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.     

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.     

Modeling the effect of the layer thickness and tissue conductivities of the head and the brain on the EEG potentials using finite element method

The influence of the thickness and specific resistance of the brain tissues and its surrounding coverings, brain sulci and anisotropy of white matter electric conductivity on the EEG potentials were modeled. The finite element method was used for simulation, which is realized in the Femlab module. During the comparison of two models with different thickness of the layers was shown the change of potentials by 40% for scull, which thickness varied by 9 mm, and for the gray matter and spinal fluid the change of potentials amounted to 15% by 3 mm variable thickness. The change of conductivity by 25% resulted in the difference of potentials amounted to 15% for the white matter and 1.5% for the cortex of the brain. During the assignment of the anisotropy in the model, by the whole volume of the white matter, sixfold difference of the potentials in comparison with application of isotropic parameters was discovered. The difference of the potentials for single heterogeneity, simulated the sulci of the brain, amounted to 10% in the heterogeneity projection point and increased during the drawing near to the "referent electrode". The model complex of the "sulci of cerebrum" gave significant contribution to the difference of the potentials and depended on the depth of dipole occurrence and nearness of the sulci complex. Significant influence of brain sulci on the EEG-potentials distribution, which can give rise to great artifacts, was discovered.     

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     

Mechanisms of magnetic stimulation of central nervous system neurons

Transcranial magnetic stimulation (TMS) is a stimulation method in which a magnetic coil generates a magnetic field in an area of interest in the brain. This magnetic field induces an electric field that modulates neuronal activity. The spatial distribution of the induced electric field is determined by the geometry and location of the coil relative to the brain. Although TMS has been used for several decades, the biophysical basis underlying the stimulation of neurons in the central nervous system (CNS) is still unknown. To address this problem we developed a numerical scheme enabling us to combine realistic magnetic stimulation (MS) with compartmental modeling of neurons with arbitrary morphology. The induced electric field for each location in space was combined with standard compartmental modeling software to calculate the membrane current generated by the electromagnetic field for each segment of the neuron. In agreement with previous studies, the simulations suggested that peripheral axons were excited by the spatial gradients of the induced electric field. In both peripheral and central neurons, MS amplitude required for action potential generation was inversely proportional to the square of the diameter of the stimulated compartment. Due to the importance of the fiber's diameter, magnetic stimulation of CNS neurons depolarized the soma followed by initiation of an action potential in the initial segment of the axon. Passive dendrites affect this process primarily as current sinks, not sources. The simulations predict that neurons with low current threshold are more susceptible to magnetic stimulation. Moreover, they suggest that MS does not directly trigger dendritic regenerative mechanisms. These insights into the mechanism of MS may be relevant for the design of multi-intensity TMS protocols, may facilitate the construction of magnetic stimulators, and may aid the interpretation of results of TMS of the CNS.     

Dipole interactions in electrofusion. Contributions of membrane potential and effective dipole interaction pressures.

The contributions of pulse-induced dipole-dipole interaction to the total pressure acting normal to the membranes of closely positioned pronase treated human erythrocytes during electrofusion was calculated. The total pressure was modeled as the sum of pressures arising from membrane potential and dipole-dipole attraction opposed by interbilayer repulsion. The dipole-dipole interaction was derived from the experimentally obtained cell polarizability. The threshold electric field amplitude necessary for fusion of pronase-treated human erythrocytes was experimentally obtained at various combinations of pulse duration, frequency, and the conductivity of the external medium. The theoretical values of the critical electric field amplitude compared favorably to the experimentally obtained threshold field amplitudes. Fusion by dc pulses may be primarily attributed to attainment of sufficiently high membrane potentials. However, with decreasing external conductivity and increasing sinusoidal pulse frequency (100 kHz-2.5 MHz), the induced dipole-dipole interactions provide the principal driving force for membrane failure leading to fusion.     

Dose response study of human exposure to 60 Hz electric and magnetic fields

This human exposure study examined the relationship between field strength and biological response and tested whether the exposure levels at which the greatest effects occur differ for different endpoints. Three matched groups of 18 men each participated in two 6 h exposure test sessions. All subjects were sham exposed in one session. In the other session, each group of subjects was exposed at a different level of combined electric and magnetic field strength (low group: 6 kV/m, 10 μT; medium group: 9 kV/m, 20 μT; and high group: 12 kV/m, 30 μT). The study was performed double blind, with exposure order counterbalanced. Significant slowing of heart rate, as well as alterations in the latency and amplitude of event-related brain potential measures derived from the electro encephalogram (EEG), occurred in the group exposed to the 9 kV/m, 20 μT combined field (medium group). Exposure at the other field strength levels had no influence on cardiac measures and differential effects on EEG activity. Significant decrements in reaction time and in performance accuracy on a time estimation task were observed only in the low group. These results provide support for the hypothesis that humans may be more responsive to some combinations or levels of field strength than to others and that such differences in responsivity may depend, in part, on the endpoint of interest. © 1994 Wiley-Liss, Inc.     

