Reducing the staircasing error in computational dosimetry of low-frequency electromagnetic fields

Comparison of Transcranial Magnetic Stimulation Dosimetry between Structured and Unstructured Grids Using Different Solvers

In recent years, the interest in transcranial magnetic stimulation (TMS) has surged, necessitating deeper understanding, development, and use of low-frequency (LF) numerical dosimetry for TMS studies. While various ad hoc dosimetric models exist, commercial software tools like SimNIBS v4.0 and Sim4Life v7.2.4 are preferred for their user-friendliness and versatility. SimNIBS utilizes unstructured tetrahedral mesh models, while Sim4Life employs voxel-based models on a structured grid, both evaluating induced electric fields using the finite element method (FEM) with different numerical solvers. Past studies primarily focused on uniform exposures and voxelized models, lacking realism. Our study compares these LF solvers across simplified and realistic anatomical models to assess their accuracy in evaluating induced electric fields. We examined three scenarios: a single-shell sphere, a sphere with an orthogonal slab, and a MRI-derived head model. The comparison revealed small discrepancies in induced electric fields, mainly in regions of low field intensity. Overall, the differences were contained (below 2% for spherical models and below 12% for the head model), showcasing the potential of computational tools in advancing exposure assessment required for TMS protocols in different bio-medical applications.

Electric Field Modeling in Personalizing Transcranial Magnetic Stimulation Interventions

The modeling of transcranial magnetic stimulation (TMS)-induced electric fields (E-fields) is a versatile technique for evaluating and refining brain targeting and dosing strategies, while also providing insights into dose-response relationships in the brain. This review outlines the methodologies employed to derive E-field estimations, covering TMS physics, modeling assumptions, and aspects of subject-specific head tissue and coil modeling. We also summarize various numerical methods for solving the E-field and their suitability for various applications. Modeling methodologies have been optimized to efficiently execute numerous TMS simulations across diverse scalp coil configurations, facilitating the identification of optimal setups or rapid cortical E-field visualization for specific brain targets. These brain targets are extrapolated from neurophysiological measurements and neuroimaging, enabling precise and individualized E-field dosing in experimental and clinical applications. This necessitates the quantification of E-field estimates using metrics that enable the comparison of brain target engagement, functional localization, and TMS intensity adjustments across subjects. The integration of E-field modeling with empirical data has the potential to uncover pivotal insights into the aspects of E-fields responsible for stimulating and modulating brain function and states, enhancing behavioral task performance, and impacting the clinical outcomes of personalized TMS interventions.

An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling

Objective.In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.Approach.We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a 'silver-standard' solution found by subsequent 4:1 global refinement of the adaptively-refined model.Main results.Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.Significance.This error has especially important implications for TES dosing prediction-where the stimulation strength plays a central role-and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

Orthopedic implants affect the electric field induced by switching gradients in MRI

PURPOSE

To investigate whether the risk of peripheral nerve stimulation increases in the presence of bulky metallic prostheses implanted in a patient's body.

METHODS

A computational tool was used to calculate the electric field (E-field) induced in a realistic human model due to the action of gradient fields. The calculations were performed both on the original version of the anatomical model and on a version modified through "virtual surgery" to incorporate knee, hip, and shoulder prostheses. Five exam positions within a body gradient coil and one position using a head gradient coil were simulated, subjecting the human model to the readout gradient from an EPI sequence. The induced E-field in models with and without prostheses was compared, focusing on the nerves and all other tissues (both including and excluding the bones from the analysis).

RESULTS

In the nerves, the most pronounced increase in the E-field (+24%) was observed around the knee implant during an abdominal MRI (Y axis readout). When extending the analysis to encompass all tissues (excluding bones), the greatest amplification (+360%) occurred around the knee implant during pelvic MRI (Z axis readout). Notable increases in E-field peaks were also identified around the shoulder and hip implants in multiple scenarios.

CONCLUSION

Based on the presented results, further investigations aimed at quantifying the threshold of nerve stimulation in the presence of bulky implants are desirable.

Outcome measures for electric field modeling in tES and TMS: A systematic review and large-scale modeling study

BACKGROUND

Electric field (E-field) modeling is a potent tool to estimate the amount of transcranial magnetic and electrical stimulation (TMS and tES, respectively) that reaches the cortex and to address the variable behavioral effects observed in the field. However, outcome measures used to quantify E-fields vary considerably and a thorough comparison is missing.

OBJECTIVES

This two-part study aimed to examine the different outcome measures used to report on tES and TMS induced E-fields, including volume- and surface-level gray matter, region of interest (ROI), whole brain, geometrical, structural, and percentile-based approaches. The study aimed to guide future research in informed selection of appropriate outcome measures.

METHODS

Three electronic databases were searched for tES and/or TMS studies quantifying E-fields. The identified outcome measures were compared across volume- and surface-level E-field data in ten tES and TMS modalities targeting two common targets in 100 healthy individuals.

