MR image reconstruction using deep density priors

Algorithms for Magnetic Resonance (MR) image reconstruction from undersampled measurements exploit prior information to compensate for missing k-space data. Deep learning (DL) provides a powerful framework for extracting such information from existing image datasets, through learning, and then using it for reconstruction. Leveraging this, recent methods employed DL to learn mappings from undersampled to fully sampled images using paired datasets, including undersampled and corresponding fully sampled images, integrating prior knowledge implicitly. In this article, we propose an alternative approach that learns the probability distribution of fully sampled MR images using unsupervised DL, specifically Variational Autoencoders (VAE), and use this as an explicit prior term in reconstruction, completely decoupling the encoding operation from the prior. The resulting reconstruction algorithm enjoys a powerful image prior to compensate for missing k-space data without requiring paired datasets for training nor being prone to associated sensitivities, such as deviations in undersampling patterns used in training and test time or coil settings. We evaluated the proposed method with T1 weighted images from a publicly available dataset, multi-coil complex images acquired from healthy volunteers (N=8) and images with white matter lesions. The proposed algorithm, using the VAE prior, produced visually high quality reconstructions and achieved low RMSE values, outperforming most of the alternative methods on the same dataset. On multi-coil complex data, the algorithm yielded accurate magnitude and phase reconstruction results. In the experiments on images with white matter lesions, the method faithfully reconstructed the lesions. Keywords: Reconstruction, MRI, prior probability, machine learning, deep learning, unsupervised learning, density estimationComment: Published in IEEE TMI. Main text and supplementary material, 19 pages tota

Whole-brain estimates of directed connectivity for human connectomics

Connectomics is essential for understanding large-scale brain networks but requires that individual connection estimates are neurobiologically interpretable. In particular, a principle of brain organization is that reciprocal connections between cortical areas are functionally asymmetric. This is a challenge for fMRI-based connectomics in humans where only undirected functional connectivity estimates are routinely available. By contrast, whole-brain estimates of effective (directed) connectivity are computationally challenging, and emerging methods require empirical validation. Here, using a motor task at 7T, we demonstrate that a novel generative model can infer known connectivity features in a whole-brain network (>200 regions, >40,000 connections) highly efficiently. Furthermore, graph-theoretical analyses of directed connectivity estimates identify functional roles of motor areas more accurately than undirected functional connectivity estimates. These results, which can be achieved in an entirely unsupervised manner, demonstrate the feasibility of inferring directed connections in whole-brain networks and open new avenues for human connectomics

Accelerated dynamic Fourier velocity encoding by exploiting velocity-spatio-temporal correlations

Objective: To describe how the information content in a Fourier velocity encoding (FVE) scan can be transformed into a very sparse representation and to develop a method that exploits the compactness of the data to significantly accelerate the acquisition. Materials and Methods: For validation, fully sampled FVE datasets were acquired in phantom and in vivo experiments. Fivefold and eightfold acceleration was simulated by using only one fifth or one eighth of the data for reconstruction in the proposed method based on the k-t BLAST framework. Reconstructed images were compared quantitatively to those from the fully sampled data. Results: Velocity spectra in the accelerated datasets were comparable to the spectra from fully sampled datasets. The detected peak velocities remained accurate even at eightfold acceleration, and the overall shape of the spectra was well preserved. Slight temporal smoothing was seen in the accelerated datasets. Conclusion: A novel technique for accelerating time-resolved FVE scan is presented. It is possible to accelerate FVE to acquisition speeds comparable to a standard time-resolved phase-contrast sca

Bandwidth, expansion, treewidth, separators, and universality for bounded degree graphs

