Momentum-weighted conjugate gradient descent algorithm for gradient coil optimization.

MRI gradient coil design is a type of nonlinear constrained optimization. A practical problem in transverse gradient coil design using the conjugate gradient descent (CGD) method is that wire elements move at different rates along orthogonal directions (r, phi, z), and tend to cross, breaking the constraints. A momentum-weighted conjugate gradient descent (MW-CGD) method is presented to overcome this problem. This method takes advantage of the efficiency of the CGD method combined with momentum weighting, which is also an intrinsic property of the Levenberg-Marquardt algorithm, to adjust step sizes along the three orthogonal directions. A water-cooled, 12.8 cm inner diameter, three axis torque-balanced gradient coil for rat imaging was developed based on this method, with an efficiency of 2.13, 2.08, and 4.12 mT.m(-1).A(-1) along X, Y, and Z, respectively. Experimental data demonstrate that this method can improve efficiency by 40% and field uniformity by 27%. This method has also been applied to the design of a gradient coil for the human brain, employing remote current return paths. The benefits of this design include improved gradient field uniformity and efficiency, with a shorter length than gradient coil designs using coaxial return paths.     

Minimum maximum temperature gradient coil design

Ohmic heating is a serious problem in gradient coil operation. A method is presented for redesigning cylindrical gradient coils to operate at minimum peak temperature, while maintaining field homogeneity and coil performance. To generate these minimaxT coil windings, an existing analytic method for simulating the spatial temperature distribution of single layer gradient coils is combined with a minimax optimization routine based on sequential quadratic programming. Simulations are provided for symmetric and asymmetric gradient coils that show considerable improvements in reducing maximum temperature over existing methods. The winding patterns of the minimaxT coils were found to be heavily dependent on the assumed thermal material properties and generally display an interesting “fish‐eye” spreading of windings in the dense regions of the coil. Small prototype coils were constructed and tested for experimental validation and these demonstrate that with a reasonable estimate of material properties, thermal performance can be improved considerably with negligible change to the field error or standard figures of merit. Magn Reson Med 70:584–594, 2013. © 2012 Wiley Periodicals, Inc.     

Constrained length minimum inductance gradient coil design

A gradient coil design algorithm capable of controlling the position of the homogeneous region of interest (ROI) with respect to the current-carrying wires is required for many advanced imaging and spectroscopy applications. A modified minimum inductance target field method that allows the placement of a set of constraints on the final current density is presented. This constrained current minimum inductance method is derived in the context of previous target field methods. Complete details are shown and all equations required for implementation of the algorithm are given. The method has been implemented on computer and applied to the design of both a 1:1 aspect ratio (length:diameter) central ROI and a 2:1 aspect ratio edge ROI gradient coil. The 1:1 design demonstrates that a general analytic method can be used to easily obtain very short gradient coil designs for use with specialized magnet systems. The edge gradient design demonstrates that designs that allow imaging of the neck region with a head-sized gradient coil can be obtained, as well as other applications requiring edge-of-cylinder regions of uniformity.     

Stream function optimization for gradient coil design.

This work presents a method applied to the design of short self-shielded gradient coils of cylindrical geometry. The method uses a hybrid technique that combines the simulated annealing and target field methods to optimize the standard stream functions. The optimized stream functions were parameterized using a few degrees of freedom to reduce the computing time. The optima stream function parameters are given for easy coil design purposes. The proposed approach is compared to the target field method. The main advantage of the present method over the target field method is its ability to enlarge the homogeneous gradient volume. In addition, the designs of short coils based on this approach have shown lower inductance than the coil design based on the target field method. The fast-simulated annealing technique presented in this work enables the gradient coil optimization in less than 3 min of computing time. Magn Reson Med 45:505-512, 2001.     

Asymmetrical gradient coil for head imaging.

This work presents a novel approach to develop dedicated transverse gradient coils for head imaging. The proposed coil design is based on the stochastic optimization of an asymmetrical stream function and improves the matching between the region-of-interest and the homogeneous gradient volume. Additionally, the electric field produced by these asymmetrical coils is 30% lower than that produced by standard symmetrical designs, which minimizes the risk of magnetostimulation of nerves in fast imaging techniques. A prototype of the asymmetrical gradient coil was built to test the method and magnetic field produced by the prototype was measured. Magnetic field measurements and electrical parameters of coils are in good agreement with theoretical calculations.     