RESULTS

In the systematic review, we extracted 308 outcome measures from 202 studies that adopted either a gray matter volume-level (n = 197) or surface-level (n = 111) approach. Volume-level results focused on E-field magnitude, while surface-level data encompassed E-field magnitude (n = 64) and normal/tangential E-field components (n = 47). E-fields were extracted in ROIs, such as brain structures and shapes (spheres, hexahedra and cylinders), or the whole brain. Percentiles or mean values were mostly used to quantify E-fields. Our modeling study, which involved 1,000 E-field models and > 1,000,000 extracted E-field values, revealed that different outcome measures yielded distinct E-field values, analyzed different brain regions, and did not always exhibit strong correlations in the same within-subject E-field model.

CONCLUSIONS

Outcome measure selection significantly impacts the locations and intensities of extracted E-field data in both tES and TMS E-field models. The suitability of different outcome measures depends on the target region, TMS/tES modality, individual anatomy, the analyzed E-field component and the research question. To enhance the quality, rigor, and reproducibility in the E-field modeling domain, we suggest standard reporting practices across studies and provide four recommendations.

Tensor-conductance model for reducing the computational artifact in target tissue for low-frequency dosimetry

Objective.In protecting human from low-frequency (<100 kHz) exposure, an induced electric field strength is used as a physical quantity for assessment. However, the computational assessment suffers from a staircasing error because of the approximation of curved boundary discretized with cubic voxels. The international guidelines consider an additional reduction factor of 3 when setting the limit of external field strength computed from the permissible induced electric field. Here, a new method was proposed to reduce the staircasing error considering the tensor conductance in human modeling for low-frequency dosimetry.Approach.We proposed a tensor-based conductance model, which was developed on the basis of the filling ratio and the direction of the tissue interface to satisfy the electric field boundary condition and reduce staircasing errors in the target tissue of a voxel human model.Main results.The proposed model was validated using two-layer nonconcentric cylindrical and spherical models with different conductivity contrasts. A comparison of induced electric field strengths with solutions obtained using an analytical formula and finite element method simulation indicated that for a wide range of conductivity ratios, staircasing errors were reduced compared with a conventional scalar-potential finite-difference method. The induced electric field in a simple anatomical head model using our approach was in good agreement with finite element method for exposure to uniform magnetic field exposure and that from coil, simulating transcranial magnetic stimulation.Significance.The proposed tensor-conductance model demonstrated that the staircasing error in an inner target tissue of a voxel human body can be reduced. This finding can be used for the electromagnetic compliance assessment and dose evaluation in electric or magnetic stimulation at low frequencies.

Analysis of Numerical Artifacts Using Tetrahedral Meshes in Low Frequency Numerical Dosimetry

Anatomical realistic voxel models of human beings are commonly used in numerical dosimetry to evaluate the human exposure to low-frequency electromagnetic fields. The downside of these models is that they do not correctly reproduce the boundaries of curved surfaces. The stair-casing approximation errors introduce computational artifacts in the evaluation of the induced electric field and the use of post-processing filtering methods is essential to mitigate these errors. With a suitable exposure scenario, this paper shows that tetrahedral meshes make it possible to remove stair-casing errors. However, using tetrahedral meshes is not a sufficient condition to completely remove artifacts, because the quality of the tetrahedral mesh plays an important role. The analyses carried out show that in real exposure scenarios, other sources of artifacts cause peak values of the induced electric field even with regular meshes. In these cases, the adoption of filtering techniques cannot be avoided.

A fast tool for the parametric analysis of human body exposed to LF electromagnetic fields in biomedical applications

A numerical procedure for analyzing electromagnetic (EM) fields interactions with biological tissues is presented. The proposed approach aims at drastically reducing the computational burden required by the repeated solution of large scale problems involving the interaction of the human body with EM fields, such as in the study of the time evolution of EM fields, uncertainty quantification, and inverse problems. The proposed volume integral equation (VIE), focused on low frequency applications, is a system of integral equations in terms of current density and scalar potential in the biological tissues excited by EM fields and/or electrodes connected to the human body. The proposed formulation requires the voxelization of the human body and takes advantage of the regularity of such discretization by speeding-up the computational procedure. Moreover, it exploits recent advancements in the solution of VIE by means of iterative preconditioned solvers and ad hoc parametric Model Order Reduction techniques. The efficiency of the proposed tool is demonstrated by applying it to a couple of realistic model problems: the assessment of the peripheral nerve stimulation, performed in terms of evaluation of the induced electric field, due to the gradient coils of a magnetic resonance imaging scanner during a clinical examination and the assessment of the exposure to environmental fields at 50 Hz of live-line workers with uncertain properties of the biological tissues. Thanks to the proposed method, uncertainty quantification analyses and time domain simulations are possible even for large scale problems and they can be performed on standard computers and reasonable computation time. Sample implementation of the method is made publicly available at https://github.com/UniPD-DII-ETCOMP/BioMOR.

