A novel method for highly linear gradient coil design based on stream function.

BACKGROUND: Magnetoencephalography (MEG) and magnetic resonance imaging (MRI) are non-invasive imaging techniques that offer effective means for disease diagnosis. A more straightforward and optimized method is presented for designing gradient coils which are pivotal parts of the above imaging systems. PURPOSE: A novel design method based on stream function combining an optimization algorithm is proposed to obtain highly linear gradient coil. METHODS: Two-dimensional Fourier expansion of the current field on the surface where the coil is located and the equipotential line of the expansion term superposition according to the number of turns of the coil are used to represent the coil shape. Particle swarm optimization is utilized to optimize the coil shape while linearity and field uniformity are used as parameters to evaluate the coil performance. Through this method, the main parameters such as input current distribution region, coil turns, desired magnetic field strength, expansion order and iteration times can be combined in a given solution space to optimize coil design. RESULTS: Simulation results show that the maximum linearity spatial deviation of the designed bi-planar x-gradient coil compared with that of target field method is reduced from 14% to 0.54%, and that of the bi-planar z-gradient coil is reduced from 8.98% to 0.52%. Similarly, that of the cylindrical x-gradient coil is reduced from 2% to 0.1%, and that of the cylindrical z-gradient coil is reduced from 0.87% to 0.45%. The similar results are found in the index of inhomogeneity error. Moreover, it has also been verified experimentally that the result of measured magnetic field is consist with simulated result. CONCLUSIONS: The proposed method provides a straightforward way that simplifies the design process and improves the linearity of designed gradient coil, which could be beneficial to realize better magnetic field in engineering applications.

Experimental validation of a PNS-optimized whole-body gradient coil.

PURPOSE: Peripheral nerve stimulation (PNS) limits the usability of state-of-the-art whole-body and head-only MRI gradient coils. We used detailed electromagnetic and neurodynamic modeling to set an explicit PNS constraint during the design of a whole-body gradient coil and constructed it to compare the predicted and experimentally measured PNS thresholds to those of a matched design without PNS constraints. METHODS: We designed, constructed, and tested two actively shielded whole-body Y-axis gradient coil winding patterns: YG1 is a conventional symmetric design without PNS-optimization, whereas YG2's design used an additional constraint on the allowable PNS threshold in the head-imaging landmark, yielding an asymmetric winding pattern. We measured PNS thresholds in 18 healthy subjects at five landmark positions (head, cardiac, abdominal, pelvic, and knee). RESULTS: The PNS-optimized design YG2 achieved 46% higher average experimental thresholds for a head-imaging landmark than YG1 while incurring a 15% inductance penalty. For cardiac, pelvic, and knee imaging landmarks, the PNS thresholds increased between +22% and +35%. For abdominal imaging, PNS thresholds did not change significantly between YG1 and YG2 (-3.6%). The agreement between predicted and experimental PNS thresholds was within 11.4% normalized root mean square error for both coils and all landmarks. The PNS model also produced plausible predictions of the stimulation sites when compared to the sites of perception reported by the subjects. CONCLUSION: The PNS-optimization improved the PNS thresholds for the target scan landmark as well as most other studied landmarks, potentially yielding a significant improvement in image encoding performance that can be safely used in humans.

Designing gradient coils with the shape derivative and the closed B-spline curves.

This study proposes a versatile and efficient optimisation method for discrete coils that induce a magnetic field by their steady currents. The prime target is gradient coils for MRI (Magnetic Resonance Imaging). The derivative (gradient) of the z-component the magnetic field, which is calculated by the Biot-Savart's law, with respect to the z-coordinate in the Cartesian xyz coordinate system is considered as the objective function. Then, the derivative of the objective function with respect to a change of coils in shape is formulated according to the concept of shape optimisation. The resulting shape derivative (as well as the Biot-Savart's law) is smoothly discretised with the closed B-spline curves. In this case, the control points (CPs) of the curves are naturally selected as the design variables. As a consequence, the shape derivative is discretised to the sensitivities of the objective function with respect to the CPs. Those sensitivities are available to solve the present shape-optimisation problem with a certain gradient-based nonlinear-programming solver. The numerical examples exhibit the mathematical reliability, computational efficiency, and engineering applicability of the proposed methodology based on the shape derivative/sensitivities and the closed B-spline curves.