Light scattering of aqueous solutions of DNA, poly(acrylic acid), and tobacco mosaic virus under alternating electric field

Two new techniques, amplitude modulation (AM) and frequency modulation (FM) of an electric field, are developed for the light-scattering study of polymer solutions under ac electric fields. The AM technique makes it possible to observe accurately the frequency dependence of the intensity changes of scattered light due to the electric field. The FM one allows us to obtain directly the frequency derivative of the intensity change. The techniques are applied to DNA, poly(acrylic acid), and tobacco mosaic virus in the frequency range from 10 Hz to 100 kHz. A low-frequency relaxation is found for both DNA and poly(acrylic acid). The obsersved relaxation time of DNA agrees with that in the dielectric relaxation of DNA, which has been attributed to the rotation of the molecule with a quasipermanent dipole. In the case of poly(acrylic acid), the relaxation strength increases with increasing degree of neutralization. TMV at a concentration of 0.1% exhibits a negative relaxation at low frequencies, which indicates the rotation of TMV aggregate with a permanent dipole along its minor axis.     

Kerr effect of charged dipolar macromolecules without condensed counterions in conducting solution.

The theoretical treatment of the Kerr constant of rigid, dipolar, conducting ellipsoidal macromolecules of O'Konski and Krause (1970. J. Phys. Chem. 74:3243) has been extended to very low ionic strength solutions for charged macromolecules. The O'Konski and Krause theoretical treatment postulated a surface conductivity directly on the surface of each macromolecule. For charged macromolecules, this surface conductivity was generally assumed to be caused by movement of condensed counterions on the macromolecules. In the present work, it has been assumed that, at very low ionic strength, the average counterion is at the Debye characteristic distance from the surface of each charged macromolecule and contributes to surface conductivity at that distance, with no additional surface conductivity on the true surface of the macromolecule. Essentially, these considerations change the calculated interaction energy of the macromolecule with an externally applied electric field via a change in both the internal field components and in the reaction field of the macromolecular dipole. The new interaction energy is used to calculate the orientation distribution function of the macromolecules in solution and this distribution function can, in principle, be used to calculate the steady state electric linear or circular dichroism, electric light scattering, anisotropy of conductivity, etc., using the appropriate theoretical treatment for each of these quantities.     

Dipole characterization of single neurons from their extracellular action potentials

The spatial variation of the extracellular action potentials (EAP) of a single neuron contains information about the size and location of the dominant current source of its action potential generator, which is typically in the vicinity of the soma. Using this dependence in reverse in a three-component realistic probe + brain + source model, we solved the inverse problem of characterizing the equivalent current source of an isolated neuron from the EAP data sampled by an extracellular probe at multiple independent recording locations. We used a dipole for the model source because there is extensive evidence it accurately captures the spatial roll-off of the EAP amplitude, and because, as we show, dipole localization, beyond a minimum cell-probe distance, is a more accurate alternative to approaches based on monopole source models. Dipole characterization is separable into a linear dipole moment optimization where the dipole location is fixed, and a second, nonlinear, global optimization of the source location. We solved the linear optimization on a discrete grid via the lead fields of the probe, which can be calculated for any realistic probe + brain model by the finite element method. The global source location was optimized by means of Tikhonov regularization that jointly minimizes model error and dipole size. The particular strategy chosen reflects the fact that the dipole model is used in the near field, in contrast to the typical prior applications of dipole models to EKG and EEG source analysis. We applied dipole localization to data collected with stepped tetrodes whose detailed geometry was measured via scanning electron microscopy. The optimal dipole could account for 96% of the power in the spatial variation of the EAP amplitude. Among various model error contributions to the residual, we address especially the error in probe geometry, and the extent to which it biases estimates of dipole parameters. This dipole characterization method can be applied to any recording technique that has the capabilities of taking multiple independent measurements of the same single units.     

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.     

The effects of heart-cavity blood resistivity and volume on endocardial potentials: theoretical predictions

Theoretical concepts regarding the potential variations within the bloodfilled cavities of the heart caused by excitation of the myocardium are scarce. In an attempt to understand these potential variations, calculations were made of the potentials due to a dipole adjacent to a disk of finite resistivity. The dipole was assumed to be in an infinite two-dimensional medium of higher resistivity. Equations for the potential inside a sphere due to an external source are also given.On the basis of the results, predictions were made on the effects of the intracardiac blood on the endocardial potentials: (1) the potential at the center of the cavity is independent of blood resistivity and equivalent to the free space potential; (2) potentials due to a tangential dipole are uniformly reduced; (3) potentials due to a radial dipole are smaller near the dipole, but greater at the far end of the dipole axis; (4) for a dipole radial to or making an angle with the cavity, potentials are reduced at some points but increased at others; (5) the potential along the transverse axis of the dipole has a constant value depending on conductivity; (6) intracardiac blood tends to smooth out potential variations within the cavity; (7) the potential depends both on dipole distance and direction; and (8) if the cavity volume increases, potentials decrease with distance from the dipole; the potential at the adjacent endocardial wall changes little.     