Exposure of Infants to Gradient Fields in a Baby MRI Scanner

In pediatric magnetic resonance imaging (MRI), infants are exposed to rapid, time-varying gradient magnetic fields, leading to electric fields induced in the body of infants and potential safety risks (e.g. peripheral nerve stimulation). In this numerical study, the in situ electric fields in infants induced by small-sized gradient coils for a 1.5 T MRI scanner were evaluated. The gradient coil set was specially designed for the efficient imaging of infants within a small-bore (baby) scanner. The magnetic flux density and induced electric fields by the small x, y, z gradient coils in an infant model (8-week-old with a mass of 4.3 kg) were computed using the scalar potential finite differences method. The gradient coils were driven by a 1 kHz sinusoidal waveform and also a trapezoidal waveform with a 250 µs rise time. The model was placed at different scan positions, including the head area (position I), chest area (position II), and body center (position III). It was found that the induced electric fields in most tissues exceeded the basic restrictions of the ICNIRP 2010 guidelines for both waveforms. The electric fields were similar in the region of interest for all coil types and model positions but different outside the imaging region. The y-coil induced larger electric fields compared with the x- and z- coils. © 2022 Bioelectromagnetics Society.

Influence of Posture and Coil Position on the Safety of a WPT System While Recharging a Compact EV

In this study, the human exposure to the magnetic field emitted by a wireless power transfer (WPT) system during the static recharging operations of a compact electric vehicle (EV) is evaluated. Specifically, the influence of the posture of realistic anatomical models, both in standing and lying positions, either inside or outside the EV, is considered. Aligned and misaligned coil configurations of the WPT system placed both in the rear and front position of the car floor are considered as well. Compliance with safety standards and guidelines has proven that reference levels are exceeded in the extreme case of a person lying on the floor with a hand close to the WPT coils, whereas the system is always compliant with the basic restrictions, at least for the considered scenarios.

Chassis Influence on the Exposure Assessment of a Compact EV during WPT Recharging Operations

In this study, the external magnetic field emitted by a wireless power transfer (WPT) system and the internal electric field induced in human body models during recharging operations of a compact electric vehicle (EV) are evaluated. The magneticfield is calculated with a hybrid scheme coupling the boundary element method with the surface impedance boundary conditions in order to fit the multiscale open-boundary characteristics of the problem. A commercial software is then used to perform numerical dosimetry. Specifically, two realistic anatomical models, both in a driving position and in a standing posture, are considered, and the chassis of the EV is modeled either as a currently employed aluminum alloy and as a futuristic carbon fiber composite panel. Aligned and misaligned coil configurations of the WPT system are considered as well. The analysis of the obtained results shows that the International Commission on Non-Ionizing Radiation Protection (ICNIRP) reference levels are exceeded in the driving position, especially for the carbon fiber chassis, whereas the system is compliant with the basic restrictions, at least for the considered scenarios.

Effect of Loudspeakers on the In Situ Electric Field in a Driver Body Model Exposed to an Electric Vehicle Wireless Power Transfer System

This study computationally evaluates the effect of loudspeakers on the in situ electric field in a driver body model exposed to the magnetic field from a wireless power transfer (WPT) system in an electric vehicle (EV), one with a body made of carbon fiber reinforced plastic (CFRP) and the other made with aluminum. A quasi-static two-step approach was applied to compute the in situ electric field. The computational results showed that the magnetic field distribution generated by the WPT is significantly altered around the loudspeakers, and shows obvious discontinuity and local enhancement. The maximum spatial-average magnetic field strength in the driver’s body was increased by 11% in the CFRP vehicle. It was 2.25 times larger than the reference levels (RL) prescribed in the International Commission of Non-Ionizing Radiation Protection (ICNIRP) guidelines in 2010. In addition, we found that the in situ electric field computed by the line- and volume-averaging methods were stable if the top 0.1% voxels are excluded. The maximum value was well below the basic restriction (BR) of the ICNIRP guidelines. Nevertheless, the presence of the loudspeaker led to increments in the electric field strength in parts of the human body, suggesting the potential influence of permissible transmitting power in the WPT system. The maximum electric field strength in the thigh and buttock with the woofer, increased by 27% in the CFRP vehicle. The arm value was up to 3 times higher than that obtained without the tweeter in the aluminum vehicle. Moreover, this study found that the maximum electric field strength depended on the location of the loudspeaker with respect to the WPT system and the separation from the driver model. Therefore, the loudspeaker should be considered when evaluating the maximum in situ electric field strength in the vehicle body design stage.

