CN110568390A - design method of biplane shimming coil - Google Patents

Abstract

The invention discloses a design method of a biplane shim coil, which comprises the steps of firstly introducing a source point grid of the biplane shim coil, ordering grid vertexes and triangular surfaces, then respectively calculating magnetic field values of 2-order shim coils on target points by adopting a spherical harmonic function, reading each vertex and each surface of the triangular grid by adopting MATLAB software, optimizing the arrangement sequence of the vertexes and the surfaces, setting the size of a lead according to a boundary element method, calculating the contribution value of a power-on lead of a source point region to a field point, restricting the energy storage and the power consumption of the biplane shim coil to be minimum, solving the current density distribution on the upper plane shim coil, and obtaining the winding shape of the biplane shim coil by a current function method. The invention adopts the design method of the biplane shimming coil with the structure, and can eliminate 2-order and above harmonic magnetic field, thereby improving the uniformity of the main magnetic field and improving the image quality of the open MRI system.

Description

design method of biplane shimming coil

Technical Field

The invention relates to the field of magnetic resonance imaging, in particular to a design method of a biplane shim coil.

Background

magnetic Resonance imaging (magnetic Resonance imaging MRI) technology is a multi-technology crossed technology, including the subjects of electromagnetism, digital signal processing, biomedicine, atomic physics and the like, compared with other medical imaging technologies, MRI has the advantages of no radiation, high resolution, clear image quality and the like, so the MRI technology has important clinical application value in medical examination, ideally, the main magnetic field of MRI equipment only has a B0 field and no other harmonic magnetic field, however, due to the existence of processing and assembling errors, a harmonic magnetic field other than a B0 field is inevitably introduced, the introduction of the harmonic magnetic field can cause poor imaging quality or even cannot image, a gradient coil can correct a 1-order harmonic magnetic field, and a magnetic field higher than the 1-order harmonic magnetic field needs a 2-order shimming coil and more than the 2-order shimming coil to eliminate, so that a B0 field reaches the range of imaging requirements.

the invention provides a design method of a biplane shim coil in order to solve the problem of main magnetic field nonuniformity of an open MRI magnet. The magnetic field of harmonic wave of 2 orders and above can be eliminated, the uniformity of the main magnetic field is improved, and the image quality of the open type MRI system is improved.

Disclosure of Invention

the invention aims to provide a design method of a biplane shim coil, which can eliminate 2-order and above harmonic magnetic field, improve the uniformity of a main magnetic field and improve the image quality of an open MRI system.

In order to achieve the purpose, the invention provides a method for designing a biplane shim coil, which comprises the following steps.

The method comprises the following steps: and (4) introducing a biplane shimming coil grid, and dividing the main gradient coil area into three-dimensional triangular grid nodes.

Step two: dividing spheres with set diameters into 16 layers, setting a test point every 11.6 degrees, and obtaining 1488 target points by using MATLAB to obtain x, y and z coordinates of the target points to obtain field coordinate points.

Step three: and determining a target point magnetic field value according to the target point coordinate value and the 2 nd order spherical harmonic coefficient, wherein the target point magnetic field value on the spherical surface is the product of the coordinate point z coordinate value and the spherical harmonic coefficient.

Step four: according to the boundary element method and the set dimensions of the biplane shim coil wires, calculating the contribution value of the electrified wire in the source point region to the target field point: discretizing the source point region into a vertex and a triangular surface, sequencing the source point vertex and the triangular surface by adopting an MATLAB sequencing program to obtain coordinate values of the discrete vertex, and calculating the contribution value of the electrified conducting wire of the source point region to the target field point according to a Biao savart formula.

step five: and calculating the power consumption of the biplane shim coil, constraining the biplane shim coil to have minimum power consumption and energy storage through a quadrprog quadratic programming method, and calculating the current value on the minimum shim coil node.

Step six: and obtaining the actual winding shape of the biplane shim coil by a flow function method.

Step seven: and solving a magnetic field value of the coil on a target point by utilizing the Bio savart theorem according to the winding shape of the shimming coil, judging whether the magnetic field value meets the error requirement of the target magnetic field value, and if not, modifying the weight coefficients of the power consumption matrix and the energy storage matrix until the magnetic field value meets the error requirement of the target magnetic field value.

