High-field animal magnetic resonance imaging superconducting magnet, gradient coil and decoupling method

Abstract

The invention relates to a high-field animal magnetic resonance imaging superconducting magnet, a gradient coil and a decoupling method. Wherein the superconducting magnet comprises two main coils, four adjusting coils and three shielding coils, and nine first-order, second-order and third-order axial superconducting shimming coils are arranged in the superconducting magnet; the gradient coil comprises an active shielding magnetic field coding coil and further comprises 11 coils in the zero-order axial direction, the second-order axial direction, the third-order axial direction and the fourth-order axial direction. Electromagnetic coupling and mechanical coupling between the superconducting magnet and the gradient coil are optimized, the basic judgment standard is that the minimum distance between coil wires is appropriate, engineering processing is feasible, and therefore the minimum stray magnetic field of the gradient coil and the minimum electromagnetic Lorentz force are obtained. Cooperative stable operation can be guaranteed without additional connection processing between the two functional parts. The superconducting magnet shielding effect is excellent, the gradient coil shielding effect is excellent, and strong Lorentz force coupling between the superconducting magnet and the gradient coil is effectively eliminated.

Description

Technical Field

[0001] The invention belongs to the field of electrical engineering theory and new technology, and specifically relates to a high-field animal magnetic resonance imaging superconducting magnet, a gradient coil and a decoupling method, which are used for animal magnetic resonance imaging research. Background Art

[0002] Animal MRI has a smaller aperture than human MRI. Unlike human MRI, which pursues more versatility, safety, and comfort, animal MRI usually emphasizes excellent performance. The detection aperture of animal MRI is small and long, and there is no need to consider the claustrophobia of the organism. Its radio frequency short-wave side effects are not obvious. It can usually provide higher main magnetic field strength and gradient magnetic field strength, and faster gradient magnetic field conversion efficiency than human MRI. Under the strong magnetic field interaction, a huge alternating Lorentz force is generated between the superconducting magnet and the gradient coil, posing a threat to the stable operation of the system. This is a common key problem of high-field MRI systems; in addition, the transient gradient magnetic field will also generate eddy currents on the superconducting magnet, which will radiate secondary magnetic fields. Therefore, the development of high-performance animal MRI systems is not only about developing high-field superconducting magnets and gradient coils themselves, but also about effectively solving the coupling problem of components during operation.

[0003] Chinese invention patent ZL201610811541.1 discloses an ultra-high field and high uniformity superconducting magnet for small animal magnetic resonance imaging. Its superconducting magnet coil includes 1 main coil, 4 adjustment coils, and 2 shielding coils. Its coil structure type is different from the present invention, and the above patent does not include a gradient coil, so there is no decoupling problem between the superconducting magnet and the gradient coil. Chinese invention patent ZL202210372215.0 discloses a superconducting magnet and gradient device for micro-animal magnetic resonance imaging. Its superconducting magnet is a non-shielded structure, its scale is small, and it does not include a shielding coil. The gradient device only includes three layers of main coils, and does not include shielding coils and shimming coils. The coupling between the superconducting magnet and the gradient device is controllable and is not considered separately. Summary of the invention

[0004] In order to solve the above technical problems, the present invention provides a high-field animal magnetic resonance imaging superconducting magnet, gradient coil and decoupling method. The design of the superconducting magnet and gradient coil fully considers the excitation safety and the need for shimming. The superconducting magnet has appropriate electromagnetic margin and is equipped with sufficient shimming coils and shimming structures. 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 object, the technical solution adopted by the present invention is as follows:

[0006] On the one hand, the present invention provides a high-field animal magnetic resonance imaging superconducting magnet, the superconducting magnet comprising: 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:

[0007] The inner main coil and the outer main coil are spiral-shaped and are nested along the same axis with separate skeleton supports;

[0008] 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 symmetry axis in the length direction of the outer main coil, the first adjustment coil and the third adjustment coil are on the same side, the second adjustment coil and the fourth adjustment coil are 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 are nested outside the outer main coil;

[0009] The superconducting shim coil includes a plurality of sub-coils, which are supported by the same frame and are nested outside the layer where the first to fourth adjustment coils are located;

[0010] The first to third shielding coils are all annular coils, supported by the same frame, and nested outside the layer where the superconducting shim coil is located. The first shielding coil is located at the midpoint of the symmetry axis in the length direction of the outer main coil, and the second shielding coil and the third shielding coil are evenly distributed on both sides of the first shielding coil.