Gaps in Knowledge Relevant to the "Guidelines for Limiting Exposure to Time-Varying Electric and Magnetic Fields (1 Hz-100 kHz)"

Sources of low-frequency fields are widely found in modern society. All wires or devices carrying or using electricity generate extremely low frequency (ELF) electric fields (EFs) and magnetic fields (MFs), but they decline rapidly with distance to the source. High magnetic flux densities are usually found in the vicinity of power lines and close to equipment using strong electrical currents, but can also be found in buildings with unbalanced return currents, or indoor transformer stations. For decades, epidemiological as well as experimental studies have addressed possible health effects of exposure to ELF-MFs. The main goal of ICNIRP is to protect people and the environment from detrimental exposure to all forms of non-ionizing radiation (NIR). To this end, ICNIRP provides advice and guidance by developing and disseminating exposure guidelines based on the available scientific research. Research in the low-frequency range began more than 40 years ago, and there is now a large body of literature available on which ICNIRP set its protection guidelines. A review of the literature has been carried out to identify possible relevant knowledge gaps, and the aim of this statement is to describe data gaps in research that would, if addressed, assist ICNIRP in further developing guidelines and setting revised recommendations on limiting exposure to electric and magnetic fields. It is articulated in two parts: the main document, which reviews the science related to LF data gaps, and the annex, which explains the methodology used to identify the data gaps.

Effects of a Wireless Charging System Built for An Electric Kick Scooter on Human Biological Tissue

In this paper, the authors present an evaluation of the electromagnetic fields generated by a static wireless charging system designed for an electric kick scooter on the human biological tissue. The guidelines on the exposure to the electromagnetic fields are previously specified. In this work, a model is designed under COMSOL multi-physics to study the effects of the magnetic field on two possible body parts of a person, which might be exposed to this field, namely the head and the hands is analysed. The magnetic flux density, the induced electrical field, the specific absorption rate, and the resulting increase of temperature of biological tissues are modelled and compared to the limits and guidelines prescribed in the regulation established to limit the exposure of people to electromagnetic fields. Furthermore, the used wireless charging system is modified to operate at higher frequencies to study its effect. The obtained results are below the guidelines and limits of exposure to the electromagnetic fields specified by the International Commission on Non-Ionizing Radiation Protection, European Commission, Institute of Electrical and Electronics Engineers and International Electrotechnical Commission.

Conditions for numerically accurate TMS electric field simulation

BACKGROUND

Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking.

OBJECTIVE

To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup.

METHOD

We benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods.

RESULTS

To achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled.

CONCLUSION

BEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.

Evaluating exposure from electric fields in a high voltage switchyard according to the EU directive

An assessment according to Directive 2013/35/EU of exposure in a 400 kV switchyard has been performed. Part of the body was exposed to electric field strength above the high action level. We therefore performed simulations of the electric fields induced in the body to assess these accoding to the exposure limit values (ELVs). The simulations show that as long as the body is not grounded nor touching any grounded metallic objects, worker exposure is compliant with the directive. When grounded metallic objects are touched with hand or foot the ELV are exceeded. The ELV is exceeded already at very low contact currents (2-3 μA) in the finger. If not appropriate measures are taken, this would lead to a severe limitation of the work tasks that can be performed in switchyards.

Impact of non-brain anatomy and coil orientation on inter- and intra-subject variability in TMS at midline

OBJECTIVE

To investigate inter-subject variability with respect to cerebrospinal fluid thickness and brain-scalp distance, and to investigate intra-subject variability with different coil orientations.

METHODS

Simulations of the induced electric field (E-Field) using a figure-8 coil over the vertex were conducted on 50 unique head models and varying orientations on 25 models. Metrics exploring stimulation intensity, spread, and localization were used to describe inter-subject variability and effects of non-brain anatomy.

RESULTS

Both brain-scalp distance and CSF thickness were correlated with weaker stimulation intensity and greater spread. Coil rotations show that for the dorsal portion of the stimulated brain, E-Field intensities are highest when the anterior-posterior axis of the coil is perpendicular to the longitudinal fissure, but highest for the medial portion of the stimulated brain when the coil is oriented parallel to the longitudinal fissure.

CONCLUSIONS

Normal anatomical variation in healthy individuals leads to significant differences in the site of TMS, the intensity, and the spread. These variables are generally neglected but could explain significant variability in basic and clinical studies.

SIGNIFICANCE

This is the first work to show how brain-scalp distance and cerebrospinal fluid thickness influence focality, and to show the disassociation between dorsal and medial TMS.

A high-resolution computational localization method for transcranial magnetic stimulation mapping

BACKGROUND

Transcranial magnetic stimulation (TMS) is used for the mapping of brain motor functions. The complexity of the brain deters determining the exact localization of the stimulation site using simplified methods (e.g., the region below the center of the TMS coil) or conventional computational approaches.

OBJECTIVE

This study aimed to present a high-precision localization method for a specific motor area by synthesizing computed non-uniform current distributions in the brain for multiple sessions of TMS.

