Electrical phosphenes: on the influence of conductivity inhomogeneities and small-scale structures of the orbita on the current density threshold of excitation

Electrical and magnetic phosphenes, perceptions of light as a result of non-adequate stimulation of the eye by electrical current or magnetic induction, respectively, are one of the cornerstones to justify limit values for extreme low-frequency fields specified by statutory regulations. However, the mechanism and place of action, as well as the excitation threshold, remain unknown until now. We suggest that the origin of phosphene excitation is the synaptic layer of the eye. The current density threshold value for electrical phosphene excitation was numerically quantified for this area on the basis of a detailed geometrical model in original submillimetre resolution and specifically measured conductivities in the LF range. The threshold values found were 1.8 Am⁻² at 60 Hz and 0.3 Am⁻² at 25 Hz. These values are comparable with values of other excitable tissues. It has been shown that the current density threshold for phosphene generation depends on small-scale structures not taken into account by previous models.     

The interference threshold of unipolar cardiac pacemakers in extremely low frequency magnetic fields

The effective induction loop area of implanted cardiac pacemaker (CPM) systems in magnetic fields was determined. The results were verified in a tank model placed in the centre of a Helmholtz-coil-arrangement. Both a left and a right pectorally implanted unipolar dual chamber CPM system were simulated. On this basis and with the results of benchmark-tests the interference thresholds for a collection of modern CPMs in extremely low frequency (ELF) magnetic fields were estimated. The investigations clearly showed that there are two loops, the CPM-lead-tissue-loop and the body loop, responsible for the magnitude of the disturbance voltage on the input of a cardiac pacemaker. The effective induction loop areas ranged from 100 to 221 cm2. For a left pectorally implanted, atrially controlled CPM system the interference thresholds for the magnetic induction lay between 16 and 552 µ T (RMS) for frequencies of the magnetic field between 10 and 250 Hz. Thus, there is a limited possibility for an interference of implanted CPMs by ELF magnetic fields in everyday life.     

The interference threshold of unipolar cardiac pacemakers in extremely low frequency magnetic fields.

The effective induction loop area of implanted cardiac pacemaker (CPM) systems in magnetic fields was determined. The results were verified in a tank model placed in the centre of a Helmholtz-coil-arrangement. Both a left and a right pectorally implanted unipolar dual chamber CPM system were simulated. On this basis and with the results of benchmark-tests the interference thresholds for a collection of modern CPMs in extremely low frequency (ELF) magnetic fields were estimated. The investigations clearly showed that there are two loops, the CPM-lead-tissue-loop and the body loop, responsible for the magnitude of the disturbance voltage on the input of a cardiac pacemaker. The effective induction loop areas rangedfrom 100 to 221 cm2. For a left pectorally implanted, atrially controlled CPM system the interference thresholds for the magnetic induction lay between 16 and 552 micro T (RMS) for frequencies of the magneticfield between 10 and 250 Hz. Thus, there is a limited possibility for an interference of implanted CPM by ELF magnetic fields in everyday life.     

Volume conductor effects on the spatial resolution of magnetic fields and electric potentials from gastrointestinal electrical activity

An analysis of the relative capabilities of methods for magnetic and electric detection of gastrointestinal electrical activity is presented. The model employed is the first volume conductor model for magnetic fields from GEA to appear in the literature. A mathematical model is introduced for the electric potential and magnetic field from intestinal electrical activity in terms of the spatial filters that relate the bioelectric sources with the external magnetic fields and potentials. The forward spatial filters are low-pass functions of spatial frequency, so more superficial external fields and potentials contain less spatial information than fields and potentials near the source. Inverse spatial filters, which are reciprocals of the forward filters, are high-pass functions and must be regularised by windowing. Because of the conductivity discontinuities introduced by low-conductivity fat layers in the abdomen, the electric potentials recorded outside these layers required more regularisation than the magnetic fields, and thus, the spatial resolution of the magnetic fields from intestinal electrical activity is higher than the spatial resolution of the external potentials. In this study, two smooth muscle sources separated by 5 cm were adequately resolved magnetically, but not resolved electrically. Thus, sources are more accurately localized and imaged using magnetic measurements than using measurements of electric potential.     

