USRE39460E1 - Asymmetric superconducting magnets for magnetic resonance imaging - Google Patents

Asymmetric superconducting magnets for magnetic resonance imaging Download PDF

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USRE39460E1
USRE39460E1 US10/283,692 US28369202A USRE39460E US RE39460 E1 USRE39460 E1 US RE39460E1 US 28369202 A US28369202 A US 28369202A US RE39460 E USRE39460 E US RE39460E
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coils
magnetic resonance
dsv
magnet
resonance system
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Stuart Crozier
David M. Doddrell
Huawei Zhao
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NMR Holdings No 2 Pty Ltd
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NMR Holdings No 2 Pty Ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
    • G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
    • G01R33/381—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using electromagnets
    • G01R33/3815—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field using electromagnets with superconducting coils, e.g. power supply therefor
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
    • G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
    • G01R33/3806—Open magnet assemblies for improved access to the sample, e.g. C-type or U-type magnets

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  • This invention relates to a method of magnet design and magnet configurations produced by the method.
  • the invention relates to asymmetric superconducting magnets for magnetic resonance imaging (MR imaging) and methods for designing such magnets.
  • MR imaging magnetic resonance imaging
  • MRI magnetic resonance imaging
  • dsv diameter spherical imaging volume
  • Conventional medical MRI systems are typically around 1.6-2.0 m in length with free bore diameters in the rnage of 8.0-1.0 m.
  • the magnet is symmetric and the midpoint of the dsv is located at the geometric center of the magnet's structure.
  • the central uniformity of symmetrical fields is often analyzed by a zonal spherical harmonic expansion.
  • FIG. 14 The basic components of a magnet system 10 useful for performing magnetic resonance investigations are shown in FIG. 14 .
  • the system of this figure is suitable for producing diagnostic images for human studies, similar systems being used for other applications.
  • System 10 includes magnet housing 12 , superconducting magnet 13 , shim coils 14 , gradient coils 16 , RF coils 18 , and patient table 20 .
  • magnet 13 serves to produce a substantially uniform field (the B 0 field) in the dsv.
  • Discussions of MRI, including magnet systems for use in conducting MRI studies, can be found in, for example, Mansfield et al., NMR in Imaging and Biomedicine, Academic Press, Orlando, Fla., 1982. See also McDougall, U.S. Pat. No. 4,689,591; McDougall et al., U.S. Pat. No. 4,701,736; Dorri et al , U.S. Pat. No. 5,416,415; Dorri et al., U.S. Pat. No. 5,428,292; and Chari et al., International Publication No. WO 94/06034.
  • the typical patient aperture of a conventional MRI machine is a cylindrical space having a diameter of about 0.6-0.8 meters, i.e., just large enough to accept the patient's shoulders, and a length of about 2.0 meters or more.
  • the patient's head and upper torso are normally located near the center of the patient aperture, which means that they are typically about a meter from the end of the magnet system.
  • the length of the magnet is a primary factor in determining the cost of an MRI machine, as well as the costs involved in the siting of such a machine.
  • MRI machines In order to be safely used, MRI machines often need to be shielded so that the magnetic fields surrounding the machine at the location of the operator are below FDA-specified exposure levels. By means of shielding, the operator can be safely sited much closer to the magnet than in an unshielded system. Longer magnets require more internal shielding and larger shielded rooms for such safe usage, thus leading to higher costs.
  • Pissanetzky has proposed an approach to field design based on a hybridized methodology incorporating ideas from finite elements, analytical techniques, and other numerical methods.
  • S. Pissanetzky “Structured coil for NMR applications,” IEEE Trans. Magn., 28, 1961-1968 (1992).
  • Thompson has illustrated a method based on a variational approach with constraints introduced by Lagrange multipliers.
  • the analytical aspects of the variational calculus were combined with numerical techniques to obtain optimal spatial coil distributions.
  • Michael R. Thompson, Robert W. Brown, and Vishnu C. Srivastava “An inverse approach to design of MRI main magnets”, IEEE Trans. Magn., 30, 108-112, (1994); and Robert W.
  • Crozier has introduced a stochastic optimization technique that was successfully used to design symmetric, compact MRI magnets. See S. Crozier and D. M. Doddrell, “Compact MRI magnet design by stochastic optimization,” J. Magn. Reson.127, 233-237 (1997); and U.S. Pat. No. 5,818,319.
