Three-dimensional Current Flow Research Articles

Modelling in vivo action potential propagation along a giant axon

A partial differential equation model for the three-dimensional current flow in an excitable, unmyelinated axon is considered. Where the axon radius is significantly below a critical value R(crit) (that depends upon intra- and extra-cellular conductivity and ion channel conductance) the resistance of the intracellular space is significantly higher than that of the extracellular space, such that the potential outside the axon is uniformly small whilst the intracellular potential is approximated by the transmembrane potential. In turn, since the current flow is predominantly axial, it can be shown that the transmembrane potential is approximated by a solution to the one-dimensional cable equation. It is noted that the radius of the squid giant axon, investigated by (Hodgkin and Huxley 1952e), lies close to R(crit). This motivates us to apply the three-dimensional model to the squid giant axon and compare the results thus found to those obtained using the cable equation. In the context of the in vitro experiments conducted in (Hodgkin and Huxley 1952e) we find only a small difference between the wave profiles determined using these two different approaches and little difference between the speeds of action potential propagation predicted. This suggests that the cable equation approximation is accurate in this scenario. However when applied to the it in vivo setting, in which the conductivity of the surrounding tissue is considerably lower than that of the axoplasm, there are marked differences in both wave profile and speed of action potential propagation calculated using the two approaches. In particular, the cable equation significantly over predicts the increase in the velocity of propagation as axon radius increases. The consequences of these results are discussed in terms of the evolutionary costs associated with increasing the speed of action potential propagation by increasing axon radius.

3차원적 전류 흐름을 고려한 FinFET의 기생 Source/Drain 저항 모델링

본 논문에서는 RSD(Raised Source/Drain)구조를 가지는 FinFET에서 3차원적 전류 흐름을 고려한 소스와 드레인의 해석적 저항모델을 제시한다. FinFET은 Fin을 통해 전류가 흐르기 때문에 소스/드레인의 기생저항이 크고 채널을 포함한 전체저항에서 중요한 부분을 차지한다. 제안하는 모델은 3차원적 전류흐름을 고려하여 contact부터 channel 직전 영역까지의 소스/드레인 저항을 나타내며 contact저항과 spreading저항의 합으로 이루어져 있다. Contact저항은 전류의 흐름을 고려한 가이드라인을 통해 작은 저항의 병렬합으로 모델링되고 spreading저항은 적분을 통해 구현했다. 제안된 모델은 3D numerical solver인 Raphael의 실험결과를 통해 검증했다. 본 연구에서 제안된 기생저항 모델을 BSIM-CMG와 같은 압축모델에 구현하여 DC 및 AC 성능 예측의 정확도를 높일 수 있을 것이다.

Cost performance trade-off in thermoelectric modules with low fractional area coverage

ABSTRACTWe report a comprehensive study of the cost of materials used in the thermoelectric module as the elements, substrate, and metal interconnect are optimized for maximum output power. The power conversion cost [$/W] is analyzed. The maximum power output is found by matching both thermal and electrical impedances to the external load and heat sink. The fractional area coverage or fill factor of the thermoelement (leg) in the module is a key factor which affects the overall cost of the waste heat recovery system. Thermal spreading resistance is a function of the thermal conductivity and the thickness of the substrates. Also the air gap between the legs contributes to parasitic heat loss from the hot to the cold substrate through heat conduction and radiative heat transfer. The optimum fill factor under atmospheric air-pressure is found to be on the order of a few percent. We also take into account the three-dimensional current flow and the effect of the metallization thickness on the series resistance in the module. Calculations identify the minimum metal trace thickness needed to have a minimum impact on output power generation.

Electrical conductivity in patterned silver–mesoporous titania nanocomposite thin films: towards robust 3D nano-electrodes

The space-resolved electrical conductivity of patterned silver nanoparticle (NP) arrays embedded in mesoporous TiO(2) thin films was locally evaluated using a conductive-tip AFM. A remarkable conductivity dependence on the film mesostructure and metal NP loading was observed, confirming a three-dimensional current flow throughout the nanocomposite.

