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

Abstract

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.

Inverse design of an organ-oriented RF coil for open, vertical-field, MR-guided, focused ultrasound surgery

“…The M and N in the series representations in Eq. (8) were set as M=N=9, which should be sufficient in terms of the accuracy of the solutions [11,20]. The coefficient λ was set as λ≈10 − 5 to keep the condition number of the matrix at the 10 9 level.…”

Designing shielded radio-frequency phased-array coils for magnetic resonance imaging

“…The target field method, first proposed by Turner, is frequently used in the design of RF coils. [5][6][7][8] A possible limitation of this inverse method [9][10][11][12] is that it assumes coils of notionally infinite length. To overcome the extra error introduced by the assumption, finite length coils can be designed without approximation by expanding the current density in a Fourier series.…”

“…[3,21,24,25] The target field method proposed for designing unshielded and shielded RF coils introduces a set of Fourier coefficients and needs a large scale of numerical calculations. [8,21] Meanwhile, the corresponding magnetic field induced by the coil designed with a minimum curvature penalty function in the specified imaging region is highly unsatisfactory. The penalty factor determines the accuracy of the solution and the complexity of coil windings.…”

“…Hence, the selection of the penalty factor is important for finding simple winding patterns with high precision. However, in the literature, [8,21,25] it is not discussed in detail. The inverse method for designing unshielded RF coils [25] is extended to the design of shielded phased-array RF coils and the selection of the penalty factor in this research.…”

A theoretical study for the inverse design of an ellipsoidal phased-array breast coil

“…By using a time-harmonic inverse method, Lawrence et al successfully designed and constructed a novel asymmetric RF coil for 4.5 T MRI systems [7] and an open head/neck RF coil to operate in a clinical 2 T system [8]. While et al [9] extend the work of Lawrence et al by considering a more general form of the current density and a new regularization penalty function. In addition, it has been combined with other methods like the boundary element method in designing RF phased array coils [10], and the deformation method in designing breast RF phased array coils [11].…”