Method for determining construction parameters of magnet structures designed to generate magnetic fields in predetermined volumes of space and method for correcting magnetic fields in predetermined volumes of space, particularly in MRI apparatus

Abstract

A method for determining construction parameters of magnet structures designed to generate magnetic fields in predetermined volumes of space, comprising the steps of: a) defining a predetermined volume of space in which a static magnetic field is to be generated; b) defining the nominal strength and profile of the magnetic field in said predetermined volume of space; c) mathematically describing the nominal magnetic field on the surface of and/or in said predetermined volume of space by using a polynomial expansion of the magnetic field-describing function, which provides a series of coefficients; d) determining the size, geometry and relative position in space of the means for generating said nominal magnetic field, with respect to the volume of space in and on which the desired, i.e. nominal magnetic field, is defined. According to the invention, the predetermined volume of space is delimited by an ideal ellipsoidal closed surface and the magnetic field is expressed by coefficients of a polynomial ellipsoidal harmonic expansion. The method may be also used as a shimming method in volumes of space ideally delimited by ellipsoidal closed surfaces, to be implemented whether or not the predetermined volume of space defined by the magnet structure is also delimited by an ideal closed surface, with an ellipsoidal or other shape.

Description

The theory and implementations at the basis of the above methods of this invention will be now described in further detail, with reference to the accompanying drawings, in which:

FIG. 1 shows a two-dimensional grid of Gaussian abscissas.

FIG. 2 shows the three-dimensional grid (continuous line) of Gaussian abscissas in Cartesian coordinates and reference ellipsoid (a=90, b=80, c=70).

FIG. 3 shows the projection of the 3D Gaussian grid in the xy plane.

FIG. 4 shows a reference ellipsoid with a Brillouin sphere.

FIG. 5 shows the profile of ellipsoidal cosine coefficients with ‘even-even’ symmetry

FIG. 6 shows the profile of ellipsoidal sine coefficients with ‘even-even symmetry’.

Claims

1. A method for determining construction parameters of magnet structures designed to generate magnetic fields in predetermined volumes of space, comprising the steps of: a) defining a predetermined volume of space in which a magnetic field is to be generated;b) defining a nominal strength and a profile of a nominal desired magnetic field in said predetermined volume of space;c) mathematically defining the nominal desired magnetic field on a surface of and/or in said predetermined volume of space by calculating a series of coefficients using a polynomial expansion of a magnetic field-describing function; andd) determining a size, a geometry and a relative position in space of a magnet structure designed to generate said nominal desired magnetic field, with respect to the predetermined volume of space in and on which the nominal desired magnetic field is definedwhereinthe predetermined volume of space is delimited by an ideal closed surface having an ellipsoidal shape, andthe magnetic field is expressed by the coefficients of the polynomial expansion in ellipsoidal harmonics.

2. A method as claimed in claim 1, wherein the magnet structure is designed with an inhomogeneity tolerance threshold of up to thousands of parts per million (ppm) and after the magnet structure is constructed, the magnet structure is subjected to a shimming correction process.

3. A method as claimed in claim 2, wherein in the shimming process an inhomogeneity of the magnetic field within the predetermined volume of space is reduced below a tolerance threshold of up to tens of ppm peak to peak, the shimming process comprising the steps of: measuring a magnetic field generated in said predetermined volume of space at several predetermined points in a grid of predetermined measuring points arranged in said predetermined volume of space delimited by the ideal closed surface;comparing the measured magnetic field with the nominal desired magnetic field within said predetermined volume of space; anddetermining a value of a magnetic moment of magnetic shims and a position thereof over one or more shim positioning grids having a predetermined position and an orientation relative to said predetermined volume of space.

4. A method as claimed in claim 3, wherein the shimming is sequentially repeated several times.

5. A method as claimed in claim 3, wherein the shim positioning grid is configured as at least one of a Cartesian grid, an annular grid formed by intersection of concentric circles and radiuses, and an ellipsoidal grid formed by a number of ellipses, one inside another, intersecting with radiuses or adjacent parallel lines.

6. A method as claimed in claim 5, wherein the ellipses of the ellipsoidal grid are concentric or confocal.

7. A method as claimed in claim 1, wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps: measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N;constructing Lamé functions from dimensions of the semiaxes up to an order of N−1;calculating normalization coefficients γnp according to the function

8. A shimming method for correcting magnetic fields in predetermined volumes of space, comprising the following steps: defining a predetermined volume of space, which is permeated by the magnetic field, by defining an ideal closed delimiting surface;measuring a magnetic field generated in said predetermined volume of space at several predetermined points in a grid of predetermined measuring points arranged in said predetermined volume of space delimited by the ideal closed surface and/or along said ideal closed surface;comparing the measured magnetic field with a nominal desired is magnetic field within said predetermined volume of space and/or over the ideal closed delimiting surface; anddetermining a value of magnetic moment of magnetic shims and a position thereof over one or more shim positioning grids having a predetermined position and an orientation relative to said predetermined volume of space,whereinthe ideal closed surface that delimits the predetermined volume of space is an ellipsoidal surface,the magnetic field is expressed by a polynomial expansion in ellipsoidal harmonics.

9. A method as claimed in claim 8, wherein the shimming is sequentially repeated several times.

10. A method as claimed in claim 8, wherein the shim positioning grid is configured as at least one of a Cartesian grid, an annular grid formed by intersection of concentric circles and radiuses, and an ellipsoidal grid formed by a number of ellipses, one inside another, intersecting with radiuses or adjacent parallel lines.

11. A method as claimed in claim 10, wherein the ellipses of the ellipsoidal grid are concentric or confocal.

12. A method as claimed in claim 8, wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps: measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N;constructing Lamé functions from dimensions of the semiaxes up to an order of N−1.calculating normalization coefficients γnp according to the function

13. A method as claimed in claim 1, wherein the ideal surface that delimits the predetermined volume of space corresponds to an ellipsoid enveloping a limb, an organ, a body part under examination, a body under examination, or an anatomic region under examination and having a size that provides a highest filling ratio in the volume of space by the limb, the organ, the body under examination, the body part under examination, or the anatomic region under examination.

14. A method as claimed in claim 1, wherein the magnetic field is a static magnetic field of an MRI apparatus, which permeates a predetermined part of the volume that is defined by a cavity designed to receive a limb, an organ, a body part under examination, a body under examination, or an anatomic region under examination.

15. A method as claimed in claim 2, wherein the shimming is sequentially repeated several times.

16. A method as claimed in claim 4, wherein the shim positioning grid is configured as at least one of a Cartesian grid, an annular grid formed by intersection of concentric circles and radiuses, and an ellipsoidal grid formed by a number of ellipses, one inside another, intersecting with radiuses or adjacent parallel lines.

17. A method as claimed in claim 1, wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps: measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N;constructing Lamé functions from dimensions of the semiaxes up to an order of N−1;calculating normalization coefficients γnp according to the function

18. A method as claimed in claim 2, wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps: measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N;constructing Lamé functions from dimensions of the semiaxes up to an order of N−1;calculating normalization coefficients γnp according to the function

19. A method as claimed in claim 3, wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps: measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N;constructing Lamé functions from dimensions of the semiaxes up to an order of N−1;calculating normalization coefficients γnp according to the function

20. A method as claimed in claim 4, wherein the calculation of the coefficients of the polynomial expansion in ellipsoidal harmonics is performed with the following steps: measuring three semiaxes of the ideal ellipsoid delimiting the predetermined volume having an order of approximation N;constructing Lamé functions from dimensions of the semiaxes up to an order of N−1;calculating normalization coefficients γnp according to the function