Multi-target field control for matrix gradient coils.

OBJECTIVE: Conventional single-target field control for matrix gradient coils will add control complexity in MRI spatial encoding, such as designing specialized fields and sequences. This complexity can be reduced by multi-target field control, which is realized by optimizing the coil structure according to target fields. METHODS: Based on the principle of multi-target field control, the X, Y and Z gradient fields can be set as target fields, and all coil elements can then be divided into three groups to generate these fields. An improved simulated annealing algorithm is proposed to optimize the coil element distribution of each group to generate the corresponding target field. In the improved simulated annealing process, two swapping modes are presented, and randomly selected with certain probabilities that are set to 0.25, 0.5 and 0.75, respectively. The flexibility of the final designed structure is demonstrated by a spherical harmonic basis up to the full second order with single-target field control. An experimental platform is built to measure the gradient fields generated by the designed structure with multi-target target control. RESULTS: With three probabilities of swapping modes, three similar coil element distributions are optimized, and their maximum magnetic field errors for generating X, Y and Z gradients are all below 5%. The structure selected for the final design is the one with a probability of 0.75, considering the coil performance and structural symmetry. The maximum error for all target fields generated by single-target field control is also below 5%. The experimental results show that the measured gradient fields along the axes have enough strength and high linearity. CONCLUSIONS: With the proposed improved simulated annealing algorithm and swapping modes, multi-target field control for matrix gradient coils is verified and achieved in this study by optimizing the coil element distribution. Moreover, this study provides a solution to simplify the complexity of controlling the matrix gradient coil in spatial encoding.

Nonlinear Gradient Field Mapping Using a Spherical Grid Phantom for 3 and 7 Tesla MR Imaging Systems Equipped with High-performance Gradient Coils.

Recent high-performance gradient coils are fabricated mainly at the expense of spatial linearity. In this study, we measured the spatial nonlinearity of the magnetic field generated by the gradient coils of two MRI systems with high-performance gradient coils. The nonlinearity of the gradient fields was measured using 3D gradient echo sequences and a spherical phantom with a built-in lattice structure. The spatial variation of the gradient field was approximated to the 3rd order polynomials. The coefficients of the polynomials were calculated using the steepest descent method. The geometric distortion of the acquired 3D MR images was corrected using the polynomials and compared with the 3D images corrected using the harmonic functions provided by the MRI venders. As a result, it was found that the nonlinearity correction formulae provided by the vendors were insufficient and needed to be verified or corrected using a geometric phantom such as used in this study.

A power efficient actively shielded two-channel transverse MRI gradient coil numerical design.

Large and fast electrical current pulses are typically applied to conventional single-channel transverse MR gradient coils. However, these pulses result in a significant amount of power losses and heating of the coils. Previously, we presented a cylindrical multi-channel Z-gradient coil design that has better power efficiency compared to the single-channel design. In this work, we further investigate the DC power advantage for a two-channel actively-shielded transverse cylindrical gradient coil over the single-channel design. The conventional coil quadrants are radially divided into two sections, one for each channel, for both the primary and shielding surfaces. The symmetric inner sections of both the primary and shielding coils are assigned to the first channel, while the outer enclosing sections for each quadrant are assigned to the second channel. Discrete wire design is employed, where quasi-elliptic functions are used to parameterize the turns of each section. The coil geometric parameters, section size, number of turns, and turn locations are used as the design optimization parameters. The coils are optimized to maximize the coil's efficiency while keeping the linearity error less than 10% and the shielding ratio above 85%. The design procedure is employed to design both the single and two-channel transverse gradient coils for comparison. Eleven different two-channel configurations having different section sizes were investigated. Results show that the power used to drive the most power-efficient two-channel coil is less than that of the single-channel design by ∼25%. Moreover, the two-channel configuration showed slightly better shielding efficiency.