A multielement RF coil for MRI guidance of interventional devices.

Accurate localization of minimally invasive devices is critical to the success of interventional procedures. Device orientation and tip position are two of the most important pieces of information needed to define device location for magnetic resonance imaging (MRI)-guided interventional procedures. While a single one-element micro coil incorporated into an interventional device has proven to be effective in some applications, it can only supply tip position information. However, multiple positions on the device are necessary to also determine its orientation. For this purpose, a novel single micro coil design with three separate winding elements that provides both the device orientation and tip position is described in this study. Definition of MR scan planes, by using the device orientation and the target tissue location, permits automatic tracking of the insertion of the device. Furthermore, devices that include this coil design are permitted to bend to a limited extent. This makes the micro coil design appropriate for many flexible interventional devices. Reliable near-real-time tracking of three points on an interventional device is demonstrated on a 0.2T MRI system with modest gradient performance. Phantom and in vivo animal experiments are used to demonstrate the utility of this new coil design.     

Longitudinal gradient coil optimization in the presence of transient eddy currents.

The switching of magnetic field gradient coils in magnetic resonance imaging (MRI) inevitably induces transient eddy currents in conducting system components, such as the cryostat vessel. These secondary currents degrade the spatial and temporal performance of the gradient coils, and compensation methods are commonly employed to correct for these distortions. This theoretical study shows that by incorporating the eddy currents into the coil optimization process, it is possible to modify a gradient coil design so that the fields created by the coil and the eddy currents combine together to generate a spatially homogeneous gradient that follows the input pulse. Shielded and unshielded longitudinal gradient coils are used to exemplify this novel approach. To assist in the evaluation of transient eddy currents induced within a realistic cryostat vessel, a low-frequency finite-difference time-domain (FDTD) method using the total-field scattered-field (TFSF) scheme was performed. The simulations demonstrate the effectiveness of the proposed method for optimizing longitudinal gradient fields while taking into account the spatial and temporal behavior of the eddy currents.     

The design and test of a new volume coil for high field imaging

A major problem in the development of high field (>100 MHz) large volume (>6000 cm³) MR coils is the interaction of the coil with the subject as well as the radiation loss to the environment. To reduce subject perturbation of the coil resonance modes, a volume coil that uses an array of freely rotating resonant elements radially mounted between two concentric cylinders was designed for operation at 170 MHz. Substantial electromagnetic energy is stored in the resonant elements outside the sample region without compromising the efficiency of the overall coil. This stored energy reduces the effect of the subject on the circuit and maintains a high Q, facilitating the tuning and matching of the coil. The unloaded Q of the coil is 680; when loaded with a head, it was 129. The ratio of 5.3 of the unloaded to loaded Q supports the notion that the efficiency of the coil was maintained in comparison with previous designs. The power requirement and signal-to-noise performance are significantly improved. The coil is tuned by a mechanism that imparts the same degree of rotation on all of the elements simultaneously, varying their degree of mutual coupling and preserving the overall coil symmetry. A thin radiofrequency shield is an integral part of the coil to reduce the radiation effect, which is a significant loss mechanism at high fields. MR images were collected at 4T using this coil design with high sensitivity and B₁, homogeneity.     

MR gradient coil heat dissipation

The temperature responses of five different gradient coil designs were modeled using simplified engineering equations and measured. The model predicts that the coil temperature approaches a maximum as an inverse exponential, where the maximum temperature is governed by two parameters: a local power density and a cooling term. The power density term is a function of position and is highest where the current paths have minimum widths and are closely packed. The cooling parameter consists of convective, conductive, and radiative components which can be controlled by (1) providing forced cooling, (2) having a coil former with high thermal conductivity and thin walls, and (3) varying the emissivity of the coil surfaces. For a given gradient strength, the average temperature rise is minimized by designing a coil with a small radius and thick copper. The model predicted the local temperature rise, which is also dependent on the current density, to within 5°C of measured values.     

