Self-shielded gradients and method of designing and producing self-shielded gradients
A self-shielded gradient adapted to be disposed within a main magnet field of an MRI scanner includes a gradient coil having a shield current distribution J s based on current density components φ n on a gradient surface where J s = ∑ n a n ϕ n . The current distribution is a predetermined value within a volume defined by a periphery of the gradient coil. The current distribution is substantially zero outside the periphery of the gradient coil. According to a method of producing a self-shielded gradient, a shield current distribution J s is determined based on current density components φ n on a gradient surface where J s = ∑ n a n ϕ n , by using an optimization technique, and a gradient coil is constructed according to the shield current distribution. The current distribution is a predetermined value within a volume defined by a periphery of the gradient coil. The current distribution is substantially zero outside the periphery of the gradient coil.
1. A method of producing a self-shielded gradient adapted to be disposed within a main magnet field of an MRI scanner, comprising:
determining a shield current distribution J s based on current density components φ n on a gradient surface where
J
s
=
∑
n
a
n
ϕ
n
,
by using an optimization technique; and
constructing a gradient coil according to the shield current distribution;
wherein the current distribution is a predetermined value within a volume defined by a periphery of the gradient coil;
wherein the current distribution is substantially zero outside the periphery of the gradient coil;
wherein the gradient is oriented along the static field direction;
wherein the gradient currents flow in at least one circular loop; and
wherein determining a shield current distribution includes determining a current density for a single current loop such that the current density is zero except at a radius of the loop.
2. The method of claim 1 , wherein the gradient surface is a plane, and each said φ n is φ n (x,y), where x and y are Cartesian coordinates on the gradient surface.
3. The method of claim 2 , wherein a corresponding primary gradient disposed within the main magnet field has a surface that is planar.
4. The method of claim 2 , wherein a corresponding primary gradient disposed within the main magnet field has a surface that is not planar.
5. The method of claim 4 , wherein the corresponding primary gradient has a surface that is a cylindrical section.
6. The method of claim 1 , wherein the gradient surface is a surface of a cylinder section, and each said φ n is φ n (r,θ), where r and θ are radial coordinates on the gradient surface representing the radius and angle of the position, respectively.
7. The method of claim 6 , wherein a corresponding primary gradient disposed within the main magnet field has a surface that is a cylindrical section.
8. The method of claim 6 , wherein a corresponding primary gradient disposed within the main magnet field has a surface that is not a cylindrical section.
9. The method of claim 8 , wherein the corresponding primary gradient has a surface that is planar.
10. The method of claim 1 , wherein determining the shield current distribution J s based on current density components φ n includes determining a current density corresponding to each current density component such that a resulting gradient field is minimized on a pole of a main magnet generating the main magnet field.
11. The method of claim 10 , further comprising determining a current density corresponding to each current density component such that a resulting gradient field is minimized on shim bars disposed at outer edges of the pole.
12. The method of claim 1 , wherein the shield current distribution is determined over a finite area.
13. The method of claim 1 , wherein φ n =δ(r−r n ){circumflex over (φ)}, wherein δ is the delta function and {circumflex over (φ)} is a unit vector along a circle.
14. The method of claim 1 , wherein determining a shield current distribution includes individually determining a current density for each of a plurality of current loops.
15. The method of claim 14 , further comprising interpolating a current density for a loop having a general radius based on a continuous shield current distribution for the plurality of current loops.
16. The method of claim 15 , wherein the plurality of current loops are concentric.
17. The method of claim 16 , wherein the radii of the respective current loops are equally-spaced.
18. The method of claim 15 , further comprising assembling current loops that are optimized to provide a substantially uniform gradient, based on the interpolated current density.
19. The method of claim 15 , further comprising optimizing gradient paths for transverse gradients based on the interpolated current density.
20. The method of claim 19 , wherein optimizing gradient paths includes optimizing positions of the gradient paths.
21. The method of claim 19 , wherein the gradient paths are optimized for a uniform gradient.
22. The method of claim 19 , further comprising optimizing positions for the longitudinal gradients.
23. The method of claim 22 , further comprising optimizing the amplitudes a n for the transverse gradients.
24. A self-shielded gradient adapted to be disposed within a main magnet field of an MRI scanner, comprising:
a gradient coil having a shield current distribution J s based on current density components φ n on a gradient surface where
J
s
=
∑
n
a
n
ϕ
n
;
wherein the current distribution is a predetermined value within a volume defined by a periphery of the gradient coil;
wherein the current distribution is substantially zero outside the periphery of the gradient coil;
wherein the gradient is oriented along the static field direction;
wherein the gradient currents flow in at least one circular loop; and
wherein the shield current distribution includes a current density for a single current loop such that the current density is zero except at a radius of the loop.
25. The self-shielded gradient of claim 24 , wherein the gradient surface is a plane, and each said φ n is φ n (x,y), where x and y are Cartesian coordinates on the gradient surface.
26. The self-shielded gradient of claim 25 , further comprising a corresponding primary gradient disposed within the main magnet field that has a surface that is planar.
27. The self-shielded gradient of claim 25 , further comprising a corresponding primary gradient disposed within the main magnet field that has a surface that is not planar.
28. The self-shielded gradient of claim 27 , wherein the corresponding primary gradient has a surface that is a cylindrical section.
29. The self-shielded gradient of claim 24 , wherein the gradient surface is a surface of a cylinder section, and each said φ n is φ n (r,θ), where r and θ are radial coordinates on the gradient surface representing the radius and angle of the position, respectively.
30. The self-shielded gradient of claim 29 , further comprising a corresponding primary gradient disposed within the main magnet field that has a surface that is a cylindrical section.
31. The self-shielded gradient of claim 29 , further comprising a corresponding primary gradient disposed within the main magnet field that has a surface that is not a cylindrical section.
32. The self-shielded gradient of claim 31 , wherein the corresponding primary gradient has a surface that is planar.
33. The self-shielded gradient of claim 24 , wherein a current density corresponds to each current density component φ n , such that a resulting gradient field is minimized on a pole of a main magnet generating the main magnet field.
34. The self-shielded gradient of claim 33 , wherein a current density corresponds to each current density component such that a resulting gradient field is minimized on shim bars disposed at outer edges of the pole.
35. The self-shielded gradient of claim 24 , wherein the shield current is distributed over a predetermined area.
36. The self-shielded gradient of claim 24 , wherein φ n =δ(r−r n ){circumflex over (φ)}, wherein δ is the delta function and {circumflex over (φ)} is a unit vector along a circle.
37. The self-shielded gradient of claim 24 , wherein the shield current distribution includes individual current densities for each of a plurality of current loops.
38. The self-shielded gradient of claim 37 , wherein the plurality of current loops are concentric.
39. The self-shielded gradient of claim 38 , wherein the radii of the respective current loops are equally-spaced.
40. The self-shielded gradient of claim 37 , wherein the current loops are optimized to provide a substantially uniform gradient, according to an interpolated current density for a loop having a general radius based on a continuous shield current distribution for the plurality of current loops.
41. The self-shielded gradient of claim 37 , further comprising gradient paths that are optimized for transverse gradients, according to an interpolated current density for a loop having a general radius based on a continuous shield current distribution for the plurality of current loops.
42. The self-shielded gradient of claim 41 , wherein the optimized gradient paths include optimized positions of the gradient paths.
43. The self-shielded gradient of claim 41 , wherein the gradient paths are optimized for a uniform gradient.
44. The self-shielded gradient of claim 41 , further comprising optimized positions for the longitudinal gradients.
45. The self-shielded gradient of claim 44 , wherein the amplitudes a n are optimized for the transverse gradients.