Abstract:
Gradient coil assemblies and shim coil assemblies are disclosed for magnetic resonance imaging (&#34;MRI&#34;) devices, wherein the coil assemblies comprise a coil support and a conductive wire having a locus described by a solution of a current continuity equation over a finite interval for which certain terms of the magnetic field expansion are equal to zero, for generating non-uniform magnetic fields. The gradient coil produces gradient fields and magnetic fields which cancel non-uniformities in the magnetic field of the magnet of the MRI device. Shim coils cancel such non-uniformities, as well. A method of manufacturing such coils is also disclosed.

Description:
FIELD OF THE INVENTION 
     The present invention relates to optimized gradient coils and shim coils for magnetic resonance scanning systems, including optimized shielded gradient coils and shim coils for use in vertical field magnetic resonance imaging systems. 
     BACKGROUND OF THE INVENTION 
     Magnetic resonance scanning systems include magnetic resonance imaging (MRI) and magnetic resonance spectroscopy (MRS) systems. These systems, and particularly those used for medical imaging, are required to develop a highly uniform magnetic field and precise and controllable time-varying gradients within that magnetic field. MRI systems typically include a magnetic structure for developing the uniform magnetic field and auxiliary coils through which currents flow in order to superimpose gradients on the magnetic field. The magnetic field uniformity is improved by the use of auxiliary correcting coils through which current flows to make corrections for non-uniformity of the magnetic field. This correcting is called &#34;shimming&#34; the magnetic field, and the correcting coils are referred to as shim coils. 
     The design of gradient coils and shim coils has received considerable attention in recent years. The design techniques used can be broadly classified in two categories. With the target field method a current distribution is established which develops a magnetic field having the target values at the specified points of space. See R. Turner, A Target Field Approach to Optimal Coil Design, J. Phys. D:Appl. Phys. 19, L147-L151 (1986). 
     An alternative method of field modification involves representing the field as a sum of orthogonal basis functions and determining the amplitude that each basis function should have in order to achieve the desired field. A coil or other conductive path is established for flowing current which is effective to generate the field described by the summation of basis functions. See F. Romeo and D. I. Hoult, Magnet Field Profiling: Analysis and Correcting Coil Design, Magnetic Resonance in Medicine 1, 44-65 (1984). 
     A particularly important class of coils in the MRI field are self-shielded gradient coils. These coils are configured to generate a desired gradient field within a region of space when current flows through the coils and so that the magnetic field outside the coils is as near to zero as possible. Self-shield gradient coils minimize the interaction between the gradient magnetic field and the MRI system structure. Various approaches to the construction of self-shielded gradient coils have been proposed. See P. Mansfield and B. Chapman, Active Magnetic Screening of Gradient Coils in MR Imaging, Journal of Magnetic Resonance 66, 573-576 (1986) and U.S. Pat. No. 4,737,716 issued to P. B. Romer, et al., for self-shielded gradient coils for nuclear magnetic resonance imaging. 
     The structure of gradient coils and shim coils for MRI systems necessarily involves departures from ideality. First, if an ideal current distribution extends to infinity, it must be truncated so it occupies a finite region of space. Coils of infinite extent are obviously not realizable and as a practical matter, the coils will be physically smaller than the MRI system overall. Secondly, the ideal current distribution is frequently a continuous current sheet which can only be approximated by a discrete distribution of current flowing through wires. Thirdly, the design methods used to determine the coil configurations and dimensions themselves introduce non-idealities into the resulting coil. In particular, the target field method yields current paths that exhibit large spatial oscillations which make the coils difficult to build. 
     It is an object of the invention to provide gradient and shim coils for MRI scanners which are optimized for the case of finite, discrete current distributions and which do not use the target field method in their design. 
     It is another object of the invention to provide a self-shielded gradient coil for MRI scanners. 
     Another object of the invention is to provide a method of manufacturing coils of the type just described. 
     SUMMARY OF THE INVENTION 
     According to the invention, a gradient coil, or shim coil assembly for magnetic resonance imaging is comprised of an insulating coil support having a major surface, and a conductive wire defining a gradient coil disposed on the coil support and having a locus described by the solution of the current continuity equation over a finite interval for which certain terms of the magnetic field expansion are equal to zero. In one preferred embodiment the insulative coil support is planer so that the conductive wire defining a gradient coil is confined to a plane. 
     In still another embodiment, the gradient coil is a self-shielded gradient coil for minimizing magnetic interaction between the gradient field and the MRI scanner in which the self-shielded gradient coil is used. 
    
