M. Martens

Insertable biplanar gradient coils for magnetic resonance imaging

Insertable planar gradient coils offer the potential for significant performance increases in magnetic resonance imaging through higher gradient strength and shorter rise times. Using variational methods to minimize inductance, and thereby to optimize switching speeds, we have analyzed and constructed a biplanar y‐gradient coil for insertion into a solenoidal magnet system where z is the magnet axis. We have also analyzed biplanar x‐gradient and z‐gradient coil designs using the same methods. These biplanar coils offer an advantage over a cylindrical coil of comparable diameter in that they achieve high gradient strengths with relatively short rise times while maintaining patient access. Although the requirement that the currents for the x gradient lie in the same plane as for the y and z gradients increases the stored energy by a factor of 3 with respect to the other two gradients, this stored energy is still smaller by a factor of 2 than that of a comparably constrained x‐gradient cylindrical coil. The biplanar coil design offers improved linearity over its single planar coil alternative. The particular designs we have investigated are generally limited to small‐volume imaging.

Dependence of Brownian and Néel relaxation times on magnetic field strength

PURPOSE In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS) the relaxation time of the magnetization in response to externally applied magnetic fields is determined by the Brownian and Néel relaxation mechanisms. Here the authors investigate the dependence of the relaxation times on the magnetic field strength and the implications for MPI and MPS. METHODS The Fokker-Planck equation with Brownian relaxation and the Fokker-Planck equation with Néel relaxation are solved numerically for a time-varying externally applied magnetic field, including a step-function, a sinusoidally varying, and a linearly ramped magnetic field. For magnetic fields that are applied as a step function, an eigenvalue approach is used to directly calculate both the Brownian and Néel relaxation times for a range of magnetic field strengths. For Néel relaxation, the eigenvalue calculations are compared to Browns high-barrier approximation formula. RESULTS The relaxation times due to the Brownian or Néel mechanisms depend on the magnitude of the applied magnetic field. In particular, the Néel relaxation time is sensitive to the magnetic field strength, and varies by many orders of magnitude for nanoparticle properties and magnetic field strengths relevant for MPI and MPS. Therefore, the well-known zero-field relaxation times underestimate the actual relaxation times and, in particular, can underestimate the Néel relaxation time by many orders of magnitude. When only Néel relaxation is present--if the particles are embedded in a solid for instance--the authors found that there can be a strong magnetization response to a sinusoidal driving field, even if the period is much less than the zero-field relaxation time. For a ferrofluid in which both Brownian and Néel relaxation are present, only one relaxation mechanism may dominate depending on the magnetic field strength, the driving frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field. CONCLUSIONS A simple treatment of Néel relaxation using the common zero-field relaxation time overestimates the relaxation time of the magnetization in situations relevant for MPI and MPS. For sinusoidally driven (or ramped) systems, whether or not a particular relaxation mechanism dominates or is even relevant depends on the magnetic field strength, the frequency (or ramp time), and the phase of the magnetization relative to the applied magnetic field.

Modeling the Brownian relaxation of nanoparticle ferrofluids: Comparison with experiment

We obtain good agreement between the calculated and measured ratio of harmonics only when the model includes nanoparticles which have a distribution in the hydrodynamic diameter - that is polydisperse. We are unable to find good agreement if the diameter of the nanoparticles is constrained to only one value - that is monodisperse. In Fig. 1 we plot the measured [3] ratios of 5th/3rd harmonics of the magnetization for samples using “100 nm” iron oxide particles (top plot) and “40 nm” iron oxide particles (bottom plot). The measurements were collected with the nanoparticles in ferrofluid solutions with a range of water/glycerol ratios corresponding to different viscosities (and therefore different Brownian relaxation times.) As described in [3] the data are plotted as a function of ωτB. Also shown in Fig. 1 are the calculations of the ratios of 5th/3rd harmonics assuming both monodisperse and polydisperse ferrofluids. Details of the calculations and parameters used in the models can be found in [5].

Search for disoriented chiral condensate at the Fermilab Tevatron

We present results from MiniMax (Fermilab T-864), a small test/experiment at the Fermilab Tevatron designed to search for the production of a disoriented chiral condensate (DCC) in p-p(bar sign) collisions at {radical}(s)=1.8 TeV in the forward direction, {approx}3.4<{eta}<{approx}4.2. Data, consisting of 1.3x10{sup 6} events, are analyzed using the robust observables developed in an earlier paper. The results are consistent with generic, binomial-distribution partition of pions into charged and neutral species. Limits on DCC production in various models are presented. (c) 2000 The American Physical Society.

Analysis of charged-particle–photon correlations in hadronic multiparticle production

In order to analyze data on joint charged-particle/photon distributions from an experimental search (T-864, MiniMax) for disoriented chiral condensate (DCC) at the Fermilab Tevatron collider, we have identified robust observables, ratios of normalized bivariate factorial moments, with many desirable properties. These include insensitivity to many efficiency corrections and the details of the modeling of the primary pion production, and sensitivity to the production of DCC, as opposed to the generic, binomial-distribution partition of pions into charged and neutral species. The relevant formalism is developed and tested in Monte-Carlo simulations of the MiniMax experimental conditions.

