Current Dipole Moment Research Articles

Understanding magnetic fields, for NMR/MRI

The basic physics of magnetic fields is presented for a target audience of NMR workers. This group often does not have formal training in electromagnetism, but could benefit from an understanding of a selected subset of topics. The focus here is on a relatively non-mathematical view, intended to deliver an intuitive understanding of the topic. The covered topics start with the fields arising from simple idealized currents, including long straight wires, short flat coils, infinite current sheets, long solenoids, and magnetic dipole moments. The generation of field gradients and shim fields is discussed. All of these can be unified by considering the divergence and curl of the magnetic field. Magnetic materials are treated, both linear magnetizable materials (including the sample itself) and permanently magnetized materials; the approaches of equivalent currents and Ampere's theorem for magnetic circuits are presented.

ALP-assisted strong first-order electroweak phase transition and baryogenesis

Axion-like particles (ALPs) can be naturally lighter than the electroweak scale. We consider an ALP that couples to the Standard Model Higgs to achieve the strong first-order electroweak phase transition. We discuss the two-field dynamics of the phase transition and the associated computation in detail and identify the viable parameter space. The ALP mass can be from the MeV to GeV scale. Baryon asymmetry can be explained by local baryogenesis without violating the current electron and atom electric dipole moment bound in most of the viable parameter space. The viable parameter space can be probed through Higgs exotic decay, rare kaon decay, the electron and atomic electric dipole moment, and the effective number of neutrinos in the cosmic microwave background in the future. The gravitational-wave signal is too weak to be detected.

A reformulation of the brain’s magneto-quasistatic approximation and a formalism for the long-distance magnetic field generated by populations of neurons

To evaluate the long-distance magnetic field generated by neurons, we propose a reformulation of the brain’s magneto-quasistatic approximation based on the Jefimenko’s time-dependent generalization of the Biot–Savart law. This differs from the traditional approach relying on Maxwell’s equations and not on their general solution. Instead of a typical length of the medium in the conventional approach, we use the signal traveling distance |r−r′¯|, from the farthest source point r′¯ to the field point r, as the proper length to define the quasistatic dynamics. We consider relatively low frequencies below a typical value fmax=100Hz. The quasistatic approximation is justified since (2πfmax)2|r−r′¯|2ϵμ0≈4×10−7≪1. We take |r−r′¯|≈0.1m, with the gray matter permittivity, previously underestimated, to be ϵ≈107ϵ0. A formalism for the long-distance magnetic field generated by neuronal populations is then developed. Each population is described as a region of small dimensions compared to the average distance from the field point. We split the impressed current density into synaptic and action potential contributions and study their magnetic field. Assuming a small contribution of the impressed currents at the region boundary surface, we obtain two equivalent expressions of the synaptic current dipole moment in terms of the scalar potential and/or its spatial derivatives. Using Maxwell–Wagner’s time, the synaptic current dipole moment of a region is also shown to be related to the electric dipole moment of each part with uniform conductivity and permittivity. Finally, the long-distance magnetic field of action potential currents is expressed in terms of the magnetic dipole moment for these currents.

Constraining CP-violating electron-gluonic operators

We present an analysis of constraints on two types of CP-odd electron-gluonic operators (ēiγ5e)GμνaGaμν and left(overline{e}eright){G}_{mu nu}^a{overset{sim }{G}}^{amu nu } from current and future electric dipole moment (EDM) experiments. The recent result from the ACME experiment using ThO molecules is used to derive an impressive lower bound on the effective scale for (ēiγ5e)GμνaGaμν at 8 TeV, assuming a QCD one-loop factor and no helicity suppression from new physics. One interesting aspect is that (ēiγ5e)GμνaGaμν contributes to the observable EDM in ThO experiment mainly through CP-odd electron-nucleon interaction rather than direct electron EDM which arises from three-loop running and matching. For left(overline{e}eright){G}_{mu nu}^a{overset{sim }{G}}^{amu nu } the current bound is much weaker and suffers from large uncertainties. We also discuss the QCD running and matching for the CP-odd electron-gluonic operators and give an estimate of the relevant nucleon matrix elements and uncertainties that are needed in the calculation.

Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0.

Recordings of extracellular electrical, and later also magnetic, brain signals have been the dominant technique for measuring brain activity for decades. The interpretation of such signals is however nontrivial, as the measured signals result from both local and distant neuronal activity. In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons. Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed. This allows for the development of computational tools implementing forward models grounded in the biophysics underlying electrical and magnetic measurement modalities. LFPy (LFPy.readthedocs.io) incorporated a well-established scheme for predicting extracellular potentials of individual neurons with arbitrary levels of biological detail. It relies on NEURON (neuron.yale.edu) to compute transmembrane currents of multicompartment neurons which is then used in combination with an electrostatic forward model. Its functionality is now extended to allow for modeling of networks of multicompartment neurons with concurrent calculations of extracellular potentials and current dipole moments. The current dipole moments are then, in combination with suitable volume-conductor head models, used to compute non-invasive measures of neuronal activity, like scalp potentials (electroencephalographic recordings; EEG) and magnetic fields outside the head (magnetoencephalographic recordings; MEG). One such built-in head model is the four-sphere head model incorporating the different electric conductivities of brain, cerebrospinal fluid, skull and scalp. We demonstrate the new functionality of the software by constructing a network of biophysically detailed multicompartment neuron models from the Neocortical Microcircuit Collaboration (NMC) Portal (bbp.epfl.ch/nmc-portal) with corresponding statistics of connections and synapses, and compute in vivo-like extracellular potentials (local field potentials, LFP; electrocorticographical signals, ECoG) and corresponding current dipole moments. From the current dipole moments we estimate corresponding EEG and MEG signals using the four-sphere head model. We also show strong scaling performance of LFPy with different numbers of message-passing interface (MPI) processes, and for different network sizes with different density of connections. The open-source software LFPy is equally suitable for execution on laptops and in parallel on high-performance computing (HPC) facilities and is publicly available on GitHub.com.

Exploring dynamical CP violation induced baryogenesis by gravitational waves and colliders

By assuming a dynamical source of CP violation, the tension between sufficient CP violation for successful electroweak baryogenesis and strong constraints from current electric dipole moment measurements could be alleviated. We study how to explore such scenarios through gravitational wave detection, collider experiments, and their possible synergies with a well-studied example.

The method of suppressing spatial filter output noise-power gain for cardiac electrical activity imaging

For non-invasive imaging of cardiac electrical activity using magnetocardiogram (MCG) data measured on human body surface, a key problem that needs to be solved is to enhance the spatial resolution of reconstructing distributed current source dipole moment strength in MCG imaging. In this paper, a beamforming method of suppressing spatial filter output noise-power gain (SONG) is proposed based on the minimum variance beamforming (MVB). The purpose is to improve the resolution of the distributed source dipole moment strength reconstruction, i.e., the ability to resolve the source for distributed current source spatial spectrum estimation, in order to enhance the resolution of the cardiac electrical activity magnetic imaging. The method offers a new spatial filter weight matrix by using a low-trace positively-semidefinite matrix that will affect the spatial filter output power, on the premise that the influence of noise spatial spectrum of spatial filter on the estimation of current source spatial spectrum has been constrained by the noise spatial spectrum intensity normalization. The positively-semidefinite matrix is specially constructed to satisfy the condition that the eigenvalue is not greater than 1 and the trace of the matrix is lower than its order, so that it can be used to constrain the spatial filter output noise-power gain for improving the robustness to noise of the source spatial spectrum estimation. In addition, a classical model of the horizontally layered conductor is used as the heart-torso model to calculate the lead-field matrix that needs to be used in source spatial spectrum estimation. The results obtained in this study are as follows. For validating the proposed method, a theoretical analysis and simulation tests of the current source reconstruction are performed, where the SONG and MVB methods are compared and a parameter of the signal-to-noise ratio is considered according to the realistic MCG data. In this paper we also give the cardiac electrical activity imaging of 36-channel cardiac magnetic field data of single-cycle from two healthy people, where a heart profile from the magnetic resonance imaging is used as a reference and adjusted to the MCG measurement system. The results show that the SONG method has ability to better resolve the current source and can observe the significant electrophysiological characteristics such as the strong electrical activity in the ventricles of the healthy people at the time of Rpeak. In summary, our proposed method can improve the visual effect of the cardiac electrical activity imaging, when the signal-to-noise ratio of the single-cycle cardiac magnetic signal is not lower than 10 dB. Therefore, this method of measuring the non-invasively imaging cardiac electrical activity is a promising one and helpful for relevant medical research and applications.

