Paper cocinas de induccion

Paper cocinas de induccion

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  Bioelectromagnetics33:695^705(2012) Exposureof the HumanBody to Professional and Domestic Induction Cooktops Comparedto the Basic Restrictions Andreas Christ,1 * Rene¤ Guldimann,2 Barbara Bˇhlmann,1 Marcel Zefferer,1 Jurriaan F.Bakker,3 Gerard C. van Rhoon,3 and Niels Kuster1,4 1 Foundation forResearchonInformationTechnologiesin Society (IT’IS), Zurich, Switzerland 2 State Secretariat forEconomicAffairs (SECO), Zurich, Switzerland 3 ErasmusMC-DanieldenHoed Cancer Center, Department of Radiation Oncology, Rotterdam,The Netherlands 4 Swiss FederalInstitute ofTechnology (ETHZ), Zurich, Switzerland We investigated whether domestic and professional induction cooktops comply with the basic restrictions defined by the International Commission on Non-Ionizing Radiation Protection (ICNIRP). Based on magnetic field measurements, a generic numerical model of an induction cooktop was derived in order to model user exposure. The current density induced in the user was simulated for various models and distances. We also determined the exposure of the fetus and of young children. While most measured cooktops comply with the public exposure limits at the distance specified by the International Electrotechnical Commission (standard IEC 62233), the majority exceeds them at closer distances, some of them even the occupational limits. The maxi- mum current density in the tissue of the user significantly exceeds the basic restrictions for the general public, reaching the occupational level. The exposure of the brains of young children reaches the order of magnitude of the limits for the general public. For a generic worst-case cooktop compliant with the measurement standards, the current density exceeds the 1998 ICNIRP basic restrictions by up to 24 dB or a factor of 16. The brain tissue of young children can be overexposed by 6 dB or a factor of 2. The exposure of the tissue of the central nervous system of the fetus can exceed the limits for the general public if the mother is exposed at occupational levels. This demonstrates that the methodology for testing induction cooktops according to IEC 62233 contradicts the basic restrictions. This evaluation will be extended considering the redefined basic restrictions proposed by the ICNIRP in 2010. Bioelectromagnetics 33:695–705, 2012. ß 2012 Wiley Periodicals, Inc. Key words: induction cooking; ELF magnetic field exposure; compliance testing; exposure of the fetus; exposure of adults and children INTRODUCTION Induction cooktops have been replacing tradi- tional gas stoves, particularly in professional kitch- ens. In comparison to traditional electric stoves, induction cooktops yield better energy efficiency and offer more flexible heating control, while avoiding the open flame and leakage risks from gas stoves. Initial studies on the exposure of the human body in the close environment of induction cooktops were not conclusive [Yamazaki et al., 2004]. However, a detailed experimental evaluation by Viellard et al. [2006] demonstrated that the incident B-field expo- sure can exceed the reference levels posed by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) [ICNIRP, 1998a] by more than a factor of 30 at close distances by devices shown to Additional supporting information may be found in the online version of this article. Grant sponsors: Swiss Federal Office of Public Health; The Netherlands Organization for Health Research and Development (ZonMw); Swiss National Fund (National Research Program 57). *Correspondence to: Andreas Christ, Foundation for Research on Information Technologies in Society (IT’IS), Zeughausstrasse 43, CH-8004 Zu¨rich, Switzerland. E-mail: [email protected] Received for review 14 August 2011; Accepted 3 May 2012 DOI 10.1002/bem.21739 Published online 1 June 2012 in Wiley Online Library (wileyonlinelibrary.com). ß 2012WileyPeriodicals,Inc.
