Free-breathing 2D cine DENSE MRI using localized signal generation, image-based navigators, motion compensation and compressed sensing

Xiaoying Cai^{1}, Xiao Chen^{2}, Yang Yang^{1}, Michael Salerno^{3}, Daniel S. Weller^{4}, Craig H. Meyer^{1}, and Frederick H. Epstein^{1}

** ^{}Pulse
sequence:** A 2D spiral cine DENSE sequence

**Self-navigation
and motion estimation:** To estimate the motion of the
heart due to respiration, low-resolution iNAV images were reconstructed for each
heartbeat by an intra-heartbeat sliding-window method using the central k-space. Two-dimensional cross-correlation was used to estimate inter-heartbeat
respiratory translation. The use of localized signal generation facilitated
automatic estimation of heart motion due to respiration, as other tissues such
as liver and chest did not generate significant signal.

**Motion
compensation and Compressed Sensing:** Motion compensation was performed
in k-space^{5 }using $$$\hat{d}_{i}=d_{i}e^{j2\pi k_{i} t_{i}}$$$ where $$$\hat{d_i}$$$ is the motion-corrected k-space data from the i-th heartbeat,
$$$d_{i}$$$ is the acquired k-space data from the i-th heartbeat, $$$k_{i}$$$ denotes the k-space trajectory of $$$d_{i}$$$, and $$$t_{i}$$$ is the 2D translation
vector computed from the iNAV images. The motion corrected data were
reconstructed using compressed sensing with low-rank constraints^{6}: $$$m=argmin_{m}\parallel F_{u}m-\hat{d} \parallel_{2}+\lambda\parallel m \parallel _* $$$, where $$$m$$$ denotes the dynamic cine DENSE images to be reconstructed, $$$F_{u}$$$ denotes non-uniform fast fourier transform (NUFFT^{7}) operator including the sampling mask and
sensitivity encoding, $$$\parallel \parallel _*$$$ denotes the
spatiotemporal low-rank constraint and $$$\lambda$$$ is a regularization parameter.

**T1-relaxation
artifact reduction:**
By applying localized signal generation, the DENSE stimulated echo signal originates
from only the heart region. However, signal due to T1 relaxation still originates
from the entire slice. Because subtraction of phase-cycled data to eliminate
the artifact-generating T1-relaxation signal is ineffective for free-breathing
acquisitions, we applied a circular band-stop k-space filter around the displacement-encoding
frequency to reduce artifacts due to T1 relaxation.

**Data
acquisition:** DENSE imaging was performed on 5
healthy volunteers using a 1.5T scanner (Avanto, Siemens) with a 5-channel coil.
Mid-ventricular short-axis DENSE datasets were collected with both
breath-holding and free-breathing. Imaging parameters were: displacement
encoding frequency k_{e} = 0.1 cyc/mm, through-plane dephasing
frequency k_{d} = 0.08 cyc/mm, temporal resolution = 28 ms, in-plane
resolution = 2.5 x 2.5 mm^{2}, slice thickness = 8 mm, localized
excitation width = 60-80 mm, field of view = 160 mm, number of spiral interleaves
per image = 4, and number of interleaves acquired per heartbeat = 2. Spiral interleaves
were rotated by the golden angle through different cardiac phases. The total
imaging time was 14 heartbeats for a full 2D dataset. Images were reconstructed
offline using MATLAB (MathWorks, MA). Both breath-holding and free-breathing
data were reconstructed using density weighted NUFFT. Free-breathing data were also
reconstructed using the proposed method (Figure 1).

**Image
Analysis:** Standard strain analysis^{2} was performed for 6 segments of
the myocardium and Bland-Altman analysis was used to estimate agreement of circumferential
strain for free-breathing and breath-holding datasets reconstructed using both NUFFT and
the proposed method.

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