Small Tip Angle Research Articles

A novel method for reducing the amount of dust produced by roadheaders based on the numerical simulation of coal breakage

Dust pollution is a serious environmental hazard during the tunneling in coal mines. Despite the presented dust control technologies, the method of reducing dust production has not been adequately investigated. This paper conducted cutting tests with various tip angles and attack angles using numerical models. A novel method for reducing the production of dust, based on the simulation results, was proposed and verified in the field experiments. The cutting force, work and crack extensions were analyzed. The concentrations of dust in laboratory tests were linked to the simulation results. The simulated results showed that the conical pick with a large tip angle could increase the cutting force and work and cause more cracks. The attack angle had a negative relation with the cutting force and work. The field experiments suggested that the amount of dust could be significantly reduced by using conical picks with a small tip angle. A slower rotation speed of the cutting head could alleviate dust hazards. The results are of momentous relevance for mine managers and researchers to reduce the production of dust during tunneling and control the dust more efficient.

Different plant species exhibit contrasting root traits and penetration to variation in soil bulk density of clayey red soil

AbstractHigh bulk density reduces yields in almost every soil and management system worldwide. Using pioneer plants was one of the practical solutions to remediate the adverse effects from high bulk density. The objectives of this research were to investigate the effect of soil bulk density on root traits and penetration of different pioneer plants (rape [Brassica napus L. cv. Huashuang 4]; deep rape [Brassica napus L. cv. Xinan 28]; lucerne [Medicago sativa L. cv. Ladino]; vetiver [Chrysopogon zizanioides L. cv. Wild]) under controlled and field conditions. Replicated field and laboratory studies were conducted in a soil composition of high clay percentage, high oxides content, and low organic matter content. Seedling and matured root traits of four plants under contrasting bulk density in controlled study and field were analyzed. Under controlled situations, soil with a bulk density of 1.4 g cm–3 had thicker roots (higher diameter) than soil with a bulk density of 1.2 g cm–3, whereas soil with a bulk density of 1.6 g cm–3 had reduced root lengths (RL), branch number, root tip angle, and root elongation rate than soil with a bulk density of 1.4 g cm–3. Similar changes of root diameter (RD) and root length density (RLD) with bulk density also appeared in the field. Generally, the penetration ability of plant species displayed in the order of vetiver > lucerne > deep rape > rape. Vetiver showed the highest penetrating ability due to its high RD (0.7 mm in field), percentage of medium roots (20–50%) and RLD, and small root tip angle to ensure penetration through hard layers. The results demonstrated that vetiver will be an effective pioneer plant for red soil management.

Viscoelastic flow-induced oscillations of a cantilevered beam in the crossflow of a wormlike micelle solution

Abstract We investigate the interactions between a cantilevered flexible beam and cross-flow of a viscoelastic fluid. Unlike Newtonian fluids, viscoelastic fluids exhibit elastic flow instabilities even in the absence of inertia. These elastic flow instabilities drive the oscillations of flexible structures placed in their flow path. In this work, the fluid–structure interactions between the flow of viscoelastic wormlike micelle solution and a flexible cantilevered beam is studied as a function of the Weissenberg number and the beam’s tip angle. At low Weissenberg numbers, the flow remained stable and the beam deflected in the direction of flow. As the Weissenberg number was increased, a separated vortex appeared upstream of the cantilever near its tip. At a critical Weissenberg number of W i = 11 , the flow became unstable. For beams with small tip angles of 0° and 25°, no oscillations were observed. However, for beams with larger tip angles of 45° and 65°, oscillatory motions coupled to the flow instability were observed, where the amplitude of the beam oscillations increased with increasing tip angle. Particle image velocimetry measurements showed that the elastic flow instability was characterized by the periodic formation of strong fluid jet that originated upstream of the beam in a region of strong extensional flow where it likely resulted from the local breakdown of the wormlike micelle solution. This jet was accompanied by a pair of counter-rotating vortices on its sides as it entrained fluid around the tip of the beam. The frequency of oscillations of the beams with large tip angles increased monotonically with Weissenberg number, while their amplitudes of oscillations initially increased with Weissenberg number before decaying to zero for W i > 20 , despite the fact that the flow remained unstable. Our results showed that oscillations were only possible when the tip of the cantilevered beam made a positive angle with respect to the primary incoming flow direction.