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  be compliant atthe measurement distance of 300 mm defined by the International Electrotechnical Commission (IEC) [IEC, 2005]. A recent publication by Kos et al. [2011] quantifies the user exposure to a specific induction cooktop. While the authors do not observe violations of the exposure limits for the eval- uated cooktop, they mention that the induced current density of the ICNIRP 1998 guidelines ‘‘could exceed the basic restrictions for induction cooktops in compliance with the IEC 62233 standard.’’ Many countries have adopted the safety guide- lines issued by the ICNIRP in 1998, as well the 2005 IEC measurement standard (IEC 62233). Besides the derived reference levels, the ICNIRP guidelines also define basic restrictions for the actual exposure of the human body. In the ICNIRP 1998 guidelines, the latter were introduced in terms of the induced current density for the head and the trunk in order to protect against peripheral nerve stimulation. A clarification of the guidelines issued shortly after their original publication, however, reduces the applicability of these restrictions to tissues of the central nervous system (CNS), that is, the brain and spinal cord [ICNIRP, 1998b]. No limits are provided for other body tissues. Due to this uncertainty, some regula- tors, for example, Switzerland, require that the basic restrictions on the current density be met in all tissues of the trunk and head as originally stated. In the recently published guidelines on low frequency exposure, the ICNIRP abandons the assessment of the averaged current density in favor of restrictions on the electric field in the body averaged over a cubical volume of 2 mm  2 mm  2 mm [ICNIRP, 2010]. Separate limits are defined for the CNS tissues of the head and for all other tissues of the body for frequencies up to 1 kHz. Above 1 kHz, the basic restrictions are identical. Since these limits have not yet been adopted by regulators, they are not investi- gated within this article but will be the subject of a follow-up study. Although a detailed exposure analysis was not carried out by Viellard et al. [2006], a simple analyti- cal approximation showed that violations of the basic restrictions on the induced current density in the body of a person in the immediate environment of the stove are likely. This study aims to close the gaps regarding compliance with the basic restrictions that are currently imposed in many countries. This will be done by assessing the current density in the hu- man body using a set of anatomical high-resolution models of adults of different heights and body mass indices. In addition, models of a pregnant woman in different gestational phases and young children whose heads are at the same height as the cooking zones will be evaluated. The incident fields are mod- eled using the results of an experimental evaluation of professional cooktops in different gastronomic kitchens and of the two domestic cooktops and the portable cooktop evaluated by Viellard et al. [2006]. In detail, the objectives of this study are to complement the analysis of the three domestic devices used in Viellard et al. [2006] by the experi- mental evaluation of the B-fields of 13 different pro- fessional cooktops at different installation sites; numerically assess the induced current density in users and bystanders using different anatomical mod- els of adults, children and pregnant women in typical and worst-case situations and postures; and discuss the exposure from the specific devices and the con- sistency of the product standard IEC 62233 with the ICNIRP 1998 basic restrictions. METHODS Experimental Methods The spatial distribution and the frequency spec- tra of the B-fields of 13 professional induction cook- tops were measured using a low frequency E- and H-field probe (EHP-200, Narda Safety Test Solu- tions, Hauppauge, NY) within a frequency range from 9 to 400 kHz. The spatial distribution was sampled in steps of 90 mm  90 mm over a surface ranging from 625 to 1795 mm above the floor (z-axis) and À450 to 360 mm from the left to right (y-axis) with zero as the center of the cooktop. These measurements were taken at distances of 0 and 300 mm from the front edge of the cabinet that hous- es the cooktops. The first distance can be regarded as the closest a user can stand without bending over the device, whereas the latter can be regarded as a distance typical of passers-by while the cooktop is operational. Additional measurements at distances of 50, 100, 150, 200, and 250 mm were taken at the location of the field maximum observed when measuring the spatial distribution at 0 mm. Figure 1 shows an overview of the references of the measure- ment distances used in this study. For the evaluation of compliance of the B-fields with safety limits, IEC 62233 defines a position 300 mm from the edge of the cooktop [IEC, 2005]. This position depends on the dimensions of the cabinet and the mounting posi- tion of the cooktop and is therefore different for all evaluated devices. Supplementary Table I shows an overview of these distances. The B-fields at the dis- tance of 300 mm are evaluated by interpolating the fields at the measured distances listed above using a curve fit. 696 Christetal. Bioelectromagnetics
