Gradient and shim coil design method based on segmented function trajectory optimization

Abstract

The present invention relates to a method for designing gradient and shim coils based on the optimization of piecewise function trajectories, belonging to the field of magnetic resonance. The method includes: a. Selecting corresponding characteristic regions and coil trajectory geometric types in the wiring area according to the specific types of gradient coils or shim coils; b. Determining characteristic points in each turn of the wire path within the characteristic region, which will construct the final overall structure of the coil through piecewise functions; c. Determining the optimization objectives and constraints according to the optimization requirements of the coil; d. Establishing the corresponding relationship between the coil structure and the magnetic field based on the Biot-Savart law, establishing a numerical optimization problem for numerical optimization, and obtaining the optimal solution parameter set that meets the requirements of step c. This method has simple and direct calculations, high programmability, low manual adjustment requirements, can easily achieve good gradient magnetic field linearity and the corresponding performance of shim coils, and is convenient for applying additional constraints.

Description

Technical Field

[0001] The present invention belongs to the field of magnetic resonance, and relates to a method for designing gradient and shim coils based on the optimization of piecewise function trajectories. Background Art

[0002] Magnetic resonance imaging (MRI) is an imaging technique widely used in medical clinical diagnosis and medical research. When a magnetic resonance imaging system works, a human body is placed in a uniform static magnetic field, and the atomic nuclei in some regions of human tissues are excited by transmitting radio frequency pulses to the human body. After the radio frequency field is removed, these excited atomic nuclei radiate radio frequency signals, which are received by an antenna. Since a gradient magnetic field is added in this process, the spatial distribution information of the human body can be obtained through the radio frequency signals, and thus a two-dimensional or three-dimensional image of the human body can be reconstructed.

[0003] Both the gradient and shim coils are important components of a magnetic resonance imaging system, and their related research has been widely concerned. The gradient coil generates linearly varying gradient magnetic fields in the x, y, and z directions for slice selection, phase encoding, and frequency encoding, so as to provide a positioning basis for image reconstruction. Therefore, in order to improve the quality of the image, the gradient coil needs to generate a gradient field with good linearity. In an MRI device, a very uniform magnetic field is required in the imaging area. The region of this uniform magnetic field is spherical. After placing the part to be imaged in this spherical region, the image of the part to be imaged can be captured through scanning. However, usually, mechanical errors and the like generated after the magnet is installed cause the magnetic field not to meet the uniformity requirements. Therefore, a set of shim coils is installed for active shimming, and each harmonic component is calculated and cancelled to further improve the magnetic field uniformity of the target region.

[0004] Nowadays, the optimization design method of gradient and shim coils usually adopts the stream function method based on the inverse problem of electromagnetic fields. However, the coil structure calculated by this method is usually relatively complex, such as a series of separated closed curves, which need to be manually reconnected before use, making the design process complex and bringing difficulties to actual manufacturing. Summary of the Invention

[0005] In view of this, the purpose of the present invention is to provide a method for designing gradient and shim coils based on the optimization of piecewise function trajectories. According to the long-term design experience of gradient and shim coils, the winding trajectory is geometrized, and characteristic parameters are extracted for optimization, thereby avoiding additional engineering errors and shortening the design process.

[0006] To achieve the above purpose, the present invention provides the following technical solutions:

[0007] A method for designing gradient and shim coils based on the optimization of piecewise function trajectories, the method comprising the following steps:

[0008] S1: Select the corresponding characteristic region and coil trajectory geometric type in the wiring area according to the specific type of the gradient coil or shim coil.

[0009] S2: Determine the characteristic points in each turn of the wire path in the characteristic region, including the intersection points Pn of the arc and the parabola or the arc and the symmetric line, the intersection points Qn of the parabola and the axis of symmetry, the intersection points Qn of the symmetric line and the axis of symmetry, and the outer diameter Rn of the arc. The final overall structure of the coil will be constructed through piecewise functions.