The invention has the beneficial effects that:

The biplane shimming coil designed by the invention can effectively eliminate 2-order and above harmonic magnetic field introduced by machining and assembling errors, and simultaneously improves the uniformity of a main magnetic field and the image quality.

The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.

drawings

Fig. 1 is a flow chart of a design method of the bi-planar shim coil of the present invention.

Fig. 2 is a schematic diagram of source region meshing of the shim coil of the present invention.

FIG. 3 is a schematic view of the imaging region target point of the present invention.

FIG. 4 is a schematic diagram of a three-dimensional display source region and imaging region target point of the present invention.

fig. 5 is a schematic diagram of the structure of a biplane Z20 shim coil of the present invention.

Fig. 6 is a schematic diagram of the structure of a biplane Z21 shim coil of the present invention.

Fig. 7 is a schematic diagram of the structure of a biplane Z22 shim coil of the present invention.

Detailed Description

Embodiments of the present invention will be further described with reference to the accompanying drawings.

the invention uses 3 groups of 2-order axial shimming coils: the design method of the biplane shim coil is introduced by Z20, Z21 and Z22 as design examples, the design flow chart is shown in figure 1, the design parameters of the biplane shim coil are set, the biplane shim coil is a triangular grid with the diameter of 0.42m and the distance is 500mm, each sphere on 100mm, 240mm and 360mm spheres is divided into 16 layers, a test point is set at intervals of 11.6 degrees, 1488 target points are set, the error is not more than 5%, and the specific design steps are as follows.

The method comprises the following steps: according to the design parameters of the set biplane shim coil, performing triangularization grid division on the shim coil by using blend 2.8 software, namely dispersing the shim coil into nodes and triangular surfaces, as shown in fig. 2. And exporting the grid nodes into an obj format, reading and sequencing the obj format file through MATLAB to obtain source point coordinate points S (x, y, z).

Step two: spheres with diameters of 100mm, 240mm and 360mm are divided, each sphere is divided into 16 layers, and test points are set every 11.6 degrees for 1488 target points, as shown in fig. 3 and 4. The x, y, z coordinates of these target points were found using MATLAB to obtain field coordinate points F (x1, y1, z 1).

Step three: determining a target point magnetic field value according to the target field point coordinate value and the 2 nd order spherical harmonic coefficient, wherein the target spherical harmonic coefficient is 5mT/m, and the target point magnetic field value on the spherical surface is the product of the coordinate point z coordinate value and the spherical harmonic coefficient, namely:

Q_z＝Q*z

In the formula, Qz is the magnetic field value of a target point in a given target area, and the unit is mT; q is a spherical harmonic coefficient of a given order, and the unit is mT/m; z is the coordinate value of the target point in the z direction and the unit is m.

Step four: and calculating the contribution value of the electrified lead of the source point region to the target field point according to a boundary element method and the set size of the biplane shim coil lead. Discretizing the source point region into a vertex and a triangular surface, and sequencing the vertex and the triangular surface of the source point by adopting an MATLAB sequencing program to obtain coordinate values S (x, y, z) of the discrete vertex.

according to the biot savart formula:

In the formulaThe contribution value of the source point lead to the field point magnetic induction intensity is obtained; mu.s₀Is a vacuum magnetic conductivity; dl is the length of the electrified lead in the source region; r is the distance from the source point to the field point; i is the current value on the source point lead; theta is an included angle between the electrified lead and a connecting line of the source point and the field point.

Step five: calculating the power consumption of the biplane shim coil, calculating the current value on the node of the minimum shim coil with the power consumption and the energy storage by adopting a quadprog function in matlab,

the coil power consumption expression is as follows:

Wherein the surface S is a discrete unit surface comprising n nodes, I_mAnd I_nCurrent values at the m-th and n-th nodes, respectively, p being the resistance of the conductor, d_rIs the thickness of the conductor. R_mnIs a resistance matrix of the gradient coil;

The coil energy storage expression is as follows:

