Off-center spherical model for dosimetry calculations in chick brain tissue

This paper presents calculations for the electric field and absorbed power density distribution in chick brain tissue inside a test tube, using an off-center spherical model. It is shown that the off-center spherical model overcomes many of the limitations of the concentric spherical model, and permits a more realistic modeling of the brain tissue as it sits in the bottom of the test tube surrounded by buffer solution. The effect of the unequal amount of buffer solution above the upper and below the lower surfaces of the brain is analyzed. The field distribution is obtained in terms of a rapidly converging series of zonal harmonics. A method that permits the expansion of spherical harmonics about an off-center origin in terms of spherical harmonics at the origin is developed to calculate in closed form the electric field distribution. Numerical results are presented for the absorbed power density distribution at a carrier frequency of 147 MHz. It is shown that the absorbed power density increases toward the bottom of the brain surface. Scaling relations are developed by keeping the electric field intensity in the brain tissue the same at two different frequencies. Scaling relations inside, as well as outside, the brain surface are given. The scaling relation distribution is calculated as a function of position, and compared to the scaling relations obtained in the concentric spherical model. It is shown that the off-center spherical model yields scaling ratios in the brain tissue that lie between the extreme values predicted by the concentric and isolated spherical models.     

Power density,field intensity,and carrier frequency determinants of RF-energy-lnduced calcium-ion efflux from brain tissue

To explain a carrier frequency dependence reported for radiofrequency (RF)-induced calcium-ion efflux from brain tissue, a chick-brain hemisphere bathed in buffer solution is modeled as a sphere within the uniform field of the incident electromagnetic wave. Calculations on a spherical model show that the average electric-field intensity within the sample remains the same at different carrier frequencies if the incident power density (P_i) is adjusted by an amount that compensates for the change in complex permittivity (?) and the change of wavelength, as a function of carrier frequency. The resulting formula for transforming P_i is seen to follow the pattern of both positive and negative demonstrations of calcium-ion efflux that have been observed at carrier frequencies of 50, 147, and 450 MHz. Indeed, all results obtained at these three frequencies, when related by P_i's that produce the same average electric-field intensity within the sample, are seen to be in agreement; no prediction is contradicted by an experiment.     

New model for the avian magnetic compass

It is proposed that the avian magnetic compass depends on the angle between the horizontal component B(h) of the geomagnetic field (GMF) and E(r), the radial electric field distribution generated by gamma-oscillations within the optic tectum (TeO). We hypothesize that the orientation of the brain relative to B(h) is perceived as a set of electric field ion cyclotron resonance (ICR) frequencies that are distributed in spatially recognizeable regions within the TeO. For typical GMF intensities, the expected ICR frequencies fall within the 20-50 Hz range of gamma-oscillation frequencies observed during visual stimulation. The model builds on the fact that the superficial lamina of the TeO receive signals from the retina that spatially map the visual field. The ICR frequencies are recruited from the local wide-band gamma-oscillations and are superposed on the tectum for interpretation along with other sensory data. As a first approximation, our analysis is restricted to the medial horizontal plane of the TeO. For the bird to fly in a preferred, previously mapped direction relative to B(h), it hunts for that orientation that positions the frequency maxima at appropriate locations on the TeO. This condition can be maintained even as B(h) varies with geomagnetic latitude during the course of long-distance flights. The magnetovisual coordinate system (straight phi, omega) overlaying the two halves of the tectal surface in a nonsymmetric way may imply an additional orienting function for the TeO over and above that of a simple compass (e.g., homing navigation as distinct from migrational navigation).     

Reduction of electrode polarization capacitance in low-frequency impedance spectroscopy by using mesh electrodes

Dielectric measurements of biological samples are obscured by electrode polarization, which at low frequencies dominates over the actual sample response. Reduction of this artifact is especially necessary in studying interactions of electric field with biological systems in the α-dispersion range. We developed a method to reduce the influence of electrode polarization by employing mesh instead of solid electrodes as sensing probes, thereby reducing the area of the double layer. The design decreases the electrode-electrolyte contact area by almost 40% while keeping the bulk sample capacitance the same. Interrogation electric fields away from the electrode surface and sensitivity are unaffected. Electrodes were microfabricated (600μm×50μm, spacing of 100μm) with and without mesh holes 7.5μm×7.5μm in size. Simulations of electric field performed using Comsol Multiphysics showed non-uniformity of the electric field within less than 1.5μm from the electrode surface, which encompasses the double layer region, but at greater distance the solid and mesh electrodes gave the same results. Mesh electrodes reduced capacitance measurements for water and KCl solutions of different concentrations at low frequencies (<10kHz), while higher frequency capacitance remained the same for both electrode types, confirming our hypothesis that this design leaves the electric field mainly unaffected. Impedance measurements at low frequencies for water and mice heart mitochondrial suspension were lower for mesh than for solid electrodes. Comsol simulations confirmed these results by showing that mesh electrodes have a greater charge density than solid electrodes, which affects conductance. These electrodes are being used for mitochondrial membrane potential studies.     