Three-dimensional current flow in a large-scale model of the cochlea and the mechanism of amplification of sound.

The mammalian inner ear uses its sensory hair cells to detect and amplify incoming sound. It is unclear whether cochlear amplification arises uniquely from a voltage-dependent mechanism (electromotility) associated with outer hair cells (OHCs) or whether other mechanisms are necessary, for the voltage response of OHCs is apparently attenuated excessively by the membrane electrical filter. The cochlea contains many thousands of hair cells organized in extensive arrays, embedded in an electrically coupled system of supporting cells. We have therefore constructed a multi-element, large-scale computational model of cochlear sound transduction to study the underlying potassium (K+) recirculation. We have included experimentally determined parameters of cochlear macromechanics, which govern sound transduction, and data on hair cells' electrical parameters including tonotopical variation in the membrane conductance of OHCs. In agreement with the experiment, the model predicts an exponential decay of extracellular longitudinal K+ current spread. In contrast to the predictions from isolated cells, it also predicts low attenuation of the OHC transmembrane receptor potential (-5 dB per decade) in the 0.2-30 kHz range. This suggests that OHC electromotility could be driven by the transmembrane potential. Furthermore, the OHC electromotility could serve as a single amplification mechanism over the entire hearing range.

Simulation of Electrical Conduction in Geomaterials by SPICE

Electrical responses of the subsurface can be used to identify geologic strata, locate anomalies, detect and delineate contamination, among many other applications. All these applications depend on the spatial variations of electrical properties in the subsurface and the resulting flow pattern of electric current. Due to the heterogeneity of the subsurface and complex boundary conditions, three-dimensional electric current flow problems are not easy to analyze, in particular when the response is frequency- and/or time-dependent. In this paper, a method of electric circuit analogy is proposed to simulate the electrical responses of geomaterials using the circuit simulator SPICE. The technique will allow simulation of more complex electrical conduction behavior of geomaterials without much extra effort. The excellent agreement between simulated results and analytical solutions developed for surface geophysical techniques establishes the viability of the method. Limitations of the approach and potential solutions to relax these limitations, and other potential applications of the technique in geosciences are also discussed.

P22.4 Investigating the mechanism of deep brain stimulation using a dynamic complex model of the head incorporated with a complete model of electrode

Background: The use of deep brain stimulation (DBS) for clinical treatment for various neurological disorders, particularly movement disorders such as Parkinson’s disease is on the increase. However, the mechanism by which this electrical stimulation acts on neuronal activity is unclear. Experimental in situ investigation of the mechanism of DBS in animal models or patients has clear limitations due to the multi-factorial nature. Objectives: Our aim is to produce an accurate computational model to simulate the current flow produced by DBS. This will increase the understanding of the precise effects of the injected current on the surrounding neural tissue and allow us to predict optimum dynamic injection and measurement protocols required to maximise the effects of DBS in a defined region of the brain. Methods: We have developed a dynamic complex head model that incorporates the complete electrode model. This model takes into account the effects of the electrode contact impedance at the interface of the electrodes. The head model is based on a realistic FEM of a human head which incorporates an estimation of the head’s tissues conductivities. Results: The results from the model yield a fuller understanding of the three-dimensional current flow in the surrounding neuronal tissues. In particular, the model shows the distribution of electric field around electrode–brain interface (EBI), depending on the characteristic magnitude, rate, impedance, and waveform of brain pulsation. Therefore this shows how this physiological modulation affects the therapeutic effect of DBS. Conclusions: A number of research groups have presented results of the electrode interface for DBS. However the previous studies have not included the correct electrode model, limiting the validity of their simulations. Inaccurate estimation of this interface effect is particularly critical when considering the dynamic properties of the current distribution and hence the effects on the neural activity.

