A high-field animal magnetic resonance imaging superconducting magnet, gradient coil, and decoupling method
By designing a multi-layer coil structure and decoupling method, the coupling problem between superconducting magnets and gradient coils in high-field animal magnetic resonance imaging systems was solved, the system stability and magnetic field uniformity were improved, and operation and maintenance were simplified.
Patent Information
- Application Number
- CN202411676715.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-22
- Publication Date
- 2025-10-10
- Estimated Expiration
- 2044-11-22
AI Technical Summary
In high-field animal magnetic resonance imaging systems, the mechanical and electromagnetic coupling problems between superconducting magnets and gradient coils have not been effectively solved, resulting in threats to system stability and magnetic field uniformity.
A superconducting magnet and gradient coil for high-field animal magnetic resonance imaging (MRI) was designed. This design employed a multi-layer coil structure and a special decoupling method, including a combination of inner and outer main coils, adjustment coils, shielding coils, and shim coils. The decoupling of the superconducting magnet and gradient coils was achieved by optimizing the wire spacing through boundary element meshing and the target field method.
It effectively reduces the Lorentz force and stray magnetic field, improves the stability of the system and the uniformity of the magnetic field, facilitates operation and maintenance, and reduces the influence of eddy current effects.
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Figure CN119480329B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application belongs to the field of electrical engineering theory and new technology, and particularly relates to a high-field animal magnetic resonance imaging superconducting magnet, gradient coil and decoupling method, which is used for animal magnetic resonance imaging research. BACKGROUND
[0002] Animal magnetic resonance imaging is smaller in aperture than human magnetic resonance imaging, and is different from human magnetic resonance imaging in pursuit of more universality, safety and comfort. Animal magnetic resonance imaging usually emphasizes excellent performance. The detection hole of animal magnetic resonance imaging is small and long, and there is no need to consider the claustrophobia of the organism. The radio frequency short wave side effect is not obvious, and animal magnetic resonance imaging can usually provide higher main magnetic field strength and gradient magnetic field strength, and faster gradient magnetic field conversion efficiency than human magnetic resonance imaging. Under the interaction of strong magnetic field, a huge alternating Lorentz force is generated between the superconducting magnet and the gradient coil, which threatens the stable operation of the system, which is a common key problem of high-field magnetic resonance imaging system. In addition, the transient transformed gradient magnetic field will also generate eddy current on the superconducting magnet, and then radiate the secondary magnetic field. Therefore, the research and development of high-performance animal magnetic resonance imaging system not only research and develop high-field superconducting magnet and gradient coil itself, but also effectively solve the coupling problem of the components during operation.
[0003] Chinese invention patent ZL201610811541.1 discloses a super-high-field high-uniformity superconducting magnet for small animal magnetic resonance imaging, which comprises 1 main coil, 4 adjusting coils and 2 shielding coils. The coil structure type is different from the present application, and the above-mentioned patent does not contain the gradient coil, and there is no decoupling problem between the superconducting magnet and the gradient coil. Chinese invention patent ZL202210372215.0 discloses a miniature animal magnetic resonance imaging superconducting magnet and gradient device, the superconducting magnet is a non-shielded structure, the scale is smaller, and it does not contain shielding coils. The gradient device only contains three layers of main coils, does not contain shielding coils and shim coils, and the coupling between the superconducting magnet and the gradient device is controllable, and it is not considered separately. SUMMARY
[0004] To solve the above technical problems, the present application provides a high-field animal magnetic resonance imaging superconducting magnet, gradient coil and decoupling method. The design of the superconducting magnet and the gradient coil fully considers the excitation safety and the need for field uniformity. The superconducting magnet has appropriate electromagnetic margin, and sufficient shim coils and shim structures are arranged. In addition, under high field strength, the mechanical and electromagnetic coupling problems between the superconducting magnet and the gradient coil are effectively solved.
[0005] To achieve the above purpose, the technical scheme adopted by the present application is as follows:
[0006] In one aspect, the present application provides a high-field animal magnetic resonance imaging superconducting magnet, comprising: an inner main coil, an outer main coil, a first adjusting coil, a second adjusting coil, a third adjusting coil, a fourth adjusting coil, a superconducting shim coil, a first shielding coil, a second shielding coil, and a third shielding coil, wherein,
[0007] The inner main coil and the outer main coil are helical and are nested along the same coaxial axis with separate skeletons.