A Statistical Robust Approach to Design Parallel Transmit Radiofrequency Excitations in MRI

In MRI, at ultrahigh field, the use of parallel transmit radiofrequency (RF) arrays is very beneficial to better control spin excitation spatially. In that framework, the so-called “universal pulse” technique, proposed recently for head imaging at 7 tesla, gives access to “plug-and-play” nonadiabatic solutions exhibiting good robustness against intersubject variations in the resonant transmit fields. This new type of solution has been defined so far as the result of numerical pulse optimizations performed across a collection of RF field maps acquired on a small population sample (pulse design database). In this work, we investigate an alternative universal pulse design approach in the linear small tip angle regime whereby the database of RF field maps is first transformed into a second-order statistical model and which then exploits a statistical robust design formalism for the optimization of the RF and magnetic field gradient waveforms. Experimental validation with an eightfold transmit RF coil for 7 tesla brain imaging shows that this new approach brings some benefit in terms of computational efficiency. Hence, for a design database composed of 35 maps, the computation time initially of 50 min could be reduced down to 3 min. The proposed statistical approach thus enables integration of large databases, presumably necessary to ensure robust solutions. Finally, it provides means to compute flip angle statistics and, along with it, simple performance metrics for quality assurance (RF pulse performance) or guidance in the optimization of TX array architectures.

Bioinspired conical design for efficient water collection from fog.

Nature is known for using conical shapes to transport the collected water from fog for consumption or storage. The curvature gradient of the conical shape creates a Laplace pressure gradient in the water droplets which drives them towards the region of lower curvature. Linear cones with linearly increasing radii have been studied extensively. A smaller tip angle cone transports water droplets farther because of higher Laplace pressure gradient. Whereas a larger tip angle with a larger surface slope transports water droplets because of higher gravitational forces. In this study, for the first time, a nonlinear cone with a concave profile has been designed with small tip angle and nonlinearly increasing radius to maximize water collection. This article is part of the theme issue 'Bioinspired materials and surfaces for green science and technology (part 2)'.

Improved chemical exchange saturation transfer imaging with real-time frequency drift correction.

To investigate the effects of frequency drift on chemical exchange saturation transfer (CEST) imaging at 3T, and to propose a new sequence for correcting artifacts attributed to B0 drift in real time. A frequency-stabilized CEST (FS-CEST) imaging sequence was proposed by adding a frequency stabilization module to the conventional non-frequency-stabilized CEST (NFS-CEST) sequence, which consisted of a small tip angle radiofrequency excitation pulse and readout of three non-phase-encoded k-space lines. Experiments were performed on an egg white phantom and 26 human subjects on a heavy-duty clinical scanner, in order to compare the difference of FS-CEST and NFS-CEST sequences for generating the z-spectrum, magnetization transfer ratio asymmetry (MTRasym ) spectrum, and amide proton transfer weighted (APTw) image. The B0 drift in CEST imaging, if not corrected, would cause APTw images and MTRasym spectra from both the phantom and volunteers to be either significantly higher or lower than the true values, depending on the status of the scanner. The FS-CEST sequence generated substantially more stable MTRasym spectra and APTw images than the conventional NFS-CEST sequence. Quantitatively, the compartmental-average APTw signals (mean ± standard deviation) from frontal white matter regions of all 26 human subjects were -0.32% ± 2.32% for the NFS-CEST sequence and -0.14% ± 0.37% for the FS-CEST sequence. The proposed FS-CEST sequence provides an effective approach for B0 drift correction without additional scan time and should be adopted on heavy-duty MRI scanners.

