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Optimized interferometric encoding of presaturated TurboFLASH B₁-mapping for pTx at 7T MRI: Application to T₁-mapping in the spinal cord

Aurelien Destruel^1,2,3, Franck Mauconduit⁴, Aurélien Massire⁵, Vincent Gras⁴, and Virginie Callot^1,2,3
¹Aix-Marseille Univ, CNRS, CRMBM, Marseille, France, ²APHM, Hôpital Universitaire Timone, CEMEREM, Marseille, France, ³iLab-Spine, International Associated Laboratory, Montréal, Canada, Marseille, France, ⁴Paris-Saclay University, CEA, CNRS, BAOBAB, NeuroSpin, Gif-sur-yvette, France, ⁵Siemens Healthcare SAS, Saint-Denis, France

Synopsis

Keywords: RF Pulse Design & Fields, Spinal Cord

One of the best solutions to B₁ inhomogeneities observed at ultra-high field MRI is to use parallel transmit techniques (pTx). However, fast and accurate knowledge of the B₁⁺ is required. The presaturated TurboFLASH (satTFL)-based B₁-mapping sequence, with interferometric encoding, has shown great promise due to its speed and reliability, but it was observed that its performance may drop when used with unconventional radiofrequency coils and applications. In this study, a novel optimization of the interferometric encoding is presented and applied to cervical spinal cord MRI at 7T. The impact of having improved B₁-maps is evaluated on pTx MP2RAGE-based T₁-mapping.

Introduction

Parallel transmit (pTx) techniques are promising solutions to mitigate B₁-related issues^1–3. As they require B₁ generated by each channel, having accurate B₁-maps is primordial. Several B₁-mapping sequences have been developed, with varying results⁴, with one of the most accurate being the actual flip angle (AFI) sequence, although it is prohibitively slow for mapping multiple RF channels⁵. Alternatively, the presaturated TurboFLASH (satTFL) method with interferometry encoding can provide fast individual B₁-maps⁴ from acquired linear combinations B₁^lc of RF channels:

$$$ B_{1 ,i}^{lc}=∑_k A_{i,k} B_{1,k} $$$ and $$$ B_{1 ,k}=∑_i (A^{-1} )_{i,k} B_{1,k}^{lc} $$$

where $$$ i $$$ is the i-th RF mode, $$$ k $$$ is the k-th RF-channel, and $$$ A$$$ is the interferometry encoding matrix. Simple $$$A$$$-matrices are used, such as ‘One-inv’ (one channel has opposite phase than others)⁶, and optimization of diagonal elements of $$$ A$$$ was proposed⁷. In this work, we evaluate the accuracy of the satTFL for cervical spinal cord compared with the AFI and apply a novel optimization of the interferometric encoding, as it was observed that B₁-inhomogeneities resulted in signal drops over all B1^lc with the used RF coil. The influence of the optimization was evaluated on in vivo quantitative T₁-mapping from MP2RAGE with pTx .

Methods

B₁-mapping was performed at 7T (TERRA, Siemens Healthcare, Germany), with a Rapid 8Tx/8Rx cervical spine coil loaded with the SAM phantom (Speag, Switzerland)⁸, and with two volunteers (Fig.3).

SatTFL was used to measure 2D-axial individual B₁-maps with interferometric acquisitions from a modified version using a Shinnar-Le Roux saturation pulse⁹ with two methods:

Interferometric¹⁰: Eight RF modes i, with and without presaturation-pulse; effective flip angle $$$β_{i}^{lc} = acos(sig_i^{sat}/sig_i^{nosat}).$$$

Hybrid^11,12: Eight RF modes i, without presaturation pulse and a single reference B₁-map, with $$$β_{i}^{lc} = β_{ref}.(sig_i^{nosat}/sig_{ref}^{nosat})$$$ and $$$β_{ref}^{lc} = acos(sig_{ref}^{sat}/sig_{ref}^{nosat}).$$$

After initial acquisitions with ‘One-inv’, the complex elements of $$$ A $$$ (interferometric: eight encoding modes; hybrid: reference + eight encoding modes) were optimized. A flow chart summarizing the methods is shown in Fig.1. The Matlab pattern search global optimization was used with ‘One-inv’ encoding as starting point, 10g-averaged specific absorption rate (SAR_10g) as constraint, and 3000 iterations. The cost function was the normalized root-mean-square error (NRMSE), inside a region-of-interest (ROI), between complex acquired individual B₁-maps and those obtained from calculated signal images:

Effective excitation and presaturation FA, α and β, were calculated by numerical integration of the Bloch equation using the measured B1.
$$$ sin_{i}^{nosat} = sin(α) + n_1 $$$ and $$$ sin_{i}^{sat} = sin(α).cos(β) + n_2 $$$ , with $$$n_1$$$ and complex Rice noise scaled to obtain SNR = 15. The signal model could be simplified as the ratio of the two images is used.

To validate the performance of the optimizations, individual B₁-maps were acquired with each optimized satTFL method, and two absolute B₁-maps were calculated. Actual flip angle (AFI) sequences were acquired with those RF shims and compared with each satTFL method to demonstrate the added value of the optimization.