Broadband Rydberg atom-based radio-frequency field sensor

Significant progress has been made in atom-based measurements of length, time, gravity and electromagnetic fields in recently years. Rydberg atom-based microwave electric field measurement, using electromagnetically induced transparency (EIT) in room temperature alkali-metal vapors, has been extensively investigated and aroused the broad interest. This approach may establish a new standard for the measurements of microwave (MW) and radio frequency (RF) electric fields.In this review, we describe the work on a new method of measuring electric fields based on quantum interference by using either cesium or rubidium atoms contained in a dielectric vapor cell. Rydberg atoms with principal quantum number n >>1 have large direct current (DC) polarizabilities and microwave transition dipole moments, thereby making them extremely sensitive to external electric fields. Using the Rydberg three-level EIT to detect the level splitting and shift that is induced by the external field, we can realize a rapid and robust self-calibration method of measuring the electric field in a frequency range from 0.01 GHz to 1000 GHz. For the MW electric field (frequency range > 1 GHz), the MW field causes the Rydberg states to split, known as an Autler-Townes splitting (A-T) effect when the applied microwave can resonate with adjacent Rydberg states. The MW coupled A-T splitting is proportional to the applied electric field strength, from which the field strength is measured. Using the EIT window, a high sensitivity of 3 μV·cm-1·Hz-1/2 and small electric field of 1 μV/cm are expected to be achieved with a modest setup, and the limitations of the sensitivity are also addressed in the review. For the RF field at frequency mj EIT lines, and avoided crossings formed with the fine-structure levels of equal mj and different J's, which is used to calibrate and measure the RF field amplitude. On the other hand, the dependence of the EIT-line strength on the RF field polarization provides a fast and robust polarization measurement of RF fields based on matching experimental data with a theoretical simulation. The measurements of minimum strengths and sensitivity of RF fields based on Rydberg atoms are one order magnitude below the values obtained by traditional antenna methods. The atom-based field measurement paves the way for determining fields through calibration-free, invariable atomic properties and miniaturization. We also propose its various potential applications in the future.

Vibrational circular dichroism from ab initio molecular dynamics and nuclear velocity perturbation theory in the liquid phase.

We report the first fully ab initio calculation of dynamical vibrational circular dichroism spectra in the liquid phase using nuclear velocity perturbation theory (NVPT) derived electronic currents. Our approach is rigorous and general and thus capable of treating weak interactions of chiral molecules as, e.g., chirality transfer from a chiral molecule to an achiral solvent. We use an implementation of the NVPT that is projected along the dynamics to obtain the current and magnetic dipole moments required for accurate intensities. The gauge problem in the liquid phase is resolved in a twofold approach. The electronic expectation values are evaluated in a distributed origin gauge, employing maximally localized Wannier orbitals. In a second step, the gauge invariant spectrum is obtained in terms of a scaled molecular moments, which allows to systematically include solvent effects while keeping a significant signal-to-noise ratio. We give a thorough analysis and discussion of this choice of gauge for the liquid phase. At low temperatures, we recover the established double harmonic approximation. The methodology is applied to chiral molecules ((S)-d2-oxirane and (R)-propylene-oxide) in the gas phase and in solution. We find an excellent agreement with the theoretical and experimental references, including the emergence of signals due to chirality transfer from the solute to the (achiral) solvent.