Formula middle surface S_mand S_nAre discrete triangular surfaces and belong to nodes n and m respectively, and the nodes n and m respectively contain W_nAnd W_mA triangle. I is_mand I_nCurrent values, μ, at the mth and nth nodes, respectively₀Is the magnetic permeability of vacuum, r^mAnd rⁿRespectively, the coordinates of the points in the triangular plane. v. of_maand v_nbWhich are the basis functions of nodes m and n, respectively. M_mnIs an energy storage matrix of the shim coils;

The quadprog function is as follows:

F＝α*I*R_mn*I’+β*I*M_mn*I’

Wherein F is an objective function, I is a discrete point current value of the source region, I' is a transposed matrix of I, R_mnIs a source region discrete point resistance matrix, M_mnthe method comprises the steps that a source region discrete point inductance matrix is adopted, and alpha and beta are respectively a resistance matrix and an inductance matrix weight coefficient;

The constraint conditions are as follows:

A*I<ε*B^t

In the formula, A is a magnetic field coefficient matrix which does not contain a node current value and is calculated by Bio savart at a target point through a source point; epsilon is the magnetic field error, epsilon is 0.05; b is^tIs the target magnetic field value; i is the node current value.

Step six: the winding shape of the biplane shim coil is calculated by a flow function method,

In the formula, S is an equipotential difference, max (I) is a maximum node current value, min (I) is a minimum node current value, and the number of turns of the N biplane shim coil windings is equal to the maximum node current value.

Step seven: and solving the magnetic field value of the coil on the target point by utilizing the Bio Saval theorem according to the winding shape of the shimming coil, and judging whether the magnetic field value meets the error requirement of the target magnetic field value. If the target magnetic field value requirement of the shimming coil is met, stopping modifying the alpha and beta weighting coefficients, otherwise, continuing the alpha and beta weighting coefficients until the linearity requirement of the gradient coil is met, and designing results are shown in fig. 5, 6 and 7.

Therefore, the invention provides a design method of the biplane shim coil, which controls the power consumption and energy storage minimization of the shim coil, restrains the magnetic field value of the shim coil on a target point, can effectively eliminate a high-order harmonic magnetic field induced by machining and assembling errors, and further improves the image quality of an open MRI system.

Finally, it should be noted that: the above embodiment is exemplified by a 2-order axial shim coil and is not limited to a 2-order shim coil, a higher-order shim coil can be designed by modifying the order in the spherical harmonic coefficient, and the above embodiment is only used for illustrating the technical solution of the present invention and is not limited thereto, although the present invention is described in detail with reference to the preferred embodiment, those skilled in the art should understand that: modifications and equivalents may be made to the invention without departing from the spirit and scope of the invention.

Claims (1)

1. A design method of a biplane shim coil is characterized in that: the method comprises the following steps:

The method comprises the following steps: leading in a biplane shimming coil grid, and dividing a main gradient coil area into three-dimensional triangular grid nodes;

step two: dividing spheres with set diameters into 16 layers, setting a test point every 11.6, and obtaining 1488 target points, and calculating x, y and z coordinates of the target points by using MATLAB to obtain a field coordinate point F (x1, y1 and z 1);

Step three: determining a target point magnetic field value according to the target point coordinate value and the 2 nd order spherical harmonic coefficient, wherein the target point magnetic field value on the spherical surface is the product of the coordinate point z coordinate value and the spherical harmonic coefficient;

step four: according to the boundary element method and the set dimensions of the biplane shim coil wires, calculating the contribution value of the electrified wire in the source point region to the target field point: discretizing the source point region into a vertex and a triangular surface, sequencing the source point vertex and the triangular surface by adopting an MATLAB sequencing program to obtain a coordinate value of the discrete vertex, and calculating a contribution value of a power-on lead of the source point region to a target field point according to a Biao savart formula;

Step five: calculating the power consumption of the biplane shimming coil, constraining the biplane shimming coil to have minimum power consumption and energy storage through a quadrprog quadratic programming method, and calculating the current value on the minimum shimming coil node;

Step six: obtaining the actual winding shape of the biplane shim coil by a flow function method;

step seven: and solving a magnetic field value of the coil on a target point by utilizing the Bio savart theorem according to the winding shape of the shimming coil, judging whether the magnetic field value meets the error requirement of the target magnetic field value, and if not, modifying the weight coefficients of the power consumption matrix and the energy storage matrix until the magnetic field value meets the error requirement of the target magnetic field value.