An FDTD model for calculation of gradient-induced eddy currents in MRI system

In most magnetic resonance imaging (MRI) systems, pulsed magnetic gradient fields induce eddy currents in the conducting structures of the superconducting magnet. The eddy currents induced in structures within the cryostat are particularly problematic as they are characterized by long time constants by virtue of the low resistivity of the conductors. This paper presents a three-dimensional (3-D) finite-difference time-domain (FDTD) scheme in cylindrical coordinates for eddy-current calculation in conductors. This model is intended to be part of a complete FDTD model of an MRI system including all RF and low-frequency field generating units and electrical models of the patient. The singularity apparent in the governing equations is removed by using a series expansion method and the conductor-air boundary condition is handled using a variant of the surface impedance concept. The numerical difficulty due to the asymmetry of Maxwell equations for low-frequency eddy-current problems is circumvented by taking advantage of the known penetration behavior of the eddy-current fields. A perfectly matched layer absorbing boundary condition in 3-D cylindrical coordinates is also incorporated. The numerical method has been verified against analytical solutions for simple cases. Finally, the algorithm is illustrated by modeling a pulsed field gradient coil system within an MRI magnet system. The results demonstrate that the proposed FDTD scheme can be used to calculate large-scale eddy-current problems in materials with high conductivity at low frequencies.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

Finite element analysis of fault bend influence on stick-slip instability along an intra-plate fault

Earthquakes have been recognized as resulting from stick-slip frictional instabilities along the faults between deformable rocks. A three-dimensional finite-element code for modeling the nonlinear frictional contact behaviors between deformable bodies with the node-to-point contact element strategy has been developed and applied here to investigate the fault geometry influence on the nucleation and development process of the stick-slip instability along an intra-plate fault through a typical fault bend model, which has a pre-cut fault that is artificially bent by an angle of 5.6degrees at the fault center. The numerical results demonstrate that the geometry of the fault significantly affects nucleation, termination and restart of the stick-slip instability along the intra-plate fault, and all these instability phenomena can be well simulated using the current finite-element algorithm.

Earthquake statistics in a Block Slider Model and a fully dynamic Fault Model

We examine the event statistics obtained from two differing simplified models for earthquake faults. The first model is a reproduction of the Block-Slider model of Carlson et al. (1991), a model often employed in seismicity studies. The second model is an elastodynamic fault model based upon the Lattice Solid Model (LSM) of Mora and Place (1994). We performed simulations in which the fault length was varied in each model and generated synthetic catalogs of event sizes and times. From these catalogs, we constructed interval event size distributions and inter-event time distributions. The larger, localised events in the Block-Slider model displayed the same scaling behaviour as events in the LSM however the distribution of inter-event times was markedly different. The analysis of both event size and inter-event time statistics is an effective method for comparative studies of differing simplified models for earthquake faults.

Overexpressed Ca-v beta 3 inhibits N-type (Ca(v)2.2) calcium channel currents through a hyperpolarizing shift of "ultra-slow" and "closed-state" inactivation

It has been shown that P auxiliary subunits increase current amplitude in voltage-dependent calcium channels. In this study, however, we found a hovel inhibitory effect of beta3 Subunit on macroscopic Ba2+ currents through recombinant N- and R-type calcium channels expressed in Xenopus oocytes. Overexpressed beta3 (12.5 ng/ cell cRNA) significantly suppressed N- and R-type, but not L-type, calcium channel currents at physiological holding potentials (HPs) of -60 and -80 mV At a HP of -80 mV, coinjection of various concentrations (0-12.5 ng) of the beta3 with Ca,.2.2alpha(1) and alpha(2)delta enhanced the maximum conductance of expressed channels at lower beta3 concentrations but at higher concentrations (>2.5 ng/cell) caused a marked inhibition. The beta3-induced Current suppression was reversed at a HP of - 120 mV, suggesting that the inhibition was voltage dependent. A high concentration of Ba-2divided by (40 mM) as a charge carrier also largely diminished the effect of P3 at -80 mV Therefore, experimental conditions (HP, divalent cation concentration, and P3 subunit concentration) approaching normal physiological conditions were critical to elucidate the full extent of this novel P3 effect. Steady-state inactivation curves revealed that N-type channels exhibited closed-state inactivation without P3, and that P3 caused an similar to40 mV negative shift of the inactivation, producing a second component with an inactivation midpoint of approximately -85 mV The inactivation of N-type channels in the presence of a high concentration (12.5 ng/cell) of P3 developed slowly and the time-dependent inactivation curve was best fit by the sum of two exponential functions with time constants of 14 s and 8.8 min at -80 mV Similar ultra-slow inactivation was observed for N-type channels Without P3. Thus, P3 can have a profound negative regulatory effect on N-type (and also R-type) calcium channels by Causing a hyperpolarizing shift of the inactivation without affecting ultra-slow and closed-state inactivation properties.