METHODS

Peritumoral mapping by TMS was conducted on patients who had intra-axial brain neoplasms located within or close to the motor speech area. The electric field induced by TMS was computed using realistic head models constructed from magnetic resonance images of patients. A post-processing method was implemented to determine a TMS hotspot by combining the computed electric fields for the coil orientations and positions that delivered high motor-evoked potentials during peritumoral mapping. The method was compared to the stimulation site localized via intraoperative direct brain stimulation and navigated TMS.

RESULTS

Four main results were obtained: 1) the dependence of the computed hotspot area on the number of peritumoral measurements was evaluated; 2) the estimated localization of the hand motor area in eight non-affected hemispheres was in good agreement with the position of a so-called "hand-knob"; 3) the estimated hotspot areas were not sensitive to variations in tissue conductivity; and 4) the hand motor areas estimated by this proposal and direct electric stimulation (DES) were in good agreement in the ipsilateral hemisphere of four glioma patients.

CONCLUSION(S)

The TMS localization method was validated by well-known positions of the "hand-knob" in brains for the non-affected hemisphere, and by a hotspot localized via DES during awake craniotomy for the tumor-containing hemisphere.

Numerical assessment of low-frequency dosimetry from sampled magnetic fields

Low-frequency dosimetry is commonly assessed by evaluating the electric field in the human body using the scalar potential finite difference method. This method is effective only when the sources of the magnetic field are completely known and the magnetic vector potential can be analytically computed. The aim of the paper is to present a rigorous method to characterize the source term when only the magnetic flux density is available at discrete points, e.g. in case of field measurements. The method is based on the solution of the discrete magnetic curl equation. The system is restricted to the independent set of magnetic fluxes and circulations of magnetic vector potential using the topological information of the computational mesh. The solenoidality of the magnetic flux density is preserved using a divergence-free interpolator based on vector radial basis functions. The analysis of a benchmark problem shows that the complexity of the proposed algorithm is linearly dependent on the number of elements with a controllable accuracy. The method proposed in this paper also proves to be useful and effective when applied to a real world scenario, where the magnetic flux density is measured in proximity of a power transformer. A 8 million voxel body model is then used for the numerical dosimetric analysis. The complete assessment is completed in less than 5 min, that is more than acceptable for these problems.

Systematic Numerical Analysis of Magnetic Field Partial Body Exposure and Comparison With Occupational Exposure Limit Values According to European Directive 2013/35/EU

According to European Directive 2013/35/EU, exposure limit values for protection against sensory and health effects are met if external electric or magnetic fields are below corresponding low and high action levels for head, trunk and limb exposure, respectively. In order to verify this assumption even for more realistic exposure situations deviating from strictly uniform fields, systematic numerical computations using anatomical body models exposed to worst-case magnetic field gradients in different body regions are conducted. Applying magnetic fields according to low action level to the head and high action level to trunk and limbs at the same time results in slightly increased in situ electric field strengths in central nervous system tissues, compared to uniform exposure at the low action level. The extent of this increase depends on field orientation, field gradient (slope from low to high action level), and relative position between body region and field gradient. While this increase does not lead to conflicts with the exposure limit values for frequencies of 50 Hz and higher, violation of corresponding exposure limit values could be observed at 16.67 Hz.

Equivalent magnetic vector potential model for low-frequency magnetic exposure assessment

In this paper, a novel source model based on a magnetic vector potential for the assessment of induced electric field strength in a human body exposed to the low-frequency (LF) magnetic field of an electrical appliance is presented. The construction of the vector potential model requires only a single-component magnetic field to be measured close to the appliance under test, hence relieving considerable practical measurement effort-the radial basis functions (RBFs) are adopted for the interpolation of discrete measurements; the magnetic vector potential model can then be directly constructed by summing a set of simple algebraic functions of RBF parameters. The vector potentials are then incorporated into numerical calculations as the equivalent source for evaluations of the induced electric field in the human body model. The accuracy and effectiveness of the proposed model are demonstrated by comparing the induced electric field in a human model to that of the full-wave simulation. This study presents a simple and effective approach for modelling the LF magnetic source. The result of this study could simplify the compliance test procedure for assessing an electrical appliance regarding LF magnetic exposure.

Magnetic Field Reference Levels for Arbitrary Periodic Waveforms for Prevention of Peripheral Nerve Stimulation