A scheme for incorporating DC magnetic fields into epidemiological studies of EMF exposure

Experimental data on calcium-ion release in chicken brain tissue suggest that biological effects of electric and magnetic fields (EMFs) are concentrated near certain “active combinations” of DC magnetic field strength and “effective” AC magnetic field frequencies. We hypothesize that active AC/DC combinations may exist and suggest that epidemiologic data, coupled with DC magnetic field measurements, may be used to identify critical exposure conditions. An empirical model is used to calculate these multiple active combinations at any given DC magnetic field strength and to define a rating system that incorporates the proximity of AC magnetic field frequencies generated by electric power lines to the new, computed effective frequencies. Such an exposure score may be useful in investigating correlations of EMF exposure with disease incidence. For 60 Hz and 50 Hz, the highest EMF exposure scores occurred at DC field strengths of 506 mG and 422 mG, respectively. The exposure score contains a factor which may be adjusted to reflect the importance of harmonics of the AC magnetic field as well as of the fundamental frequency. Using this factor, we consider two important special cases consistent with chick brain data: 1) we consider active pairs associated with all detectable harmonics (up to 660 Hz) without regard to relative intensity of the harmonics, and 2) we use the relative intensities of the AC field frequencies to adjust their contribution to the exposure score. © 1993 Wiley-Liss. Inc.     

Measurement of small mechanical vibrations of brain tissue exposed to extremely-low-frequency electric fields

Electromagnetic fields can interact with biological tissue both electrically and mechanically. This study investigated the mechanical interaction between brain tissue and an extremely-low-frequency (ELF) electric field by measuring the resultant vibrational amplitude. The exposure cell is a section of X-band waveguide that was modified by the addition of a center conductor to form a small TEM cell within the waveguide structure. The ELF signal is applied to the center conductor of the TEM cell. The applied ELF electric field generates an electrostrictive force on the surface of the brain tissue. This force causes the tissue to vibrate at a frequency equal to twice the frequency of the applied sinusoidal signal. An X-band signal is fed through the waveguide, scattered by the vibrating sample, and detected by a phase-sensitive receiver. Using a time-averaging spectrum analyzer, a vibration sensitivity of approximately 0.2 nmp-p can be achieved. The amplitude of the brain tissue vibrational response is constant for vibrational frequencies below 50 Hz; between 50 and 200 Hz resonant phenomena were observed; and above 200 Hz the amplitude fall-off is rapid.     

An analytical model for the calculation of the change in transmembrane potential produced by an ultrawideband electromagnetic pulse

The electric field pulse shape and change in transmembrane potential produced at various points within a sphere by an intense, ultrawideband pulse are calculated in a four stage, analytical procedure. Spheres of two sizes are used to represent the head of a human and the head of a rat. In the first stage, the pulse is decomposed into its Fourier components. In the second stage, Mie scattering analysis (MSA) is performed for a particular point in the sphere on each of the Fourier components, and the resulting electric field pulse shape is obtained for that point. In the third stage, the long wavelength approximation (LWA) is used to obtain the change in transmembrane potential in a cell at that point. In the final stage, an energy analysis is performed. These calculations are performed at 45 points within each sphere. Large electric fields and transmembrane potential changes on the order of a millivolt are produced within the brain, but on a time scale on the order of nanoseconds. The pulse shape within the brain differs considerably from that of the incident pulse. Comparison of the results for spheres of different sizes indicates that scaling of such pulses across species is complicated.     

Brain stimulation using electromagnetic sources: theoretical aspects.

We prove that, at the frequencies generally proposed for extracranial stimulation of the brain, it is not possible, using any superposition of external current sources, to produce a three-dimensional local maximum of the electric field strength inside the brain. The maximum always occurs on a boundary where the conductivity jumps in value. Nevertheless, it may be possible to achieve greater two-dimensional focusing and shaping of the electric field than is currently available. Towards this goal we have used the reciprocity theorem to present a uniform treatment of the electric field inside a conducting medium produced by a variety of sources: an external magnetic dipole (current loop), an external electric dipole (linear antenna), and surface and depth electrodes. This formulation makes use of the lead fields from magneto- and electroencephalography. For the special case of a system with spherically symmetric conductivity, we derive a simple analytic formula for the electric field due to an external magnetic dipole. This formula is independent of the conductivity profile and therefore embraces spherical models with any number of shells. This explains the "insensitivity" to the skull's conductivity that has been described in numerical studies. We also present analytic formulas for the electric field due to an electric dipole, and also surface and depth electrodes, for the case of a sphere of constant conductivity.     