Theoretical investigation of convective instability in inclined and fluid-saturated three-dimensional fault zones.

The convective instability of pore-fluid flow in inclined and fluid-saturated three-dimensional fault zones has been theoretically investigated in this paper. Due to the consideration of the inclined three-dimensional fault zone with any values of the inclined angle, it is impossible to use the conventional linear stability analysis method for deriving the critical condition (i.e., the critical Rayleigh number) which can be used to investigate the convective instability of the pore-fluid flow in an inclined three-dimensional fault zone system. To overcome this mathematical difficulty, a combination of the variable separation method and the integration elimination method has been used to derive the characteristic equation, which depends on the Rayleigh number and the inclined angle of the inclined three-dimensional fault zone. Using this characteristic equation, the critical Rayleigh number of the system can be numerically found as a function of the inclined angle of the three-dimensional fault zone. For a vertically oriented three-dimensional fault zone system, the critical Rayleigh number of the system can be explicitly derived from the characteristic equation. Comparison of the resulting critical Rayleigh number of the system with that previously derived in a vertically oriented three-dimensional fault zone has demonstrated that the characteristic equation of the Rayleigh number is correct and useful for investigating the convective instability of pore-fluid flow in the inclined three-dimensional fault zone system. The related numerical results from this investigation have indicated that: (1) the convective pore-fluid flow may take place in the inclined three-dimensional fault zone; (2) if the height of the fault zone is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone stabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; (3) if the thickness of the stratum is used as the characteristic length of the system, a decrease in the inclined angle of the inclined fault zone destabilizes the three-dimensional fundamental convective flow in the inclined three-dimensional fault zone system; and that (4) the shape of the inclined three-dimensional fault zone may affect the convective instability of pore-fluid flow in the system. (C) 2004 Published by Elsevier B.V.

Independent roles of calcium and voltage-dependent potassium currents in controlling spike frequency adaptation in lateral amygdala pyramidal neurons

The calcium-dependent afterhyperpolarization (AHP) that follows trains of action potentials is responsible for controlling action potential firing patterns in many neuronal cell types. We have previously shown that the slow AHP contributes to spike frequency adaptation in pyramidal neurons in the rat lateral amygdala. In addition, a dendritic voltage-gated potassium current mediated by Kv1.2-containing channels also suppresses action potential firing in these neurons. In this paper we show that this voltage-gated potassium current and the slow AHP act together to control spike frequency adaptation in lateral amygdala pyramidal neurons. The two currents have similar effects on action potential number when firing is evoked either by depolarizing current injections or by synaptic stimulation. However, they differ in their control of firing frequency, with the voltage-gated potassium current but not the slow AHP determining the initial frequency of action potential firing. This dual mechanism of controlling firing patterns is unique to lateral amygdala neurons and is likely to contribute to the very low levels of firing seen in lateral amygdala neurons in vivo.