  • the design of superconducting MRI magnets requires the consideration of various parameters. These include: central magnetic field strength, peak field in the superconductors, spatial homogeneity within the dsv, geometrical constraints, weight, and cost.
  • the challenge in designing a compact magnet is the retention of high homogeneity conditions in the dsv, as magnet homogeneity is strongly dependent on the overall length of the coil structure.
  • the invention in accordance with certain of its aspects provides a magnetic resonance system for producing MR images comprising an asymmetric superconducting magnet which produces a magnetic field which is substantially homogeneous over a dsv having a diameter greater than or equal to 40 centimeters, said magnet having a longitudinal axis (e.g., the “z-axis”) and comprising a plurality of current carrying coils which surround the axis, are distributed along the axis, and define a turn distribution function T(z) which varies with distance z along the axis and is equal to the sum of the number of turn in all coils at longitudinal position z, wherein:
  • the longitudinal extent “L” of the plurality of coils defines first and second ends for the superconducting magnet, which, for example, can be spaced apart by a distance which is less than or equal to 1.4 meters and greater than or equal to 0.3 meters,
  • the midpoint “M” of the dsv is spaced from the first end by a distance “D” which is less than or equal to 40 centimeters (preferably, less than or equal to 35 centimeters), and
  • the turn distribution function T(z) has a maximum value which occurs at a longitudinal location that is closer to the first end than to the second end.
  • the turn distribution function must exhibit substantially larger values near said first end.
  • the maximum value of the turn distribution function T(z) occurs at the first end, although in some cases in can be displaced to some extent from that end.
  • the turn distribution function is calculated by summing the number of turns of all coils surrounding a particular longitudinal position regardless of the radial locations of the coils and regardless of the direction in which current flows through the coils (i.e., the turn distribution function is a count of the number of turns in all coils without regard to winding direction).
  • the turn distribution function combines the effects of what would be referred to in classical MRI magnet design as primary and shielding coils, but does not include shim coils or gradient coils.
  • the terms “primary” and “shielding” coils are, in general, not particularly meaningful since the coils of the magnet take on a variety of radial locations, axial locations, and winding directions in order to achieve the desired dsv characteristics, as well as, desired overall magnet geometry (e.g., the magnitude of “L”), desired stray field levels external to the magnet (e.g., stray field levels less than 5 ⁇ 10 ⁇ 4 Tesla at all locations greater than 6 meters from the midpoint M of the dsv), and desired peak field strengths within the coils of the magnet (e.g., a peak magnetic field strength within the current carrying coils of less than 8.5 Tesla).
  • desired overall magnet geometry e.g., the magnitude of “L”
  • desired stray field levels external to the magnet e.g., stray field levels less than 5 ⁇ 10 ⁇ 4 Tesla at all locations greater than 6 meters from the midpoint M of the dsv
  • desired peak field strengths within the coils of the magnet e.g.
  • the MRI magnet will have a plurality of radially-stacked coils at the first end which are wound to carry currents in opposite directions.
  • at least one of the radially-stacked coils can be wound so as to carry current in a first direction and at least two others of those coils can be wound so as to carry current in a second direction opposite to the first direction.
  • these two coils are located radially adjacent to one another.
  • the radially innermost and radially outermost of the radially-stacked coils are wound to carry current in the same direction.
  • the invention provides a method of designing magnets for use in magnetic resonance imaging comprising the steps of:
  • a method for designing a superconducting magnet having a longitudinal axis which lies along the z-axis of a three dimensional coordinate system which comprises:
  • At least one cylindrical surface for current flow (e.g., 2 to 6 surfaces), said surface being located at a radius r 1 from the longitudinal axis and having a preselected length L along said axis;
  • step (d) selecting an initial set of coil geometries for the superconducting magnet using the vector J r1 (z) of current densities obtained in step (c);
  • step (e) determining final coil geometries for the superconducting magnet using a non-linear optimization technique applied to the initial set of coil geometries of step (d).
  • the selected at least one cylindrical surface for current flow has a first end and a second end, and step (b) in addition to requiring a specified homogeneity of the magnetic field in the z-direction over the dsv, also requires that:
  • the dsv has a midpoint closer to the first end than to the second end;
  • the magnitude of the stray magnet fields produced by the superconducting magnet at at least one location external to the superconducting magnet is less than a specified level;
  • constraints (a), (b), and (c) are simultaneously applied, along with the basic constraint that the magnetic field has a specified homogeneity in the z-direction over the dsv.