Protein purification by Off-Gel electrophoresis

A novel free-flow protein purification technique based on isoelectric electrophoresis is presented, where the proteins are purified in solution without the need of carrier ampholytes. The gist of the method is to flow protein solutions under an immobilised pH gradient gel (IPG) through which an electric field is applied perpendicular to the direction of the flow. Due to the buffering capacity of the IPG gel, proteins with an isoelectric point (pI) close to pH of the gel in contact with the flow chamber stay in solution because they are neutral and therefore not extracted by the electric field. Other proteins will be charged when approaching the IPG gel and are extracted into the gel by the electric field. Both a demonstration experiment with pI markers and a simulation of the electric field distribution are presented to highlight the principle of the system. In addition, an isoelectric fractionation of an Escherichia coli extract is shown to illustrate the possible applications.     

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.     

Frequency-dependent effects in an alternating electric field on an isolated frog heart

An isolated frog heart placed in a special chamber with Ringer solution (pH 7.2) was stimulated by electric field at a frequency of 0.3-4.0 Hz with graphite electrodes immersed in the solution. Unusual resonance phenomena were observed during a progressive increase or decrease of the stimulation frequency: the amplitude of the mechanical responses of the preparation rose at multiple frequencies of stimulation, whereas the frequency of the responses remained unchanged.     

Membrane electropermeabilization effects of frequency and membrane surface order on liposome leakage

Liposomes containing fluorescence marker were exposed to an alternating electric field of 80 V peak to peak square electric waves at different frequencies 0.01, 1, and 100 kHz to perturb the liposome permeation. The efflux of fluorescence dye after application of the electric field was measured by recording the fluorescence emission due to the complex formation reaction between the fluorescence dye and calcium ions in the bulk medium solution. Two independent sets of experiments were conducted: 1) calcium ions were present during electropulsation; and 2) they were added after electric field application. Two parameters, fluorescence emission intensity and increment of temperature of the solution in the chamber, were studied. The effect of membrane surface order on the fluorescence dye leakage from the liposomes was studied by addition of urea at threshold concentration before the liposomes sealed. The data demonstrate the existence of frequency dependency window at 1 kHz. Furthermore, the data were interpreted according to the theory of interactions of electromagnetic fields with highly polarized and deformed materials such as liposome particles. The urea caused an enhancement of the fluorescence dye leakage at frequency of 100 kHz. This effect could be explained as a decrease of the membrane binding rigidity due to the disordering effect of urea on the membrane lipid surface. Our conclusion is that the frequency and the membrane surface order are additional parameters that influence the processes of membrane electropermeabilization.     

An ephaptic transmission model of CA3 pyramidal cells: an investigation into electric field effects

Extracellular electric fields existing throughout the living brain affect the neural coding and information processing via ephaptic transmission, independent of synapses. A two-compartment whole field effect model (WFEM) of pyramidal neurons embedded within a resistive array which simulates the extracellular medium i.e. ephapse is developed to study the effects of electric field on neuronal behaviors. We derive the two linearized filed effect models (LFEM-1 and LFEM-2) from WFEM at the stable resting state. Through matching these simplified models to the subthreshold membrane response in experiments of the resting pyramidal cells exposed to applied electric fields, we not only verify our proposed model’s validity but also found the key parameters which dominate subthreshold frequency response characteristic. Moreover, we find and give its underlying biophysical mechanism that the unsymmetrical properties of active ion channels results in the very different low-frequency response of somatic and dendritic compartments. Following, WFEM is used to investigate both direct-current (DC) and alternating-current field effect on the neural firing patterns by bifurcation analyses. We present that DC electric field could modulate neuronal excitability, with the positive field improving the excitability, the modest negative field suppressing the excitability, but interestingly, the larger negative field re-exciting the neuron back into spiking behavior. The neuron exposed to the sinusoidal electric field exhibits abundant firing patterns sensitive to the input frequency and intensity. In addition, the electrical properties of ephapse can modulate the efficacy of field effect. Our simulated results are qualitatively in line with the relevant experimental results and can explain some experimental phenomena. Furthermore, they are helpful to provide the predictions which can be tested in future experiments.     

Experimental investigation on neural cell survival after dielectrophoretic trapping

Negative dielectrophoretic forces can effectively be used to trap cortical rat neurons. The creation of dielectrophoretic forces requires electric fields of high non-uniformity. High electric field strengths, however, can cause excessive membrane potentials by which cells may unrecoverably be changed or it may lead to cell death. In a previous study it was found that cells trapped at 3 Vtt/14 MHz did not change morphologically as compared to cells that were not exposed to the electric field. This study investigates the viability of fetal cortical rat neurons after being trapped by negative dielectrophoretic forces at frequencies up to 1 MHz. A planar quadrupole micro-electrode structure was used for the creation of a non-uniform electric field. The sinusoidal input signal was varied in amplitude (3 and 5 Vtt) and frequency (10 kHz-1 MHz). The results presented in this paper show that the viability of dielectrophoretically trapped postnatal cortical rat cells was greatly frequency dependent. To preserve viability frequencies above 100 kHz (at 3 Vtt) or 1 MHz (5 Vtt) must be used.     