Phase alignment of multiple surface coil data for reduced bandwidth and reconstruction requirements

Multiple element surface coils are often used in clinical MRI to increase the image signal-to-noise ratio (S/N). Use of multicoils typically requires increased net sampling bandwidth and data processing for each coil element. A phase-alignment technique is described which combines the signals from all coil elements before image reconstruction, greatly relaxing the technical requirements of the standard multicoil methods. Hardware and software implementations allow reduction of the reconstruction requirement to that of a single coil. The hardware implementation additionally allows a significant reduction in the net sampling bandwidth. The method is applicable to high speed MRI techniques, as demonstrated in phantoms and volunteers.     

Practical design of a high-strength breast gradient coil

A high-strength three-axis local gradient coil set was constructed for MRI of the breast. Gradient fields with good uniformity (<10% deviation from the desired gradient) over most of the volume required for breast imaging were generated with efficiencies of up to 3.3 mT/m/A. The coils will allow diffusion breast imaging in clinically acceptable examination times. The electrical design, water cooling system, and fabrication techniques are described. Preliminary tests of the coil included images of a grid phantom and diffusion measurements in a short-T₂ agarose gel phantom.     

Analytic approach to the design of transverse gradient coils with co-axial return paths.

Transverse gradient coils with co-axial return paths offer reduced acoustic noise compared with standard cylindrical gradient coils, due to local force balancing, and can also easily be made to have a length to diameter ratio that is less than one. Analytic expressions for the magnetic field and vector potential generated by this type of coil are described here, along with a formula for calculating the coil inductance. It is shown that these expressions allow the implementation of powerful analytic methods of coil design, as well as the incorporation of active magnetic screening. It is also demonstrated how the mathematics specifies the best parameters to use when designing coils with small numbers of elements. A head gradient coil for use at 3.0 T has been designed using the analytic approach described here. The process of coil design and construction is outlined and the performance of the coil in comparison with a similar standard cylindrical coil is described.     

Minimax current density gradient coils: Analysis of coil performance and heating

Standard gradient coils are designed by minimizing the inductance or resistance for an acceptable level of gradient field nonlinearity. Recently, a new method was proposed to minimize the maximum value of the current density in a coil additionally. The stated aim of that method was to increase the minimum wire spacing and to reduce the peak temperature in a coil for fixed efficiency. These claims are tested in this study with experimental measurements of magnetic field and temperature as well as simulations of the performance of many coils. Experimental results show a 90% increase in minimum wire spacing and 40% reduction in peak temperature for equal coil efficiency and field linearity. Simulations of many more coils indicate increase in minimum wire spacing of between 50 and 340% for the coils studied here. This method is shown to be able to increase coil efficiency when constrained by minimum wire spacing rather than switching times or total power dissipation. This increase in efficiency could be used to increase gradient strength, duty cycle, or buildability. Magn Reson Med, 2012. © 2011 Wiley Periodicals, Inc.     

Design and evaluation of shielded gradient coils.

Techniques are described for the design of shielded gradient coils for superconducting MRI systems. These design methods are suited for constructing the most efficient gradient coil that meets a specified homogeneity requirement. Tradeoffs in coil design of efficiency with coil size and gap size are discussed. Residual eddy currents from coils constructed with a finite number of wires are calculated and give guidelines for the construction of efficient, whole-body gradient coils.     

Three-dimensional time-of-flight MR angiography with a specialized gradient head coil

A gradient head coil has been developed, incorporating two independent gradients within the conventional body coil of the magnetic resonance (MR) system, with reduced rise times (200 μsec) and maximum amplitudes of 37 and 18 mT/m in the z and y directions, respectively. This gradient coil was systematically evaluated by testing two-dimensional (2D) and three-dimensional (3D) time-of-flight (TOF) MR angiography sequences applied to a pulsatile flow phantom simulating a carotid stenosis and the intracranial vasculature. When standard 2D and 3D TOF MR angiography techniques were used to image the carotid stenosis model, dramatic signal loss in the stenotic segment and a large flow void distal to the stenosis were seen. The shorter (3.8 msec) absolute echo times (TEs) achievable with the gradient coil in 3D sequences substantially reduced the phase dispersion and associated signal loss in the region of stenosis. Shorter TEs alone (3.2 msec) did not minimize signal loss, and firstorder flow compensation in the read and section-select directions provided further improvements (despite slightly longer TEs). Reduction of TEs in 2D sequences yielded relatively poor results regardless of the refocusing scheme or TE. This study confirms the predicted benefits of a dedicated coil with improved gradient capabilities for 3D MR angiography. The study suggests the limitations of 2D TOF MR angiography in the evaluation of severe stenoses.     