Guidelines for prevention of peripheral nerve stimulation from exposure to low frequency magnetic fields have been developed by standard-setting bodies. Exposure limits or reference levels (RLs) are typically set in terms of the maximum root-mean-square amplitude of a sinusoidal waveform; however, environmental flux densities are often periodic, non-sinusoidal waveforms. This work presents a procedure for deriving RLs for any generalized periodic waveform using the empirical nerve-stimulation threshold data obtained from human volunteer MRI experiments. For this purpose, the "Law of Electrostimulation" (LOE), which sets forth conditions of a waveform necessary to trigger the action potential required to depolarize cell membranes, is applied to various waveforms. The results of the LOE analysis are waveform-specific, amplitude thresholds of stimulation that are found in terms of the empirically-derived rheobase threshold time-rate-of-change flux density and chronaxie from trapezoidal pulse MRI experiments. The thresholds are converted to amplitude RLs in two asymptotic frequency regimes as per the usual practice in standard setting. The resulting RLs have the same frequency dependence as in existing standards (i.e., inverse-frequency below a transition frequency and flat above). It is shown that the transition frequency is dependent only on the shape of the waveform. Both sinusoidal and non-sinusoidal waveforms have identical peak-to-peak amplitude RLs above their respective transition frequencies. Below these frequencies, all peak-to-peak amplitude RLs have the same functional dependence on frequency when the frequency is normalized to the waveform-specific transition frequency. This results in simple criteria for testing the amplitude of any arbitrary periodic waveform against potential for stimulation. These criteria are compared to guidance given for non-sinusoidal waveforms in the ICNIRP 1 Hz-100 kHz exposure standard.

The effects of human height and mass on the calculated induced electric fields at 50 Hz for comparison with the EMF Directive 2013/35/EU

A worker's height and mass can significantly affect the way in which incident low frequency electric and magnetic fields are absorbed in the body. To investigate this, several anatomically realistic human models were produced for heights between 1.56 and 1.96 m and masses between 33 and 113 kg. The human models were derived from the MAXWEL surface-based phantom, the model previously used in the EMF Directive 2013/35/EU Practical Guide to demonstrate how induced electric fields in the body are calculated. Computer simulations were carried out to calculate the low frequency EMF directive exposure limit value (ELV) quantities, i.e. the induced electric fields, in these human model variations from exposure to external 50 Hz magnetic and electric fields. The computational work showed that simple relationships relating the human model's height/weight with the induced electric fields in tissue types such as bone, fat, muscle, brain, spinal cord and retina could be developed. Calculations of parameters that affected absorption and fields required to produce the EMF Directive ELVs were carried out and compared with the action levels (ALs). It was found that the ALs generally provided a conservative estimate of the ELVs for the various human models and exposure situations studied.

Electric field induced in the human body by uniform 50 Hz electric or magnetic fields: bibliography analysis and method for conservatively deriving measurable limits

Health guidelines for electric and magnetic fields in the low frequency range define exposure limits for electric and magnetic fields in terms of induced electric field in the human body, which is not directly measurable, requiring use of dosimetry. However many parameters, such as human models, calculation codes and post-processing methods influence the calculation results. Based upon many published papers and therefore covering a wide range of these influence parameters, this paper proposes a method for conservatively deriving measurable levels of electric and magnetic fields equivalent to the basic restrictions. Following this method, we found that, regarding exposure to uniform fields, the ICNIRP 2010 occupational basic restrictions are equivalent to a 2 mT and 7 mT magnetic field and to a 35 kV m^-1 and 35 kV m^-1 electric field at 50 Hz when applied respectively to the central and peripheral nervous system.

Low-frequency electrical dosimetry: research agenda of the IEEE International Committee on Electromagnetic Safety

This article treats unsettled issues in the use of numerical models of electrical dosimetry as applied to international limits on human exposure to low-frequency (typically  <  100 kHz) electromagnetic fields and contact current. The perspective in this publication is that of Subcommittee 6 of IEEE-ICES (International Committee on Electromagnetic Safety) Technical Committee 95. The paper discusses 25 issues needing attention, fitting into three general categories: induction models; electrostimulation models; and human exposure limits. Of these, 9 were voted as 'high priority' by members of Subcommittee 6. The list is presented as a research agenda for refinements in numerical modeling with applications to human exposure limits. It is likely that such issues are also important in medical and electrical product safety design applications.

Direct control of the temperature rise in parallel transmission by means of temperature virtual observation points: Simulations at 10.5 Tesla

PURPOSE

A method using parallel transmission to mitigate B1+ inhomogeneity while explicitly constraining the temperature rise is reported and compared with a more traditional SAR-constrained pulse design.

METHODS

Finite difference time domain simulations are performed on a numerical human head model and for a 16-channel coil at 10.5 Tesla. Based on a set of presimulations, a virtual observation point compression model for the temperature rise is derived. This compact representation is then used in a nonlinear programming algorithm for pulse design under explicit temperature rise constraints.

RESULTS

In the example of a time-of-flight sequence, radiofrequency pulse performance in some cases is increased by a factor of two compared with SAR-constrained pulses, while temperature rise is directly and efficiently controlled. Pulse performance can be gained by relaxing the SAR constraints, but at the expense of a loss of direct control on temperature.

CONCLUSION

Given the importance of accurate safety control at ultrahigh field and the lack of direct correspondence between SAR and temperature, this work motivates the need for thorough thermal studies in normal in vivo conditions. The tools presented here will possibly contribute to safer and more efficient MR exams.

