Teodora Chitiboi^{1}, Li Feng^{1}, Rebecca Ramb^{2}, Ricardo Otazo^{1}, and Leon Axel^{1}

Arrhythmia is often a significant challenge to acquiring diagnostic quality cardiac MRI. While discarding atypical cardiac cycles can exclude short-lived arrhythmic events, such as premature ventricular contractions (PVCs), this fails for atrial fibrillation (Afib), where subjects have an irregular cardiac cycle pattern. Harnessing the potential of the XD-GRASP MRI technique to reconstruct continuously acquired data with cardiac and respiratory phase as extra dimensions, we propose to additionally classify cardiac cycles for Afib patients according to their preload state, and simultaneously reconstruct the different types of arrhythmic cycles in a five-dimensional image space.

Patients
underwent free-breathing continuous acquisition, using a steady-state free
precession sequence, with golden-angle radial sampling scheme, for a
single-slice mid-ventricular short axis cine. Imaging was performed on a 1.5T
scanner (Aera, Siemens, Erlangen, Germany), TR/TE=2.8/1.4ms, FOV=320×320mm^{2}, 128 readout points per spoke, spatial resolution 2×2mm^{2},
slice thickness 8mm, acquisition time 2min.

Breathing
and cardiac motion-related signals were separately extracted from the image data,
after a "real-time" KWIC reconstruction.^{4} Cardiac signal was derived
from an automatically detected region around the heart. The breathing motion signal
was extracted from an automatically determined image block with strongest
periodic signal in the breathing range (0.2-0.4Hz). Data was grouped into 5 respiratory phases using probabilistic
k-means, which minimizes the intra-class
variance.

Classifying cardiac cycles by length
of RR interval is common but suboptimal, as it may group together cycles
with different cardiac state. It was shown that, in Afib, cardiac function
can be predicted by previous cycle dynamics.^{5} Since the P wave is
absent, the amount of preload of the LV is mainly determined by the
length of diastole during the previous cardiac cycle (LD). The preload is, in
turn, correlated with the next cycle’s ejection fraction. Based on this
observation, we use LD-dependent preload as a measure of self-similarity for
cardiac cycles in Afib, which ensures a similar blood pool size for
corresponding cardiac cycles. Cardiac cycles were thus classified by their
preload state, computed as LD (Fig.2.). The number of distinct classes was
heuristically determined from the LD distribution (3 to 6). To facilitate joint
multidimensional reconstruction, reconstructed cardiac cycles were equally resampled
into 15 cardiac phases.

After rebinning data in the three
extra dimensions (cardiac phase, arrhythmic cycle type, and respiratory phase),
each reconstructed image frame has a variable degree of undersampling (30 to 80
spokes per frame). Joint reconstruction was performed
using XD-GRASP by iterative optimization.^{3} The optimal
“sparsifiable” multidimensional image $$$d$$$ for all acquired data $$$y$$$ was
found by:$$d=argmin\parallel
E(d)-y\parallel_2+\lambda_1\phi_d\parallel
T_1(d)\parallel_1+\lambda_2\phi_d\parallel T_2(d)
\parallel_1w_2+\lambda_3\phi_d\parallel T_3(d)\parallel_1$$where $$$E$$$ is the sampling function (including coil sensitivities),
$$$T_{1,2,3}$$$ are total variation functions computed separately over the
cardiac, respiratory, and cardiac cycle type dimensions, as sparsity
transforms, and $$$\lambda_{1,2,3}$$$ are regularizing parameters. The probabilistic result of k-means classification was used to implement weighted view sharing along the
respiratory dimension $$$w_2$$$,
for the highly
undersampled respiratory states. To
account for the variable undersampling, the additional $$$\phi_d=1/n_s$$$ weighting
term is inversely proportional to the number of spokes $$$n_s$$$ in
each frame.

1. Piekarski E, Chitiboi T, Ramb R, Feng L, Axel L. Use of self-gated radial cardiovascular magnetic resonance to detect and classify arrhythmias (atrial fibrillation and premature ventricular contraction). JCMR 2016; 18(1):83.

2.Wolf PA, Abbott RD, Kannel WB. Atrial fibrillation as an independent risk factor for stroke: the Framingham Study. Stroke 1991;22:983-988

3. Feng L, Axel L, Chandarana H, Block KT, Sodickson DK, Otazo R. XD‐GRASP: Golden‐angle radial MRI with reconstruction of extra motion‐state dimensions using compressed sensing. MRM 2016; 75(2):775-88.

4. Song HK, Dougherty L. k‐Space weighted image contrast (KWIC) for contrast manipulation in projection reconstruction MRI. MRM 2000;44(6):825-32.

5. Rawles JM. A mathematical model of left ventricular function in atrial fibrillation. International journal of bio-medical computing. 1988 Oct 1;23(1-2):57-68.

Fig. 1. Five-dimensional space where image
frames are ordered by their cardiac phase (cardiac dimension), relative breathing position
(respiratory dimension), and by preload from previous cardiac cycle of varying
duration (Afib cycle dimension). The MR images are jointly reconstructed in
this space.

Fig.2. Cardiac signal and labeled different types of
cardiac cycles (different colors) according to LD (the length of the filling phase of the previous
cycle).

Fig.3. End-diastolic
(left) and end-systolic (right) cardiac phases for consecutive arrhythmic
cardiac cycles reconstructed from patient with atrial fibrillation. The cardiac
cycles are sorted by the amount of preload in the Afib cycle dimension. Cardiac cycles with larger preload
(larger blood pool in the end-diastolic phase) correspondingly contract more
vigorously in the end-systolic phase. (animated)

Fig.4. Comparison
between 4D reconstruction in cardiac and
respiratory dimensions (top 4) and 5D reconstruction with additional Afib cycle type dimension (bottom 4) of ED cardiac phases at different respiratory positions. In
the 4D reconstruction, by combining cardiac cycles with different preloads and
lengths, the ED phases are more blurry. In the 5D reconstruction, although 4 times more cardiac cycles are reconstructed in the added dimension, sharpness is qualitatively improved through better
data sorting. Additionally, different cardiac cycle dynamic can be inspected along the Afib dimension.