Monica Sigovan^{1}, Gastao Cruz^{2}, Torben Schneider^{3}, Juan Felipe Perez-Juste Abascal^{1}, Cyril Mory^{1}, Guruprasad Krishnamoorty^{4}, Rene Botnar^{2}, Philippe Douek^{1,5}, Claudia Prieto^{2}, and Loic Boussel^{1,5}

Clinical diagnosis based on thoracic blood flow using three-dimensional cardiac-resolved (4D) phase contrast PC-MRI is limited by long acquisition times, due to the need of respiratory gating. In addition, gating does not provide potentially important physiological information, the variation of flow within the respiratory cycle. To address these challenges we developed a 5D (4D respiratory-resolved) PC-MRI sequence combining 3D radial k-space sampling, respiratory self-gating, and compressed sensing reconstruction. Our preliminary results demonstrate respiratory related changes in blood flow in healthy subjects. The proposed method may potentially refine diagnosis in congenital heart disease by assessing the respiratory related blood flow variations.

Clinical assessment of thoracic blood flow using three-dimensional cardiac-resolved (4D) phase contrast MRI (PC-MRI) has been limited by long acquisition times, due in part to the need of respiratory gating. Standard pencil beam respiratory gating is highly inefficient since data is only acquired during a specific phase of the respiratory cycle, leading to prolonged scan times. Moreover, gated acquisitions do not provide potentially important physiological information on the variation of flow with the respiratory cycle.

Respiratory self-gating has the potential to enable velocity measurements at different phases of the respiratory cycle without any data rejection. Our goal was to develop a respiratory self-gated 3D radial 5D (4D respiratory-resolved) flow MRI sequence and study the respiratory related variability of blood flow velocity in the thoracic aorta.

We implemented a 3D radial trajectory based on a spiral phyllotaxis
pattern for k-space sampling similar to that proposed by Piccini et al.^{1}
on a 1.5T Philips Ingenia system (Philips, Best, The Netherlands). The
trajectory has several advantages for flow imaging: minimal eddy currents
compared to other 3D radial sampling patterns, intrinsic self-navigation, and
isotropic resolution. We combined the trajectory with bipolar gradients on 3
fixed spatial directions for velocity encoding.

Imaging was performed on 3 healthy subjects using the implemented 3D
radial sequence and a standard Cartesian 4D flow acquisition. The Cartesian
acquisition was performed using pencil beam respiratory gating and prospective
cardiac triggering in an oblique plane encompassing the thoracic aorta with the
following parameters: TFE factor 2, turbo direction Y, k-t BLAST factor 8, TE/TR
= 1.9/4.3 ms, flip angle = 6◦, VENC = 240 cm/s; FOV = 320x320x100 mm^{3},
2.5 mm isotropic voxel size, bandwidth = 723 Hz. The 3D radial acquisition was free-running
interleaved (8 projections per interleaf) and performed with the following
parameters: TE/TR 2.5/6.0 ms, flip angle = 6◦, VENC = 240 cm/s, FOV = 340x340x340
mm^{3}, 2.5 mm isotropic voxel size, bandwidth = 723 Hz. A total of
54096 radial readouts were acquired in 6762 interleaves. Each projection was
repeated 4 times for velocity measurements using Hadamard encoding.

The respiratory self-gated (SG) signal was derived independently for
each velocity encoding step as the time variation of the z coordinate of the
center of mass of the image^{2}, computed from the first projection of
each interleaf using a conjugate gradient method with L1 regularization. Using
the respiratory SG signal, data was separated in 3 respiratory phases with
equal number of projections per bin. Subsequently, each respiratory phase was
binned in 8 cardiac phases using the ECG signal. Respiratory- and
cardiac-resolved images were reconstructed offline from
undersampled data (R ~ 9) using a
compressed sensing^{3} algorithm implemented in Matlab (The Mathworks,
Inc, Natick, MA) using first order finite differences as sparsifying transforms
in space ($$$\triangledown_{s}$$$) and time ($$$\triangledown_{t}$$$), for both cardiac and
respiratory dimensions:

$$\hat{I_{b}}=arg min_{I_{b}}\left\{\parallel EI_{b} - K_{b}\parallel_2^2 + \lambda_{s}\parallel \triangledown_{s}I_{b}\parallel_{1} + \lambda_{c}\parallel \triangledown_{t}I_{b}\parallel_{1}+ \lambda_{r}\parallel \triangledown_{t}I_{b}\parallel_{1}\right\}$$

where $$${I_{b}}$$$ is a temporally resolved image at a given cardiac and respiratory phase, $$$E$$$ is the encoding operator, $$$K_{b}$$$ is the undersampled k-space data and $$$ \lambda_{s}, \lambda_{c}, \lambda_{r}$$$ are regularization weights.

[1] D. Piccini et al, “Spiral phyllotaxis: the natural way to construct a 3D radial trajectory in MRI”, Magnetic Resonance in Medicine 66:1049–1056 (2011)

[2] O. Wieben et al, “Correcting for Translational Motion in 3D Projection Reconstruction”, Proc. Intl. Soc. Mag. Reson. Med 9 (2001) #737

[3] Lustig, Michael, et al., “Sparse MRI: The application of compressed sensing for rapid MR imaging.” Magn. Reson. Med. 2007; Vol. 58:1182-1195

[4] H. Korperich et al, “Differentiation of impaired from preserved hemodynamics in patients with Fontan circulation using real-time phase-velocity cardiovascular Magnetic Resonance”, J Thorac Imaging, 32 (2017) 159-168

Figure
1. Representative cardiac, respiratory, and velocity resolved images acquired
with the new 3D radial sequence. Maps of the velocity vectors projections in
the Feet-Head direction are presented at peak systole for the 3 reconstructed
respiratory phases. The corresponding magnitude image of the end-expiration
phase is presented on the left.

Figure 2. Temporal MIP of computed Phase Contrast Angiography obtained
from the standard Cartesian acquisition (left) and the respiratory resolved 3D
radial acquisition (right) obtained in end-inspiration (green) and end-expiration
(pink). The overlay image demonstrates displacement of the ascending aorta due
to respiratory motion. No displacement of the descending aorta can be observed.