Gradient Coil Design Research Articles

Design method of transverse gradient coils based on nonuniform rational B-spline (NURBS) curves.

To propose a hybrid transverse gradient coil design method that leverages current density-based methods and nonuniform rational B-spline (NURBS) curves to optimize the performance and manufacturability of gradient coils. Our method begins by generating an initial wire configuration using a density-based method. Then, we fit NURBS curves to the configuration, and adjust the control parameters of these curves to meet performance requirements. To ensure adequate spacing and even distribution of wires, an objective function utilizing the sigmoid function to modulate the distances between adjacent wires is constructed. Critical factors including gradient efficacy, linearity, eddy current, and torque, are incorporated as constraints. The piecewise nature of the curves provides the flexibility to independently control specific segments without impacting others. We validated our method by designing three shielded transverse gradient coils: a whole-body coil, an ultra-short whole-body coil, and an ultra-short asymmetric head coil. The primary design objectives were to improve linearity and maintain gradient efficiency. All optimized coils demonstrated significant linearity across large diameters of spherical volumes (DSVs), while gradient efficiency, eddy currents, and torque were well-balanced. The objective function effectively managed the wire concentrations required for high linearity, ensuring even wire arrangement and adequate spacing. We leveraged the flexibility of the curves to individually tailor wire paths for specific objectives, such as preventing interference between coils and passive shimming and accommodating wire connections and cooling circuits. This method provides a versatile and effective approach for designing high-performance and manufacturable gradient coils.

Design and Performance Analysis of Gradient Coil for High-Field HTS REBCO MRI Magnet

Design and Performance Analysis of Gradient Coil for High-Field HTS REBCO MRI Magnet

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

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. A novel design method based on stream function combining an optimization algorithm is proposed to obtain highly linear gradient coil. 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. 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. 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.

Numerical design of transverse gradient coil with transformed magnetic gradient field over an effective imaging area

Numerical design of transverse gradient coil with transformed magnetic gradient field over an effective imaging area

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

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. 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). 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. 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.

Developing an AI-empowered head-only ultra-high-performance gradient MRI system for high spatiotemporal neuroimaging

Recent advances in neuroscience requires high-resolution MRI to decipher the structural and functional details of the brain. Developing a high-performance gradient system is an ongoing effort in the field to facilitate high spatial and temporal encoding. Here, we proposed a head-only gradient system NeuroFrontier, dedicated for neuroimaging with an ultra-high gradient strength of 650 mT/m and 600 T/m/s. The proposed system features in 1) ultra-high power of 7MW achieved by running two gradient power amplifiers using a novel paralleling method; 2) a force/torque balanced gradient coil design with a two-step mechanical structure that allows high-efficiency and flexible optimization of the peripheral nerve stimulation; 3) a high-density integrated RF system that is miniaturized and customized for the head-only system; 4) an AI-empowered compressed sensing technique that enables ultra-fast acquisition of high-resolution images and AI-based acceleration in q-t space for diffusion MRI (dMRI); and 5) a prospective head motion correction technique that effectively corrects motion artifacts in real-time with 3D optical tracking. We demonstrated the potential advantages of the proposed system in imaging resolution, speed, and signal-to-noise ratio for 3D structural MRI (sMRI), functional MRI (fMRI) and dMRI in neuroscience applications of submillimeter layer-specific fMRI and dMRI. We also illustrated the unique strength of this system for dMRI-based microstructural mapping, e.g., enhanced lesion contrast at short diffusion-times or high b-values, and improved estimation accuracy for cellular microstructures using diffusion-time-dependent dMRI or for neurite microstructures using q-space approaches.

