Calculation of induced current densities for humans by magnetic fields from electronic article surveillance devices.

This paper illustrates the use of the impedance method to calculate the electric fields and current densities induced in millimetre resolution anatomic models of the human body, namely an adult and 10- and 5-year-old children, for exposure to nonuniform magnetic fields typical of two assumed but representative electronic article surveillance (EAS) devices at 1 and 30 kHz, respectively. The devices assumed for the calculations are a solenoid type magnetic deactivator used at store checkouts and a pass-by panel-type EAS system consisting of two overlapping rectangular current-carrying coils used at entry and exit from a store. The impedance method code is modified to obtain induced current densities averaged over a cross section of 1 cm2 perpendicular to the direction of induced currents. This is done to compare the peak current densities with the limits or the basic restrictions given in the ICNIRP safety guidelines. Because of the stronger magnetic fields at lower heights for both the assumed devices, the peak 1 cm2 area-averaged current densities for the CNS tissues such as the brain and the spinal cord are increasingly larger for smaller models and are the highest for the model of the 5-year-old child. For both the EAS devices, the maximum 1 cm2 area-averaged current densities for the brain of the model of the adult are lower than the ICNIRP safety guideline, but may approach or exceed the ICNIRP basic restrictions for models of 10- and 5-year-old children if sufficiently strong magnetic fields are used.

Currents induced in anatomic models of the human for uniform and nonuniform power frequency magnetic fields.

We have used the quasi-static impedance method to calculate the currents induced in the nominal 2 x 2 x 3 and 6 mm resolution anatomically based models of the human body for exposure to magnetic fields at 60 Hz. Uniform magnetic fields of various orientations and magnitudes 1 or 0.417 mT suggested in the ACGIH and ICNIRP safety guidelines are used to calculate induced electric fields or current densities for the various glands and organs of the body including the pineal gland. The maximum 1 cm(2) area-averaged induced current densities for the central nervous system tissues, such as the brain and the spinal cord, were within the reference level of 10 mA/m(2) as suggested in the ICNIRP guidelines for magnetic fields (0.417 mT at 60 Hz). Tissue conductivities were found to play an important role and higher assumed tissue conductivities gave higher induced current densities. We have also determined the induced current density distributions for nonuniform magnetic fields associated with two commonly used electrical appliances, namely a hair dryer and a hair clipper. Because of considerably higher magnetic fields for the latter device, higher induced electric fields and current densities were calculated.

Inter-laboratory comparison of numerical dosimetry for human exposure to 60 Hz electric and magnetic fields.

In recent years, with the availability of high resolution models of the human body, numerical computations of induced electric fields and currents have been made in more than one laboratory for various exposure conditions. Despite the verification of computational methods, questions are often asked about the reliability of these data. In this paper, computational results from two laboratories that presented data in compatible formats are compared, supplemented with additional data from the third laboratory. Two exposures to uniform fields at 60 Hz are evaluated. The human body models used in the computations are different and so are the computation al methods and codes. There are some differences in the conductivity values used for some of the tissues, as well. The results of the comparison confirm that these data are reliable, as the overall agreement is reasonably good and the differences can be rationally explained. This comparison also underscores the importance of accurate data on the dielectric properties of tissues.

Specific absorption rates and induced current densities for an anatomy-based model of the human for exposure to time-varying magnetic fields of MRI.

A 6-mm resolution, 30-tissue anatomy-based model of the human body is used to calculate specific absorption rate (SAR) and the induced current density distributions for radiofrequency and switched gradient magnetic fields used for MRI, respectively. For SAR distributions, the finite-difference time-domain (FDTD) method is used including modeling of 16-conductor birdcage coils and outer shields of dimensions that are typical of body and head coils and a new high-frequency head coil proposed for the 300-400 MHz band. SARs at 64, 128, and 170 MHz have been found to increase with frequency (f) as f(k) where k is on the order of 1.1-1.2. The tables of the calculated maximum 1 kg and 100 g SAR may be used to calculate the maximum RF currents and/or magnetic fields that may be used in order not to exceed the safety guidelines. Because of the low frequencies associated with switched gradient magnetic fields, a quasi-static impedance method is used for calculation of induced current densities that are compared with the safety guidelines.

Comparison of numerical and experimental methods for determination of SAR and radiation patterns of handheld wireless telephones.

