The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.     

Comparison of coupling of humans to electric and magnetic fields with frequencies between 100 Hz and 100 kHz

Recent laboratory and epidemiological results have stimulated interest in the hypothesis that human beings may exhibit biological responses to magnetic and/or electric field transients with frequencies in the range between 100 Hz and 100 kHz. Much can be learned about the response of a system to a transient stimulation by understanding its response to sinusoidal disturbances over the entire frequency range of interest. Thus, the main effort of this paper was to compare the strengths of the electric fields induced in homogeneous ellipsoidal models by uniform 100 Hz through 100 kHz electric and magnetic fields. Over this frequency range, external electric fields of about 25–2000 V/m (depending primarily on the orientation of the body relative to the field) are required to induce electric fields inside models of adults and children that are similar in strength to those induced by an external 1 μT magnetic field. Additional analysis indicates that electric fields induced by uniform external electric and magnetic fields and by the nonuniform electric and magnetic fields produced by idealized point sources will not differ by more than a factor of two until the sources are brought close to the body. Published data on electric and magnetic field transients in residential environments indicate that, for most field orientations, the magnetic component will induce stronger electric fields inside adults and children than the electric component. This conclusion is also true for the currents induced in humans by typical levels of 60 Hz electric and magnetic fields in U.S. residences. Bioelectromagnetics 18:67–76, 1997. © 1997 Wiley-Liss, Inc.     

有限元法计算各向异性介质球头模型电位分布

在脑电正问题研究中,脑神经元所产生的电活动可用电流偶极子来模拟.本文提出把大脑看作各向异性介质球,即同时考虑电容效应、电导效应对脑内电流偶极子产生的电位的影响,并用有限元法推导出偶极子在各向异性介质球模型中的电位分布计算公式.结果表明介质的电容效应对电位分布是有影响的,反映了大脑活组织电特性,对外来不同频率的信号刺激有不同的响应.同时有限元法对大脑内某一区域内电位分布求解表明,测量较深层组织的电特性变化敏感的特点,可获得更多的测量信息.     

Miniature-probe measurements of electric fields induced by 60 Hz magnetic fields in rats

Extremely-low-frequency (ELF) magnetic fields interact with an animal by inducing internal electric fields, which represent the internal dose from an external exposure. In this study, an electric field probe of approximately 2 mm resolution was used to measure fields induced in rat carcasses by a 60 Hz magnetic field at 1 mT. With the rat lying on its side, the probe was inserted through a small hole in the body wall, and scanned at 5 mm increments from the side with frontal and axial exposure (field horizontal) and from the front with lateral exposure (field vertical). The induced electric field declined from a maximum at the entrance to the abdomen and crossed zero to negative (180° phase shift) values within the body as expected. In general, the magnitudes of the measurements inside the abdomen were less than expected from whole-body calculations that used homogeneous-ellipsoidal models of a rat in the three orientations. The low measurements did not appear to be explained by perpendicular field components, by conductivity differences between the tissue and the probe path, or by air in the lungs. The low measurements probably result from inhomogeneities in actual rats that include conductivity differences between tissues and biological membranes. For example, an alternative model considered the abdominal cavity to be electrically isolated from the body by the diaphragm and the peritoneum and calculations from this model were in better agreement with the measurements inside the abdomen (than were the whole-body calculations). Therefore, inhomogeneities in conductivity and biomembranes such as the peritoneum should be considered in order to fully understand ELF-induced field dosimetry. © 1996 Wiley-Liss, Inc.     

Model Studies of the Magnetocardiogram

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid.     

The influence of local tissue conductivity changes on the magnetoencephalogram and the electroencephalogram.

We examined the influence of local tissue conductivity changes in the vicinity of a dipolar source on the neuromagnetic field and the electric scalp potential using a high resolution finite element method model of the human head. We found that the topology of both the electric scalp potential and the neuromagnetic field (and consequently dipole localization) is influenced significantly by conductivity changes only in voxels adjacent to the source. Conductivity changes in these voxels yield a greater change in the amplitude of the magnetic field (and consequently in the dipole strength) than in the amplitude of the electric potential.     

On the calculation of magnetic fields based on multipole modeling of focal biological current sources.