[0008] The first adjusting coil, the second adjusting coil, the third adjusting coil, and the fourth adjusting coil are all annular coils, are uniformly distributed on both sides of the midpoint of the lengthwise symmetry axis of the outer main coil, the first adjusting coil and the third adjusting coil are on the same side, the second adjusting coil and the fourth adjusting coil are on the same side, the first adjusting coil, the second adjusting coil, the third adjusting coil, and the fourth adjusting coil are supported by the same skeleton and are nested outside the outer main coil.
[0009] The superconducting shim coil comprises a plurality of sub-coils, is supported by the same skeleton, and is nested outside the layer where the first to fourth adjusting coils are located.
[0010] The first to third shielding coils are all annular coils, are supported by the same skeleton, and are nested outside the layer where the superconducting shim coil is located, the first shielding coil is located at the midpoint of the lengthwise symmetry axis of the outer main coil, and the second shielding coil and the third shielding coil are uniformly distributed on both sides of the first shielding coil.
[0011] Further, the inner main coil and the outer main coil have the same length.
[0012] Further, the first adjusting coil and the second adjusting coil have the same inner and outer diameters, the third adjusting coil and the fourth adjusting coil have the same inner and outer diameters, the first adjusting coil and the second adjusting coil have the same width, the third adjusting coil and the fourth adjusting coil have the same width, and the width of the first adjusting coil and the second adjusting coil is smaller than the width of the third adjusting coil and the fourth adjusting coil.
[0013] Further, the superconducting shim coil comprises nine sub-coils arranged from inside to outside, namely Z2 superconducting shim coil, Z1 superconducting shim coil, Z3 superconducting shim coil, X superconducting shim coil, Y superconducting shim coil, ZX superconducting shim coil, ZY superconducting shim coil, X2-Y2 superconducting shim coil, and XY superconducting shim coil.
[0014] Further, the first to third shielding coils have the same inner and outer diameters.
[0015] Further, the first shielding coil is wider than the second shielding coil and the third shielding coil located at both ends, and the second shielding coil and the third shielding coil have the same width.
[0016] In another aspect, the present application provides a high-field animal magnetic resonance imaging gradient coil, which comprises 11 sub-coils, several water pipes for cooling and iron shim uniformity slots, each sub-coil is coaxially nested from inside to outside, which are: the inner layer main coil of the X gradient coil, the inner layer main coil of the Y gradient coil, the water pipe, the inner layer main coil of the Z gradient coil, the X2-Y2 gradient coil, the XY gradient coil, the ZX gradient coil, the ZY gradient coil, the Z0 gradient coil, the Z2 gradient coil, the Z3 gradient coil, the Z4 gradient coil, the iron shim uniformity slot, the water pipe, the outer layer shielding coil of the Z gradient coil, the outer layer shielding coil of the X gradient coil, and the outer layer shielding coil of the Y gradient coil, wherein,
[0017] The Z0 gradient coil is zero-order, the Z gradient coil, the X gradient coil and the Y gradient coil are first-order, the Z2 gradient coil, the ZX gradient coil, the ZY gradient coil, the X2-Y2 gradient coil and the XY gradient coil are second-order, the Z3 gradient coil is third-order, and the Z4 gradient coil is fourth-order.
[0018] Further, the first-order Z gradient coil, the X gradient coil and the Y gradient coil are magnetic field encoding coils.
[0019] Further, the outer diameter of the gradient coil is not more than 292mm, and the inner diameter of the gradient coil is not more than 170mm.