An integrated target field framework for point-of-care halbach array low-field MRI system design.

OBJECTIVE: Low-cost low-field point-of-care MRI systems are used in many different applications. System design has correspondingly different requirements in terms of imaging field-of-view, spatial resolution and magnetic field strength. In this work an iterative framework has been created to design a cylindrical Halbach-based magnet along with integrated gradient and RF coils that most efficiently fulfil a set of user-specified imaging requirements. METHODS: For efficient integration, target field methods are used for each of the main hardware components. These have not been used previously in magnet design, and a new mathematical model was derived accordingly. These methods result in a framework which can design an entire low-field MRI system within minutes using standard computing hardware. RESULTS: Two distinct point-of-care systems are designed using the described framework, one for neuroimaging and the other for extremity imaging. Input parameters are taken from literature and the resulting systems are discussed in detail. DISCUSSION: The framework allows the designer to optimize the different hardware components with respect to the desired imaging parameters taking into account the interdependencies between these components and thus give insight into the influence of the design choices.

Peripheral nerve stimulation informed design of a high-performance asymmetric head gradient coil.

PURPOSE: Peripheral nerve stimulation (PNS) limits the image encoding performance of both body gradient coils and the latest generation of head gradients. We analyze a variety of head gradient design aspects using a detailed PNS model to guide the design process of a new high-performance asymmetric head gradient to raise PNS thresholds and maximize the usable image-encoding performance. METHODS: A novel three-layer coil design underwent PNS optimization involving PNS predictions of a series of candidate designs. The PNS-informed design process sought to maximize the usable parameter space of a coil with <10% nonlinearity in a 22 cm region of linearity, a relatively large inner diameter (44 cm), maximum gradient amplitude of 200 mT/m, and a high slew rate of 900 T/m/s. PNS modeling allowed identification and iterative adjustment of coil features with beneficial impact on PNS such as the number of winding layers, shoulder accommodation strategy, and level of asymmetry. PNS predictions for the final design were compared to measured thresholds in a constructed prototype. RESULTS: The final head gradient achieved up to 2-fold higher PNS thresholds than the initial design without PNS optimization and compared to existing head gradients with similar design characteristics. The inclusion of a third intermediate winding layer provided the additional degrees of freedom necessary to improve PNS thresholds without significant sacrifices to the other design metrics. CONCLUSION: Augmenting the design phase of a new high-performance head gradient coil by PNS modeling dramatically improved the usable image-encoding performance by raising PNS thresholds.

Overview of Methods for Noise and Heat Reduction in MRI Gradient Coils.

Magnetic resonance imaging (MRI) gradient coils produce acoustic noise due to coil conductor vibrations caused by large Lorentz forces. Accurate sound pressure levels and modeling of heating are essential for the assessment of gradient coil safety. This work reviews the state-of-the-art numerical methods used in accurate gradient coil modeling and prediction of sound pressure levels (SPLs) and temperature rise. We review several approaches proposed for noise level reduction of high-performance gradient coils, with a maximum noise reduction of 20 decibels (dB) demonstrated. An efficient gradient cooling technique is also presented.

Characterisation of a split gradient coil design induced systemic imaging artefact on 0.35 T MR-linac systems.

