GTF at 11.7 T (Iseult), 10.5 T (CMRR), and on the classic 7 T Magnetom

Figure 3 presents the GTF acquired on a classic 7 T Magnetom as well as 11.7 T initially on Iseult (other characteristics listed in Table 1) and at 10.5 T at CMRR (in its nominal configuration, i.e., with third-order shim coils disconnected). The 11.7 T result was the one reported in [8], i.e., without the lead tube and with the third-order shim coils connected (nominal configuration). The data revealed at first a supra-linear amplification of the peak at 1350 Hz when going from 10.5 to 11.7 T. Although an intensification of the peak versus field strength was to be expected because of increased gradient–magnet interactions, such drastic amplification suggested that other factors were important.

Fig. 3

Illustration of the 1350 Hz strong resonance on the gradient Z axis observed on Iseult at 11.7 T. a GTF spectra (magnitude) over the − 7 and + 7 kHz range. b Zoom on the 1–2 kHz range showing the main resonance. Comparisons are provided with a measurement at 10.5 T (CMRR) and 7 T (Classic Magnetom at NeuroSpin)

EPI waveform measurements

Some analysis of field measurements was performed in the time domain to get more insight about the effects induced by the peaks and dips visible in the GTF spectra. Figure 4 reports EPI waveforms measured with a field camera at 7 T on Iseult, at 7 T on a Terra and on the classic 7 T Magnetom when first (ES = 0.37 ms) and third (ES = 1.11 ms) harmonics of the EPI train excite the 1350 Hz mechanical resonance. One can see that the vibrations distort the EPI plateaus and that gradient oscillations can even persist after the train. Of course, because there is no data acquisition in that period, the latter are not strictly problematic for faithful spatial encoding but instead illustrate better the impact of vibrations on the field, because eddy currents alone would yield exponentially decaying fields [13]. A zoom into the superposed measurements on the gradient plateaus also reveals a transient behavior hypothesized to be due to mechanical damping, because of the order of magnitude of the time-constants, which yields a characteristic time comparable to the duration of the EPI train, making phase correction pre-scans [17, 18] possibly inaccurate. The oscillations after the train here were comparable on 7 T Iseult and 7 T Terra, while the classic 7 T Magnetom yielded smaller oscillations. The decline of the amplitude of the EPI plateaus along the train with the first harmonic is also more severe on the Terra and Iseult than on the classic Magnetom, at the same field strength. This suggests similarities between the two former systems, 7 T Iseult and 7 T Terra, regarding this particular problem. Despite an overshoot at the beginning of the EPI plateaus with the classic Magnetom 7 T, field perturbations with the third harmonic excitation oscillate more with the 7 T Terra and 7 T Iseult around the center of k-space.

Fig. 4

EPI field perturbations observed at 7 T when exciting the 1350 Hz resonance on the Z gradient axis. Left: 1st harmonic (ES = 0.37 ms) excitation, right: third harmonic (ES = 1.11 ms) excitation. A zoom on the plateaus (purple boxes) and on the oscillations after the EPI train (green boxes) is provided in each case, with the same color coding. The plateaus along the EPI train are superposed at the bottom. The yellow–black, orange–brown, light and dark blue plots in the zoom correspond to the Magnetom, Iseult, and Terra measurements. The darker the color for each group, the earlier the plateau occurs in the EPI train. Units are in mT/m in all figures. On the left, the red curve of the oscillation after the EPI train was interrupted to leave visible the Terra data

Mechanical coupling alterations

Figure 5 reports the accelerations versus frequency measured on the SC72 gradient coil and the Iseult magnet bore at 7 T when pulsing on the gradient Z axis at 1 mT/m and with the ND (green) and NB (pink) Sylodyn pads. The mechanical resonance at 1350 Hz is clearly visible. Interestingly, the vibration spectra of the gradient coil are quasi-identical in the two scenarios while coupling to the bore has been significantly reduced using the NB (pink) Sylodyn. Figure 5d shows the GTF magnitude around the main resonance in the different configurations, where very little difference was found. The result of the mechanical simulation identified the closest resonance at 1415 Hz, in reasonable agreement with the experimental data, and is illustrated in Figure 5c. The mode is labeled (0,2) indicating 0 and 2 half-wavelengths in the circumferential and axial directions. It is called a breathing mode because displacements perpendicular to the z axis maintain cylindrical symmetry. The data shows that mechanical coupling was significantly altered but yet the field response remained highly similar. Insertion of wooden wedges and removing the passive shim tray also had little effect on the field response. The reader should note that a tune-up of the PID controller of the GPA was repeated systematically in each condition so that small differences can be the result of the slight variations in regulator tuning. In the end, the data convincingly shows that the mechanical coupling between the gradient coil and the magnet was not responsible for the main peak intensity in the GTF spectrum located at 1350 Hz in Fig. 3.