[0010] S3: Determine the optimization objectives and constraints according to the optimization requirements of the coil, including magnetic field linearity, magnetic field deviation from the target field, gradient efficiency, minimum line spacing, stray magnetic field in the specified area, and resistance.

[0011] S4: Establish the correspondence between the coil structure and the magnetic field based on the Biot-Savart law, and establish a numerical optimization problem according to S3. Use algorithms such as the interior point method for numerical optimization to obtain the optimal solution that meets the requirements of S3, that is, the optimal characteristic point parameter set.

[0012] Optionally, in S1, for the Z-gradient coil and the Z 2 -(X 2 +Y 2 ) / 2 shim coil, the characteristic region is the entire circular wiring domain, and the coil geometric type is involute.

[0013] For the X-gradient coil, Y-gradient coil, XZ shim coil, and YZ shim coil, the characteristic region is half of the circular wiring domain, and the coil geometric type is a combination of arcs, variable radius arcs, and parabolas.

[0014] For the X 2 -Y 2 shim coil and 2XY shim coil, the characteristic region is a quarter of the circular wiring domain, and the coil geometric type is a combination of arcs, variable radius arcs, and symmetric lines.

[0015] Optionally, in S2, for the Z-gradient coil and the Z 2 -(X 2 +Y 2 ) / 2 shim coil, the characteristic points are composed of the set R = {R1, R2,..., RN}, which represents the intersection points of each turn of the involute and the axis of symmetry.

[0016] For the remaining coils, the characteristic points are composed of the sets P = {P1, P2,..., PN}, Q = {Q1, Q2,..., QN}, and R = {R1, R2,..., RN}. P represents the intersection points of the parabola and the axis of symmetry, Q represents the intersection points of the parabola or the symmetric line and the arc, and R represents the outer diameter of a certain turn of the arc.

[0017] Optionally, in S2, if there is an acute angle at the intersection of the parabola and the arc and at the intersection of the symmetry line and the axis of symmetry, take the tangent at the adjacent points and make a connecting arc to achieve smoothing processing.

[0018] Optionally, the design method is used for gradient and shim coils of a bi-planar permanent magnet, electromagnetic, or superconducting magnetic resonance imaging system, including 3 types of gradient coils: X-direction gradient coil, Y-direction gradient coil, and Z-direction gradient coil, and 5 types of higher-order shim coils: XZ shim coil, YZ shim coil, X 2 -Y 2 shim coil, 2XY shim coil, and Z 2 -(X 2 +Y 2 ) / 2 shim coil.

[0019] The beneficial effects of the present invention are as follows: It solves the problems brought by the traditional design method of gradient and shim coils in the MRI system, such as the complex winding structure, the need to manually modify the wire connection of each separated turn of the coil, and the resulting magnetic field error and the complication of the design process. Based on piecewise functions, the present invention geometrizes the coil trajectory. By optimizing the characteristic parameter set, it realizes the optimization of the overall winding trajectory with smooth connection of each turn of the coil directly, without additional manual wire modification. At the same time, by establishing and solving a non-linear numerical optimization problem, the present invention makes the optimization goal flexible, and can simultaneously consider various performances of the coil for optimization under the condition of meeting the self-defined constraints.

[0020] Other advantages, objectives, and features of the present invention will be described to some extent in the subsequent specification, and to some extent, will be obvious to those skilled in the art based on the study of the following text, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the following specification. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be described in detail preferably with reference to the accompanying drawings, where:

[0022] Figure 1 Schematic diagram of the bipolar magnet and gradient and shim coil structure for magnetic resonance imaging;

[0023] Figure 2 Function geometric segmentation schematic diagram of the present invention applicable to X-gradient coil, Y-gradient coil, XZ shim coil, and YZ shim coil;

[0024] Figure 3 For the present invention applicable to Z 2 -(X 2 +Y 2) / 2 shimming coil and Z-gradient coil function geometric segmentation schematic diagram;

[0025] Figure 4 This invention is applicable to X 2 -Y 2 shimming coil and 2XY shimming coil geometric segmentation schematic diagram;