Design and construction of gradient coils for an MRI-guided small animal radiation platform

Small animal radiation experiments use a dedicated hardware platform to deliver radiation to small animals to support pre-clinical radiobiological studies. Image guidance is critical to achieve experiment accuracy. MR-based image guidance became recently available in human radiation therapy by integrating an MR scanner with a medical linear accelerator. Our group is developing a small animal MR-guidance system for pre-clinical radiation studies using a unique low-field unilateral magnet design. In this paper, we reported our design, construction, and characterization of split gradient coils for the MRI scanner. The coils were designed to have a 4 cm gap to allow the radiation beam to pass through for radiation experiments. We designed the coil patterns by solving an optimization problem. We constructed the coils by printing molds for the designed coil patterns using 3D printing technology and wiring the coils following the pattern. We measured parameters of the coils to characterize their performance. The coils achieved a linear magnetic field throughout a 4 cm spherical region of interest. The slew rates were 8640 and 1970 T/m⋅s, and the efficiencies were 1.2 and 0.21 mT/m⋅A for the Y-coil and X-coil, respectively. Preliminary imaging with the coils on our proposed system validates spatial encoding functions of the developed coils.

Retracted: Acoustic Control through Gradient Coil Design Using a Finite-Difference-Based Method for MRI

Retracted: Acoustic Control through Gradient Coil Design Using a Finite-Difference-Based Method for MRI

The possible influence of third-order shim coils on gradient–magnet interactions: an inter-field and inter-site study

ObjectiveTo assess the possible influence of third-order shim coils on the behavior of the gradient field and in gradient–magnet interactions at 7 T and above.Materials and methodsGradient impulse response function measurements were performed at 5 sites spanning field strengths from 7 to 11.7 T, all of them sharing the same exact whole-body gradient coil design. Mechanical fixation and boundary conditions of the gradient coil were altered in several ways at one site to study the impact of mechanical coupling with the magnet on the field perturbations. Vibrations, power deposition in the He bath, and field dynamics were characterized at 11.7 T with the third-order shim coils connected and disconnected inside the Faraday cage.ResultsFor the same whole-body gradient coil design, all measurements differed greatly based on the third-order shim coil configuration (connected or not). Vibrations and gradient transfer function peaks could be affected by a factor of 2 or more, depending on the resonances. Disconnecting the third-order shim coils at 11.7 T also suppressed almost completely power deposition peaks at some frequencies.DiscussionThird-order shim coil configurations can have major impact in gradient–magnet interactions with consequences on potential hardware damage, magnet heating, and image quality going beyond EPI acquisitions.

Design of cylindrical saddle-shaped transverse gradient coils with small aspect ratios and high linearity for micro comagnetometers

Design of cylindrical saddle-shaped transverse gradient coils with small aspect ratios and high linearity for micro comagnetometers

Design of gradient coils based on the target field method in a high-permeability shield considering sidewall apertures

The combination of high-permeability ferrite and coils is often used to nullify ambient magnetic fields and is widely used in applications such as magnetic resonance imaging and high-sensitivity magnetic sensors. We propose the design method of transverse gradient coils based on the target field method in a high-permeability shield considering sidewall apertures (TFM-HPSCSA), which are installed in the ferrite shield to zero the residual magnetic field gradient. TFM-HPSCSA coils enable an innovative combination of magnetic field gradient linearity and structural luminescence. The coil current density distribution is set to avoid the central sidewall apertures. As a result, the contour distribution of the stream function under the optimized weight coefficients is calculated to obtain the wire alignments of the dBy/dx, dBy/dy and dBy/dz gradient coils. The deviations of the experimentally measured values from the finite element simulations of the three types coils are 0.63%, 1.17% and 0.48%, respectively, which verified the validity and the accuracy of the proposed method. In comparison to the traditional saddle gradient coil designed under the free space condition, the proposed dBy/dx coil produces a 30.5% improvement in the percentage range of regions with 5% magnetic field gradient nonlinearity. The increased linear range of the gradient magnetic field contributes to the improvement of the residual field nulling range in magnetic sensors and magnetic shielding systems in practical applications.

Gradient coil design with enhanced shielding constraint for a cryogen-free superconducting MRI system

The relatively fragile low-temperature stability of cryogen-free superconducting magnetic resonance imaging (MRI) magnets requires the careful management of exogenous heat sources. A strongly shielded gradient magnetic field is important for the optimal operation of cryogen-free MRI systems. In this study, we present an enhanced shielding method incorporating a regionalized stray field constraining strategy. By optimizing the constraint parameters, we could develop engineering-feasible gradient coil schemes without increasing system complexity but with the stray field intensity reduced by half. In real measurement in an integrated MRI system, the developed gradient assembly demonstrated good performance and supported to output images of excellent quality. Our findings suggested that the proposed method could potentially form a useful design paradigm for cryogen-free MRI magnets.

