Optimized interferometric encoding of presaturated TurboFLASH B₁ mapping for parallel transmission MRI at 7 T: Preliminary application for quantitative T₁ mapping in the spinal cord

2.1 Acquisition of the B₁ maps

The 2D-satTFL were acquired using a custom sequence with a Shinnar-Le Roux saturation pulse to mitigate slice cross-interference³² and enable the import of external encoding matrices.

After deriving the magnitude of $$$ {B}_i^{lc} $$$ from $$$ {\beta}_i^{lc} $$$, its phase relative to the transmit RF phase of the first acquired RF mode $$$ \left({\mathrm{sig}}_{\mathrm{ref}}^{\mathrm{nosat}}\right) $$$ was obtained by extracting the phase difference between $$$ {\mathrm{sig}}_i^{\mathrm{nosat}} $$$ and $$$ {\mathrm{sig}}_{\mathrm{ref}}^{\mathrm{nosat}} $$$.

The individual channel B₁ maps were then obtained according to Eq. 2. The signals corresponding to different pTx pre-saturation (if any) and excitation pulses were acquired as repetitions of turbo-FLASH acquisition using the following sequence parameters: resolution: 5 × 5 × 2.5 mm³, matrix size = 48 × 36, 48 slices acquired in an interleaved manner, TE = 1.81 ms, FA readout α = 5° (Sinc pulse with duration = 0.8 ms), FA presaturation β = 60° (minimum phase Shinnar-Le Roux pulse with duration = 5 ms, time bandwidth product = 9, and pass-band ripple 1%). The time TR between two consecutive turbo-FLASH acquisitions was 15 s, allowing for the magnetization to fully recover. In addition, B₀ maps were acquired as they were used during the calculation of FA distribution when optimizing the encoding matrix and the pTx pulses (sequence parameters: 3D multi-echo gradient echo, resolution: 2.5 × 2.5 × 2.5 mm³, TE₁/TE₂/TE₃/TR = 5/6.5/8/300 ms, FA = 20°, TA = 2 min 52 s).

An initial satTFL was acquired using “One-inv” encoding ($$$ {\mathrm{B}}_1^{\mathrm{acq}} $$$) to calculate each channel B₁, with a reference voltage calculated based on the average FA inside a region of interest (ROI) approximating the cervical cord (C1–C7) in the phantom and including C1–T1 in vivo. Although not shown, a comparison between the Fourier and One-inv encoding¹¹ showed that the latter produced higher quality B₁ maps.

Data from four healthy volunteers (two males and two females, with age and weight range = [28, 33] years and [55, 90] kg, respectively) were acquired. The satTFL B₁ maps acquired with “One-inv” were denoised using block matching with 4D filtering (BM4D)³³ separately on the real and imaginary components, and were considered as ground truth during the optimization of the matrix $$$ A $$$. The satTFL was optimized for all four volunteers simultaneously, aiming to find a preliminary proof-of-concept “generic” optimized satTFL, as an alternative to subject-specific optimization.

2.2 Optimization of the encoding matrix

As a preliminary step to isolate the effect of matrix amplitude on the accuracy of the encoding, the optimization only allowed linear scaling of the One-inv modes, giving an optimized matrix $$$ A $$$_opt,linear. A full optimization of all elements of the encoding matrix $$$ A $$$ was then performed to generate $$$ A $$$_opt,full, using One-inv as starting point. In addition to the encoding matrix, the optimization calculated the required reference voltage, which was then used during the acquisitions. A summary of the method is shown in Figure 1. In addition, the condition (Cond) of the different optimized matrices was calculated because this metric represents the tendency of a matrix to amplify noise.

2.3 Validation of the optimization

2.4 Preliminary application for pTx quantitative T₁ mapping

Following the comparison with the AFI, the potential of using the optimized satTFL was evaluated by measuring quantitative T₁ maps (T₁q) from MP2RAGE,²¹ using the sequence parameters described in Massire et al.¹⁹ (coronal acquisition, FA₁/FA₂ = 4/5, TE/TR = 2.4/5000 ms, TI₁/TI₂ = 700/2400 ms, FOV = 260 mm, number of slices = 192). The reference T₁q (T₁q^ref) was obtained after standard MP2RAGE acquisition (using Shim_def and an hyperbolic secant 4 adiabatic inversion pulse) and included correction for B₁-induced bias of the T₁. Its calculation assumed an inversion efficiency of 1, as previously done.¹⁹ Different pTx-MP2RAGE²¹ were then acquired with pulses calculated from hybrid satTFL with One-inv (the default protocol on our MR scanner) and optimized encoding. Importantly, only the latter included a correction for the bias between satTFL and AFI, showing the combined effects of the matrix optimization and the AFI-based bias correction. T₁q were calculated without correcting the T₁ for B₁-induced bias, leading to T₁q^One-inv and T₁q^opt,corr, respectively. Denoising using BM4D was applied to all T₁q.

