Field Strength Gradient Research Articles

A Macroscopic Model for the Diffusion MRI Signal Accounting for Time-Dependent Diffusivity

Diffusion magnetic resonance imaging (dMRI) encodes water displacement due to diffusion and is a powerful tool for obtaining information on the tissue microstructure. An important quantity measured in dMRI in each voxel is the apparent diffusion coefficient ($ADC$), and it is well established from imaging experiments that, in the brain, in vivo, the $ADC$ is dependent on the measured diffusion time. To aid in the understanding and interpretation of the $ADC$, using homogenization techniques, we derived a new asymptotic model for the dMRI signal from the Bloch--Torrey equation governing the water proton magnetization under the influence of diffusion-encoding magnetic gradient pulses. Our new model was obtained using a particular choice of scaling for the time, the biological cell membrane permeability, the diffusion-encoding magnetic field gradient strength, and a periodicity length of the cellular geometry. The $ADC$ of the resulting model is dependent on the diffusion time. We numerically validated this model for a wide range of diffusion times for two-dimensional geometrical configurations.

Simultaneous iterative reconstruction technique software for spectral–spatial EPR imaging

Continuous wave electron paramagnetic resonance imaging (EPRI) experiments often suffer from low signal to noise ratio. The increase in spectrometer time required to acquire data of sufficient quality to allow further analysis can be counteracted in part by more processing effort during the image reconstruction step. We suggest a simultaneous iterative reconstruction algorithm (SIRT) for reconstruction of continuous wave EPRI experimental data as an alternative to the widely applied filtered back projection algorithm (FBP). We show experimental and numerical test data of 2d spatial images and spectral–spatial images. We find that for low signal to noise ratio and spectral–spatial images that are limited by the maximum magnetic field gradient strength SIRT is more suitable than FBP.

Patterns of Intersecting Fiber Arrays Revealed in Whole Muscle with Generalized Q-Space Imaging

The multiscale attributes of mammalian muscle confer significant challenges for structural imaging in vivo. To achieve this, we employed a magnetic resonance method, termed “generalized Q-space imaging”, that considers the effect of spatially distributed diffusion-weighted magnetic field gradients and diffusion sensitivities on the morphology of Q-space. This approach results in a subvoxel scaled probability distribution function whose shape correlates with local fiber orientation. The principal fiber populations identified within these probability distribution functions can then be associated by streamline methods to create multivoxel tractlike constructs that depict the macroscale orientation of myofiber arrays. We performed a simulation of Q-space input parameters, including magnetic field gradient strength and direction, diffusion sensitivity, and diffusional sampling to determine the optimal achievable fiber angle separation in the minimum scan time. We applied this approach to resolve intravoxel crossing myofiber arrays in the setting of the human tongue, an organ with anatomic complexity based on the presence of hierarchical arrays of intersecting myocytes. Using parameters defined by simulation, we imaged at 3T the fanlike configuration of the human genioglossus and the laterally positioned merging fibers of the styloglossus, inferior longitudinalis, chondroglossus, and verticalis. Comparative scans of the excised mouse tongue at 7T demonstrated similar midline and lateral crossing fiber patterns, whereas histological analysis confirmed the presence and distribution of these myofiber arrays at the microscopic scale. Our results demonstrate a magnetic resonance method for acquiring and displaying diffusional data that defines highly ordered myofiber patterns in architecturally complex tissue. Such patterns suggest inherent multiscale fiber organization and provide a basis for structure-function analyses in vivo and in model tissues.

