Sophie Schauman^{1}, Joseph G. Woods^{1,2}, Mark Chiew^{1}, and Thomas W. Okell^{1}

^{1}Wellcome Centre for Integrative Neuroimaging, NDCN, University of Oxford, Oxford, United Kingdom, ^{2}Department of Radiology, University of California San Diego, La Jolla, CA, United States

Time-encoded (TEnc) dynamic ASL angiography is a method that provides high SNR, dynamic information about the blood supply to the brain. However, as is commonly the case with all ASL-based methods, multiple repeat encodings are required to fully sample the information required to decode the dynamic angiographic data. Here we apply spatial sparsity and temporal smoothness constraints to reconstruct highly under-sampled TEnc data, and demonstrate that high fidelity, high resolution ASL angiography can be performed in a fraction of the time it takes using conventional methods.

There are two main approaches to acquiring the temporal information of the bolus’ passage through the arterial tree. The simplest method is to acquire continuously after each labelling (tag or control) block for the desired readout duration and split up the data into a number of frames. This approach requires small flip angles to prevent signal attenuation from each RF pulse during the readout. The other approach is to use time-encoding (TEnc), where the labelling is modulated to carry temporal information

Typically, multiple repeats of each labelling condition are acquired to fully sample each frame. Here we propose an accelerated approach that can reconstruct under-sampled TEnc dynamic ASL data in a compressed sensing framework, leveraging both the spatial sparsity and temporal smoothness of angiographic data to greatly reduce the required scan time.

- A naïve re-gridding of the non-cartesian data using the NUFFT
^{4}. - Non-Cartesian SENSE parallel imaging reconstruction
- Compressed sensing reconstruction with sparsity in decoded image space and a temporal smoothness constraint

$$cost=\frac{1}{2}|Ex-d|_{2}^{2}+\lambda_{1}|x|_{1}+\frac{1}{2}\lambda_{2}|\nabla{}x|^2_{2}$$

where E is the overall encoding operator (including time-encoding, coil sensitivities, and Fourier encoding), x is the angiographic data, d is the measured k-space data, and ∇ is the temporal finite difference operator. The parameters $$$\lambda_1$$$ and $$$\lambda_2$$$ weight the spatial sparsity and temporal smoothness constraints, respectively. This cost function was minimized using FISTA, For the SENSE reconstruction, both $$$\lambda_1$$$ and $$$\lambda_2$$$were set to 0. Coil sensitivity profiles were estimated from the data averaged across readout frames and time-encodings using the adaptive combine approach

Future directions will include 3D angiography, allowing for even higher acceleration factors, and combining TEnc schemes with vessel-encoding7or perfusion imaging8in a constrained reconstruction framework.

This work was supported by funding from the Engineering and Physical Sciences Research Council (EPSRC) and Medical Research Council (MRC) [grant numberEP/L016052/1].

The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z). MC (RF201617\16\23) and TO (RF/132) are supported by the Royal Academy of Engineering

1.Suzuki Y, Teeuwisse WM, Schmid S, Helle M, Cauteren M Van, Osch MJP Van. Improving 4D pCASL angiography by combining Hadamard time-encoding with Look-Locker readout. In: Proc. Intl. Soc. Mag. Reson. Med. 22. ; 2014. p. 6460.2. Woods JG, Schauman SS, Chiew M, Chappell MA, Okell TW. Optimization of time-encoded pseudo-continuous ASL angiography with a variable flip-angle scheme. In: Proceedings 27th Scientific Meeting, ISMRM. Montreal, Canada; 20193.Schauman SS, Chiew M, Okell TW. Highly accelerated vessel‐selective arterial spin labeling angiography using sparsity and smoothness constraints. Magn Reson Med 2019:mrm.27979 doi: 10.1002/mrm.27979.4. Fessler JA, Sutton BP. Nonuniform fast Fourier transforms using min-max interpolation. IEEE Transactions on Signal Processing 2003;51:560–574 doi: 10.1109/TSP.2002.807005.5. Pruessmann, Klaas P, M Weiger, P Börnert, and P Boesiger. “Advances in Sensitivity Encoding with Arbitrary K-Space Trajectories.” Magnetic Resonance in Medicine46, no. 4, 2001: 638–516. Walsh, D O, A F Gmitro, and M W Marcellin. “Adaptive Reconstruction of Phased Array MR Imagery.” Magnetic Resonance in Medicine43, no. 5, 2000: 682–907.Wong, Eric C. “Vessel-Encoded Arterial Spin-Labeling Using Pseudocontinuous Tagging.” Magnetic Resonance in Medicine 58, no. 6, 2007: 1086–91 8. Okell, Thomas W. “Combined Angiography and Perfusion Using Radial Imaging and Arterial Spin Labeling.” Magnetic Resonance in Medicine 81, no. 1, 2019: 182–94

Schematic diagram of time-encoding scheme and associated sampling patterns for various under-sampling factors. The 3 time-encoding blocks and 3 readout frames combine to form 9 total effective post-labelling delays.

Figure 2 – Reconstructions at acceleration factor 12 using the sparse (CS), gridding (Adjoint), and SENSE methods. Insets highlight the small subtle vessel features that are well captured in the CS reconstruction, but either missing or only partially captured in the SENSE and gridding reconstructions.

Figure 3 - Comparison of dynamics at an early, mid and late PLDs, for the gridding (Adjoint), SENSE and sparse (CS) reconstructions (R=12). Blurring and residual aliasing can be seen in the Adjoint reconstruction, whereas the SENSE images appear noisy and lacking vessel contrast. The CS reconstructions show significantly improved vessel delineation, particularly at the late PLD.

Figure 4 - Temporal mean of the sparse reconstruction at varying acceleration factors, ranging from fully sampled (R=1) to single-shot (R=46). At R=12 and R=23, considerable detail and image fidelity are preserved, while requiring significantly shorter acquisition times.