Intravenous anaesthetics inhibit nicotinic acetylcholine receptor-mediated currents and Ca2+ transients in rat intracardiac ganglion neurons

1 The effects of intravenous (i.v.) anaesthetics on nicotinic acetylcholine receptor (nAChR)-induced transients in intracellular free Ca2+ concentration ([Ca2+](i)) and membrane currents were investigated in neonatal rat intracardiac neurons. 2 In fura-2-loaded neurons, nAChR activation evoked a transient increase in [Ca2+](i), which was inhibited reversibly and selectively by clinically relevant concentrations of thiopental. The half-maximal concentration for thiopental inhibition of nAChR-induced [Ca2+](i) transients was 28 muM, close to the estimated clinical EC50 (clinically relevant (half-maximal) effective concentration) of thiopental. 3 In fura-2-loaded neurons, voltage clamped at -60mV to eliminate any contribution of voltage-gated Ca2+ channels, thiopental (25 muM) simultaneously inhibited nAChR-induced increases in [Ca2+](i) and peak current amplitudes. Thiopental inhibited nAChR-induced peak current amplitudes in dialysed whole-cell recordings by - 40% at - 120, -80 and -40 mV holding potential, indicating that the inhibition is voltage independent. 4 The barbiturate, pentobarbital and the dissociative anaesthetic, ketamine, used at clinical EC50 were also shown to inhibit nAChR-induced increases in [Ca2+](i) by similar to40%. 5 Thiopental (25 muM) did not inhibit caffeine-, muscarine- or ATP-evoked increases in [Ca2+](i), indicating that inhibition of Ca2+ release from internal stores via either ryanodine receptor or inositol-1,4,5-trisphosphate receptor channels is unlikely. 6 Depolarization-activated Ca2+ channel currents were unaffected in the presence of thiopental (25 muM), pentobarbital (50 muM) and ketamine (10 muM). 7 In conclusion, i.v. anaesthetics inhibit nAChR-induced currents and [Ca2+](i) transients in intracardiac neurons by binding to nAChRs and thereby may contribute to changes in heart rate and cardiac output under clinical conditions.

Voltage-dependent inhibition of recombinant NMDA receptor-mediated currents by 5-hydroxytryptamine

1 The effect of 5-HT and related indolealkylamines on heteromeric recombinant NMDA receptors expressed in Xenopus oocytes was investigated using the two-electrode voltage-clamp recording technique. 2 In the absence of external Mg2+ ions, 5-HT inhibited NMDA receptor-mediated currents in a concentration-dependent manner. The inhibitory effect of 5-HT was independent of the NR1a and NR2 subunit combination. 3 The inhibition of glutamate-evoked currents by 5-HT was use- and voltage-dependent. The voltage sensitivity of inhibition for NR1a+NR2 subunit combinations by 5-HT was similar, exhibiting an e-fold change per similar to20 mV, indicating that 5-HT binds to a site deep within the membrane electric field. 4 The inhibition of the open NMDA receptor by external Mg2+ and 5-HT was not additive, suggesting competition between Mg2+ and 5-HT for a binding site in the NMDA receptor channel. The concentration-dependence curves for 5-HT and 5-methoxytryptamine (5-MeOT) inhibition of NMDA receptor-mediated currents are shifted to the right in the presence of external Mg2+. 5 The related indolealkylamines inhibited glutamate-evoked currents with the following order of inhibitory potency: 5-MeOT = 5-methyltryptamine > tryptamine > 7-methyltryptamine > 5-HTmuch greater than tryptophan melatonin. 6 Taken together, these data suggest that 5-HT and related compounds can attenuate glutamate-mediated excitatory synaptic responses and may provide a basis for drug treatment of excitoxic neurodegeneration.

Thermal and electrical currents in nanoscale electronic interferometers

We theoretically study thermal transport in an electronic interferometer comprising a parallel circuit of two quantum dots, each of which has a tunable single electronic state which are connected to two leads at different temperature. As a result of quantum interference, the heat current through one of the dots is in the opposite direction to the temperature gradient. An excess heat current flows through the other dot. Although locally, heat flows from cold to hot, globally the second law of thermodynamics is not violated because the entropy current associated with heat transfer through the whole device is still positive. The temperature gradient also induces a circulating electrical current, which makes the interferometer magnetically polarized.