The GRAPE method³⁷ was used to calculate the nonselective excitation (duration = 500 μs) and non-adiabatic inversion (duration = 7500 ms) pTx pulses. This method uses parametrization-free RF waveforms and 3D gradient trajectories to lower the NMRSE between the calculated and target FAs inside the ROI used in the satTFL optimization.Optimization of the excitation and inversionpulses were performed in parallel (calculation time of about 2 min on a DELL Precision 7560).

3.1 Optimization of the encoding matrix

Figure 2 shows the magnitude and phase of different $$$ A $$$-matrices used for the interferometry and hybrid satTFL in the SAM phantom and in vivo. All optimizations increased the magnitude of $$$ A $$$, with maximum values of 2.04 for the linear optimization of One-inv, and 2.98 for the full optimization of hybrid satTFL. Substantially larger amplitudes were reached when only considering the SAR_10g and/or FA constraints compared with the linear optimization of One-inv. However, mean amplitudes of the encoding matrices with maximum constraints(interferometry: 1.35, hybrid: 2) were similar to the mean amplitude reached after full optimization (interferometry: 1.33, hybrid: 2.13). The optimized mean ± SD of the phases of the diagonal (off diagonal, respectively) elements were, in the phantom: interferometry:−101° ± 26° (48° ± 46); hybrid: −46° ± 20° (126° ± 41°); in vivo: −93° ± 31° (76° ± 43°). Because the hybrid encoding method only relies on a single reference mode with presaturation (line 1 of the optimized hybrid matrices), higher RF mode amplitudes were reached for the encoding modes (lines 2–8 of the optimized hybrid matrices) compared with the interferometry approach. Although not constrained, the conditions after optimization were close to Cond(One-inv) = 3, with the exception of the full optimization using the interferometry approach (Cond = 5.52). The stopping criteria was reached in about 1 h when using data from a single subject.

An intermediate step of the B₁-map reconstruction is shown in Figure 3, as the $$$ {\mathrm{B}}_1^{\mathrm{lc}} $$$ (shown as sagittal FA maps) with the One-inv and optimized hybrid satTFL on a volunteer, using the matrix shown in Figure 2C. The red contour shows the ROI in which the accuracy and robustness of the B₁ was optimized, illustrating that the One-inv encoding included almost no signal below the black dotted line, which represents the region under the C6 cervical level. After optimization, some of the RF modes generated signal in this region, providing information that can be used in the reconstruction of the individual-channel B₁.

This observation was confirmed in Figure 4, which displays the effect of the optimization on the individual hybrid satTFL B₁ maps on volunteer 1. B₁ maps are shown before denoising to better appreciate the impact of the optimization of the encoding. Although One-inv and optimized-satTFL provide similar results above the C6 cervical level (black dotted line), a qualitative comparison shows improvements in the magnitude for lower cord levels, displaying as a reduction of noise. In particular, a substantial difference between One-inv and optimized satTFL was observed for channel 4 in those regions, where very poor signal was partially recovered using the optimized satTFL acquisition. Although not included in the optimization, improvements were also noticed in some regions outside the ROI (black arrows). Similar phase distributions were obtained with the different methods. Results on phantom are shown in Figure S1.

Figure 5 shows, for every channel, the difference between the BM4D-denoised B₁ maps (available in Figure S2) and the “raw” B₁ maps (Figure 4). The denoising operation notably improves the measured B₁⁺ of every channel while preserving the distribution. As indicated by the average noise level inside the ROI, denoising has a more pronounced effect on One-inv due to lower noise robustness of this strategy. An average noise reduction factor of 27.5% (up to 44% for channel 4) was obtained with optimized encoding.

3.2 Validation of the optimization

Figure 6 shows scatter plots comparing acquired AFI and calculated FA maps from the hybrid satTFL, with different encoding methods for the SAM phantom (Figure 6A) and for volunteers 1 and 2 (Figure 6B). The comparisons combine results from different RF shims, as described in the Methods section, and includes FA inside the ROI which were higher than 10°. Results show that the One-inv encoding leads to relatively high deviation from the AFI, for a wide range of FA, for all calibrations and scaling, even when similar amplitudes were used in the encoding matrices (see Figure 2). This deviation is somewhat reduced using “One-inv optimized” (phantom only); yet, a full interferometric matrix optimization further reduces this deviation (SD) for both the interferometry and hybrid methods. Scaling of the One-inv to reach maximum SAR_10g constraints is shown in Figure S3.