Analysis of Magnetohydrodynamic Generator Power Generation

The three-dimensional current and fluid flow characteristics of diagonally connected magnetohydrodynamics generators are studied by means of numerical solutions. The formulation solves the Navier-Stokes equations in conjunction with the magnetic diffusion equation and a two-equation turbulence model on a hybrid unstructured grid. The current is obtained from Ampere's law, and a generalized Ohm's law is used to include the Hall effect. A flux-split upwind discretization is used for the convective terms along with a nonconservative correction that drives the divergence of the magnetic field to zero. Physical difficulties with boundary conditions are removed by extending the computational domain into the far field to encompass the plasma channel, the conducting and dielectric walls, and the surrounding air. The fluid flow and magnetic field solvers can be updated in loosely or closely coupled fashion depending on the magnetic Reynolds number. Results are shown for supersonic flow generators with both constant and diverging area channels. Properties are based on equilibrium table lookup for combustion gas products with potassium seedant.

Three-dimensional Numerical Analysis of a Liquid Metal MUD Generator

Three-dimensional numerical analysis of a liquid metal MHD generator has been carried out. The three-dimensional structures of the electromagnetic field and fluid flow in the MHD generator have been clarified, and the effect of the electrode width on the performance has been also examined, taking account of the current flow in the electrode. Structures of the electromagnetic field and fluid flow are complicated owing to the three-dimensional current flow, induced magnetic field, and Lorentz force. The highest performance is found to be obtained when the width of electrode is equal to that of the generator. The performance predicted from three-dimensional analysis is somewhat lower than that from two-dimensional analysis because of the larger input power. The increase in the input power is attributed to the increase in Lorentz force caused by less reduced magnetic flux density and to the additional friction loss on the insulator walls (x-y plane).

Impact of three-dimensional lateral current flow on ultrashallow spreading resistance profiles

The spreading resistance probe (SRP) is a widely used measurement tool for electrical characterization of Si structures. From the measured spreading resistance depth profile, the underlying electrically active dopant profile can be extracted through the application of a series of specific software corrections. In this letter, it is shown that for sub-100 nm deep structures a new type of correction is needed in order to account for the impact of three-dimensional lateral current flow through the conductive surface sublayers located above the actual measurement depth.

A triangle-shaped nanoscale metal–oxide–semiconductor device

A new fabrication process for ultrasmall high-current-density metal–oxide–semiconductor transistors is proposed. The device fabrication is based on anisotropic wet etching of silicon using bonded and etched back silicon-on-insulator (BESOI) material and a self-adjusting polysilicon gate technology. The special feature in the design of the transistor is a small silicon wire with a triangular instead of a planar cross section connecting the source and drain areas. Applying a moderate voltage to the poly-gate, a high electric field is built up in the top of the triangle which increases the volume of the conducting channel below the gate. For normal operating conditions, the three-dimensional current flow allows smaller lateral dimensions of the device that offers higher integration. Because of the BESOI material, faster device performance is expected. The physical principle is discussed and the basic fabrication techniques are described. First electrical investigations of the transistors operating at room temperature are presented providing evidence that the current density is considerably higher than in planar transistors.

Subsurface electrical impedance imaging: measurement strategy, image reconstruction and in vivo results

In conventional cross-sectional electrical impedance tomography, most of the spatial information is concentrated at the periphery of the image, close to the measurement electrodes. Increasing the number of electrodes tends not to increase the poor resolution at the centre of the cross-sectional image due to the physics of three-dimensional current flow. In this work an alternative approach, INSEIT (imaging near the surface by electrical impedance tomography), is explored in which the image plane lies at a selected depth in the object parallel to a surface electrode array. This approach has been investigated using a prototype data measurement system. The preliminary in vivo results include subsurface images of respiration, the gastro-intestinal tract and limb blood flow.

Numerical and experimental analysis of eddy current testing for a tube with cracks

A novel method for calculating the impedance signal in eddy current testing (ECT) for a tube with surface cracks is developed using the two-dimensional current vector potential method. Three-dimensional current flow around a surface crack is approximated by introducing quasi-conductivity in the crack region. A final matrix relating the current vector potentials is obtained by decreasing the width of the crack to zero, and then the elements in the crack region are not necessary any longer. Numerical results show good agreement with the experimental ones, which indicates the validity of the proposed method and the possibility of designing a more efficient probe of ECT using the code.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Shallow, small area, TiSi2 contacts to n+ and p+ silicon

Shallown + andp + doped source/drain contacts to silicon as small as 300 × 200 nm have been fabricated using an optimized silicided (TiSi2) contact technology. Well behaved structural and electrical characteristics were found. The electrical series resistance through two of such contacts from metal to metal through the semiconductor contacts increases rapidly for contact sizes below the transfer length of the contact (about 0.5 μm). This resistance increase is critically dependent on the contact resistivity and three-dimensional current flow patterns.