Fig. 5

Mechanical coupling alteration results on Iseult operated at 7 T. Subplots (a) and (b) show the accelerations measured on the gradient coil and the bore tube, respectively, with green (ND) and pink (NB) Sylodyn pads. Subplot (c) reports the deformation returned from a mechanical simulation as a breathing mode being the closest resonance matching the experimental data. Subplot (d) reports the magnitude of the GTF measurement around the 1350 Hz resonance in the various conditions where mechanical coupling was altered, showing little differences

GPA and third-order shim coil influence results

Figure 6 reports the magnitude and phase of the GTF on Iseult at 11.7 T, 10.5 T (CMRR), 9.4 T (MPI, Tuebingen), 7 T Terra (McGill, Montreal), 7 T Terra Plus (SFVA), and 7 T classic Magnetom (CEA NeuroSpin). Data were separated into two groups for clarity, i.e., with the GPA XXL with no third-order shim coils connected and the GPA 90/22 with third-order shim coils connected, the nominal configurations. The data are plotted on the same scale to emphasize the differences between the two scenarios. There is clearly a distinct behavior where for instance the 1350 Hz peak at 7 T with the GPA 90/22 (Terra) with connected third-order shim is higher than the one obtained at 9.4 T and 10.5 T with the GPA XXL with third-order shim disconnected, despite a lower field strength, especially in the phase response. For the same GPA XXL, the peak tends to become moderately higher with field strength (from 7 to 9.4 T and 10.5 T). Overall, the data of Fig. 6, thus, highlighted two potential key differences, i.e., GPA and third-order shim configurations, between the setups that could affect the results.

Fig. 6

Self-term Z GTF measurements for the SC72 whole-body gradient coils when driven by the GPA 90/22 (third-order shim connected) versus GPA XXL (third-order shim disconnected) at various field strengths. a, b Magnitude and c, d phase in the GTFs are provided

Current measurements on Iseult

The results of Fig. 6 show a different gradient field behavior between two setups involving different GPAs and third-order shim connections, as characterized by the field camera technology. To gain further insight, current measurements were performed directly on the GPAs on Iseult at 0 T (GPA 90/22), Iseult at 7 T (GPA 90/22) and on the classic Magnetom 7 T (GPA XXL). Results are displayed in Fig. 7. At 0 T, there are no vibrations and, therefore, there are no oscillations at the end of the EPI train. The currents, however, oscillate in the presence of the main field and are larger with the GPA 90/22 with connection to the third-order shim coil versus the GPA XXL with no connection, respectively, for the same field strength. With an echo-spacing of 0.37 ms, the main frequency of the EPI waveform drives the 1350 Hz mechanical resonance with deformation pictured in Fig. 5c. At the end of the train, the system is released and vibrates predominantly at the same frequency, given this eigenmode initial condition. The data, therefore, are consistent with the gradient field oscillations shown in Fig. 4.

Fig. 7

Current measurements on the GPA during an EPI sequence with ES = 0.37 ms. The absence of oscillations at 0 T confirmed the influence of the vibrations on the current. The GPA XXL (classic Magnetom) with no third-order shim coils connected led to smaller oscillations than the GPA 90/22 with third-order shim coils connected when both used at the same field strength of 7 T

Impact of third-order shim coils

The results of Fig. 6 indicated that both the GPA type and the third-order shim coils configuration could possibly play a role. To attempt to solve the puzzle, a GPA XXL was, therefore, installed and configured on Iseult and the GIRF measurements were repeated at 11.7 T. But little differences were found. The separation made in Fig. 6 (left: GPA 90/22, right: GPA XXL), thereby simply reflected the chronology of events and current knowledge when the experiments were carried out. Therefore, after showing that the GPA type barely had any influence, the GPA 90/22 was reinstalled with the third-order shim connected or disconnected to the filter plate inside the Faraday cage on the gradient side. The results are reported in Fig. 8. Connection to the third-order shim cabinet, even with its amplifier disabled, had major impact on the GTF (results shown both for Terra 7 T and Iseult 11.7 T). A similar measurement was performed with the second-order shim coils disconnected but little differences were observed. A Skope dynamic field camera was also employed to reconstruct the dynamic third-order spherical harmonics fields for better accuracy and SNR at 11.7 T, when driving the Z gradient axis. The most dominant Z3 (⇒5Z3-3ZR2) term is shown in Fig. 8c which reveals matching peaks with the self-term, suggesting current circulation in the corresponding shim coil at the resonance frequencies when the latter is connected to the filter plate. Figure 8d also reports the measurement of the power deposition (renormalized for 70 mT/m, assuming power deposition is proportional to the square of the gradient amplitude, as verified experimentally before) in the Iseult He bath at 11.7 T versus frequency for the gradient Z axis between 1300 and 2000 Hz: with green (ND) Sylodyn (third-order shim coils connected) and pink (NB) Sylodyn (third-order shim coils connected and disconnected). The pink (NB) Sylodyn had a non-negligible but still relatively smaller impact on the results. This shows that mechanical coupling played a role, yet smaller, and that the interaction mostly responsible for the power deposition is electromagnetic, the 1350 Hz mechanical resonance yet remaining the root cause. The cryogenic measurement with the pink (NB) Sylodyn pads and with the third-order shim coils connected was conducted only over the frequency range of most interest for this work (1300–1400 Hz), because of the stress it engenders on the gradient cables and gradient coil.

