Analysis of Motion and Eddy Currents with 3D Cones Reordering for Whole-Heart Coronary MR Angiography

Mario O. MalavĂ©^{1}, Nii Okai Addy^{1}, R. Reeve Ingle^{1}, Joseph Y. Cheng^{1}, Corey A. Baron^{1}, and Dwight G. Nishimura^{1}

We have developed an alternating-TR steady state free precession (SSFP) coronary MR angiography (CMRA) sequence using a 3D cones k-space trajectory [1]. A consideration during the data acquisition is the ordering and position of the cone readouts. Specifically, we would like to acquire cone readouts in a fashion that exhibits incoherent motion artifacts while minimizing eddy current effects with SSFP. In this work, motion and eddy current artifacts were investigated with simulations, metric measures, and in vivo scans for three different cone acquisition schemes: sequential, multidimensional golden means (MDGM) [2], and phyllotaxis [3].

Cone Trajectory Design:

The
cones trajectories were designed using 10,980 readouts to image a 28x28x14 cm^{3}
field of view (FOV) with 1.2 mm isotropic resolution. Each cone readout has an
initial radial traversal (exiting polar angle < φ, θ>), followed by a
spiral-like traversal [4]. The different design methods, shown in Fig. 1, that were evaluated include
sequential, MDGM [2] without and with pairing [5], and phyllotaxis [3].

Design Analysis:

The scan was segmented over each heartbeat where a specified number of cone readouts was acquired. For any given segment, the distribution of cones should have uniform spread in k-space while minimizing eddy currents when using SSFP. Two metrics were used for analyzing distribution uniformity and eddy current sensitivity: relative standard deviation (RSD) (Eqn. 1) and average distance measure (Eqn. 2) [6]. N, HB, and Nseg represent total cones, total heartbeats, and cones per heartbeat respectively. $$(Eqn.1)RSD=\frac{\sqrt{\frac{1}{N\cdot4}\cdot\sum_{i=1,j=1}^{i=N,j=4}(d_{j,i}-\mu_{d})^{2}}}{\mu_{d}}\cdot100$$ $$\mu_{d}=\frac{1}{N\cdot4}\cdot\sum_{i=1,j=1}^{i=N,j=4}d_{j,i}$$ $$(Eqn.2)Avg.Dist.=\frac{1}{HB}\sum_{i=1:Nseg:N}^{N}\frac{1}{Nseg-1}\sum_{j=1}^{Nseg-1}d_{i(i+j)}$$ For a uniformly spread distribution, the variation and the average distance between neighboring points are minimized and maximized respectively. Thus, the RSD would give smaller values for more uniformly spread distributions. The eddy current sensitivity is defined by calculating the average distance between points (exiting angles) within each heartbeat. Thus, lower values demonstrate that the distribution is more robust to eddy currents [5,6].

To analyze motion for the different acquisition ordering methods, the point spread function (PSF) was calculated with an added superior/inferior (S/I) motion component. For each PSF, S/I motion data, obtained retrospectively from 2D image-based navigators (iNAVs) [1], was added using a linear phase term on the cone readouts for each heartbeat.

In vivo scans were performed on a 1.5T GE scanner using an 8-channel cardiac receiver coil. All design methods acquired 18 cones per heartbeat with a total of 610 heartbeats.

Simulation:

The RSD measure can be seen for four different cones trajectory designs in Fig. 2a. The RSD, with a nearest neighbor of four, shows that the phyllotaxis design has better distribution uniformity. The sequential design becomes more uniform when the total number of cones is increased.

The average distance measure is also shown for the different cone trajectories in Fig. 2b. As expected, the MDGM without pairing performed the worst due to the large jumps in k-space within each heartbeats. Using “pairing” [5] can help to alleviate the k-space jumps (eddy currents) as shown. Both MDGM methods, and phyllotaxis perform better than sequential ordering until more cones are used (~300 total heartbeats with 18 cones each).

The PSFs for sequential ordering and phyllotaxis design methods are shown in Fig. 3. In the coronal and sagittal slice, the motion artifacts are more concentrated along the vertical axis for sequential whereas the motion is incoherently spread around the center of k-space for phyllotaxis.

Experimental:

In Fig. 4, the central sagittal, coronal, and axial slices for an in vivo scan are shown. Similar to the PSFs, the sequential acquisition shows more coherent motion artifacts.

In Fig. 5, the right coronary artery (RCA), left coronary artery (LCA), and left anterior descending (LAD) are shown for all three cones acquisition methods. In the images, the phyllotaxis acquisition resulted in sharper coronaries due to the design uniformity and negligible eddy current effects. The MDGM with pairing method introduced eddy current artifacts shown by degraded image quality in the ventricles, and signal loss in the coronaries.

NIH T32 HL007846, NIH R01 HL127039, GE Healthcare

[1] Wu, HH., et al, MRM 2012 [2] Chan, R., et al, MRM 2009 [3] Malavé, M., et al, ISMRM 2015 [4] Gurney, P., et al, MRM 2006 [5] Bieri, O., et al, MRM 2005 [6] Piccini, D., et al, MRM 2011

Fig. 1. The plots above show how the exiting angle is defined (a) with
the respective top
views of sequential/MDGM (b), and
phyllotaxis (c) polar angle patterns for each cone readout on the unit sphere.
In (d-f), all 18
readouts for the 5^{th}
heartbeat are shown for all three methods: sequential (d), multidimensional
golden means with pairing (e) and phyllotaxis (f).

Fig. 2. The
plots above show the RSD (a) and average distance measure (b) for 4 different
cone design methods when acquiring 18 cones per heartbeat. Better uniformity
(lower RSD) is important for scan efficiency to minimize oversampling while
satisfying Nyquist
throughout the scan volume. Also, abrupt changes in x, y and z gradients
can produce eddy current artifacts [5]; therefore, a lower average distance per
heartbeat can alleviate these effects.

Fig. 3. The images above show the PSFs (with S/I
motion) of central sagittal, coronal, and axial
slices for sequential (a-c) and phyllotaxis (d-f) acquisition methods. In the
sagittal and coronal slices, motion artifacts are more concentrated
along the vertical axis for sequential whereas the motion is
incoherently spread around the center of k-space for phyllotaxis.

Fig. 4. The images above show in vivo data for central sagittal, coronal, and axial slices when
using sequential (a-c) and phyllotaxis (d-f) acquisition methods before
correcting for motion. Similar to the PSFs, sagittal and the coronal slices are
worse for sequential (a, b) compared to phyllotaxis (d, e). The
effectiveness of motion correction will depend on the acquisition method due to
the resulting motion artifacts: more coherent artifacts for sequential compared
to phyllotaxis.

Fig. 5. The
images above show sequential (a, d), MDGM with pairing (b, e) and phyllotaxis
(c, f) acquisitions after retrospectively correcting for rigid-body translation
[1]. The RCA (yellow arrows) and LAD (red arrows) have better signal quality
for phyllotaxis (c, f) followed by sequential (a, d) and less signal for MDGM
(b, e). The RCA (blue arrows) also has better contrast for phyllotaxis (f)
while sequential (d) has motion blurring and slightly less blurring for MDGM
(e).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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