Olivier Jaubert^{1}, Gastao Cruz^{1}, Torben Schneider^{2}, Rene Botnar^{1}, Daniel Rueckert^{3}, and Claudia Prieto^{1}

Magnetic Resonance Fingerprinting (MRF) estimates multi-parametric maps simultaneously
with short acquisition times. Cardiac MRF has been recently proposed to
quantify myocardial T_{1} and T_{2} maps for 2D single-phase
cardiac imaging. This ECG-triggered breath–hold approach provides a
single-phase cardiac image and uses a non-continuous (segmented) acquisition.
Here we sought to investigate myocardial MRF at multiple cardiac phases from a
continuous acquisition, which could simultaneously provide cardiac function and
quantitative tissue characterisation. The proposed approach was evaluated in
simulations and healthy subjects, considering eight cardiac phases per cycle.

*Acquisition.* A pseudo-balanced SSFP^{3}
(pSSFP) golden radial acquisition with inversion recovery (IR) pulses applied
throughout the acquisition, to ensure sufficient encoding for multiple cardiac
phases, was developed. The flip angle (FA) pattern was similar to the one in^{4}
and was repeated during the scan. TR was
computed as to preserve the pSSFP conditions (Fig.1), while TE was fixed for simplicity. ECG signal was used to
retrospectively bin the data into to different cardiac phases (Fig.2).

*Reconstruction*: Parallel imaging, low
rank inversion^{5}, soft-weighting^{6} and locally low rank
regularisation^{7} were combined to reconstruct multiple phases of the
cardiac cycle. This was achieved by solving:

$$\hat{\textit{I}_c}=\underset{I_c}{\mathrm{argmin}}\Vert W_c(\textbf{E} \textbf{U}_{Rc}\textit{I}_c-\textbf{K}_c)\Vert_2^2+\lambda\sum_{b}\Vert\textbf{R}_{b}\textit{I}_c\Vert_*$$

where $$$\hat{\textit{I}_c}$$$ is the compressed time-point image series
at cardiac phase *c*, **E**
is the SENSE encoding operator, **K**_{c}
is the acquired k-space data at phase *c*,
**U**_{Rc} is the low rank operator obtained truncating
(to the appropriate rank R) a
singular value decomposition of the soft-weighted MRF dictionary at phase c, $$$\textbf{R}_{b}$$$ thresholds the singular value
decomposition of an image block ** b** and $$$\lambda$$$
controls the regularization strength. The soft-weights for
cardiac phase

$$W_c(t)=\begin{cases}1\quad,\quad if\quad |t-t_c|<\frac{S_c}2\\e^{-\alpha(m(t)-m(t_c)) }\quad,\quad if\quad e^{-\alpha(m(t)-m(t_c))}>\tau\quad and\quad |t-t_c|>\frac{S_c}2\\0 \quad, \quad otherwise\end{cases}$$

where $$$\alpha$$$ is
a scaling factor, $$$\tau$$$ a threshold value to discard low weighted time-points,$$$S_c$$$ the size of phase *c*,$$$m(t)$$$ the cardiac
motion model and $$$t_c$$$ the center of phase *c*. An estimation of the cardiac motion $$$m(t)$$$ is obtained from the data itself by an
intermediate zero-filled CINE reconstruction (Fig.2), enabling identification
of the quiescent and motion intensive periods of the cardiac cycle. A dot
product matching between the reconstructed data and the soft-weighted
dictionary^{8} was applied to obtain the T_{1} and T_{2}
maps.

*Experiments:* A digital static
cardiac phantom (MRXCAT^{9}) was simulated using realistic T_{1}
and T_{2} values for myocardium, blood and liver, and a model $$$m(t)$$$ for a
heart-rate of 53 beats/minute. Motion was not considered in the simulations to
isolate the effects of the encoding and the proposed reconstruction. IR pulses
and FA pattern were repeated every 2.92s, considering a 29.5 sec scan. Four
healthy subjects were scanned in a 1.5T Philips MR scanner using anterior and posterior coils (28-channels). Acquisition parameters included: TE=2ms, 4380 time-points,
one spoke per time-point, 2x2 mm^{2} resolution, 300x300 mm^{2}
FOV and 10 mm slice thickness, 6 repetitions of IR and flip angle train, acquisition
time=17.7s compatible with a breath-hold. $$$\alpha$$$ and $$$\tau$$$ were set empirically for both
simulations and in-vivo
reconstructions.
For both cases, eight cardiac phases were retrospectively reconstructed, with R=8,
b=7 and local rank threshold=5% of the maximum singular value.

This work was supported by:

-Philips Healthcare,

-EPSRC programme Grant (EP/P001009/1),

-FONDECYT 1161055,

-King’s College London & Imperial College London EPSRC Centre for Doctoral Training in Medical Imaging (EP/L015226/1).

1.Ma D et al, Nature 2013;495:187-192

2. Hamilton et al, MRM 2017;77: 1446–1458.

3. Asslander et al, MRM, 2017;77(3):1151–1161

4. Asslander et al, arXiv, 2017;1703.00481

5. McGivney et al, IEEE Trans Med Imaging 2014;33(12):2311-22

6. Johnson et al, MRM, 2012;67:1600-1608

7. Cao et al, MRM, 2017;78:1579–1588

8. Cruz et al, ISMRM 2018, submitted

9. Wissmann L et al,JCMR 2014;16:63.

10. Reiter et al, Radiology 2014;271:365–372.

Figure 1. One repetition of the flip angle train and
repetition time train containing 730 values for an acquisition time of 2.92s
per repetition. Each repetition of the pattern is preceded by an IR and the TE
is fixed at 2ms.

Figure 2. Proposed
MORE-MRF framework. **a)** A 1D cardiac motion model m(t) is estimated from an
intermediate retrospectively ECG-gated zero-filled reconstruction. ECG signal is
also used to retrospectively assign the time-points to different cardiac phases.**
b)** Weights for the proposed reconstruction are obtained from the estimated
cardiac motion model (Eq.2). Soft-weights (lines) are compared to a hard-weight
(bars) approach. **c)** MORE-MRF reconstruction is performed combining soft-weights
and regularized low rank reconstruction of T1 and T2 maps
for each cardiac phase.

Figure 3. T1
(first row) and T2 (second row) maps from cardiac phases 1, 3, 5 and
7 from simulated data reconstructed with MORE-MRF. Good quality T1
and T2 maps are obtained for all cardiac phases. T1 and T2 maps are
visually consistent with ground truth maps (last column) throughout the
different cardiac phases. Cardiac motion was not considered in the simulations
to isolate the effects of the proposed encoding and the soft-weighted
reconstruction.

Figure 4.
T1 and T2
errors in comparison to ground truth values for all cardiac phases with the proposed
approach. Values were measured on a region of interest of the simulated
myocardium. Bias under 6 % were obtained for all cardiac phases for both T1 and
T2 values. Error on all phases was measured at 5.9±32.5ms and 0.05±0.50ms for T1 and T2 respectively. A
higher bias is observed in T1 for the first phase, which coincides
with the acquisition of the first inversion pulse.

Figure 5
. In-vivo MORE-MRF. T1 and T2 maps for
eight cardiac phases in a healthy subject. Septal myocardium values were measured
as 922±65ms and 42±7.9ms throughout the
cycle for T1 and T2 respectively. Functional cardiac contraction and relaxation
can be observed throughout the cardiac cycle. Blood behaviour was not modelled,
therefore values are expected to differ from phase to phase.