Sensitivity of the amplitude of the single muscle fibre action potential to microscopic volume conduction parameters

A microscopic model of volume conduction was applied to examine the sensitivity of the single muscle fibre action potential to variations in parameters of the source and of the volume conductor, such as conduction velocity, intracellular conductivity and intracellular volume fraction. The model results show that the sensitivity to the intracellular and extracellular conductivity depends on the distance from the source. The action potential amplitude is strongly influenced by the intracellular volume fraction. In this frequency-dependent model the amplitude is influenced by the conduction velocity to a smaller degree than predicted by previous studies, which use a noncapacitive homogeneous volume conductor model.     

Electric fields induced in a spherical volume conductor by temporally varying magnetic field gradients

A homogeneous spherical volume conductor is used as a model system for the purpose of calculating electric fields induced in the human head by externally applied time-varying magnetic fields. We present results for the case where magnetic field gradient coils, used in magnetic resonance imaging (MRI), form the magnetic field, and we use these data to put limits on the rates of gradient change with time needed to produce nerve stimulation. The electric field is calculated analytically for the case of ideal longitudinal and transverse linear field gradients. We also show results from computer calculations yielding the electric field maps in a sphere when the field gradients are generated by a real MRI gradient coil set. In addition, the effect of shifting the sphere within each gradient coil volume is investigated. Numerical analysis shows similar results when applied to a model human head.     

A new magnetic resonance electrical impedance tomography (MREIT) algorithm: the RSM-MREIT algorithm with applications to estimation of human head conductivity

We have developed a new magnetic resonance electrical impedance tomography (MREIT) algorithm, the RSM-MREIT algorithm, for noninvasive imaging of the electrical conductivity distribution using only one component of magnetic flux density. The proposed RSM-MREIT algorithm uses the response surface methodology (RSM) algorithm for optimizing the conductivity distribution through minimizing the errors between the measured and calculated magnetic flux densities. A series of computer simulations has been conducted to assess the performance of the proposed RSM-MREIT algorithm to estimate electrical conductivity values of the scalp, the skull and the brain tissue, in a three-shell piecewise homogeneous head model. Computer simulation studies were conducted in both a spherical and realistic-geometry head model with a single variable (the brain-to-skull conductivity ratio) and three variables (the conductivity of the brain, the skull, and the scalp). The relative error between the target and estimated head conductivity values was less than 12% for both the single-variable and three-variable simulations. These promising simulation results demonstrate the feasibility of the proposed RSM-MREIT algorithm in estimating electrical conductivity values in a piecewise homogeneous head model of the human head, and suggest that the RSM-MREIT algorithm merits further investigation.     

On the magnetic field and the electrical potential generated by bioelectric sources in an anisotropic volume conductor

The electrical conductivity in biological tissue is often dependent on the direction of the fibres. In the paper the influence of this anisotropic nature on the electrical potential and magnetic field generated by a current dipole is studied analytically. Three different methods are discussed. The volume conductor is described by piecewise homogeneous compartments and the interfaces between compartments are either parallel or perpendicular to one of the principal axes. To illustrate the methods, the influence of the anisotropic nature is computed for a two-layered medium. It turns out that the influence on both the potential and the magnetic field cannot be ignored. However, for some commonly used models of the head and torso, a certain component of the magnetic field is not influenced by the anisotropy.     

The presence of unknown layer of skin and fat is an obstacle to a correct estimation of the motor unit size from surface detected potentials

To overcome problems with a strong distance-dependence of the motor unit potentials (MUPs), different methods to estimate the MU location and size have been proposed. Distance-independence of the exponent of the power function, that describes the MUP distance decline, and homogeneity of the volume conductor, are assumed in all methods. Some of them consider the exponent value as unique, irrespective of persons, muscles and their functional state. One method estimates the current exponent value. We evaluate this method by computer simulation of MUPs in infinite and semi-infinite volume conductor. Our results show that although the first assumption is not fulfilled, it does not affect considerably the estimate of the MU location and size obtained for infinite or semi-infinite homogeneous volume conductor. The errors of the MU location can be insignificant even in inhomogeneous volume conductor with a layer of lower conductivity (skin and fat) between the muscle tissue and electrode. The accurate location of the MU electrical axis is, however, not a sufficient condition for a correct MU size estimation that depends considerably on actual parameters of the layer. Thus, the surface EMG could hardly be considered as non-invasive alternative to macro EMG for detection of the enlarged MUs.     

