Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

The sparsity which is implicit in MR images is exploited to significantly undersample k -space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain–for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressedsensing, images with a sparse representation can be recovered from randomly undersampled k -space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the 1 norm of a transformed image, subject to data

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Sparse MRI: The application of compressed sensing for rapid MR imaging.

The invention relates to a method of parallel imaging for obtaining images by means of magnetic resonance (MR). The method includes the simultaneous measurement of sets of MR singals by an array of receiver coils, and the reconstruction of individual receiver coil images from the sets of MR signals. In order to reduce the acquisition time, the distance between adjacent phase encoding lines in k-space is increased, compared to standard Fourier imaging, by a non-integer factor smaller than the number of receiver coils. This undersampling gives rise to aliasing artifacts in the individual receiver coil images. An unaliased final image with the same field of view as in standard Fourier imaging is formed from a combination of the individual receiver coil images whereby account is taken of the mutually different spatial sensitivities of the receiver coils at the positions of voxels which in the receiver coil images become superimposed by aliasing. This requires the solution of a linear equation by means of the generalised inverse of a sensitivity matrix. The reduction of the number of phase encoding lines by a non-integer factor compared to standard Fourier imaging provides that different numbers of voxels become superimposed (by aliasing) in different regions of the receiver coil images. This effect can be exploited to shift residual aliasing artifacts outside the area of interest.

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SENSE: Sensitivity Encoding for fast MRI

In this study, a novel partially parallel acquisition (PPA) method is presented which can be used to accelerate image acquisition using an RF coil array for spatial encoding. This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD-AUTO-SMASH reconstruction techniques. As in those previous methods, a detailed, highly accurate RF field map is not needed prior to reconstruction in GRAPPA. This information is obtained from several k-space lines which are acquired in addition to the normal image acquisition. As in PILS, the GRAPPA reconstruction algorithm provides unaliased images from each component coil prior to image combination. This results in even higher SNR and better image quality since the steps of image reconstruction and image combination are performed in separate steps. After introducing the GRAPPA technique, primary focus is given to issues related to the practical implementation of GRAPPA, including the reconstruction algorithm as well as analysis of SNR in the resulting images. Finally, in vivo GRAPPA images are shown which demonstrate the utility of the technique.

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Generalized autocalibrating partially parallel acquisitions (GRAPPA).

Functional magnetic resonance imaging (fMRI) is currently the mainstay of neuroimaging in cognitive neuroscience. Advances in scanner technology, image acquisition protocols, experimental design, and analysis methods promise to push forward fMRI from mere cartography to the true study of brain organization. However, fundamental questions concerning the interpretation of fMRI data abound, as the conclusions drawn often ignore the actual limitations of the methodology. Here I give an overview of the current state of fMRI, and draw on neuroimaging and physiological data to present the current understanding of the haemodynamic signals and the constraints they impose on neuroimaging data interpretation.

What we can do and what we cannot do with fMRI

State-of-the-art MR-PET scanners allow simultaneous data acquisition. However, image reconstruction is performed separately and results are only combined at the visualization stage. PET images are reconstructed using a variant of EM and MR data are reconstructed using an inverse Fourier transform or iterative algorithms for parallel imaging or compressed sensing. We propose a new iterative joint reconstruction framework based on multi-sensor compressed sensing that exploits anatomical correlations between MR and PET.

Joint reconstruction is motivated by the fact that MR and PET are based on the same anatomy. High resolution MR information can be used to enhance the PET reconstruction and MR artifacts are not present in the PET image. Therefore a dedicated reconstruction can exploit the incoherence of artifacts in the joint space. Our approach uses a nonlinear constrained optimization problem. In each iteration OSEM enforces data consistency of the current solution with measured PET rawdata. An l1-norm based joint sparsity term exploits anatomical correlations. MR data consistency is enforced with the MR forward operator, consisting of coil sensitivity modulation and a (non-uniform) Fourier transform. Data were acquired on a clinical 3T MR-PET unit (Siemens Biograph mMR). 10 mCi 18F-FDG were injected followed by a 60min list mode scan. 3D MP-RAGE was used for MR data acquisition: TR=2300ms, TE=2.98ms, TI=900ms, FA=9°, acceleration factor 2, 24 ACS lines, 256 matrix, voxel size=1×1×1mm3, 192 slices.

Joint MR-PET reconstruction improves resolution in PET images when structures are aligned with MR. PET signal information cannot be improved in regions showing no distinctive MR contrast, but it is also not influenced falsely. The availability of simultaneously-acquired MR and PET data will also enable incorporation of dynamic correlations and motion correction into the joint reconstruction framework. We expect that this provides additional enhancements to the information content of multimodality studies.

https://link.springer.com/content/pdf/10.1186%2F2197-7364-1-S1-A26.pdf

Joint reconstruction of simultaneously acquired MR-PET data with multi sensor compressed sensing based on a joint sparsity constraint

The brain after COVID-19: Compensatory neurogenesis or persistent neuroinflammation?