A Stream Function Smoothing Method for the Design of MRI Gradient Coils on Non-Developable Surfaces.

Insert gradient coils with similar imaging body shapes typically have smaller dimensions and higher spatial efficiency. This often allows the gradient coils the achievement of stronger and faster gradient fields. Thus, improving existing methods to make them applicable to the design of MRI gradient coils on complex surfaces has also become a challenge. This article proposes an algorithm that smooths the implicitly expressed stream function based on the intrinsic surface Laplace-Beltrami operator. This algorithm can be used to simplify the design procedure of MRI gradient coils on non-developable surfaces. The following steps are performed by the proposed algorithm: an initial design of the stream function configuration, extraction of the surface mesh, discretization of the surface smoothing operator, and a smoothing of the contour lines. To evaluate the quality of the smoothed streamline configuration, several technical parameter metrics-including magnetic field accuracy, coil power consumption, theoretical minimum wire spacing, and the maximum curvature of the contour lines-were evaluated. The proposed method was successfully validated in a design gradient coil on both developable and non-developable surfaces. All examples evolved from an initial value with a locally non-smooth and complex topological configuration to a smooth result while maintaining high magnetic field accuracy.

Design and construction of new small gradient coils for mouse MRI

We represent small Z- and Y-gradient coils with higher gradient strength and slew rate for mouse MRI. The coil geometries are optimized based on predetermined conditions for the gradient strength and slew rate in terms of minimum power consumption and acceptable linearity for the variation of the magnetic fields using the particle swarm optimization algorithm in computer simulation technology. The simulation results verify that the magnitudes of the field strength and slew rate have reached up to and for the Z-gradient coil and increased to and for the Y-gradient coil, respectively. Furthermore, the optimal geometry of the Z-gradient coil derived from a simulation study was then fabricated, and its parameters were measured using a Hall sensor. The gradient strength and slew rate of the fabricated Z-gradient coil were measured at and , respectively, which have only a 9% difference from the corresponding simulated parameters.

Hybrid optimal design method for magnetic field coils under magnetic shielding boundary

A novel strategy for designing uniform magnetic field and gradient magnetic field coils considering the boundary effect of magnetic shielding is proposed in this study. This strategy uses intelligent optimization algorithm to skillfully transform the complex coil design problem into the spatial optimization problem of individual population. The mirror method is combined with Green’s function to accurately calculate the magnetic field, and the target field method (TFM) is combined with the whale optimization algorithm to optimize the stream functions using adaptive ridge regression. The minimum fitness function is defined as the real-time magnetic field relative error, and the optimal ridge coefficient is continuously obtained by determining the current density coefficient. The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM, with reductions ranging from 12.2% to 0.11% (Bx coil), 0.3% to 0.02% (Bz coil), 20% to 10% (dBx/dz coil) and 2.9% to 2.4% (dBz/dz coil). The strategy has been effectively validated by analytical simulations and experimental results, and is expected to be applied to the design of uniform field coils and gradient coils for ultra-high precision atomic sensors.

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 in Z (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, the R in 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.

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

To demonstrate systematic, linear algebra-based, dimensional analysis to derive a scaling relationship among the design parameters of MRI gradient and harmonic shim coils. The dimensions of five physical quantities relevant for gradient coil design (inductance, gradient amplitude, inner diameter [ ], 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. 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 . 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 . 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. 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.

Design of High Linearity and Low Power Gradient Coil Based on Magnetic Field Harmonic Analysis Method

Design of High Linearity and Low Power Gradient Coil Based on Magnetic Field Harmonic Analysis Method

Gradient Coil Design and Optimization for an Ultra-Low-Field MRI System

Gradient Coil Design and Optimization for an Ultra-Low-Field MRI System