Electricity: magnetically operated switches – magnets – and electr – Magnets and electromagnets – Magnet structure or material
Reexamination Certificate
2002-09-04
2003-12-16
Barrera, Ramon M. (Department: 2832)
Electricity: magnetically operated switches, magnets, and electr
Magnets and electromagnets
Magnet structure or material
C335S299000, C324S320000
Reexamination Certificate
active
06664879
ABSTRACT:
1. FIELD OF THE INVENTION
This invention relates to shim coils. In particular, the invention relates to shim coils suitable for use in magnetic resonance applications that generate tesseral fields located asymmetrically in a finite-length coil. A method for the design of such shim coils of the type useful for Magnetic Resonance applications is described. The method involves a type of target-field approach, but the exact geometry of the shim coils is treated without approximation. In particular, the fact that shim coils are of finite length is catered for. Although illustrated herein in terms of shim coils, the methods of the invention can also be used to design essentially any type of coil which is to be used to produce a desired magnetic field, including, without limitation, gradient coils and H
0
-producing coils.
2. BACKGROUND TO THE INVENTION
In magnetic resonance imaging (MRI) applications, a patient is placed in a strong and homogeneous static magnetic field, causing the otherwise randomly oriented magnetic moments of the protons, in water molecules within the body, to precess around the direction of the applied field. The part of the body in the homogeneous region of the magnet is then irradiated with radio-frequency (RF) energy, causing some of the protons to change their spin orientation. When the RF energy source is removed, the protons in the sample return to their original configuration, inducing a measurable signal in a receiver coil tuned to the frequency of precession. This is the magnetic resonance (MR) signal. Most importantly, the frequency at which protons absorb the RF signal depends on the background magnetic field.
In practice, the presence of the patient's body perturbs the strong magnetic field slightly, and so shim coils are used to correct the field, to give the best possible final image. The field within a specified target volume (the diameter of the sensitive volume, or DSV) is typically represented in terms of spherical harmonics, and so impurities in the field are analyzed in terms of the coefficients of an expansion in these harmonics. Shim coils are therefore designed to correct a perturbed magnetic field by producing a particular spherical harmonic that can be added to the background magnetic field, so as to cancel the effect of a certain harmonic caused by an impurity. Many of these coils may be present in a particular MRI device, and each may have its own power supply, to produce the required current flow.
The major task associated with the design of these shim coils is to determine the precise windings on the coil that will produce the desired magnetic field within the coil. One method, due to Turner (1986,
A target field approach to optimal coil design
, J. Phys. D: Appl. Phys. 19, 147-151), is to specify a desired target field inside the cylinder, at some radius less than the coil radius. Fourier transform methods are then used to find the current density on the surface of the coil, required to give the desired target field. This method has been widely used and is successful in applications, but it is based on the approximation that the coil is, in some sense, infinite in length so that the Fourier transform technique can be applied. Finite-length coils can be simulated in this technique by adding a constraint that the current density must fall to zero outside some finite interval, and this is discussed by Turner in U.S. Pat. No. 5,289,151. Nevertheless, coils of finite length are not natural to this approach, and in some circumstances smoothing functions have to be incorporated in the Fourier transform so as to guarantee its convergence.
A related method for overcoming the difficulty associated with coils of finite length has been advanced by Forbes, Crozier and Doddrell in Australian Provisional Patent Application PQ9787 (see U.S. Pat. No. 6,377,148 B1) and Forbes and Crozier (2001,
Asymmetric zonal shim coils for Magnetic Resonance applications
, Med. Phys. 28, 1644-1651). The technique employs a target-field approach and builds in the finite length of the coils by making use of a Fourier series technique. This approach involves approximations, but is capable of designing coils for asymmetrically located fields in a very systematic way.
An alternative method for the design of coils of finite length is the stochastic optimization approach pioneered by Crozier and Doddrell (1993,
Gradient
-
coil design by simulated annealing
, J. Magn. Reson. A 103, 354-357). This approach seeks to produce a desired field in a given volume (the DSV) using optimization methods to adjust the location of certain loops of wire and the current flowing in those loops. The method is very robust, since it uses simulated annealing as its optimization strategy, and it can incorporate other constraints in a straightforward manner by means of a Lagrange-multiplier technique. Coils of genuinely finite length are accounted for without approximation by this technique, and it therefore has distinct advantages over the target field method (and alternative methods based on finite-elements). Since it relies on a stochastic optimization strategy, it can even cope with discontinuous objective functions, and so can accommodate adding or removing loops of wire during the optimization process. The method has the drawback that the stochastic optimization technique can take many iterations to converge, and so can be expensive of computer time. In addition, the technique is undoubtedly more difficult to apply to the design of coils that produce more complicated magnetic fields, such as those involved in higher-order spherical harmonics with tesseral components.
It is an object of the invention to provide coil structures that generate desired fields internal or external to the coil structure, that may be symmetric or non-symmetric with respect to that structure. For example, in connection with certain preferred embodiments, it is an object of the invention to provide coil structures that generate desired fields within certain specific and asymmetric portions of the coil structure.
It is a further object of the invention to provide a general systematic method for producing any desired zonal or tesseral or otherwise shaped magnetic field within and/or outside a coil, taking the finite length of the coil into account without approximation.
3. SUMMARY OF THE INVENTION
In one broad form, the invention provides a method for the design of coils for the production of magnetic fields. For example, such coils can be shim coils of the type suitable for use in Magnetic Resonance applications. The method involves a type of target-field approach, but the exact geometry of the coils is treated without approximation. In particular, the fact that coils are of finite length is catered for.
Target fields of any desired type may be specified, and may involve zonal and tesseral harmonics or any other specified field shape. The method of this invention can be used to design the coil windings needed to produce the specified target field. In this approach, there is complete freedom in the choice of target field. For example, there is no requirement to restrict the target field to any one spherical harmonic. The method is therefore able to design coils in which the region of interest is located asymmetrically with respect to the coil length. In addition, to improve the accuracy of the fields produced by the coil, the design methodology of this invention can match desired target fields at two or more different target radii, which preferably are co-axial.
In one embodiment, the invention provides a method for designing a coil, e.g., a tesseral shim coil for a magnetic resonance system, where the coil extends from −L to +L along a longitudinal axis which lies along the z-axis of a three dimensional coordinate system, and the method comprises the steps of:
(a) selecting a cylindrical surface having a radius r=a for calculating current densities for the coil (the “r=a surface”), the surface surrounding the longitudinal axis and extending from −L to +L;
(b) selecting a
Crozier Stuart
Forbes Lawrence Kennedy
Barrera Ramon M.
Klee Maurice M.
NMR Holdings No. 2 Pty Limited
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