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  For the accuratepositioning of the probe, a foam plastic wall with mounting holes was used (Fig. 1 in the Online Supplementary Material). The mechanical stability of the wall was considered when determining the number and the spatial density of the holes. The orthogonal current loops of the EHP-200 probe, which pick up the vector components of the B-field, are not concentric. They have a diameter of approximately 31 mm. The center of the loop of the z-component of the B-field, which is the dominant component for all the cases investigated here, has an offset of approximately 42 mm from the frontal sur- face of the probe case. This offset was considered when normalizing the field distribution of the numer- ical model to the measured cases. Only fields in the front of the cooktops were evaluated. During the measurements, the active cook- ing zones were loaded with a reference vessel (270 mm diameter, 145 mm height) that was filled with 3 L of water. The water that evaporated during the measurements was refilled. The cooking zones were operated at maximum power. Only the maxi- mum values of the power control cycles of the cook- ing zones were considered. The decay of the B-fields with distance was assessed at the location of the maximum of each device. Additional measurements were carried out with different vessels and off-center positions on the cooking zone. The impact of the loading on the B-field strength used for the dosimet- ric evaluations was added as an offset in the dosimet- ric evaluation. Eleven of the 13 cooktops (#1–#11) were fixed installations. Cooktop #12 was a portable device with a single cooking zone, and Cooktop #13 was a wok installed in a fixed housing. In addition to the professional cooktops, the three domestic devices referred to as cooktops #14– #16, originally evaluated in Viellard et al. [2006], were also used for the dosimetric assessment of the current density induced in the user. These devices were measured with an ELT-400 probe (Narda Safety Test Solutions) positioned using a DASY 4 Dosimet- ric Assessment System (Schmid & Partner Engineer- ing, Zu¨rich, Switzerland). Numerical Exposure Modeling In the low frequency range, where the relevant dimensions of the computational domain are signifi- cantly smaller than the free space wavelength, the magnetic vector potential A can be assumed to be decoupled from the electric field E. As a conse- quence, A can be calculated using Biot–Savart’s law, and since the divergence of the current density van- ishes and conduction currents are dominant in the hu- man body for the application in this article, E can be calculated from the scalar potential F, which is given by: Àr Á srF ¼ jvr Á ðsAÞ with s as the tissue conductivity and v as the angular frequency of the fields of the induction cooktop. A is calculated using a Biot–Savart solver, and the finite element method is used to solve for F. The Biot–Savart solver and the finite element algorithm are implemented in SEMCAD Â 14.2 (Schmid & Partner Engineering). Unlike typical finite element methods, the implemen- tation used here operates on rectilinear meshes like the finite-difference time-domain method [Taflove and Hagness, 2000]. In this way, complex anatomical models can easily be rendered by adapting the mesh resolution. A description of the low frequency solver and its validation can be found in Capstick et al. [2008]. Alternative methods for the calculation of the exposure of the human body were proposed in the past, which evaluated the scalar potential F using finite-difference approximations [Dawson et al., 1997; Liu et al., 2003], frequency-scaling [Gandhi and Chen, 1992], or modeling the human body as an impedance network [Orcutt and Gandhi, 1988]. The recent study by Kos et al. [2011] applies the finite element method used here. The dosimetric results were assessed in terms of the current density maximum (peak current densi- ty) in different body tissues. The ICNIRP 1998 guidelines define the basic restrictions for the current density as the average over a cross section of 1 cm2 . The orientation of the cross section is perpendicular to the currents flowing through it. An algorithm to calculate this average current density was imple- mented for the post-processing of the simulation results. The algorithm determines the direction of the current density vector on each grid node. The current density is then integrated on a circular surface that is perpendicular to this vector and has the required Fig.1. Sketch ofaninduction cooktopwith fourintegrated circular cooking zones built into a cabinet. The measurement distances are 0 and 300 mmfromtheedgeofthe cabinet. ExposuretoInductionCooktops 697 Bioelectromagnetics