The lack of evidence for ELF magnetic-field effects on bilayer membranes and reconstituted membrane channels

The effects of low-frequency (10-500 Hz) magnetic fields on the electrical properties of channel-free bilayer membranes, and on the single-channel conductance and macroscopic gating characteristics of porin channels incorporated into membranes, have been studied for field strengths in the range 10-100 microT. The field conditions that could in theory give rise to 'cyclotron resonance' effects were also studied. No evidence has been found to support the concept that cyclotron resonance and membrane ion channel effects are involved in the reported biological effects of ELF magnetic fields.     

Effects of 50 Hz electromagnetic fields on electroencephalographic alpha activity, dental pain threshold and cardiovascular parameters in humans

Recent studies indicate that exposure to extremely low frequency magnetic fields (ELF MFs) influences human electroencephalographic (EEG) alpha activity and pain perception. In the present study we analyse the effect on electrical EEG activity in the alpha band (8-13 Hz) and on nociception in 40 healthy male volunteers after 90-min exposure of the head to 50 Hz ELF MFs at a flux density of 40 or 80 microT in a double-blind randomized sham-controlled study. Since cardiovascular regulation is functionally related to pain modulation, we also measured blood pressure (BP) and heart rate (HR) during treatment. Alpha activity after 80 microT magnetic treatment almost doubled compared to sham treatment. Pain threshold after 40 microT magnetic treatment was significantly lower than after sham treatment. No effects were found for BP and HR. We suggest that these results may be explained by a modulation of sensory gating processes through the opioidergic system, that in turn is influenced by magnetic exposure.     

Sensitivity of EEG and MEG measurements to tissue conductivity

Monitoring the electrical activity inside the human brain using electrical and magnetic field measurements requires a mathematical head model. Using this model the potential distribution in the head and magnetic fields outside the head are computed for a given source distribution. This is called the forward problem of the electro-magnetic source imaging. Accurate representation of the source distribution requires a realistic geometry and an accurate conductivity model. Deviation from the actual head is one of the reasons for the localization errors. In this study, the mathematical basis for the sensitivity of voltage and magnetic field measurements to perturbations from the actual conductivity model is investigated. Two mathematical expressions are derived relating the changes in the potentials and magnetic fields to conductivity perturbations. These equations show that measurements change due to secondary sources at the perturbation points. A finite element method (FEM) based formulation is developed for computing the sensitivity of measurements to tissue conductivities efficiently. The sensitivity matrices are calculated for both a concentric spheres model of the head and a realistic head model. The rows of the sensitivity matrix show that the sensitivity of a voltage measurement is greater to conductivity perturbations on the brain tissue in the vicinity of the dipole, the skull and the scalp beneath the electrodes. The sensitivity values for perturbations in the skull and brain conductivity are comparable and they are, in general, greater than the sensitivity for the scalp conductivity. The effects of the perturbations on the skull are more pronounced for shallow dipoles, whereas, for deep dipoles, the measurements are more sensitive to the conductivity of the brain tissue near the dipole. The magnetic measurements are found to be more sensitive to perturbations near the dipole location. The sensitivity to perturbations in the brain tissue is much greater when the primary source is tangential and it decreases as the dipole depth increases. The resultant linear system of equations can be used to update the initially assumed conductivity distribution for the head. They may be further exploited to image the conductivity distribution of the head from EEG and/or MEG measurements. This may be a fast and promising new imaging modality.     

Magnetic stimulation of axons in a nerve bundle: Effects of current redistribution in the bundle

Recently, we developed a model of magnetic stimulation of a concentric axon in an anisotropic nerve bundle. In that earlier paper, we considered a single axon surrounded by a nerve bundle represented as a homogeneous anisotropic monodomain medium. In this paper we extend our previous calculations to examine excitation of axons within a nerve bundle without neglecting the presence of other axons in the nerve bundle. A three-dimensional axial symmetry volume conductor model is used to determine the transmembrane potential response along an axon due to induced electric fields produced by a toroidal coil. Our principal objective is to examine the effect of current redistribution to other axons in the bundle on excitation characteristics. We derive the transmembrane potential along an axon for two currently available models of current redistribution: the biodomain model and the spatial-frequency monodomain model. Results indicate that a reduction in the transmembrane potential along an axon due to the presence of other nerve fibers in the bundle is observed. Axons located at the periphery of a nerve bundle have lower thresholds and different excitation sites compared with axons located near the center of a nerve bundle.     

