Eddy currents in a transverse MRI gradient coil

Abstract

A transverse gradient coil (x-or y-coil) of an MRI-scanner is modeled as a network of curved circular strips placed at the surface of a cylinder. The current in this network is driven by a time-harmonic source current. The low frequency applied allows for an electro-quasi-static approach. The strips are thin and the current is assumed to be uniformly distributed in the thickness direction. For the current distribution in the width direction of the strips, an integral equation is derived. Its logarithmically singular kernel represents inductive effects related to the occurrence of eddy currents. For curved circular strips of width much smaller than the radius of the cylinder one may locally replace the curved circular strip by a tangent plane circular strip. This plane geometry preserves the main characteristics of the transverse current distribution through the strips. The current distribution depends strongly on the in-plane curvature of the strips. The Petrov-Galerkin method, using Legendre polynomials, is applied to solve the integral equation and shows fast convergence. Explicit results are presented for two examples: a set of 1 strip and one of 10 strips. The results show that the current distributions are concentrated near the inner edges and that resulting edge-effects, both local and global, are non-symmetric. This behavior is more apparent for higher frequencies and larger in-plane curvatures. Results have been verified by comparison with finite-element results.

Eddy currents in MRI gradient coils configured as rings and patches

“…The source current is incorporated in the model via Ohm's law (including source currents; see [15,Eq. 6…”

“…They consist of strips that are placed spirally on the surface of a cylinder. For curved circular strips of width much smaller than the radius of the cylinder, one may locally replace the curved circular strip by a tangent-plane circular strip, as described in [15].…”

Gradient coil design and intra-coil eddy currents in MRI systems

“…The time-varying gradient field produced by the switched gradient coils induces undesirable time-varying eddy currents in the nearby conductive materials such as cryostat, RF shield and the gradient coils themselves. These eddy currents result in many deleterious effects, such as ohmic heating, mechanical vibration and acoustic noise in conductive parts in MRI scanners [11,12].…”

“…Due to the skin and proximity effects, the current density tends to be non-uniform across the width of the conductor [12] and it is known that these effects increase with the frequency [12], especially in the modern MRI scanner, the gradient coils are usually etched or machined using wide copper sheet for power dissipation purpose [82]. Not taking into account the skin and proximity effects may lead to inaccurate modelling of the magnetic field profile expected from the gradient coil design.…”

“…To study edge-effects, a mathematical model that explains coupling between tracks was developed by Kroot [12,89,132]. However, in his work, only the current distribution in strips and islands were studied, but the effects caused by a non-uniform current density distribution along the track width on the coil parameters and field harmonics were not considered.…”