Objective. The aim of this work was to highlight and characterize a systemic 'star-like' artefact inherent to the low field 0.35 T MRIdian MR-linac system, a magnetic resonance guided radiotherapy device. This artefact is induced by the original split gradients coils design. This design causes a surjection of the intensity gradient inZ(or head-feet) direction. This artefact appears on every sequence with phase encoding in the head-feet direction.Approach. Basic gradient echo sequence and clinical mandatory bSSFP sequence were used. Three setups using manufacturer provided QA phantoms were designed: two including the linearity control grid used for the characterisation and a third including two homogeneity control spheres dedicated to the artefact management in a more clinical like situation. The presence of the artefact was checked in four different MRidian sites. The tested parameters based on the literature were: phase encoding orientation, slab selectivity, excitation bandwidth (BWRF), acceleration factor (R) and phase/slab oversampling (PO/SO).Main results. The position of this artefact is constant and reproducible over the tested MRIdian sites. The typical singularity saturated dot or star is visible even with the 3D slab-selection enabled. A management is proposed by decreasing the BWRF, theRin head-feet direction and increasing the PO/SO. The oversampling can be optimized using a formula to anticipate the location of artefact in the field of view.Significance. The star-like artefact has been well characterised. A manageable solution comes at the cost of acquisition time. Observed in clinical cases, the artefact may degrade the images used for the RT planning and repositioning during the treatment unless corrected.

A z-gradient array coil with a dedicated active-shielded array coil for MRI.

PURPOSE: An array-based z-gradient coil with a set of programmable power amplifiers can outperform a conventional z-gradient coil and make it highly customizable with a broader range of tunable features. METHODS: A dynamically adjustable imaging volume can be achieved using a pair of independent arrays and a modified optimization procedure based on analytic equations. Two modes of operation are provided: (a) standard mode that resembles a conventional coil; (b) advanced mode, where all performance parameters can be adjusted employing a controllable feeding mechanism. Commercial software is used to demonstrate the validity and feasibility of the proposed coil. RESULTS: Primary and shield array diameters are 24 and 30 cm, both of which comprise 12 bundles of 10 turns copper wires. Maximum feeding voltage/current is 250 V/100 A for all array elements. Four distinct magnetic profiles are provided: (a) conventional profile with 140 mm diameter spherical region of interest, 120 mT/m gradient, and up to 4500 T/m/s slew rate; (b) profile of 200 mT/m, 70 mm region of interest, and up to 6900 T/m/s slew rate; (c) 60 mm axially shifted 70 mm region of interest with 120 mT/m strength and 3600 T/m/s slew rate; and (d) profile of 370 mT/m, 120 mm region of interest, and 3700 T/m/s slew rate when the active shield is reverse fed. CONCLUSION: By using an active-shielded gradient array coil, the magnetic field profile of the imaging volume can be adjusted dynamically, and it can provide new features and a wide range of field profiles for diverse applications in MRI.

Systematic Dimensional Analysis of the Scaling Relationship for Gradient and Shim Coil Design Parameters.

PURPOSE: To demonstrate systematic, linear algebra-based, dimensional analysis to derive a scaling relationship among the design parameters of MRI gradient and harmonic shim coils. THEORY AND METHODS: The dimensions of five physical quantities relevant for gradient coil design (inductance, gradient amplitude, inner diameter [ d$$ d $$ ], current, and the permeability of free space) were decomposed into fundamental units, and their exponents were arranged into a dimensional matrix. The resulting set of homogenous equations was solved using standard linear algebraic methods. Inclusion of the number of turns as an additional unit yielded a 5 × 5 dimensional matrix with a unique, nontrivial solution. The analysis was extended to harmonic shim coils. The gradient coil scaling relationship was compared with data from 24 published gradient coil sets. RESULTS: Only when the unit of turns was included did the linear algebra-based analysis uniquely produce the known scaling relationship that gradient inductance is proportional to gradient efficiency squared times d5$$ {d}^5 $$ . By applying the same methodology to an lth order shim coil, a novel result is obtained: Shim inductance is proportional to its efficiency squared times d2l+3$$ {d}^{2l+3} $$ . The predicted power-law relationship between inductance-normalized gradient efficiency and the diameter accounted for > 92% of the efficiency variation of the surveyed gradient coils. A dimensionless parameter is proposed as an intrinsic figure-of-merit of gradient coil efficiency. CONCLUSION: Systematic application of linear algebra-based dimensional analysis can provide new insight in gradient and shim coil design by revealing fundamental scaling relations and helping to guide the design and comparison of coils with different diameters.

Accelerating Brain Imaging Using a Silent Spatial Encoding Axis.

