A hybrid, inverse approach to the design of magnetic resonance imaging magnets

Passive Shimming of MRI Static Magnetic Field Using Regularization of Truncated Singular Value Decomposition

PURPOSE

To develop a new shimming calculation method, which can calculate iron piece placements rapidly to make the magnetic field homogeneous at intended homogeneity and then to make the shimming working time short.

MATERIALS AND METHODS

The shimming calculation yields magnetic moment (MM) distribution, which is calculated by the truncated singular value decomposition (SVD) from the measured magnetic field. The MM distribution is described by a superposition of eigenmodes obtained by SVD of a response matrix from the moment distributions to magnetic fields at the field of view (FOV). The homogeneity is regulated by a truncation number of the superposed eigenmodes. The magnetic moments are converted into iron volumes with the assumption of saturated magnetization and the iron pieces are placed according to the calculation results. Since the SVD calculation can be done in advance, the computational time at the shimming site is short.

RESULTS

Trial applications on a 0.5T magnetic resonance imaging (MRI) magnet were done using the new shimming calculation method, which was proved to work well. However, since the iron piece volumes had tolerances, the work was repeated until enough homogeneity was obtained. As a result, an intended homogeneity of 8.9 ppm (peak-to-peak) on 40 cm diameter spherical surface was successfully obtained from measured homogeneity of 543 ppm with short computational and working time.

CONCLUSION

The test shimming work showed that the developed shimming calculation method with truncated SVD regularization is applicable to the shimming work on the MRI magnets.

Electromagnetic computation and modeling in MRI

Electromagnetic (EM) computational modeling is used extensively during the development of a Magnetic Resonance Imaging (MRI) scanner, its installation, and use. MRI, which relies on interactions between nuclear magnetic moments and the applied magnetic fields, uses a range of EM tools to optimize all of the magnetic fields required to produce the image. The main field magnet is designed to exacting specifications but challenges in manufacturing, installation, and use require additional tools to maintain target operational performance. The gradient magnetic fields, which provide the primary signal localization mechanism, are designed under another set of complex design trade-offs which include conflicting imaging performance specifications and patient physiology. Gradients are largely impervious to external influences, but are also used to enhance main field operational performance. The radiofrequency (RF) magnetic fields, which are used to elicit the signals fundamental to the MR image, are a challenge to optimize for a host of reasons that include patient safety, image quality, cost optimization, and secondary signal localization capabilities. This review outlines these issues and the EM modeling used to optimize MRI system performance.

Globally optimal superconducting magnets part I: minimum stored energy (MSE) current density map

An optimal current density map is crucial in magnet design to provide the initial values within search spaces in an optimization process for determining the final coil arrangement of the magnet. A strategy for obtaining globally optimal current density maps for the purpose of designing magnets with coaxial cylindrical coils in which the stored energy is minimized within a constrained domain is outlined. The current density maps obtained utilising the proposed method suggests that peak current densities occur around the perimeter of the magnet domain, where the adjacent peaks have alternating current directions for the most compact designs. As the dimensions of the domain are increased, the current density maps yield traditional magnet designs of positive current alone. These unique current density maps are obtained by minimizing the stored magnetic energy cost function and therefore suggest magnet coil designs of minimal system energy. Current density maps are provided for a number of different domain arrangements to illustrate the flexibility of the method and the quality of the achievable designs.

Shim design using a linear programming algorithm

The advent of open magnetic resonance imaging (MRI) scanners and dedicated MRI scanners tailored to specific body parts has led to an increasing number of noncylindrical MRI scanner geometries, for which noncylindrical gradients and shims are needed. These new scanner geometries are driving the need for fast, flexible shim design methods that can design shim coils for any geometry. A linear programming (LP) algorithm was developed to design minimum-power resistive shim coils on an arbitrary surface. These coils can be designed to produce any order shim field over an arbitrarily shaped target region, which can be placed anywhere within the coil. The resulting designs are relatively sparse and can be readily constructed. This algorithm was used to design and construct a seven-coil cylindrical shim set for a knee imaging magnet with a cylindrical homogeneous region. The algorithm was then used to design shim coils for a biradial head imager with an asymmetrically located spherical target region for brain imaging.

