D. P. The effect of gelled-pad design on the performance of electrosurgical
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A trial solution to the remaining term of equation A.1 is as follows:
cðz; rÞ ¼ Az þ B: But the conditions at the top and bottom of the cylinder lead to the following: Top: 0 ¼ AlþB, Bottom: V0 ¼ B. Therefore, C ¼ 2V0z/lþV0, and
Figure A1. A cylindrical representation of a finger contacting a metallic electrode with a surface area greater than the finger’s cross section.
Next, by symmetry @ 2c/@ f 2 ¼ 0, and the second term drops.
@c V0 ¼s ; @z l
where Ez is the electric field in the z-direction (Er and Ef ¼ 0). According to the uniqueness theorem, there is only one solution that satisfies the boundary conditions of constant and known potential at the ends and @ c/ @r ¼ 0 at r ¼ a. Since this solution satisfies all of the boundary conditions, the assumption that @ c/@r ¼ 0 for 0 , r , a is validated. The current density is thus uniform over the cross section at the finger–electrode interface. This result is consistent with the results in Olsen et al. for a conductive post positioned in a waveguide(20).
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JZ ¼ sEz ¼ s
doi:10.1093/rpd/nct311
RADIOFREQUENCY CONTACT CURRENTS: SENSORY RESPONSES AND DOSIMETRY Robert Kavet1, R. A. Tell2 and R. G. Olsen3 1 Electric Power Research Institute, 3420 Hillview Avenue, Palo Alto, CA 94304, USA 2 Richard Tell Associates, Inc., 350 Falcon Ridge Parkway, Suite 103, Mesquite, NV 89027, USA 3 School of Electrical Engineering and Computer Science, Washington State University, Pullman, WA 99164-2752, USA *Corresponding author: [email protected]
The process of setting science-based exposure standards (or guidelines) for radiofrequency (RF) contact current exposure has been disadvantaged by a lack of relevant data. The authors first review the essential features and results of the available studies and illustrate the apparent discrepancies among them. Then, they examine the manner in which current was administered in these studies and suggest as to how the physical relationship of a contacting finger to the current electrode may play a role in affecting sensory thresholds specific to those configurations. A major factor in this analysis relates to whether current density is uniformly distributed across the contact area or whether an electrode’s ‘edge effects’ enhance currents with a net effect of decreasing apparent thresholds, when expressed as the bulk current entering a subject. For an exposure with a clear hazard potential, thresholds of human sensory response to RF currents require further investigation.
INTRODUCTION Exposure to radiofrequency (RF) contact current (about 100 kHz) may result from contact of part of the body, usually one or both hands or fingers with (a) a conductive object that is directly energised from a power source (e.g. an active antenna), or (b) a passive conductor indirectly energised by an RF field, which is referred to as ‘re-radiation’. These scenarios may also include exposure to an RF spark discharge—or an arc—that may bridge the gap between the conductor and the finger or hand just prior to the point at which actual physical contact with the conductor occurs, or upon breaking contact. Either continuous current via contact or an arc may inflict an adverse reaction (tissue heating to the point of pain or a burn). An important distinction is that the arc produces its effect immediately, whereas with a continuous current in the absence of an arc, an individual can often sense the temperature rise in tissue and withdraw contact before an injury occurs. An extensive amount of research has dealt with the potential biological effects associated with the direct coupling of RF fields with living bodies(1 – 3). Far less attention has been accorded to dose –effect characteristics of the sensory responses (e.g. perception, pain or aversion) to RF contact current, which presents a potentially hazardous condition that can precede a burn injury. This paper (a) reviews the studies that have addressed thresholds of sensory responses to continuous RF contact currents, (b) addresses the apparent discrepancies in reported thresholds for perception
and pain responses (c) and reflects on the adequacy of the available data for setting exposure standards for RF contact current.