  • magnet configurations suitable for use in MR imaging are produced by above method.
  • FIG. 1a is a schematic view of a cylindrical surface on which current density calculations are performed. The figure also shows the parameters used in the calculations, as well as a dsv which is symmetrically located relative to the ends of an MRI magnet.
  • FIG. 1b is a schematic view of an MRI magnet having an asymmetrically-located dsv.
  • FIG. 2 is a view of a graph of current density oscillations with an initial coil configuration superimposed upon it.
  • FIG. 3 is a flow chart useful in describing and understanding the method of the invention.
  • FIGS. 4a and 4b show plots of current density for different regularization parameters and of relative error in field distribution for these regularization parameters.
  • FIGS. 5a and 5b are plots of normalized current density for magnets of different lengths.
  • FIG. 5c is a plot of normalized field distribution along the z-axis for the magnets of different lengths of FIGS. 5a and 5b .
  • FIG. 5d is a plot of the relative errors for the magnets of different lengths of FIGS. 5a and 5b .
  • FIG. 6 is a plot of maximum current density versus the relaxation factor ⁇ .
  • FIG. 7 is a view showing sample points over a dsv at which field strength can be determined.
  • FIGS. 8a , 8 b, and 8 c show field distributions and coil configurations for a non-linear optimization with five coils for a magnet having a length of 1.3 m, nine coils for a magnet having a length of 1 m, and seven coils for a magnet having a length of 0.8 m, respectively.
  • FIG. 8d is a plot of peak relative error for the configurations of FIGS. 8a , 8 b, and 8 c.
  • FIG. 9 illustrates the relationship between the field strength in the dsv, the transport current in all coils, and the maximum peak field in the coils.
  • FIG. 10a is a plot showing field distribution and coil configuration for a magnet having an asymmetrically positioned dsv.
  • FIG. 10b is a perspective view of the coil configuration shown in FIG. 10 a.
  • FIG. 11a shows current densities for a two layer asymmetric magnet, with the more rapidly varying current density being the inner layer and the less rapidly varying current density being the outer layer.
  • FIG. 12a shows current densities for another two layer asymmetric magnet, with the more rapidly varying current density being the inner (first) layer and the less rapidly varying current density being the outer (second) layer.
  • FIG. 12b is a plot showing field distribution and coil configuration for a magnet designed based on the current densities of FIG. 12 a.
  • FIG. 12c shows the 5 ⁇ 10 ⁇ 4 Tesla external stray field contour for the magnet of FIG. 12 b.
  • FIG. 12d shows the peak field distribution within the coils of the magnet of FIG. 12 b.
  • FIG. 12e is the turn distribution function T(z) of the magnet of FIG. 12 b.
  • FIG. 13a shows current densities for a three layer symmetric magnet.
  • FIG. 13b is a plot showing field distribution and coil configuration for a magnet designed based on the current densities of FIG. 13 a. Currents flowing in one direction are shown by filled blocks and currents flowing in the opposite direction are shown by open blocks.
  • FIG. 13c shows the 5 ⁇ 10 ⁇ 4 Tesla external stray field contour for the magnet of FIG. 13 b.
  • FIG. 13d shows the peak field distribution within the coils of the magnet of FIG. 13 b.
  • FIG. 14 is a schematic diagram of a prior art MRI machine.
  • the present invention relates to asymmetric MRI magnets and methods for designing such magnets.
  • the design technique involves two basic steps: (1) use of a current density analysis to obtain a first estimate of coil locations, and (2) use of non-linear optimization to obtain a final coil configuration.
  • the method aspects of the invention are discussed below in terms of a single current density layer, it being understood that the invention is equally applicable to, and, in general, will be used with multiple current density layers.
  • FIG. 3 illustrates the overall numerical procedure of the invention with reference to the various equations presented below.
  • the structure of a clinical MRI magnet comprises an air-cored coil.
  • the first step in the method of the invention is to find a source current density which is constrained to the surface of a cylinder of fixed length.
  • a current density J needs to be found which will produce a homogeneous magnetic field over the dsv.
  • the most effective basis unit is a single circular current loop J(R, ⁇ )d ⁇ . It then follows from Maxwell's equations that the magnetic induction dB(r,z) for a static field can be derived from the magnetic vector potential dA(r,z) according to the formula (see FIG.