Planar gradient coil design by scaling the spatial frequencies of minimum-inductance current density

Gradient coil inductance has been remarkably reduced by the minimum-inductance design technique, which minimizes the magnetic energy stored by the gradient coil. The planar gradient coil designed by this technique, however, often has poor magnetic field linearity. Scaling the spatial frequencies of the current density function derived by this method, the magnetic field linearity of the planar gradient coil can be greatly improved with a small sacrifice of gradient coil inductance. A figure of merit of the planar gradient coil has been found to be improved by scaling the spatial frequencies.     

Multiple-region gradient arrays for extended field of view, increased performance, and reduced nerve stimulation in magnetic resonance imaging.

This article presents a novel design for magnetic resonance imaging (MRI) gradient systems. This design may allow the development of MRI scanners that are capable of imaging large regions with high performance while minimizing the potential for nerve stimulation. The general concept of the gradient system is that spatial oscillation is incorporated such that each gradient coil creates multiple, approximately linear gradient regions that oscillate in gradient polarity. Separate radiofrequency (RF) coil arrays are designed to be sensitive to the signals within each linear region and thus allow signal measurements to be obtained separately from each region. Enabling image acquisition in the transition region that separates each pair of adjacent linear regions requires a second gradient system with imaging regions that overlap and coincide with the transition regions of the first gradient system. Imaging the extended field of view (FOV) is accomplished by interleaved operation of the two gradient systems. Simulated annealing is used to create designs for both longitudinal and transverse gradient systems with two imaging regions.     

Design and fabrication of a three-axis edge ROU head and neck gradient coil.

The design, fabrication, and testing of a complete three-axis gradient coil capable of imaging the human neck is described. The analytic method of constrained current minimum inductance (CCMI) was used to position the uniform region of the gradient coil adjacent to and extending beyond the physical edge of the coil. The average gradient efficiency of the three balanced axes is 0.37 mT/m/A and the average inductance is 827 microH. With maximum amplifier current of 200A and receive signal sweep width of +/-125 kHz, the average minimum FOV using this gradient set is 7.9 cm. The completed coil has an inner diameter of 32 cm, an outer diameter of 42 cm, and a length (including cabling connections) of 80 cm. The entire coil was built in-house. The structure is actively water cooled. Heating measurements were made to characterize the thermal response of the coil under various operating conditions and it was determined that a continuous current of 100A could be passed through all three axes simultaneously without increasing the internal coil temperature by more than 23 degrees C. Eddy current measurements were made for all axes. With digital compensation, the gradient eddy current components could be adequately compensated. A large B(o) eddy current field is produced by the Gz axis that could be corrected through the use of an auxiliary B(o) compensation coil. Preliminary imaging results are shown in both phantoms and human subjects.     

Superelliptical insert gradient coil with a field‐modifying layer for breast imaging

Many MRI applications such as dynamic contrast‐enhanced MRI of the breast require high spatial and temporal resolution and can benefit from improved gradient performance, e.g., increased gradient strength and reduced gradient rise time. The improved gradient performance required to achieve high spatial and temporal resolution for this application may be achieved by using local insert gradients specifically designed for a target anatomy. Current flat gradient systems cannot create an imaging volume large enough to accommodate both breasts; further, their gradient fields are not homogeneous, dropping off rapidly with distance from the gradient coil surface. To attain an imaging volume adequate for bilateral breast MRI, a planar local gradient system design has been modified into a superellipse shape, creating homogeneous gradient volumes that are 182% (G_x), 57% (G_y), and 75% (G_z) wider (left/right direction) than those of the corresponding standard planar gradient. Adding an additional field‐modifying gradient winding results in an additional improvement of the homogeneous gradient field near the gradient coil surface over the already enlarged homogeneous gradient volumes of the superelliptical gradients (67%, 89%, and 214% for G_x, G_y, and G_z respectively). A prototype y‐gradient insert has been built to demonstrate imaging and implementation characteristics of the superellipse gradient in a 3 T MRI system. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.