Magnetic fields in QCD vacuum: A lattice view

We review the basic phenomena in QCD subject to strong magnetic fields which are accessible in experiment and can be also studied in lattice QCD simulations: enhanced fluctuations of electric current and electric dipole moment, the negative magnetoresistivity and the inverse magnetic catalysis. We comment on the possibility of experimental detection of negative magnetoresistivity by analysing the angular distributions of dilepton pairs in off-central heavy-ion collisions.

Relating follicly-challenged compact stars to bald black holes: A link between two no-hair properties

Compact stars satisfy certain no-hair relations through which their multipole moments are given by their mass, spin and quadrupole moment. These relations are approximately independent of their equation of state, relating pressure to density. Such relations are similar to the black hole no-hair theorems, but these possess event horizons inside which information that led to their formation can hide. Compact stars do not possess horizons, so whether their no-hair relations are related to the black hole ones is unclear. We investigate how the two relations are related by studying relations among multipole moments for compact stars with anisotropic pressure as a toy model, which allows such stars to be more compact than those with isotropic pressure. We here show numerically that the compact star no-hair relations approach the black hole ones as the compactness approaches that of a black hole. We also prove analytically that the current dipole moment exactly reaches the black hole limit quadratically in compactness as strongly-anisotropic stars approach the black hole limit. We moreover show that compact stars become progressively oblate in this limit, even if prolate at low compactness due to strong anisotropies.

Invariance in current dipole moment density across brain structures and species: Physiological constraint for neuroimaging

Although anatomical constraints have been shown to be effective for MEG and EEG inverse solutions, there are still no effective physiological constraints. Strength of the current generator is normally described by the moment of an equivalent current dipole Q. This value is quite variable since it depends on size of active tissue. In contrast, the current dipole moment density q, defined as Q per surface area of active cortex, is independent of size of active tissue. Here we studied whether the value of q has a maximum in physiological conditions across brain structures and species. We determined the value due to the primary neuronal current (qprimary) alone, correcting for distortions due to measurement conditions and secondary current sources at boundaries separating regions of differing electrical conductivities. The values were in the same range for turtle cerebellum (0.56–1.48nAm/mm2), guinea pig hippocampus (0.30–1.34nAm/mm2), and swine neocortex (0.18–1.63nAm/mm2), rat neocortex (~2.2nAm/mm2), monkey neocortex (~0.40nAm/mm2) and human neocortex (0.16–0.77nAm/mm2). Thus, there appears to be a maximum value across the brain structures and species (1–2nAm/mm2). The empirical values closely matched the theoretical values obtained with our independently validated neural network model (1.6–2.8nAm/mm2 for initial spike and 0.7–3.1nAm/mm2 for burst), indicating that the apparent invariance is not coincidental. Our model study shows that a single maximum value may exist across a wide range of brain structures and species, varying in neuron density, due to fundamental electrical properties of neurons. The maximum value of qprimary may serve as an effective physiological constraint for MEG/EEG inverse solutions.

Structure predicts function: Combining non-invasive electrophysiology with in-vivo histology

We present an approach for combining high resolution MRI-based myelin mapping with functional information from electroencephalography (EEG) or magnetoencephalography (MEG). The main contribution to the primary currents detectable with EEG and MEG comes from ionic currents in the apical dendrites of cortical pyramidal cells, aligned perpendicularly to the local cortical surface. We provide evidence from an in-vivo experiment that the variation in MRI-based myeloarchitecture measures across the cortex predicts the variation of the current density over individuals and thus is of functional relevance. Equivalent current dipole locations and moments due to pitch onset evoked response fields (ERFs) were estimated by means of a variational Bayesian algorithm. The myeloarchitecture was estimated indirectly from individual high resolution quantitative multi-parameter maps (MPMs) acquired at 800μm isotropic resolution. Myelin estimates across cortical areas correlated positively with dipole magnitude. This correlation was spatially specific: regions of interest in the auditory cortex provided significantly better models than those covering whole hemispheres. Based on the MPM data we identified the auditory cortical area TE1.2 as the most likely origin of the pitch ERFs measured by MEG. We can now proceed to exploit the higher spatial resolution of quantitative MPMs to identify the cortical origin of M/EEG signals, inform M/EEG source reconstruction and explore structure–function relationships at a fine structural level in the living human brain.