[0011] Furthermore, the inner main coil and the outer main coil have the same length.

[0012] Furthermore, 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.

[0013] Furthermore, 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.

[0014] Furthermore, the inner and outer diameters of the first to third shielding coils are consistent.

[0015] Furthermore, the first shielding coil is wider than the second shielding coil and the third shielding coil located at two ends, and the second shielding coil and the third shielding coil have the same width.

[0016] On the other hand, the present invention provides a high-field animal magnetic resonance imaging gradient coil, the gradient coil comprises 11 sub-coils, a plurality of water pipes for cooling and iron sheet shim grooves, the sub-coils are coaxially nested from the inside to the outside, respectively: an inner main coil of an X gradient coil, an inner main coil of a Y gradient coil, a water pipe, an inner main coil of a Z gradient coil, an X2-Y2 gradient coil, an XY gradient coil, a ZX gradient coil, a ZY gradient coil, a Z0 gradient coil, a Z2 gradient coil, a Z3 gradient coil, a Z4 gradient coil, an iron sheet shim grooves, a water pipe, an outer shielding coil of the Z gradient coil, an outer shielding coil of the X gradient coil, and an outer shielding coil of the Y gradient coil, wherein:

[0017] 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.

[0018] Furthermore, the first-order Z gradient coil, X gradient coil, and Y gradient coil are magnetic field encoding coils.

[0019] Furthermore, 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.

[0020] In a third aspect, the present invention provides a high-field animal magnetic resonance imaging superconducting magnet and a gradient coil decoupling method, which is applied to the aforementioned high-field animal magnetic resonance imaging superconducting magnet and a 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 a rubber sheet is placed at the contact point. The decoupling between the superconducting magnet and the gradient coil is achieved according to the following steps:

[0021] In the first step, the two cylindrical shells where the main coil and shielding 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;

[0022] The second step is to calculate the Lorentz force F(x) on the triangular boundary element grid based on the coil structure of the superconducting magnet, which is a function of the stream function value x to be solved on the grid node;

[0023] The third step is to write the Lorentz force F(x) into the objective function of the gradient coil design;

[0024] Step 4: Set the minimum acceptable spacing between the gradient coil wires to d, and set the maximum stray magnetic field initial value of the gradient coil in the cylindrical surface area of ​​the inner diameter of the superconducting magnet cold shield to s0;

[0025] Step 5: Use the target field method to design the gradient coil and calculate the minimum spacing d1 between the wires. 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.

[0026] Step 6: If |d1-d|≤0.2mm is satisfied, the first-order gradient coil structure is output;

[0027] 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 boundary element meshes using triangles, and the other single-layer coils are output using the target field method.

[0028] The present invention has the following beneficial technical effects:

[0029] The shielding effect of the superconducting magnet of the present invention is outstanding. The shielding structure of 3 coils is adopted, and the range of 5 Gauss lines is significantly narrowed, especially at the upper end of the magnet, where the 5 Gauss lines are close to the magnet coil, which is convenient for operations such as lead plugging and unplugging, refrigerator maintenance, etc.; the gradient coil stray magnetic field minimization control method can effectively reduce the eddy current secondary magnetic field effect generated by the transient gradient magnetic field on the superconducting magnet; the Lorentz force minimization method between the superconducting magnet and the gradient coil can effectively prevent the gradient coil from shaking, while the traditional method is to extend the gradient coil to the end plate of the superconducting magnet to achieve the fixed connection between the two. The present invention does not require such a structure, and only needs to place the gradient coil in the superconducting magnet warm hole and pad it with a rubber sheet. In addition, sufficient shimming coils are placed inside the superconducting magnet and the gradient coil to prevent the magnetic field uniformity from being greatly improved under harsh initial magnetic field conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is the overall cross-sectional structure of the superconducting magnet and gradient coil;