Spatially restricted biological current distributions, like the primary neuronal response in the human somatosensory cortex evoked by electric nerve stimulation, can be described adequately by a current multipole expansion. Here analytic formulas are derived for computing magnetic fields induced by current multipoles in terms of an nth-order derivative of the dipole field. The required differential operators are given in closed form for arbitrary order. The concept is realized in different forms for an expansion of the scalar as well as the dyadic Green's function, the latter allowing for separation of those multipolar source components that are electrically silent but magnetically detectable. The resulting formulas are generally applicable for current sources embedded in arbitrarily shaped volume conductors. By using neurophysiologically relevant source parameters, examples are provided for a spherical volume conductor with an analytically given dipole field. An analysis of the signal-to-noise ratio for multipole coefficients up to the octapolar term indicates that the lateral extent of cortical current sources can be detected by magnetoencephalographic recordings.     

Characteristic features of electron-ion collisions in strong electric fields

The classical motion of an electron in the Coulomb field of an ion and in a uniform external electric field is analyzed. A nondimensionalization method that makes it possible to study electron motion in arbitrarily strong electric fields is proposed. The possible electron trajectories in the plane of motion in a static field are classified. It is noted that, from a practical standpoint, the most interesting trajectories are snakelike trajectories, which are absent in the problem with a weak external field. An adiabatic approximation for transverse electron motions in quasistatic (strong) fields is constructed. A one-dimensional equation of motion is derived that accounts for transverse electron oscillations and the increase in the effective electron mass as an electron approaches an ion. An analytic model is used to calculate the spectra of bremsstrahlung generated by individual electrons. The calculated results are shown to agree well with the results of direct numerical integration of the basic equations. It is predicted that, at frequencies higher than the frequency of the incident light, pronounced peaks can appear in the spectrum of the transverse dipole moment of an electron; as a result, an electron is expected to effectively emit radiation at these frequencies in the direction of the external field.     

Lorentz force electrical impedance tomography

This article describes a method called Lorentz Force Electrical Impedance Tomography. The electrical conductivity of biological tissues can be measured through their sonication in a magnetic field: the vibration of the tissues inside the field induces an electrical current by Lorentz force. This current, detected by electrodes placed around the sample, is proportional to the ultrasonic pressure, to the strength of the magnetic field and to the electrical conductivity gradient along the acoustic axis. By focusing at different places inside the sample, a map of the electrical conductivity gradient can be established. In this study, experiments were conducted on a gelatin phantom and on a beef sample, successively placed in a 300 mT magnetic field and sonicated with an ultrasonic transducer focused at 21 cm emitting 500 kHz bursts. Although all interfaces are not visible, in this exploratory study a good correlation is observed between the electrical conductivity image and the ultrasonic image. This method offers an alternative to detecting pathologies invisible to standard ultrasonography.     

Effects of cavities on EEG dipole localization and their relations with surface electrode positions

Effects of cavities in the human head on EEG dipole localization have been investigated by computer simulation. The human head is represented by a homogeneous spherical conductor including an eccentric spherical cavity which approximates effects of actual cavities inside the head. The homogeneous sphere model is used for assessing the effects caused by neglecting the cavity in the volume conductor model in the inverse dipole fitting procedure. Four electrode configurations have been examined to investigate their relation to the EEG inverse dipole solution. After examination of 2520 dipoles in the brain, the effects of cavities in the human head are found to be negligible when the dipole is located in the cortex or in the subcortex. When the dipole is located in the brain stem, the EEG inverse dipole solution is strongly affected by the cavity and is sensitive to the electrode configuration on the scalp. The EEG inverse dipole solution in the deep brain is sensitive to inhomogeneity in the lower part of the head when a single positive or negative potential pole is observed by the electrodes on the scalp, and at the same time is sensitive to the extent of the scalp covered by the electrodes. In conclusion, the electrodes should cover as much of the upper scalp as possible for deep source localization.     

Investigation of the temporal and spatial dynamics of muscular action potentials through optically pumped magnetometers

AimThis study aims to simultaneously record the magnetic and electric components of the propagating muscular action potential.MethodA single-subject study of the monosynaptic stretch reflex of the musculus rectus femoris was performed; the magnetic field generated by the muscular activity was recorded in all three spatial directions by five optically pumped magnetometers. In addition, the electric field was recorded by four invasive fine-wire needle electrodes. The magnetic and electric fields were compared by modelling the muscular anatomy of the rectus femoris muscle and by simulating the corresponding magnetic field vectors.ResultsThe magnetomyography (MMG) signal can reliably be recorded following the stimulation of the monosynaptic stretch reflex. The MMG signal shows several phases of activity inside the muscle, the first of which is the propagating muscular action potential. As predicted by the finite wire model, the magnetic field vectors of the propagating muscular action potential are generated by the current flowing along the muscle fiber. Based on the magnetic field vectors, it was possible to reconstruct the pinnation angle of the muscle fibers. The later magnetic field components are linked to the activation of the contractile apparatus.InterpretationMMG allows to analyze the muscle physiology from the propagating muscular action potential to the initiation of the contractile apparatus. At the same time, this methods reveals information about muscle fiber direction and extend. With the development of high-resolution magnetic cameras, that are based on OPM technology, it will be possible to image the function and structure of the biomagnetic field of any skeletal muscle with high precision. This method could be used both, in clinical medicine and also in sports science.     