Capturing exchange using periodic radiofrequency irradiation

The dynamics of spin system coupled by chemical exchange between two sites with different chemical shifts during periodic radiofrequency (RF) irradiation was here investigated. When the instantaneous π-flip of effective frequency during the course of frequency sweep was applied, a significant increase of exchange-induced relaxation rate constants was observed for small tip angle of magnetization in the laboratory frame of reference. This increase of the rate constants corresponds to the side bands generated by the periodic irradiation during the RF pulses. The exchange - induced relaxation rate constants depend on the exchange conditions, the RF power and the irradiation period. The described phenomenon promises applications for studying protein dynamics and for generating exchange specific relaxation contrasts in MRI.

Squeezed Trajectory Design for Peak RF and Integrated RF Power Reduction in Parallel Transmission MRI.

High peak RF amplitude and excessive specific absorption rate (SAR) are two critical concerns for hardware implementation and patient safety in scientific and clinical research for high field MRI using parallel transmissions (pTX). In this paper, we introduce a squeezing strategy to reduce peak RF amplitude and integrated RF power via direct reshaping of the k-space trajectory. In the existing peak RF / integrated RF power optimization methods gradient amplitude or slew rate is reduced, but the k-space trajectory remains unchanged. Unlike these traditional methods, we worked directly in the excitation k-space to reshape k-space traversal by a squeezing vector in order to achieve peak RF and total RF power optimization, using a particle swarm optimization algorithm. The squeezing strategy was applied to the conventional variable density spiral (CVDS) and the variable rate selective excitation (VERSE) trajectories, dubbed SVDS (squeezed variable density spiral) and SVERSE (squeezing trajectory with VERSE), respectively, for different excitation profiles of small or large tip angles. Pulse acceleration and off-resonance effects were evaluated for an 8-ch pTX via Bloch simulation. CVDS, VERSE, SVDS, and SVERSE pulses were implemented on a 3T scanner with a 2-ch pTX. Phantom and in vivo experiments were performed for reduced FOV (rFOV) imaging. The results show that SVDS pulses simultaneously reduce integrated RF power and peak RF by about 30% on average compared to CVDS pulses for a square pattern ( $80\times80$ mm2) with flip angles of 30°, 90°, and 180°. Compared with the VERSE method under the same peak RF constraints, the SVDS method reduces integrated RF power by an average of 20% for small tip excitations for profiles of slice, rectangular, square, and circle, and has slightly reduced excitation accuracy slightly (about 0.6%, from 6.8% to 7.4%). The SVERSE method shortens the duration of the VERSE pulse by 12.8% at large ti p angle (180°). Feasibility for rFOV imaging was demonstrated with phantom and in vivo experiments with squeezed pulses.

Puncture performance of sharpen microneedles by using inclined contact UV lithography

Microneedles is one of important future dispensing device for vaccination and diabetes. Solid microneedles is of wide application as it have also been designed to be coated with a drug for releasing into the skin by dissolution. Hard biodegradable polylactic acid (PLA) microneedles is suitable for solid microneedles because PLA provides safety in case microneedles accidentally break in the skin. The puncture performance of more sharpen microneedles have been demonstrated in this study. To make small tip radius and sharp tip angle to penetrate the skin from the viewpoints of ease of needling is key point on design of master mold. SU-8 mold manufactured by inclined contact UV lithography have been used for fabricating microneedles. To make designed small tip and shape tip angle on master mold, liquid impregnation method was introduced. Exposure value and developing time were optimized. Microneedles patch was replicated by molding PLA from dimethylpolysiloxane mold. The tip radius of pyramid microneedle was 3 μm and the tip angle of sold polymer microneedle was 18°, and these data were smallest tip radius and angle that have seen in all references. On imprint lithography process, thermoforming process was performed in the vacuum temperature chamber. As duration under decompressing in the vacuum temperature chamber was longer, the defects ratio of PLA microneedles became smaller. Microneedles patch was punctured into a mouse and human skins in high probability that is more than 80% after pressing the patch into the skin.

Design of spectral-spatial phase prewinding pulses and their use in small-tip fast recovery steady-state imaging.