PURPOSE: To characterize the acceleration capabilities of a silent head insert gradient axis that operates at the inaudible frequency of 20 kHz and a maximum gradient amplitude of 40 mT/m without inducing peripheral nerve stimulation. METHODS: The silent gradient axis' acquisitions feature an oscillating gradient in the phase-encoding direction that is played out on top of a cartesian readout, similarly as done in Wave-CAIPI. The additional spatial encoding fills k-space in readout lanes allowing for the acquisition of fewer phase-encoding steps without increasing aliasing artifacts. Fully sampled 2D gradient echo datasets were acquired both with and without the silent readout. All scans were retrospectively undersampled (acceleration factors R = 1 to 12) to compare conventional SENSE acceleration and acceleration using the silent gradient. The silent gradient amplitude and the readout bandwidth were varied to investigate the effect on artifacts and g-factor. RESULTS: The silent readout reduced the g-factor for all acceleration factors when compared to SENSE acceleration. Increasing the silent gradient amplitude from 31.5 mT/m to 40 mT/m at an acceleration factor of 10 yielded a reduction in the average g-factor (gavg ) from 1.3 ± 0.14 (gmax  = 1.9) to 1.1 ± 0.09 (gmax  = 1.6). Furthermore, reducing the number of cycles increased the readout bandwidth and the g-factor that reached gavg  = 1.5 ± 0.16 for a readout bandwidth of 651 Hz/pixel and an acceleration factor of R = 8. CONCLUSION: A silent gradient axis enables high acceleration factors up to R = 10 while maintaining a g-factor close to unity (gavg  = 1.1 and gmax  = 1.6) and can be acquired with clinically relevant readout bandwidths.

Analysis of coil element distribution and dimension for matrix gradient coils.

OBJECTIVE: The goal of this work is to analyze the influence of the distributions and dimensions of the coil elements and to present a method for improving the performance of the matrix gradient coil. METHODS: Three typical models (five structures in total) are presented, and a double-layer biplanar matrix gradient coil is used to install coil elements. Two metrics, namely, the role of coil elements and mutual inductance between coil elements, are proposed to assess the performance of coil systems. An optimization approach to design matrix gradient coils is introduced based on analyzing the distributions and dimensions of coil elements. The flexibility of the magnetic field generation of the designed coil structure is demonstrated by generating full third-order spherical harmonic fields and different oblique gradient fields. RESULTS: Matrix gradient coils with suitable distributions are capable of generating target magnetic fields. The role of coil elements quantitatively illustrates that the coil elements have different impacts on generating magnetic fields. Increasing the coil element dimension within a certain range can reduce the mutual inductance between coil elements and improve the performance of the coil system. The designed novel double-layer biplanar matrix gradient coil achieves an acceptable performance in generating different magnetic fields. CONCLUSIONS: The proposed metrics can provide theoretical support for designing matrix gradient coils and evaluating their performance. The role of coil elements contributes to analyzing the distributions of coil elements to decrease the number of coil elements and power amplifiers. The mutual inductance between coil elements can be a reference for designing the dimensions of coil elements.

Analysis on matrix gradient coil modeling.

OBJECTIVE: The current distribution of the matrix gradient coil can be optimized via matrix gradient coil modeling to reduce the Lorentz force on individual coil elements. Two different modeling approaches are adopted, and their respective characteristics are summarized. METHODS: The magnetic field at each coil element is calculated. Then, the Lorentz force, torque, and deformation of the energized coil element in the magnetic field are derived. Two modeling approaches for matrix gradient coil, namely, optimizing coil element current (OCEC) modeling and optimizing coil element Lorentz force (OCEF) modeling, are proposed to reduce the Lorentz force on individual coil elements. The characteristics of different modeling approaches are compared by analyzing the influence of the weighting factor on the performance of the coil system. The current, Lorentz force, torque, and deformation results calculated via different modeling approaches are also compared. RESULTS: Coil element magnetic fields are much weaker than the main magnetic field, and their effect can be ignored. Matrix gradient coil modeling with different regularization terms can help to decrease the current and Lorentz force of coil elements. The performance of the coil system calculated via different modeling approaches is similar when suitable weighting factors are adopted. The two modeling approaches, OCEC and OCEF, can better reduce the maximum current and Lorentz force on individual coil elements compared with the traditional modeling approach. CONCLUSIONS: Different modeling approaches can help to optimize the current distribution of coil elements and satisfy various requirements while maintaining the performance of the coil system.

