Using Monte Carlo simulation, we analyse the behaviour of two-dimensional hard rods in four different types of geometric confinement: (i) a slit pore where the particles are confined between two parallel walls with homeotropic anchoring; (ii) a hybrid slit pore formed by a planar and a homeotropic wall; square cavities that frustrate the orientational order by imposing either (iii) homeotropic or (iv) planar wall anchoring. We present results for the state diagram as a function of the packing fraction and the degree of confinement. Under extreme confinement, unexpected states appear with lower symmetries than those of the corresponding stable states in bulk, such as the formation of states that break the anchoring constraints or the symmetry imposed by the surfaces. In both types of square cavities, the particles form disclinations at intermediate densities. At high densities, however, the elastic stress is relaxed via the formation of domain walls where the director rotates abruptly by 90°.

The extension of the NLINV algorithm for SMS data was implemented and successfully demonstrated in combination with a Cartesian and radial SMS-FLASH sequence. Magn Reson Med 79:2057-2066, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Robustness against data inconsistencies, imaging artifacts and acquisition speed are crucial factors limiting the possible range of applications for magnetic resonance imaging (MRI). Therefore, we report a novel calibrationless parallel imaging technique which simultaneously estimates coil profiles and image content in a relaxed forward model. Our method is robust against a wide class of data inconsistencies, minimizes imaging artifacts and is comparably fast, combining important advantages of many conceptually different state-of-the-art parallel imaging approaches. Depending on the experimental setting, data can be undersampled well below the Nyquist limit. Here, even high acceleration factors yield excellent imaging results while being robust to noise and the occurrence of phase singularities in the image domain, as we show on different data. Moreover, our method successfully reconstructs acquisitions with insufficient field-of-view. We further compare our approach to ESPIRiT and SAKE using spin-echo and gradient echo MRI data from the human head and knee. In addition, we show its applicability to non-Cartesian imaging on radial FLASH cardiac MRI data. Using theoretical considerations, we show that ENLIVE can be related to a low-rank formulation of blind multi-channel deconvolution, explaining why it inherently promotes low-rank solutions.

Cardiac Magnetic Resonance Imaging (MRI) is time-consuming and error-prone. To ease the patient's burden and to increase the efficiency and robustness of cardiac exams, interest in methods based on continuous steady-state acquisition and self-gating has been growing in recent years. Self-gating methods extract the cardiac and respiratory signals from the measurement data and then retrospectively sort the data into cardiac and respiratory phases. Repeated breathholds and synchronization with the heart beat using some external device as required in conventional MRI are then not necessary. In this work, we introduce a novel self-gating method for radially acquired data based on a dimensionality reduction technique for time-series analysis (SSA-FARY). Building on Singular Spectrum Analysis, a zero-padded, time-delayed embedding of the auto-calibration data is analyzed using Principle Component Analysis. We demonstrate the basic functionality of SSA-FARY using numerical simulations and apply it to in-vivo cardiac radial single-slice bSSFP and Simultaneous Multi-slice radiofrequency-spoiled gradient echo measurements, as well as to Stack-of-Stars bSSFP measurements. SSA-FARY reliably detects the cardiac and respiratory motion and separates it from noise. We utilize the generated signals for high-dimensional image reconstruction using parallel imaging and compressed sensing with in-plane wavelet and (spatio-)temporal total-variation regularization.

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Purpose To develop a simple and robust tool for the estimation of gradient delays from highly undersampled radial k‐space data. Theory In radial imaging gradient delays induce parallel and orthogonal trajectory shifts, which can be described using an ellipse model. The intersection points of the radial spokes, which can be estimated by spoke‐by‐spoke comparison of k‐space samples, distinctly determine the parameters of the ellipse. Using the proposed method (RING), these parameters can be obtained using a least‐squares fit and utilized for the correction of gradient delays. Methods The functionality and accuracy of the proposed RING method is validated and compared to correlation‐based gradient‐delay estimation from opposing spokes using numerical simulations, phantom and in vivo heart measurements. Results In all experiments, RING robustly provides accurate gradient delay estimations even for as few as three radial spokes. Conclusions The simple and straightforward to implement RING method provides accurate gradient delay estimation for highly undersampled radial imaging.

Purpose A novel subspace‐based reconstruction method for frequency‐modulated balanced steady‐state free precession (fmSSFP) MRI is presented. In this work, suitable data acquisition schemes, subspace sizes, and efficiencies for banding removal are investigated. Theory and Methods By combining a fmSSFP MRI sequence with a 3D stack‐of‐stars trajectory, scan efficiency is maximized as spectral information is obtained without intermediate preparation phases. A memory‐efficient reconstruction routine is implemented by introducing the low‐frequency Fourier transform as a subspace which allows for the formulation of a convex reconstruction problem. The removal of banding artifacts is investigated by comparing the proposed acquisition and reconstruction technique to phase‐cycled bSSFP MRI. Aliasing properties of different undersampling schemes are analyzed and water/fat separation is demonstrated by reweighting the reconstructed subspace coefficients to generate virtual spectral responses in a post‐processing step. Results A simple root‐of‐sum‐of‐squares combination of the reconstructed subspace coefficients yields high‐SNR images with the characteristic bSSFP contrast but without banding artifacts. Compared to Golden‐Angle trajectories, turn‐based sampling schemes were superior in minimizing aliasing across reconstructed subspace coefficients. Water/fat separated images of the human knee were obtained by reweighting subspace coefficients. Conclusions The novel subspace‐based fmSSFP MRI technique emerges as a time‐efficient alternative to phase‐cycled bSFFP. The method does not need intermediate preparation phases, offers high SNR and avoids banding artifacts. Reweighting of the reconstructed subspace coefficients allows for generating virtual spectral responses with applications to water/fat separation.

Conclusion:Motion-resolved myocardial T 1 mapping during free-breathing with good accuracy, precision and repeatability can be achieved by combining inversion-recovery radial FLASH, self-gating and a calibrationless motion-resolved model-based reconstruction.