Synopsis

Keywords: Myocardium, Diffusion Tensor Imaging

Nyquist ghosting is a common artefact in echo planar imaging (EPI), typically corrected using separately acquired reference data. Here we demonstrate that reference free Nyquist ghost correction algorithms based on entropy and Ghost/Object ratio minimization can outperform navigator based methods and improve imaging efficiency for in vivo diffusion tensor cardiovascular magnetic resonance.

Introduction

Echo planar imaging (EPI) is subject to Nyquist ghosting due to misalignment of the forward and reverse lines of k-space. These artefacts are commonly corrected using the well-established three line navigators¹ methods. Alternatively, reference-free methods have demonstrated Nyquist ghost correction without the need to acquire additional reference scans in the breast and brain^2-3. Diffusion tensor cardiovascular magnetic resonance (DT-CMR) typically relies on single shot EPI acquisitions with separately acquired phase correction navigators, which reduce the efficiency of this already time consuming mehtod⁴. This work aims to investigate and compare the performance of a standard navigator-based method, to referenceless entropy based², and the Ghost/Object minimization³ method in application to DT-CMR.

Method

Acquisition
DT-CMR systolic, breath hold, motion compensated Spin Echo⁵ (SE) and STEAM⁴ EPI data were acquired in the mid-ventricular short axis from 16 healthy volunteers. The "b0" image is acquired with b ~ 30 s⋅mm⁻² followed by 6 diffusion encoding directions with 2 repetitions at b = 150 s⋅mm^-2 and 8 to 10 repetitions with 450 s⋅mm⁻² and 600 s⋅mm⁻² for SE and STEAM respectively. The imaging parameters are as follow: TE = 62 ms and 22 ms for SE and STEAM respectively, field of view 360 by 135 mm², TR = 2 cardiac cycles, 2442 Hz/pixel bandwidth, 2.8 by 2.8 mm² or 1.4 by 1.4 mm² with zero padding, GRAPPA x2, and no partial Fourier used. The field of view was reduced in the phase encode direction by making the 1st (and 2nd for STEAM) RF pulse slice selective in the phase encode direction.

Reconstruction
The raw data were reconstructed offline using 4 methods 1) uncorrected, 2) navigator based ghost correction 3) entropy based ghost correction 4) Ghost/Object minimization.
Method 1: GRAPPA⁶ kernels were trained on the ghosted reference data and then applied on the aliased dataset.
Method 2: A linear fit was first performed on the savgol filtered (order 4) phase difference obtained from the navigators in the hybrid space (1D inverse Fourier transform along frequency encode direction) to obtain the phase correction offset and slope. This phase shift is then applied to the data followed by an standard GRAPPA in plane reconstruction.
Method 3: Brute force search was used find the phase correction offset and slope corresponding to the minimum image entropy. This phase correction was applied before GRAPPA reconstruction as in 2.
Method 4: Reconstruction as for method 3, but the cost function is replaced with f,
$$f^{-1} = \sum_{x,y} F_{med 2D} \frac{|I_{x,y}|}{|I'_{x,y}|}$$
where $F$ is the 2D median filter, $I$ is the measured image in image space$(x,y)$, and $I'$ is the copy of $I$ shifted by half field of view in the phase encoding direction.
The phase errors between even and odd lines (after FFT along FE) were modelled with a linear fit for all methods. The Nyquist Ghost intensity is measured using the relative intensity outside the spin or stimulated echo field of view as shown in figure 1. DT-CMR data is processed using in-house MATLAB (Mathworks, Natick, Massachusetts, USA) software.

Result

Examples of ghost correction for all 4 methods are shown in Figure 2. The average ghost intensity for the entropy( 0.0790$\pm$0.0303) and Ghost/Object (0.0797$\pm$0.0305) methods are significantly lower (p<0.005) than that of the navigator based method (0.1210$\pm$0.0439) as shown in figure 3. The performance is also consistent across all diffusion weightings and sequence types. Examples of the DT-CMR maps are shown in figure 4 for all correction methods, and the averaged DT-CMR measures are compared in figure 5.

Discussion

Correction methods show reduction in ghosting over the uncorrected image set, particularly the referenceless based corrections. As for the DT-CMR maps in figure 5, the increased FA and reduced MD using the referenceless methods are consistent with an increase in the SNR of the diiffusion weighted images^7-8.
Referenceless methods such as the entropy and Ghost/Object minimisation are robust and efficient, because they do not require additional reference scans, which saves acquisition time. The scan time reduction provided by the referenceless methods allows at least 8 additional images to be acquired in the same amount of time in our clinical research DT-CMR protocol. However, when using the entropy based method, care must be taken when setting the search range of the phase offset parameter, as the result may deviate from the true ghost correction parameters if the range is too large and the algorithm will try to enhance the ghost and remove the parent object. As a result, the cost function for the Ghost/Object method may be preferred for a more stable outcome when the reduced phase field of view method can be used.
In conlusion, although the computational cost is higher for the referenceless methods, the image quality improvement and acquisition time saving makes these methods valuable additions to the DT-CMR image reconstruction pipeline, paving the way for clinically feasible in vivo DT-CMR.

Acknowledgements

The authors would like to thank the research radiographers Raj Soundarajan and Gover Simon for their immense support and guidance in data acquistion.