Some recent developments in both the numerical and experimental methods for determination of SARs and radiation patterns of handheld wireless telephones are described, with emphasis on comparison of results using the two methods. For numerical calculations, it was possible to use the Pro-Engineer CAD Files of cellular telephones for a realistic description of the device. Also, we used the expanding grid formulation of the finite-difference time-domain (FDTD) method for finer-resolution representation of the coupled region, including the antenna, and an increasingly coarser representation of the more-distant, less-coupled region. Together with the truncation of the model of the head, this procedure led to a saving of computer memory needed for SAR calculations by a factor of over 20. Automated SAR and radiation pattern measurement systems were used to validate both the calculated 1-g SARs and radiation patterns for several telephones, including some research test samples, using a variety of antennas. Even though widely different peak 1-g SARs were obtained, ranging from 0.13 to 5.41 W/kg, agreement between the calculated and the measured data for these telephones, five each at 835 and 1900 MHz, was excellent and generally within +/-20% (+/-1 dB). An important observation was that for a maximum radiated power of 600 mW at 800/900 MHz, which may be used for telephones using AMPS technology, the peak 1-g SARs can be higher than 1.6 W/kg unless antennas are carefully designed and placed further away from the head.

Head and neck resonance in a rhesus monkey--a comparison with results from a human model.

The use of primates for examining the effects of electromagnetic radiation on behavioural patterns is well established. Rats have also been used for this purpose. However, the monkey is of greater interest as its physiological make-up is somewhat closer to that of the human. Since the behavioural effects are likely to occur at lower field strengths for resonant absorption conditions for the head and neck, the need for determination of resonance frequencies for this region is obvious. Numerical techniques are ideal for the prediction of coupling to each of the organs, and accurate anatomically based models can be used to pinpoint the conditions for maximum absorption in the head in order to focus the experiments. In this paper we use two models, one of a human male and the other of a rhesus monkey, and find the mass-averaged power absorption spectra for both. The frequencies at which highest absorption (i.e. resonance) occurs in both the whole body and the head and neck region are determined. The results from these two models are compared for both E-polarization and k-polarization, and are shown to obey basic electromagnetic scaling principles.

Comparison of cardiac-induced endogenous fields and power frequency induced exogenous fields in an anatomical model of the human body.

Time-domain potentials measured at 64 points on the surface of a large canine heart, considered comparable with those of a human heart, were used to calculate the electric fields and current densities within various organs of the human body. A heterogeneous volume conductor model of an adult male with a resolution of approximately 6 mm3 and 30 segmented tissue types was used along with the admittance method and successive over-relaxation to calculate the voltage distribution throughout the torso and head as a function of time. From this time-domain voltage description, values of [E(t)] and [J(t)] were obtained, allowing for maximum values to be found within the given tissues of interest. Frequency analysis was then used to solve for [E(f)] and [J(f)] in the various organs, so that average, minimum and maximum values within specific bandwidths (0-40, 40-70 and 70-100 Hz) could be analysed. A comparison was made between the computed results and measured data from both EKG waveforms and isopotential surface maps for validation, with good agreement in both amplitude and shape between the computed and measured results. These computed endogenous fields were then compared with exogenous fields induced in the body from a 60 Hz high-voltage power line and a 60 Hz uniform magnetic field of 1 mT directed from the front to the back of the body. The high-voltage power line EMFs and 1 mT magnetic field were used as 'bench' marks for comparison with several safety guidelines for power frequency (50/60 Hz) EMF exposures. The endogenous electric fields and current densities in most of the tissues (except for organs in close proximity to the heart, for example lungs, liver, etc) in the frequency band 40-70 Hz were found to be considerably smaller, between 5% and 10%, than those induced in the human body by the electric and magnetic fields generated by the 60 Hz sources described above.

Power deposition in the head and neck of an anatomically based human body model for plane wave exposures.

At certain frequencies, when the human head becomes a resonant structure, the power absorbed by the head and neck, when the body is exposed to a vertically polarized plane wave propagating from front to back, becomes significantly larger than would ordinarily be expected from its shadow cross section. This has possible implications in the study of the biological effects of electromagnetic fields. Additionally the frequencies at which these resonances occur are not readily predicted by simple approximations of the head in isolation. In order to determine these resonant conditions an anatomically based model of the whole human body has been used, with the finite-difference time-domain (FDTD) algorithm to accurately determine field propagation, specific absorption rate (SAR) distributions and power absorption in both the whole body and the head region (head and neck). This paper shows that resonant frequencies can be determined using two methods. The first is by use of the accurate anatomically based model (with heterogeneous tissue properties) and secondly using a model built from parallelepiped sections (for the torso and legs), an ellipsoid for the head and a cylinder for the neck. This approximation to the human body is built from homogeneous tissue the equivalent of two-thirds the conductivity and dielectric constant of that of muscle. An IBM SP-2 supercomputer together with a parallel FDTD code has been used to accommodate the large problem size. We find resonant frequencies for the head and neck at 207 MHz and 193 MHz for the isolated and grounded conditions, with absorption cross sections that are respectively 3.27 and 2.62 times the shadow cross section.

Calculation of electric fields and currents induced in a millimeter-resolution human model at 60 Hz using the FDTD method.

