2-D Respiration Navigation Framework for 3-D Continuous Cardiac Magnetic Resonance Imaging

We extended a previously proposed prototypical method for 3-D free-breathing, continuous, cardiac MRI [5]. Data is collected during multiple cardiac and respiration phases. The Cartesian phase encoding (PE) plane is incoherently undersampled with samples on pseudo-spiral spokes, each starting in the $k$-space center (Fig. 1). We adapted this scheme to sample 2-D respiration motion information: Every $t=1\,s$, data is sampled on the $k_{z}=0$, $k_{y}=-u/2,...,0,...,u/2$ line, where $u$ is number of samples on one pseudo-spiral spoke. This leads to a fully sampled $k$-space center with size $u\times v$, where $v$ is the length of the $k_{x}$-line, the remaining positions are zero-filled. The 2-D navigation signals are planes within the imaged 3-D volume, mainly orientated in the AP and SI direction. These readouts are simultaneously used for navigation and reconstruction of the 3-D dynamic volumes, avoiding additional scan time for navigation. All acquired readouts after a navigation signal $i$ and prior to the next navigation signal $i+1$ are considered to have the same motion state as the navigation signal $i$.

All 2-D navigation signals from single coils are transformed to the spatial domain with the 2-D inverse Fourier transform (iFT) and are combined with the sum-of-squares (SoS) resulting in final low-resolutional navigation images, $N_{1},...,N_{I}$, where $I$ is the total number of navigation images. The 2-D respiration motion in AP and SI direction can be observed there (Fig. 3). For the selection of one respiration state, following steps are applied: (1) The first navigation image is selected as reference $N_{\text{ref}}$ with $R$ different regions of interest (ROIs) $N_{\text{refROI}_{1}},...,N_{\text{refROI}_{R}}$ with observable motion. (2) For each ROI the correlation coefficients $CC$ between $N_{\text{refROI}_{1}},...,N_{\text{refROI}_{R}}$ and $N_{\text{ROI}_{1}},...,N_{\text{ROI}_{R}}$ in each $N_{2},...,N_{I}$ are calculated, while moving the ROI within a selected search window on $N_{2},...,N_{I}$. The spatial positions of $N_{\text{ROI}_{1}},...,N_{\text{ROI}_{R}}$ in $N_{2},...,N_{I}$ with the highest $CC$ result in the $x$ and $y$ shifts for the two motion directions compared to the $N_{\text{refROI}_{1}},...,N_{\text{refROI}_{R}}$, yielding the current motion vector $\vec{m_{ir}}=(\hat{x}_{ir},\hat{y}_{ir})^{\top}$ for each $N_{2},...,N_{I}$ and each $N_{\text{ROI}_{1}},...,N_{\text{ROI}_{R}}$. (3) We assume that each ROI will mainly contain one direction of motion (e.g., a ROI on the chest wall will contain mainly AP motion). PCA is applied on all motion vectors from step (2) to select the dominant 1-D shifts from each ROI, resulting in a combined $\vec{m_{comb}}=(\hat{x}_{ir_{\max}},\hat{y}_{ir_{\max}})^{\top}$ for each $N_{2},...,N_{I}$, where $r_{\max}$ is the selected ROI for one particular motion direction ($x$ or $y$). (4) Different motion states and the amount of respective navigation images for each state are computed. All readouts from the state with the most frequent occurence are selected for reconstruction, which is based on a previously proposed prototypical Compressed Sensing framework combined with spatiotemporal Wavelet regularization [8].

We acquired a 3-D free-breathing, continuous in-vivo scan from one volunteer (female, 55 years) after written consent was obtained. Data was acquired with the proposed prototypical sequence in short-axis orientation and balanced steady-state free precession readouts on a $1.5\,T$ scanner (MAGNETOM Aera, Siemens Healthcare, Erlangen, Germany) with these parameters: Field-of-view: $310\times 310\times 86\,mm$, spatial resolution: $1.8^{3}\,mm$, flip angle: 46 ^∘, echo time: $1.7\,ms$, repetition time: $3.3\,ms$, scan time: $5.3\,min$. Cardiac signal from an external ECG device was used to bin the data into cardiac phases [5]. We selected $R=2$ navigation ROIs, which correspond mainly to AP (green ROI in Fig. 3) and SI motion (red ROI in Fig. 3). A search window of $\pm$ 25 pixels in $x$, $y$ directions on $N_{2},...,N_{I}$ was used. The $\vec{m_{comb}}$ was selected with $\hat{x}=2$ (from green ROI with a principal component coeffiecent of 0.99) and $\hat{y}=1$ (from red ROI with a principal component coeffiecent of 0.99) with 39.9 % of all data (108/339 navigation images). We compared three different reconstructions: (1) Without respiration compensation (No Nav), (2) with 1-D navigation (1-D Nav), with respiration motion extracted from central 1-D $k$-space lines [5] (Fig. 3) and (3) with our proposed 2-D navigation (2-D Nav). For the quantitative evaluation, three commonly used image quality metrics in motion compensation [9] were applied (Tab. 1): (1) Histogram entropy $H$, (2) total variation $TV$ and (3) wavelet-based estimation of the standard deviation of Gaussian noise distribution $\sigma_{\text{Noise}}$ [10].

Figure 4 shows one slice resolved into different cardiac phases from 3-D volumes reconstructed with different approaches. Our 2-D based navigation shows a visually sharper image quality compared to the other reconstructions, especially in the cardiac region (marked with orange box for cardiac phase 2). For all quantitative metrics shown in Tab. 1, the 2-D based navigation approach yields superior results. The Student’s $t$-test results confirm that the differences in the image quality between the approaches are statistically significant ($p$-value $<0.05$).