Introduction

It is crucial to demonstrate a robust correlation of the simulated and manufactured parallel-transmit (pTx) arrays performances to release the currently-use very restrictive safety margins (5x more restrictive compared to single-Tx for commercial coils). Up to date, pTx is not extensively used due to heavy local specific-absorption-rate (SAR) restrictions on the acquisition parameters. In this work, we studied three simulation setup configurations to investigate the role of design parameters on the correspondence of the simulated and experimental scattering matrix and individual and shimmed B₁⁺-field maps with similar amplitude and phase pTx RF pulse settings for the manufactured pTx dipole array with in-house manufactured phantom.

Methods

The three simulation configurations are following:
Configuration 1: 8pTx-dipole array¹ with the exact circuit layout including copper traces and printed-circuit board (Fig.2A). In co-simulation, the lumped elements were defined as inductors or capacitors. To include component losses, capacitors were assigned a general Q-factor of 1500². In addition, to mimic RF losses along the line from RF power amplifiers to the coil input, a series resistor was added to both inductors (Fig.2A&D) in co-simulation.
Configuration 2: 8pTx-dipole array with the exact circuit layout only. Note that the simulated model was similar as in configuration 1, but the capacitors were considered lossless, and no resistors were included (Fig.2B&E).
Configuration 3: 8pTx-dipole array simulated with co-simulation method³ only (Fig.2C). Instead of the exact circuit layout, each dipole included only the source which was defined as a matching circuit in co-simulation with one series inductor and one parallel capacitor (Fig.2F). This is a common approach in the field to spare computational time and power.
The built eight dipoles were tuned and matched to 297.2MHz and the experimental scattering matrix (S-matrix) was acquired using a purpose-designed phantom⁴. Reflection (S_i,i) and coupling curves were recorded. MR acquisitions were performed on phantom on a 7T MR scanner (MAGNETOM Terra,Siemens,Germany). The B₁⁺-field distribution was acquired⁵ in circularly polarized (CP) mode, C2P mode (reversed CP phases), and one RF shimmed configuration. Individual B₁⁺-field maps (magnitude/phase) were acquired⁶. Combined and individual B₁⁺-field maps were normalized to 1kW total output power at RF amplifiers. The individual phase maps were computed relative to the shimmed combined RF phase map.
Electromagnetic field simulations were performed using a finite-difference time-domain (FDTD) simulation software (Sim4life 6.2,ZMT,Switzerland) for the 8pTx-dipole array. The simulated impedance data was exported to a co-simulation software (Optenni,Finland) to tune/match the dipoles.
For the three configurations, the S-matrix was optimized to match the experimental S-matrix for the reflection coefficients (S_i,i), and 1^st (S_i,j) and 2^nd (S_i,j+1) coupling terms. The simulated optimized S-matrix was compared to the experimental values. Simulated S-curves were computed in configuration 1.
Simulated individual B₁⁺-field maps were computed and were normalized, per channel, to the corresponding averaged measured B₁⁺-field value. The three combined maps in CP, C2P, and RF shimmed configurations were calculated using the same RF phases applied in measurements. Difference maps were calculated, and the normalized root-mean-square error (NRMSE) was computed between simulated and measured B₁⁺-field maps.

Results

In configuration 1, an average relative difference of 1.1% was found between simulated and experimental S_i,i values, 4.2% for S_i,j, and 9.4% for S_i,j+1 (Fig.3B). The experimental/simulated S-curves presented a similar shape although the difference between 1^st and 2^nd coupling curves were more pronounced with the simulated data (Fig.3C-F). In the same configuration setup, the simulated individual B₁⁺-field magnitude maps were remarkably well correlated with the experimental results. Notably, the regions where the B₁⁺-field is canceled were similar (Fig.4A). The NRMSE values for individual B₁⁺-field maps ranged from 2% to 4.8%. An averaged difference of 15 degrees was found between simulated and experimental individual phase maps. The simulated B₁⁺-field maps in CP, C2P, and shimmed modes were comparable to the experimental maps, using the exact same phases. NRMSE values of 6.2%, 10.3%, and 7.5% were observed between experimental and simulated maps in CP, C2P, and shimmed modes, respectively.
In configurations 2 and 3, the average relative difference with experimental S-parameters was increased to 44% and 43%, respectively, for S_i,j values. Clear coupling was visible between the dipoles in the simulated individual B₁⁺-field maps and NRMSE values ranged from 5.3% to 7.3% in configuration 2 and 3.9% to 6.4% in configuration 3. The averaged phase difference was about 13 degrees in both configurations.

Discussion and Conclusion

In this study, we introduced a model to include RF losses in the simulations for an 8pTx-dipole array. The effectiveness of the model to accurately predict the B₁⁺-field patterns was assessed, qualitatively and quantitatively, through a comparison with experimental data.
Including component losses and a series resistor into the co-simulation circuit model highly contributed to getting a robust correlation between the experimental and simulated S-matrices. Input power is damped by the resistors, and consequently, the B₁⁺-field efficiency of the simulated dipoles is decreased. The coupling between dipoles is therefore decreased in the simulated model. Nevertheless, the need for individual scaling indicates that additional sources of RF losses may have to be considered. We conclude that using the co-simulation approach and the proposed model for RF losses, a robust correlation is achieved between simulated and experimental data using the 8pTx-dipole array at 7T.

Acknowledgements

This work was supported by core funding from the Wellcome/EPSRC Centre for Medical Engineering [WT203148/Z/16/Z], the Wellcome Trust Collaboration in Science grant [WT201526/Z/16/Z], and by the National Institute for Health Research (NIHR) Biomedical Research Centre based at Guy’s and St Thomas’ NHS Foundation Trust and King’s College London and/or the NIHR Clinical Research Facility. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care.