A layer model for RF penetration, heating, and screening in NMR

Abstract A solvable layer model is presented for the problem of a conducting, dielectric object in the presence of an external RF magnetic field. The corresponding structure permits exact analytic solutions for currents, fields, and image response. This provides a testing ground for certain transmission and receiving issues in magnetic resonance imaging, including RF power deposition, high-frequency screening, and other wavelength effects. Free-space wavelength effects can be accounted for exactly in this solution. A successful comparison with phantom measurements indicates that the model is an adequate guide of what to expect for more realistic geometries at high frequencies and can be extended to mimic actual body layers. The general results exhibit less penetration and heating effects than expected. The layer model is useful for demonstrating the in vivo extraction of electrical tissue properties and for tests and comparisons of various numerical methods.

Conduction cooled magnet design for 1.5 T, 3.0 T and 7.0 T MRI systems

Main magnets for magnetic resonance imaging (MRI) are largely constructed with low temperature superconducting material. Most commonly used superconductors for these magnets are niobium-titanium (NbTi). Such magnets are operated at 4.2 K by being immersed in a liquid helium bath for long time operation. As the cost of liquid helium has increased threefold in the last decade and the market for MRI systems is on average increasing by more than 7% every year, there is a growing demand for an alternative to liquid helium. Superconductors such as magnesium-diboride (MgB2) and niobium-tin (Nb3Sn) demonstrate superior current carrying quality at higher critical temperatures than 4.2 K. In this article, electromagnetic designs for conduction cooled main magnets over the range of medium field strengths (1.5 T) to ultrahigh field strengths (7.0 T) are presented. These designs are achieved by an improved functional approach coming from a series of developments by the present research group and using properties of the state-of-the-art second generation MgB2 wires and Nb3Sn wires developed by Hyper Tech Research Inc. The MgB2 magnet designs operated at different field strengths demonstrate excellent homogeneity and shielding properties at an operating temperature of 10 K. At ultrahigh field, the high current density on Nb3Sn allowed by the larger magnetic field on wire helps to reduce the superconductor volume in comparison with high field NbTi magnet designs. This allows for a compact magnet design that can operate at a temperature of 8 K. Overall, the designs created show promise in the development of conduction cooled dry magnets that would reduce dependence on helium.

An MRI elliptical coil with minimum inductance

The authors present an application to elliptical coordinates of Turners target field method. Coils are designed with their inductance minimized subject to constraints on the magnetic field. This is of value, for example, in magnetic resonance imaging (MRI) where it is desired that high-strength gradient coils be rapidly switched on and off. Green functions and associated computational tools in elliptic coordinates are developed. The authors also discuss the advantages of elliptically cylindrical coils compared with circularly cylindrical coils for whole-body MRI applications.

Numerical study on the quench propagation in a 1.5 T MgB2 MRI magnet design with varied wire compositions

To reduce the usage of liquid helium in MRI magnets, magnesium diboride (MgB2), a high temperature superconductor, has been considered for use in a design of conduction cooled MRI magnets. Compared to NbTi wires the normal zone propagation velocity (NZPV) in MgB2 is much slower leading to a higher temperature rise and the necessity of active quench protection. The temperature rise, resistive voltage, and NZPV during a quench in a 1.5 T main magnet design with MgB2 superconducting wire was calculated for a variety of wire compositions. The quench development was modeled using the Douglas–Gunn method to solve the 3D heat equation. It was determined that wires with higher bulk thermal conductivity and lower electrical resistivity reduced the hot-spot temperature rise near the beginning of a quench. These improvements can be accomplished by increasing the copper fraction inside the wire, using a sheath material (such as Glidcop) with a higher thermal conductivity and lower electrical resistivity, and by increasing the thermal conductivity of the wires insulation. The focus of this paper is on the initial stages of quench development, and does not consider the later stages of the quench or magnet protection.

A multiscale and multiphysics model of strain development in a 1.5 T MRI magnet designed with 36 filament composite MgB2 superconducting wire

High temperature superconductors such as MgB2 focus on conduction cooling of electromagnets that eliminates the use of liquid helium. With the recent advances in the strain sustainability of MgB2, a full body 1.5 T conduction cooled magnetic resonance imaging (MRI) magnet shows promise. In this article, a 36 filament MgB2 superconducting wire is considered for a 1.5 T fullbody MRI system and is analyzed in terms of strain development. In order to facilitate analysis, this composite wire is homogenized and the orthotropic wire material properties are employed to solve for strain development using a 2D-axisymmetric finite element analysis (FEA) model of the entire set of MRI magnet. The entire multiscale multiphysics analysis is considered from the wire to the magnet bundles addressing winding, cooling and electromagnetic excitation. The FEA solution is verified with proven analytical equations and acceptable agreement is reported. The results show a maximum mechanical strain development of 0.06% that is within the failure criteria of −0.6% to 0.4% (−0.3% to 0.2% for design) for the 36 filament MgB2 wire. Therefore, the study indicates the safe operation of the conduction cooled MgB2 based MRI magnet as far as strain development is concerned.