The finite-difference time-domain (FDTD) method has previously been used to calculate induced currents in anatomically based models of the human body at frequencies ranging from 20 to 915 MHz and resolutions down to about 1.25 cm. Calculations at lower frequencies and higher resolutions have been precluded by the huge number of time steps that would be needed in these simulations. This paper describes a method used to overcome this problem and efficiently calculate induced currents in an MRI-based, 6-mm-resolution model of the human under a high-voltage transmission line. This model is significantly higher resolution than the 1.31-cm-resolution model previously used; therefore, it can be used to pinpoint locations of peak current densities in the body. Proposed safety guidelines would allow external electric fields of 10 kV/m and 25 kV/m for exposure to 60 Hz fields of the general public and workers, respectively. For this external electric field exposure of 10 kV/m, local induced current densities as high as 20 mA/m2 are found in the head and trunk with even higher values (above 150 mA/m2) in the legs. These currents are considerably higher than the 4 or even 10 mA/m2 that have been suggested in the various safety guidelines, thus indicating an inconsistency in the proposed guidelines. In addition, several ratios of E/H typical of power line exposures were examined, and it was found that the vertical electric field couples strongly to the body, whereas the horizontal magnetic field does not.

Induced current and SAR distributions for a worker model exposed to an RF dielectric heater under simulated workplace conditions.

We have used the finite-difference time-domain method to calculate the distributions of absorbed energy for a 1.34 x 1.34 x 1.4 cm resolution anatomically based model of the human body for exposure to leakage electromagnetic fields of a radiofrequency dielectric heater operating at 40.68 MHz. To simulate workplace conditions, the dielectric heater is assumed to be placed in a screen room and different operator postures, such as standing or sitting on a wooden or metal stool with hands on sides or extended toward the radiofrequency heater, are considered. To obviate the problem of having to model a fairly large volume of the screen room of assumed dimensions 2.13 x 3.05 x 2.13 m, we have used a uniform finer grid of points for the finite-difference time-domain method for the closely coupled region consisting of the front region of the heater and the human model, while a newly developed expanding-grid finite-difference time-domain formulation is used elsewhere. This results in a saving of both the memory and computation times by almost a factor of four. The average rates of energy absorption are given for the whole body, selected parts of the body, and various organs. As expected, the foot currents and the rates of energy absorption are higher with the screen room for sitting postures where the upper parts of the body are in higher electromagnetic fields, and for hands extended toward the heater.

A memory efficient method of calculating specific absorption rate in CW FDTD simulations.

Specific absorption rate (SAR) distributions in man models are often calculated using the finite-difference time-domain (FDTD) method. The traditional method of calculating SAR requires calculation and storage of the three electric field components in each cell and is therefore very time- and memory-intensive. A new algorithm, based on the mass-normalized time-averaged energy distribution, is presented in this paper. This new method of calculating SAR requires 1/6 of the memory and a small fraction of the computer time of the traditional method. The accuracy of the two methods is shown to be virtually identical. In addition to improving the efficiency of SAR distribution calculations, the memory requirements are virtually eliminated for calculations of layer-averaged or organ-averaged SAR.

Electric field and current density distributions induced in an anatomically-based model of the human head by magnetic fields from a hair dryer.

We have used the impedance method to calculate the induced electric (E) fields and current densities (J) for the spatially varying vector magnetic fields due to a hair dryer. In this method, applicable for low-frequency exposures where the quasi-static approximation may be made, the biological body or the exposed parts thereof are represented by a three-dimensional (3-D) network of impedances whose individual values are obtained from the electrical properties sigma, epsilon r for the various tissues. We have measured the 3-D variations of the 50-Hz magnetic fields from a typical hair dryer and found that the various components correlate well with those for a helical coil. The non-uniform magnetic fields thus obtained are used to calculate the induced E and J with a resolution of 1.31 cm for the model of the head and neck. The induced E values are compared with the fields endogenous to the body and the minimum detectable E-field limits based on the cellular thermal noise model proposed by Weaver and Astumian (1990, 1992).

Induced electric currents in models of man and rodents from 60 Hz magnetic fields.

Induced electric currents in models of man, rat and mouse from 60 Hz magnetic fields are computed using the impedance method. The models all have realistic shapes, and in the case of rodents, a homogeneous average tissue conductivity is assumed. The model of man is analyzed for two cases, a homogeneous average tissue conductivity and a heterogeneous model, both consisting of 1.3 cm cubical tissue cells whose conductivities are representative of the tissue within the cube. The results for various models and species, as well as different orientations of the magnetic field, are compared. The data presented are useful as the first step in dosimetry for 60 Hz magnetic fields, and for interspecies scaling of biological interactions related to the tissue induced electric currents.

Radio frequency currents induced in the human body for medium-frequency/high-frequency broadcast antennas.