A contribution to MRI safety testing related to gradient-induced heating of medical devices.

PURPOSE: To theoretically investigate the feasibility of a novel procedure for testing the MRI gradient-induced heating of medical devices and translating the results into clinical practice. METHODS: The concept of index of stress is introduced by decoupling the time waveform characteristics of the gradient field signals from the field spatial distribution within an MRI scanner. This index is also extended to consider the anisotropy of complex bulky metallic implants. Merits and drawbacks of the proposed index of stress are investigated through virtual experiments. In particular, the values of the index of stress evaluated for realistic orthopedic implants placed within an ASTM phantom are compared with accurate heating simulations performed with 2 anatomic body models (a man and a woman) implanted through a virtual surgery procedure. RESULTS: The manipulation of the proposed index of stress allows to identify regions within the MRI bore where the implant could affect the safety of the examinations. Furthermore, the conducted analysis shows that the power dissipated into the implant by the induced eddy currents is a dosimetric quantity that estimates well the maximum temperature increase in the tissues surrounding the implant. CONCLUSION: The results support the adoption of an anisotropic index of stress to regulate the gradient-induced heating of geometrically complex implants. They also pave the way for a laboratory characterization of the implants based on electrical measurements, rather than on thermal measurements. The next step will be to set up a standardized experimental procedure to evaluate the index of stress associated with an implant.

A silent gradient axis for soundless spatial encoding to enable fast and quiet brain imaging.

PURPOSE: A novel silent imaging method is proposed that combines a gradient insert oscillating at the inaudible frequency 20 kHz with slew rate-limited gradient waveforms to form a silent gradient axis that enable quiet and fast imaging. METHODS: The gradient insert consisted of a plug-and-play (45 kg) single axis z-gradient, which operated as an additional fourth gradient axis. This insert was made resonant using capacitors and combined with an audio amplifier to allow for operation at 20 kHz. The gradient field was characterized using field measurements and the physiological effects of operating a gradient field at 20 kHz were explored using peripheral nerve stimulation experiments, tissue heating simulations and sound measurements. The imaging sequence consisted of a modified gradient-echo sequence which fills k-space in readout lanes with a width proportional to the oscillating gradient amplitude. The feasibility of the method was demonstrated in-vivo using 2D and 3D gradient echo (GRE) sequences which were reconstructed using a conjugate-gradient SENSE reconstruction. RESULTS: Field measurements yielded a maximum gradient amplitude and slew rate of 40.8 mT/m and 5178T/m/s at 20 kHz. Physiological effects such as peripheral nerve stimulation and tissue heating were found not to be limiting at this amplitude and slew rate. For a 3D GRE sequence, a maximum sound level of 85 db(A) was measured during scanning. Imaging experiments using the silent gradient axis produced artifact free images while also featuring a 5.3-fold shorter scan time than a fully sampled acquisition. CONCLUSION: A silent gradient axis provides a novel pathway to fast and quiet brain imaging.

A Huygens' surface approach to rapid characterization of peripheral nerve stimulation.