Induction of kinetochore-positive and kinetochore-negative micronuclei in CHO cells by ELF magnetic fields and/or X-rays

To test the genotoxic effects of extremely low frequency (ELF) magnetic fields, the induction of micronuclei by exposure to ELF magnetic fields and/or X-rays was investigated in cultured Chinese hamster ovary (CHO) cells, using the cytokinesis block method. Micronuclei derived from acentric fragments or from whole chromosomes were evaluated by immunofluorescent staining using anti-kinetochore antibodies from the serum of scleroderma (CREST syndrome) patients. A 60 Hz ELF magnetic field at 5 mT field strength was applied, either before or after 1 Gy X-ray irradiation or without additional X-ray irradiation. No statistically significant difference in the frequency of micronuclei in CHO cells was observed between a sham exposure (no exposure to an ELF magnetic field) and a 24 h ELF magnetic field exposure. Exposure to an ELF magnetic field for 24 h before X-ray irradiation or for 18 h after X-ray irradiation did not affect the frequency of X-ray-induced micronuclei. However, the number of kinetochore-positive micronuclei was significantly increased in the cells subjected to X-ray irradiation followed by ELF magnetic field exposure, but not in the cells treated with ELF magnetic field exposure before X-ray irradiation, compared with exposure to X-rays alone. The number of spontaneous kinetochore-positive and kinetochore-negative micronuclei was not affected by exposure to an ELF magnetic field alone. Our data suggest that exposure to an ELF magnetic field has no effect on the number of spontaneous and X-ray-induced micronuclei. However, ELF magnetic field exposure after but not before X-ray irradiation may somehow accelerate X-ray-induced lagging of whole chromosomes (or centric fragments) in CHO cells.     

Magnetophosphenes: a quantitative analysis of thresholds

Low-frequency and transient magnetic fields of moderate flux densities are known to generate visual phenomena, so-called magnetophosphenes. In the present study, time-variable very low frequency (10–50 Hz) electromagnetic fields of moderate flux density (0–40 mT) were used to induce magnetophosphenes. The threshold values for these phosphenes were determined as a function of the frequency of the magnetic field both in normal subjects and colour defective ones. Maximum sensitivity occurred at a frequency of approximately 20–30 Hz, and with broad-spectrum light the threshold flux density was 10–12 mT. The threshola values were found to be dependent upon the intensity and the spectral distribution of the background light. Sensitivity decreased during dark adaptation. In certain respects deutans differed from subjects with normal colour vision. Possible mechanisms for generation of magnetophosphenes are discussed. The present magnetic threshold curves show a close resemblance to corresponding curves obtained by electric stimulation at various frequencies provided the electric thresholds are divided by the a.c. frequency. These problems are under current investigation in our laboratory. This is in full agreement with the assumption that the fluctuating magnetic field affects retinal neurons by inducing currents which polarise synaptic terminals.     

Tissue heterogeneity as a mechanism for localized neural stimulation by applied electric fields

We investigate the heterogeneity of electrical conductivity as a new mechanism to stimulate excitable tissues via applied electric fields. In particular, we show that stimulation of axons crossing internal boundaries can occur at boundaries where the electric conductivity of the volume conductor changes abruptly. The effectiveness of this and other stimulation mechanisms was compared by means of models and computer simulations in the context of transcranial magnetic stimulation. While, for a given stimulation intensity, the largest membrane depolarization occurred where an axon terminates or bends sharply in a high electric field region, a slightly smaller membrane depolarization, still sufficient to generate action potentials, also occurred at an internal boundary where the conductivity jumped from 0.143 S m(-1) to 0.333 S m(-1), simulating a white-matter-grey-matter interface. Tissue heterogeneity can also give rise to local electric field gradients that are considerably stronger and more focal than those impressed by the stimulation coil and that can affect the membrane potential, albeit to a lesser extent than the two mechanisms mentioned above. Tissue heterogeneity may play an important role in electric and magnetic 'far-field' stimulation.     