[0026] Figure 5 Wiring schematic diagrams of each gradient and shimming coil completed in the design of this invention; (a) is the X-gradient coil; (b) is the Y-gradient coil; (c) is the Z-gradient coil; (d) is the Z 2 -(X 2 +Y 2 ) / 2 shimming coil; (e) is the XZ shimming coil; (f) is the YZ shimming coil; (g) is the X 2 -Y 2 shimming coil; (h) is the 2XY shimming coil. Specific implementation manners

[0027] The following uses specific specific examples to illustrate the implementation manners of this invention. Those skilled in the art can easily understand other advantages and effects of this invention from the content disclosed in this specification. This invention can also be implemented or applied through other different specific implementation manners. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this invention. It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of this invention in a schematic manner. Without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0028] Among them, the attached drawings are only for illustrative purposes, showing only schematic diagrams, not physical diagrams, and cannot be understood as a limitation to this invention; in order to better illustrate the embodiments of this invention, some components in the attached drawings will be omitted, enlarged or reduced, which does not represent the size of the actual product; for those skilled in the art, it is understandable that some well-known structures and their descriptions in the attached drawings may be omitted.

[0029] In the attached drawings of the embodiments of this invention, the same or similar reference numerals correspond to the same or similar components; in the description of this invention, it should be understood that if there are terms such as "upper", "lower", "left", "right", "front", "rear", etc. indicating the orientation or position relationship, they are based on the orientation or position relationship shown in the attached drawings, and are only for the convenience of describing this invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, the terms describing the position relationship in the attached drawings are only for illustrative purposes and cannot be understood as a limitation to this invention. For those of ordinary skill in the art, the specific meanings of the above terms can be understood according to specific circumstances.

[0030] The method of the present invention relates to a method for designing gradient and shim coils for magnetic resonance imaging. Among them, the structure of the biplanar MRI system is as shown in Figure 1 . Among them, the magnet is installed in the upper and lower yokes, and the gradient and shim coils are installed inside the magnet. The central region is the target imaging region (Region of Interest, ROI), and as high as possible main magnetic field uniformity and gradient magnetic field linearity are required in this region. The purpose of the present invention is to optimize the gradient coil and the shim coil to meet the above requirements.

[0031] Figure 1 Schematic diagram of the structure of a bipolar magnet, gradient and shim coils for magnetic resonance imaging; Figure 2 Schematic diagram of the functional geometric segmentation of the X-gradient coil, Y-gradient coil, XZ shim coil and YZ shim coil of the present invention; Figure 3 For the Z 2 -(X 2 +Y 2 ) / 2 shim coil and Z-gradient coil; Figure 4 For the X 2 -Y 2 shim coil and 2XY shim coil; Figure 5 Schematic diagram of the winding of each gradient and shim coil designed by the present invention; (a) is the X-gradient coil; (b) is the Y-gradient coil; (c) is the Z-gradient coil; (d) is the Z 2 -(X 2 +Y 2 ) / 2 shim coil; (e) is the XZ shim coil; (f) is the YZ shim coil; (g) is the X 2 -Y 2 shim coil; (h) is the 2XY shim coil.

[0032] Example 1

[0033] Taking the X-gradient coil as an example, the design method of the gradient coil for magnetic resonance imaging of the present invention includes the following steps:

[0034] S1. Refer to Figures 1 to 2 . The gradient coil is distributed on the XOY plane, and the wiring surface is disk-shaped. Since the X-gradient coil has symmetry, the right half of the wiring area is selected as the characteristic area, and the coil geometric types combined with arcs, variable radius arcs and parabolas are selected.

