Robust 3D Bloch-Siegert based B1+ mapping using Multi-Echo General Linear Modelling
Nadège Corbin1, Julio Acosta-Cabronero1, Shaihan J Malik2, and Martina F Callaghan1

1Wellcome Centre for Human Neuroimaging, UCL Institute of Neurology, London, United Kingdom, 2School of Biomedical Engineering & Imaging Sciences, King’s College London, London, United Kingdom


Robust quantification of the longitudinal relaxation rate (R1)—a widely used proxy marker of myelin content—requires highly accurate and precise estimation of the RF transmit field (B1+). The Bloch-Siegert shift (BSS) is a B1+-mapping method that allows calibration data to be acquired with the same spoiled gradient-echo readout used for variable flip angle R1 mapping. Here we show that systematic differences in steady state phase, caused by the interleaved nature typically adopted, lead to bias or loss of precision, but that these effects can be corrected for using a multi-echo approach and GLM fitting to isolate the BSS phase.


The longitudinal relaxation rate (R1) is a useful marker of myelination enabling study of the structure-function relationship1,2. To achieve robust quantification and sensitivity to subtle inter-individual differences, highly accurate and precise estimation of the transmit field (B1+) is required. The Bloch-Siegert Shift (BSS)3 is a B1+-mapping procedure that uses off-resonance pulses to impart B1+-dependent phase. This phase can be isolated by acquiring two images using BSS pulses of opposite off-resonance frequency. The acquisition of these images is typically interleaved to increase robustness to long term phase inconsistencies, e.g. subject motion4 or scanner drift5. However, interleaving introduces an additional phase difference between the two acquisitions that causes bias in the B1+ map. These effects can be corrected by extracting the BSS-specific phase using a multi-echo acquisition with a general linear model (GLM) estimation procedure6


The phase of the steady-state signal of an interleaved BS acquisition (Fig.1a) was simulated as a function of pulse number using the procedure outlined in Fig.2a. The difference between opposite off-resonance frequency readouts prior to the BS pulse was also calculated. This was done to isolate any phase difference present from shot-to-shot that was not induced by the BSS. The impact of RF spoiling and TR was investigated. Phantom and in vivo experiments were conducted to verify the simulation results (protocol details in Fig.1d). All B1+ maps were reconstructed in real-time using Gadgetron7. These maps were calculated in two ways:

-The “classic” approach estimates B1+ efficiency from the phase difference between the echoes immediately following the BS pulses of opposite polarity (one measurement per BS-pulse frequency): $$$ \Phi_{BSS}=\frac{\Phi_{Diff}}{2}$$$

-The “GLM” approach isolates the phase specific to the BSS by fitting a GLM to the multi-echo data (Fig.1b,c): $$$\Phi_{BSS}=\beta_{BSS}$$$

$$$\Phi_{BSS}$$$ was then used to estimate B1+ ($$$B_1^+\propto \sqrt{\Phi_{BSS}}$$$).

For each estimation technique and protocol, errors were calculated with respect to a reference B1+ map acquired with TR=100ms and RF spoiling.


Numerical simulations showed that the alternating off-resonance frequency of the BS pulse introduced an alternating phase across pulses(Fig.2b-c) that resulted in a phase discrepancy between the steady state of interleaved TRs (Fig.2d-e). This phase difference is present prior to the application of the BS pulse and will therefore manifest as a bias in the B1+ estimation when using the “classic” approach. This bias is predicted to be present with or without RF spoiling, but to be smaller using RF spoiling and/or with longer TR.

The results of phantom experiments were consistent with this. “Classic” B1+ maps contained bias when RF spoiling was not used (Fig.3a) that was greatly reduced by using RF spoiling. However, an additional source of variability, not predicted by the simulations, led to a broadening of the B1+ error histogram in the latter case. These effects (both bias and variance) were corrected by the GLM approach (Fig.3b). B1+ bias was also observed in vivo when not using RF spoiling (Fig.4a-b). In agreement with the phantom experiments, the GLM approach reduced both B1+ bias and variance with respect to the long-TR reference measurement.