Three-dimensional finite element solution for biopotentials: erythrocyte in an applied field

The use of the finite-element method in the analysis of bioelectric phenomena is demonstrated. The problem studied is three-dimensional steady current flow around an erythrocyte in an extracellular medium. The finite-element equations for the electrical field problem are derived and mesh generation and the use of a heat-conduction code for analysis are described. Spherical cell geometry, allowing an analytical solution, is also modeled to guide in mesh creation and error estimation for the case of erythrocyte geometry. The results are shown as contour plots of potential on the erythrocyte surface. The maximum transmembrane potential calculated for the erythrocyte is 22% lower than that of the sphere, a significant finding since spherical geometry is often used in studies involving the effect of applied electrical fields on cells. >

Ionospheric and field-aligned current systems in the auroral zone: a concise review

During the last few years our knowledge about the real three-dimensional current flow in the auroral zone has been significantly increased due to new improved measurements, especially those made by ground-based magnetometer networks, coherent and incoherent auroral radars, sounding rockets and low-altitude satellites. Combination of two or even more of those data sets (e.g. electron densities and electric and magnetic fields) allowed for a rather accurate determination of the distribution of Hall, Pedersen and Birkeland currents in the auroral zone. In this review an attempt is made to summarize the present knowledge about the distribution of conductivity, electric field and current flow in the auroral zone as well for the large-scale electrojet systems as for the comparatively smaller current systems associated with quiet and active aurora, i.e. discrete arcs, auroral break-ups, westward travelling surges and omega bands.

Joint two-dimensional observations of ground magnetic and ionospheric electric fields associated with auroral zone currents. 2. Three-dimensional current flow in the morning sector during substorm recovery.

By using two-dimensional observations of ground magnetic perturbations with the Scandinavian Magnetometer Array and by incorporating some simultaneous electric field observations made by the STARE radars, an attempt is made to model the threedimensional current system in the late morning sector during a substorm recovery phase on February 16, 1977. During the recovery phase of substorm activity a localized region of net upward field-aligned current drifts to the east. This current is apparently carried by drift precipitation of energetic electrons which has been observed earlier by balloon and satellite spectrometers under the same geophysical conditions. The precipitating electrons responsible for the upward field-aligned current seem to shortcircuit the westward electrojet Hall current and cause its divergence up magnetic field lines. Equatorward of the auroral oval the precipitating electrons create a high-conducting channel where an eastward current is flowing. This current is probably a Cowling current and is decreasing in the eastward direction. While it remains open how this current is fed into the ionosphere, we content that the total eastward current is also diverging up magnetic field lines.

Atmospheric solar tides and their electrodynamic effects—II. The equatorial electrojet

The global-scale dynamo solution in Part I is used to determine a full three-dimensional solution within the equatorial electrojet. Inclusion of vertical currents near the magnetic equator nearly doubles the magnetic variation obtained from the thin-shell dynamo model, relaxing the need for E-region diurnal wind speeds as large as those required by previous workers to reproduce the S q current system. This occurs because the electrojet is broadened both vertically and in its north-south extent when three-dimensional current flow is permitted. The underlying physics of this enhancement of the electrojet intensity over that predicted by the thin-shell approximation is discussed. The three-dimensional electrojet structure confirms salient features of simpler noontime meriodional-plane electrojet models, if these are extended to couple with local time variations of the polarization field generated by global dynamo action. By including local winds in our electrojet model, we are able to simulate the double-peaked structures observed near the magnetic equator by rocket-borne magnetometers. The model is also utilized as an aid in elucidating other electrojet phenomena, including the occurrence of plasma instabilities and the counter-electrojet.