Detunable wireless resonator arrays for TMJ MRI: A comparative study.

Temporomandibular Joint Magnetic Resonance Imaging (TMJ MRI) is crucial for diagnosing temporomandibular disorders (TMDs). This study advances the use of inductively coupled wireless coils to enhance imaging quality in TMJ MRI. After investigating multiple wireless resonator configurations, including a 1-loop design with a loop diameter of 9 cm, a 2-loop design with each loop having a diameter of 7 cm, and a 3-loop design with each loop having a diameter of 5 cm, our findings indicate that the 3-loop configuration achieves the optimal signal-to-noise ratio (SNR), surpassing other wireless arrays. Bilateral deployment of wireless coils further amplifies SNR, enabling superior visualization of TMJ structures, particularly with the 3-loop design. This cost-effective and comfortable solution, featuring a detunable design, eliminates the need for system parameter adjustments. The study indicates broad adaptability across MRI platforms, enhancing TMJ imaging for routine clinical diagnostics of TMDs.

A detunable wireless resonator insert for high-resolution TMJ MRI at 1.5 T.

MRI is essential for evaluating and diagnosing various conditions affecting the temporomandibular joint (TMJ) and surrounding structures, as it provides highly detailed images that enable healthcare professionals to assess the joints and surroundings in great detail. While commercial MRI scanners typically come equipped with basic receive coils, such as the head receive array, RF coils tailored for specialized applications like TMJ MRI must be obtained separately. Consequently, TMJ MRI scans are often conducted using the head receive array, yet this configuration proves suboptimal due to the lack of specialized coils. In this study, we introduce a simple, low-cost, and easy-to-reproduce wireless resonator insert to enhance the quality of TMJ MRI at 1.5 T. The wireless resonator shows a significant improvement in signal-to-noise ratio (SNR) and noticeably better imaging quality than the head array alone configuration in both phantom and in vivo images.

Detunable wireless Litzcage coil for human head MRI at 1.5 T.

Inductively coupled radiofrequency (RF) coils are an inexpensive and simple method to realize wireless RF coils in magnetic resonance imaging (MRI), which can significantly ease the MRI scan setup and improve patient comfort because they do not require bulky components such as cables, baluns, preamplifiers, and connectors. However, volume-type wireless coils are typically operated in transmit/receive mode because detuning such coils is much more challenging due to their complex structure and multiple resonant modes. Meanwhile, adding too many detuning circuits to a wireless coil would decrease the coil's quality factor, impair the signal-to-noise ratio, and increase the cost. In this work, we proposed, constructed, and tested a novel wireless volume coil based on the Litzcage design for 1.5-T head imaging. Being an inductively coupled coil, it has a much simpler structure, resulting in a lighter weight and less bulky design. Despite its simpler structure, it exhibits comparable imaging performance with a commercial receive array, providing an alternative to conventional wired coils with a high cost and complex structure. The unique figure-of-8 conductor pattern within the rungs ensures that the proposed wireless Litzcage can be efficiently detuned with minimal detuning circuits.

Miniature and flexible Bazooka balun for high-field MRI.

Flexible coils offer improved patient comfort and better imaging quality. However, rigid and bulky baluns in RF coils limit flexibility and manufacturing. A miniaturized and flexible balun design was proposed to address this issue. It replaced rigid components with an ultra-flexible rubber tube and a flexible coaxial capacitor. Simulations validated the concept, and bench tests confirmed its performance, including a measured common-mode rejection ratio of -15.8 dB. The flexible balun was integrated into a 4-channel coil array, evaluating impedance changes caused by the "hand effect." Compared to coils without the balun, the flexible coil with the proposed balun showed improved robustness in impedance matching and inter-element couplings. Transmit efficiency of the flexible coil with the balun was compared to coils without a balun and with a rigid, shielded cable trap. Results demonstrated that the proposed balun circuit maintained high transmit efficiency. Overall, the flexible balun design offers a promising solution for improving the flexibility and performance of RF coil arrays in MRI applications.

Dark band artifact in transcranial MR-guided focused ultrasound: Mechanism and mitigation with passive crossed wire antennas.

