An inverse method for designing RF phased array coils in MRI—theoretical considerations

Abstract

Phased array coils afford a number of advantages over RF volume coils, including a high SNR over a large field of view. In this paper, a time-harmonic inverse method is presented for the theoretical design of RF phased arrays. The method allows any array size to be considered, for which a homogeneous magnetic field is desired within some spherical target region within the coils. An ill-conditioned integral equation is solved using regularization, whereby the error between induced and target magnetic fields is minimized along with an additional constraint related to the curvature of the coil windings. The ability to focus the RF field to arbitrary locations within the coil volume is incorporated into the model and a number of examples are displayed. Attention is also given to the polarization of the induced field, with the direction of linear polarization investigated along with circular polarization. Phased arrays comprising smooth windings that are able to induce highly homogeneous magnetic fields are displayed and discussed for a range of array sizes, and for several different field focusing and polarization considerations.

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

“…Fujita et al [7] directly gave the expressions according to their experiences with and to the principles of MRI [7]. Lawrence et al [8], While et al [9,10] and Li et al [11] all gave the expressions according to the requirements of their research. In the current study, the expressions were given according to a strictly analytical deduction from the stream function, which was related to the coil windings.…”

“…The same penalty function was chosen because the resulting current density is easier to implement [10]. Then, the function R= F+ λP (λ is a coefficient) was used instead of the function F to solve the coefficients.…”

“…Thus, the method given in their research cannot be used to inversely design an RF coil with the ultrasound aperture for the MRgFUS system. Recently, more progress was made by Lawrence et al [8] and While et al [9,10]. They developed the inverse methods to design an RF coil in a high field.…”

Designing MR Shim Arrays With Irregular Coil Geometry: Theoretical Considerations

“…A similar representation for the stream function was used in previous work on RF phased array design [20]. All features of interest for the array can be defined in terms of the stream function coefficients ψ kq m n in (1).…”

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

“…In this study, we extend the inverse design model of While et al [12] further to extend breast RF phased array coils from cylindrical geometries to tailored shapes. The aim of this paper is to provide a theoretical design for a RF phased-array breast coil with ellipsoidal geometry.…”