Cardio-respiratory motion-corrected 3D cardiac water-fat MRI using model-based image reconstruction

2.1 Overview image reconstruction workflow

A schematic overview of the reconstruction workflow used is given in Figure 1. Several image reconstruction and motion estimation steps are performed where each of the steps incorporates information obtained in the previous ones.

The surrogate signals necessary for relating the data to the individual motion states are available in the form of an ECG for cardiac motion (Figure 1A) or a self-navigator, which is extracted from the acquired k-space data for respiration (Figure 1B). Data are either binned based on the cardiac phase or respiratory amplitude.

The respiratory self-navigator was obtained from the data itself. The readouts at the phase encoding point k_y = k_z = 0 are extracted and Fourier transformed along the readout yielding a time-resolved projection of the 3D image volume onto the foot-head axis. The temporal resolution of this navigator depends on the time intervals in which the phase encoding point k_y = k_z = 0 is sampled, which in this work yielded a resolution of 48*T_R = 394 ms.

From these data, the respiratory surrogate signal is extracted using principal component analysis (PCA) over the readout- and receiver channel dimension where the component with the largest singular value was selected as the respiratory signal. Subsequently, it was interpolated to the resolution of T_R using a spline interpolation.

Coil sensitivity profiles were estimated from the acquired data³³ and no coil calibration scan was required.

For the estimation and correction of motion, a two-step strategy is applied. Both respiratory and cardiac motion-resolved images are reconstructed, and the 4D motion is estimated for both motion modes individually. First, the data are reconstructed resolving the respiratory motion, followed by a registration step extracting a respiratory motion model (Figure 1C). Subsequently, this respiration model is included in the reconstruction of cardiac-resolved images, followed again by registration to model the cardiac motion (Figure 1D). The images underlying the cardiac motion estimation are, however, already corrected for respiratory motion. Cardio-respiratory motion is then generated by combining the two individual motion modes by concatenation of cardiac and respiratory motion to yield both cardiac and respiratory motion-corrected and water-fat separated images (Figure 1E). Details on the individual steps are described in the following.

All reconstructions were performed using a custom implementation in MATLAB (The Mathworks, Natick, MA) and Python.³⁴

2.2 Motion-resolved model-based water-fat separated image reconstruction

A reconstruction using this approach and cost function and data acquisition with a stack-of-stars trajectory has previously been proposed as XD-GRASP.^{18, 19, 30} In this work, however, the sampling of non-cartesian data points is not performed in the readout direction but the phase-encoding direction instead.

The field off-resonance map $$$ \Phi $$$ used in the forward model was computed using the three individual echoes using a dedicated region-growing algorithm¹⁴ before the reconstruction and kept constant concerning the optimization afterward.

2.3 Motion-corrected model-based water-fat separated Image reconstruction

2.4 Synergistic registration

2.5 Combination of cardiac and respiratory motion correction

To perform simultaneous cardiac and respiratory motion correction, the data are double binned such that the motion index $$$ m $$$ is comprised of a respiratory and cardiac motion state: $$$ m=\left(r,c\right) $$$. As the motion transformation is not estimated on double-binned reconstructed images, but the cardiac motion is only estimated in end-exhale to apply both motion models at the same time, the cardiac motion model must be transformed from the end-exhale motion state into the other respiratory motion states by concatenation of respiratory and cardiac motion transform: $$$ {T}_{\left(r,c\right)}={T}_c\circ {T}_r $$$.

This ensures that the correction of the heartbeat is moved to the individual respiratory motion states. This combination of motion modes is possible if the respiratory motion is an affine transformation in the regions where the heartbeat is corrected. This can be assumed to be true for the central region of the thorax where the heart executes a respiratory-induced combination of translation and rotation.

