Electricity: magnetically operated switches – magnets – and electr – Magnets and electromagnets – Magnet structure or material
Reexamination Certificate
2001-08-27
2002-04-23
Barrera, Ramon M. (Department: 2832)
Electricity: magnetically operated switches, magnets, and electr
Magnets and electromagnets
Magnet structure or material
C335S299000, C324S320000
Reexamination Certificate
active
06377148
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to shim coils for magnetic resonance applications. In particular, the invention is directed to the design of asymmetric shim coils for magnetic resonance imaging machines.
BACKGROUND OF 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. The net magnetization of the spin ensemble is nutated away from the direction of the applied static magnetic field by the applied RF energy. The component of this net magnetization orthogonal to the direction of the applied static magnetic field acts to induce 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 precess around the applied static field depends on the background magnetic field. Since this is designed to vary at each point in the sample in an imaging experiment, it follows that the frequency of the MR signal likewise depends on location. The signal is therefore spatially encoded, and this fact is used to construct the final image.
In practice, construction tolerances mean that MR magnets do not generate perfectly homogeneous fields over the DSV (the specified Diameter-Sensitive Volume; also referred to herein as the “predetermined shimming volume”) and therefore require some adjustment of the field purity which is achieved by shimming. In addition, 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 the 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. Correction coils are therefore designed to produce a particular magnetic field shape that can be added to the background magnetic field, so as to cancel the effect of one or more of these spherical harmonics. 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. Zonal shim coils are those that possess complete azimuthal symmetry; that is, have the same current density around the periphery of the cylinder for each point along its length.
The main design task associated with these correction 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; U.S. Pat. No. 4,896,129), 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 suffers from three significant drawbacks. Firstly, the method does not allow the length of the coil to be specified in advance. Secondly, so that the Fourier-transform technique can be applied to finite length coils, the target fields must be moderated or smoothed in some way, so that the Fourier transforms converge, and this can introduce unnecessary errors and complications. Thirdly, because the coils in this approach are not given an explicit length, there is no straightforward way of using this method to design asymmetrically locates target fields in a coil of finite length.
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 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.
It is an object of this invention to provide coil structures that generate desired fields within certain specific, and asymmetric portions of the overall coil.
It is a further object of the present invention to provide a general systematic method for producing a desired zonal magnetic field within the coil, but using a technique that retains the simplicity of a direct analytical approach. In connection with this object, the desired zonal magnetic field can be located symmetrically or asymmetrically with respect to the overall geometry of the coil.
SUMMARY OF THE INVENTION
In one broad form, the invention provides a method for the design of symmetric and asymmetric zonal shim coils of a MR device. The method uses Fourier-series to represent the magnetic field inside and outside a specified volume. Typically, the volume is a cylindrical volume of length 2 L and radius a within the MR device. The current density on the cylinder is also represented using Fourier series. This approximate technique ignores “end effects” near the two ends of the coil, but gives an accurate representation of the fields and currents inside the coil, away from the ends.
Any desired field can be specified in advance on the cylinder's radius, over some portion (e.g., a non-symmetric 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.
For example, the desired target field in an asymmetric position of the cylindrical volume is represented as a periodic function of period equal to twice the length of the coil (i.e. 4 L). The extended periodic target field can be represented as an even periodic extension about an end of the coil. 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. In another broad form, the invention provides asymmetric zonal shim coils for MR systems. Asymmetric shim coils can be used in conventional MR systems or in the newly developed asymmetric magnets, such as the magnets of U.S. Pat. No. 6,140,900.
Thus, in accordance with certain of its aspects, the invention provides a zonal shim coil (e.g., a member of a shim set) having (i) a longitudinal axis (e.g., the z-axis) and (ii) a predetermined shimming volume (the dsv), and comprising a plurality of current-carrying windings which surround and are spaced along the longitudinal axis, said coil producing a magnetic field, the longitudinal component of which is given by:
B
z
(
r
,
θ
)
=
∑
n
=
0
∞
r
n
(
a
n0
P
n0
(
cos
θ
)
)
where a
n0
are the amplitudes of the zonal harmonics, P
n0
(cos &thgr;) are Legendre polynomials, n is the order of the polynomial, and r and &thgr; are radial and azimuthal coordinates, respectively;
wherein:
(i) the coil generates at least one predetermined zo
Crozier Stuart
Doddrell David Michael
Forbes Lawrence Kennedy
Barrera Ramon M.
Klee Maurice M.
NMR Holdings No. 2 Pty Limited
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