We hypothesised that the increased variance observed when using RF spoiling may be due to imperfect specification of the RF phase. To test this hypothesis, we acquired FID signals (with the same sequence, but only playing out the excitation pulse and spoiler gradient) in vivo and on phantoms using different RF spoiling increments (0°,117°,137°), TRs (35ms,100ms) and excitation flip angles (6°,15°). We computed the FID phases as a function of pulse number for the two interleaves. Consistent with our hypothesis, both in vivo and phantom experiments confirmed that phase variability observed with RF spoiling is deterministic, dependent on the RF spoiling increment, can be decreased with increasing TR or reducing the excitation flip angle and induces a spurious phase difference between the two interleaves.


In this study we found that the classic BSS approach suffers from large B1+ biases (without RF spoiling) and increased variance (with RF spoiling). The GLM approach robustly isolated the B1+-specific phase leading to more precise and unbiased estimation.


B1+ mapping with interleaved BS-pulses offers greater robustness to motion and scanner drift. However, the systematic difference of the BS-pulse frequency across TRs leads to a systematic difference in the steady-state phase for the two conditions that cannot be distinguished from the B1+-specific phase using the classic BSS approach. We demonstrated that this effect can be reduced using RF spoiling, but at the cost of sensitivity to any errors in pulse phase definition. Using a multi-echo acquisition and fitting a GLM offers robustness to both effects, enabling precise and accurate transmit field mapping, which is crucial for quantitative MRI.


The Wellcome Centre for Human Neuroimaging is supported by core funding from the Wellcome [203147/Z/16/Z].


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Fig.1:The sequence diagram of the modified 3D-multi-echo-gradient-echo is illustrated in (a). Two echoes were acquired prior to, and six echoes after the Bloch-Siegert pulse, which was flanked by crushers to destroy any inadvertent on-resonance excitation and minimize excitation flip angle dependency8. A GLM was used to model the phase variation across echoes (b). The model coefficients obtained with the phantom (c) highlight phase accrued due to the Bloch-Siegert shift,(βBSS), B0 field inhomogeneity,(βΔω0), alternating readout polarity,(βOdd/Even), initial phase offsets,(βOffset1Offset1), and an additional phase caused by the block of crushers and BS pulse and independent of the sign of the pulse frequency (βAdd). (d)List of sequence parameters.

Fig.2: a) Pipeline of the numerical descriptions and the values of the parameters. b) Impact of the TR on the phase acquired prior to the BS pulse, across pulses with alternating off-resonance frequency between pulses, in case of RF spoiling (c ) or not (b). Difference between the phases (before BS pulse) of the two interleaves with opposite off-resonance frequencies in the case of RF spoiling turned on (e) or off (d). A phase difference of 0 is expected to fulfil the requirements of the classic BS method.

Fig.3: Histograms of the difference in B1 relative to the reference B1 map acquired on phantom. All B1 maps (including the reference map) are either calculated with the classic method (a) or the GLM method (b). (c) Percentage of difference between the B1 maps computed with the GLM and the Classic methods for the reference map (TR=100ms), showing the consistency of the two methods at long TR.

Fig.4: (a) B1 maps computed with the classic approach (First row) and the GLM method (Third raw). Difference of the B1 maps computed with the Classic method (Second row) and the GLM method (Fourth row) relative to the reference map (RF Spoiling, TR of 100 ms) computed with the classic method and the GLM method, respectively. (b-c) Histograms of the difference in B1 relative to the reference B1 map acquired in vivo. All the B1 maps (including the reference map) are either calculated with the classic method (b) or the GLM method (c).

Fig.5: FID phase of the two interleaves acquired on phantom (left) and in vivo (right) in several configurations described in the table. The BS pulse and all gradients apart from the spoiler were turned off. With Rf spoiling, the phase of the two interleaves are different when RF spoiling is used, the pattern of variation is reproducible across runs (b,c). The pattern depends on the RF spoiling increment (c,d). The amplitude decreases as TR increases (b,e) or the flip angle decreases (b,f). Without RF spoiling, a phase variation is observed in vivo but is the same across interleaves and likely due to physiological sources.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)