Computational dosimetry for child and adult human models due to contact current from 10 Hz to 110 MHz

This study computationally investigates in situ electric field due to low-frequency contact current and specific absorption rate (SAR) due to high-frequency contact currents in a realistic child model and compared with those in the adult model. The in situ electric fields and SAR in the child model are found to exceed the corresponding values in the adult. At the finger tip, the electric field and SAR due to contact currents, both at the ICNIRP reference levels and IEEE Maximum Permissible Exposures, are well beyond the corresponding basic restrictions. In the remaining part, the largest difference was observed in spinal tissue, and the smallest effect was in the heart. With respect to brain and skin conductivities, one needs to strongly consider which values of tissue properties are used to interpret one's results. The in situ electric fields resulting from contact with the metal plane are similar to those for contact with the wire.

Dosimetric Uncertainties: Magnetic Field Coupling to Peripheral Nerve

The International Commission on Non-ionizing Radiation Protection (ICNIRP) and the Institute for Electrical and Electronic Engineers (IEEE) have established magnetic field exposure limits for the general public between 400 Hz (ICNIRP)/759 Hz (IEEE) and 100 kHz to protect against adverse effects associated with peripheral nerve stimulation (PNS). Despite apparent common purpose and similarly stated principles, the two sets of limits diverge between 3.35-100 kHz by a factor of about 7.7 with respect to PNS. To address the basis for this difference and the more general issue of dosimetric uncertainty, this paper combines experimental data of PNS thresholds derived from human subjects exposed to magnetic fields together with published estimates of induced in situ electric field PNS thresholds to evaluate dosimetric relationships of external magnetic fields to induced fields at the threshold of PNS and the uncertainties inherent to such relationships. The analyses indicate that the logarithmic range of magnetic field thresholds constrains the bounds of uncertainty of in situ electric field PNS thresholds and coupling coefficients related to the peripheral nerve (the coupling coefficients define the dosimetric relationship of external field to induced electric field). The general public magnetic field exposure limit adopted by ICNIRP uses a coupling coefficient that falls above the bounds of dosimetric uncertainty, while IEEE's is within the bounds of uncertainty toward the lower end of the distribution. The analyses illustrate that dosimetric estimates can be derived without reliance on computational dosimetry and the associated values of tissue conductivity. With the limits now in place, investigative efforts would be required if a field measurement were to exceed ICNIRP's magnetic field limit (the reference level), even when there is a virtual certainty that the dose limit (the basic restriction) has not been exceeded. The constraints on the range of coupling coefficients described in this paper could facilitate a re-evaluation of ICNIRP and IEEE dose and exposure limits and possibly lead toward harmonization.

Human exposure standards in the frequency range 1 Hz To 100 kHz: the case for adoption of the IEEE standard

Differences between IEEE C95 Standards (C95.6-2002 and C95.1-2005) in the low-frequency (1 Hz-100 kHz) and the ICNIRP-2010 guidelines appear across the frequency spectrum. Factors accounting for lack of convergence include: differences between the IEEE standards and the ICNIRP guidelines with respect to biological induction models, stated objectives, data trail from experimentally derived thresholds through physical and biological principles, selection and justification of safety/reduction factors, use of probability models, compliance standards for the limbs as distinct from the whole body, defined population categories, strategies for central nervous system protection below 20 Hz, and correspondence of environmental electric field limits with contact currents. This paper discusses these factors and makes the case for adoption of the limits in the IEEE standards.

On the issues related to compliance assessment of ICNIRP 2010 basic restrictions

This article discusses technical issues related to compliance assessment of ICNIRP 2010 basic restrictions. Several difficulties are identified in this study when assessing the spatial average and 99th percentile value of the electric field. These issues are mainly attributed to the lack of clarity in the guideline specifications, which leads to inadequate or irreproducible results. Effects on compliance results due to such ambiguous procedures are hereby investigated, with particular focus on technical issues rather than biological ones. Examples spanning from simple canonical test cases to realistic applications have been selected to highlight the strong variability in dosimetry results. Based on our findings, revisiting the ICNIRP 2010 guidelines is strongly recommended, and proposed alternative solutions are outlined.

Experimental and numerical assessment of low-frequency current distributions from UMTS and GSM mobile phones

The evaluation of the exposure from mobile communication devices requires consideration of electromagnetic fields (EMFs) over a broad frequency range from dc to GHz. Mobile phones in operation have prominent spectral components in the low-frequency (LF) and radio-frequency (RF) ranges. While the exposure to RF fields from mobile phones has been comprehensively assessed in the past, the LF fields have received much less attention. In this study, LF fields from mobile phones are assessed experimentally and numerically for the global system for mobile (GSM) and universal mobile telecommunications system (UMTS) communication systems and conclusions about the global (LF and RF) EMF exposure from both systems are drawn. From the measurements of the time-domain magnetic fields, it was found that the contribution from the audio signal at a normal speech level, i.e., -16 dBm0, is the same order of magnitude as the fields induced by the current bursts generated from the implementation of the GSM communication system at maximum RF output level. The B-field induced by currents in phones using the UMTS is two orders of magnitude lower than that induced by GSM. Knowing that the RF exposure from the UMTS is also two orders of magnitude lower than from GSM, it is now possible to state that there is an overall reduction of the exposure from this communication system.

