Minimizing eddy currents induced in the ground plane of a large phased-array ultrasound applicator for echo-planar imaging-based MR thermometry

Abstract

Background: The study aims to investigate different ground plane segmentation designs of an ultrasound transducer to reduce gradient field induced eddy currents and the associated geometric distortion and temperature map errors in echo-planar imaging (EPI)-based MR thermometry in transcranial magnetic resonance (MR)-guided focused ultrasound (tcMRgFUS).

Methods: Six different ground plane segmentations were considered and the efficacy of each in suppressing eddy currents was investigated in silico and in operando. For the latter case, the segmented ground planes were implemented in a transducer mockup model for validation. Robust spoiled gradient (SPGR) echo sequences and multi-shot EPI sequences were acquired. For each sequence and pattern, geometric distortions were quantified in the magnitude images and expressed in millimeters. Phase images were used for extracting the temperature maps on the basis of the temperature-dependent proton resonance frequency shift phenomenon. The means, standard deviations, and signal-to-noise ratios (SNRs) were extracted and contrasted with the geometric distortions of all patterns.

Results: The geometric distortion analysis and temperature map evaluations showed that more than one pattern could be considered the best-performing transducer. In the sagittal plane, the star (d) (3.46 ± 2.33 mm) and star-ring patterns (f) (2.72 ± 2.8 mm) showed smaller geometric distortions than the currently available seven-segment sheet (c) (5.54 ± 4.21 mm) and were both comparable to the reference scenario (a) (2.77 ± 2.24 mm). Contrasting these results with the temperature maps revealed that (d) performs as well as (a) in SPGR and EPI.

Conclusions: We demonstrated that segmenting the transducer ground plane into a star pattern reduces eddy currents to a level wherein multi-plane EPI for accurate MR thermometry in tcMRgFUS is feasible.

Keywords: Echo-planar imaging; Eddy currents; Focused ultrasound; MR thermometry; Phased-array transducer; Proton resonance frequency shift.

Fig. 1

Magnitude image of an EPI scan (a) with phase encoding direction in anterior/posterior direction of a sagittal slice of a gel phantom mounted inside the transducer setup (c). The distortions also occur when changing the readout direction from a head to foot direction (b). c Phased-array transducer setup with a dedicated eight-channel phased-array receive coil and water cooling pipes for circulating water through the transducer

Fig. 2

a Picture of the ground plane and a close up where the soldered joints are highlighted with the white arrows. b Picture of a CAD model of the copper layer of the ground plane, illustrating the soldering of seven segments to a continuous surface. The CAD model in b is used in FEM simulations to predict the induced eddy currents on its surface. c Schematic of the FEM model (full shield and primary y-coil) of the depicted MRI system. The hemisphere in the iso-center demonstrates the positioning of the transducer ground plane inside the gradient coil

Fig. 3

(Top) Picture showing transducer mockup model containing reference plastic hemisphere (red arrow) and ADNI phantom (green arrow). (Middle) Pictures of different copper patterns attached to the outside of the hemisphere: a reference without copper sheet, b solid copper surface (one segment, average surface of segment ≈1413 cm²), c seven-segment clinical pattern (average surface of segments ≈199 cm²), d star pattern (32 segments, average surface of segments ≈37 cm²), e ring pattern (16 segments, average surface of segment ≈92 cm²), and f a combined star-ring pattern (64 segments, average surface of segment ≈27 cm²). (Bottom) Modeled patterns of FEM simulations with 36 (d), 17 (e), and 54 segments, respectively. Black arrows indicate the points of view of the ground planes when plotting the current densities in Fig. 4

Fig. 4

(Top) Densities of currents induced on the surfaces of the transducer ground planes when pulsing the y-gradient coil (scale 0 to 40 kA/m²). Current densities are plotted for patterns (b) to (f). Only one fourth of the model is shown given the symmetry boundary conditions in the FEM simulations. (Bottom) Calculated maximum gradient strengths on a 20-cm sphere inside the FOV of the gradient model, plotted for all segmentation patterns described in Fig. 3 (reference gradient strength g _ref = 49.44 mT/m)

Fig. 5

(Top) Sagittal images of patterns (a) to (f) in SPGR with calculated temperature maps. (Middle) Sagittal images of patterns (a) to (f) in EPI with calculated temperature maps. The mean and standard deviations were calculated on 2585 voxels of predefined region of interest. (Bottom) Geometric distortion maps created by masks to generate about 5000 voxels. Two different color scales are used to facilitate comparison

Fig. 6

SNR expressed as 1/σ (ordinate) plotted against the standard deviation of geometric distortion expressed in millimeters (abscissa) in SPGR (top) and EPI (bottom) for the sagittal (left), axial (center), and coronal (right) planes for all scenarios (a) to (f). The desired design space comprises high SNR and small geometric distortion error bars centered at 0 °C

Fig. 7

(Top) Axial images of patterns (a) to (f) in SPGR with calculated temperature maps. (Middle) Axial images of patterns (a) to (f) in EPI with calculated temperature maps. The mean and standard deviations were calculated on 7488 voxels of a predefined region of interest. (Bottom) Geometric distortion maps created by masks to generate about 2500 voxels

Fig. 8

(Top) Coronal images of patterns (a) to (f) in SPGR with calculated temperature maps. (Middle) Coronal images of patterns (a) to (f) in EPI with calculated temperature maps. The mean and standard deviations were calculated on 1458 voxels of a predefined region of interest. (Bottom) Geometric distortion maps created by masks to generate about 4000 voxels. Two different color scales are used to facilitate comparisons