Spectrally selective "prewinding" radiofrequency pulses can counteract B0 inhomogeneity in steady-state sequences, but can only prephase a limited range of off-resonance. We propose spectral-spatial small-tip angle prewinding pulses that increase the off-resonance bandwidth that can be successfully prephased by incorporating spatially tailored excitation patterns. We present a feasibility study to compare spectral and spectral-spatial prewinding pulses. These pulses add a prephasing term to the target magnetization pattern that aims to recover an assigned off-resonance bandwidth at the echo time. For spectral-spatial pulses, the design bandwidth is centered at the off-resonance frequency for each spatial location in a field map. We use these pulses in the small-tip fast recovery steady-state sequence, which is similar to balanced steady-state free precession. We investigate improvement of spectral-spatial pulses over spectral pulses using simulations and small-tip fast recovery scans of a gel phantom and human brain. In simulation, spectral-spatial pulses yielded lower normalized root mean squared excitation error than spectral pulses. For both experiments, the spectral-spatial pulse images are also qualitatively better (more uniform, less signal loss) than the spectral pulse images. Spectral-spatial prewinding pulses can prephase over a larger range of off-resonance than their purely spectral counterparts. Magn Reson Med 79:1377-1386, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Simultaneous use of linear and nonlinear gradients for B1+ inhomogeneity correction.

The simultaneous use of linear spatial encoding magnetic fields (L-SEMs) and nonlinear spatial encoding magnetic fields (N-SEMs) in B1+ inhomogeneity problems is formulated and demonstrated with both simulations and experiments. Independent excitation k-space variables for N-SEMs are formulated for the simultaneous use of L-SEMs and N-SEMs by assuming a small tip angle. The formulation shows that, when N-SEMs are considered as an independent excitation k-space variable, numerous different k-space trajectories and frequency weightings differing in dimension, length, and energy can be designed for a given target transverse magnetization distribution. The advantage of simultaneous use of L-SEMs and N-SEMs is demonstrated by B1+ inhomogeneity correction with spoke excitation. To fully utilize the independent k-space formulations, global optimizations are performed for 1D, 2D RF power limited, and 2D RF power unlimited simulations and experiments. Three different cases are compared: L-SEMs alone, N-SEMs alone, and both used simultaneously. In all cases, the simultaneous use of L-SEMs and N-SEMs leads to a decreased standard deviation in the ROI compared with using only L-SEMs or N-SEMs. The simultaneous use of L-SEMs and N-SEMs results in better B1+ inhomogeneity correction than using only L-SEMs or N-SEMs due to the increased number of degrees of freedom.

Experimental study on the single grit interaction behaviour and brittle–ductile transition of grinding with a diamond micro-grinding tool

This study presents new information on single grit interaction behaviour and its brittle–ductile transition in micro-grinding single crystal silicon using a single grit diamond tool. A model to describe the energy interaction between the cutting behaviour of a single grit and the workpiece in micro-grinding is established based on the single grit geometry model, which was indicated in Fig. 1a, the critical condition of the volume of material removed and the conservation of energy. The tip angle of the single-point diamond tool has been considered. To reveal the material removal mechanism of micro-grinding, a series of scratching experiments, which conducted with a low cutting speed (0.036 to 0.6 m/s), have been performed in this study. The fractures of the micro-grooves machined using single-point diamond tools have been examined by a microscope and a surface profilometer, thus revealing different processing modes (brittle and ductile). The variation curves of the fracture length c have been presented on the condition of different tool tip angles θ (60° and 120°). It is found that the fracture size of grooves machined by a grit with a blunt angle is comparatively larger than that of a grit with a sharp angle for the same scratching parameters. The scratching speed v and penetration depth p0 have a direct effect on the fracture length c, which increases obviously with the rising of v and p0. The critical condition has been investigated based on the experimental results; the blunt grit (with a larger tip angle: θ = 120°) and the sharp grit (with a smaller tip angle: θ = 60°) have different brittle–ductile transitions and different critical cutting depths, which are 334 nm (θ = 60°) and 607 nm (θ = 120°), respectively. The effects of the scratching speed v are investigated. The brittle–ductile transitions of the different scratching speeds have been compared. The relationship between the fracture length c and the volume of material removed in unit time V has been discussed; V is an important measuring constant for the fracture formation and critical ductile cutting condition. This study reveals the mechanism of the single grit interaction in micro-grinding with an ultra-small grinding tool and provides theoretical and experimental validation for ductile micro-grinding of single crystal silicon.

