Spiral MRI Trajectory Design with Frequency Constraint

. However, lowering β reduces the slew rate which can result in a greatly increased spiral duration T. Therefore, a three-domain parameterisation is proposed with an initial frequency-limited domain, followed by two domains adapted from the Heid solutions (3) (Eqn. (3)). The value of B in the modified constant angular velocity spiral φF was found by numerical optimisation. In order to include also the spectral width associated with the duration of the first domain τ1, an additional condition is introduced (Eqn. (4)) that is fulfilled in an iterative procedure. Methods Simulations were based on a Fourier analysis of the gradient waveforms. Synthetic k-space data was generated by discrete FT of an object, and images were reconstructed using standard gridding. Real data was acquired on a Bruker BioSpec at 7 T and reconstructed using measured trajectories. Results Fig. 1 shows simulation results for three different designs using G = 40 mT/m, S = 600 T/m/s, and D = 10 cm. A single-shot protocol with matrix size 32 was chosen as the investigated effects are most prominent at the spiral start. The Cline design without frequency limitation (top) exhibits the two domains where gradient and slew rate amplitudes are normalised to their limits while the maximum frequency of 16 kHz is scaled to 1. Also the Fourier analysis shows high frequencies which are damped by the filter representing the frequency response of the gradient system. Due to the damping the actual gradient is reduced (see design plot), the trajectory has a reduced density in the centre, and the reconstructed image is corrupted. In the second design based on Cline (middle) the application of the frequency constraint with F = 5 kHz limits f (plotted normalised with F), which can also be observed in the Fourier analysis. Only negligible gradient damping occurs, resulting in an improved trajectory and a clean image. However, the reduced slew rate leads to a considerably increased duration T. In the 3-domain design (bottom) F was set to 3 kHz according to the plateau of the filter function. The three domains can be noticed in the design plot with the frequency running close to the limit throughout the first domain and decreasing afterwards. Correspondingly, the intensity drops at the limit in the spectrum. The trajectory is realised as desired, providing the same image quality as before at an only moderately increased T compared to the original design. With the same set of designs, experiments were performed with G = 134 mT/m, S = 6130 T/m/s, and D = 7 cm, resulting in T = 2.2 ms (F = ∞), 5.8 ms (F = 15 kHz), and 2.6 ms (F = 10 kHz). Without frequency limitation similar artefacts as in the simulation occur, which are removed for the improved designs (Fig. 2). The advantage of the shorter acquisition with the 3-domain design becomes obvious by the absence of the off-resonance blurring due to a field distortion close to the imaged slice.