2.6 Parameters in image reconstruction workflow

In a first step, the respiratory self-navigator is extracted and used to bin the data into N_resp = 6 respiratory motion states based on respiratory amplitude with a 10% overlap between adjacent bins. This yielded an undersampling factor of three for respiratory reconstruction. Binning for respiration (as well as cardiac motion later) was performed by adaptively choosing the bin width, such that all bins contain the same amount of data points to ensure a similar undersampling artifact level upon reconstruction. The binned data are reconstructed into water and fat content using a TV and TVT regularization strength of $$$ {\lambda}_{TV}=0.05 $$$ and $$$ {\lambda}_{TVT}=0 $$$. The resulting image series are subsequently registered using the dual water-fat registration defined in Equation (2) with (w, ΔB, $$$ \rho $$$) = (0.7, 8, 0) yielding motion fields that describe the respiratory motion model. In a second step, the data are binned into N_card = 12 cardiac motion states based on cardiac phase using the ECG signal. For cardiac binning, a 0% overlap between adjacent bins was used. This yielded an undersampling factor of 6 for the cardiac reconstruction. The resulting data are reconstructed into water and fat modes using a regularization strength of $$$ {\lambda}_{TV} $$$=0.025 and $$$ {\lambda}_{TVT} $$$=0.05 while simultaneously applying the previously generated respiration model for respiratory MoCo. The resulting image series resolves the heartbeat motion, and each image itself is already free of artifacts caused by respiration. The image registration with (w, ΔB, $$$ \rho $$$) = (0.5, 2, 2*10⁻³) was applied to determine the cardiac motion fields. Eventually, both motion models were combined into a cardio-respiratory motion model and applied to reconstruct a single, motion-free fat and water separated image. Finally, three reconstructions were compared: the motion-averaged (AVG), respiratory-corrected, cardiac-averaged (r-MCIR), and the cardio-respiratory corrected (cr-MCIR). Each was reconstructed with $$$ {\lambda}_{TV} $$$=0.015 (as there is only one reconstructed, motion-corrected image TVT regularization cannot be performed, i.e. $$$ {\lambda}_{TVT}=0.\Big) $$$

2.7 Trajectory

Sampling k-space using a radial phase encoding (RPE) trajectory has been proposed before and used in several cardiac imaging applications.^{29, 39, 40} An RPE trajectory performs parallel, cartesian readouts that are arranged in a non-cartesian pattern in the phase-encoding plane of k-space.

For this work, a novel trajectory was implemented, which aims to generate a phase encoding sampling scheme more suitable for compressed sensing applications. It should have a uniform and random distribution after the data are binned into cardiac or respiratory motion states, but at the same time provide ideal coverage of the phase encoding plane when all sampled data points are used in an MCIR. Since the readouts are parallel and cartesian samples the subsequent analysis considers phase encoding points only.

We present a phase encoding sampling strategy for RPE that decouples radial and angular undersampling for the arrangement of the phase encoding points. The resulting trajectory is shown in Figure 2.

Where $$$ \Phi =\frac{1+\sqrt{5}}{2} $$$ is the golden ratio and mod the modulo operator on floating-point numbers. This angle-dependent shift applies the principle of golden-ratio increments previously used in the angular direction for radial-readout⁴¹ or RPE sampling³⁹ to the radial direction. Hence, the points are arranged on infinitely interleaved circles where no two points have the same distance to the center of the phase encoding plane. However, as the readout in the center point of the k_y-k_z-plane, which is required for robust motion binning and self-navigation, is shifted away from its position at k_y = k_z = 0, the readout of the first radial point of each angle (n_r = -N_r/2) is used to acquire k_y = k_z = 0. This yields a pattern in the phase encoding plane of the arrangement of sunflower seeds. This pattern was previously generated with a spiral readout.⁴²

During the acquisition, this decouples the notion of the radial FOV from the radial sampling distance $$$ dr: $$$ an undersampling of the radial direction by a factor of F_r can be compensated by an angular oversampling by a factor of $$$ {\mathrm{F}}_{\upvarphi} $$$, i.e., $$$ {\mathrm{N}}_r\to {N}_r/{F}_r $$$ while $$$ {\mathrm{N}}_{\upvarphi}\to {\mathrm{N}}_{\upvarphi}\cdotp {\mathrm{F}}_{\upvarphi} $$$. The gaps in the radial direction are automatically filled by the additional angles, leaving the sampling pattern invariant. The temporal order of the sampling and the generation of the pattern are shown in Supporting Information Videos S1–S3, which are available online, for an example trajectory of N_r = 64, $$$ {N}_{\upvarphi}=\uppi \cdotp {N}_r $$$ and $$$ {\mathrm{F}}_{\mathrm{r}}={\mathrm{F}}_{\upvarphi}\in \left[1,4\right] $$$.

This particular pattern is only generated using a radial shift as above for linear angle increments $$$ d\upvarphi =\frac{\uppi}{N_{\upvarphi}} $$$. However, in this work, a golden-angle increment was used: $$$ d{\upvarphi}_{\mathrm{gold}}=\uppi \left(\Phi -1\right) $$$. Assuming a homogenous angular distribution after sampling all angles with $$$ d{\upvarphi}_{\mathrm{gold}} $$$ the same pattern can be generated by reordering the shift according to $$$ \Delta {\left({n}_{\upvarphi}\right)}_{gold}={\left(-1\right)}^{U\left({n}_{\upvarphi}\right)}\Delta \left(\Pi \left({n}_{\upvarphi}\right)\right) $$$, where $$$ \Pi \left({n}_{\upvarphi}\right) $$$ is the permutation that sorts the sampled angles into a linearly increasing order and $$$ U\left({n}_{\upvarphi}\right)=\left(\operatorname{Re}\left({\mathrm{e}}^{\mathrm{i}\ {\mathrm{n}}_{\upvarphi}\ \mathrm{d}{\upvarphi}_{\mathrm{gold}}}\right)>0\right) $$$ accounts for the direction of the shift.