Primary Fields and Screening Currents of gl (2/2) non-unitary conformal field theory

The non-semisimple gl(2)k current superalgebra in the standard basis and the corresponding non-unitary conformal field theory are investigated. Infinite families of primary fields corresponding to all finite-dimensional irreducible typical and atypical representations of gl(212) and three (two even and one odd) screening currents of the first kind are constructed explicitly in terms of ten free fields. (C) 2004 Elsevier B.V All rights reserved.

Extension of dynamic model of impulse behavior of concentrated grounds at high currents

A dynamic model which describes the impulse behavior of concentrated grounds at high currents is described in this paper. This model is an extension of previous models in that it can successfully account for the surge behavior of concentrated grounds over a much wider range of current densities. It is able to describe the well known effect of ionization of soil as well as the observed effect of discrete breakdowns and filamentary arc paths at much higher currents. Results of verification against experimental results are also presented.

Analysis of transient eddy currents in MRI using a cylindrical FDTD method

Most magnetic resonance imaging (MRI) spatial encoding techniques employ low-frequency pulsed magnetic field gradients that undesirably induce multiexponentially decaying eddy currents in nearby conducting structures of the MRI system. The eddy currents degrade the switching performance of the gradient system, distort the MRI image, and introduce thermal loads in the cryostat vessel and superconducting MRI components. Heating of superconducting magnets due to induced eddy currents is particularly problematic as it offsets the superconducting operating point, which can cause a system quench. A numerical characterization of transient eddy current effects is vital for their compensation/control and further advancement of the MRI technology as a whole. However, transient eddy current calculations are particularly computationally intensive. In large-scale problems, such as gradient switching in MRI, conventional finite-element method (FEM)-based routines impose very large computational loads during generation/solving of the system equations. Therefore, other computational alternatives need to be explored. This paper outlines a three-dimensional finite-difference time-domain (FDTD) method in cylindrical coordinates for the modeling of low-frequency transient eddy currents in MRI, as an extension to the recently proposed time-harmonic scheme. The weakly coupled Maxwell's equations are adapted to the low-frequency regime by downscaling the speed of light constant, which permits the use of larger FDTD time steps while maintaining the validity of the Courant-Friedrich-Levy stability condition. The principal hypothesis of this work is that the modified FDTD routine can be employed to analyze pulsed-gradient-induced, transient eddy currents in superconducting MRI system models. The hypothesis is supported through a verification of the numerical scheme on a canonical problem and by analyzing undesired temporal eddy current effects such as the B-0-shift caused by actively shielded symmetric/asymmetric transverse x-gradient head and unshielded z-gradient whole-body coils operating in proximity to a superconducting MRI magnet.

Dynamic rupture in a 3-D particle-based simulation of a rough planar fault

An appreciation of the physical mechanisms which cause observed seismicity complexity is fundamental to the understanding of the temporal behaviour of faults and single slip events. Numerical simulation of fault slip can provide insights into fault processes by allowing exploration of parameter spaces which influence microscopic and macroscopic physics of processes which may lead towards an answer to those questions. Particle-based models such as the Lattice Solid Model have been used previously for the simulation of stick-slip dynamics of faults, although mainly in two dimensions. Recent increases in the power of computers and the ability to use the power of parallel computer systems have made it possible to extend particle-based fault simulations to three dimensions. In this paper a particle-based numerical model of a rough planar fault embedded between two elastic blocks in three dimensions is presented. A very simple friction law without any rate dependency and no spatial heterogeneity in the intrinsic coefficient of friction is used in the model. To simulate earthquake dynamics the model is sheared in a direction parallel to the fault plane with a constant velocity at the driving edges. Spontaneous slip occurs on the fault when the shear stress is large enough to overcome the frictional forces on the fault. Slip events with a wide range of event sizes are observed. Investigation of the temporal evolution and spatial distribution of slip during each event shows a high degree of variability between the events. In some of the larger events highly complex slip patterns are observed.