Purpose The aim of this study was to compare the wave‐CAIPI (controlled aliasing in parallel imaging) trajectory to the Cartesian sampling for accelerated free‐breathing 4D lung MRI. Methods The wave‐CAIPI k‐space trajectory was implemented in a respiratory self‐gated 3D spoiled gradient echo pulse sequence. Trajectory correction applying the gradient system transfer function was used, and images were reconstructed using an iterative conjugate gradient SENSE (CG SENSE) algorithm. Five healthy volunteers and one patient with squamous cell carcinoma in the lung were examined on a clinical 3T scanner, using both sampling schemes. For quantitative comparison of wave‐CAIPI and standard Cartesian imaging, the normalized mutual information and the RMS error between retrospectively accelerated acquisitions and their respective references were calculated. The SNR ratios were investigated in a phantom study. Results The obtained normalized mutual information values indicate a lower information loss due to acceleration for the wave‐CAIPI approach. Average normalized mutual information values of the wave‐CAIPI acquisitions were 10% higher, compared with Cartesian sampling. Furthermore, the RMS error of the wave‐CAIPI technique was lower by 19% and the SNR was higher by 14%. Especially for short acquisition times (down to 1 minute), the undersampled Cartesian images showed an increased artifact level, compared with wave‐CAIPI. Conclusion The application of the wave‐CAIPI technique to 4D lung MRI reduces undersampling artifacts, in comparison to a Cartesian acquisition of the same scan time. The benefit of wave‐CAIPI sampling can therefore be traded for shorter examinations, or enhancing image quality of undersampled 4D lung acquisitions, keeping the scan time constant.

We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

Purpose The aim of this study was to investigate the acceleration potential of wave‐CAIPI (controlled aliasing in parallel imaging) for 4D flow MRI, provided that image quality and precision of flow parameters are maintained. Methods The 4D flow MRIs with acceleration factor R = 2 were performed on 10 healthy volunteers, using both wave‐CAIPI and standard Cartesian/2D‐CAIPI sampling for reference. In addition, 1 patient with known aortic valve stenosis was examined. The flow rate (Q), net flow (Qnet), peak velocity )(vmax, and net average through‐plane velocity (v¯⊥) were calculated in eight analysis planes in the ascending and descending aorta. The acquisitions were retrospectively undersampled (R = 6), and deviations of flow parameters and hemodynamic flow patterns were evaluated. Results Flow parameters measured with an undersampled wave‐CAIPI trajectory showed considerably smaller deviations to the references than the 2D‐CAIPI images. For vmax, the mean absolute differences were )(6.02±2.08 cm/s versus )(14.36±5.68 cm/s; for Qnet, the mean absolute differences were )(3.67±1.40 ml versus )(5.87±1.91 ml for wave‐CAIPI versus 2D‐CAIPI, respectively. Noise calculations indicate that the 2D‐CAIPI sampling exhibits a 43±38% higher average noise level than the wave‐CAIPI technique. Qualitative discrepancies in hemodynamic flow patterns, visualized through streamlines, particle traces and flow velocity vectors, could be reduced by using the undersampled wave‐CAIPI trajectory. Conclusion Use of wave‐CAIPI instead of 2D‐CAIPI sampling in retrospectively 6‐fold accelerated 4D flow MRI enhances the precision of flow parameters. The acquisition time of 4D flow measurements could be reduced by a factor of 3, with minimal differences in flow parameters.