SENSORY RESPONSES TO CONTACT CURRENT: EXPERIMENTAL STUDIES Experimental data on human reactions to contact current at 100 kHz or above have been reported by Chatterjee et al.,(4) Rogers(5) and Dalziel and Mansfield(6), with the key features of each study summarised in Table 1. As will be reported later, greater contact current thresholds are observed for grasp compared with touch contact. This is attributable to the relatively larger cross section of tissue exposed to a given level of current for grasp compared with touch contact, and thus lower current densities, which are responsible directly for local heating. Chatterjee et al.(4) published the only peer-reviewed paper to present data describing sensory responses of human subjects to RF currents of .200 kHz(4). Chatterjee noted that, ‘the sensation for frequencies below 100 kHz was one of tingling or pricking, localized in the area adjacent to the region of contact on the finger or hand. [For frequencies greater than 100 kHz] [t]he sensation was one of warmth or heat in the area below and around the plate electrode in the case of finger contact, and in the hand and wrist regions in the case of grasping contact’. The wrist, which has the smallest cross-sectional area (of soft tissue), in the current pathway for grasp is, thus, the site most prone to heating. Note that for testing touch thresholds,
# The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
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Received 14 June 2013; revised 31 October 2013; accepted 6 November 2013
Table 1. Comparison of RF contact current perception studies. Chatterjee 197 F and 170 C (18 –70 y old) 18–35: 70 F, 59 C 36–50: 66 F, 55 C 51–70: 61 F, 56 C 10-y-old thresholds inferred by body size scaling from males
Rogers
Touch: 28 F Hold (‘Grasp’): 28 F, 4 C; 72–76 % of males 30 y old
50 ‘persons’
10 and 30 kHz, 0.1, 0.3, 1 and 3 MHz
200 kHz
2, 5, 10, 15 and 20 MHz
Index Touch: fingertip Grasp: palm
Index Back of finger; fingertip, but no data presented
Contact with
Touch: square copper block Grasp: brass rod
Middle Touch: ‘fingertip’ but very possibly the finger pad Hold (‘Grasp’): palm (probably) Touch/tap: copper plate Hold (‘Grasp’): number 8-copper wire
Contact dimension
Touch: 25 mm2, i.e. ,fingertip area for threshold study; 144 mm2 for impedance measurements Grasp: cylindrical brass rod 1.5 cm diameter, 14 cm long
Touch/tap: probably .fingertip area (i.e. finger pad) Grasp: number-8 copper wire (3.264 mm diameter)
18 mm diameter; length of tube . width of finger
Saline-moistened contact? Approach
Yes
Yes
Yes
Subthreshold
Subthreshold
Subthreshold
Perception
‘just felt a sensation’
‘mean value of current just causing sensation’
‘barely perceptible sensation’
Pain
‘the sensation was so uncomfortable that they would definitely not want to hold on to or touch the electrode’
NA
‘discomfort was felt’
Reporting
Perception versus current w/error bars
Probit plots
Histograms
Brass tube
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Frequency Finger for touch Part of finger/hand
SENSORY RESPONSES TO RF CURRENT
Subjects
Dalziel
R. KAVET ET AL. Table 2. Median response thresholds for males and females averaged (i.e. GM) for each from 100 kHz to 3 MHz, with male-to-female and pain-to-perception ratios (based on graphical data in Chatterjee et al.(4)). Response Touch perception (mA) Touch pain (mA) Pain:perception Grasp perception (mA) Grasp pain (mA)
F
C
F:C
39.8 49.2 1.24
36.3 45.3 1.25
1.10 1.09 —
290 360
229 286
1.27 —
Figure 1. Summary of sensory thresholds from Chatterjee et al.,(4) showing the geometric mean of male and female adult thresholds.
Chatterjee had the subjects contact a square 25-mm2 copper block with the saline-moistened tip of the index finger; the fingertip thus extended well beyond the electrode’s edge. To establish a more exact frequency at which the transition from electrostimulation to a warming sensation occurs, the investigators tested a subset of subjects who reported ‘tingling’ exclusively (i.e. electrostimulation) at 50 kHz. They state that, ‘at 70 kHz, some subjects felt tingling and some felt warmth. When the current was raised slightly for those subjects who reported tingling, the sensation changed to one of warmth’. The exposures in this and the two studies described later were continuous sinusoids, that is, they had a 100 % duty cycle; for lower duty cycles, the current threshold for warming would increase, and the initial response would be electrostimulation(7). The authors layered Chatterjee’s graphs for the three endpoints (touch perception, touch pain and grasp perception in Figures 4–6 in their paper) on an enlarged grid to enable us to derive a graphically based estimate of their data. The charted data points are treated as medians, that is, the estimated geometric mean (GM) for an assumed lognormal distribution. To provide a general comparison of the thresholds across the three endpoints, the authors averaged the male and female thresholds for each endpoint at each frequency to represent a mixed cohort of adults (Figure 1). As observed, the threshold profiles ‘flatten’ out to some degree between 100 kHz and 3 MHz. Accordingly, for male –female comparisons in this frequency range, gender-specific thresholds were calculated as the GM of the medians at each frequency. Thresholds representing the three endpoints for a mixed adult population were calculated as the GM of the values for each gender. The thresholds for male subjects were greater than those for females with a greater difference between
genders for grasp than for touch (Table 2). Apparent gender differences have been shown to be an artefact of an underlying body size relationship, rather than gender per se(8). The threshold for touch pain was 25 % greater than that for perception, and in a related observation, the investigators noted for a subset of subjects tested (N¼9) that, ‘when the current was adjusted to a value equal to the perception threshold, pain was reported typically within 10–20 s’. To determine the between-subjects range of adult sensory sensitivity to RF currents for touch perception and touch pain and for grasp, the authors estimated the geometric standard deviations (GSDs) from the published figures. For each gender/response combination (e.g. female/touch pain), the authors computed the GM of the GSDs for the four frequencies tested from 100 kHz to 3 MHz. Using the pooled value of male and female GSDs as the within-group GSD, and the differences between male and female GMs (each also averaged from 100 kHz to 3 MHz as noted earlier) as the between-group GSD, an overall ‘adult’ GSD was computed for each response type based on a standard ANOVA approach. This computation assumed equal sample sizes for male and female groups to represent an evenly mixed cohort of adults. Under the assumption of relatively constant thresholds for each sensory response from 100 kHz through 3 MHz, these computations allowed a view of the range of adult sensitivities in a single graphic (Figure 2). The authors project that for Chatterjee’s exposure scenario, roughly one in a hundred adult persons would have thresholds of 24.3 mA (or less) for touch perception, 31.0 mA for touch pain and 149 mA for grasp perception (i.e. 1st percentile thresholds). The value of 185 mA for grasp pain was derived by multiplying the grasp perception median threshold by the ratio of the median touch pain to median touch perception. The figure also indicates the 0.1th and 50th percentile values. In 1950, Dalziel and Mansfield reported on thresholds of current perception from 60 Hz to 200 kHz for
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Grasp pain ¼ grasp perception` pain:perception.