We establish relations between the bandwidth and the treewidth of bounded degree graphs G, and relate these parameters to the size of a separator of G as well as the size of an expanding subgraph of G. Our results imply that if one of these parameters is sublinear in the number of vertices of G then so are all the others. This implies for example that graphs of fixed genus have sublinear bandwidth or, more generally, a corresponding result for graphs with any fixed forbidden minor. As a consequence we establish a simple criterion for universality for such classes of graphs and show for example that for each gamma>0 every n-vertex graph with minimum degree ((3/4)+gamma)n contains a copy of every bounded-degree planar graph on n vertices if n is sufficiently large

Temperature distribution in a gas-solid fixed bed probed by rapid magnetic resonance imaging

Controlling the temperature distribution inside catalytic fixed bed reactors is crucial for yield optimization and process stability. Yet, in situ temperature measurements with spatial and temporal resolution are still challenging. In this work, we perform temperature measurements in a cylindrical fixed bed reactor by combining the capabilities of real-time magnetic resonance imaging (MRI) with the temperature-dependent proton resonance frequency (PRF) shift of water. Three-dimensional (3D) temperature maps are acquired while heating the bed from room temperature to 60~$^{\circ}$C using hot air. The obtained results show a clear temperature gradient along the axial and radial dimensions and agree with optical temperature probe measurements with an average error of $\pm$ 1.5~$^{\circ}$C. We believe that the MR thermometry methodology presented here opens new perspectives for the fundamental study of mass and heat transfer in gas-solid fixed beds and in the future might be extended to the study of reactive gas-solid systems

Mono‐planar T‐Hex: Speed and flexibility for high‐resolution 3D imaging

The aim of this work is the reconciliation of high spatial and temporal resolution for MRI. For this purpose, a novel sampling strategy for 3D encoding is proposed, which provides flexible k-space segmentation along with uniform sampling density and benign filtering effects related to signal decay. Methods For time-critical MRI applications such as functional MRI (fMRI), 3D k-space is usually sampled by stacking together 2D trajectories such as echo planar imaging (EPI) or spiral readouts, where each shot covers one k-space plane. For very high temporal and medium to low spatial resolution, tilted hexagonal sampling (T-Hex) was recently proposed, which allows the acquisition of a larger k-space volume per excitation than can be covered with a planar readout. Here, T-Hex is described in a modified version where it instead acquires a smaller k-space volume per shot for use with medium temporal and high spatial resolution. Results Mono-planar T-Hex sampling provides flexibility in the choice of speed, signal-to-noise ratio (SNR), and contrast for rapid MRI acquisitions. For use with a conventional gradient system, it offers the greatest benefit in a regime of high in-plane resolution <1 mm. The sampling scheme is combined with spirals for high sampling speed as well as with more conventional EPI trajectories. Conclusion Mono-planar T-Hex sampling combines fast 3D encoding with SNR efficiency and favorable depiction characteristics regarding noise amplification and filtering effects from urn:x-wiley:07403194:media:mrm28979:mrm28979-math-0003 decay, thereby providing flexibility in the choice of imaging parameters. It is attractive both for high-resolution time series such as fMRI and for applications that require rapid anatomical imaging

Increased cerebral blood volume in small arterial vessels is a correlate of amyloid-β-related cognitive decline

The protracted accumulation of amyloid-β (Aβ) is a major pathologic hallmark of Alzheimer's disease and may trigger secondary pathological processes that include neurovascular damage. This study was aimed at investigating long-term effects of Aβ burden on cerebral blood volume of arterioles and pial arteries (CBVa), possibly present before manifestation of dementia. Aβ burden was assessed by 11C Pittsburgh compound-B positron emission tomography in 22 controls and 18 persons with mild cognitive impairment (MCI), [ages: 75(±6) years]. After 2 years, inflow-based vascular space occupancy at ultra-high field strength of 7-Tesla was administered for measuring CBVa, and neuropsychological testing for cognitive decline. Crushing gradients were incorporated during MR-imaging to suppress signals from fast-flowing blood in large arteries, and thereby sensitize inflow-based vascular space occupancy to CBVa in pial arteries and arterioles. CBVa was significantly elevated in MCI compared to cognitively normal controls and regional CBVa related to local Aβ deposition. For both MCI and controls, Aβ burden and follow-up CBVa in several brain regions synergistically predicted cognitive decline over 2 years. Orbitofrontal CBVa was positively associated with apolipoprotein E e4 carrier status. Increased CBVa may reflect long-term effects of region-specific pathology associated with Aβ deposition. Additional studies are needed to clarify the role of the arteriolar system and the potential of CBVa as a biomarker for Aβ-related vascular downstream pathology

