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.

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.

Continuous-variable Einstein-Podolsky-Rosen paradox with traveling-wave second-harmonic generation

The Einstein-Podolsky-Rosen paradox and quantum entanglement are at the heart of quantum mechanics. Here we show that single-pass traveling-wave second-harmonic generation can be used to demonstrate both entanglement and the paradox with continuous variables that are analogous to the position and momentum of the original proposal.

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.

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.

Removable singularities for p-harmonic maps: The subquadratic case

We prove a removable singularity theorem for p-harmonic maps in the subquadratic case. The theorem states that an isolated singularity of a weakly p-harmonic map is removable if the energy is sufficiently small in a neighbourhood of the singularity.

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.

A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.

Reply to comment by A. G. J. Hilberts and P. A. Troch on "Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling"

We thank Hilberts and Troch [2006] for their comment on our paper [Cartwright et al, 2005]. Before proceeding with our specific replies to the comments we would first like to clarify the definitions and meanings of equations (1)-(3) as presented by Hilberts and Troch [2006]. First, equation (1) is the fundamental definition of the (complex) effective porosity as derived by Nielsen and Perrochet [2000]. Equations (2) and (3), however, represent the linear frequency response function of the water table in the sand column responding to simple harmonic forcing. This function, which was validated by Nielsen and Perrochet [2000], provides an alternative method for estimating the complex effective porosity from the experimental sand column data in the absence of direct measurements of h_(tot) (which are required if equation (1) is to be used).