  • dB(r,z,R, ⁇ ) ⁇ dA(r,z,R, ⁇ ) (1)
  • (r,z) is the field position coordinate
  • (R, ⁇ ) is source location
  • the radius R is usually fixed as a system requirement and B z is the only field component of interest in the dsv.
  • the technique of the invention only considers the magnetic field distribution along the Z-axis in the first instance, with other points in the dsv being considered later in the process.
  • the boundary ⁇ is divided into n parts ⁇ j .
  • J ⁇ will converge to the solution of (16) as ⁇ 0, provided that ⁇ 2 ⁇ 0 no less rapidly than ⁇ .
  • L is chosen in such a way that it will help to suppress wild oscillations in functions J for which ⁇ AJ ⁇ tilde over (B) ⁇ . However, this effect should not be too strong so that all oscillations in J are damped out.
  • Equation (19) is a n ⁇ n linear system, and the LU decomposition method (see, for example, W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Fannery, “Numerical Recipes in C”, Cambridge University Press, 683-688 (1992)) can be used with iterative improvement to compute the function J when the condition ⁇ AJ ⁇ tilde over (B) ⁇ is satisfied.
  • the structure must be refined.
  • the magnetic field produced by a coil having many turns of wire can be computed in the same way as above. All that is required is to apply the Biot-Savart law, and integrate along each turn in the (short) solenoids. However, if a very large number of turns are involved, this procedure becomes prohibitively expensive for optimization in terms of computer time.
  • An alternative approach is therefore used for computing the magnetic field produced by a circular coil that contains a large number of turns wound onto a solenoid of rectangular cross section.
  • N is the total number of the coils
  • (r,0,z) is the field location
  • (R j , ⁇ j ,w j ,h j ) are the coordinates of the coil
  • M r and M z are the kernels of the summation.
  • m ⁇ n is chosen so that equation (23) is an over-determinate system.
  • the process of the invention as described above is preferably practiced on a digital computer system configured by suitable programming to perform the various computational steps.
  • the programming can be done in various programming languages known in the art.
  • a preferred programming language is the C language which is particularly well-suited to performing scientific calculations.
  • Other languages which can be used include FORTRAN, BASIC, PASCAL, C ++ , and the like.
  • the program can be embodied as an article of manufacture comprising a computer usable medium, such as a magnetic disc, an optical disc, or the like, upon which the program is encoded.
  • the computer system can comprise a general purpose scientific computer and its associated peripherals, such as the computers and peripherals currently being manufactured by DIGITAL EQUIPMENT CORPORATION, IBM, HEWLETT-PACKARD, SUN MICROSYSTEMS, SGI or the like.
  • the numerical procedures of the invention can be implemented in C-code and performed on a Silicon Graphics Origin 2000 system.
  • the processing portion of the computer system should have the following characteristics: a processing rate of 25 million floating point operations per second; a word length of 32 bits floating point, at least sixty four megabytes of memory, and at least 100 megabytes of disk storage.
  • the system should include means for inputting data and means for outputting the results of the magnet design both in electronic and visual form.
  • the output can also be stored on a disk drive, tape drive, or the like for further analysis and/or subsequent display.
  • FIG. 4a shows the current density distributions corresponding to different values of ⁇ .
  • FIG. 4b The relative error in the field distribution is illustrated in FIG. 4b , where it is seen that as ⁇ 0, the error goes to zero.
  • the normalized magnetic field distributions are presented in FIG. 5 c and the relative errors are exhibited in FIG. 5 d. These results highlight the fact that the magnetic fields are very homogeneous in the controlled subdomain with maximal relative errors between +1 and ⁇ 1 ppm for all the cases. The maximal relative error is inversely proportional to ⁇ .
  • the peak current J max is located at the end of the magnet.
  • the maximum current density versus the relaxation factor ⁇ is given in FIG. 6 , which shows that as ⁇ 0 the peak current density J max becomes extremely large. This indicates that at least one large coil is required at the end of magnet.
  • the current densities shown in FIGS. 5 (a) and 5 (b) are converted into coil configurations using the non-linear optimization technique described above.
  • L 0.8 m
  • 1.0 m and 1.5 m the radius of the free bore
  • R 0.5 m
  • 150 sample points evenly spaced over the dsv and including its surface were selected as exemplified in FIG. 7 .
  • the constant target field B z was set to 1.0 Tesla at each sample point of the dsv.