Stability of toroidal magnetic fields in stellar interiors

We present 3D MHD simulations of purely toroidal and mixed poloidal-toroidal magnetic field configurations to study the behavior of the Tayler instability. For the first time the simultaneous action of rotation and magnetic diffusion are taken into account and the effects of a poloidal field on the dynamic evolution of unstable toroidal magnetic fields is included. In the absence of diffusion, fast rotation (rotation rate compared to Alfv\'en frequency) is able to suppress the instability when the rotation and magnetic axes are aligned and when the radial field strength gradient p < 1.5. When diffusion is included, this system turns unstable for diffusion dominated and marginally diffusive dominated regions. If the magnetic and rotation axes are perpendicular to each other the stabilizing effect induced by the Coriolis force is scale dependent and decreases with increasing wavenumber. In toroidal fields with radial field gradients bigger than p > 1.5, rapid rotation does not suppress the instability but instead introduces a damping factor to the growth rate in agreement with the analytic predictions. For the mixed poloidal-toroidal fields we find an unstable axisymmetric mode, not predicted analytically, right at the stability threshold for the non-axisymmetric modes; it has been argued that an axisymmetric mode is necessary for the closure of the Tayler-Spruit dynamo loop.

Concept of a Generator for the Selection and Focus Field of a Clinical MPI Scanner

We present a concept for a combined selection and focus field generator for whole-body magnetic particle imaging (MPI). Predictions for field of view, gradient field strength, slew rate, and power consumption are calculated and discussed with the help of finite-element simulations.

Study on the photodetachment wave packet dynamics of H- ion in a gradient electric field

Using the combination of the time-dependent perturbation theory and the closed-orbit theory, we put forward a calculation formula for the autocorrelation function of H ion in a gradient electric field, and then calculate and analyze the autocorrelation function of the system. Especially, we discuss the effect of laser pulse width, electric field strength and the electric field gradient on the autocorrelation function of H ion in a gradient electric field. It is demonstrated that when the laser pulse width is very narrow, far less than the period of the detached electron, the quantum wave packet revival phenomenon is significant. A series of sharp reviving peaks appear in the autocorrelation function, which are caused by the interference between the returning electron wave packets travelling along the closed orbit and the outgoing electron wave packets. However, with the increase of laser pulse width, the quantum wave packet revival phenomenon becomes weakened. When the difference between the pulse width and the period of the closed orbit is not very large, the reviving peaks in the autocorrelation function become widely spread gradually and the oscillatory structures get flattened. This correspondence will vanish finally due to the interference between the adjacent peaks. In addition, our study also suggests that the background electric field strength and the electric field gradient in the gradient electric field can also have significant effects on the autocorrelation function. With the increase of background electric field strength and electric field gradient, the period of the detached electron's closed orbit gets shorter, the number of the revival peaks in the autocorrelation function is increased gradually, and the quantum wave packet revival phenomenon will be enhanced. Therefore, we can control the autocorrelation function of the hydrogen negative ion by changing the laser pulse width and the external electric field strength. Our results will provide some reference values for the experimental research on the wave packet dynamic property of atoms or ions in external fields.

Analysis of eddy currents induced by transverse and longitudinal gradient coils in different tungsten collimators geometries for SPECT/MRI integration.

We investigated the temporal variation of the induced magnetic field due to the transverse and the longitudinal gradient coils in tungsten collimators arranged in hexagonal and pentagonal geometries with and without gaps between the collimators. We modeled x-, y-, and z-gradient coils and different arrangements of single-photon emission computed tomography (SPECT) collimators using FEKO, a three-dimensional electromagnetic simulation tool. A time analysis approach was used to generate the pulsed magnetic field gradient. The approach was validated with measurements using a 7T MRI scanner. Simulations showed an induced magnetic field representing 4.66% and 0.87% of the applied gradient field (gradient strength = 500 mT/m) for longitudinal and transverse gradient coils, respectively. These values can be reduced by 75% by adding gaps between the collimators for the pentagonal arrangement, bringing the maximum induced magnetic field to less than 2% of the applied gradient for all of the gradient coils. Characterization of the maximum induced magnetic field shows that by adding gaps between the collimators for an integrated SPECT/MRI system, eddy currents can be corrected by the MRI system to avoid artifact. The numerical model was validated and was proposed as a tool for studying the effect of a SPECT collimator within the MRI gradient coils.

