Patrick Metze^{1}, Tobias Speidel^{2}, Kilian Stumpf^{1}, and Volker Rasche^{1,2}

In this work we present a reconstruction technique based on $$$k$$$-space subtraction of static image parts to acquire real-time cardiac images. The static part is estimated with a sliding window reconstruction of the region outside of the heart to account for respiratory motion. The reduced field of view, i.e. the region of interest, is then reconstructed using a standard SENSE reconstruction, resulting in a temporal resolution of under 40 ms. The image quality is sufficient to estimate functional values in accordance with the BH-CINE reference standard.

The reconstruction process is illustrated in figure 1 and described in the following. The sliding window width is set to five fully sampled images for the acquisitions, resulting in 720 ms temporal resolution.

The target $$$k$$$-space consists of $$$n$$$ EPI trains (equally spaced), the fully sampled $$$k$$$-space consists of $$$N$$$ trains. The acceleration factor $$$R$$$ is then calculated as

$$R=\frac{N}{n}.$$

The raw (full FOV) data is available in the same dimensions. $$$\textrm{ksp}_i$$$ denotes the full FOV $$$k$$$-space of the $$$i$$$-th frame ($$$i=1 … I$$$). The $$$j$$$-th ($$$j=1 … I/R$$$) fully sampled image is then

$$\textrm{img}_{\textrm{full},j}= \textrm{FT}\left[ \sum_{i=(j-1)R+1}^{jR} \textrm{ksp}_i \right].$$

The $$$k$$$-space of the static part of the image is created with the dynamic region set to 0 in image space:

$$\textrm{ksp}_{\textrm{static},j}=\textrm{FT}^{-1}\left[ \textrm{img}_{\textrm{full},j} (\textrm{dyn. reg.}=0) \right].$$

The sliding window of width $$$w$$$ ($$$w$$$ uneven, WLOG) is then calculated in $$$k$$$-space according to

$$\textrm{ksp}_{\textrm{sw},k}=\frac{1}{w}
\sum_{ind=k-\lfloor\frac{w}{2}\rfloor}^{k+\lfloor\frac{w}{2}\rfloor}
\textrm{ksp}_{\textrm{static},ind}$$

with $$$k=\lceil\frac{w}{2}\rceil ... J-\lfloor\frac{w}{2}\rfloor $$$ .

Finally, the rFOV $$$k$$$-space can be calculated as

$$\textrm{ksp}_{\textrm{dynamic},i} = \textrm{ksp}_i -\textrm{ksp}_{\textrm{sw},k}(\textrm{PE}_{\textrm{ksp}_i})$$

with $$$\textrm{PE}_{\textrm{ksp}_i}$$$ denoting the phase
encode steps (non-zero $$$k$$$-space lines)
of $$$\textrm{ksp}_i$$$, $$$i=R\lceil\frac{w}{2}\rceil ... I-R\lfloor\frac{w}{2}\rfloor$$$ and $$$k=\lfloor\frac{i}{R}\rfloor$$$. For further
acceleration the rFOV reconstruction is based on standard Cartesian SENSE^{3}.
To reduce the influence of subcutaneous fat, the sequence was combined with a
1-2-1 binomial fat suppression pulse. The flip angle was chosen to maximize contrast
between myocardium and the blood pool.
Imaging is performed
using an interleaved EPI sequence with the parameters given in table 1. All
imaging experiments were performed on a 1.5 T clinical whole-body scanner (Philips
Achieva, Best, The Netherlands) with a maximum gradient strength of 21 mT/m per
channel and a maximum slew rate of 180 T/m/s. All data were acquired with a
32-element SENSE Cardiovascular array coil.
The method was tested
in three healthy volunteers, acquiring three short axis slices. Images are
compared against standard SENSE reconstructed images from the same dataset and
the BH-CINE images. Functional parameters of the left ventricle have been
calculated with Segment (Medviso AB, Lund, Sweden).

The ability of the sw-rFOV method to reconstruct RT cardiac images could be shown. Image quality is reduced and the contrast is degraded compared to BH-CINE acquisition. This can be partly explained by the superior b-SSFP contrast generation. However, it could be shown that the rFOV technique allows for higher undersampling factors and therefore higher temporal resolutions than a pure parallel imaging ansatz. Functional parameters are in line with the reference values, a Wilcoxon test showed no significant differences. It should be noted, that differences might be due to minor slice displacement between BH and RT imaging.

Compared to saturation pulse techniques sw-rFOV imaging holds two major advantages: lower SAR values and a higher probability of auxiliary findings. As opposed to other real-time imaging techniques, such as CS or Deep Learning, sw-rFOV relies on simple cartesian reconstruction and does neither need training data nor a carefully chosen regularization parameter and is very resource efficient in terms of reconstruction speed.

(1) Fredrickson, Jill O., and Norbert J. Pelc. "Temporal resolution improvement in dynamic imaging." Magnetic resonance in medicine 35.4 (1996): 621-625.

(2) Weingärtner, Sebastian, and Moeller, Steen and Akcakaya, Mehmet “Feasibility of Ultra-high Simultaneous Multi-slice and In-plane Accelerations for Cardiac MRI Using Outer Volume Suppression and Leakage-Blocking Reconstruction”, ISMRM 2018, 0359

(3) Pruessmann, Klaas P., et al. "SENSE: sensitivity encoding for fast MRI." Magnetic resonance in medicine 42.5 (1999): 952-962

Figure 1: Reconstruction
process for sliding window rFOV imaging. The sw-reconstruction images are not
taken from the same series to better illustrate respiratory motion. The
interleaved EPI acquisition is chosen in a way to facilitate reconstruction,
i.e. the acceleration factor (product of SENSE factor and rFOV reduction) has
to be known to choose the multiplier accordingly. On the average image the rFOV
can be selected, an implementation setting rFOV to 1/nth of the PE
direction is also feasible.

Figure 2: Example
still images of conventional imaging, sw-rFOV reconstruction and standard SENSE
reconstruction of the EPI dataset (a). The sw-rFOV reconstruction process shows
clear advantages over SENSE imaging with the same temporal resolution. This is
also illustrated by m-mode images (b) of the two methods. The SENSE images are
corrupted by noise, making it very difficult to assess cardiac motion.

Figure 3: Quantitative
image comparison (sw-rFOV vs. BH-CINE). While SNR in the LV blood pool (a) is higher
for the BH-CINE images, the SNR for myocardium (b) is higher in sw-rFOV images.
In terms of CNR (c), the conventional images also hold advantages over the
sw-rFOV reconstruction of EPI images. The sharpness measures should be
considered with caution, as double edges or streaking artifacts might lead to
higher values for the Sobel metric. However, the Sobel edge index (d) indicates
slightly better performance of the conventional images, while the signal
increase (e) seems to be steeper in sw-rFOV reconstruction.

Table 1: Parameters
for the EPI and the BH-CINE sequence. The temporal
resolution in sw-rFOV reconstruction is 2 TR = 36.52 ms.

Table 2: Functional
parameters derived from sw-rFOV reconstructed EPI images and the reference
BH-CINE acquisition with corresponding p-values for the Shapiro-Wilk test for paired differences and the Wilcoxon test. Although values for end diastolic, systolic and stroke volume are lower in EPI and the ejection fraction is higher, none of the differences are statistically significant.