2.8 Data acquisition

Nine patients were scanned on a 1.5T Siemens Avanto using a 32-channel cardiac phased coil array. Patients included in the study were suffering from myocarditis or muscular dystrophy. The study was conducted in accordance with the Declaration of Helsinki, each patient provided informed written consent.

Data were acquired with a 3D three-echo Dixon (TR = 8.,2 ms, TE = 2.90 ms, 4.48 ms, 6.06 ms, α = 15°, acquisition time [TA] = 13:26 min) FLASH sequence. The reconstructed FOV in each direction was 288 mm at a 1.5 mm isotropic resolution, covering the entire thorax. Fourier encoding was performed with the readout ($$$ {k}_x\Big) $$$ along the head-foot direction and for the $$$ {k}_y-{k}_z $$$ directions using the sunflower trajectory as described above The radial direction was undersampled by F_r = 4 and a total of 2048 different phase encoding angles were sampled.

Data acquisition was carried out during free breathing without cardiac triggering. Patients' ECG signals were recorded. Each patient was given a T₁ contrast agent for clinical reasons before the data acquisition (0.2 mmol/kg ProHance, except for patient 9, 0.15 mmol/kg Regadenoson).

Water-fat separated images were acquired in two-, three-, and four-chamber views using a standard ECG-triggered 2D Cartesian acquisition scheme in three patients. The proposed 3D acquisition was then reformatted to these orientations and compared.

Additional, a qualitative assessment was performed regarding a retrospectively gated reconstruction. To this end, data from the three cardiac motion frames with the largest motion and the end-inhale phase were excluded and the resulting reconstructions were compared qualitatively to using all acquired data.

2.9 Computation of local image sharpness

To assess the effect of motion correction on the image quality, the sharpness of small structures in the fat images was evaluated.^43-46 An example for one patient in one view is depicted in Supporting Information Figure S1. To this end, the fat images were reformatted to two- and four-chamber view and a Canny edge detection algorithm was applied to the reformatted fat images to generate the local magnitude of the image edges. Two fat structures from each view were marked with a curve of length l. Both the edge magnitude and the image magnitude were subsequently extracted along this curve in a 10-pixel corridor, yielding a patch of size l x 10 whose central line is the marked curve. The extracted patches for both image and edge values were averaged along the direction of the curve and the maximum was computed over the width of the patch, yielding the values (img) and (edg) for the image and edge information respectively. Finally, the edge sharpness was defined as $$$ \Sigma =\frac{\mathrm{edg}}{img}. $$$ This sharpness score was evaluated for four different locations each yielding the score $$$ {\Sigma}_{\mathrm{l}} $$$, two locations in two-chamber and two- in four-chamber view. Exemplary locations for one patient are depicted in Figure 8. For each patient, the sharpness score was the average sharpness over all four locations.

Additionally, a comparison of the image sharpness between the 2D ECG-triggered reference images and reformatted 3D AVG and cr-MCIR reconstructions was performed for the patients in which the reference was available(patients 1, 2, and 3).

3.1 Qualitative evaluation of water-fat reconstructions

Motion-resolved reconstructions for two patients are displayed in Figure 3. For both patients, water and fat images in end-exhale, end-inhale, diastole and systole are displayed. One patient is shown in sagittal and one in coronal view to highlight the 3D isotropic resolution of the acquired data.

For both patients, changes in the anatomy due to respiratory motion are visible in water and fat reconstructions. In the cardiac-resolved images, the respiration has been corrected as indicated by the position of the liver and diaphragm. For patient 8, the contraction of the heart from the diastolic to systolic phase is visible both in water and fat images.

In Figure 4, the effect of the estimated motion fields for example patient is shown as coordinate transformations from exhale to inhale for respiration and diastole to systole for cardiac motion. The motion transformations do not show non-physical properties such as overlapping coordinate lines and are well-regularized. The successful transport of the cardiac motion along the path defined by the respiratory motion can be seen in the combined cardio-respiratory motion field.