Multi-objective optimization of gradient coil for benchtop magnetic resonance imaging system with high-resolution

Significant high magnetic gradient field strength is essential to obtaining high-resolution images in a benchtop magnetic resonance imaging (BT-MRI) system with permanent magnet. Extending minimum wire spacing and maximum wire width of gradient coils is one of the key solutions to minimize the maximum current density so as to reduce the local heating and generate higher magnetic field gradient strength. However, maximum current density is hard to optimize together with field linearity, stored magnetic energy, and power dissipation by the traditional target field method. In this paper, a new multi-objective method is proposed to optimize the maximum current density, field linearity, stored magnetic energy, and power dissipation in MRI gradient coils. The simulation and experimental results show that the minimum wire spacings are improved by 159% and 62% for the transverse and longitudinal gradient coil respectively. The maximum wire width increases from 0.5 mm to 1.5 mm. Maximum gradient field strengths of 157 mT/m and 405 mT/m for transverse and longitudinal coil are achieved, respectively. The experimental results in BT-MRI instrument demonstrate that the MRI images with in-plane resolution of 50 μm can be obtained by using the designed coils.

Probing of susceptibility structures through the distant dipolar field effect

In this paper, the utilization of the distant dipolar field (DDF) signal to extract the properties of susceptibility structures over a subvoxel length scale is investigated. Numerical simulations are performed to study a system of randomly distributed blood vessels with a susceptibility offset inside a voxel. It is shown that the DDF signal of the system as a function of the strength of the correlation gradient field manifests a peak that depends on the volume ratio, size, and susceptibility offset of the blood vessels. In particular, the location of the signal peak is found to vary as powers of these parameters. As a result, by varying the strength of the correlation gradient field, the characteristic properties of the blood vessels can be extracted from the peak position of the DDF signal. It is also found that, for a given volume ratio of the blood vessels, a smaller size of the blood vessels can be probed when the susceptibility offset is increased. Nevertheless, it is demonstrated that, owing to the broad width of the signal peak, the DDF effect generally cannot be used for the preferential selection of the signal arising from the blood vessels on the length scale determined by the correlation length.

Solid-state STRAFI NMR probe for material imaging of quadrupolar nuclei

Stray field imaging (STRAFI) has provided an alternative imaging method to study solid materials that are typically difficult to obtain using conventional MRI methods. For small volume samples, image resolution is a challenge since extremely strong gradients are required to examine narrow slices. Here we present a STRAFI probe for imaging materials with quadrupolar nuclei. Experiments were performed on a 19.6T magnet which has a fringe field gradient strength of 72T/m, nearly 50 times stronger than commercial microimagers. We demonstrate the ability to acquire 7Li 1D profiles of liquid and solid state lithium phantoms with clearly resolved features in the micrometer scale and as a practical example a Li ion battery electrode material is also examined.

On-line capillary electrophoresis for enhanced detection sensitivity of feline panleukopenia virus

A rapid on-line capillary electrophoresis (CE) method for highly sensitive detection of DNA molecules with specific lengths was developed based on the combination of base stacking (BS) and programmed field strength gradients (PFSG). The BS method has been performed for on-column concentration to improve detection sensitivity without any modification of the CE system. PFSG increased the electrophoretic velocity of DNA molecules, which effectively decreased analysis time. Using the BS and PFSG combination, the amplified PCR product (340-bp DNA) of cats infected with feline panleukopenia virus was detected within 6.5min. Detection sensitivity (∼10-fold) was enhanced compared to conventional CE analysis. The combined on-line CE/BS-PFSG methodology could be an effectively rapid analysis technique for the highly sensitive detection of disease-related specific DNA molecules.

Determination of mean droplet sizes of water-in-oil emulsions using an Earth’s field NMR instrument

The use of the Earth’s magnetic field (EF) to conduct nuclear magnetic resonance (NMR) experiments has a long history with a growing list of applications (e.g. ground water detection, diffusion measurements of Antarctic sea ice). In this paper we explore whether EFNMR can be used to accurately and practically measure the mean droplet size (〈a〉) of water-in-oil emulsions (paraffin and crude oil). We use both pulsed field gradient (PFG) measurements of restricted self-diffusion and T2 relaxometry, as appropriate. T2 relaxometry allows the extension of droplet sizing ability below the limits set by the available magnetic field gradient strength of the EFNMR apparatus. A commercially available bench-top NMR spectrometer is used to verify the results obtained using the EFNMR instrument, with good agreement within experimental error, seen between the two instruments. These results open the potential for further investigation of the application of EFNMR for emulsion droplet sizing.

