Modeling assemblies of biological cells exposed to electric fields

Gap junctions are channels through the cell membrane that electrically connect the interiors of neighboring cells. Most cells are connected by gap junctions, and gaps play an important role in local intercellular communication by allowing for the exchange of certain substances between cells. Gap communication has been observed to change when cells are exposed to electromagnetic (EM) fields. In this work, the authors examine the behavior of cells connected by gap junctions when exposed to electric fields, in order to better understand the influence of the presence of gap junctions on cell behavior. This may provide insights into the interactions between biological cells and weak, low-frequency EM fields. Specifically, the authors model gaps in greater detail than is usually the case, and use the finite element method (FEM) to solve the resulting geometrically complex cell models. The responses of gap-connected cell configurations to both dc and time harmonic fields are investigated and compared with those of similarly shaped (equivalent) cells. To further assess the influence of the gap junctions, properties such as gap size, shape, and conductivity are varied. The authors' findings indicate that simple models, such as equivalent cells, are sufficient for describing the behavior of small gap connected cell configurations exposed to dc electric fields. With larger configurations, some adjustments to the simple models are necessary to account for the presence of the gaps. The gap junctions complicate the frequency behavior of gap-connected cell assemblies. An equivalent cell exhibits lowpass behavior. Gaps effectively add a bandstop filter in series with the low-pass behavior, thus lowering the relaxation frequency. The characteristics of this bandstop filter change with changes to gap properties. Comparison of the FEM results to those obtained with simple models indicates that more complex models are required to represent gap-connected cells     

Second-order model of membrane electric field induced by alternating external electric fields

With biological cells exposed to ac electric fields below 100 kHz, external field is amplified in the cell membrane by a factor of several thousands (low-frequency plateau), while above 100 kHz, this amplification gradually decreases with frequency. Below 10 MHz, this situation is well described by the established first-order theory which treats the cytoplasm and the external medium as pure conductors. At higher frequencies, capacitive properties of the cytoplasm and the external medium become increasingly important and thus must be accounted for. This leads to a broader, second-order model, which is treated in detail in this paper. Unlike the first-order model, this model shows that above 10 MHz, the membrane field amplification stops decreasing and levels off again in the range of tens (high-frequency plateau). Existence of the high-frequency plateau could have an important impact on present theories of high-frequency electric fields effects on cells and their membranes.     

Maximum surface and bulk electric fields at breakdown for planar and beveled devices

Techniques previously presented for predicting breakdown voltage on planar devices with and without a field ring and in negative beveled devices are greatly extended so that the peak bulk and surface electric fields at breakdown can now be predicted. In addition, new techniques are described which for the first time allow the peak bulk and surface electric fields to be predicted for all positive and double positive beveled devices. Using this paper it becomes possible to predict peak bulk and surface electric fields as well as breakdown voltage for all planar and beveled devices. This is accomplished by the use or normalization procedures which allow dependencies on the substrate doping, junction depth, surface concentration, junction curvature, and bevel angle to be reduced to a single dependence. It is shown that the positive bevel is most effective in reducing surface electric fields with the negative bevel, double positive bevel, and the field ring for planar devices in decreasing order of effectiveness.     

The effect of trench corner shapes on local stress fields: athree-dimensional finite-element modeling study

Local stress fields associated with deep trench structures are modeled in three dimensions utilizing a finite-element method. A model consisting of a SiO₂-filled deep trench residing in a silicon substrate is utilized, and stress is generated by differential thermal contraction. It is shown that corner regions, especially convex, `outside' corners, dramatically enhance the elastic energy density and shear stresses locally compared to noncorner regions. The effects of the specific corner geometry on these local stress fields is then investigated and it is shown that subtle geometric changes can yield substantial decreases in the magnitude and lateral extent of the fields     

Effects of induced electric fields on finite neuronal structures: asimulation study

An analysis is presented of magnetic stimulation of finite length neuronal structures using computer simulations. Models of finite neuronal structures in the presence of extrinsically applied electric fields indicate that excitation can be characterized by two driving functions: one due to field gradients and the other due to fields at the boundaries of neuronal structures. It is found that boundary field driving functions play an important role in governing excitation characteristics during magnetic stimulation. Simulations indicate that axons whose lengths are short compared to the spatial extent of the induced field are easier to excite than longer axons of the same diameter. Simulations also indicate that independent cellular dendritic processes are probably not excited during magnetic stimulation. Analysis of the temporal distribution of induced fields indicates that the temporal shape of the stimulus waveform modulates excitation thresholds and propagation of action potentials     

Finite-difference modeling of the anisotropic electric fields generated by stimulating needles used for catheter placement

The use of peripheral nerve blocks to control pain is an increasing practice. Many techniques include the use of stimulating needles to locate the nerve of interest. Though success rates are generally high, difficulties still exist. In certain deeper nerve blocks, two needles of different geometries are used in the procedure. A smaller needle first locates a nerve bundle, and then is withdrawn in favor of a second, larger needle used for injection. The distinct geometries of these needles are shown to generate different electric field distributions, and these differences may be responsible for failures of the second needle to elicit nerve stimulation when placed in the same location as the first. A 3-D finite-difference method has been employed to numerically calculate the electric field distributions for a commercial set of stimulating needles.     