[0035] S2. Let the total number of turns of the characteristic region be N, and select a set of characteristic points consisting of P = {P1, P2, …, PN}, Q = {Q1, Q2, …, QN}, and R = {R1, R2, …, RN}, where P represents the intersection points of the parabola or symmetric line and the arc, Q represents the intersection points of the parabola and the axis of symmetry, and R represents the outer diameter of the arc of a certain turn. For the nth turn of the coil, its composition is shown in Figure 2 . Pn’ is the symmetric point of Pn about the x-axis, α is the angle between the connecting line of any point on the parabola and Qn and the x-axis, θ is the deflection angle of any point on the arc relative to the x-axis, and δ is the deflection angle of any point on the variable-radius arc relative to the x-axis. Then the parametric equations of the variable-radius arc, parabola, and arc can be respectively expressed as:

[0036]

[0037]

[0038]

[0039] In the formula, r (n) is the abscissa of Rn, Δr is the difference between r of this turn (n) and r of the next turn (n+1) , p x (n) and p y (n) are respectively the abscissa and ordinate of Pn, and q (n) is the abscissa of Qn. In addition, since there is an acute angle at the connection of the parabola and the arc at the dotted line in the figure, tangents are taken at adjacent points to make a connecting arc for smoothing processing.

[0040] S3. According to the optimization requirements of the coil, determine the optimization objectives and constraints. In this example, it is required to generate a target gradient magnetic field of 5 mT / m, and its magnetic field non-linearity is not greater than 5%. In addition, it is required that the line spacing Δl between adjacent two lines is at least 4 mm. First, based on the Biot-Savart law, with the current as the variable, the magnetic field at a certain point in the target region can be expressed as:

[0041]

[0042] Take m observation points uniformly on the surface of the ROI, then the magnetic field intensity of each observation point can be obtained from the above formula. The optimization problem of the coil is thus established, which seeks the optimal solution that makes the Z component of the magnetic field at each observation point differ as little as possible from the target magnetic field, that is:

[0043]

[0044] S4. Solve the above problems through numerical algorithms. In this example, the interior point method is adopted. Obtain the optimal solutions of each characteristic point set through computer program optimization, and construct the coil structure based on this for simulation verification. The optimized coil trajectory is as Figure 5 shown in (a), with its maximum magnetic field non-linearity of 2.12% and driving current of 18.14 A. The above optimization results make the linearity of the gradient magnetic field in the target area reach the optimal.

[0045] Example 2

[0046] Taking the shim coil of Z 2 -(X 2 +Y 2 ) / 2 as an example, the design method of the shim coil for magnetic resonance imaging of the present invention includes the following steps:

[0047] S5. Refer to Figure 1 , Figure 3 . The shim coil is distributed on the XOY plane, and the wiring surface is disk-shaped. Select the entire wiring area as the characteristic area and the involute as the coil geometry type.

[0048] S6. Let the total number of turns of the characteristic area be N, select the set R = {R1, R2,..., RN} as the characteristic point set, Rn represents the starting radius of a certain turn of the involute, and δ is the deflection angle of any point on the variable radius arc relative to the x-axis. The involute starts from Rn and transitions clockwise to the radius Rn+1 of the next turn, and its parametric equation is expressed as:

[0049]

[0050] where r (n) is the abscissa of Rn, and Δr is the difference between r (n) of this turn and r (n+1) of the next turn.

[0051] S7. According to the optimization requirements of the coil, determine the optimization objectives and constraints. In this example, it is required that the shim coil generates a second-order magnetic field with the characteristic of Z 2 -(X 2 +Y 2 ) / 2 in the target area, and the secondary component of the field strength after the second-order decomposition is not higher than 5%. In addition, it is required that the line spacing Δl between adjacent two lines is at least 4 mm. Uniformly take m observation points on the surface of the ROI, and the magnetic field intensity of each observation point can be obtained by formula (4). The optimization problem of the coil is thus established, which seeks the optimal solution that makes the Z component of the magnetic field at each observation point differ as little as possible from the target magnetic field, that is:

[0052]