Purpose The aim of this study was to evaluate the effect of integrated high-permittivity materials (HPMs) on excitation homogeneity and global specific absorption rate (SAR) for transmit arrays at 7T. Methods A rapid electrodynamic simulation framework was used to calculate L-curves associated with excitation of a uniform 2D profile in a dielectric sphere. We used ultimate intrinsic SAR as an absolute performance reference to compare different transmit arrays in the presence and absence of a layer of HPM. We investigated the optimal permittivity for the HPM as a function of its thickness, the sample size, and the number of array elements. Results Adding a layer of HPM can improve the performance of a 24-element array to match that of a 48-element array without HPM, whereas a 48-element array with HPM can perform as well as a 64-element array without HPM. Optimal relative permittivity values changed based on sample and coil geometry, but were always within a range obtainable with readily available materials (er = 100-200). Conclusion Integration of HPMs could be a practical method to improve RF shimming performance, alternative to increasing the number of coils. The proposed simulation framework could be used to explore the design of novel transmit arrays for head imaging at ultra-high field strength. Magn Reson Med 80:391-399, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Approaching ultimate intrinsic specific absorption rate in radiofrequency shimming using high-permittivity materials at 7 Tesla.

Purpose Most clinical MR examinations require acquisition of different image contrasts. For abdominal exams, the scans are conventionally performed as separate acquisitions using respiratory gating or repeated breath holding, which can be time-inefficient and challenging for patients. Here, a hybrid imaging approach is described that creates T2 - and T1 -weighted images from a single scan and allows for free-breathing acquisition. Theory and methods T2 -weighted data is collected using 3D fast spin-echo (FSE) acquisition with motion-robust radial stack-of-stars sampling. The wait time between the FSE trains is used to acquire T1 -weighted gradient-echo (GRE) data. Improved robustness is achieved by extracting a respiratory signal from the GRE data and using it for motion-weighted reconstruction. Results As validated in simulations and phantom scans, GRE acquisition in the wait time has minor effect on the signal strength and contrast. Volunteer scans at 1.5T showed that T2 - and T1 -weighted hybrid imaging is feasible during free-breathing. Furthermore, it has been demonstrated in a patient that hybrid imaging with T1 -weighted Dixon acquisition is possible. Conclusion The described hybrid sequence enables comprehensive T2 - and T1 -weighted imaging in a single scan. In addition to free-breathing abdominal examination, it promises value for clinical applications that are frequently affected by motion artifacts.

Hybrid T2 - and T1 -weighted radial acquisition for free-breathing abdominal examination.

Purpose: The analysis of optimized spin ensemble trajectories for relaxometry in the hybrid state. 
Methods: First, we constructed visual representations to elucidate the differential equation that governs spin dynamics in hybrid state. Subsequently, numerical optimizations were performed to find spin ensemble trajectories that minimize the Cramer-Rao bound for $T_1$-encoding, $T_2$-encoding, and their weighted sum, respectively, followed by a comparison of the Cramer-Rao bounds obtained with our optimized spin-trajectories, as well as Look-Locker and multi-spin-echo methods. Finally, we experimentally tested our optimized spin trajectories with in vivo scans of the human brain. 
Results: After a nonrecurring inversion segment on the southern hemisphere of the Bloch sphere, all optimized spin trajectories pursue repetitive loops on the northern half of the sphere in which the beginning of the first and the end of the last loop deviate from the others. The numerical results obtained in this work align well with intuitive insights gleaned directly from the governing equation. Our results suggest that hybrid-state sequences outperform traditional methods. Moreover, hybrid-state sequences that balance $T_1$- and $T_2$-encoding still result in near optimal signal-to-noise efficiency. Thus, the second parameter can be encoded at virtually no extra cost. 
Conclusion: We provide insights regarding the optimal encoding processes of spin relaxation times in order to guide the design of robust and efficient pulse sequences. We find that joint acquisitions of $T_1$ and $T_2$ in the hybrid state are substantially more efficient than sequential encoding techniques.

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Daniel K. Sodickson

Papers

Joint reconstruction of simultaneously acquired MR-PET data with multi sensor compressed sensing based on a joint sparsity constraint

The brain after COVID-19: Compensatory neurogenesis or persistent neuroinflammation?

Approaching ultimate intrinsic specific absorption rate in radiofrequency shimming using high-permittivity materials at 7 Tesla.

Hybrid T2 - and T1 -weighted radial acquisition for free-breathing abdominal examination.

Optimized Quantification of Spin Relaxation Times in the Hybrid State