Slice‐selective adiabatic magnetization T2‐preparation (SAMPA) for efficient T2‐weighted imaging at ultrahigh field strengths

At high field, T2 -weighted (T2 w) imaging is limited by transmit field inhomogeneity and increased radiofrequency power deposition. In this work, we introduce SAMPA (Slice-selective Adiabatic Magnetization T2 PrepAration) and demonstrate its use for efficient brain T2 w imaging at 7 Tesla (T). SAMPA was designed by subsampling an optimized B1 insensitive rotation (BIR4) waveform with small tip angle linear subpulses. To perform T2 w imaging, SAMPA was inserted before a fast gradient echo acquisition. The off-resonance behavior, B1 robustness, and slice selectivity of the novel T2 preparation module were analyzed using Bloch simulations. The performance of SAMPA for T2 w imaging was demonstrated in phantom experiments as well as in the brains of healthy volunteers at 7T. Based on simulations, the proposed design operates at peak B1 of 15 μT and higher, within a 400 Hz bandwidth. T2 values were in strong agreement with spin echo-based T2 mapping in phantom experiments. Whole brain, interleaved multislab three-dimensional imaging could be acquired with 0.8 mm3 isotropic resolution in 5:36 min per T2 weighting. Compared with previous adiabatic T2 preparation techniques, SAMPA allows for slice-selectivity, which can lead to efficient and robust acquisitions for T2 w imaging at high field. Magn Reson Med 76:1741-1749, 2016. © 2015 International Society for Magnetic Resonance in Medicine.

Fast three-dimensional inner volume excitations using parallel transmission and optimized k-space trajectories.

To design short parallel transmission (pTx) pulses for excitation of arbitrary three-dimensional (3D) magnetization patterns. We propose a joint optimization of the pTx radiofrequency (RF) and gradient waveforms for excitation of arbitrary 3D magnetization patterns. Our optimization of the gradient waveforms is based on the parameterization of k-space trajectories (3D shells, stack-of-spirals, and cross) using a small number of shape parameters that are well-suited for optimization. The resulting trajectories are smooth and sample k-space efficiently with few turns while using the gradient system at maximum performance. Within each iteration of the k-space trajectory optimization, we solve a small tip angle least-squares RF pulse design problem. Our RF pulse optimization framework was evaluated both in Bloch simulations and experiments on a 7T scanner with eight transmit channels. Using an optimized 3D cross (shells) trajectory, we were able to excite a cube shape (brain shape) with 3.4% (6.2%) normalized root-mean-square error in less than 5 ms using eight pTx channels and a clinical gradient system (Gmax = 40 mT/m, Smax = 150 T/m/s). This compared with 4.7% (41.2%) error for the unoptimized 3D cross (shells) trajectory. Incorporation of B0 robustness in the pulse design significantly altered the k-space trajectory solutions. Our joint gradient and RF optimization approach yields excellent excitation of 3D cube and brain shapes in less than 5 ms, which can be used for reduced field of view imaging and fat suppression in spectroscopy by excitation of the brain only. Magn Reson Med 76:1170-1182, 2016. © 2015 Wiley Periodicals, Inc.

First and second order derivatives for optimizing parallel RF excitation waveforms

For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly. This way the magnetization created by an excitation pulse can be written as a concatenation of rotations applied to the initial magnetization. For fixed gradient trajectories, the problem of finding parallel RF waveforms, which minimize the difference between achieved and desired magnetization on a number of voxels, can thus be represented as a finite-dimensional minimization problem. We use quaternion calculus to formulate this optimization problem in the magnitude least squares variant and specify first and second order derivatives of the objective function. We obtain a small tip angle approximation as first order Taylor development from the first order derivatives and also develop algorithms for first and second order derivatives for this small tip angle approximation. All algorithms are accompanied by precise floating point operation counts to assess and compare the computational efforts. We have implemented these algorithms as callback functions of an interior-point solver. We have applied this numerical optimization method to example problems from the literature and report key observations.