PURPOSE: Peripheral nerve stimulation (PNS) modeling has a potential role in designing and operating MRI gradient coils but requires computationally demanding simulations of electromagnetic fields and neural responses. We demonstrate compression of an electromagnetic and neurodynamic model into a single versatile PNS matrix (P-matrix) defined on an intermediary Huygens' surface to allow fast PNS characterization of arbitrary coil geometries and body positions. METHODS: The Huygens' surface approach divides PNS prediction into an extensive pre-computation phase of the electromagnetic and neurodynamic responses, which is independent of coil geometry and patient position, and a fast coil-specific linear projection step connecting this information to a specific coil geometry. We validate the Huygens' approach by performing PNS characterizations for 21 body and head gradients and comparing them with full electromagnetic-neurodynamic modeling. We demonstrate the value of Huygens' surface-based PNS modeling by characterizing PNS-optimized coil windings for a wide range of patient positions and poses in two body models. RESULTS: The PNS prediction using the Huygens' P-matrix takes less than a minute (instead of hours to days) without compromising numerical accuracy (error ≤ 0.1%) compared to the full simulation. Using this tool, we demonstrate that coils optimized for PNS at the brain landmark using a male model can also improve PNS for other imaging applications (cardiac, abdominal, pelvic, and knee imaging) in both male and female models. CONCLUSION: Representing PNS information on a Huygens' surface extended the approach's ability to assess PNS across body positions and models and test the robustness of PNS optimization in gradient design.

Design of a high-performance non-linear gradient coil for diffusion weighted MRI of the breast.

Diffusion-weighted imaging (DWI) in the female breast is a magnetic resonance imaging (MRI) technique that complements clinical routine protocols, and that might provide an independent diagnostic value for specific clinical tasks in breast imaging. To further improve specificity of DWI in the breast, stronger and faster diffusion weighting is advantageous. Here, a dedicated gradient coil is designed, targeted at diffusion weighting in the female breast, with the peak gradient magnitude exceeding that of the current clinical MR scanners by an order of a magnitude. Design of application-tailored gradient coils in MRI has recently attracted increased attention. With the target application in mind, the gradient coil is designed on an irregularly shaped semi-open current-carrying surface. Due to the coil former closely fitting the non-spherical target region, non-linear encoding fields become particularly advantageous for achieving locally exceptionally high gradient strengths. As breast tissue has a predominantly isotropic cellular microstructure, the direction of the diffusion-weighting gradient may be allowed to vary within the target volume. However, due to the quadratic dependency of the b-factor on the gradient strength, variation of the gradient magnitude should be carefully controlled. To achieve the above design goals the corresponding multi-objective optimization problem is reformulated as a constrained optimization, allowing for flexible and precise control of the coil properties. A novel constraint is proposed, limiting gradient magnitude variation within every slice while allowing for variations in both the direction of the gradient within the slice and the magnitude across the slices. These innovations enable the design of a unilateral coil for diffusion weighting in the female breast with local gradient strengths exceeding 1 T/m with highly homogeneous diffusion weighting for imaging in the coronal slice orientation.

Parametric modeling of steady-state gradient coil vibration: Resonance dynamics under variations in cylinder geometry.

Gradient coil (GC) vibration is the root cause of many problems in MRI adversely affecting scanner performance, image quality, and acoustic noise levels. A critical issue is that GC vibration will be significantly increased close to any GC mechanical resonances. It is well known that altering the dimensions of a GC fundamentally affects the mechanical resonances excited by the GC windings. The precise nature of the effects (i.e., how the resonances are affected) is however not well understood. The purpose of the present paper is to study how the mechanical resonances excited by closed whole-body Z-gradient coils are affected by variations in cylinder geometry. A mathematical Z-gradient coil vibration model recently developed and validated by the authors is used to theoretically study the resonance dynamics under variation(s) in cylinder: (i) length, (ii) mean radius, and (iii) radial thickness. The forced-vibration response to Lorentz-force excitation is in each case analyzed in terms of the frequency response of the GC cylinder's displacement. In cases (i) and (ii), the qualitative dynamics are simple: reducing the cylinder length and/or mean radius causes all mechanical resonances to shift to higher frequencies. In case (iii), the qualitative dynamics are much more complicated with different resonances shifting in different directions and additional dependencies on the cylinder length. The more detailed dynamics are intricate owing to the fact that resonances shift at comparatively different rates and this leads to several novel and theoretically interesting predicted effects. Knowledge of these effects advance our understanding of the basic mechanics of GC vibration and offer practically useful insights into how such vibration may be passively reduced.