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  dimensions of 1cm2 . The maximum of the values of all grid nodes is reported as the peak average current density. The numerical uncertainty with respect to grid resolution and size of the averaging surface is shown in Tables V and VI of the Online Supple- mentary Material. The evaluation of the average current density can be restricted to particular body tissues. This is used to quantify the exposure of the brain and spinal cord, for example. In the following sections of this article, the brain and the spinal cord will be referred to as the CNS. In a recent publication by Dimbylow [2008], problems were reported for the evaluation of the average current density in the spinal cord because the cross sectional area of the spinal cord can be less than 1 cm2 for significant parts along its length. If the evaluation of the current density is restricted to particular tissues (e.g., the CNS) such that the required cross section cannot be reached, only the contributions of current densities from those tissues are considered for the averaging. EXPERIMENTAL RESULTS The spatial distribution of the B-field at the cab- inet edge of one of the measured cooktops is shown in Figure 2 as an example, together with its spectral content. For all measured cooktops the dominant spectral component lies at approximately 20 kHz. Most cooktops show even and odd harmonics throughout the entire measurement range (up to 400 kHz). Their amplitudes are always a factor of 10 or more below the amplitude of the fundamental frequency. Therefore, the higher harmonics are not considered for the numerical assessment of the induced current density. Only a harmonic signal of 20 kHz is used. As the probe reference point has an offset with respect to the center of the loop for the z-component, the correction for the offset and its uncertainty have been determined as follows. The B-field of a generic cooking zone model was integrated over the loop diameter and compared to the B-field at the probe reference point as a function of the distance to the cooking zone. The ratio of the integrated B-field and the B-field at the reference point changes as a function of the field gradient and therefore depends on the distance to the cooking zone. The mean value for the offset correction is 1.1 (averaging over all measured positions along the z-axis). The maxi- mum deviation from this average is 1.1 and is con- sidered in the uncertainty evaluation (Supplementary Table IV) as a rectangular distribution. Figure 3 shows the maximum B-field ampli- tudes of the 13 professional induction cooktops eval- uated directly at the cabinet edge and at a distance of 300 mm from the cooktop edge at their operational frequency of 20 kHz. The positions (y À z coordi- nates as specified in Figs. 1 and 2) of the maxima in the plane at the cabinet edge and in the plane at a distance of 300 mm coincide within the spacing of the probe mounting positions in the measurement wall (Fig. 1 in the Online Supplementary Material). At 300 mm, most devices were found to be compliant with the ICNIRP 1998 reference level of 6.25 mT for the general public, although their field strengths vary by more than a factor of 30. Immedi- ately in front of the cabinet (0 mm), all but two Fig. 2. Measured B-field of one of the cooktops normalized to the occupational ICNIRP limit (30.7 mT). Left: frontal plane at the cabinet edge; right: spectrum of the signal at different distances. 698 Christetal. Bioelectromagnetics
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  devices are withinthe more relaxed occupational limits of 30.7 mT; significant differences between the professional (#1–#13) and domestic devices (#14–#16) could not be observed. Also, the maxi- mum B-field amplitudes could not be correlated with the nominal power of the different devices. The pow- er consumption was not monitored during the meas- urements because the primary source of exposure is the magnetic field. The magnetic field amplitude does not only depend on the power but also on the complex impedance of the loaded coil. In addition, the impact on the B-field was eval- uated for loading conditions with different vessels, which were also positioned off the center of the cooking zone. Vessels that are not particularly speci- fied for use with induction cooktops were included as well. For almost all devices, increased field strengths could be observed with respect to the standard con- figuration specified in IEC 62233. Supplementary Table II summarizes the results. In the worst case, an increase of more than a factor of 4.5 was found (#14). NUMERICAL EXPOSURE EVALUATION Exposure Configurations For the assessment of the current density in- duced in the body, six non-pregnant and three preg- nant anatomical whole-body models were selected for the dosimetric analysis by considering the body mass range of people working in professional kitch- ens. Models of young children were also included. All models are based on the computer-aided design representation of the organ surfaces and up to 80 dif- ferent tissue types are represented (up to 17 in the fetus models1 ). The non-pregnant models were developed from magnetic resonance (MR) images of volunteers [Christ et al., 2009, 2010]. Their details are: ‘‘Fats’’: male, 37 years, 1.78 m, 120 kg; ‘‘Duke’’: male, 34 years, 1.74 m, 70 kg; ‘‘Ella’’: female, 26 years, 1.60 m, 58 kg; ‘‘Louis’’: male, 14 years, 1.65 m, 50 kg; ‘‘Thelonious’’: male, 6 years, 1.17 m, 20 kg; ‘‘Roberta’’: female, 5 years, 1.08 m, 18 kg. The models of the pregnant woman are based on the model ‘‘Ella.’’ For the development of the fetus and womb during the different gestational phases, images from various sources were used. The fetus models represent the 3rd, 7th, and 9th gesta- tional month. Their masses are 15, 1700, and 2700 g, respectively. For the model in the 3rd month, a generic model based on images in the available scientific literature, for example, Levine [2005], was integrated into the womb of the model ‘‘Ella,’’ which was scaled in order to accommodate the fetus. The outer shape of the model was not changed. For the development of the model in the 7th month, MR images of the torso of a pregnant woman were seg- mented and integrated into the model. The model of the 9th month is based on that of the 7th month, but the fetus model was replaced by a model of a scaled newborn [Petoussi-Henss et al., 2002]. The dimen- sions of the abdominal region of the mother model were increased in order to accommodate the larger Fig. 3. Measured maxima of the B-field of 16 induction cooktops (professional and domestic) at the cabinet edge and 300 mm from the edge of the cooktop at their operational frequency of 20 kHz (not considering harmonics). Error bars indicate the measurement uncertainty (k ¼ 1) of 16% (1.3 dB, devices #1^#13) and 9% (0.8 dB, devices #14^#16) as given in Supplementary Table IV, excludingthe contributionofthenumericalrepresentationofthemeasureddevices. 1 The fetal tissues include bladder, bone, brain, eyes, fat, gall blad- der, heart, intestines, kidney, liver, lung, muscle, subcutaneous adipose tissue, skin, spinal cord, spleen, and stomach. It should be noted that not all three fetus models distinguish all tissues. ExposuretoInductionCooktops 699 Bioelectromagnetics
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  fetus. Figure 2of the Online Supplementary Material shows an overview of all anatomical models used in this study. The tissue conductivities for the simula- tions at 20 kHz are based on Gabriel et al. [1996]. The current densities in the bodies of the ana- tomical models were simulated using a generic cook- ing zone model that could be adapted to the incident fields of the measured devices. For the four non- pregnant models, the cooking zone was placed at distances of 10–310 mm from the body in steps of 100 mm (measured horizontally from the rim of the cooking zone to the closest point of the skin). It was placed both in front of and behind the models. The default height of the cooking zone model was 850 mm above ground. For the assessment of the un- certainty of the results with respect to the body height and position of the user, the height of the cooking zone was also varied in steps of Æ100 mm and moved to the left in steps of 100 mm. The results of these evaluations are considered only in the uncertainty budget (Tables IV–VI in the Online Sup- plementary Material) and not reported individually. For the evaluation of the exposure of the two models of young children, the same configurations as for the adults were used but the height of the coils was adjusted to their foreheads. This corresponds to body heights of approximately 1.0 m and to an age range of 3–4.5 years for boys and girls [Kromeyer- Hauschild et al., 2001]. Figure 3 in the Online Supplementary Material shows the different configu- rations. They were used for the evaluation of the uncertainty and variability of the exposure (Tables IV–VI in the Online Supplementary Material). Additional scenarios were analyzed in order to assess the effect of the posture of the body when op- erating the induction cooktop. The models ‘‘Duke’’ and ‘‘Ella’’ were bent over the hob at angles of 22.58 and 458. For these configurations, the closest distance from the rim of the cooking zone to the skin of the model was also 10 mm. Again, these evaluations were considered only in the uncertainty budget. For the assessment of the current density induced in the fetus and in the womb of the pregnant women mod- els, the cooking zone was placed at three different heights in the center of the abdomen. Again, the min- imum distance to the skin was 10 mm. The distance increased in steps of 100 mm, and the height changed by Æ100 mm. The changes in exposure for these positions were considered in the evaluation of the uncertainty and variability (Tables IV–VI in the Online Supplementary Material). In addition, the hands of the model ‘‘Duke’’ were positioned above the center and above the rim of the cooking zone. The vertical distances of the hand to the cooking zone were 50, 100, and 150 mm. Two horizontal positions were analyzed (above the center and above the rim). The results of the evaluation of the expo- sure of the hands are discussed below. Modeling of the Incident B-Fields In the experimental evaluation of the B-fields, a number of cooktops were evaluated both under the loading conditions defined by IEC 62233 [IEC, 2005] and with a large series of different vessels rep- licating several realistic exposure