Ali Sadr^{1}, Stefan Kroboth^{1}, Elmar Fischer^{1}, Feng Jia^{1}, Sebastian Littin^{1}, Huijun Yu^{1}, Jürgen Hennig^{1}, and Maxim Zaitsev^{1}

Undersampled trajectories were optimized for parallel imaging with explicit consideration of the RF coil sensitivities in order to complement the RF coil elements. A second-order approximation of pixel variance was used as a metric to evaluate encoding trajectories and also serves as the cost function in the optimization problem, solved using Simulated Annealing. The metric was implemented on a Graphical Processing Unit (GPU) to accelerate computations. The developed method was evaluated on two test cases with Cartesian and radial sampling for isotropic and anisotropic fields-of-view. Resulting optimized trajectories led to improved image quality, more uniform SNR and reduced g-factors.

[1] Layton, K. J., Kroboth, S., Jia, F., Littin, S., Yu, H. and Zaitsev, M. (2016), Trajectory optimization based on the signal-to-noise ratio for spatial encoding with nonlinear encoding fields. Magn Reson Med, 76: 104–117. doi: 10.1002/mrm.25859

[2] Layton, K. J., Morelande, M., Farrell, P.M, Moran, B., Johnston, L.A. (2012), Performance analysis for magnetic resonance imaging with nonlinear encoding fields. IEEE Transactions on Medical Imaging 31 (2), 391-404

[3] David Smith. Compressed sensing MRI phantom. 2018. url: https://github.com/davidssmith/csphantom (visited on 07/29/2018) (cit. on p. 28).

[4] Stefan Kroboth. Accelerated Reconstruction Toolbox for MRI. 2018. url:https://github.com/stefan-k/ARTBOX (visited on 08/21/2018) (cit.on p. 51).

[5] Peder EZ Larson, Paul T Gurney, and Dwight G Nishimura. “Anisotropicfield-of-views in radial imaging.” In: IEEE transactions on medical imaging27.1 (2008), pp. 47–57 (cit. on pp. 46, 51).

Table.1: This table shows the execution time of a single cost function evaluation on a GPU ($$$t_{GPU}$$$), one CPU ($$$t_{1CPU}$$$) and 24 CPUs ($$$t_{24CPU}$$$) for five trajectories with different numbers of k-space samples and two coil arrays with 8 and 32 elements, respectively. (Due to hardware limitations, four elements of the table (filled by hyphens) could not be measured.) The table illustrates that the GPU implementation is about two hundred times faster than the CPU code executed on a single CPU and five times faster than the CPU code executed on 24 CPUs.(GPU-model: Nvidia-P100, CPU-model: Intel-Xeneon 2.1Ghz)

Fig.1: Measured sensitivity
maps of (a) the 32-element and (b) the 8-element RF receive coil array. Due to
the arbitrary absolute scaling of maps the color bars are omitted.

Fig.2: The optimization was initialized with (a)42 equally distributed readouts (6-fold undersampled Cartesian). (b)Optimized trajectories after 391 iterations of the SA algorithm. Movement of the readouts was restricted to the vertical (phase encoding) axis. All results were optimized for an 8-element coil array (Fig.1a). Reconstructed images for the initial and optimized trajectory are shown in (c) and (d), respectively. The g-factor maps (e and f) were scaled to the maximum value of both unoptimized and optimized maps while the SNR maps (g and h) were scaled to the maximum of the optimized maps in order to better illustrate the differences.

Fig.3:The performed optimization was initialized with (a)32 equally distributed readouts (8-fold undersampled Cartesian). (b)Optimized trajectories after 420 iterations of the SA algorithm. Movement of the readouts was restricted to the vertical (phase encoding) axis. All results were optimized for a 32-element coil array (Fig.1b). The reconstructed images for the initial and optimized trajectory are shown in (c) and(d), respectively. The g-factor maps (e and f) were scaled to the maximum value of both unoptimized and optimized maps while the SNR maps (g and h) were scaled to the maximum of the optimized maps in order to better illustrate the differences.

Fig.4:The performed optimization was initialized with (a)12 readouts distributed with the golden-angle scheme. (b)Optimized trajectories after 1867 iterations. The annealing function was only allowed to rotate the readouts about the central point of k-space. All results were optimized for a 32-element coil array (Fig.1b). Reconstructed images for the initial and optimized trajectory are shown in (c) and (d), respectively. The g-factor maps (e and f) were scaled to the maximum value of both unoptimized and optimized maps while the SNR maps (g and h) were scaled to the maximum of the optimized maps in order to better illustrate the differences.