A review of analytically determined electric fields and currents induced in the human body when exposed to 50-60-Hz electromagnetic fields

In this review paper, analytical methods are used to determine the electric field and current induced in the conducting human body when this is exposed to an electromagnetic field at extremely low frequencies (ELFs) or very low frequencies (VLFs). This is done by treating it as a parasitic antenna when this is modeled successively as a sphere, an ellipsoid, and a cylinder. Because the body is electrically very short at ELF and VLF, the axial current depends primarily on the length of the body. Comparison with the ellipsoidal shape shows that the induced current is virtually independent of the cross-sectional shape. It is concluded that the axial current induced in the cylinder is a good approximation of the current induced in an actual body with the same length and mean cross sectional area. References to persons standing on the earth and with the arms raised are given. The significance of the accurate knowledge of induced currents and fields for biomedical purposes is discussed.     

Measurement of r63 for ADP up to electric breakdown

The measurement of the electro-optic coefficient r63 at constant stress for ammonium dihydrogen phosphate is described. A novel form of electro-optic modulator is employed, with an optically transparent electrode system. The results obtained show no variation of the electro-optic coefficient with field strength up to electric breakdown at 200kV/cm.     

Comparison of the absorption characteristics of block and prolate spheroidal models of man exposed to near fields of short electric dipole

It is shown that the average specific absorption rates (SAR's) in a prolate spheroidal model of man are essentially the same as those for a block model of man irradiated by a short electric dipole at 27.12 MHz, even in the near fields. For purposes of average SAR, this allows use of the simpler and less expensive prolate spheroidal calculations.     

Imaging mass lesions by vibro-acoustography: modeling and experiments

Vibro-acoustography is a recently developed imaging method based on the dynamic response of to low-frequency vibration produced by of ultrasound radiation force. The main differentiating feature of this method is that the image includes information about the dynamic properties of the object at the frequency of the vibration, which is normally much lower than the ultrasound frequency. Such information is not available from conventional ultrasound imaging. The purpose of this study is to evaluate the performance of vibro-acoustography in imaging mass lesions in soft tissue. Such lesions normally have elastic properties that are different from the surrounding tissue. Here, we first present a brief formulation of image formation in vibro-acoustography. Then we study vibro-acoustography of solid masses through computer simulation and in vitro experiments. Experiments are conducted on excised fixed liver tissues. Resulting images show lesions with enhanced boundary and often with distinctive textures relative to their background. The results suggest that vibro-acoustography maybe a clinically useful imaging modality for detection of mass lesions.     

Increased avalanche breakdown voltage and controlled surface electric fields using a junction termination extension (JTE) technique

Extremely high breakdown voltages with very low leakage current have been achieved in plane and planar p-n junctions by using an ion-implemented junction extension for precise control of the depletion region charge in the junction termination. A theory is presented which shows a greatly improved control of both the peak surface and bulk electric fields in reverse biased p-n junctions. Experimental results show breakdown voltages greater than 95 percent of the ideal breakdown voltage with lower leakage currents than corresponding unimplanted devices. As an example, diodes with a normal breakdown voltage of 1050 V and a 0.5 mA leakage current become 1400 V (1450 ideal) devices with a 5 µA leakage current. Applications of the junction termination technique is feasible in MOS technology, but is more attractive in power devices where reduced surface fields are as important as the extremely high breakdown voltages. Reduced surface fields allow more flexibility in passivation techniques, two of which we have used to date. Our results also show that the implant can be activated at a variety of temperatures with a good degree of success; process flexibility being the goal of these tests.     

Determination of nonuniform diffusion length and electric field in semiconductors

A method is proposed that purports to measure the non-uniform diffusion lengthL(x)in the presence of an arbitrary electric fieldE_{x}(x). A point source of carrier generation (as a model for an electron beam) scans across the sample in the thickness direction x while the induced currents are measured at two reverse-biased junctions sandwiching the sample.L(x)and(E_{x} micro_{p} + D_{p})/D_{p}can be deduced from the currents. If only one collecting junction is present, one of the two functions may be deduced provided that the other is known; in addition, the surface recombination velocity at the other boundary may be determined in the presence of arbitraryL(x)andE_{x}(x). With additional scanning in theyandzdirections, quasi three-dimensional mapping is possible.     

Accurate modeling of lossy nonuniform transmission lines by using differential quadrature methods

This paper discusses an efficient numerical approximation technique, called the differential quadrature method (DQM), which has been adapted to model lossy uniform and nonuniform transmission lines. The DQM can quickly compute the derivative of a function at any point within its bounded domain by estimating a weighted linear sum of values of the function at a small set of points belonging to the domain. Using the DQM, the frequency-domain Telegrapher's partial differential equations for transmission lines can be discretized into a set of easily solvable algebraic equations. DQM reduces interconnects into multiport models whose port voltages and currents are related by rational formulas in the frequency domain. Although the rationalization process in DQM is comparable with the Pade approximation of asymptotic waveform evaluation (AWE) applied to transmission lines, the derivation mechanisms in these two disparate methods are significantly different. Unlike AWE, which employs a complex moment-matching process to obtain rational approximation, the DQM requires no approximation of transcendental functions, thereby avoiding the process of moment generation and moment matching. Due to global sampling of points in the DQM approximation, it requires far fewer grid points in order to build accurate discrete models than other numerical methods do. The DQM-based time-domain model can be readily integrated in a circuit simulator like SPICE.     

