Introduction

The Zero Echo-Time (ZTE) pulse sequence was originally developed to image flowing liquids [1]. Its serendipitous properties include minimal acoustic noise [2] and the ability to capture signals from protons with ultra-short relaxation times [3]. However, as illustrated in figure 1 a TE of 0 cannot be achieved in practice and there is a short dead-time gap of several microseconds. This leads to a few missing samples in the centre of k-space, which can result in large reconstruction artefacts depending on scan parameters. Existing methods to correct this artefact acquire either an extra low-resolution k-space or additional single-point acquisitions [3]. These data points may have different T₂* decay or spoiling properties, and hence merging it with the high-resolution k-space data is not always straightforward.

Modern MRI scans are generally acquired using multi-channel coils, and parallel imaging exploits data redundancy between these to synthesise deliberately un-acquired k-space data [4]. We hypothesised that parallel-imaging could instead be used to fill the dead-time gap. In this work, we demonstrate the feasibility of this method in phantoms and in-vivo brain images. We name this method ZTE IN-filling From Autocalibration NeighbourhooD ELements (ZINFANDEL).

Methods

To fill the dead-time gap, we reduce the gold-standard GRAPPA framework from two dimensions to one dimension and apply it to each acquired radial spoke, as illustrated in figure 2. Each spoke contains N_r samples across N_c channels, the first N_g points fall in the dead-time gap, and we set N_s to the number of source points for the kernel. We choose the N_l closest points to the dead-time gap to act as the calibration region. In comparison to 2D GRAPPA, N_l is generally quite small so to increase the number of calibration points we use the N_k closest spokes, assuming the kernel only varies slowly in the angular direction.

In the calibration step we divide the calibration region into sets consisting of a target point and the contiguous N_s source points and formulate the calibration source S (N_c*N_s by N_l*N_k) and target T (N_c by N_l*N_k) matrices. We then solve for the weight matrix W using the equation
$$
\textbf{T}=\textbf{W}\textbf{S}\quad\quad\quad\quad (1)
$$
In the synthesis step we fill a single point in the gap by applying equation 1 to the N_s closest points. We iterate this process across all spokes and then iterate again until the dead-time gap is completely filled. We empirically found that this looping order, which progressively updates the kernel weights as points are filled, had better performance than training a single kernel per spoke [5].

To demonstrate this method we used a ZTE sequence implemented on a 3T MR750 scanner (GE Healthcare, Chicago, IL) and 32-channel head coil (Nova Medical). We scanned a spherical water phantom at 2 mm isotropic resolution, 220x220x220 mm FoV, FA 1°, with read-out bandwidths of ±41.67 kHz and ±15.625 kHz (2x oversampled) corresponding to dead-time gaps of 3 and 2 samples respectively. We also scanned a volunteer at 3 mm isotropic resolution, 216x216x126 mm FoV, FA 1°, ±31.25 kHz (dead-time gap 3) and separately with a 12-channel head coil and IR-prepared ZTE sequence, 1 mm isotropic resolution, 220 mm isotropic FoV, FA 2°, TI450 ms. All scans were acquired with a low-resolution k-space for comparison [6]. Scans were acquired with an angular under-sampling factor of 𝜋 relative to Cartesian sampling, except the 3 mm scan which had a further factor of 2.

Images were reconstructed using RIESLING (https://github.com/spinicist/riesling). The raw k-space data was first compressed to 16 or 8 channels [7], ZINFANDEL applied using N_k=5, N_s=5, N_l=16, and finally images reconstructed on a 2x oversampled grid and root-sum-squares channel combination [8]. Images were additionally reconstructed both without applying ZINFANDEL and with the low-resolution k-space instead for comparison.

Results & Discussion

Figure 3 shows the water phantom reconstructed at two bandwidths and dead-time gaps. At both bandwidths when the dead-time gap is unfilled a significant artefact manifests as a low-intensity region in the center of the phantom and high intensity outside of the phantom. Filling the dead-time gap with either ZINFANDEL or the low-resolution k-space removes the artefact.

Figures 4 & 5 show the brain scan, which show artifactual high intensity in the void spaces when the dead-time gap is unfilled. These are very strong in the 3 mm image, which is also blurred due to the extreme angular under-sampling. ZINFANDEL corrects these artefacts and restores signal to the parenchyma.

There are some residual low spatial frequency differences between ZINFANDEL and the reference low-resolution k-space method. However, these are at least partially to be expected as the low-resolution k-space is acquired with a reduced gradient amplitude. This corresponds to different T₂* decay weighting [3], a different slab profile [9], and different spoiling due to the reduced gradient. For the brain scan, no obvious anatomical detail is present in the difference image, suggesting a high fidelity reconstruction with ZINFANDEL.

Conclusion

We have demonstrated that ZINFANDEL is a viable method of filling dead-time gaps up to three samples. Where ZTE scans are acquired with a multi-channel coil this could make ZTE sequences and reconstruction more flexible and straightforward, as no additional data must be acquired.

Acknowledgements

This work was supported by the Wellcome/EPSRC Centre for Medical Engineering [WT 203148/Z/16/Z] and the NIHR Clinical Research Facility at King's College Hospital. MC is supported by the Royal Academy of Engineering (RF201617\16\23).