Two-spoke placement optimization under explicit specific absorption rate and power constraints in parallel transmission at ultra-high field

The spokes method combined with parallel transmission is a promising technique to mitigate the B1+ inhomogeneity at ultra-high field in 2D imaging. To date however, the spokes placement optimization combined with the magnitude least squares pulse design has never been done in direct conjunction with the explicit Specific Absorption Rate (SAR) and hardware constraints. In this work, the joint optimization of 2-spoke trajectories and RF subpulse weights is performed under these constraints explicitly and in the small tip angle regime. The problem is first considerably simplified by making the observation that only the vector between the 2 spokes is relevant in the magnitude least squares cost-function, thereby reducing the size of the parameter space and allowing a more exhaustive search. The algorithm starts from a set of initial k-space candidates and performs in parallel for all of them optimizations of the RF subpulse weights and the k-space locations simultaneously, under explicit SAR and power constraints, using an active-set algorithm. The dimensionality of the spoke placement parameter space being low, the RF pulse performance is computed for every location in k-space to study the robustness of the proposed approach with respect to initialization, by looking at the probability to converge towards a possible global minimum. Moreover, the optimization of the spoke placement is repeated with an increased pulse bandwidth in order to investigate the impact of the constraints on the result. Bloch simulations and in vivo T2∗-weighted images acquired at 7T validate the approach. The algorithm returns simulated normalized root mean square errors systematically smaller than 5% in 10s.

Balanced SSFP-like steady-state imaging using small-tip fast recovery with a spectral prewinding pulse.

Small-tip fast recovery (STFR) imaging has been proposed recently as a potential alternative to balanced steady-state free precession (bSSFP). STFR relies on a tailored "tip-up" radio-frequency pulse to achieve comparable signal level as bSSFP, but with reduced banding artifacts and transient oscillations, and is compatible with magnetization-preparation pulses. Previous STFR implementations used two-dimensional or three-dimensional pulses spatially tailored to the accumulated phase calculated from a B0 field map, making the steady-state STFR signal contain some T2* weighting. Here, we propose to replace the spatially tailored pulse with a recently introduced spectrally selective "pre-winding" pulse that is precomputed to a target frequency range. The proposed "spectral-STFR" sequence produces T2/T1-weighted images similar to bSSFP, but with reduced banding and potentially other benefits. We investigated the steady-state signal properties of spectral-STFR using simulations, and phantom and human volunteer experiments. Our simulation and experimental results showed that the spectral-STFR sequence has similar signal level and tissue contrast as bSSFP, but has a wider passband and more consistent banding profiles across different tissues (e.g., less hyperintense signal at band edges for low flip angles). Care is needed in designing the spectral radio-frequency pulse to ensure that the small tip angle approximation holds during radio-frequency transmission. Spectral-STFR has similar tissue contrast as bSSFP but a wider passband and more consistent cerebrospinal fluid/brain tissue contrast across the passband. The spectral-STFR sequence is a potential alternative to bSSFP in some applications. Compared to a spatially tailored STFR sequence, spectral-STFR can be precomputed, is easier to implement in practice, and potentially has more uniform image contrast and minimal T2* weighting.

3D printed, bio-inspired prototypes and analytical models for structured suture interfaces with geometrically-tuned deformation and failure behavior