SENSORY RESPONSES TO RF CURRENT
a sample of adults touching or tapping a copper plate with the middle finger, or holding (i.e. grasping) a number-8 wire (3.26 mm diameter) (Table 1)(6). They observed that, ‘[t]he touching and tapping contact tests using frequencies between 100,000 and 200,000 cycles [i.e. Hz] brought forth the opinion from all subjects that the sensation caused by the higher frequencies was one of heat rather than the muscle stimulation noted at the low frequencies’. They further observed that, ‘the change in sensation [heating] is a definite change, rather than the gradual changes experienced at frequencies below 100,000 cycles’. Finally, observing the clear difference in sensory experience above and below 100 kHz, Dalziel and Mansfield reported that ‘When currents of 100,000 or more cycles were adjusted to values slightly less than the perception values and maintained constant, perception was reported after an interval of several seconds. In contrast, for frequencies less than 100,000 cycles, currents of slightly less than the perception value were not perceived after an interval of several minutes’. Dalziel and Mansfield reported a median perception threshold at 70 kHz (based on 19 males) of 101.5 mA for holding the wire; the investigators extrapolated their plot to 100 kHz with a threshold the authors estimate from the graphic (not shown) to be 148 mA. For touching a copper plate (they use the term ‘copper block’ in their figures and ‘plate’ in text) with a finger, the median perception threshold was 43.8 mA at 100 kHz and 63.6 mA at 200 kHz (25 males). The thresholds for tapping contacts were lower than those for continuous touch. They attribute this to ‘accommodation’ wherein desensitisation occurs as exposure continues. The authors derived the 1st percentile thresholds from the graphs for touch and grasp in Dalziel and Mansfield (Figures 4 and 5 in the original publication), who provided the 0.5th percentile, in addition
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Figure 2. Summary of probits for touch and grasp estimated from the 100 kHz to 3 MHz data in the graphs in Chatterjee et al.(4).
to the 50th and 99.5th percentiles. For touch, which extended to 200 kHz, the plots did not appear to flatten above 100 kHz as Chatterjee et al.(4) had observed. From Figure 2, which presents the results from Chatterjee et al., the authors computed ratios of the 50th to 1st percentile of 1.56 and 1.73 for touch and grasp, respectively (some refer to this ratio as the ‘slope factor’(9)), representing males and females pooled from 100 kHz to 3 MHz. In Dalziel and Mansfield, and using log-transformed data for our calculations, this ratio for touch was 2.57 at 100 kHz and 1.48 at 200 kHz. For grasp, Dalziel and Mansfield’s ratio was 1.45 at 100 kHz, the highest frequency reported, whereas Figure 2 reflects a median to 1st percentile ratio of 1.73 for males and females pooled from 100 kHz to 3 MHz in Chatterjee et al. Despite these differences, the consistency between the two studies just discussed allows a generalisation that, for continuous sinusoidal currents, the transition from electrostimulation to warming sensations occurs at 100 kHz. In a workshop proceeding, Rogers reported on sensory thresholds for a group of 50 adult subjects contacting an 18-mm-diameter brass tube electrode with the back of their index finger(5). The distinction between the electrodes and mode of touch contact in the Chatterjee and Rogers studies (Figure 3) is critical to the discussion later, which addresses the discrepancies in their respective results. The endpoint identified by Rogers as ‘let-go’ appears to be functionally equivalent to that identified by Chatterjee as ‘pain’. Rogers explained that for each subject, he measured the threshold of perception, as well as another endpoint that he called discomfort in one paragraph, and let-go in another. In most literature on electric shock, the ‘let-go’ threshold refers to grip tetanus of a grasped conductor—a very painful condition. Equating ‘discomfort’ with ‘let-go’ at first seemed contradictory. With further reflection, it seems likely that Rogers’ subjects were responding to a condition in which they could not tolerate the stimulus, and consequently felt compelled to cease contact, that is, to let go of the energised conductor. Such terminology is said to have been common in the UK at the time of Rogers’ study. However, the authors cannot provide absolute certainty on this point. The authors were kindly provided numerical transcriptions of the histograms in Rogers’ report by Dr. B. J. Klauenberg and colleagues. The authors assigned the midpoint current value of each of Rogers’ histogram bars (e.g. 25, 35, 45 mA, etc.) to the number of individuals within the respective bar. To estimate the 1st percentile threshold for the perception and let-go responses, the authors first assumed that for each of these two responses, the probit distributions at each frequency maintain the same shape (are parallel to one another, the same assumption adopted for analysing Chatterjee et al.); analysing
R. KAVET ET AL.
Figure 4. Probit distributions from Rogers data(5) for perception (triangles) and let-go (open squares). Also shown are the regression lines for each: linear for perception and quadratic for let-go.