[0020] In a third aspect, the present application provides a high-field animal magnetic resonance imaging superconducting magnet and gradient coil decoupling method, which is applied to the aforementioned high-field animal magnetic resonance imaging superconducting magnet and high-field animal magnetic resonance imaging gradient coil. The gradient coil is placed in the superconducting magnet, the center positions of the two coincide, and the contact place is padded with a rubber sheet. The decoupling between the superconducting magnet and the gradient coil is realized by the following steps:
[0021] Firstly, the two layers of cylindrical shells where the main coils and shielding coils of the first-order Z gradient coil, the X gradient coil and the Y gradient coil are located are meshed with triangles as boundary elements;
[0022] Secondly, the Lorentz force F(x) on the triangular boundary element mesh is calculated according to the coil structure of the superconducting magnet, which is a function of the flow function value x to be solved at the grid node;
[0023] Thirdly, the Lorentz force F(x) is written into the objective function of the gradient coil design;
[0024] Fourthly, the minimum acceptable distance d between the conductors of the gradient coil is set, and the initial value s0 of the maximum stray magnetic field of the gradient coil in the cylindrical surface region of the cold shield of the superconducting magnet is set;
[0025] Fifth step, the gradient coil is designed by using the target field method and the minimum distance d1 between the conductors is calculated, whether the condition |d1-d|<=0.2mm is satisfied is evaluated, if not, the shielding constraint is tightened, that is, s0 is reduced, the gradient coil is redesigned and the minimum distance d1 between the conductors is calculated, and the cycle is executed;
[0026] Sixth step, if the condition |d1-d|<=0.2mm is satisfied, the first-order gradient coil structure is outputted;
[0027] Seventh step, the single-layer cylindrical shell where other single-layer coils included in the gradient coil are located is meshed by using a triangle as a boundary element, and the other single-layer coils are outputted by using the target field method.
[0028] The present application has the following beneficial technical effects:
[0029] The superconducting magnet has prominent shielding effect, the shielding structure of 3 coils is adopted, the 5-gauss line range is significantly narrowed, especially at the upper end of the magnet, the 5-gauss line is close to the magnet coil, which is convenient for lead plug-in, refrigerator maintenance and other operations; the minimum control method of the gradient coil stray magnetic field can effectively reduce the eddy current secondary magnetic field effect of the transient gradient magnetic field on the superconducting magnet; the minimum method of the Lorentz force between the superconducting magnet and the gradient coil can effectively avoid the gradient coil from shaking, and the traditional method is to extend the gradient coil to the end plate of the superconducting magnet to realize the fixation of the two, the present application does not need such structure, only needs to place the gradient coil on the rubber sheet on the pad in the superconducting magnet temperature hole. In addition, the superconducting magnet and the gradient coil are internally provided with sufficient shim coils for greatly improving the magnetic field uniformity under the condition of severe initial magnetic field. BRIEF DESCRIPTION OF DRAWINGS
[0030] Figure 1 It is the overall cross-sectional structure of the superconducting magnet and the gradient coil;
[0031] Figure 2 It is a 3 / 4 model of the three-dimensional structure of the superconducting magnet;
[0032] Figure 3 It is the three-dimensional structure of each sub-coil of the superconducting shim coil;
[0033] Figure 4 It is the three-dimensional structure of each sub-coil of the gradient coil.
[0034] Reference signs:
[0035] 1, inner main coil, 2, outer main coil, 3, first adjusting coil, 4, second adjusting coil, 5, third adjusting coil, 6, fourth adjusting coil, 7, superconducting shim coil, 8, first shield coil, 9, second shield coil, 10, third shield coil, 11, superconducting magnet cold shield, 12, superconducting magnet vacuum vessel, 13, gradient coil, 14, rubber sheet, 7a, Z2 superconducting shim coil, 7b, Z1 superconducting shim coil, 7c, Z3 superconducting shim coil, 7d, X superconducting shim coil, 7e, Y superconducting shim coil, 7f, ZX superconducting shim coil, 7g, ZY superconducting shim coil, 7h, X2-Y2 superconducting shim coil, 7i, XY superconducting shim coil, 13a, X gradient coil, 13b, Y gradient coil, 13c, Z gradient coil, 13d, X2-Y2 gradient coil, 13e, XY gradient coil, 13f, ZX gradient coil, 13g, ZY gradient coil, 13h, Z0 gradient coil, 13i, Z2 gradient coil, 13j, Z3 gradient coil, 13k, Z4 gradient coil. DETAILED DESCRIPTION
[0036] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application.
