Variable density sampling based on physically plausible gradient waveform. Application to 3D MRI angiography

Performing k-space variable density sampling is a popular way of reducing scanning time in Magnetic Resonance Imaging (MRI). Unfortunately, given a sampling trajectory, it is not clear how to traverse it using gradient waveforms. In this paper, we actually show that existing methods [1, 2] can yield large traversal time if the trajectory contains high curvature areas. Therefore, we consider here a new method for gradient waveform design which is based on the projection of unrealistic initial trajectory onto the set of hardware constraints. Next, we show on realistic simulations that this algorithm allows implementing variable density trajectories resulting from the piecewise linear solution of the Travelling Salesman Problem in a reasonable time. Finally, we demonstrate the application of this approach to 2D MRI reconstruction and 3D angiography in the mouse brain.Comment: IEEE International Symposium on Biomedical Imaging (ISBI), Apr 2015, New-York, United State

Gradient waveform design for variable density sampling in Magnetic Resonance Imaging

Fast coverage of k-space is a major concern to speed up data acquisition in Magnetic Resonance Imaging (MRI) and limit image distortions due to long echo train durations. The hardware gradient constraints (magnitude, slew rate) must be taken into account to collect a sufficient amount of samples in a minimal amount of time. However, sampling strategies (e.g., Compressed Sensing) and optimal gradient waveform design have been developed separately so far. The major flaw of existing methods is that they do not take the sampling density into account, the latter being central in sampling theory. In particular, methods using optimal control tend to agglutinate samples in high curvature areas. In this paper, we develop an iterative algorithm to project any parameterization of k-space trajectories onto the set of feasible curves that fulfills the gradient constraints. We show that our projection algorithm provides a more efficient alternative than existinf approaches and that it can be a way of reducing acquisition time while maintaining sampling density for piece-wise linear trajectories

A projection algorithm for gradient waveforms design in Magnetic Resonance Imaging

International audienceCollecting the maximal amount of information in a given scanning time is a major concern in Magnetic Resonance Imaging (MRI) to speed up image acquisition. The hardware constraints (gradient magnitude, slew rate, ...), physical distortions (e.g., off-resonance effects) and sampling theorems (Shannon, compressed sensing) must be taken into account simultaneously, which makes this problem extremely challenging. To date, the main approach to design gradient waveform has consisted of selecting an initial shape (e.g. spiral, radial lines, ...) and then traversing it as fast as possible using optimal control. In this paper, we propose an alternative solution which first consists of defining a desired parameterization of the trajectory and then of optimizing for minimal deviation of the sampling points within gradient constraints. This method has various advantages. First, it better preserves the density of the input curve which is critical in sampling theory. Second, it allows to smooth high curvature areas making the acquisition time shorter in some cases. Third, it can be used both in the Shannon and CS sampling theories. Last, the optimized trajectory is computed as the solution of an efficient iterative algorithm based on convex programming. For piecewise linear trajectories, as compared to optimal control reparameterization, our approach generates a gain in scanning time of 10% in echo planar imaging while improving image quality in terms of signal-to-noise ratio (SNR) by more than 6 dB. We also investigate original trajectories relying on traveling salesman problem solutions. In this context, the sampling patterns obtained using the proposed projection algorithm are shown to provide significantly better reconstructions (more than 6 dB) while lasting the same scanning time

Phase Relaxed Localized Excitation Pulses for Inner Volume Fast Spin Echo Imaging

PURPOSE: To design multidimensional spatially selective radiofrequency (RF) pulses for inner volume imaging (IVI) with three‐dimensional (3D) fast spin echo (FSE) sequences. Enhanced background suppression is achieved by exploiting particular signal properties of FSE sequences. THEORY AND METHODS: The CPMG condition dictates that echo amplitudes will rapidly decrease if a 90° phase difference between excitation and refocusing pulses is not present, and refocusing flip angles are not precisely 180°. This mechanism is proposed as a means for generating additional background suppression for spatially selective excitation, by biasing residual excitation errors toward violating the CPMG condition. 3D RF pulses were designed using this method with a 3D spherical spiral trajectory, under‐sampled by factor 5.6 for an eight‐channel PTx system, at 3 Tesla. RESULTS: 3D‐FSE IVI with pulse durations of approximately 12 ms was demonstrated in phantoms and for T(2)‐weighted brain imaging in vivo. Good image quality was obtained, with mean background suppression factors of 103 and 82 ± 6 in phantoms and in vivo, respectively. CONCLUSION: Inner Volume Imaging with 3D‐FSE has been demonstrated in vivo with tailored 3D‐RF pulses. The proposed design methods are also applicable to 2D pulses. Magn Reson Med 76:848–861, 2016. © 2015 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicin

Fast Large-Tip-Angle Multidimensional and Parallel RF Pulse Design in MRI

Large-tip-angle multidimensional radio-frequency (RF) pulse design is a difficult problem, due to the nonlinear response of magnetization to applied RF at large tip-angles. In parallel excitation, multidimensional RF pulse design is further complicated by the possibility for transmit field patterns to change between subjects, requiring pulses to be designed rapidly while a subject lies in the scanner. To accelerate pulse design, we introduce a fast version of the optimal control method for large-tip-angle parallel excitation. The new method is based on a novel approach to analytically linearizing the Bloch equation about a large-tip-angle RF pulse, which results in an approximate linear model for the perturbations created by adding a small-tip-angle pulse to a large-tip-angle pulse. The linear model can be evaluated rapidly using nonuniform fast Fourier transforms, and we apply it iteratively to produce a sequence of pulse updates that improve excitation accuracy. We achieve drastic reductions in design time and memory requirements compared to conventional optimal control, while producing pulses of similar accuracy. The new method can also compensate for nonidealities such as main field inhomogeneties.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86004/1/Fessler12.pd

Optimal Control and Synchronization of Dynamic Ensemble Systems

Ensemble control involves the manipulation of an uncountably infinite collection of structurally identical or similar dynamical systems, which are indexed by a parameter set, by applying a common control without using feedback. This subject is motivated by compelling problems in quantum control, sensorless robotic manipulation, and neural engineering, which involve ensembles of linear, bilinear, or nonlinear oscillating systems, for which analytical control laws are infeasible or absent. The focus of this dissertation is on novel analytical paradigms and constructive control design methods for practical ensemble control problems. The first result is a computational method %based on the singular value decomposition (SVD) for the synthesis of minimum-norm ensemble controls for time-varying linear systems. This method is extended to iterative techniques to accommodate bounds on the control amplitude, and to synthesize ensemble controls for bilinear systems. Example ensemble systems include harmonic oscillators, quantum transport, and quantum spin transfers on the Bloch system. To move towards the control of complex ensembles of nonlinear oscillators, which occur in neuroscience, circadian biology, electrochemistry, and many other fields, ideas from synchronization engineering are incorporated. The focus is placed on the phenomenon of entrainment, which refers to the dynamic synchronization of an oscillating system to a periodic input. Phase coordinate transformation, formal averaging, and the calculus of variations are used to derive minimum energy and minimum mean time controls that entrain ensembles of non-interacting oscillators to a harmonic or subharmonic target frequency. In addition, a novel technique for taking advantage of nonlinearity and heterogeneity to establish desired dynamical structures in collections of inhomogeneous rhythmic systems is derived

RF Pulse Design for Parallel Transmission in Ultra High Field Magnetic Resonance Imaging

Magnetic Resonance Imaging (MRI) plays an important role in visualizing the structure and function of the human body. In recent years, ultra high magnetic field (UHF) MRI has emerged as an attractive means to achieve significant improvements in both signal-to-noise ratio (SNR) and contrast. However, in vivo imaging at UHF is hampered by the presence of severe B1 and B0 inhomogeneities. B1 inhomogeneity leads to spatial non-uniformity excitation in MR images. B0 inhomogeneity, on the other hand, produces blurring, distortions and signal loss at tissue/air interfaces. Both of them greatly limit the applications of UHF MRI. Thus mitigating B1 and B0 inhomogeneities is central in making UHF MRI practical for clinical use. Tailored RF pulse design has been demonstrated as a feasible means to mitigate the effects of B1 and B0 inhomogeneities. However, the primary limitation of such tailored pulses is that the pulse duration is too long for practical clinical applications. With the introduction of parallel transmission technology, one can shorten the pulse duration without sacrificing excitation performance. Prior reports in parallel transmission were formulated using linear, small-tip-angle approximation algorithms, which are violated in the regime of nonlinear large-tip-angle excitation. The overall goal of this dissertation is to develop effective and fast algorithms for parallel transmission UHF RF pulses design. The key contributions of this work include 1) a novel large-tip-angle RF pulse design method to achieve significant improvements compared with previous algorithms; 2) implementing a model-based eddy current correction method to compensate eddy current field induced on RF shield for parallel transmission and leading to improved excitation and time efficiency; 3) developing new RF pulse design strategy to restore the lost signal over the whole brain and increase BOLD contrast to brain activation in T2*-weighted fMRI at UHF. For testing and validation, these algorithms were implement on a Siemens 7T MRI scanner equipped with a parallel transmission system and their capabilities for ultra high field MRI demonstrated, first by phantom experiments and later by in vivo human imaging studies. The contributions presented here will be of importance to bring parallel transmission technology to clinical applications in UHF MRI