Current FDA-approved transcranial MR-guided focused ultrasound (tcMRgFUS) transducers cause a curved dark band in 3 T brain images that runs through midbrain targets of ablative treatments for essential tremor and other applications, and signal is reduced by at least 25% elsewhere in the brain. This limits the set of scans that can be performed to guide and assess the effects of treatment. An electromagnetic simulation study was performed to elucidate the mechanisms causing the dark band. Based on the results, a pair of passive antennas in a "propeller-beanie" configuration were designed to manipulate the reflected waves to avoid signal cancellation within the brain. The antennas were optimized and validated with in-vivo experiments and hydrophone measurements. The simulation study revealed that the dark band is caused by RF waves reflected from the transducer's ground plane, which cancel with incoming waves from the scanner's body coil. The passive antennas shifted the dark band out of the brain and increased transmit efficiency in the center of brain 2.3 times while improving field homogeneity by 50%. They also increased receive sensitivity and SNR in anatomic and temperature imaging. They caused no detectable distortion in hydrophone-measured focal pressure profiles. The conductive ground planes and coupling media used in tcMRgFUS and other piezoelectric FUS transducers interact with a 3 T scanner's RF fields to reduce transmit efficiency and SNR. For tcMRgFUS scenario, "propeller beanie" passive reflecting antennas alleviated these effects. This could make a broader set of imaging sequences available to guide tcMRgFUS treatment.

Implantable, Bioresorbable Radio Frequency Resonant Circuits for Magnetic Resonance Imaging.

Magnetic resonance imaging (MRI) is widely used in clinical care and medical research. The signal-to-noise ratio (SNR) in the measurement affects parameters that determine the diagnostic value of the image, such as the spatial resolution, contrast, and scan time. Surgically implanted radiofrequency coils can increase SNR of subsequent MRI studies of adjacent tissues. The resulting benefits in SNR are, however, balanced by significant risks associated with surgically removing these coils or with leaving them in place permanently. As an alternative, here the authors report classes of implantable inductor-capacitor circuits made entirely of bioresorbable organic and inorganic materials. Engineering choices for the designs of an inductor and a capacitor provide the ability to select the resonant frequency of the devices to meet MRI specifications (e.g., 200 MHz at 4.7 T MRI). Such devices enhance the SNR and improve the associated imaging capabilities. These simple, small bioelectronic systems function over clinically relevant time frames (up to 1 month) at physiological conditions and then disappear completely by natural mechanisms of bioresorption, thereby eliminating the need for surgical extraction. Imaging demonstrations in a nerve phantom and a human cadaver suggest that this technology has broad potential for post-surgical monitoring/evaluation of recovery processes.

Improving Specific Absorption Rate Efficiency and Coil Robustness of Self-Decoupled Transmit/Receive Coils by Elevating Feed and Mode Conductors.

Self-decoupling technology was recently proposed for radio frequency (RF) coil array designs. Here, we propose a novel geometry to reduce the peak local specific absorption rate (SAR) and improve the robustness of the self-decoupled coil. We first demonstrate that B1 is determined by the arm conductors, while the maximum E-field and local SAR are determined by the feed conductor in a self-decoupled coil. Then, we investigate how the B1, E-field, local SAR, SAR efficiency, and coil robustness change with respect to different lift-off distances for feed and mode conductors. Next, the simulation of self-decoupled coils with optimal lift-off distances on a realistic human body is performed. Finally, self-decoupled coils with optimal lift-off distances are fabricated and tested on the workbench and MRI experiments. The peak 10 g-averaged SAR of the self-decoupled coil on the human body can be reduced by 34% by elevating the feed conductor. Less coil mismatching and less resonant frequency shift with respect to loadings were observed by elevating the mode conductor. Both the simulation and experimental results show that the coils with elevated conductors can preserve the high interelement isolation, B1+ efficiency, and SNR of the original self-decoupled coils.

Low-cost inductively coupled stacked wireless RF coil for MRI at 3 T.

Inductively coupled RF coils are an inexpensive and simple method to realize wireless RF coils in MRI. They are low cost and can greatly ease the MR scan setup and improve patient comfort, since they do not require bulky components such as cables, baluns, preamplifiers, and connectors. Previous works have typically used single-layer loops as wireless coils. In this work, we present a novel wireless coil, where two loops are stacked and decoupled with a shared capacitor. We found that such a stacked structure could increase the coil efficiency and SNR. Compared with the single-layer wireless coil, both electromagnetic simulation and MR experiment results demonstrate that the stacked wireless coil has a considerable SNR improvement of approximately 35%.