Power laws from linear neuronal cable theory: power spectral densities of the soma potential, soma membrane current and single-neuron contribution to the EEG.

Power laws, that is, power spectral densities (PSDs) exhibiting behavior for large frequencies f, have been observed both in microscopic (neural membrane potentials and currents) and macroscopic (electroencephalography; EEG) recordings. While complex network behavior has been suggested to be at the root of this phenomenon, we here demonstrate a possible origin of such power laws in the biophysical properties of single neurons described by the standard cable equation. Taking advantage of the analytical tractability of the so called ball and stick neuron model, we derive general expressions for the PSD transfer functions for a set of measures of neuronal activity: the soma membrane current, the current-dipole moment (corresponding to the single-neuron EEG contribution), and the soma membrane potential. These PSD transfer functions relate the PSDs of the respective measurements to the PSDs of the noisy input currents. With homogeneously distributed input currents across the neuronal membrane we find that all PSD transfer functions express asymptotic high-frequency power laws with power-law exponents analytically identified as for the soma membrane current, for the current-dipole moment, and for the soma membrane potential. Comparison with available data suggests that the apparent power laws observed in the high-frequency end of the PSD spectra may stem from uncorrelated current sources which are homogeneously distributed across the neural membranes and themselves exhibit pink () noise distributions. While the PSD noise spectra at low frequencies may be dominated by synaptic noise, our findings suggest that the high-frequency power laws may originate in noise from intrinsic ion channels. The significance of this finding goes beyond neuroscience as it demonstrates how power laws with a wide range of values for the power-law exponent α may arise from a simple, linear partial differential equation.

Action potentials contribute to epileptic high-frequency oscillations recorded with electrodes remote from neurons

ObjectiveThe importance of epileptic high-frequency oscillations (HFOs) in electroencephalogram (EEG) is growing. Action potentials generating some HFOs are observed in the vicinity of neurons in experimental animals. However electrodes that are remote from neurons, as in case of clinical situations, should not record action potentials. We propose to resolve this question by a realistic simulation of epileptic neuronal network. MethodsThe rat dentate gyrus with sclerosis was simulated in silico. We computed the current dipole moment generated by each granule cell and the field potentials in a measurement area far from neurons. ResultsThe dentate gyrus was stimulated through synaptic input to evoke discharges resembling interictal epileptiform discharges, which had superimposed HFOs⩽295Hz that were recordable with remote electrodes and represented bursts of action potentials of granule cells. The increase in power of HFOs was associated with the progression of sclerosis, the reduction of GABAergic inhibition, and the increase in cell connectivity. Spectral frequency of HFOs had similar tendencies. ConclusionsHFOs recorded with electrodes remote from neurons could actually be generated by clusters of action potentials. SignificanceThe phenomenon of action potentials recorded with remote electrodes can possibly extend the clinical meaning of EEG.

Simultaneous measurement of tunneling current and atomic dipole moment on Si(111)-(7 × 7) surface by noncontact scanning nonlinear dielectric microscopy

Non-contact scanning nonlinear dielectric microscopy (NC-SNDM) can resolve the topography and dipole moment distribution of a Si(111)-(7 × 7) surface on an atomic level. We discuss the origin of the atomic contrast in dipole moment images based on simultaneously acquired time-averaged tunneling current images. The dipole moment images are found to have the same characteristics as the simultaneously acquired current images. This similarity between these two images does not originate from circuit crosstalk since it is suppressed by our circuit design that decouples the tip-sample capacitance and the tunneling current. Constant-height images also indicate that the atomic contrast is not artificially caused by feedback crosstalk. These results suggest that the atomic contrast is due to the variation in the tip-sample capacitance caused by modulation of atomic dipole moments by the local density of states of the surface.