Computation of neuromagnetic fields using finite-element method and Biot-Savart law

The finite-element method in combination with the Biot-Savart law is described to compute the magnetic field distribution generated by a dipolar source within a homogeneous volume conductor of an arbitrary shape. In order to calculate the three independent components of the magnetic field outside the volume conductor by means of the Biot-Savart law, the distribution of the current throughout the medium is required. A finite-element mesh is constructed using four-node tetrahedral elements. The potential in each node is computed numerically by the finite-element method using the proper continuity conditions across the boundaries. The gradient of the potential denotes the current density within an element. The components of the magnetic induction are calculated by numerical integration, applying the current density within the tetrahedrons. Simulations are carried out to assess the numerical accuracy for a homogeneous spherical volume conductor. Errors of 3% can be obtained with a locally refined spherical mesh containing about 1000 nodes, for dipoles at any depth and any orientation. A homogeneous realistically shaped model with the shape of the inside of the skull is obtained from magnetic resonance images.     

Effects of volume conductor and source configuration on simulated magnetogastrograms

Recordings of the magnetic fields (MFs) arising from gastric electrical activity (GEA) have been shown to be able to distinguish between normal and certain abnormal GEA. Mathematical models provide a powerful tool for revealing the relationship between the underlying GEA and the resultant magnetogastrograms (MGGs). However, it remains uncertain the relative contributions that different volume conductor and dipole source models have on the resultant MFs. In this study, four volume conductor models (free space, sphere, half space and an anatomically realistic torso) and two dipole source configurations (containing 320 moving dipole sources and a single equivalent moving dipole source) were used to simulate the external MFs. The effects of different volume conductor models and dipole source configurations on the MF simulations were examined. The half space model provided the best approximation of the MFs produced by the torso model in the direction normal to the coronal plane. This was despite the fact that the half space model does not produce secondary sources, which have been shown to contribute up to 50% of the total MFs when an anatomically realistic torso model was used. We conclude that a realistic representation of the volume conductor and a detailed dipole source model are likely to be necessary when using a model-based approach for interpreting MGGs.     

Modeling and source localization of MEG activities

Summary During the past decade, substantial advances in the understanding of the functional organization of the human brain have been made through the technique of MEG topographic mapping. Most of these investigations were concerned with the estimation and localization of sources which were modeled as single current dipoles positioned in a semi-infinite volume conductor with homogeneous conductivity. However, the sources in the brain are complex, and the head as a volume conductor consists of different materials with different electrical conductivities. The influence of these inhomogeneities on the MEG topography is studied by a computer simulation, modeling the sources as single or multiple dipoles located in inhomogeneous volume conductors. The computer simulation suggests some important aspects in estimation of source localization. The sources of MEG activities in human subject during sleep are also studied. A comparison of simulated MEG topographic patterns with measured data suggests that the sources of K-complexes can be modeled by two current dipoles. Sources for delta waves are analyzed by the FFT technique. The results show that the frequency distributions are different for delta waves measured by MEG and EEG techniques, leading us to conclude that at least two different sources are present. The MEG measurements have an advantage to provide important information concerning brain function which cannot be obtained using the EEG measurements.This work was supported in part by grants 63850090 and 01790390 from the Ministry of Education Science and Culture, Japan, and by grants from Nakatani Electric Measuring Technology Association, and the Mitsubishi Foundation.     

脑磁图研究的若干理论问题(上)——基本电磁学方程及脑磁正问题

本文概述了脑磁技术的发展历程、现状及潜在的临床价值。详细阐述了脑磁研究中使用的基本电磁学理论 ,包括描述电磁规律最基本的麦克斯韦方程组 ,生物电磁研究中麦氏方程的准静态近似条件 ,介质分区域均匀时计算电场、磁场的 Geselowitz公式。在准静态近似条件下 ,讨论了原在电流密度 (Primary current density)与脑外磁场的线性关系。阐述了脑磁正问题中常用的球对称导体模型解及基于真实头模型的边界元方法解。