scenarios. Differen- ces in the field distribution in the measurement planes were observed due to different cooking zone configurations or loading with different vessels, for example (Supplementary Table II). These differences would not permit the accurate evaluation of a partic- ular cooktop without significant modeling and valida- tion efforts under a number of representative loading configurations. Because it is not the objective of this article to evaluate the compliance of particular induc- tion cooktops, the most generic approach has been chosen to model the spatial characteristics of the magnetic field distribution. Thus, the amplitude range of the induced current density can be quantified for realistic exposure scenarios. The applied cooking zone model consists of ten concentric loops with a constant current. The distance between the loops is 10 mm. In the radial direction (r), the B-field ampli- tude decays approximately with 1/r3 [Yamazaki et al., 2004]. In order to assess the exposure of the anatomi- cal models for the B-field amplitudes of the different measured devices (Fig. 3), the current density, which was evaluated using the generic cooking zone at dis- tances from 10 to 310 mm in the x-direction from the coil (Fig. 1), was scaled to match the B-field amplitudes of the measured devices at different mea- surement distances and the actual distance between the coil of the cooking zone and the measurement location. For each measured device, a scale factor was derived. Figure 4 shows the B-fields for each of the devices fitted to the B-field of the generic cook- ing zone at the different locations of the measure- ments.2 Considering the distances to the rim of the cooking zone, the agreement of the measured values at all evaluated distances in the x-direction is gener- ally satisfactory using a single scale factor for each device. The uncertainty of the representation of the amplitudes and field decay of the measured cooktops 2 Between two and eight points in the x-direction were evaluated depending on the different devices. Up to four measurement points per device are shown in Figure 4. 700 Christetal. Bioelectromagnetics
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  by the genericmodel was assessed as 17% (1.4 dB; Supplementary Table IV). DOSIMETRIC RESULTS Induced Current Density for the Generic Cooking Zone Model Figure 5 shows the normalized peak average current density for the six non-pregnant models as a function of the distance from the generic cooking zone model. For the definition of the distance refer- ence, a spacing of 50 mm between the rim of the cooking zone and the front edge of the cooktop is assumed. No additional space between the cooktop edge and the cabinet edge is added, which is a valid assumption for typical stand-alone devices. The cur- rent of the cooking zone was normalized to a B-field strength of 6.25 mT at a distance of 300 mm from the cooktop edge (i.e., 450 mm from the center point of the cooking zone). Like this, the generic cooking zone corresponds to a worst-case device that is com- pliant with the exposure limits for the general public when tested according to IEC 62233. At the operational frequency of 20 kHz, the limit for the induced current averaged over 1 cm2 is 40 mA/m2 for the general public and 200 mA/m2 for occupational exposure. When considering the cur- rents in all body tissues, the exposure limits for the general public are reached at distances between 200 and 250 mm for the adult models, and the abdominal region is the most exposed. For very close distances (<50 mm), even the occupational limits can be exceeded. The current density maxima typically oc- cur in tissues with comparatively high conductivity such as muscle, the penis, or walls of the gall bladder or small intestine. The maxima are not necessarily located at the closest location to the cooking zone model. For the two models of the children whose heads directly face the cooking zone model, the cur- rent density maximum can also occur in the vitreous humor. The current density of the two child models is about a factor of 2 below the values observed for the adults in their abdominal regions. Supplementary Table III lists those tissues in which the current den- sity maxima are typically observed, together with their conductivities at 20 kHz. The current density in the CNS of the adult and adolescent models is approximately a factor of 10 below the current density averaged over all tissues for all observed cases (Fig. 6). Even when standing directly at the cabinet edge the basic restrictions are not reached. For these exposure conditions, the cur- rent density maximum is located in the lower part of the spinal cord, which is at a comparatively large distance from the coil. For young children whose heads are at the same height as the cooktop, the basic restrictions for the general public are violated at distances below 60 mm, with the current density maximum located in the brain. When standing imme- diately at the cooktop, the current densities in the CNS can exceed the basic restrictions by approxi- mately a factor of 2. For the models of the pregnant woman and