Controlling chaotic behavior of heavy to light hole mixingtunneling by external electric fields

Oscillatory and chaotic motion of heavy to light hole mixing tunneling in asymmetric coupled quantum-well structures can be controlled by an external electric field. Chaotic behavior occurs if the heavy-hole state in the first well is aligned with the light-hole state in the second well under a significant in-plane vector k_∥. Oscillatory motion is recovered if the external electric field disrupts the alignment between the heavy-hole state in the first well and the light-hole state in the second well     

Calculation of electric fields due to lines of charge

The amplitude of the electric field due to a straight line segment of uniform electric charges is shown to be given by E=2q (4πDε₀)^-1 sen (α/2) where q is the linear charge density, α is the viewing angle (from the observation point to the filament extremities), and D is the distance to the filament; furthermore, the direction of the vector E lies on the bisector of the viewing angle. This result can greatly reduce the computation time in the analysis of EMC (electromagnetic compatibility) problems involving static or quasi-static charge distributions     

Propagation of centimeter and millimeter spin-dipolar waves in nonuniform magnetic fields

Propagation of exchangeless spin-dipolar waves (SDW) of centimeter (f ～ 3-20 GHz) and millimeter (f ～ 30–60 GHz) wavelength ranges in ferrite films into nonuniform magnetic fields was researched analytically and numerically. Applied magnetic field is directed along film plane and it is slightly nonuniform in this plane. Proposed SDW propagation in magnetic fields was researched with complex geometric optics. We have shown a possibility of SDW type transformation from superficial SDW into backward volume SDW along propagation trajectory in both centimeter and millimeter wavelength range. An influence of electromagnetic delay on SDW propagation in nonuniform magnetic fields is essential in millimeter wavelength range and it can modify wave trajectories.     

The finite-element modeling of three-dimensional electromagneticfields using edge and nodal elements

An efficient and accurate finite-element method is presented for computing transient as well as time-harmonic electromagnetic fields in three-dimensional configurations containing arbitrarily inhomogeneous media that may be anisotropic. To obtain accurate results with an optimum computational efficiency, both consistently linear edge and consistently linear nodal elements are used for approximating the spatial distribution of the field. Compared with earlier work, the formulation is generalized by adding a method for explicitly modeling the normal continuity along interfaces that are free of surface charge. In addition, the conditions for efficiently solving time-harmonic problems using a code designed for solving transient problems are discussed. A general and simple method for implementing arbitrary inhomogeneous absorbing boundary conditions for modeling arbitrary incident fields is introduced     

Thickness dependent dielectric breakdown of PECVD low-k carbon doped silicon dioxide dielectric thin films: modeling and experiments

The experimental results obtained on the dielectric strength E_B of carbon doped silicon dioxide thin films for various film thicknesses using I-V measurements with metal-insulator-semiconductor structures suggest a new relationship between the film thickness d and the dielectric strength E_B, i.e. E_B∝(d−d_c)⁻ⁿ. This inverse power law relationship indicates the existence of a critical thickness d_c which may correspond to an ultimate thickness limit below which the rate of detrapping of electron charges exceeds the rate of trapping and no dielectric breakdown can be observed. The newly obtained inverse power law relationship appears to be general since it is also supported by other published dielectric strength data for both amorphous and polycrystalline polymer thin films.     

Control of magnetostatic waves in thin films by means of spatially nonuniform bias fields

Although magnetostatic wave devices normally employ spatially uniform magnetic bias, control of important features of the modes is afforded through judicious use of dc field gradients. Such control can be the basis for new forms of microwave signal processors.Gradients in either the field magnitude, direction, or both can be employed to affect wave dispersion or mode spectra. This is done to control prespecified characteristics such as frequency, rf energy distribution, impedance, and the velocity of energy propagation.Very general mathematical analyses of both the forward volume wave and surface wave geometries are developed for cases where the effective magnetic bias has, depending upon the mode, transverse spatial variation along either the ferrite film width or thickness caused by the applied field, saturation magnetization, magnetic anisotropy — or some combination.Computer simulation has been used to obtain eigenfrequencies and eigenmodes when the bias is uniform or nonuniform. The latter cases reveal that a great deal of control over the mode energy distributions can be exercised by the proper choice of gradients. For example, a forward volume wave can be forced to have strong field-displacement characteristics that are either nearly reciprocal or very strongly nonreciprocal.This research was supported, in part, by the Joint Services Electronic Program (JSEP) under Contract DAAG29-83-K-0003 administered by the Research Laboratory of Electronics (RLE); the National Science Foundation under Grant 8008628-DAR; and STAS 0356 administered by the Battelle Research Triangle Park Office.