Oscillation spectrum of an electron gas with a small density fraction of ions

The problem is solved of the stability of a nonneutral plasma that completely fills a waveguide and consists of magnetized cold electrons and a small density fraction of ions produced by ionization of the atoms of the background gas. The ions are described by an anisotropic distribution function that takes into account the characteristic features of their production in crossed electric and magnetic fields. By solving a set of Vlasov-Poisson equations analytically, a dispersion equation is obtained that is valid over the entire range of allowable electric and magnetic field strengths. The solutions to the dispersion equation for the m = +1 main azimuthal mode are found numerically. The plasma oscillation spectrum consists of the families of Trivelpiece-Gould modes at frequencies equal to the frequencies of oblique Langmuir oscillations Doppler shifted by the electron rotation and also of the families of “modified” ion cyclotron (MIC) modes at frequencies close to the harmonics of the MIC frequency (the frequencies of radial ion oscillations in crossed fields). It is shown that, over a wide range of electric and magnetic field strengths, Trivelpiece-Gould modes have low frequencies and interact with MIC modes. Trivelpiece-Gould modes at frequencies close to the harmonics of the MIC frequency with nonnegative numbers are unstable. The lowest radial Trivelpiece-Gould mode at a frequency close to the zeroth harmonic of the MIC frequency has the fastest growth rate. MIC modes are unstable over a wide range of electric and magnetic field strengths and grow at far slower rates. For a low ion density, a simplified dispersion equation is derived perturbatively that accounts for the nonlocal ion contribution, but, at the same time, has the form of a local dispersion equation for a plasma with a transverse current and anisotropic ions. The solutions to the simplified dispersion equation are obtained analytically. The growth rates of the Trivelpiece-Gould modes and the behavior of the MIC modes agree with those obtained by numerical simulation.     

Characteristics of transverse electric and magnetic field transmission cells at extremely low frequencies

Transverse electric and magnetic field (TEM) cells are often designed to subject samples to electromagnetic radiation of intrinsic impedance (E/H) that is the same as in free space, 377 omega. Earlier work has shown this value to be correct for the RF region above about 2 kHz. In this study, measurements of magnetic fields in the extremely low frequency regions and at DC indicate the E/H ratio to be around 300 omega for frequencies less than 2 kHz in cells of a particular design. This lower value indicates that care should be taken in estimating AC magnetic field intensities from electric field measurements in TEM cells at frequencies below 2 kHz.     

Effect of dissipative processes on the dispersion and instability of drift waves in a fine-stratified semiconductor structure

The damping of waves of the charge carrier density in a periodic semiconductor structure in an external electric field is investigated under the assumption that the period of the structure is much smaller than the electromagnetic radiation wavelength. The threshold conditions for the instability of carrier density waves propagating obliquely to the direction of the electric current are obtained. The existence of a resistive instability that can develop at drift velocities both higher and lower than the plasmon phase velocity is predicted.     

Effects of a brain tumor in a dispersive human head on SAR and temperature rise distributions due to RF sources at 4G and 5G frequencies

In this paper, effects of a brain tumor located in a dispersive human head model on specific absorption rate (SAR) and temperature rise distributions due to different types of RF sources at 4G and 5G cellular frequencies are investigated with the use of a multiphysics model. This multiphysics model analyzes the dispersive human head with the brain tumor and provides the SAR and temperature rise distributions in the head due to the RF source operated at 4G and 5G cellular frequencies in a single finite-difference time-domain simulation. An adjacent antenna operated at 4G and 5G cellular frequencies to the human head is considered as the RF source for near-field exposure, while a plane wave field radiated by base stations operated at 4G and 5G cellular frequencies is considered as the RF source for far-field exposure. Numerical results show that the brain tumor in the head slightly affects the SAR and temperature rise distributions due to different RF sources at 4G and 5G cellular frequencies.     

B-form and A-form DNA in an electric field

The structures of B-form and A-form DNA are studied in 0–70 and 70–80% ethanol solutions, respectively, in an electric field, using linear dichroism. The limiting reduced linear dichroism data of B-form DNA are chain length dependent in 0% ethanol solution. However, there is no such chain length dependence of the limiting reduced linear dichroism of the A-form. Our reslts also suggest that (1) the transition moments at 260 nm lie within the plaxe of the DNA bases, (2) the two allomorphs (A and B forms) of the long chain DNA in solution in the electric field are like the respective classica forms.