The magnetic and electric fields induced by superparamagnetic magnetite in honeybees

Hairs on the abdomen of honeybees contain dendrites and a rod and ring structure composed of black particles, presumed to be superparamagnetic (SPM) magnetite. The rod and ring were divided into compartments and each compartment approximated by a dipole. The magnetic fields were calculated at a point P at various locations for a change of the external geomagnetic field from zero to 0.5 G in 0.1 s. The magnetite amplifies the external field at the rod/ring-dendrite interface. The induced electric field and potential difference for a small circular area are in the order of 10^–7 V/m and 10^–13 V respectively. Mechanisms are proposed for amplifying the electric fields in the dendrite and in an integrating nerve fibre. A hypothesis is developed for associative learning of visual and magnetic stimuli. If magnetic and visual inputs are associated in the ganglion and in the brain, very small changes of either magnetic or visual inputs could be perceived. A bee could sequentially follow the images associated with magnetic gradients on a cloudy day and find the food source.This paper is dedicated to the memory of the late Prof. Dr. W. Reichardt, an outstanding scientist and personality, who will be greatly missed by all who knew him and his work     

The Effect of Electrical Deformation Forces on the Electropermeabilization of Erythrocyte Membranes in Low- and High-Conductivity Media

Electrical breakdown of erythrocytes induces hemoglobin release which increases markedly with decreasing conductivity of the pulse medium. This effect presumably results from the transient, conductivity-dependent deformation forces (elongation or compression) on the cell caused by Maxwell stress. The deformation force is exerted on the plasma membrane of the cell, which can be viewed as a transient dipole induced by an applied DC electric field pulse. The induced dipole arises from the free charges that accumulate at the cell interfaces via the Maxwell-Wagner polarization mechanism. The polarization response of erythrocytes to a DC field pulse was estimated from the experimental data obtained by using two complementary frequency-domain techniques. The response is very rapid, due to the highly conductive cytosol. Measurements of the electrorotation and electrodeformation spectra over a wide conductivity range yielded the information and data required for the calculation of the deformation force as a function of frequency and external conductivity and for the calculation of the transient development of the deformation forces during the application of a DC-field pulse. These calculations showed that (i) electric force precedes and accompanies membrane charging (up to the breakdown voltage) and (ii) that under low-conductivity conditions, the electric stretching force contributes significantly to the enlargement of ``electroleaks' in the plasma membrane generated by electric breakdown. Received: 12 December 1997/Revised: 13 March 1998     

Does direction of induced electric field or current provide a test of mechanism involved in nerve regeneration?

We suggest an experimental comparison of two directions for applying the time-varying magnetic fields which have been found to speed spontaneous regeneration of injured peripheral nerves and in attempts to repair spinal cord injuries. Time-varying magnetic fields induce currents in a plane perpendicular to the magnetic field direction. The lower conductivity of the spinal cord's sheath (dura matter) or of the myelin sheath of peripheral nerves would seem to confine the induced electric fields and currents to the spinal cord or nerve itself. The proposed comparison could allow choosing between two possible modes of action of the fields: (1) Magnetically-induced electric fields or currents may be encouraging ion flow or otherwise helping enzyme, channel or other interactions at the cell membrane, as is thought to be the case in field stimulation of healing in bone. This mechanism should be independent of field direction. (2) Work in developing organisms and with fields applied to nerve cells in vitro has shown that neurite growth is guided parallel to both endogenous and external electric fields. This mechanism would be effective when induced electric fields are parallel, but not when they are perpendicular to the nerve. Any experimental test should seek to produce as close as possible to the same induced current intensity with both field directions. Possible confounding factors, as well as breakdowns in the assumptions of the simple model presented here, would have to be considered. This proposal was motivated by a recent report in which the authors listed a changed field direction as one of several possible reasons for an unsuccessful experiment.     