fetus, the averaged current density is shown in Figure 7. Among the investigated cases, Fig. 4. Simulated B-field in front of the model of the generic cooking zone normalized to a B-field amplitude of 6.25 mT at a distance of 300 mm from the cooktop edge (50 mm from the rim of the generic cooking zone). Measured results are scaled to matchamplitudeandslope. Fig. 5. Peakaverage currentdensitiesofallnon-pregnant models in all body tissues normalized to the B-field of 6.25 mTat a dis- tance of 300 mm from the cooktop edge (50 mm from the rim of the generic cooking zone). Symbols represent the simulation results at the different positions and the lines show exponential curve fits. Closest distance at which the current densities were evaluated is 10 mm from the rim of the cooking zone. This result has been included in the exponential curve fit but is outside the scope of the x-axis (À50 mm) of this figure and Figures 6^8. ExposuretoInductionCooktops 701 Bioelectromagnetics
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  mother and fetussuffer the highest exposure in the 9th gestational month. The current density maximum typically occurs in the tissue of the uterus because of its high conductivity (Supplementary Table III). Current densities in the tissue of the mother model, immediately at the edge of the cooktop, are approxi- mately a factor of 16 above the ICNIRP limit for the general public when considering all tissues. With the exception of the fetus in the 3rd gestational month, the current densities in the fetal tissue reach limits for the general public at 100–170 mm when averag- ing over the entire body and exceed them by up to a factor of 6 at the cooktop edge. If only the CNS tis- sue is considered, the limits are a factor of 2.5 below the basic restrictions for the general public (Fig. 8). Considering the exposure of pregnant women in working environments, it is debatable whether the oc- cupational limits or the limits for the general public should be applied to protect the fetus. Scaling the results of Figure 8 to a device that is only compliant with the occupational B-field limits (30.7 mT at 300 mm distance), shows that the exposure of the CNS tissue of the fetus can exceed the exposure lim- its for the general public if the mother is exposed in an occupational environment. It should, however, be noted that the brains of the fetus models are not ori- ented toward the cooking zone (Fig. 2 in the Online Supplementary Material). The exposure of the hand above the cooking zone almost reaches the occupa- tional limit at distances from 50 mm above the cook- ing zone (Fig. 9), both for centered position and above the rim. Normalization to the B-Field Amplitudes of the Measured Devices In order to assess the exposure in persons in the close environment at the B-field levels of the different induction cooktops discussed above and in Fig. 6. Peakaverage currentdensitiesofallnon-pregnant models in the CNS tissues normalized to the B-field of 6.25 mTat a dis- tance of 300 mm from the cooktop edge (50 mm from the rim of the generic cooking zone). Symbols represent the simulation results at the different positions and the lines show exponential curvefits. Fig. 7. Peak average current density of the pregnant models in thethreegestationalphasesandthefetusesoverallbody tissues, normalized to the B-field of 6.25 mTat a distance of 300 mm from the cooktop edge (50 mm from the rim of the generic cooking zone). Symbols represent the simulation results and the lines showexponentialcurvefits. Fig. 8. Peak average current density in the CNS tissues of the fetuses normalized to the B-field of 6.25 mT at a distance of 300 mmfromthe cooktopedge (50 mmfromtherimofthegener- ic cooking zone). Symbols represent the simulation results and thelinesshowexponentialcurvefits. 702 Christetal. Bioelectromagnetics
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  Viellard et al.[2006], the exponential fit shown in Figures 5–8 was used to correlate the averaged cur- rent density maximum with the measurement results. The field strengths at the particular distances to the rims of the cooking zones were derived by normaliz- ing these current densities with the scaling factors derived above. In addition, the increase in field strength for worst-case loading conditions was ap- plied (Supplementary Table II). Figure 10 shows the exposure average of the anatomical models for which the maximum current density was observed for the generic cooking zone (Figs. 5–8), normalized to the incident B-fields of the measured devices at three dif- ferent distances. At 30 mm from the cabinet edge, parts of the user’s body are assumed to protrude above the cabinet; at the cabinet edge, the user is assumed to touch the cabinet without any protruding regions of his body; and 300 mm from the cabinet edge is the maximum distance at which the fields were measured (this distance is regarded as typical for bystanders). Figure 5 shows that the exposure of the non- pregnant models at the largest distance (300 mm from the cabinet) is always compliant with the basic Fig. 9. Peakaverage current densityinthehandofthemodel‘‘Duke’’at different distancesandposi- tions above the hobs normalized to the B-field of 6.25 mTat 300 mm from the edge of the generic cooktop. Fig.10. Peak average current density in the CNS and all tissues of the anatomical models (most relevant cases ofthis figure and Figs.8 and 9), normalized to the average ofthe measured devices at À30,0, and 300 mm from the edge ofthe device.Hatched barsindicate the range from the best- totheworst-casedevice.Expandeduncertainty (k ¼ 2) ofthemeasurementandsimulationresults is 6.0 dB for themodelsoftheadultsandchildren (SupplementaryTableV), and 6.4 dB for thefetus models (SupplementaryTableVI). ExposuretoInductionCooktops 703 Bioelectromagnetics
