Echo Train Pulse Sequences

A referenceless Nyquist ghost correction workflow for echo planar imaging of hyperpolarized [1‐13C]pyruvate and [1‐13C]lactate

“…Half‐field of view (FOV) ghosting in EPI images is induced by: 1) group delays between readout gradients and signal acquisition; and 2) eddy currents in the readout direction 25. These result in a zero‐order phase error and a phase error that depends on the position in the readout direction ( x axis).…”

“…The phase error accumulated as a result of a group delay is equivalent to the effect of a first‐order short time constant eddy current in the readout gradient and is also included in Equation (1). The phase error θ has alternating polarities in even and odd k ‐space lines, resulting in Nyquist ghosting25: $\hat{\mathsf{\rho }}=\mathrm{sans-serif-italic\rho }\left(\mathsf{x},\mathsf{y}\right)sans-serif-italiccos\left(\mathrm{sans-serif-italic\theta }\left(\mathsf{x}\right)\right)+\mathrm{sans-serif-italici\rho }\left(\mathsf{x},\mathrm{sans-serif-italicy}-\frac{\mathsf{N}}{\mathsf{2}}\right)sans-serifsin\left(\mathrm{sans-serif-italic\theta }\left(\mathsf{x}\right)\right)$where ρ is the ideal image, $\hat{\rho }$ is the reconstructed image, N is the number of phase‐encoding steps and x / y are the coordinates in the ideal image in the frequency‐ and phase‐encoding directions, respectively. In short, the ideal image splits into a real one, at the original location, and an imaginary one, half a FOV away.…”

“…The proposed workflow was compared with three other phase correction methods: 1) direct 13 C reference scan25; 2) integrated 13 C reference echoes31; and 3) 1 H reference scan 27. The pulse sequences used in these experiments are shown in Figure 1B, C. The 13 C imaging sequence acquired a 2D EPI k ‐space, starting with an excitation pulse and slice selection gradient, followed by a train of 20 bipolar readout gradients and, simultaneously, a train of 19 blipped phase‐encoding gradients.…”

“…Echo planar imaging (EPI) is often used as it is fast (subsecond), minimizes RF pulse exposure (only a single shot is required for a 2D image), produces artefacts that are easier to correct because of the Cartesian k‐space, and there are well‐established methods for image reconstruction. However, a drawback of EPI is Nyquist ghosting in the phase‐encoding direction, caused mainly by eddy currents,24 which result in the accumulation of opposite phase errors in odd and even k ‐space lines 25. Fly‐back designs avoid bipolar readout gradients and misalignment between alternate k ‐space lines26; however, they are more prone to geometric distortions and give a lower signal‐to‐noise ratio (SNR) 27…”

“…In proton magnetic resonance imaging (MRI), this can be achieved by acquiring a reference dataset with the phase‐encoding gradients turned off 25. This method, however, is less desirable for hyperpolarized 13 C MRI because a time point is sacrificed in the acquisition of a full EPI reference scan.…”