Thermal noise calculation method for precise estimation of the signal-to-noise ratio of ultra-low-field MRI with an atomic magnetometer

In recent years, there has been considerable interest in developing an ultra-low-field magnetic resonance imaging (ULF-MRI) system using an optically pumped atomic magnetometer (OPAM). However, a precise estimation of the signal-to-noise ratio (SNR) of ULF-MRI has not been carried out. Conventionally, to calculate the SNR of an MR image, thermal noise, also called Nyquist noise, has been estimated by considering a resistor that is electrically equivalent to a biological-conductive sample and is connected in series to a pickup coil. However, this method has major limitations in that the receiver has to be a coil and that it cannot be applied directly to a system using OPAM. In this paper, we propose a method to estimate the thermal noise of an MRI system using OPAM. We calculate the thermal noise from the variance of the magnetic sensor output produced by current-dipole moments that simulate thermally fluctuating current sources in a biological sample. We assume that the random magnitude of the current dipole in each volume element of the biological sample is described by the Maxwell–Boltzmann distribution. The sensor output produced by each current-dipole moment is calculated either by an analytical formula or a numerical method based on the boundary element method. We validate the proposed method by comparing our results with those obtained by conventional methods that consider resistors connected in series to a pickup coil using single-layered sphere, multi-layered sphere, and realistic head models. Finally, we apply the proposed method to the ULF-MRI model using OPAM as the receiver with multi-layered sphere and realistic head models and estimate their SNR.

Can power laws in macroscopic and microscopic neural recordings be explained by the cable properties of neurons?

Can power laws in macroscopic and microscopic neural recordings be explained by the cable properties of neurons?

Inversion of self-potential of idealized bodies’ anomalies using particle swarm optimization

The particle swarm optimization (PSO) method was applied to the inversion of single and multiple self-potential (SP) data anomalies caused by buried bodies with simple geometry like spheres, cylinders and inclined sheets. The inversion parameters are the depth of the body, the location of the anomaly, the electric current dipole moment, the polarization angle or the inclination angle and the half-width in the sheet-like body case. The algorithm was tested on synthetic data with single and multiple SP anomalies and applied to two experimental data from Surda area (India) and Vilarelho da Raia (Portugal). The inversion results showed good agreement with the previous results obtained using other techniques. The great advantage of the PSO method is that it is fast and does not require assumptions about the shape of the source of the SP anomaly.

Intrinsic dendritic filtering gives low-pass power spectra of local field potentials

The local field potential (LFP) is among the most important experimental measures when probing neural population activity, but a proper understanding of the link between the underlying neural activity and the LFP signal is still missing. Here we investigate this link by mathematical modeling of contributions to the LFP from a single layer-5 pyramidal neuron and a single layer-4 stellate neuron receiving synaptic input. An intrinsic dendritic low-pass filtering effect of the LFP signal, previously demonstrated for extracellular signatures of action potentials, is seen to strongly affect the LFP power spectra, even for frequencies as low as 10 Hz for the example pyramidal neuron. Further, the LFP signal is found to depend sensitively on both the recording position and the position of the synaptic input: the LFP power spectra recorded close to the active synapse are typically found to be less low-pass filtered than spectra recorded further away. Some recording positions display striking band-pass characteristics of the LFP. The frequency dependence of the properties of the current dipole moment set up by the synaptic input current is found to qualitatively account for several salient features of the observed LFP. Two approximate schemes for calculating the LFP, the dipole approximation and the two-monopole approximation, are tested and found to be potentially useful for translating results from large-scale neural network models into predictions for results from electroencephalographic (EEG) or electrocorticographic (ECoG) recordings.