Figure 5. Geometric means and lower 1st percentile values for perception and pain based on histograms in the Rogers report, and the analysis from Figure 4 and that described in the text (5).
each response separately was necessitated by the fact that the probit distributions for perception were different from those for let-go ( p , 0.0001), as discussed later. The authors then computed (using Excel), for each of the five frequencies—2, 5, 10, 15 and 20 MHz—the 2nd-through-98th percentile threshold current values in increments of two percentiles. For each frequency and percentile value, the current thresholds were normalised to the respective
frequency-specific GM threshold current (Ithresh/ IGM). For each percentile value, this normalised statistic was averaged across the five frequencies. For each response, these values were plotted with the vertical axis a probit of a normal distribution (distributed as the number of standard deviations from the GM), and the horizontal axis in terms of log10(Ithresh/IGM). On inspection, the distribution of the perception data points appeared linear (i.e. lognormal), and the let-go
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Figure 3. Difference between Chatterjee et al.(4) and Rogers(5) with respect to electrode contact. The bottom left (right) schematic is a simplified equivalent of the upper left (right) drawing.
SENSORY RESPONSES TO RF CURRENT
curve data appeared to have a quadratic component, and each was regressed accordingly (Figure 4). The regression equations were extrapolated to the 1st percentile level on the vertical axis, with the result that the 1st percentile threshold current was 50.5 % of the GM for perception, and 62.9 % of the GM for let-go (Figure 5). Rogers stated that his result: ‘indicates an approximate average hazard threshold current of 200 mA for the band 2–20 MHz. It was noted that perception and let-go currents for finger-tip contact were about twice those for back-of-finger contact and even higher for large area contact with the palm’. The plots in Figure 5 reflect that the distribution of let-go thresholds in the Rogers study were, for the most part, ,200 mA, with 1 % of the population projected to have a threshold of 89.4 mA at 2 MHz increasing to 133 mA at 20 MHz. For perception, the thresholds were largely ,100 mA, with 1 % of the
population projected to have a threshold of 25.3 mA at 2 MHz increasing to 53.8 mA at 20 MHz. For purposes of comparison, the median sensory threshold data from the three studies discussed earlier have been graphed together. For touch perception and grasp (Figure 6, left and right), the data from Chatterjee and Dalziel virtually overlap with relatively minor exceptions. With little overlap of the frequency ranges studied by Chatterjee and Rogers for touch perception and touch pain (let-go) (Figure 6, top left and right), the reasons for the differences between the two with respect to both thresholds and slope are not immediately apparent. The next section addresses a possible basis for these discrepancies, as well as for the doubling of threshold for fingertip contact relative to back-of-the-finger in the Rogers study.
FACTORS AFFECTING SENSORY THRESHOLDS The process of setting exposure standards for RF contact current has necessarily relied on the small set
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Figure 6. Comparison of median touch thresholds across the three studies reviewed (left); comparison of median pain thresholds from Chatterjee and Rogers (right); comparison of median grasp thresholds from Chatterjee and Dalziel & Mansfield (D&M) (middle)(4 – 6).
R. KAVET ET AL.
SAR ¼
2 Javg ; sr
Figure 7. Iso-effect thresholds for pain and burn in human skin. (Adapted from Dewhirst et al.(10)) (Data points from Dewhirst et al., and regressions performed for this paper.)
ð1Þ
where Javg represents the average current density through a tissue cross section with area, A; Javg ¼I/A (A m22); I is current (A); A is cross-sectional area (m2); s, tissue conductivity (S m21) and r, tissue density (kg m23). Under an adiabatic assumption, which is probably an acceptable assumption for brief finger contact, the rise in tissue temperature, DT (8C) over time, Dt (s), is calculated as follows: DT ¼
SAR Dt; c
ð2Þ
where c is the heat capacity of the affected tissue (Joules kg21 8C21). Dewhirst et al. published a comprehensive review of thermal thresholds in skin, reporting that a skin temperature of 44 to 488C for on the order of 6 s produces pain, and an increase to 53 to 598C for between 6 and 30 s will initiate the onset of blistering (i.e. a low grade burn)(10). An adaptation of the key curves from Dewhirst et al. describing pain and blistering skin temperature/time thresholds together with regressions of those curves performed for this paper are shown in Figure 7. As an example, using the properties of connective tissue [r ¼ 1500 kg m23; c ¼ 2400 (Joules kg21 8C21), and at 0.1 –30 MHz, s ffi 0.4 S m21](11) to represent the fingertip, one would calculate a temperature increase of 6.88C for a 140mA current distributed uniformly over a 1-cm2 contact area for 5 s. Thus, for perception or pain resulting from finger contact, the SAR and local increase in tissue temperature depends on the properties (s, r and c) of epidermal and subdermal tissue at the immediate site of electrode contact (for grasp contact, not dealt with in this discussion, the wrist is most likely the primary
Figure 8. SAR at the tissue interface with a 1-cm2 electrode as a function of tissue conductivity, s, and mass density, r.
