Introduction

Proton magnetic resonance spectroscopy (MRS) is a powerful technique that can measure levels of neurochemicals in the brain, non-invasively. MRS at higher magnetic field strengths (> 3 T) provides improved sensitivity and increased spectral dispersion, resulting in improved spectral quantification. However, higher field strengths also result in larger chemical shift displacement (CSD) artifacts, but can be minimized by high bandwidth (BW) RF pulses. Gradient modulated RF pulses, specifically gradient offset independent adiabaticity (GOIA) pulses¹, have been shown to provide an order of magnitude improvement in CSD, relative to an adiabatic full passage (AFP) counterpart, while operating at clinically compatible peak and time averaged power requirements. Thus, short duration GOIA pulses (with T_p < 4 ms) are routinely used to realize short echo time (TE) LASER/sLASER localization methods for MRS and MRSI^2,3. In this work we investigate performance of short GOIA pulses subject to asynchrony between RF and GM waveforms.

Theory

In comparison to AFP pulses, gradient modulated pulses require a time-varying gradient field. Proper operation of gradient-modulated RF pulses necessitates that the RF amplitude AM(τ), RF frequency FM(τ), and gradient GM(τ) modulations experienced within the region of interest (ROI) are synchronized and reproduced without distortion. High fidelity can be compromised if slew rate of the GM waveform approaches the maximum slew rate of the system gradients, and if other imperfections such as gradient oscillations are present. Furthermore, insufficient sampling of the gradient waveform was recently reported to degrade localization profiles with spatial offset⁴. In this work we limit the practical considerations to effects due to asynchronous pulsation of the RF and gradient waveforms. Noting that AM(τ) and GM(τ) functions are part of the RF pulse, an asynchrony can be present between the RF amplifier and gradient amplifier leading to a situation where the gradient function experimentally is
GM_exp(τ) = GM(τ + δ) (1)
where δ is defined such that a positive/negative delay corresponds to the gradient waveform leading/lagging the RF pulse, respectively. Here
GM(τ) = GA·F₃(τ) (2)
where GA is the gradient amplification factor, and F₃(τ) is the gradient modulation waveform for a given GOIA RF pulse. Spatial translation of the inversion profile is achieved by modifying the RF pulse FM according to
FM(τ) = A·F₂(τ) + Δν_RF·F₃(τ) (3)
Whereby Δν_RF represent the frequency offset required for an equivalent BW non-GM RF pulse.

Methods

1-D Bloch simulations of M_z/M₀ vs B₁ amplitude were generated for a previously described 3 ms GOIA-WURST (12-4, 7) pulse⁵ subjected to a delay between RF and GM waveforms. A sLASER MRS method was developed, utilizing the GOIA-WURST(12-4,7) pulse to evaluate localization profiles with varying delays experimentally. All MR experiments were performed on a 4 T 94 cm Medspec scanner (Bruker corporation. Ettlingen, Germany).

Results

Simulated localization profiles for a 3 ms GOIA-WURST(12-4,7) pulse are illustrated in Figure 1 with spatial offsets and δ delays. The peak B₁ amplitude was set at 0.95 kHz (a ~10% overdrive relative to B_{1, 95%}). The top row of localization profiles demonstrates that a δ delay spanning -50 to +50 µs has negligible effect on localization performance for non-translated voxel placements. However, translation along the y-axis (middle and bottom rows) results in a distorted profile along the y-axis and reduced signal amplitude when | δ | > 0 and are accentuated with increased RF offset or increased lead/lag between gradient and RF components. Experimental localization profiles with the GOIA-WURST (12,4-7) pulse, similar to those in Figure 1, for an 8 cm offset with δ delays spanning - 50 to + 50 µs is illustrated in Figure 2. Below each 2D profile the corresponding x-projection, and y-projection are illustrated. Similar to simulation findings, the y-projection is reduced for δ < 0, and elongated for δ > 0. Simulation findings demonstrate that a discrepancy in x and y dimensions for an isotropic voxel (in 2D) to be a result of |δ| > 0, and can easily be calibrated out by comparing x and y projection slice bandwidths as illustrated in the lower panel of Figure 2. Based on a third order polynomial fit of BW as a function of δ, δ was determined to be + 39.5 ± 1.2 µs, specific to our Bruker 4 T system. The undesired localization of |δ| > 0 can be partially compensated with increased peak B₁ as illustrated in Figure 3, hence calibration should be performed at a B₁ ~ B_{1, 95%} to maintain sensitivity to the profile distortion.

Discussion

A discrepancy of δ = ± 20 µs between RF and GM waveforms was directly observable with 40 x 40 mm² voxel projections acquired at a 30 kHz RF offset (8 cm translation) for the 3 ms GOIA-WURST (12,4-7) pulse. This demonstrates that a projection-based calibration is practical and straightforward on clinical systems utilizing short GOIA pulses. The GOIA pulse under test, and its phase reversed counterpart can alternatively be used to calibrate δ, whereby δ needs to be adjusted till identical localization profiles are achieved with both pulses at a large RF offset.

Acknowledgements

This research was supported by NIH grant R01- EB014861.