RF shielding designs for birdcage coils for preclinical MRI at 9.4 T.

Birdcage coils are widely used in preclinical MRI as they perform well, allow for quadrature drive, and can provide a homogeneous transmit field. Unlike in larger bore scanners, an RF shield is essential to avoid strong cross-talk with gradient coils that are in close proximity. However, gradient switching induces eddy currents that heat the shield and coil and impair the temporal signal-to-noise ratio (tSNR). The motivation of this study is to investigate the performance of different designs of RF shields on a birdcage coil used for high resolution functional MRI of small primates at 9.4 T. We found the choice of materials for RF shields significantly affected ghosting and tSNR in fMRI scans. Both ultrathin foils and a slotted pattern reduce eddy currents and improve imaging quality. Our results also demonstrate that a 9-um-thick copper foil is sufficiently thin to reduce the eddy current effects for high-resolution fMRI scans and there is no need for high-cost 4-um-thick foil. For slotted shields, our results demonstrate that the number of slots should be carefully considered, and an excessive number of slots can lead to a lower SNR and tSNR. We believe the results from this study can be used as a reference to design future RF coil shields selection for preclinical scanners.

Bench to bore ramifications of inter-subject head differences on RF shimming and specific absorption rates at 7T.

PURPOSE: This study shows how inter-subject variation over a dataset of 72 head models results in specific absorption rate (SAR) and B1+ field homogeneity differences using common shim scenarios. METHODS: MR-CT datasets were used to segment 71 head models into 10 tissue compartments. These head models were affixed to the shoulders and neck of the virtual family Duke model and placed within an 8 channel transmit surface-loop array to simulate the electromagnetic fields of a 7T imaging experiment. Radio frequency (RF) shimming using the Gerchberg-Saxton algorithm and Circularly Polarized shim weights over the entire brain and select slices of each model was simulated. Various SAR metrics and B1+ maps were calculated to demonstrate the contribution of head variation to transmit inhomogeneity and SAR variability. RESULTS: With varying head geometries the loading for each transmit loop changes as evidenced by changes in S-parameters. The varying shim conditions and head geometries are shown to affect excitation uniformity, spatial distributions of local SAR, and SAR averaging over different pulse sequences. The Gerchberg-Saxton RF shimming algorithm outperforms circularly polarized shimming for all head models. Peak local SAR within the coil most often occurs nearest the coil on the periphery of the body. Shim conditions vary the spatial distribution of SAR. CONCLUSION: The work gives further support to the need for fast and more subject specific SAR calculations to maintain safety. Local SAR10g is shown to vary spatially given shim conditions, subject geometry and composition, and position within the coil.

On the design and manufacturing of miniaturized microstripline power splitters for driving multicoil transmit arrays with arbitrary ratios at 7 T.

The purpose of the current study was to implement unequal microstrip power splitters for parallel transmission at 7 T that are optimized for size and loss and that can be configured for a wide range of power ratios. The splitters will enable the use of more transmit coils without a corresponding increase in the number of transmit channels or amplifiers to control specific absorption rate, shorten RF pulses, and shim inhomogeneous RF fields. Wilkinson unequal power splitters based on a novel microstrip network design were optimized to minimize their size under 8 cm in length and 9 cm in width, enabling them to be included in coil housing or cascaded in multiple stages. Splitters were designed and constructed for a wide range of output power ratios at 298 MHz. Simulations and bench tests were performed for each ratio, and a methodology was established to adapt the designs to other ratios and frequencies. The designs and code are open source and can be reproduced as is or reconfigured. The single-stage designs achieved good matches and isolations between output ports (worst isolation -15.9 dB, worst match -15.1 dB). A two-stage cascaded (one input to four outputs) power splitter with 1:2.5, 1:10, 1:3, and 1:6 ratio outputs was constructed. The worst isolation between output ports was -19.7 dB in simulation and the worst match of the three ports was -17.8 dB. The measured ratios for one- and two-stage boards were within 10% of the theoretical ratios. The power-handling capability of the smallest trace was approximately 70 W. Power loss for the one- and two-stage boards ranged from 1% to 3% in simulation compared with 5.1% to 7.2% on the bench. It was concluded that Wilkinson unequal microstrip power splitters can be implemented with a small board size (low height) and low loss, and across a wide range of output power ratios. The splitters can be cascaded in multiple stages while maintaining the expected ratios and low loss. This will enable the construction of large fixed transmit array-compression matrices with low loss.