  • the resulting continuous current density function shown in FIG. 5a is clearly oscillating.
  • the final solution also gives 5 positive coils, however, the over all length of the magnet reduces to 1.3 m during refinement.
  • FIG. 8 c The other coils coalesced or cancelled during the refinement process, illustrating the strong non-linear behavior between magnet structure and generated magnetic field.
  • the peak relative error is presented in FIG. 8d , which illustrates the worst situation of the field on the surface of the dsv. Note that the current density distributions of FIG. 5 only guarantee the homogeneity of the B z field on the Z-axis within the dsv so that testing the homogeneity on the surface of the dsv represents a worst case analysis.
  • the solution was, not surprisingly, different from that when only the Z-axis fields were considered.
  • the magnitude of the error in homogeneity was reduced for this case compared with the case where B z was specified only on axis.
  • the final solution for the coil structure had the same general topology as that predicted by the initial current density analysis. This illustrates the advantage of using the current density analysis as the starting point for determining the coil configuration.
  • the peak fields and current densities must be within working limits of NbTi or other available superconductors.
  • the relations between the field strength in the dsv and the transport current and the peak field in the superconductor is illustrated in FIG. 9 , which concludes, not surprisingly, that a long magnet is easier to build than a short one.
  • FIG. 10 Using the techniques of the invention, a compact asymmetric MRI magnet design was optimized. The result is given in FIG. 10 and Table 2, wherein Table 2A gives performance results and Table 2B gives the coil structure, dimensions, and current directions.
  • the constant target field ⁇ dot over (B) ⁇ z was set to 1.0 Tesla. This design had a volume rms inhomogeneity of about 8 ppm over a dsv of 45 cm, the epoch of which was 11.5 cm from the end of the magnet.
  • This magnet structure is buildable and the peak fields and current densities are within working limits for NbTi superconductors.
  • the contour plot of magnetic field in FIG. 10a illustrates the position and purity of the dsv.
  • FIG. 10b provides a perspective view of the final magnet structure.
  • FIG. 11b shows the resultant homogeneity for a 45 cm dsv having its epoch 12 cm from one end of the magnet.
  • the data of this figure shows that a suitably homogeneous field was achieved. Moreover, the stray field was reduced to 5 gauss (5 ⁇ 10 ⁇ 4 Tesla) on a distorted ellipsoid having a major axis radius of approximately 5 m and a minor axis radius of approximately 3 m measured from the center (midpoint) of the dsv.
  • FIGS. 12 and 13 illustrate the use of two current layers for an asymmetric system (FIG. 12 and Table 3) and three current layers for a symmetric system (FIG. 13 ).
  • panel a shows the current density determined using the current density analysis
  • panel b shows the final coil configuration after non-linear optimization, as well as the position and purity of the dsv
  • panel c shows the stray field contour at 5 gauss
  • panel d shows the peak field distribution in the superconducting coils.
  • FIG. 12e shows the turn distribution function for the magnet of FIG. 12 b. As can be seen in this figure, the turn distribution function has its maximum value at the left hand end of the magnet, i.e., the end towards which the dsv is displaced.
  • the turn distribution function has its maximum value at the left hand end of the magnet, i.e., the end towards which the dsv is displaced.
  • FIGS. 12 and 13 are readily buildable using available superconducting materials and conventional techniques.
  • a hybrid numerical method has been provided which can be used to design compact, symmetric MRI magnets as well as compact, asymmetric magnets.
  • the method can be used to obtain a compact MRI magnet structure having a very homogeneous magnetic field over a central imaging volume in a clinical system of approximately 1 meter in length, which is significantly shorter than current designs.
  • the method provides compact MRI magnet structures with relaxation factors ⁇ 0.40, so that the dsv region can be located as close as possible to the end of the magnet. In this way, the perception of claustrophobia for the patient is reduced, better access to the patient by attending physicians is provided, and the potential for reduced peripheral nerve stimulation due to the requisite gradient coil configuration is achieved.
  • the method uses an inverse approach wherein a target homogeneous region is specified and is used to calculate a continuous current density on the surface of at least one cylinder that will generate a desired field distribution in the target region.
  • This inverse approach to is akin to a synthesis problem.
  • the inverse current density approach is combined with non-linear numerical optimization techniques to obtain the final coil design for the magnet.
  • the field calculation is performed by a semi-analytical method.

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