In clinical practice, abdominal dynamic contrast-enhanced (DCE) MRI is performed using multiple breath-hold acquisitions over a period of minutes. In particular iterative reconstruction techniques have brought continuous free-breathing acquisitions with high spatio-temporal resolution into clinical range [1]. This is not only desirable for patient comfort and robustness, but also aims at quantitative imaging. One promising strategy is to resolve motion-states as an additional dimension in the reconstruction [2, 3, 4]. Here we present a Cartesian acquisition strategy with a motion-state detection based on additional navigation scans. The latter are aligned with preparation pulses and come at practically no time cost. Motion-states are determined by clustering the imaging scans based on those navigation signals.

A prototypical 3D Cartesian spoiled Volume-Interpolated Breath-hold Examination (VIBE) GRE sequence supporting spectral fat suppression was extended to support variable-density sampling of the phase-encoding plane as well as the acquisition of a navigation signal as follows: For multiple time points, the sampling is generated in ascending order according to a Gaussian distribution, guaranteeing that at each time point the expectation value for acquiring a phase-encoding step differs from its actual acquisition number by at most one. The set of phase-encoding steps is assigned to the echo trains following the fat preparation pulses. For navigation, an additional GRE module is played out after each fat suppression pulse differing from the imaging scans only in the readout. The latter is put in head-feet direction.

Using a generalized k-means algorithm, the navigation signal is clustered into $$$N$$$ motion-states by minimizing

$$ \min_{\{\mathcal{C}_{c,r}\}, \{\mathbf{m}_{c,r}\}} \left(\sum_{c=1}^{N} \sum_{r=1}^{R} \sum_{i\in\mathcal{C}_{c,r}} \vert \mathbf{S}_{i,r} - \mathbf{m}_{c,r} \vert^2 + \alpha \sum_{c=1}^{N} \sum_{r=1}^{R-1} \vert \mathbf{m}_{c,r+1} - \mathbf{m}_{c,r} \vert^2\right)\,,$$

with $$$\mathbf{S}_{i,r}$$$ being the $$$i$$$th navigation scan at the $$$r$$$th time point. The optimization is performed for each coil element and the configuration yielding the best relative improvement compared to the accumulated variance is picked. The obtained motion-states $$$\{\mathcal{C}_{c,r}\}$$$ are sorted and assigned to the whole respective echo train. The navigation signal is obtained practically without loss in acquisition time as dummy scans and/or inversion time are conventionally put between fat preparation and imaging scans. As a result the imaging scans $$$\mathbf{D}(\mathbf{k},r,i)$$$ are indexed by $$$\mathbf{k}$$$-space, time point and motion-state. The corresponding 3d+time+motion-state image volumes $$$\mathbf{I}(\mathbf{x},r,i)$$$ are reconstructed by optimizing

$$ \min_{\mathbf{I}}\left(\Vert\mathbf{F}\mathbf{I}-\mathbf{D}\Vert_2^2+\lambda\Vert\mathbf{W}\mathbf{I}\Vert_1\right)\,,$$

with $$$\mathbf{W}$$$ being a redundant wavelet transformation, $$$\lambda$$$ the regularization strength and $$$\mathbf{F}$$$ consisting of multiplication with coil-sensitivities, Fourier transformation and masking.

In addition a reconstruction using a fixed gating acceptance for a single motion-state was considered and is referred to as hard-gating. The optimization problem above is then modified to finding the best subset of given size at each time point.

A DCE-MRI scan of the liver was performed in free breathing on a clinical 3T scanner (MAGNETOM Skyra, Siemens Healthcare, Erlangen, Germany). Parameters of the VIBE acquisition included FoV = 380x345x192mm³, image matrix = 320x290x64, TE/TR= 1.8/3.76ms, flip angle = 10°, 6-fold acceleration in the phase-encoding with the probability distribution of the variable sampling at the borders dropping to 1/5 of its central value as well as 16 time points with a temporal resolution of 11,57s each. Reconstruction was performed using a C++ prototype for the case of 6 motion-states and for a gating acceptance of 40%, respectively.

The acquired navigation signal corresponds to projections in head-feet direction with the same excitation volume as the imaging scans. Fig. 1 shows the magnitude and the phase of the navigation signal as a function of time for the picked coil element. The navigation signal shows clear periodic motion that may be attributed to the liver and which is most extreme during contrast injection at the 3rd time point. Also depicted is the clustering for 6 motion-states as well as a sorting according to motion-states for each time point.

Reconstructed images close to the liver dome are shown in Fig. 2 and 3. The hard-gated reconstruction shows good results at time points with moderate motion and signal change. However, at time point 3 with contrast arrival and stronger breathing motion, the motion-resolved reconstruction gives better image quality for the exhaled state. The motion-resolved reconstruction also shows fewer vessels at later time points which indicates less blurring in the through-plane direction.

Our initial results indicate that free-breathing liver DCE becomes feasible for Cartesian acquisitions when imaging scans are clustered according to motion-states. With reconstruction times and image volumes scaling at least linear in the motion-states, future investigation should focus on finding a good compromise for the number of motion-states as well as time points. Also a variable number of motion-states or a combination with hard-gating seems conceivable.