[0037] As shown in the drawings, Figures 1-2 The superconducting magnet of the present application includes an inner main coil 1, an outer main coil 2, a first adjusting coil 3, a second adjusting coil 4, a third adjusting coil 5, a fourth adjusting coil 6, a superconducting shim coil 7, a first shield coil 8, a second shield coil 9, and a third shield coil 10. Among them,
[0038] The inner main coil 1 and the outer main coil 2 are spiral-shaped and have the same length, and are respectively supported by a separate framework to be nested along the same axis, that is, the radius of the inner main coil 1 is smaller than that of the outer main coil 2. The first adjusting coil 3, the second adjusting coil 4, the third adjusting coil 5, and the fourth adjusting coil 6 are all annular coils, which surround the outer main coil 2 and are uniformly distributed on both sides of the midpoint of the length direction symmetry axis of the outer main coil 2, wherein the diameters of the first adjusting coil 3 and the second adjusting coil 4 are the same, the diameters of the third adjusting coil 5 and the fourth adjusting coil 6 are the same, the widths of the first adjusting coil 3 and the second adjusting coil 4 are the same, the widths of the third adjusting coil 5 and the fourth adjusting coil 6 are the same, the width of the first adjusting coil 3 and the second adjusting coil 4 is smaller than that of the third adjusting coil 5 and the fourth adjusting coil 6, the first adjusting coil 3 and the third adjusting coil 5 are on the same side, the second adjusting coil 4 and the fourth adjusting coil 6 are on the same side, and the first adjusting coil 3, the second adjusting coil 4, the third adjusting coil 5, and the fourth adjusting coil 6 are supported by one framework and nested outside the outer main coil 2; without loss of generality, as shown in the drawings, there is a gap between each layer. Figures 1-2
[0039] As Figure 3 shown, the superconducting shimming coil 7 contains 9 sub-coils, arranged from inside to outside, nested outside the layers where the first to fourth adjusting coils 3-6 are located, respectively Z2 superconducting shimming coil 7a, Z1 superconducting shimming coil 7b, Z3 superconducting shimming coil 7c, X superconducting shimming coil 7d, Y superconducting shimming coil 7e, ZX superconducting shimming coil 7f, ZY superconducting shimming coil 7g, X2-Y2 superconducting shimming coil 7h, XY superconducting shimming coil 7i, the 9 sub-coils are supported by a framework; the first to third shielding coils 8-10 have consistent inner diameter and consistent outer diameter, and are annular coils, nested outside the layers where the superconducting shimming coils are located, the first shielding coil 8 is wider than the second shielding coil 9 and the third shielding coil 10 located at both ends, the first shielding coil 8 is located at the midpoint of the length direction symmetry axis of the outer main coil 2, the second shielding coil 9 and the third shielding coil 10 are uniformly distributed on both sides of the first shielding coil 8, the second shielding coil and the third shielding coil have the same width, and the first to third shielding coils are supported by a framework.
[0040] As Figure 4 shown, the three-dimensional structure of each sub-coil of the gradient coil, each sub-coil of the gradient coil is coaxially nested together from inside to outside, containing a cooling water pipe and an iron sheet shimming slot in the middle, and the arrangement from inside to outside is as follows: the inner layer of the X gradient coil 13a (i.e. the main coil), the inner layer of the Y gradient coil 13b (i.e. the main coil), the water pipe, the inner layer of the Z gradient coil 13c (i.e. the main coil), the X2-Y2 gradient coil 13d, the XY gradient coil 13e, the ZX gradient coil 13f, the ZY gradient coil 13g, the Z0 gradient coil 13h, the Z2 gradient coil 13i, the Z3 gradient coil 13j, the Z4 gradient coil 13k, the iron sheet shimming slot, the water pipe, the outer layer of the Z gradient coil 13c (i.e. the shielding coil), the outer layer of the X gradient coil 13a (i.e. the shielding coil), the outer layer of the Y gradient coil 13b (i.e. the shielding coil). The Z0 gradient coil 13h is zero order, the Z gradient coil 13c, the X gradient coil 13a and the Y gradient coil 13b are first order, the Z2 gradient coil 13i, the ZX gradient coil 13f, the ZY gradient coil 13g, the X2-Y2 gradient coil 13d, the XY gradient coil 13e are second order, the Z3 gradient coil 13j is third order, and the Z4 gradient coil 13k is fourth order. Among them, the first order Z gradient coil 13c, X gradient coil 13a and Y gradient coil 13b are magnetic field encoding coils, also play the role of room temperature shimming, each coil contains a main coil and a shielding coil; the rest of the gradient coils are only used for room temperature shimming function. The outer diameter of the gradient coil 13 is not more than 292 mm, and the inner diameter of the gradient coil 13 is not more than 170 mm.