Fig. 8

Impact of the third-order shim coils. GTF a magnitude and b phase self-term responses are shown for the Terra 7 T and Iseult 11.7 T systems (third-order shim coils connected and disconnected). Subplot c shows the most important third-order spherical harmonics (R2 = X2 + Y2 + Z.2) response measured with a dynamic field camera on Iseult at 11.7 T with the third-order shim coils connected vs. disconnected (same color legend). Subplot d reports the power deposition measurement in the He bath of Iseult at 11.7 T between 1300 and 2000 Hz (renormalized for 70 mT/m)

Figure 8c suggests current flowing in the third-order shim coils when driving the Z gradient coil at some particular frequencies. To further confirm this behavior, current measurements through each individual third-order shim coil were repeated with current clamps on Iseult at 11.7 T with an EPI waveform with H–F read-out axis and ES = 0.37 ms (1/2ES = 1350 Hz), when the shim coils are connected fully, i.e., all the way to their shim amplifiers. The results are plotted in Fig. 9 and reveal indeed currents oscillating at the same frequency. One can observe again a transient regime. In such instance, therefore, the 3-line reference method before the EPI train cannot capture well the field perturbations occurring in the center of k-space.

Fig. 9

Currents flowing in the Z gradient and in the third-order shim coils when the 1350 Hz mechanical resonance is excited. The current in the Z gradient coil has been scaled down by a factor of 20 to superpose it to the other waveforms

Figure 10 reports the GTF measurement performed at 10.5 T (CMRR) with and without the third-order shim coils connected. The data again demonstrate a significantly different behavior between the two scenarios. Nevertheless, although clearly a difference remains at 1350 Hz, one can see another significant difference at 1950 Hz. Although other differences may not have been identified yet, this is possibly a result of the shim filters which are of a different generation on this system (classic Magnetom versus Terra), which can affect the current flow.

Fig. 10

GTF measurements (Z self-term) on the SC72 gradient coil at 10.5 T at CMRR with third-order shim coils connected versus disconnected. a Magnitude and b phases are shown

Lastly, to gain further understanding a vibration measurement of the gradient coil was performed on Iseult when ramping from 0 to 11.7 T at every Tesla, again with the third-order shim coils connected or disconnected, when pulsing at 1 mT/m on the Y or Z gradient axes. The results are presented in Fig. 11. Interestingly, the gradient coil vibrates more at 1350 Hz when the third-order shim coils are disconnected. The same behavior can be observed for the banana mode at 570 Hz on the Y gradient axis. When normalized to the response characterized at 1 T, the vibration versus B0 yields distinctly different behaviors reported in Fig. 11c. When the third-order shim coils are disconnected, vibrations at those frequencies grow linearly with B0. When they are connected, they reach a plateau at around 8 T as in [8, 20].

Fig. 11

SC72 gradient coil vibration results versus third-order shim coil configuration (connected or disconnected). Results for a GZ and b GY are provided for 1 mT/m excitation and at 11.7 T. The normalized accelerations versus B0 are reported in (c) for the Z breathing (1350 Hz) and the Y banana (570 Hz) modes, revealing distinctly different behaviors with respect to the third-order shim coil configuration

Spoiler waveform measurements

Figure 12 shows field monitoring measurements of gradient spoilers typically used in anatomical imaging, e.g., the MPRAGE, with Iseult 11.7 T and Terra 7 T (third-order shim coils connected and disconnected). Gradient oscillations persist after the spoiler event ending at 1 ms. The gradient field oscillation roughly corresponds to a 100 Hz field variation offset at 5 cm from isocenter in the Z direction at 7 T on the Terra. The oscillations are reduced by disconnecting the third-order shim coils on both scanners.

Fig. 12

Gradient oscillations measured after a gradient spoiler of 40 mT/m. The main oscillation frequency observed in all four SC72 whole-body gradient scenarios (i.e., Iseult 11.7 T and Terra 7 T with third-order shim coils connected, Iseult 11.7 T and Terra 7 T with third-order shim coils disconnected) was 1350 Hz