    
     BRIEF DESCRIPTION OF THE DRAWING 
     FIG. 1 illustrates the coordinate system used in the specification; 
     FIG. 2 is a plan view of the current contours and conductor paths of a gradient coil according to the invention; 
     FIG. 3 is a plan view of the current contours and conductor paths of a shim coil according to the invention; 
     FIG. 4 is a vertical elevation of a pair of magnet poles in an MRI system showing gradient coil and image current positions; 
     FIGS. 5 and 6 are plan views respectively showing one quadrant of the current contours and conductor paths of a gradient and shield coil for a self-shielded gradient coil according to the invention; 
     FIG. 7 is a top view of a gradient coil assembly according to the invention approximating the current contours of FIG. 2, including a portion 22 with a cut-out section 24; and 
     FIG. 8 is a perspective view of portion 22 of FIG. 7. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     The following discussion uses a spherical coordinate system which is shown in FIG. 1. In the coordinate system the position of a point P is determined relative to an origin O by the three parameters θ, φ, and ρ. The point P lies within an imaginary plane S which is a distance from the origin O. Within the plane S the position of the point P is determined by azimuth angle φ and the radius vector ρ. The line of sight from the origin O to the point P makes an angle θ with respect to the distance line from the origin to the plane S. The spherical coordinate system was chosen because the preferred embodiments of coils disclosed below are for an MRI system having a vertical field magnet in which the coils are provided in pairs each adjacent a respective magnet pole face. Accordingly, one coil will be described as lying within the imaginary plane S and the second coil in a second imaginary plane (not shown) at a distance of -a from the origin O. 
     The desired gradient coil shape and dimensions are determined by first representing the magnetic field as a summation of the orthogonal set of basis functions, determining the spatial relationship between the field and the current which generates it and finally solving for the current density. The current density is also represented by orthogonal basis functions (not necessarily the same as those used to represent the magnetic field). 
     Spherical Harmonic Representation of the Field 
     We represent the static field B z  in an MRI magnet by a sum of spherical harmonics ##EQU1## where the Y nm  are spherical harmonics according to the Bethe definition in which x=cos θ 
     
         Y.sub.nm =(1/2π).sup.1/2 p.sub.nm (x)exp(imφ)       2 
    
     and where ##EQU2## 
     Relationship Between Field and Current 
     Consider currents on planes above and below the imaging volume. The current density J(φ,ρ) must satisfy the two-dimensional continuity equation, 
     
         ∂Jφ/∂φ=∂ρ·J.rho./∂ρ=O                                    4 
    
     where ρ and φ are the radial and angular coordinates as shown in FIG. 1. Current lies on a first plane at z=a and a second plane at z=-a. 
     We employ a current density described by a summation of sine and cosine functions and which is non-zero over a finite region only. A current density that satisfies the continuity equation (4) can be written as ##EQU3## where 
     
         c=π/(ρ.sub.m -ρ.sub.o) 
    
     where q and k are integers and ρ m  and ρ o  are the maximum and minimum radii. 
     One needs only consider one k value at a time to design gradient coils and most shim coils. When k=1, the solution for the current density yields the x-gradient coil. When k=0, one obtains a z-gradient coil or a constant. By rotating 90 degrees, an x-gradient coil becomes a y-gradient coil. 
     Shim coils are obtained the same way for k&gt;2. Rotation by 45 degrees transforms an x 2  -y 2  shim coil into a 2xy shim coil. Third order shim current densities can be rotated 30 degrees to produce other useful shims. It is convenient to use the above current density for all terms and rotate it to get shim terms not covered by the formula. 
     Given the current density, we calculate the magnetic gradient or shimming field from 
     