[0041] In use, the gradient coil 13 is placed in the superconducting magnet, with its center position coinciding with the center position of the superconducting magnet. The gradient coil 13 is shorter than the superconducting magnet, and the rubber pads 14 are provided at the positions where the two ends of the gradient coil 13 contact the superconducting magnet. Due to the special design described above, the gradient coil does not need to be extended and fixed in the conventional manner.
[0042] The superconducting magnet is placed in a cryogenic container, which comprises a cold shield 11 and a vacuum container 12. The inner hole of the vacuum container 12 is the warm hole of the superconducting magnet, and the diameter is 300 mm.
[0043] Based on the special design of the superconducting magnet and the gradient coil described above, the mechanical coupling and the electromagnetic coupling between the two are minimized in the following way:
[0044] In the first step, the two layers of cylindrical shells where the main coils and the shield coils included in the first-order Z gradient coil 13c, the X gradient coil 13a, and the Y gradient coil 13b are located are meshed with triangles as boundary elements;
[0045] In the second step, the Lorentz force F(x) on the triangular boundary element mesh is calculated based on the coil structure of the superconducting magnet, which is a function of the flow function value x to be solved at the grid nodes;
[0046] In the third step, the Lorentz force F(x) is written into the objective function of the gradient coil design;
[0047] In the fourth step, the minimum acceptable distance between the gradient coil wires is set as d, and the initial value of the maximum stray magnetic field of the gradient coil in the cylindrical surface region of the inner diameter of the superconducting magnet cold shield is set as s0;
[0048] In the fifth step, the gradient coil is designed using the target field method, and the minimum distance d1 between the wires is calculated. It is evaluated whether |d1-d|≤0.2mm is satisfied. If not, the shielding constraint is tightened, i.e., s0 is reduced, the gradient coil is redesigned, and the minimum distance d1 between the wires is calculated. This cycle is repeated.
[0049] In the sixth step, if |d1-d|≤0.2mm is satisfied, the gradient coil structure is output.
[0050] In the seventh step, the single-layer cylindrical shell where the other single-layer coils included in the gradient coil are located is meshed with triangles as boundary elements, and the other single-layer coils are output using the target field method.
[0051] The above-described specific embodiments further illustrate the purpose, technical solutions, and beneficial effects of the present application. It should be understood that the above-described specific embodiments are merely examples of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.
Claims
1. A high-field animal magnetic resonance imaging superconducting magnet, characterized in that: The superconducting magnet includes: an inner main coil, an outer main coil, a first adjustment coil, a second adjustment coil, a third adjustment coil, a fourth adjustment coil, a superconducting shim coil, a first shielding coil, a second shielding coil, and a third shielding coil, wherein: The inner and outer main coils are spiral-shaped and nested along the same axis using separate skeleton supports. The first adjustment coil, the second adjustment coil, the third adjustment coil, and the fourth adjustment coil are all annular coils, evenly distributed on both sides of the midpoint of the longitudinal symmetry axis of the outer main coil, with the first adjustment coil and the third adjustment coil on the same side, and the second adjustment coil and the fourth adjustment coil on the same side. The first adjustment coil, the second adjustment coil, the third adjustment coil, and the fourth adjustment coil are supported by the same frame and nested outside the outer main coil; The superconducting shim coil includes a plurality of sub-coils supported by the same frame and nested outside the layer where the first to fourth adjustment coils are located; The first to third shielding coils are all annular coils, supported by the same frame, and nested outside the layer where the superconducting shim coils are located. The first shielding coil is located at the midpoint of the longitudinal symmetry axis of the outer main coil, and the second and third shielding coils are evenly distributed on both sides of the first shielding coil.
2. A high-field animal magnetic resonance imaging superconducting magnet according to claim 1, characterized in that: The inner main coil and the outer main coil have the same length.
3. A high-field animal magnetic resonance imaging superconducting magnet according to claim 1, characterized in that: The inner and outer diameters of the first adjustment coil and the second adjustment coil are the same, the inner and outer diameters of the third adjustment coil and the fourth adjustment coil are the same, the widths of the first adjustment coil and the second adjustment coil are the same, the widths of the third adjustment coil and the fourth adjustment coil are the same, and the widths of the first adjustment coil and the second adjustment coil are smaller than the widths of the third adjustment coil and the fourth adjustment coil.