EEG and implanted sources in the brain

Localisation procedures are based on models of the EEG that are relatively simple. The models are based on assumptions and choices of parameters that can be mistaken. Thus, it is crucial to validate the localisation procedures used in EEG. One of the options is to use the data obtained with electrodes that are implanted within the brain of an epileptic patient as part of the pre-surgical evaluation. When one of two neighbouring electrodes is used as a current source and the other as a current sink this can be regarded as a current dipole. The current injected has to be below the threshold for activation of cells. The position of this dipole can be deduced from magnetic resonance or X-ray images. The current dipole gives rise to a potential distribution at the scalp that can be measured by EEG. The measurements can be compared with the potential distribution that is calculated in a forward computation. Another method is to use the measured potential at the scalp to localize the source and to compare the result with the actual position of the dipole. In this paper the measured potential distributions at the scalp due to implanted dipoles were used to evaluate different volume conductor models. Since intracerebral and subdural electrodes were introduced through trephine holes over the fronto-central areas, and the diameter of the holes was rather large, approximately 23 mm, special effort was put into modelling the skull. Two important assumptions could be validated in this study: the electric currents within the head are Ohmic and a dipole can be used to model the induced electric activity of pairs of contacts on subdural electrodes or intra cerebral electrodes.     

Temporal variation of the static electric field inside an animal cage

The temporal variation of a static electric field inside an animal cage was investigated with a newly developed small, simple field meter. The field inside the cage was found to be highly dependent on the surface conductivity of the dielectric material. As the surface of the cage became dirty because of animal occupancy, the static electric field inside it became considerably smaller from the moment the field was turned on. Clean cages also modified the static electric field inside them, the field decaying from an initial to a much lower value over several hours. The mechanism of field attenuation for both cases is surface leakage. Surface leakage for a clean cage takes place much more slowly than for a dirty cage. This was confirmed by measuring DC insulation resistance. To examine this phenomenon further, the field in a metal cage with high electrical conductivity was measured. The static electric field inside the metal cage was also found to be reduced. An improved cage design that avoids these problems, is suggested for the study of the biologic effects of static electric fields.     

Optically pumped magnetometers disclose magnetic field components of the muscular action potential

AimAiming at analysing the signal conduction in muscular fibres, the spatio-temporal dynamics of the magnetic field generated by the propagating muscle action potential (MAP) is studied.MethodIn this prospective, proof of principle study, the magnetic activity of the intrinsic foot muscle after electric stimulation of the tibial nerve was measured using optically pumped magnetometers (OPMs). A classical biophysical electric dipole model of the propagating MAP was implemented to model the source of the data. In order to account for radial currents of the muscular tubules system, a magnetic dipole oriented along the direction of the muscle was added.ResultsThe signal profile generated by the activity of the intrinsic foot muscles was measured by four OPM devices. Three OPM sensors captured the spatio-temporal magnetic field pattern of the longitudinal intrinsic foot muscles. Changes of the activation pattern reflected the propagating muscular action potential along the muscle. A combined electric and magnetic dipole model could explain the recorded magnetic activity.InterpretationOPM devices allow for a new, non-invasive way to study MAP patterns. Since magnetic fields are less altered by the tissue surrounding the dipole source compared to electric activity, a precise analysis of the spatial characteristics and temporal dynamics of the MAP is possible. The classic electric dipole model explains major but not all aspects of the magnetic field. The field has longitudinal components generated by intrinsic structures of the muscle fibre. By understanding these magnetic components, new methods could be developed to analyse the muscular signal transduction pathway in greater detail. The approach has the potential to become a promising diagnostic tool in peripheral neurological motor impairments.     

Return current in encephalography. Variational principles.

The encephalographic problem of finding the electric potential V and the return current associated with any assumed primary current, Jp, is put in the form of a variational principle. With Jp and the conductivity specified, the correct V is one which makes an integral quantity P[V] a maximum. The terms in P[V] are related to the rates at which work is done by the electric field on the primary and return currents. It is shown that there is a unique solution for the electric field, and it satisfies the conservation of energy; this condition can serve as a check on any numerical solution. With the conductivity a different constant in different regions, the variational principle is recast in terms of the charge density on the surfaces of discontinuity. An iteration-variation method for finding the solution is outlined, and possible computational advantages over other approaches are discussed.     

On the thermodynamic characterization of membrane gating particles by their Boltzmann distribution

The characterizations of gating particles of ionic channels in nerve membranes by their equivalent valencies and their electric dipole moment changes are compared. The gating particle is represented as a system of electric charges in fixed positions in an external electric field and the potential energy of such a system is calculated in the approximation of a constant electric field. The proper expression of the Boltzmann distribution of the gating particles is presented. It is shown that the dipole moment of transition of the gating particle is the only proper thermodynamic (macroscopic) characteristics of the gating particles based on the available experimental information and does not depend on any microscopic assumption as the equivalent valency does.