site of thermal sensations even though the proximal site of contact is the palm). Tissue conductivity, s, is a function of frequency that varies among tissue types. s is thus an important factor in quantifying SAR (equation 1) across a frequency spectrum. Tissue density, r, and heat capacity, c, also vary across tissue types, but do not exhibit a frequency dependency. Because most anatomical sites consist of a mix of tissue types, a single type is unlikely to completely determine the time rate of thermal energy deposition. Various investigators have selected default values for these quantities to illustrate a general principle about tissue heating(12), whereas others have categorised tissues as having high, medium or low water content, selecting conductivity, and tissue density values to represent each(13, 14). Figure 8 shows how SAR from a current of 200 mA uniformly distributed over a 1-cm2 cross section of skin varies across a realistic joint range of tissue conductivity and tissue density, with a likelihood that the actual value would fall in this
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of studies reviewed in the previous section. Given the differences among the three studies with respect to study design and procedures (reviewed in Table 1), in addition to discrepancies in their results, standard setting is disadvantaged by an absence of a larger pool of information on thresholds of sensory responses to RF contact current. Nonetheless, it is instructive to examine possible reasons for apparently divergent results, especially between the Chatterjee and Rogers studies. The fundamental biophysical interaction between RF current and tissue may be expressed by the formula for specific absorption rate (SAR) (W kg21), the same quantity used to express dose rate in tissue (or whole body) from exposure to RF fields. For RF contact current,
SENSORY RESPONSES TO RF CURRENT
parameter space. Using these SAR values and a range of realistic heat capacities, the skin temperature could rise between 2.5 and 16.78C with a 2-s exposure (Figure 9). As a relatively simple example, one can propose how site-specific s could explain the doubling of thresholds for fingertip compared with the back of the finger in the Rogers study. Assuming uniform current flow across the contact cross section (more on this below), one could expect relatively higher conductivity in the fingertip, because it is padded with soft tissue, compared with the back of the index finger with a relatively thinner epithelia and bone immediately below the point of contact. With similar tissue densities and heat capacities assumed for the two sites, together with the same physical contact area assigned to both sites (equations 1 and 2), the higher conductivity in the fingertip would lead to a higher perception threshold for the fingertip, as was the case reported by Rogers; this analytical approach is expanded upon in the ensuing discussion. In addition to the part of a finger in contact with the electrode and its tissue properties just discussed, the factors that can affect experimental results may include: the size of the physical contact area, the subjective response criteria specific to each study and the manner in which subcutaneous heat and pain receptors are distributed and process and integrate sensory input from RF current. However, the greatest potential source of uncertainty relevant to the differences between Chatterjee’s and Rogers’ results may be related to the physical relationship of the skin to the electrode (see Figure 3). In the Chatterjee study, a moistened index fingertip was applied to a square 25-mm2 electrode. Thus, the fingertip entirely covered the area of the contact electrode. Studies concerned with electrosurgery and defibrillation have described the edge effects associated with skin burns from these procedures. When the
Figure 10. Modelled current density 0.5 mm under a square defibrillating electrode as a function of the relative distance from the electrode centre to the edge along horizontal and diagonal axes (see inset). The electrode modelled was 8.86 cm on each side with a resistivity of the interface of 20 V-m, and total interface resistance of ,2.5 V. The curves represent the current densities along the ‘Across’ and ‘Diagonal’ trajectories in one quadrant of the figure. Adapted from Krasteva et al.(17)
skin area extends beyond the outer bound of the contacting electrode, current density maxima—and thus greater burn risks—are concentrated at the edge of the electrode. For example, Kim et al. developed a computer model of current associated with a rectangular dispersive electrode (10` 12 cm) applied to the thigh, reporting that 45 % of the total current passed through the outer 26 % of the electrode’s area(15). Similarly, Wiley and Webster calculated that 50 % of the current from a circular electrosurgical electrode contacting skin is concentrated in the outer ring that accounts for 25 % of the electrode’s crosssectional area(16). Krasteva and Papzov calculated the current density in tissue directly beneath a square defibrillation electrode located on a single layer of tissue with resistivity 20 V-m and total resistance of ,2.5 V(17). Although the electrode was 8.86 cm on each side placed over the thorax, it is instructive to relate their results to Chatterjee’s experimental configuration (Figure 3). As illustrated in Figure 10, these investigators reported that the current density in the tissue below the centre of an edge and a corner reached, respectively, about three and six times the current density in the centre of the electrode (and in both cases, the current in tissue spread beyond the outer border of the electrode). In a subsequent paper, Kim et al. reported an inverse relationship between the extent of an edge effect and the resistivity of a gel layer introduced between an electrode and the skin (with the skin extending beyond the gel layer’s periphery)(18). In other words, a gel layer of relatively greater resistivity produced a more uniform current density across the
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Figure 9. Temperature increase in tissue after 2 s as a function of SAR for three values of tissue heat capacity.