4. The high-field animal magnetic resonance imaging superconducting magnet according to claim 1, characterized in that: The superconducting shim coil includes 9 sub-coils, which are arranged from the inside to the outside, namely, Z2 superconducting shim coil, Z1 superconducting shim coil, Z3 superconducting shim coil, X superconducting shim coil, Y superconducting shim coil, ZX superconducting shim coil, ZY superconducting shim coil, X2-Y2 superconducting shim coil, and XY superconducting shim coil.
5. The high-field animal magnetic resonance imaging superconducting magnet according to claim 1, characterized in that: The inner and outer diameters of the first to third shielding coils are consistent.
6. The high-field animal magnetic resonance imaging superconducting magnet according to claim 1, characterized in that: The first shielding coil is wider than the second shielding coil and the third shielding coil located at both ends, and the second shielding coil and the third shielding coil have the same width.
7. A high-field animal magnetic resonance imaging gradient coil, characterized in that: The gradient coil includes 11 sub-coils, several water pipes for cooling and iron shim slots, and the sub-coils are coaxially nested from the inside to the outside, namely: the inner main coil of the X gradient coil, the inner main coil of the Y gradient coil, the water pipe, the inner main coil of the Z gradient coil, the X2-Y2 gradient coil, the XY gradient coil, the ZX gradient coil, the ZY gradient coil, the Z0 gradient coil, the Z2 gradient coil, the Z3 gradient coil, the Z4 gradient coil, the iron shim slots, the water pipe, the outer shielding coil of the Z gradient coil, the outer shielding coil of the X gradient coil, and the outer shielding coil of the Y gradient coil, wherein, The Z0 gradient coil is zero order, the Z gradient coil, X gradient coil, and Y gradient coil are first order, the Z2 gradient coil, ZX gradient coil, ZY gradient coil, X2-Y2 gradient coil, and XY gradient coil are second order, the Z3 gradient coil is third order, and the Z4 gradient coil is fourth order.
8. The high-field animal magnetic resonance imaging gradient coil according to claim 7, characterized in that: The first-order Z gradient coil, X gradient coil, and Y gradient coil are magnetic field encoding coils.
9. The high-field animal magnetic resonance imaging gradient coil according to claim 7, characterized in that: The outer diameter of the gradient coil does not exceed 292 mm, and the inner diameter of the gradient coil does not exceed 170 mm.
10. A method for decoupling a superconducting magnet and gradient coil for high-field animal magnetic resonance imaging, the method being applied to the superconducting magnet for high-field animal magnetic resonance imaging described in claims 1-6 and the gradient coil for high-field animal magnetic resonance imaging described in claims 7-9. The method comprises placing the gradient coil in the superconducting magnet with their centers overlapping and a rubber sheet placed where they touch. Decoupling between the superconducting magnet and the gradient coil is achieved by the following steps: In the first step, the two cylindrical shells where the main coil and shield coil of the first-order Z gradient coil, X gradient coil, and Y gradient coil are located are divided into boundary element meshes using triangles; The second step is to calculate the Lorentz force F(x) on the triangular boundary element mesh based on the coil structure of the superconducting magnet, which is a function of the stream function value x to be solved at the mesh node; The third step is to write the Lorentz force F(x) into the objective function of the gradient coil design; The fourth step is to set the minimum acceptable spacing between the gradient coil wires to d, and set the initial value of the maximum stray magnetic field of the gradient coil in the cylindrical area of the inner diameter of the superconducting magnet cold shield to s0; Step 5: Use the target field method to design the gradient coil and calculate the minimum spacing d1 between the wires. Then evaluate whether |d1-d|≤0.2mm is satisfied. If not, tighten the shielding constraint (i.e., reduce s0), redesign the gradient coil, and calculate the minimum spacing d1 between the wires. Repeat this process. Step 6: If |d1-d|≤0.2mm is satisfied, the first-order gradient coil structure is output; In the seventh step, the single-layer cylindrical shell where the other single-layer coils included in the gradient coil are located is divided into triangles by boundary element meshing, and the target field method is used to output the other single-layer coils.
Citation Information
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