[0031] Figure 2 It is a 3 / 4 model of the three-dimensional structure of a superconducting magnet;

[0032] Figure 3 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 numerals:

[0035] 1. Inner main coil, 2. Outer main coil, 3. First adjustment coil, 4. Second adjustment coil, 5. Third adjustment coil, 6. Fourth adjustment coil, 7. Superconducting shim coil, 8. First shielding coil, 9. Second shielding coil, 10. Third shielding coil, 11. Superconducting magnet cold shield, 12. Superconducting magnet vacuum container, 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 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 invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0037] like Figure 1-Figure 2 As shown, the superconducting magnet of the present invention comprises an inner main coil 1, an outer main coil 2, a first adjustment coil 3, a second adjustment coil 4, a third adjustment coil 5, a fourth adjustment coil 6, a superconducting shim coil 7, a first shielding coil 8, a second shielding coil 9, and a third shielding coil 10.

[0038] The inner main coil 1 and the outer main coil 2 are spiral-shaped and have the same length. They are supported by separate skeletons and 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 adjustment coil 3, the second adjustment coil 4, the third adjustment coil 5 and the fourth adjustment coil 6 are all annular coils, surrounding the outer main coil 2, and are evenly distributed on both sides of the midpoint of the symmetry axis in the length direction of the outer main coil 2, wherein the first adjustment coil 3 and the second adjustment coil 4 have the same diameter, the third adjustment coil 5 and the fourth adjustment coil 6 have the same diameter, the first adjustment coil 3 and the second adjustment coil 4 have the same width, the third adjustment coil 5 and the fourth adjustment coil 6 have the same width, the first adjustment coil 3 and the second adjustment coil 4 have less width than the third adjustment coil 5 and the fourth adjustment coil 6, the first adjustment coil 3 and the third adjustment coil 5 are on the same side, the second adjustment coil 4 and the fourth adjustment coil 6 are on the same side, the first adjustment coil 3, the second adjustment coil 4, the third adjustment coil 5 and the fourth adjustment coil 6 are supported by a skeleton and nested outside the outer main coil 2; without loss of generality, as Figure 1-Figure 2 As shown, there are gaps between the layers.

[0039] like Figure 3 As shown, the superconducting shim coil 7 includes 9 sub-coils, which are arranged from the inside to the outside and nested outside the layer where the first to fourth adjustment coils 3-6 are located, namely, Z2 superconducting shim coil 7a, Z1 superconducting shim coil 7b, Z3 superconducting shim coil 7c, X superconducting shim coil 7d, Y superconducting shim coil 7e, ZX superconducting shim coil 7f, ZY superconducting shim coil 7g, X2-Y2 superconducting shim coil 7h, and XY superconducting shim coil 7i, and the 9 sub-coils are supported by a skeleton; the first to third shielding coils 8-10 have the same inner diameter and outer diameter, are all annular coils, and are nested outside the layer where the superconducting shim 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 evenly 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 skeleton.

[0040] like Figure 4 As shown in FIG. 1 , the three-dimensional structure of each sub-coil of the gradient coil is shown. The sub-coils of the gradient coil are nested together from the inside to the outside on the same axis, and a cooling water pipe and an iron sheet shim groove are included in the middle. The arrangement from the inside to the outside is: 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 shim groove, 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), and 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, and 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, the X gradient coil 13a, and the Y gradient coil 13b are magnetic field encoding coils, and also play the room temperature shimming function. Each coil includes a main coil and a shielding coil; the remaining gradient coils are only used for the room temperature shimming function. The outer diameter of the gradient coil 13 does not exceed 292mm, and the inner diameter of the gradient coil 13 does not exceed 170mm.

[0041] When in use, the gradient coil 13 is placed in the superconducting magnet, and its center position coincides with the center position of the superconducting magnet. The gradient coil 13 is shorter than the superconducting magnet, and rubber sheets 14 are placed where the two ends of the gradient coil 13 contact the superconducting magnet. Due to the above special design, the gradient coil does not need to be extended and fixed in a conventional manner.

