The ability to design and assemble 3-dimensional structures from colloidal particles is limited by the absence of specific directional bonds. As a result, complex or low-coordination structures, common in atomic and molecular systems, are rare in the colloidal domain. Here we demonstrate a general method for creating the colloidal analogues of atoms with valence: colloidal particles with chemically functionalized patches that can form highly directional bonds.These "colloidal atoms" possess all the common symmetries-and some uncommon ones-characteristic of hybridized atomic orbitals, including sp, sp 2 , sp 3 , sp 3 d, sp 3 d 2 , and sp 3 d 3 . Functionalizing the patches with DNA with single-stranded sticky ends makes the interactions between patches on different particles programmable, specific, and reversible, thus facilitating the self-assembly of particles into "colloidal molecules," including "molecules" with triangular, tetrahedral, and other bonding symmetries. Because colloidal dynamics are slow, the kinetics of molecule formation can be followed directly by optical microscopy. These new colloidal atoms should enable the assembly of a rich variety of new micro-structured materials. 2 IntroductionThe past decade has seen an explosion in the kinds of colloidal particles that can be synthesized 1,2 , with many new shapes, such as cubes 3 , clusters of spheres 4-6 and dimpled particles 7,8 reported. Because the self-assembly of these particles is largely controlled by their geometry, only a few relatively simple crystals have been made: face-centered and body-centered cubic crystals and variants 9 . Colloidal alloys increase the diversity of structures [10][11][12] , but many structures remain difficult or impossible to make. For example, the diamond lattice, predicted more than 20 years ago to have a full 3-dimensional photonic band gap 13 , still cannot be made by colloidal self-assembly because it requires 4-fold coordination. Without directional bonds, such low-coordination states are unstable.

Purpose To develop a fast and flexible free-breathing dynamic volumetric MRI technique, iterative Golden-angle RAdial Sparse Parallel MRI (iGRASP), that combines compressed sensing, parallel imaging, and golden-angle radial sampling. Methods Radial k-space data are acquired continuously using the golden-angle scheme and sorted into time series by grouping an arbitrary number of consecutive spokes into temporal frames. An iterative reconstruction procedure is then performed on the undersampled time series where joint multicoil sparsity is enforced by applying a total-variation constraint along the temporal dimension. Required coil-sensitivity profiles are obtained from the time-averaged data. Results iGRASP achieved higher acceleration capability than either parallel imaging or coil-by-coil compressed sensing alone. It enabled dynamic volumetric imaging with high spatial and temporal resolution for various clinical applications, including free-breathing dynamic contrast-enhanced imaging in the abdomen of both adult and pediatric patients, and in the breast and neck of adult patients. Conclusion The high performance and flexibility provided by iGRASP can improve clinical studies that require robustness to motion and simultaneous high spatial and temporal resolution.

Purpose To develop a novel framework for free-breathing MRI called XD-GRASP, which sorts dynamic data into extra motion-state dimensions using the self-navigation properties of radial imaging and reconstructs the multidimensional dataset using compressed sensing. Methods Radial k-space data are continuously acquired using the golden-angle sampling scheme and sorted into multiple motion-states based on respiratory and/or cardiac motion signals derived directly from the data. The resulting under-sampled multidimensional dataset is reconstructed using a compressed sensing approach that exploits sparsity along the new dynamic dimensions. The performance of XD-GRASP is demonstrated for free-breathing three-dimensional (3D) abdominal imaging, two-dimensional (2D) cardiac cine imaging and 3D dynamic contrast-enhanced (DCE) MRI of the liver, comparing against reconstructions without motion sorting in both healthy volunteers and patients. Results XD-GRASP separates respiratory motion from cardiac motion in cardiac imaging, and respiratory motion from contrast enhancement in liver DCE-MRI, which improves image quality and reduces motion-blurring artifacts. Conclusion XD-GRASP represents a new use of sparsity for motion compensation and a novel way to handle motions in the context of a continuous acquisition paradigm. Instead of removing or correcting motion, extra motion-state dimensions are reconstructed, which improves image quality and also offers new physiological information of potential clinical value.