Non-invasive lipid measurement in living insects using NMR microscopy

Nuclear magnetic resonance (NMR) microscopy allows us to image and quantify the distribution of NMR-active nuclei in living specimens. Using high-field NMR microscopy at a magnetic field strength of 14.1 T and strong gradients up to 3 T m(-1), we show that separation of fat and water nuclear resonances in living insects can be achieved. In contrast to destructive conventional photometric and mass measurements, we demonstrate exemplarily in the European spruce bark beetle that NMR can be efficiently used to quantify absolute fat and water content in living insects. Additionally, anatomic images with a spatial in-plane resolution up to 10 μm and with high soft tissue contrast were acquired. We demonstrate that fat distribution and fat consumption of living insects can be obtained by magnetic resonance imaging (MRI). This enables future research to address questions where single individuals have to be measured several times, which is not possible with conventional destructive methods.

Multilayer high-aspect-ratio RF coil for NMR applications

Microcoils offer a high degree of mass sensitivity and high magnetic field gradient strength in magnetic resonance microscopy applications. This paper presents a novel multilayer high-aspect-ratio metal fabrication process that can be used to fabricate a nanoliter-volume radio frequency (RF) saddle coil with an embedded flow-through fluidic channel for nuclear magnetic resonance (NMR) applications. The fabrication process is based on repeated electroplating processes and structure release processes. The achieved aspect ratio of the developed RF saddle coil is 4 with a structure line width of 25 μm. The resistance of the RF coil and the 1H spectrum line width have been measured and are found to be 0.7 Ω and 350 Hz, respectively. Our results indicate that this novel fabrication process for RF microcoils is feasible for NMR applications.

Fast Microchip Electrophoresis Using Field Strength Gradients for Single Nucleotide Polymorphism Identification of Cattle Breeds

A microchip electrophoresis (ME) method was developed using a programmed field strength gradients (PFSG) for the single nucleotide polymorphism (SNP) based fast identification of cattle breeds. Four different Korean cattle (Hanwoo) and Holstein SNP markers amplified by allele-specific polymerase chain reaction were separated in a glass microchip filled with 0.5% poly(ethyleneoxide) (<TEX>$M_r$</TEX> = 8 000 000) by PFSG as follows: 750 V/cm for 0 - 14 s, 166.7 V/cm for 14 - 31 s, 83.3 V/cm for 31 - 46 s, and 750 V/cm for 46 - 100 s. The cattle breeds were clearly distinguished within 45 s. The ME-PFSG method was 7 times and 5 times faster than the constant electric field ME method and the capillary electrophoresis- PFSG method, respectively, with a high resolving power (<TEX>$R_s$</TEX> = 5.05 - 9.98). The proposed methodology could be a powerful tool for the fast and simultaneous determination of SNP markers for various cattle breeds with high accuracy.

Microchip electrophoretic separation for the fast diagnosis of Anaplasma phagocytophilum infection in cattle

We report a diagnostic method for Anaplasma phagocytophilum (A. phagocytophilum) infection in cattle using a nested PCR and microchip electrophoresis (ME). A. phagocytophilum causes human granulocytic anaplasmosis and granulocytic ehrlichiosis, which are emerging tick-borne zoonotic diseases. Nested PCR was used to amplify genomic DNA samples extracted from cattle blood. The amplified PCR products were analyzed under a sieving gel matrix of 0.7% poly(ethyleneoxide) (M(r)=8,000,000) in a conventional glass microchip. In the ME assay, A. phagocytophilum was analyzed within 35 s with a relative standard deviation of 1.30% (n=5) using a programmed field strength gradient (PFSG) as follows: 615.3 V/cm for 0-24 s, 66.7 V/cm for 24-34 s, 615.3 V/cm for 34-100 s. The ME-PFSG assay was clinically validated by comparing the 16S rRNA gene levels obtained by this method with those measured using conventional slab gel electrophoresis performed with ten cattle blood samples suspected of A. phagocytophilum infection. In contrast to slab gel electrophoresis, the proposed ME-PFSG methodology had increased sensitivity (200-450 pg/microL), a faster analysis time (<35 s), and required a smaller sample volume (approximately 162 fL).