MRI with phaseless encoding

Purpose Fourier encoded MRI signal is complex and, therefore, sensitive to uncontrolled phase variations caused, e.g., by object motion. An alternative encoding is proposed which leads to phaseless (positive real) signals and allows the phase fluctuations to be removed by simple magnitude calculation before the Fourier transform. Theory and Methods Phaseless encoding uses harmonic modulation of the longitudinal magnetization with different frequencies and phases before excitation. It can be combined with Fourier encoding of complementary dimensions to produce, e.g., a 3D version of echo planar imaging insensitive to intershot phase variations. It can also be mixed with Fourier encoding of the same dimension allowing a high‐resolution image to be obtained from magnitude‐reconstructed low‐resolution components. The latter is a generalization of the super‐resolution MRI with microscopic tagging proposed recently. Improved reconstruction for this technique was adopted from its optical analogue, harmonic excitation light microscopy (HELM). Results Artifact free images were obtained despite phase fluctuations caused by random receiver reference and object motion during diffusion weighting. Proposed reconstruction of mixed‐encoded data reaches higher resolution than the original super‐resolution method

Algebraic method to synthesize specified modal currents in ladder resonators: Application to noncircular birdcage coils

Purpose: Detectors such as birdcage coils often consist of networks of coupled resonant circuits that must produce specified magnetic field distributions. In many cases, such as quadrature asymmetric insert body coils, calculating the capacitance values required to achieve specified currents and frequencies simultaneously is a challenging task that previously had only approximate or computationally inefficient solutions. Theory and Methods: A general algebraic method was developed that is applicable to linear networks having planar representations such as birdcage coils, transverse electromagnetic (TEM) coils, and numerous variants of ladder networks. Unlike previous iterative or approximate methods, the algebraic method is computationally efficient and determines current distribution and resonant frequency using a single matrix inversion. The method was demonstrated by specifying irregular current distributions on a highly elliptical birdcage coil at 3 Tesla. Results: Measurements of the modal frequency spectrum and transmit field distribution of the two specified modes agrees with the theory. Accuracy is limited in practice only by how accurately the matrix of self and mutual inductances of the network is known. Conclusion: The algebraic method overcomes the inability of the existing inductance equalization method to account for all elements of the inductance matrix and the inability to accommodate modal currents that are not (co)sinusoidal

Lattice permutation for reducing motion artifacts in radial and spiral dynamic imaging.

Radial and spiral trajectories exhibit favorable characteristics for dynamic imaging. Nevertheless, changes in image contents during acquisition lead to inconsistencies in the k-space data, which are manifested as streaks or spiral artifacts, respectively. This work proposes the concept of lattice permutation to reorder the data segments for artifact suppression. This acts to reshuffle the alias pattern along the temporal frequency axis. The proposed approach is well suited to sliding window reconstruction, although more sophisticated methods are also possible. For typical image series where the signal energies are concentrated in the low temporal frequencies, the permutation displaces most of the aliased signals from the low temporal frequencies to the high temporal frequencies, where they are attenuated by sliding window reconstruction, while the signals in the low temporal frequencies are mostly contaminated by aliasing from the much weaker signals in the higher temporal frequencies. This results in considerably reduced artifacts without any increase in scan time. In practice, lattice permutation achieves similar artifact suppression as the bit-reversed order, but with a less stringent restriction on the number of segments. At the same time, it provides a more powerful approach to controlling the alias pattern exactly. Results from real-time cardiac imaging are demonstrated