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compared with back-of-finger contact, but no data were provided. For fingertip contact with the brass tube in the Rogers study, the authors will assume that the physical contact area was greater than Chatterjee’s, the current was uniform across the contact area and the conductivities of the underlying fingertip tissues were comparable to Chatterjee’s. The authors sought to understand the Rogers –Chatterjee discrepancy by determining which combinations of (1) the ratio of the respective physical contact areas, (2) Jeff, associated with enhancement of current density at an electrode’s edge (in Chatterjee’s case), with Jeff ¼1 signifying no edge effect (uniform current density) and (3) the relative tissue conductivities (sRog/sChat, the authors explained earlier why they believe this ratio is 1.0), could result in the identical local SAR in each study, and therefore ideally the same sensory threshold, even though the absolute values of their respective contact current exposures differed. Thus, IRog/IChat yielding the same SARs was plotted against combinations of Jeff and sRog/sChat for scenarios in which the physical contact area in the Rogers study was 2, 4 and 6 times the area in the Chatterjee study (the ‘Area Ratio’). The results plotted in 3D surface charts (Figure 11) reflect that IRog/IChat is directly proportional to both the area ratio and Jeff and to (sRog/sChat)0.5. The results indicate clearly that, with the authors’ stated assumptions, Rogers and Chatterjee could achieve the same sensory thresholds with very different current magnitudes. Except for one case, IRog/IChat was greater than unity, with a maximum value of 24 (the exception was when ‘Area Ratio’ ¼ 2, Jeff ¼ 1 and sRog/sChat ¼ 0.10). For the brass tube electrode used in the Rogers study, the authors have shown using electrostatic theory, which is appropriate in this case, that no edge enhancement effects occur for either back-of-thefinger or fingertip contacts (see Appendix). Rogers’ observation of a doubling of the current threshold for fingertip relative to back-of-the-finger contact would thus occur, according to this simple model, when the ratio of the fingertip (ft) to back-of-finger (bf ) physical contact areas, Aft/Abf, multiplied by the square root of the fingertip to back-of-finger conductivities, (sft/sbf )0.5, equals 2.0. Given in all likelihood that Aft/Abf is not vastly different than 1.0, the conductivity ratio would be a key factor with a doubling of current threshold occurring when the fingertip’s conductivity was 4-fold greater than the conductivity of the back of the finger. A factor suggested earlier as partially responsible for discrepant study results (i.e. Chatterjee versus Rogers), but not dealt with at a quantitative level, concerns the possible differential sensitivity of heat and pain receptors in the tissue proximally exposed to RF current. Thus, if the net effect of the concentration of temperature and pain receptor free nerve
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gel –skin boundary, compared with a layer of lesser resistivity. This observation was consistent with an earlier result reported by Caruso et al.(19) Thus, given these results, and the much lower resistivities of the electrode in the Chatterjee study and saline relative to the skin, moistening the fingertip with saline in that study should have had a negligible effect on the edge effect produced by the electrode. A different result, however, would be expected in the Rogers study, in which the moistened back of the index finger was applied to an 18-mm-diameter brass tube (Figure 3). In this scenario, the tube extends beyond the boundary of the contact in the vertical direction, whereas in the direction transverse to the tube, the finger separates from the tube due to the latter’s curvature with a small air gap in between (Figure 3). At the frequencies of interest here ( ,25 MHz), the air gap can be considered to be an insulator since its reactance is high compared with the conductance of the finger. Hence, the conductor is larger than the contact area between conductor and finger. Given that all dimensions are small compared with a wavelength, the electric field (and hence current) in the finger can be found using electrostatic theory. The Appendix describes how the current in this case is uniformly distributed across a homogeneous finger (it is assumed that the conductor and the far end of the finger are at a constant potential). The point of this exercise is to show that the edge effects (that is, highly non-uniform currents) characteristic of the case for which the finger is larger than the contact area between conductor and finger do not occur in this case. A similar result has been demonstrated theoretically and empirically by Olsen et al.(20) for a conducting post positioned across the narrow dimension of a waveguide exposed to a uniform electric field parallel to the post. Given this background, the current into the back of the finger in the Rogers scenario would be regarded as relatively uniform, a view also supported by Lewis and Wasserstrom(21). Thus, when the skin extends beyond an electrode’s edge, as would be in the case of the Chatterjee study, the total current through the electrode does not appear to represent a perception or pain stimulus as an absolute quantity, but is equivalent to a greater current were it ideally distributed uniformly over the contact area. To this end, the authors established a dimensionless parameter, Jeff, to represent the current density linked to sensory response as a multiple of Javg (see Equation 1). For perception and pain (‘let-go’), the authors estimate from their analysis of the published graphs that Rogers’ thresholds at 2 MHz were, respectively, 1.33 and 3.26 times greater than Chatterjee’s thresholds at 3 MHz (see Figure 6); this ratio of thresholds is referred to here as IRogers/IChatterjee. Also, according to Rogers, the threshold values in his experiment roughly doubled when fingertip contact was
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CONCLUSION
endings, their proximity to the skin surface and the efficiency with which they are recruited to transmit sensory input to the central nervous system is enhanced at tissue site 1 compared with tissue site 2, with all else equal (e.g. contact area, s, etc.), then one would expect lower RF current sensory thresholds at tissue site 1. Whether or not these factors would be dominant or subordinate to the factors discussed earlier in quantitative terms remains uncertain.