Particle size, magnetic field, and blood velocity effects on particle retention in magnetic drug targeting

A physics-based model of a general magnetic drug targeting (MDT) system was developed with the goal of realizing the practical limitations of MDT when electromagnets are the source of the magnetic field. The simulation tracks magnetic particles subject to gravity, drag force, magnetic force, and hydrodynamic lift in specified flow fields and external magnetic field distributions. A model problem was analyzed to determine the effect of drug particle size, blood flow velocity, and magnetic field gradient strength on efficiency in holding particles stationary in a laminar Poiseuille flow modeling blood flow in a medium-sized artery. It was found that particle retention rate increased with increasing particle diameter and magnetic field gradient strength and decreased with increasing bulk flow velocity. The results suggest that MDT systems with electromagnets are unsuitable for use in small arteries because it is difficult to control particles smaller than about 20 microm in diameter.

Effect of Head Field Gradient on Nonlinear Transition Shift in Perpendicular Recording

A modified test of the fifth harmonic measurement for nonlinear transition shift (NLTS) is used to study the influence of the head field properties on some parametric data and signal-to-noise ratio (SNR) performances in perpendicular recording. Particularly, the NLTS properties of two different writer head designs were evaluated in connection with their recording performances. It was revealed that the NLTS properties are sensitive to both the head field strength and head field gradient and thus affect the SNR and bit error rate (BER) performances strongly, especially at high linear density.

Pulsed Field Gradient Nuclear Magnetic Resonance Study of Time-Dependent Diffusion Behavior and Exchange of Lipids in Planar-Supported Lipid Bilayers

This work reports the direct experimental observation of lipid exchange between liquid-ordered domains and their liquid-disordered surroundings in 3-component planar-supported multibilayers (1,2-dioleoyl-sn-glycerol-3-phosphocholine/1,2-dipalmitoyl-sn-glycero-3-phosphocholine/cholesterol). The measurements of lipid lateral diffusion and exchange were carried out using proton pulsed field gradient (PFG) NMR spectroscopy with high field strength (17.6 T) and high gradient amplitudes (up to 30 T/m). Application of large gradients affords the use of sufficiently small diffusion times under the condition that the width of the gradient pulses is much smaller than the diffusion time. As a result, PFG NMR studies of time-dependent diffusion behavior in lipid bilayers become possible over submicrometer length scales of displacements, which are comparable with the domain size. Comparison of the PFG NMR diffusion data and the corresponding results of dynamic Monte Carlo simulations allowed for the estimation of domain boundary permeability and domain size at temperatures near the transition temperature for the studied bilayers.

Magnetic nanoparticle migration in microfluidic two-phase flow

Continuous separation of superparamagnetic nanoparticles in a microfluidic system has numerous applications, especially in novel sensors based technology platforms. We have studied a simple microfluidic system with two fluidic inlets, resulting in two-phase flow of identical aqueous fluids. Magnetic nanoparticles were entrained in de-ionized water entering one inlet channel, while the other inlet channel had only de-ionized water input. The application of a magnetic field using a simple permanent magnet causes increased migration of nanoparticles into the pure fluid channel. In the absence of the magnetic field, the particles are able to diffuse into the particle free phase. A steady state convection diffusion model describes the transport of nanoparticles in the microchannel. Particle velocities are estimated from magnetic and hydrodynamic interaction forces. It is shown how particle separation is affected by Péclet number, channel length to width ratio, and magnetic field strength and field gradient. Experiments were conducted with three particle sizes, 1000, 500, and 100 nm. Results revealed a significant discrepancy between theoretical and experimental particle separations under the applied magnetic field. A correction term was introduced into the magnetic force equation. Experiment and theory could be reconciled with the insight that the correction term scales linearly with the volume of the nanoparticle core.