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  restrictions for thegeneral public even when includ- ing all body tissues for the current averaging. At close distances, the exposure limits for the general public can be exceeded by more than a factor of 5 (distance < 50 mm; Fig. 5). When considering CNS tissues only, the basic restrictions for the general public can be reached for the child models (Theloni- ous and Roberta) at close distances from the cabinet edge when allowing for the overall uncertainty of this evaluation. The combined numerical and experi- mental uncertainty was assessed as 6.0 dB (k ¼ 2; Supplementary Table V) or as 0.50–2.0 of the provid- ed exposure with a confidence interval of 95%. The exposure of the mother and fetus models exceeds the basic restrictions for the general public by a factor of 6 for the mother and 3.5 for the fetus when standing at the cabinet edge, if considering all body tissues. Given the numerical and experimental uncertainty, the violation of the occupational limits can be regarded as likely for the devices with high B-fields. For CNS tissues of the fetus, the induced current density can reach the order of magnitude of the basic restrictions when taking into account the uncertainty. The combined numerical and experimen- tal uncertainty for the exposure of the fetus was assessed as 6.4 dB (k ¼ 2; Supplementary Table VI) or as 0.48–2.1 of the provided exposure with a confi- dence interval of 95%. In general, the current density reported by Kos et al. [2011] lies in the order of magnitude of the results shown in Figure 10. Howev- er, a direct comparison is difficult because the cook- tops analyzed by Kos et al. [2011] operate at 35 kHz whereas the nominal frequency of all cooktops con- sidered in this study is 20 kHz. DISCUSSION AND CONCLUSIONS The measured B-fields of 13 professional in- duction cooktops and the three domestic devices evaluated in Viellard et al. [2006] were evaluated ex- perimentally. The field strengths are compliant with exposure limits for the general public when measured at 300 mm from the cooktops as specified by IEC 62233 [IEC, 2005]. Due to the high field gradients, the measured B-fields reach—or violate—the occupa- tional exposure limits at short distances from the cooking zone. The current densities induced in the human body were modeled using a generic worst- case cooking zone model and different anatomical models including adults, pregnant women, and chil- dren. The current densities reached the exposure lim- its according to the ICNIRP 1998 guidelines for the general public at 300 mm from the cooktop. The results were then scaled to the measured B-field levels of the professional and domestic cooktops. The findings can be summarized as follows: Most of the measured cooktops are compliant with the field limits for public exposure at a distance of 300 mm from the cooktop. Due to the high field gradients in the close environment of the cooking zone, most devices exceed these limits at closer distances. When considering the entire body of the exposed user for the current density averaging, the basic restrictions of the current density for the general public can be sig- nificantly exceeded and reach occupational levels. A generic worst-case cooktop which is compliant at the measurement distance specified by IEC 62233 can lead to current densities that exceed the basic restric- tions for the general public by a factor of 16. The brain tissue of young children can be overexposed by a factor of 2 with respect to the basic restrictions for the general public if they come close to the cooktop. If exposure limits of the general public apply to the fetus of a mother in a working environment, the cur- rent density in the CNS tissue of the fetus can exceed the basic restrictions while they are still fulfilled for the mother. To summarize, the IEC 62233 standard does not sufficiently protect exposed persons according to the basic restrictions defined by the ICNIRP 1998 guide- lines, which are enforced in many countries. The high field gradients in the close environment of in- duction cooktops need be considered very carefully. It should be noted that a recent ICNIRP statement defines different basic restrictions in terms of the electric field in the entire body and proposes higher reference levels for the incident B-field [ICNIRP, 2010]. Electric field limits have already been estab- lished by the IEEE [2002]. 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