High-Density MRI RF Arrays Using Mixed Dipole Antennas and Microstrip Transmission Line Resonators.

OBJECTIVE: High-density multi-coil arrays are desirable in MRI because they provide high signal-to-noise ratios (SNR), enable highly accelerated parallel imaging, and provide more uniform transmit fields at high fields. For high-density arrays such as a head array with 16 elements in a row, popular dipole antennas and microstrip transmission line (also referred to as "MTL") resonators both have severe coupling issues. METHODS: In this work, we show that dipoles and MTLs have naturally low coupling and propose a novel array configuration in which they are interleaved. We first show the electromagnetic (EM) coupling between a single dipole and a single MTL across different separations in bench tests. Then we validate and analyze this through EM simulations. Finally, we construct a 16-channel mixed dipole and MTL array and evaluate its performance on the bench and through MRI experiments. RESULTS: Without any decoupling treatments, the worst coupling between a dipole and an MTL was only -15.8 dB when their center-to-center distance was 4.7 cm (versus -5.4 dB for two dipole antennas and -6.0 dB for two MTL resonators). Even in a dense 16-channel mixed array, the inter-element isolation among all elements was better than -14 dB. CONCLUSION: This study reveals, analyzes, and validates a novel finding that the popular dipole antennas and MTL resonators used in ultrahigh field MRI have naturally low coupling. SIGNIFICANCE: These findings will simplify the construction of high-density arrays, enable new applications, and benefit imaging performance in ultrahigh field MRI.

Resistor-free and one-board-fits-all ratio adjustable power splitter for add-on RF shimming in high field MRI.

Ratio adjustable power splitter (RAPS) circuits were recently proposed for add-on RF shimming. Previous RAPSs split the input RF signal with a Wilkinson splitter or 50-Ω-terminated hybrid coupler into two branches, delay these two signals with cable/microstrip line phase shifters, and recombine them with another hybrid coupler. They require resistors to provide high output isolation and a cable/microstrip line library to realize desired splitting ratios. Here we propose a novel resistor-free RAPS circuit in which the Wilkinson splitter/50-Ω-terminated hybrid is replaced with a resistor-free T-junction splitter. A novel sliding mechanism was employed to further combine the T-junction's output arms with subsequent phase shifters and realize a one-board-fits-all design. The resistor-free RAPS was theoretically analyzed, simulated, and validated on workbench and MRI experiments. The resistor-free RAPS's splitting ratio has a tan/cot dependence on the phase/length difference between the T-junction output arms. The ratio can be continuously adjusted to any value by sliding the input arm without additional cable/microstrip libraries, largely saving time and effort when determining the best RF weights in practice. The fabricated resistor-free RAPS has a compact size, excellent input impedance matching, and a low insertion loss. Potential safety concerns caused by unwanted power dissipation on RF resistors are eliminated. The simulation and MRI experiments demonstrated that the resistor-free RAPS functions well on a widely-used Tx coil.

Dual-Tuned Lattice Balun for Multi-Nuclear MRI and MRS.

Balun or trap circuits are critical components for suppressing common-mode currents flowing on the outer conductors of coaxial cables in RF coil systems for Magnetic Resonance Imaging (MRI) and Magnetic Resonance Spectroscopy (MRS). Common-mode currents affect coils' tuning and matching, induce losses, pick up extra noise from the surrounding environment, lead to undesired cross-talk, and cause safety concerns in animal and human imaging. First proposed for microwave antenna applications, the Lattice balun has been widely used in MRI coils. It has a small footprint and can be easily integrated with coil tuning/matching circuits. However, the Lattice balun is typically a single-tuned circuit and cannot be used for multi-nuclear MRI and MRS with two RF frequencies. This work describes a dual-tuned Lattice balun design that is suitable for multi-nuclear MRI/MRS. It was first analyzed theoretically to derive component values. RF circuit simulations were then performed to validate the theoretical analysis and provide guidance for practical construction. Based on the simulation results, a dual-tuned balun circuit was built for 7T 1H/23Na MRI and bench tested. The fabricated dual-tuned balun exhibits superior performance at the Larmor frequencies of both 1H and 23Na, with less than 0.15 dB insertion loss and better than 17 dB common-mode rejection ratio at both frequencies.