Exposure of high resolution fetuses in advanced pregnant woman models at different stages of pregnancy to uniform magnetic fields at the frequency of 50 Hz

Extremely low frequency magnetic fields (ELF-MF) have been considered as a possible risk factor for childhood leukemia by several epidemiological studies. In this work the exposure assessment of fetuses at 3, 7 and 9 months of Gestational Age (GA) to differently polarized uniform magnetic fields at the frequency of 50 Hz by means of high resolution numerical models of pregnant women is carried out. This set of models is used to analyze the fetal tissue-specific induced electric fields and current densities as a function of both the incident magnetic field polarization and the GA.

Evaluation of the induced electric field and compliance procedure for a wireless power transfer system in an electrical vehicle

In this study, an induced electric field in a human body is evaluated for the magnetic field leaked from a wireless power transfer system for charging an electrical vehicle. The magnetic field from the wireless power transfer system is modelled computationally, and its effectiveness is confirmed by comparison with the field measured in a previous study. The induced electric field in a human standing around the vehicle is smaller than the allowable limit prescribed in international guidelines, although the magnetic field strength in the human body is locally higher than the allowable external field strength. Correlation between the external magnetic field and the induced electric field is confirmed to be reasonable at least in the standing posture, which is the case discussed in the international standard. Based on this finding, we discussed and confirmed the applicability of a three-point magnetic field measurement at heights of 0.5, 1.0, and 1.5 m for safety compliance.

Computational dosimetry for grounded and ungrounded human models due to contact current

This study presents the computational dosimetry of contact currents for grounded and ungrounded human models. The uncertainty of the quasi-static (QS) approximation of the in situ electric field induced in a grounded/ungrounded human body due to the contact current is first estimated. Different scenarios of cylindrical and anatomical human body models are considered, and the results are compared with the full-wave analysis. In the QS analysis, the induced field in the grounded cylindrical model is calculated by the QS finite-difference time-domain (QS-FDTD) method, and compared with the analytical solution. Because no analytical solution is available for the grounded/ungrounded anatomical human body model, the results of the QS-FDTD method are then compared with those of the conventional FDTD method. The upper frequency limit for the QS approximation in the contact current dosimetry is found to be 3 MHz, with a relative local error of less than 10%. The error increases above this frequency, which can be attributed to the neglect of the displacement current. The QS or conventional FDTD method is used for the dosimetry of induced electric field and/or specific absorption rate (SAR) for a contact current injected into the index finger of a human body model in the frequency range from 10 Hz to 100 MHz. The in situ electric fields or SAR are compared with the basic restrictions in the international guidelines/standards. The maximum electric field or the 99th percentile value of the electric fields appear not only in the fat and muscle tissues of the finger, but also around the wrist, forearm, and the upper arm. Some discrepancies are observed between the basic restrictions for the electric field and SAR and the reference levels for the contact current, especially in the extremities. These discrepancies are shown by an equation that relates the current density, tissue conductivity, and induced electric field in the finger with a cross-sectional area of 1 cm(2).

The role of skin conductivity in a low frequency exposure assessment for peripheral nerve tissue according to the ICNIRP 2010 guidelines

Based on numerical computations using commercially available finite difference time domain code and a state-of-the art anatomical model of a 5-year old child, the influence of skin conductivity on the induced electric field strength inside the tissue for homogeneous front-to-back magnetic field exposure and homogeneous vertical electric field exposure was computed. Both ungrounded as well as grounded conditions of the body model were considered. For electric field strengths induced inside CNS tissue the impact of skin conductivity was found to be less than 15%. However, the results demonstrated that the use of skin conductivity values as obtainable from the most widely used data base of dielectric tissue properties and recommended by safety standards are not suitable for exposure assessment with respect to peripheral nerve tissue according to the ICNIRP 2010 guidelines in which the use of the induced electric field strengths inside the skin is suggested as a conservative surrogate for peripheral nerve exposure. This is due to the fact that the skin conductivity values derived from these data bases refer to the stratum corneum, the uppermost layer of the skin, which does not contain any nerve or receptor cells to be protected from stimulation effects. Using these skin conductivity values which are approximately a factor 250-500 lower than skin conductivity values used in studies on which the ICNIRP 2010 guidelines are based on, may lead to overestimations of the induced electric field strengths inside the skin by substantially more than a factor of 10. However, reliable conductivity data of deeper skin layers where nerve and preceptor cells are located is very limited. It is therefore recommended to include appropriate background information in the ICNIRP guidelines and the dielectric tissue property databases, and to put some emphasis on a detailed layer-specific characterization of skin conductivity in near future.