Synopsis

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.

Introduction

The longitudinal relaxation rate (R₁) is a useful marker of myelination enabling study of the structure-function relationship^1,2. 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

Methods

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.

Results

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.

Discussion

Conclusion

Acknowledgements

References

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