[0053] S8. Solve the above problems through numerical algorithms. In this example, the interior point method is adopted. The optimal solution of the feature point set is obtained through computer program optimization, and the coil structure is constructed based on this to conduct simulation verification. The optimized coil trajectory is as shown in Figure 5 (d). After the magnetic field is decomposed by the second-order series, the maximum component is Z 2 -(X 2 +Y 2 ) / 2, and the coefficient of the secondary component accounts for 0.12% of the coefficient of the main component. The above optimization results make the Z 2 -(X 2 +Y 2 ) / 2 magnetic field in the target area reach the optimum.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not restrictive. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the purpose and scope of the present technical solution, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A gradient and shim coil design method based on the optimization of a piecewise function trajectory, characterized in that: The method comprises the following steps: S1: Select a corresponding characteristic region and a coil trajectory geometric type in the wiring region according to the specific type of the gradient coil or the shimming coil; S2: Determine the characteristic points in each turn of the wire path corresponding in the characteristic region, including the intersection point P of the arc and the parabola or the arc and the symmetric line, the intersection point Q of the parabola and the axis of symmetry or the symmetric line and the axis of symmetry, and the outer diameter D of a certain turn of the arc, and construct the final overall structure of the coil through a piecewise function; S3: Determine the optimization objectives and constraints according to the optimization requirements of the coil, including magnetic field linearity, magnetic field deviation degree relative to the target field, gradient efficiency, minimum line spacing, stray magnetic field in the specified region, and resistance; S4: Establish the correspondence between the coil structure and the magnetic field based on the Biot-Savart law, establish a numerical optimization problem according to S3, and use the interior point method algorithm for numerical optimization to obtain the optimal solution that meets the requirements of S3, that is, the optimal characteristic point parameter set; In S1, for the Z-gradient coil and the Z 2 -(X 2 +Y 2 ) / 2 shimming coil, the characteristic region is selected as the entire circular wiring domain, and the coil geometry type is an involute; For the XZ shimming coil and the YZ shimming coil, the characteristic region selects a half-circular wiring domain, and the coil geometric type is a combination of an arc, a variable-radius arc, and a parabola; For X 2 -Y 2 For the shimming coil and the 2XY shimming coil, the characteristic region selects a quarter-circular wiring domain, and the coil geometric type is a combination of arcs, arcs with variable radii, and symmetric straight lines; In S2, for the Z-gradient coil and the Z 2 -(X 2 +Y 2 ) / 2 shimming coil, the characteristic points are composed of the set R = {R1, R2,..., RN}, representing the intersection points of each turn of the involute and the symmetry axis; For the remaining coils, the characteristic points are composed of the sets P = {P1, P2,..., PN}, Q = {Q1, Q2,..., QN}, D = {D1, D2,..., DN}, where P represents the intersection point of the arc and the parabola or the arc and the symmetric line, Q represents the intersection point of the parabola and the axis of symmetry or the symmetric line and the axis of symmetry, D represents the outer diameter of a certain turn of the arc; N is the total number of turns in the characteristic region; In S2, if there is an acute angle at the connection of the intersection of the parabola and the arc or the intersection of the symmetric line and the axis of symmetry, take the tangent at the adjacent points and make a connecting arc to achieve smoothing; The parametric equations of the variable-radius arc, the parabola, and the arc are respectively expressed as: where d (n) is the abscissa of Dn, and Δr is the difference between the present turn d (n) and the next turn d (n+1) , p x (n) and p y (n) are the abscissa and ordinate of Pn respectively, and q (n) is the abscissa of Qn; δ is the deflection angle of any point on the variable-radius arc relative to the x-axis; α is the angle between the connection line of any point on the parabola and Qn and the x-axis; θ is the deflection angle of any point on the arc relative to the x-axis; The described design method is used for the gradient and shim coils of a bi-planar permanent magnet, electromagnetic, or superconducting magnetic resonance imaging system, including 1 type of gradient coil: the Z-direction gradient coil, and 5 types of higher-order shim coils: the XZ shim coil, the YZ shim coil, the X 2 -Y 2 shim coil, the 2XY shim coil, and the Z 2 -(X 2 +Y 2 ) / 2 shim coil.

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