To further evaluate the influence of the optimized satTFL, MP2RAGE-based T₁-maps were finally acquired using pTx pulses calculated from the different hybrid satTFL¹³, and compared with standard acquisition with vendor RF pulses, and B₁⁺-correction⁸.

Results

Fig.2 shows sagittal views of the calculated and measured B₁-maps, and the contour of the ROI in which the B₁ reliability was optimized. Results show a substantially better match with the AFI in the region of low FA after optimization, corresponding to lower cord levels (white arrows). This led to lower accuracy outside the ROI, however this signal is not used in the targeted applications.

Fig.3 confirms those observations, showing a scatter plot of calculated B₁ maps compared with the AFI. Although the One-inv and Optimized methods have similar accuracies around FA=50° to 60°, substantial improvement of the match is observed at lower FA (phantom) and higher FA (in vivo) after optimization.

A quantification of this observation is shown in Table.1 (top), as the NMRSE and percentage errors compared with the AFI, showing that reduction of errors up to 46% was achieved. The hybrid Optimized method provided the best accuracy and fastest acquisition.

Fig.4 shows T₁-maps at three cervical levels, showing greater GM/WM contrast with pTx pulses. Table.1 (bottom) shows that pTx MP2RAGE provides results within inter-session reproducibility without need to correct for B₁-inhomogeneity, with more reliable results when using optimized satTFL.

Discussion and Conclusion

This study shows that although satTFL provides fast and accurate B₁-maps, it deteriorates in some regions with the commonly used ‘One-inv’ (using the C-spine RF coil). This impacts the prediction of absolute B₁-maps in low SNR regions when using pTx, which can be observed in quantitative T₁ measures. Optimizing the amplitude and phase of the matrix $$$ A $$$ greatly improves accuracy inside ROI.

Because of the large number of degrees-of-freedom (128 and 144 for Interferometry and Hybrid methods, respectively), the stopping criteria was reached in about 1h. Rather than a patient-specific optimization, the optimization of the matrix $$$ A $$$ should be calculated offline including a wide range of acquired in-vivo B₁-maps to find a ‘universal’ solution, similar to universal pTx pulses used in the brain¹. Future works will further investigate in-vivo results, and the reliability of the optimization between anatomies.

Acknowledgements

This work was supported by ARSEP, Institut Marseille Imaging, A*midex and France Life Imaging.

References

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Figures

Figure 1: Flow chart of the study. (A) Optimization of the encoding matrix for the ‘Interferometry’ and ‘Hybrid’ methods. SAR_10g, averaged over 6 minutes and 10s, was used as an optimization constraint using custom virtual observation points¹⁴.Sequence parameters were: 2D satTFL: 5×5×2.5mm³, TE/TR = 1.81/15000 ms, FA readout = 5°, FA presaturation = 60°, TA = 15s per RF mode; 3D AFI: 5×5×2.5mm3, TE = 3.06/4.93/7, TR =130 ms, FA = 60°, TA = 5min 49s per RF mode. (B) Validation / evaluation of the performance of the One-inv and optimized satTFL compared with the AFI sequence for two RF shims.

Figure 2: Sagittal views of the B₁-maps (shown as FA maps) calculated in a phantom (placed upside-down for better coil loading) from Interferometry (A,B) and Hybrid (B,C), with One-inv or Optimized, and AFI (E); and in a volunteer (female, 32yo, 86kg) from Hybrid: (F) One-inv and (G) Optimized, and (H) AFI. The red contour shows the ROI in which the B₁ accuracy was optimized (mimicking the spinal cord in the phantom, from C1 to C7 in vivo), ignoring the values outside. The white arrows show the region of greater improvement between One-inv and Optimized.

Figure 3: Scatter plot of the interferometry and hybrid satTFL B₁-mapping methods compared with the AFI, inside the ROI (Phantom: RF shim provided by the coil manufacturer and a random amplitude and phase shim; In vivo: manufacturer RF shim, 2 volunteers (female, 28yo, 55kg; female, 32yo, 86kg)).

Table 1: NRMSE, mean percentage error with AFI ± standard deviation (std) and acquisition time of different B₁-mapping methods, in a phantom and on two volunteers; T₁ measured at threecervical levels with T₁-maps from MP2RAGE, using pTx pulses calculated from corresponding methods. The T₁ was averaged over the cross-sectional area of the cord, including GM and WM. The mean values are compared with T₁ obtained with vendor RF pulses and B₁-correction⁸, for which inter-session reproducibility was previously estimated around 2 to 3%. Higher std could result from better GM/WM contrast.

Figure 4: Sagittal view of the T₁ map derived from an MP2RAGE (acquired in coronal orientation, resolution = 0.7mm iso, TE/TR = 2.5/5000 ms, TI₁/TI₂ = 700/2400 ms)⁸ with pTx pulses optimizing the FA inside a ROI from C1 to C7 (the signal/inhomogeneities outside the ROI are ignored); corresponding axial views acquired with (left) vendor pulses, and custom pTx pulses calculated from the satTFL with One-inv (center) and Optimized (right) interferometric encoding. Greater contrast between white and gray matter is observed with pTx pulses, with less than half the CP SAR_10g.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)

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DOI: https://doi.org/10.58530/2023/4415