Cholesterol effect on the dipole potential of lipid membranes

The effect of cholesterol removal by methyl-beta-cyclodextrin on the dipole potential, psi(d), of membrane vesicles composed of natural membrane lipids extracted from the kidney and brain of eight vertebrate species was investigated using the voltage-sensitive fluorescent probe di-8-ANEPPS. Cyclodextrin treatment reduced cholesterol levels by on average 80% and this was associated with an average reduction in psi(d) of 50 mV. Measurements of the effect of a range of cholesterol derivatives on the psi(d) of DMPC lipid vesicles showed that the magnitude of the effect correlated with the component of the sterol's dipole moment perpendicular to the membrane surface. The changes in psi(d) observed could not be accounted for solely by the electric field originating from the sterols' dipole moments. Additional factors must arise from sterol-induced changes in lipid packing, which changes the density of dipoles in the membrane, and changes in water penetration into the membrane, which changes the effective dielectric constant of the interfacial region. In DMPC membranes, the cholesterol-induced change in psi(d) was biphasic, i.e., a maximum in psi(d) was observed at approximately 35-45 mol %, after which psi(d) started to decrease. We suggest that this could be associated with a maximum in the strength of DMPC-cholesterol intermolecular forces at this composition.     

电磁场对青蛙骨骼肌单根肌纤维效应的研究

电磁场对完整和去膜青蛙肌纤维作用的比较研究表明,交变电场通过改变膜电位引起肌肉收缩,在此过程中收缩蛋白质的空间位置而非自身构象发生变化,横桥尤其是S－2片段,在伴随横桥从弱耦合状态向强耦合状态过渡时远离粗肌丝而向细肌丝运动,使其与粗肌丝骨架的平均取向比松弛状态或静息状态时相对增大．一般强度恒定磁场对肌纤维膜电位状态及肌纤维内部蛋白质分子的运动及其相互作用影响极其微弱．     

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.     

Electrorheological modeling of the permeabilization of the stratum corneum: theory and experiment.

Experimentally observed changes in the conductivity of skin under the influence of a pulsing electric field were theoretically analyzed on the basis of a proposed electrorheological model of the stratum corneum (SC). The dependence of relative changes in conductivity on the amplitude of electric field and timelike parameters of applied pulses or pulse trains have been mathematically described. Statistical characteristics of phenomena of transient and long-term electroporation of SC were taken into consideration. The time-dependent decreases of skin resistance depicted by the models were fitted to experimental data for transient and long-term skin permeabilization by electric pulses. The results show two characteristic times and two spectra of characteristic energies for transient and long-term permeabilizations. The rheological parameters derived from the fittings agreed with those reported elsewhere for biological membranes.     

Comparison of excitation and emission ratiometric fluorescence methods for quantifying the membrane dipole potential

We are interested in developing fluorescence methods for quantifying lateral variations in the dipole potential across cell surfaces. Previous work in this laboratory showed that the ratio of fluorescence intensities of the voltage-sensitive dye di-8-ANEPPS using excitation wavelengths at 420 and 520 nm correlates well with measurements of the dipole potential. In the present work we evaluate the use of di-8-ANEPPS and an emission ratiometric method for measuring dipole potentials, as Bullen and Saggau (Biophys. J. 65 (1999) 2272-2287) have done to follow changes in the membrane potential in the presence of an externally applied field. Emission ratiometric methods have distinct advantages over excitation methods when applied to fluorescence microscopy because only a single wavelength is needed for excitation. We found that unlike the excitation ratio, the emission ratio does not correlate with the dipole potential of vesicles made from different lipids. A difference in the behaviour of the emission ratio in saturated compared to unsaturated lipid vesicles was noted. Furthermore, the emission ratio did not respond in the same way as the excitation ratio when cholesterol, 6-ketocholestanol, 7-ketocholesterol, and phloretin were added to dimyristoylphosphatidylcholine (DMPC) vesicles. We attribute the lack of correlation between the emission ratio and the dipole potential to simultaneous changes in membrane fluidity caused by changes in membrane composition, which do not occur when the electric field is externally applied as in the work of Bullen and Saggau. Di-8-ANEPPS can, thus, only be used via an excitation ratiometric method to quantify the dipole potential.     

形状识别的功能定位和时间过程:功能磁共振与脑电结合的研究

通过结合具有高空间分辨率的功能磁共振成像（fMRI）和具有高时间分辨率的128导脑电事件相关电位（ERP）两项技术,测量了视皮层腹侧区域对图形形状识别任务反应的空间定位和时间过程。fMRI的实验结果表明,图形的形状和觉引起了腹测GTi／GF皮层区域的兴奋。进一步,基于fMRI兴奋区域的种子偶极子模型拟合的的ERP动态定位分析的结果和自由运动的偶极子模型拟合的ERP定位分析结果表明：GTi／GF区域活动的时间发生在刺激呈现之后132－176ms时间段,峰值150ms左右,相应于ERP的N1成分。这些结果在人类大脑皮层上同时确定了视觉通路中涉及图形形状识别的兴奋区域和兴奋的时间过程。