Coronary MR angiography (MRA) has recently shown promising results in relatively large patient cohorts [1]. However, it still remains mostly confined to research use at a small number of experienced academic centers. Free-breathing whole-heart coronary MRA commonly uses navigators to counteract the effects of respiratory motion [2], but suffers from lengthy and unpredictable acquisition times. Conversely, self-navigation (SN) [3-5] promises 100% scan efficiency, but requires motion correction over a broad range of respiratory displacements, which may introduce image artifacts. We hypothesize that sparse reconstruction algorithms can be exploited to reconstruct respiratory motion-resolved 3D images of the heart without the need for breath-holding, navigators, self-navigated respiratory correction, or complex 3D motion correction.First, a proof of principle acquisition on an in-house-built moving phantom (sinusoidal motion amplitude=3cm) was performed to assess the performance of the proposed motion-resolved sparse reconstruction. Subsequently, examinations in N=11 healthy volunteers and M=7 patients were performed on a 1.5T clinical MRI scanner (MAGNETOM Aera, Siemens Healthcare, Erlangen, Germany). In all cases, a T2-prepared, fat-saturated prototype 3D radial phyllotaxis bSSFP imaging sequence [6] was acquired segmented and ECG-triggered. Parameters: TR/TE=3.1/1.56ms, FOV=(220mm)³, matrix=192³, voxel size=(1.15mm)³, RF excitation angle 115°, and receiver bandwidth 898 Hz/Px. A total of ~12,000 radial readouts were acquired in 400-600 heartbeats during free-breathing with 100% scan efficiency. Using a respiratory signal directly extracted from the imaging data via modulations of the k-space center amplitude [7], individual signal-readouts were binned according to the respiratory state at which they were acquired (Fig. 1). The resulting series of undersampled 3D respiratory states were reconstructed using an eXtra-Dimensional Golden-angle RAdial Sparse Parallel imaging (XD-GRASP) [8] algorithm, which exploits sparsity along the newly created respiratory-state dimension. Datasets for 4 and 6 respiratory states (phases) were reconstructed. Image quality of the end-expiratory phase was compared to 1D respiratory self-navigation for coronary vessel sharpness [9], visible length and diagnostic quality on a scale from 0=non-visible to 2=diagnostic. Patient datasets were visually assessed in comparison to 1D self-navigation and, when available, to X-ray angiography.Respiratory motion-resolved XD-GRASP reconstruction (both 4- and 6-phase) effectively suppresses respiratory motion artifacts both in the phantom acquisition and in free-breathing whole-heart coronary MRA (Fig.2). In the phantom, the average of 10 measurements resulted in a 2.73±0.3cm displacement between the two extreme states. In volunteers, average vessel sharpness and length were always superior for the respiratory-resolved datasets, reaching statistical significance (p<0.05) for the left main coronary artery (LM), the proximal- and mid-left anterior descending artery (LAD) (e.g. sharpness of mid-LAD 40.8±9.1% vs 34.9±10.2%), and the mid-right coronary artery (RCA). LM+LAD length was also significantly increased with respect to 1D self-navigation. The ratio of diagnostic coronary segments increased from 41/88 to 61/88 and 56/88 for the 4- and 6-phase reconstructions (Fig. 3a). The 4-phase XD-GRASP reconstruction reached 100% diagnostic quality for LM, proximal-LAD, and proximal-RCA. All numerical results are reported in Fig 4. Example reconstructions from patient datasets are shown in Fig 3b.Respiratory motion-resolved XD-GRASP reconstruction provides a powerful alternative to conventional navigators or self-navigation. Although a larger number of motion states (6-phase versus 4-phase) can better resolve respiratory motion and reduce blurring, this is also associated with higher degrees of undersampling. The numerical results show comparable image quality for both motion-resolved reconstructions. The high correlation along the respiratory direction enables improved performance when compared to conventional sparse reconstructions exploiting spatial correlation only. This confirms that sparse reconstruction is typically more effective with dynamic than with static data (movies are easier to compress than images). The golden-angle arrangement of the 3D radial phyllotaxis trajectory intrinsically facilitates the extraction of the respiratory motion signal from the image data (all readouts cross the k-space center) and provides flexibility in data sorting (quasi-uniform spatial sampling over time –and therefore over respiratory bins– is facilitated). Simultaneously, the golden angle rotation ensures incoherence along the respiratory dimension, required for XD-GRASP reconstruction (the data are sufficiently distinct in different motion states, since the same k-space profile is never acquired twice). Although the end-expiratory 3D volume of the XD-GRASP reconstruction was selected for analysis, the motion-resolved datasets contain abundant anatomic information across the whole respiratory cycle, which may be further exploited (Fig.5).XD-GRASP provides a highly promising alternative to navigator approaches for respiratory motion artifact suppression. Instead of discarding data or enforcing motion models for motion correction, XD-GRASP makes constructive use of all respiratory phases to improve image quality, and achieves superior quality compared to 1D respiratory self-navigation. The phyllotaxis trajectory and XD-GRASP reconstruction provide a synergistic combination that may lead coronary MRA closer to clinical practice.