Objective The objectives of this study were to develop a new method for free-breathing contrast-enhanced multiphase liver magnetic resonance imaging (MRI) using a combination of compressed sensing, parallel imaging, and radial k-space sampling and to demonstrate the feasibility of this method by performing image quality comparison with breath-hold cartesian T1-weighted (conventional) postcontrast acquisitions in healthy participants. Materials and Methods This Health Insurance Portability and Accountability Act–compliant prospective study received approval from the institutional review board. Eight participants underwent 3 separate contrast-enhanced fat-saturated T1-weighted gradient-echo MRI examinations with matching imaging parameters: conventional breath-hold examination with cartesian k-space sampling volumetric interpolate breath hold examination (BH-VIBE) and free-breathing acquisitions with interleaved angle-bisection and continuous golden-angle radial sampling schemes. Interleaved angle-bisection and golden-angle data from each 100 consecutive spokes were reconstructed using a combination of compressed sensing and parallel imaging (interleaved-angle radial sparse parallel [IARASP] and golden-angle radial sparse parallel [GRASP]) to generate multiple postcontrast phases. Arterial- and venous-phase BH-VIBE, IARASP, and GRASP reconstructions were evaluated by 2 radiologists in a blinded fashion. The readers independently assessed quality of enhancement (QE), overall image quality (IQ), and other parameters of image quality on a 5-point scale, with the highest score indicating the most desirable examination. Mixed model analysis of variance was used to compare each measure of image quality. Results Images of BH-VIBE and GRASP had significantly higher QE and IQ values compared with IARASP for both phases (P < 0.05). The differences in QE between BH-VIBE and GRASP for the arterial and venous phases were not significant (P > 0.05). Although GRASP had lower IQ score compared with BH-VIBE for the arterial (3.9 vs 4.8; P < 0.0001) and venous (4.2 vs 4.8; P = 0.005) phases, GRASP received IQ scores of 3 or more in all participants, which was consistent with acceptable or better diagnostic image quality. Conclusion Contrast-enhanced multiphase liver MRI of diagnostic quality can be performed during free breathing using a combination of compressed sensing, parallel imaging, and golden-angle radial sampling.

For patients with impaired breath-hold capacity and/or arrhythmias, real-time cine MRI may be more clinically useful than breath-hold cine MRI. However, commercially available real-time cine MRI methods using parallel imaging typically yield relatively poor spatio-temporal resolution due to their low image acquisition speed. We sought to achieve relatively high spatial resolution (~2.5mm × 2.5mm) and temporal resolution (~40ms), to produce high-quality real-time cine MR images that could be applied clinically for wall motion assessment and measurement of left ventricular (LV) function. In this work, we present an 8-fold accelerated real-time cardiac cine MRI pulse sequence using a combination of compressed sensing and parallel imaging (k-t SPARSE-SENSE). Compared with reference, breath-hold cine MRI, our 8-fold accelerated real-time cine MRI produced significantly worse qualitative grades (1–5 scale), but its image quality and temporal fidelity scores were above 3.0 (adequate) and artifacts and noise scores were below 3.0 (moderate), suggesting that acceptable diagnostic image quality can be achieved. Additionally, both 8-fold accelerated real-time cine and breath-hold cine MRI yielded comparable LV function measurements, with coefficient of variation < 10% for LV volumes. Our proposed 8-fold accelerated real-time cine MRI with k-t SPARSE-SENSE is a promising modality for rapid imaging of myocardial function.

5D whole-heart sparse imaging represents a robust and promising framework for simplified comprehensive cardiac MRI without the need for breath-hold and motion correction. Magn Reson Med 79:826-838, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

The introduction of compressed sensing for increasing imaging speed in MRI has raised significant interest among researchers and clinicians, and has initiated a large body of research across multiple clinical applications over the last decade. Compressed sensing aims to reconstruct unaliased images from fewer measurements than that are traditionally required in MRI by exploiting image compressibility or sparsity. Moreover, appropriate combinations of compressed sensing with previously introduced fast imaging approaches, such as parallel imaging, have demonstrated further improved performance. The advent of compressed sensing marks the prelude to a new era of rapid MRI, where the focus of data acquisition has changed from sampling based on the nominal number of voxels and/or frames to sampling based on the desired information content. This paper presents a brief overview of the application of compressed sensing techniques in body MRI, where imaging speed is crucial due to the presence of respiratory motion along with stringent constraints on spatial and temporal resolution. The first section provides an overview of the basic compressed sensing methodology, including the notion of sparsity, incoherence, and non-linear reconstruction. The second section reviews state-of-the-art compressed sensing techniques that have been demonstrated for various clinical body MRI applications. In the final section, the paper discusses current challenges and future opportunities.

Conventional diffusion (ΔR2(t))=2Dt gives way to subdiffusion (ΔR2(t))∼t(μ), 0<μ<1 when the waiting time distribution φ(τ) is nonintegrable. We have studied a model system, colloidal particles functionalized with DNA "sticky ends" diffusing on a complementary coated surface. We observe a crossover from subdiffusive to conventional behavior for (ΔR2(t)) and φ(τ) as temperature is increased near the particle-surface melting temperature consistent with a simple Gaussian distribution of sticky ends. Our results suggest that any system with randomness in its binding energy should exhibit subdiffusive behavior as it unbinds. This will strongly affect the kinetics of self-assembly.