         B=(μ.sub.o /4π)∇×|dV&#39;J(r&#39;)/|r-r&#39;|7 
    
     where J(r&#39;) is the current density (in vector form) obtained from the solution of the continuity equation provided by Equations 5 and 6, r&#39; is the distance from the origin 0 to a point on the coil in the plane S in FIG. 1, and r is the distance from the origin to a point in space between the origin 0 and the plane S. By expanding 1/|r-r&#39;|in Equation 7 in spherical harmonics, it can be shown that the z- component of the magnetic gradient or shimming field is ##EQU4## where P n ,k-1 is an associated Legendre polynomial. 
     Values of the coefficients of the mathematical expansion representative of the current distribution (Equations 5 and 6) which null out predetermined terms in the mathematical expansion of the magnetic field (Equation 8) are calculated to determine the current distribution which will generate the desired non-uniform magnetic field. 
     The coefficients in the mathematical expansion representive of the current distribution to be approximated by the set of windings can be determined by solving a matrix equation. The matrix equation comprises a rectangular matrix having rows equal to the amplitudes of the expansion coefficients of the magnetic field produced by current distributions corresponding to single terms in the expansion for current distribution, having one row for each component in the expansion for the magnetic field component along the static field direction. The rectangular matrix is multiplied by a first column matrix whose elements are the amplitudes of the terms in the expansion of the current distribution. The rectangular and column matrices are set equal to a second column matrix whose elements are the amplitudes corresponding to the terms in the expansion of the magnetic field which produce a desired linear magnetic field variation of the component along the static field. 
     EXAMPLES 
     The equations for the current density, and hence the current, can be solved by well known numerical methods on a digital computer. Alternatively, convenient commercially available equation solver programs which will run on a personal computer can be used. These equation solver programs accept as input the equations to be solved in symbolic form and do not require the user to program the computer in order to obtain a solution. Two such programs of sufficient power are Mathematica (TM) and Maple V (TM). 
     FIG. 2 shows the current contours for an x-gradient (or y-gradient) coil for a vertical field MRI system having circular poles. The physical gradient coil would comprise conductors, such as wires, disposed along the contours shown and electrically connected in series. The current contours are drawn to scale. 
     FIG. 7 is a top view of a gradient coil assembly 10 according to the present invention, wherein wire 12 approximates the current contour above the x-axis of FIG. 2 and wire 13 approximates the current contour below the x-axis. The wires 12, 13 are supported by an insulative support 14, which is planar in this embodiment. The wires 12, 13 may be disposed on the surface of the support 14, or embedded in grooves 16 in the surface of the support 14. A current source 18, 20 is connected to the ends of each wire 12, 13, respectively. The wires 12, 13 could be connected in series with a single current source, as mentioned above and known in the art. FIG. 7 includes a portion 22 having a cut-out section 24. FIG. 8 is a perspective view of the portion 22 and cut-out section 24, showing the grooves 16 and wire 13. A gradient coil system would typically comprise a plurality of coils supported by a plurality of insulative supports. 
     FIG. 3 shows the current contours for a shim field for x 2  -y 2  field terms, corresponding to k=2. The physical shim coil would likewise comprise conductors disposed along the contour lines and electrically connected in series. The current contours are drawn to scale. 
     FIG. 4 illustrates a pair of ferromagnetic poles 1,2 of a vertical field MRI system. A pair of gradient coils 3,4 are positioned at distances ±a, respectively, from the center of the gap between the magnet poles 1,2. The poles have respective pole faces positioned at distances ±b from the gap center where b&gt;a. In this preferred embodiment the pole faces are circular. 
     An electrical current between two perfectly conducting planes produces an infinite number of image currents. In the following discussion the ferromagnetic poles 1,2 will be treated as conducting planes at their pole faces, i.e. at distance b from the gap center. It is desired to add a companion set of coils at ±b so that the magnetic field outside the gap, z&gt;b, will be as low as possible. Thus, self shielded gradients would be realized. 
     The tangential component H t  of the magnetic intensity at z=±b resulting from the gradient coil current is computed. Image currents in planes on opposite sides of the gap must be taken into account when computing H t . Because images further from the center contribute less to the field, only a finite number need be considered. 
     For transverse gradient coils and poles separated by a distance 2b, positive images are located at 
     
         z-=(2j-1)b+(-1).sup.j (b-a) 
    
     where j=1,2,3 . . . , and negative images are located at 
     
         z-=(2j-1)b-(b-a). 
    
     For a longitudinal or z-gradient coil positive images are located at 
     
         z-=(2j-1)b-(-1).sup.j (b-a), 
    
     and negative images occur at 
     
         z-=(2j-1)b+(b-a). 
    
     Once H t  is determined the current density needed at z=±b to shield the magnetic field, e.g. the shield coils, is solved simply from 
     
         J.sub.t =H.sub.t xn. 
    
     FIGS. 5 and 6 respectively show one quadrant of the current contours for an x-gradient coil and the x-gradient shield coil. The current contours in both FIGS. 5A and 5B are drawn to scale both within each Fig. and relative to each other. The physical gradient and shield coils are realized by connecting the contours of each coil electrically in series and by connecting the two coils electrically in series. A pair of such gradient coil-shield coil sets, when a current flows through them, will result in a gradient magnetic field within the magnet gap with at most a substantially attenuated field at the pole faces. Consequently, the pair of gradient coil-shielded coil sets constitutes a pair of self-shielded gradient coils. 
     A quiet gradient coil system for magnetic resonance imaging scanners can be provided by securing a conductive wire within a surface groove of an insulative support with a securing means which reduces gradient coil flexure and resultant audible noise caused by current pulses flowing through the gradient coil. The means for securing may comprise an adhesive material disposed within the groove, such as the grooves 16 of the support 14 of FIGS. 7 and 8. As in FIGS. 7 and 8, the insulative support may be planar. The means for securing may also comprise a second planar insulative member disposed on the planar surface of the planar insulative support. The second planar insulative member is maintained against the planar surface of the insulative support to secure the wire 13 within the surface groove 16 of the support 14. The means for securing may also comprise the walls of the surface groove 14, wherein the surface groove 14 is dimensioned to provide a friction fit between the wire 13 and the walls of the groove 16.