Geometrically structured interfaces in nature possess enhanced, and often surprising, mechanical properties, and provide inspiration for materials design. This paper investigates the mechanics of deformation and failure mechanisms of suture interface designs through analytical models and experiments on 3D printed polymer physical prototypes. Suture waveforms with generalized trapezoidal geometries (trapezoidal, rectangular, anti-trapezoidal, and triangular) are studied and characterized by several important geometric parameters: the presence or absence of a bonded tip region, the tip angle, and the geometry. It is shown that a wide range (in some cases as great as an order of magnitude) in stiffness, strength, and toughness is achievable dependent on tip bonding, tip angle, and geometry. Suture interfaces with a bonded tip region exhibit a higher initial stiffness due to the greater load bearing by the skeletal teeth, a double peak in the stress–strain curve corresponding to the failure of the bonded tip and the failure of the slanted interface region or tooth, respectively, and an additional failure and toughening mechanism due to the failure of the bonded tip. Anti-trapezoidal geometries promote the greatest amplification of properties for suture interfaces with a bonded tip due the large tip interface area. The tip angle and geometry govern the stress distributions in the teeth and the ratio of normal to shear stresses in the interfacial layers, which together determine the failure mechanism of the interface and/or the teeth. Rectangular suture interfaces fail by simple shearing of the interfaces. Trapezoidal and triangular suture interfaces fail by a combination of shear and tensile normal stresses in the interface, leading to plastic deformation, cavitation events, and subsequent stretching of interface ligaments with mostly elastic deformation in the teeth. Anti-trapezoidal suture interfaces with small tip angles have high stress concentrations in the teeth and fail catastrophically by tooth failure, whereas larger tip angles exhibit a shear failure of the interfaces. Therefore, larger tip angles and trapezoidal or triangular geometries promote graceful failure, and smaller tip angles and anti-trapezoidal geometries promote more brittle-like failure. This dependence is reminiscent of biological systems, which exhibit a range of failure behaviors with limited materials and varied geometry. Triangular geometries uniquely exhibit uniform stress distributions in its teeth and promote the greatest amplification of mechanical properties. In both the bonded and unbonded cases, the predictions from the presented analytical models and experimental results on 3D printed prototypes show excellent agreement. This validates the analytical models and allows for the models to be used as a tool for the design of new materials and interfaces with tailored mechanical behavior.

Fast low-specific absorption rate B0 -mapping along projections at high field using two-dimensional radiofrequency pulses.

At 7 Tesla (T), conventional static field (B0 ) projection mapping techniques, e.g., FASTMAP, FASTESTMAP, lead to elevated specific absorption rates (SAR), requiring longer total acquisition times (TA). In this work, the series of adiabatic pulses needed for slab selection in FASTMAP is replaced by a single two-dimensional radiofrequency (2D-RF) pulse to minimize TA while ensuring equal shimming performance. Spiral gradients and 2D-RF pulses were designed to excite thin slabs in the small tip angle regime. The corresponding selection profile was characterized in phantoms and in vivo. After optimization of the shimming protocol, the spectral linewidths obtained after 2D localized shimming were compared with conventional techniques and published values from (Emir et al NMR Biomed 2012;25:152-160) in six different brain regions. Results on healthy volunteers show no significant difference (P > 0.5) between the spectroscopic linewidths obtained with the adiabatic (TA = 4 min) and the new low-SAR and time-efficient FASTMAP sequence (TA = 42 s). The SAR can be reduced by three orders of magnitude and TA accelerated six times without impact on the shimming performances or quality of the resulting spectra. Multidimensional pulses can be used to minimize the RF energy and time spent for automated shimming using projection mapping at high field.

On Variant Strategies to Solve the Magnitude Least Squares Optimization Problem in Parallel Transmission Pulse Design and Under Strict SAR and Power Constraints

Parallel transmission is a very promising candidate technology to mitigate the inevitable radio-frequency (RF) field inhomogeneity in magnetic resonance imaging at ultra-high field. For the first few years, pulse design utilizing this technique was expressed as a least squares problem with crude power regularizations aimed at controlling the specific absorption rate (SAR), hence the patient safety. This approach being suboptimal for many applications sensitive mostly to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem then was first formulated in 2007. Despite its importance and the availability of other powerful numerical optimization methods, the MLS problem yet has been faced almost exclusively by the pulse designer with the so-called variable exchange method. In this paper, we investigate various two-stage strategies consisting of different initializations and nonlinear programming approaches, and incorporate directly the strict SAR and hardware constraints. Several schemes such as sequential quadratic programming, interior point methods, semidefinite programming and magnitude squared least squares relaxations are studied both in the small and large tip angle regimes with RF and static field maps obtained in vivo on a human brain at 7T. Convergence and robustness of the different approaches are analyzed, and recommendations to tackle this specific problem are finally given. Small tip angle and inversion pulses are returned in a few seconds and in under a minute respectively while respecting the constraints, allowing the use of the proposed approach in routine.