Minimal artifact actively shimmed metallic needles in MRI.

PURPOSE: Signal voids caused by metallic needles pose visualization and monitoring challenges in many MRI applications. In this work, we explore a solution to this problem in the form of an active shim insert that fits inside a needle and corrects the field disturbance (ΔB0 ) caused by the needle outside of it. METHODS: The ΔB0 induced by a 4 mm outside-diameter titanium needle at 3T is modeled and a two-coil orthogonal shim set is designed and fabricated to shim the ΔB0 . Signal recovery around the needle is assessed in multiple orientations in a water phantom with four different pulse sequences. Phase stability around the needle is assessed in an ex-vivo porcine tissue dynamic gradient echo experiment with and without shimming. Additionally, heating of the shim insert is assessed under 8 min of continuous operation with 1A current and concurrent imaging. RESULTS: An average recovery of ~63% of lost signal around the needle across orientations is shown with active shimming with a maximum current of 1.172 A. Signal recovery and correction of the underlying ΔB0 is shown to be independent of imaging sequence. Needle-induced phase gradients outside the perceptible signal void are also minimized with active shimming. Temperature rise of up to 0.9° Celsius is noted over 8 min of continuous 1A active shimming operation. CONCLUSION: A sequence independent method for minimization of metallic needle induced signal loss using an active shim insert is presented. The method has potential benefits in a range of qualitative and quantitative interventional MRI applications.

Design and construction of an interchangeable RF coil system for rodent spinal cord MR imaging at 9.4 T.

Rodent models of spinal cord injury (SCI) have been widely used in pre-clinical studies. Injuries may occur at different levels of the lumbar and thoracic cord, and the number of segments injured and their depths may vary along the spine. It is thereby challenging to build one universal RF coil that exhibits optimal performance for all spinal cord imaging applications, especially in an animal scanner with small in-bore space and limited hardware configurations. We developed an interchangeable RF coil system for a 9.4 T small animal MRI scanner, in which the users can select an optimal coil specialized for imaging specific parts of a rat spine. We also developed the associated animal management device for immobilization and positioning. The whole system allows ease of RF coil exchange, animal fixation, and positioning, and thus reduces the animal preparation time before the MRI scan significantly. Compared to a commercial general-purpose 2-cm-diameter coil that was used in our previous studies, the specialized coil optimized for Sprague-Dawley rat lumbar spinal cord imaging exhibits up to 2.4 times SNR improvement.

Hybrid-pair ratio adjustable power splitters for add-on RF shimming and array-compressed parallel transmission.

PURPOSE: A ratio adjustable power splitter (RAPS) circuit was recently proposed for add-on RF shimming and array-compressed parallel transmission. Here we propose a new RAPS circuit design based on off-the-shelf components for improved performance and manufacturability. THEORY AND METHODS: The original RAPS used a pair of home-built Wilkinson splitter and hybrid coupler connected by a pair of connectorized coaxial cables. Here we propose a new hybrid-pair RAPS (or HP-RAPS) circuit that replaces the home-built circuits with two commercially available hybrid couplers and replaces connectorized cables with interchangeable microstrip lines. We derive the relation between the desired splitting ratio and the required phase shifts for HP-RAPS and investigate how to generate arbitrary splitting ratios using paired meandering and straight lines. Several HP-RAPSs with different splitting ratios were fabricated and tested on the workbench and MRI experiments. RESULTS: The splitting ratio of an HP-RAPS circuit has a tan or cot dependence on the meandering line's additional length compared to the straight line. The fabricated HP-RAPSs exhibit accurate splitting ratios as expected (<4% deviations) and generate transmit fields that well agree with predicted fields. They also demonstrated a low insertion loss of 0.33 dB, high output isolation of -26 dB, and acceptable impedance matching of -16 dB. CONCLUSION: A novel HP-RAPS circuit was developed and implemented. It is easy-to-fabricate/reproduce with minimal expertise. It also preserves the features of the original RAPS circuit (ratio-adjustable, small footprint, etc.) with lower insertion loss.

Sensitivity and specificity of CEST and NOE MRI in injured spinal cord in monkeys.