Motion-corrected images for two patients are shown in Figure 5. Both fat and water images are shown for AVG, r-MCIR, and cr-MCIR from left to right. Regions, where improvements in the fat structure are visible, are depicted in a separately zoomed-in square. Cyan arrows indicate additional locations where motion-blurring in the epicardial fat structures is visibly reduced by the application of the proposed motion-corrected image reconstruction. Patient 1 shows a reduction of motion blurring after the application of the respiratory model, especially in the abdominal region. Motion blurring due to the heartbeat can be further reduced by an additional application of the cardiac motion model in both epicardial fat structures as well as for the coronary vessel. Patient 6 shows very strong blurring in the motion-averaged case, of which the abdominal fat and the structure at the apex could be improved with respiratory MoCo. Cardiac MoCo could further improve the basal fat structure. A similar improvement can be also seen in the complimentary water image where the coronary arteries become visible using cr-MCIR. In addition to a reduction in blurring also respiratory motion artifacts in the ventricle are reduced with MoCo.

A comparison between 2D clinical acquisitions in two-, three-, and four-chamber view and 3D fat cr-MCIR reconstructions reformatted to the same views are displayed for two patients in Figure 6. The depiction of fat structures acquired is comparable between both scans. Nevertheless, it is important to note that the 2D data were acquired during a breath-hold using cardiac triggering and hence might show a different motion state than cr-MCIR.

Supporting Information Figure S3 shows the effect of retrospective motion gating in one example patient. It can be seen that the exclusion of data with large motion amplitudes increases the visibility of fine structures for AVG and r-MCIR reconstruction, however, not for cr-MCIR. This, however, is accompanied by a loss in overall image quality as fewer data were available for the reconstruction. Different levels in undersampling artifacts between AVG gated and (c)r-MCIR images are likely to occur since the reconstructed k-space is not oversampled after gating and motion-correction can potentially increase undersampling artifacts.²⁶ Furthermore, a comparison between AVG, AVG-gated and cr-MCIR in two-chamber view is depicted for three patients in Supporting Information Figure S4. While for one patient gating was very effective in removing most of the motion-artifacts, the patients showed residual motion artifacts in the AVG gated reconstructions. In contrast, motion correction was able to remove more motion-artifacts in all three patients than gating.

A patient with fat-infiltration in the septum is displayed in Figure 7. The reconstructed fat images are displayed in axial and sagittal views for both AVG and cr-MCIR. It can be observed that MoCo led to an improved depiction of the fat in the sagittal view. The sagittal slice shows the fine structure of the fat infiltration strongly blurred for the AVG reconstruction. In addition, many motion-artifacts make it difficult to identify these small structures. The proposed cr-MCIR reduced motion artifacts and blurring and strongly improved the visibility of the fat infiltration. This can also be seen in a water-fat overlay of the sagittal slice.

3.2 Quantitative evaluation of image sharpness

A quantitative assessment of the fat structure sharpness $$$ \Sigma $$$ is displayed in Figure 8. On the left, the locations where the sharpness is evaluated are shown for patient 4 on cr-MCIR fat images. On the right, the values of $$$ \Sigma $$$ are displayed for AVG, r-MCIR, and cr-MCIR. The distributions show an increase in sharpness for the inclusion of each motion type. The increase in sharpness due to cardiac motion correction is smaller compared to respiratory motion correction.

A comprehensive overview of the measured values is given in Table 1. The effect of r-MCIR leads to an increase in fat structure $$$ \Sigma $$$ for every patient, with improvements ranging between 1% and 81% with 32% ± 24% on average. The effect of additional cardiac MoCo is highly patient-specific. For some patients, it can further improve $$$ \Sigma $$$ by 31% for other patients it does not lead to any further improvement. On average cardiac MoCo increase $$$ \Sigma $$$ by 15% ± 11%.

The result of the statistical tests between AVG and r-MCIR of as well as cr-MCIR led to p-values p_rMCIR=0.008 and p_crMCIR = 0.008, also between r-MCIR and cr-MCIR the p-value was p_card = 0.008. This suggests that correcting for both the respiratory and the cardiac motion yields a significant improvement in the fat structure $$$ \Sigma $$$ of the overall heart.

The quantitative comparison is presented in Supporting Information Figure S2. In this patient subset, the sharpness increases between AVG and cr-MCIR reconstructions on average by 38%, and the reference data shows an increased sharpness by 19% compared to the cr-MCIR reconstruction.

The effect of gating on the sharpness metric was assessed by comparing the sharpness metric of AVG, AVG-gated, and cr-MCIR. While gating increased the sharpness metric mean by 16% from AVG to AVG-gated, it was increased further by 25% in cr-MCIR (Supporting Information Figure S5).