Toward shielding improvements in MRI gradients and other systems

A new method is described for reducing the shielding-error function in the 'supershielding' approach to designing MRI systems. The method is thus shown to lead to significantly better shielding and better control of eddy current effects associated with gradient coils. To illustrate this technique, a set of results for a z-gradient coil is presented. A generalization to non-standard geometries can be made in a straightforward manner with the new method. The usefulness of the relationship of all fringe-field quantities to the shielding-error function is emphasized. The formal limit of perfect shielding in a 'least-squares' sense is shown for a simple strip-shield model along with a numerical eigenvalue study for comparison with the theoretical limit.

Asymmetric zonal shim coils for magnetic resonance applications

A method is presented for the systematic design of asymmetric zonal shim coils for magnetic resonance applications. Fourier-series methods are used to represent the magnetic field inside and outside a circular cylinder of length 2L and radius a. The current density on the cylinder is also represented using Fourier series. Any desired field can be specified in advance on the cylinder's radius, over some nonsymmetric portion pL<z<qL of the coil's length (-1<p<q<1). Periodic extension of the field is used, in a way that guarantees the continuity of the field, and therefore gives good convergence of the Fourier series. All that is required is to calculate the Fourier coefficients associated with the specified desired field, and from these, the current density on the coil and the magnetic field components then follow automatically. The method is illustrated by applying it to three sample zonal coil designs, namely, linear, quadratic, and cubic fields located asymmetrically in the coil. Current densities and corresponding coil winding patterns are shown for these three illustrative cases. Field calculations directly from the coil patterns and spherical harmonic deconvolutions of these fields indicate that the example designs match the theory well. Asymmetric shim coils can be used in conventional symmetric MRI magnets, particularly those architected for "head-only" studies. One of their major applications is expected to be in the newly developed asymmetric magnet systems.

Compact clinical MRI magnet design using a multi-layer current density approach

In this work, a new method of optimization is successfully applied to the theoretical design of compact, actively shielded, clinical MRI magnets. The problem is formulated as a two-step process in which the desired current densities on multiple, co-axial surface layers are first calculated by solving Fredholm equations of the first kind. Non-linear optimization methods with inequality constraints are then invoked to fit practical magnet coils to the desired current densities. The current density approach allows rapid prototyping of unusual magnet designs. The emphasis of this work is on the optimal design of short, actively-shielded MRI magnets for whole-body imaging. Details of the hybrid numerical model are presented, and the model is used to investigate compact, symmetric, and asymmetric MRI magnets. Magnet designs are presented for actively-shielded, symmetric magnets of coil length 1.0 m, which is considerably shorter than currently available designs of comparable dsv size. Novel, actively-shielded, asymmetric magnet designs are also presented in which the beginning of a 50-cm dsv is positioned just 11 cm from the end of the coil structure, allowing much improved access to the patient and reduced patient claustrophobia. Magn Reson Med 45:331-340, 2001.

Application of the SUSHI method to the design of gradient coils

An approach to potential improvements in magnetic field shielding for a gradient coil system with cylindrical geometry is presented, utilizing "supershielding" conditions for the currents on both the primary and the secondary coils. It is demonstrated that the field can be strongly suppressed everywhere outside a cylindrical shield coil radius, even though the finite-length active shield only partially surrounds a primary coil. The supershielding method, which is aimed at controlling eddy currents, still has sufficient freedom to maintain the desired magnetic field behavior inside the imaging volume. The trade-off is an additional primary current oscillation and increased current peaks and field energy. This method has been applied to design short transverse and axial gradient coils, giving substantially improved shielding compared to an apodization method. Magn Reson Med 45:147-155, 2001.