PURPOSE: The sensitivity and accuracy of chemical exchange saturation transfer (CEST) and nuclear Overhauser enhancement (NOE) effects for assessing injury-associated changes in cervical spinal cords were evaluated in squirrel monkeys. Multiple interacting pools of protons, including one identified by an NOE at -1.6 ppm relative to water (NOE(-1.6)), were derived and quantified from fitting proton Z-spectra. The effects of down-sampled data acquisitions and corrections for non-specific factors including T1, semi-solid magnetization transfer, and direct saturation of free water (DS), were investigated. The overall goal is to develop a protocol for rapid data acquisition for assessing the molecular signatures of the injured spinal cord and its surrounding regions. METHODS: MRI scans were recorded of anesthetized squirrel monkeys at 9.4 T, before and after a unilateral dorsal column sectioning of the cervical spinal cord. Z-spectral images at 51 different RF offsets were acquired. The amplitudes of CEST and NOE effects from multiple proton pools were quantified using a six-pool Lorenzian fitting of each Z-spectrum (MTRmfit). In addition, down-sampled data using reduced selections of RF offsets were analyzed and compared. An apparent exchange-dependent relaxation (AREXmfit) method was also used to correct for non-specific factors in quantifying regional spectra around lesion sites. RESULTS: The parametric maps from multi-pool fitting using the complete sampling data (P51e) detected unilateral changes at and around the injury. The maps derived from selected twofold down-sampled data with appropriate interpolation (P26sI51) revealed quite similar spatial distributions of different pools as those obtained using P51e at each resonance shift. Across 10 subjects, both data acquisition schemes detected significant decreases in NOE(-3.5) and NOE(-1.6) and increases in DS(0.0) and CEST(3.5) at the lesion site relative to measures of the normal tissues before injury. AREXmfit of cysts and other abnormal tissues at and around the lesion site also exhibited significant changes, especially at 3.5, -1.6 and -3.5 ppm RF offsets. CONCLUSION: These results confirm that a reduced set of RF offsets and down sampling are adequate for CEST imaging of injured spinal cord and allow shorter imaging times and/or permit additional signal averaging. AREXmfit correction improved the accuracy of CEST and NOE measures. The results provide a rapid (~13 mins), sensitive, and accurate protocol for deriving multiple NOE and CEST effects simultaneously in spinal cord imaging at high field.

Optimization of a quadrature birdcage coil for functional imaging of squirrel monkey brain at 9.4T.

A quadrature transmit/receive birdcage coil was optimized for squirrel monkey functional imaging at the high field of 9.4 T. The coil length was chosen to gain maximum coil efficiency/signal-to-noise ratio (SNR) and meanwhile provide enough homogenous RF field in the whole brain area. Based on the numerical simulation results, a 16-rung high-pass birdcage coil with the optimal length of 9 cm was constructed and evaluated on phantom and in vivo experiments. Compared to a general-purpose non-optimized coil, it exhibits approximately 25% in vivo SNR improvement. In addition to the volume coil, details about how to design and construct the associated animal preparation system were provided.

k-Space Domain Parallel Transmit Pulse Design.

PURPOSE: To accelerate the design of (under- or oversampled) multidimensional parallel transmission pulses. METHODS: A k-space domain parallel transmission pulse design algorithm was proposed that produces a sparse matrix relating a complex-valued target excitation pattern to the pulses that produce it, and can be finely parallelized. The algorithm was applied in simulations to the design of 3D SPINS pulses for inner volume excitation in the brain at 7 Tesla. It was characterized in terms of the dependence of computation time, excitation error, and required memory on algorithm parameters, and it was compared to an iterative spatial domain pulse design method in terms of computation time, excitation error, Gibbs ringing, and ability to compensate off-resonance. RESULTS: The proposed algorithm achieved approximately 80% faster pulse design compared to the spatial domain method with the same number of parallel threads, with the tradeoff of increased excitation error and RMS RF amplitude. It reduced the memory required to store the design matrix by 99% compared to a full matrix solution. Even with a coarse design grid, the algorithm produced patterns that were free of Gibbs ringing. It was similarly sensitive to k-space undersampling as the spatial domain method, and was similarly capable of compensating for off-resonance. CONCLUSIONS: The proposed k-space domain algorithm accelerates and finely parallelizes parallel transmission pulse design, with a modest tradeoff of excitation error and RMS RF amplitude.