[0042] The superconducting magnet is placed in a cryogenic container, which includes a cold shield 11 and a vacuum container 12. The inner hole of the vacuum container 12 is a warm hole of the superconducting magnet, and its diameter is 300 mm.

[0043] Based on the specially designed superconducting magnet and gradient coil described above, the mechanical coupling and electromagnetic coupling between the two are minimized in the following manner:

[0044] The first step is to divide the two cylindrical shells where the main coil and the shielding coil of the first-order Z gradient coil 13c, X gradient coil 13a, and Y gradient coil 13b are located by using triangles for boundary element meshing;

[0045] The second step is to calculate the Lorentz force F(x) on the triangular boundary element grid based on the coil structure of the superconducting magnet, which is a function of the stream function value x to be solved on the grid node;

[0046] The third step is to write the Lorentz force F(x) into the objective function of the gradient coil design;

[0047] Step 4: Set the minimum acceptable spacing between the gradient coil wires to d, and set the maximum stray magnetic field initial value of the gradient coil in the cylindrical surface area of ​​the inner diameter of the superconducting magnet cold shield to s0;

[0048] Step 5: Use the target field method to design the gradient coil and calculate the minimum spacing d1 between the wires. 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.

[0049] Step 6: 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 divided into boundary element meshes using triangles, and the other single-layer coils are output using the target field method.

[0051] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A high-field animal magnetic resonance imaging superconducting magnet, characterized in that: The superconducting magnet comprises: 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 main coil and the outer main coil are spiral-shaped and are nested along the same axis with 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 symmetry axis in the length direction of the outer main coil, the first adjustment coil and the third adjustment coil are on the same side, the second adjustment coil and the fourth adjustment coil are 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 are nested outside the outer main coil; The superconducting shim coil includes a plurality of sub-coils, which are supported by the same frame and are 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 coil is located. The first shielding coil is located at the midpoint of the symmetry axis in the length direction of the outer main coil, and the second shielding coil and the third shielding coil 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 first adjustment coil and the second adjustment coil have the same inner and outer diameters, the third adjustment coil and the fourth adjustment coil have the same inner and outer diameters, the first adjustment coil and the second adjustment coil have the same widths, the third adjustment coil and the fourth adjustment coil have the same widths, 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. A 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. A 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. A 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 two 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, a plurality of water pipes for cooling and iron sheet shim grooves, and the sub-coils are coaxially nested from the inside to the outside, and are respectively: an inner main coil of the X gradient coil, an inner main coil of the Y gradient coil, a water pipe, an inner main coil of the Z gradient coil, an X2-Y2 gradient coil, an XY gradient coil, a ZX gradient coil, a ZY gradient coil, a Z0 gradient coil, a Z2 gradient coil, a Z3 gradient coil, a Z4 gradient coil, an iron sheet shim groove, a water pipe, an outer shielding coil of the Z gradient coil, an outer shielding coil of the X gradient coil, and an 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 a gradient coil for high-field animal magnetic resonance imaging, applied to a superconducting magnet for high-field animal magnetic resonance imaging as described in claims 1-6 and a gradient coil for high-field animal magnetic resonance imaging as described in claims 7-9, wherein the gradient coil is placed in the superconducting magnet, the centers of the two coincide, and a rubber sheet is placed at the contacting part, and the decoupling between the superconducting magnet and the gradient coil is achieved according to the following steps: In the first step, the two cylindrical shells where the main coil and shielding 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 grid based on the coil structure of the superconducting magnet, which is a function of the stream function value x to be solved on the grid node; The third step is to write the Lorentz force F(x) into the objective function of the gradient coil design; Step 4: Set the minimum acceptable spacing between the gradient coil wires to d, and set the maximum stray magnetic field initial value of the gradient coil in the cylindrical surface 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. 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 boundary element meshes using triangles, and the other single-layer coils are output using the target field method.

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