FUNDING Much of this work was supported by the Electric Power Research Institute. R. G. Olsen and R. A. Tell also contributed personal resources to this effort. The authors thank J. Patrick Reilly for helpful insights at the inception of this paper. REFERENCES
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1. AGNIR. Health effects from radiofrequency electromagnetic fields. Report of the independent Advisory Group on Non-ionising Radiation. RCE-20, Health Protection Agency (2012).
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Figure 11. The ratio of current in the Rogers configuration to the current in the Chatterjee configuration that would produce the same SAR as a function of the ratio of conductivities (sRog/sChat), the effective current density in the Chatterjee configuration given edge effects (Jeff ) (no edge effect assumed for Rogers) over a range of Rogers:Chatterjee ‘Area Ratios’ of 2 (top), 4 (middle) and 6 (bottom).
IEEE’s Standard 95.1 for exposure to fields from 3 kHz to 300 GHz(22) proposed a hierarchy of RF effects from the ‘practical perspective of managing RF safety issues within industrial environments’. Out of six possible effects, RF shocks and burn ranked first as ‘the most harmful RF exposure hazard’. It was followed in order of priority by: localised RF heating effects, surface heating effects, whole body heating effects, microwave hearing effects and low-level effects (i.e. effects at exposure levels that do not cause thermal effects). The amount of research invested into potential effects on health and safety from RF field and current exposures appears to have been roughly related to this hierarchical order in an inverse manner. Although RF currents have been examined from the perspective of harnessing them for electrosurgical cutting, tissue coagulation(23) and defibrillation(17), little attention has been accorded to potential effects of RF contact currents from environmental sources. The hierarchical order of hazard from RF exposures described earlier is based more on anecdotal incidents of RF current-induced injury than on a well-developed body of research literature. This paper has reviewed the studies upon which standard setting has had to rely and has attempted to reconcile apparent discrepancies in the results from experiments in human subjects. The organisations that have published RF exposure limits to date (ICNIRP and IEEE) have made an effort to apply the data from this limited literature in as responsible a manner as possible in the authors’ opinion(22, 24). However, the studies the authors reviewed employed different methodologies, and there were no experimental observations of .20 MHz, even though current versions of both the ICNIRP Guideline for RF and the IEEE Standard for RF extend the frequency range for RF current limits to 110 MHz. Future well-designed and well-controlled studies with human subjects would contribute valuably to assuring that RF contact current exposure limits are specified at levels that provide for a safe environment.
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20.
21. 22.
23. 24.
dispersive electrodes. J. Biomech. Eng. 104, 324–329 (1982). Olsen, R. G., Geithman, G. A. and Schrader, D. H. A microwave irradiation chamber for scientific studies on agricultural products. IEEE Trans. Microwave Theory Tech. 25, 428– 433 (1977). Lewis, J. A. and Wasserstrom, E. The field singularity at the edge of an electrode on a semiconductor surface. Bell Syst. Tech. J. 1183– 1194 (July –Aug 1970). IEEE. IEEE standard for safety levels with respect to human exposure to radio frequency electromagnetic fields, 3 kHz to 300 GHz. Institute of Electrical and Electronic Engineers, IEEE Std. C95.1 (2005). Bussiere, R. L. Principles of Electrosurgery, Tektran Incorporated (1997). ICNIRP. International commission on non-ionizing radiation protection. Guidelines for limiting exposure to time-varying electric, magnetic, and electromagnetic fields (up to 300 GHz). Health Phys. 74, 494– 522 (1998).
APPENDIX: CURRENT DENSITY IN A FINGER CONTACTING A LARGE-AREA ELECTRODE The object of this exercise is to determine whether it is fair to assume that the current density through a finger at the interface between it and a large metallic electrode is uniform across that interface. Consider a cylinder of tissue representing a finger in good electrical contact with a large metallic plate (see Figure A1), where it is assumed that all dimensions are small compared with a wavelength so that electrostatic theory can be applied. The solution is required to satisfy the Laplace equation: r2 c ¼
1@ @c 1 @2c @2c r þ 2 2þ 2 ¼0; r @r r @w @r @z
ðA:1Þ
where c ¼ c(z, r, f ), the potential at a given location within the finger (volts). First assume that conduction currents in the finger are much larger than displacement currents ði.e. s 2pfe0 Þ where f represents frequency (Hz) and 10 represents permittivity of free space (8.854` 10 –12 F m21). For typical bulk tissue conductivities (0.2 to 0.6 S m21), this inequality is satisfied at the frequencies of interest. For example, if s ¼ 0.4 S m21, s/(2pf10) ¼ 288 at 25 MHz. Given the dominance of conduction currents, virtually no current passes through the cylinder’s sides, i.e. @ c/@r ¼ 0 at r ¼ a. Since the finger is thin, it will be assumed (to be validated later) that @ c/@r ¼ 0 for 0 , r , a and the first term drops from equation A.1.