As previously reported, a linear bias was measured between the AFI and the satTFL,³⁸ justifying the need for a linear correction of the satTFL. A linear regression model fit was performed for all methods, showing superior R² after optimization (from R² = 0.90 to 0.98, and R² = 0.84 to 0.89 for the hybrid satTFL on phantom and in vivo, respectively, excluding results from Hybrid: One-inv maximum SAR_10g). Although only combined data is shown, the differences between the linear slopes of volunteers 1 and 2 with Shim_def were 10% and less than 1%, based on One-inv and optimized-satTFL, respectively, indicating that a unique linear correction could be used for different subjects after optimization. Because AFI may be inaccurate in the low FA regime,^{6, 8} Figure S4 also shows results when considering FA greater than 20°. However, excluding FA between 10° and 20° only led to variations lower than 1% in the slope of the linear correction.

Table 1 complements those results with a comparison between the different methods based on the NRMSE and MPE metrics, for FA > 20°. Without linear correction, similar NRMSE and MPE were observed with different encoding methods, although increasing the reference voltage or optimizing the encoding matrix reduced the SD of the MPE by up to 63%. With linear correction of the fully optimized encoding matrices, the MPE was reduced to less than 3.7% (phantom) and to around 12% (in vivo). Finally, different scaling of One-inv led to MPE greater than 5% and up to 57% larger SD compared with $$$ A $$$_opt,full. The NRMSE from One-inv to corrected optimized-satTFL was reduced by approximately 60% and 40% in phantom and in vivo, respectively. Because the hybrid encoding method achieved better results than interferometry encoding with a lower acquisition time, it was exclusively used for the following sections of this study.

Finally, Figure 7 illustrates the benefit of optimizing and using linear correction for the hybrid satTFL. FA maps were calculated with different RF shims and were compared with acquired AFI. The main benefit of the optimization can again be observed in the lower section of the ROI, where the One-inv encoding sometimes leads to poor prediction of the FA due to insufficient information from the $$$ {\mathrm{B}}_1^{\mathrm{lc}} $$$.

3.3 Preliminary application for pTx quantitative T₁ mapping

Table 2 (top) shows T₁q^ref, calculated from the reference MP2RAGE (vendor pulses and B₁-bias correction) and from pTx-MP2RAGE using basic One-inv encoding (T₁q^One-inv), and optimized encoding followed by linear correction (T₁q^opt,corr) in the phantom. FA maps calculated during the GRAPE optimization are shown in Figure S5. An important bias was measured when using κ = 1 between the reference and pTx T₁q calculations, with mean T₁q^ref = 1219 ms and mean T₁q^{opt,corr, κ = 1} = 1102 ms (this difference of almost 10% is greater than intersubject or intersession variability of T₁q¹⁹). For this exploratory study, it was chosen to empirically calibrate κ relative to T₁q_ref to reduce this bias. This calibration was done by matching the mean T₁q over the whole ROI in the phantom for the two methods and was estimated to κ = 0.89. However, even lower T₁ were measured from the MP2RAGE based on One-inv, with a remaining global error of 12.6% after calibration. Furthermore, greater SD inside the ROI was measured from the pTx-MP2RAGE.

Figure 8 shows in vivo T₁q (volunteer 1), acquired and reconstructed in the same conditions as for the phantom experiments. The mean T₁ over the whole cord, using the vendor pulses and Shim_def values with B₁⁺ correction and κ = 1, was found equal to 1205 ± 87 ms (it is worth noting that, for volunteer 1, FA deviations from the target FA value were up to 50%; no correction from these heterogeneities would have led to T₁q errors up to 12%). The mean T₁ over the whole cord using the optimized pTx-MP2RAGE with linear correction and κ = 0.89 was found equal to 1173 ± 112 ms. Table 2 (bottom) shows a quantitative comparison of the measured T₁ values averaged over the gray matter and white matter in the different cervical levels. Whereas T₁q^One-inv substantially underestimated the T₁, with errors of about 8% in C2–C7, and almost 19% in C1, T₁q^{opt,corr, κ = 0.89} presented good agreement with T₁q^ref, with deviations of about 4% in the C1–C3 levels and lower than 2% for C4–C7 levels. Finally, it is worth noting that the reference MP2RAGE was acquired using 100% SAR availability (corresponding to the maximum SAR authorized in first-level mode of operation), whereas pTx-MP2RAGE only required 49% (corresponding to nearly the maximum SAR in normal mode of operation).