Radio frequency currents in the human body, induced by high-frequency and medium-frequency high-power broadcast antennas, were studied theoretically and experimentally. An analytical formula was derived to calculate the foot currents in a grounded semispheroidal model of the human body. The model agrees within 30% with the results given by the standard formula presented by Gandhi on the basis of measurements with humans. Near 100 kHz, the model predicts a decrease of 14% of the current dissipated in the human body, which is due to the beta relaxation of the cells. The effect of the body and foot-contact impedances were studied with the aid of a simplified equivalent circuit which showed that the body impedance does not considerably affect the foot current below 10 MHz. The normalized foot currents measured in front of the broadcast antennas were within 30% agreement of the currents calculated with the Gandhi formula from the electric fields measured at a height of 1 m. The foot currents are induced by vertical electric fields for both medium-frequency and high-frequency antennas in spite of a strong horizontal component in the latter case. The distance at which the occupational exposure limit of 200 mA was exceeded in the worst (maximum coupling) case was 50 m for the high-frequency antenna and < 14 m for the medium-frequency antenna. In the latter case, the radio frequency shocks resulting from touching ungrounded metallic bodies impose a practical limit to about 40 m.

Specific absorption rates and induced current distributions in an anatomically based human model for plane-wave exposures.

We have previously reported local, layer-averaged, and whole-body-averaged specific absorption rates and induced currents for a 5,628-cell anatomically based model of a human for plane-wave exposures 20-100 MHz (Chen and Gandhi 1989). Using a higher resolution, 45,024-cell model of the human body, calculations have now been extended to 915 MHz using the finite-difference time-domain method. Because of the higher resolution of the model, it has been possible to calculate specific absorption rates for various organs (brain, eyes, heart, lungs, liver, kidneys, and intestines) and for various parts of the body (head, neck, torso, legs, and arms) as a function of frequency in the band 100-915 MHz. Consistent with some of the experimental data in the literature, the highest part-body-averaged specific absorption rate for the head and neck region (as well as for the eyes and brain) occurs at 200 MHz for the isolated condition and at 150 MHz for the grounded condition of the model. Also observed is an increasing specific absorption rate for the eyes for frequencies above 350 MHz due to the superficial nature of power deposition at increasing frequencies.

Numerical simulation of annular-phased arrays of dipoles for hyperthermia of deep-seated tumors.

We have used the finite-difference time domain (FDTD) method to calculate the SAR distributions from an annular-phased array of eight dipole antennas coupled through water "boluses" in anatomically based three-dimensional models of the human body. We evaluated the effect of tapered bolus chambers, frequency (100-120 MHz), dipole length (17-30 cm), and phase and amplitude of power to the various dipoles on the ability to focus energy in the region of deep-seated tumors in the prostate and the liver. Assuming tumor conductivity and permittivity to be similar or slightly higher than surrounding normal tissues, calculations indicate that adjustment of the noted parameters should result in considerable improvement in focusing of SAR distributions in tumor-bearing regions. If such calculations can be shown to correctly predict empirical measurements from complex inhomogeneous (although not necessarily anatomically correct) phantoms, they may be useful for hyperthermia treatment planning based on patient-specific anatomic models.

Numerical dosimetry at power-line frequencies using anatomically based models.

We have used the finite-difference time-domain (FDTD) method to calculate induced current densities in a 1.31-cm (nominal 1/2 in) resolution anatomically based model of the human body for exposure to purely electric, purely magnetic, and combined electric and magnetic fields at 60 Hz. This model based on anatomic sectional diagrams consists of 45,024 cubic cells of dimension 1.31 cm for which the volume-averaged tissue properties are prescribed. It is recognized that the conductivities of several tissues (skeletal muscle, bone, etc.) are highly anisotropic for power-line frequencies. This has, however, been neglected in the first instance and will be included in future calculations. Because of the quasi-static nature of coupling at the power-line frequencies, a higher quasi-static frequency f' may be used for irradiation of the model, and the internal fields E' thus calculated can be scaled back to the frequency of interest, e.g., 60 Hz. Since in the FDTD method one needs to calculate in the time domain until convergence is obtained (typically 3-4 time periods), this frequency scaling to 5-10 MHz for f' reduces the needed number of iterations by over 5 orders of magnitude. The data calculated for the induced current and its variation as a function of height are in excellent agreement with the data published in the literature. The average current densities calculated for the various sections of the body for the magnetic field component (H) are considerably smaller (by a factor of 20-50) than those due to the vertically polarized electric field component when the ratio E/H is 377 ohms. We have also used the previously described impedance method to calculate the induced current densities for the anatomically based model of the human body for the various orientations of the time-varying magnetic fields, namely from side to side, front to back, or from top to bottom of the model, respectively.