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2. EFHRAN. European health risk assessment network on electromagnetic fields exposure, risk analysis of human exposure to electromagnetic fields (revised). European Commission, Report D2 (2012). 3. SCENIHR. Scientific committee on emerging and newly identified health risks, health effects of exposure to EMF. European Commission (2009). 4. Chatterjee, I., Wu, D. and Gandhi, O. P. Human body impedance and threshold currents for perception and pain for contact hazard analysis in the VLF-MF band. IEEE Trans. Biomed. Eng. 33, 486 –494 (1986). 5. Rogers, S. J. Radiofrequency burn hazards in the MF/HF band. In: Proceedings of a Workshop on the Protection of Personnel Against Radiofrequency Electromagnetic Radiation, Mitchell, J.C., ed. Brooks Air Force Base, Texas, U.S. Air Force School of Aerospace Medicine, Aerospace Medical Division, 1981, pp. 76–89. 6. Dalziel, C. F. and Mansfield, T. H. Effect of frequency on perception currents. AIEE Trans. 69, 1162–1168 (1950). 7. Reilly, J. P. and Diamant, A. M. Electrostimulation. Artech House (2011). 8. Reilly, J. P. Applied Bioelectricity: From Electrical Stimulation to Electropathology. Springer (1998). 9. IEEE. IEEE standard for safety levels with respect to human exposure to electromagnetic fields, 0 –3 kHz. Institute of Electrical and Electronic Engineers, IEEE Std. C95.6 (2002). 10. Dewhirst, M. W., Viglianti, B. L., Lora-Michiels, M., Hanson, M. and Hoopes, P. J. Basic principles of thermal dosimetry and thermal thresholds for tissue damage from hyperthermia. Int. J. Hyperthermia. 19, 267– 294 (2003). 11. Hasgall, P. A., Neufeld, E., Gosselin, M. C., Klingenbo¨ck, A. and Kuster, N. IT’IS database for thermal and electromagnetic parameters of biological tissues, Version 2.2. www.itis.ethz.ch/database 11 July 2012. 12. Olsen, R. G., Schneider, J. B. and Tell, R. A. Radio frequency burns in the power system workplace. IEEE Trans. Power. Deliv. 26, 352 –359 (2011). 13. Chen, J. Y. and Gandhi, O. P. Thermal implications of high SAR’s in the body extremities at the ANSI-recommended MF-VHF safety levels. IEEE Trans. Biomed. Eng. 35, 435– 441 (1988). 14. Gandhi, O. P., Chen, J. Y. and Riazi, A. Currents induced in a human being for plane-wave exposure conditions 0– 50 MHz and for RF sealers. IEEE Trans. Biomed. Eng. 33, 757 –767 (1986). 15. Kim, Y., Webster, J. G. and Tompkins, W. J. Simulated and experimental studies of temperature elevation around electrosurgical dispersive electrodes. IEEE Trans. Biomed. Eng. 31, 681 –692 (1984). 16. Wiley, J. D. and Webster, J. G. Analysis and control of the current distribution under circular dispersive electrodes. IEEE Trans. Biomed. Eng. 29, 381–385 (1982). 17. Krasteva, V. T. and Papazov, S. P. Estimation of current density distribution under electrodes for external defibrillation. Biomed. Eng. Online. 1, 7 (2002). 18. Kim, Y., Fahy, J. B. and Tupper, B. J. Optimal electrode designs for electrosurgery, defibrillation, and external cardiac pacing. IEEE Trans. Biomed. Eng. 33, 845– 853 (1986). 19. Caruso, P. M., Pearce, J. A. and DeWitt, D. P. The effect of gelled-pad design on the performance of electrosurgical
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A trial solution to the remaining term of equation A.1 is as follows:
cðz; rÞ ¼ Az þ B: But the conditions at the top and bottom of the cylinder lead to the following: Top: 0 ¼ AlþB, Bottom: V0 ¼ B. Therefore, C ¼ 2V0z/lþV0, and
Figure A1. A cylindrical representation of a finger contacting a metallic electrode with a surface area greater than the finger’s cross section.
Next, by symmetry @ 2c/@ f 2 ¼ 0, and the second term drops.
@c V0 ¼s ; @z l
where Ez is the electric field in the z-direction (Er and Ef ¼ 0). According to the uniqueness theorem, there is only one solution that satisfies the boundary conditions of constant and known potential at the ends and @ c/ @r ¼ 0 at r ¼ a. Since this solution satisfies all of the boundary conditions, the assumption that @ c/@r ¼ 0 for 0 , r , a is validated. The current density is thus uniform over the cross section at the finger–electrode interface. This result is consistent with the results in Olsen et al. for a conductive post positioned in a waveguide(20).
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JZ ¼ sEz ¼ s
