阅读说明：本技术 基于阵列线圈的磁场补偿方法及设备 (Magnetic field compensation method and equipment based on array coil ) 是由 徐雅洁 余颖聪 王亚 杨晓冬 于 2020-04-29 设计创作，主要内容包括：本发明公开了一种基于阵列线圈的磁场补偿方法及设备,该方法包括以下步骤：1)根据待补偿磁场类型,选择对应的磁场分解方法,获取目标磁场的分解结果；2)选择电流分布曲面,并建立阵列线圈中每个线圈内的电流密度函数,分解电流密度函数；3)建立从电流密度的流函数中各个基函数与目标磁场分解得到的基函数之间的关系；4)建立目标磁场分布优化函数；5)根据得到的优化函数获取目标磁场的阵列线圈的参数优化结果,从而确定流函数分布和线圈结构。本发明通过这种结合了目标磁场分布特征的优化设计,能够有效的减少补偿线圈数量,降低涡流效应,提高阵列线圈电流效率,优化磁场补偿的方案；能适应多种类的目标待补偿磁场分布,实现动态磁场补偿的目的。(The invention discloses a magnetic field compensation method and equipment based on an array coil, wherein the method comprises the following steps: 1) selecting a corresponding magnetic field decomposition method according to the type of the magnetic field to be compensated to obtain a decomposition result of the target magnetic field; 2) selecting a current distribution curved surface, establishing a current density function in each coil in the array coils, and decomposing the current density function; 3) establishing a relation between each basis function in the current function of the current density and a basis function obtained by decomposing a target magnetic field; 4) establishing a target magnetic field distribution optimization function; 5) and obtaining a parameter optimization result of the array coil of the target magnetic field according to the obtained optimization function, thereby determining the flow function distribution and the coil structure. According to the invention, through the optimization design combined with the distribution characteristics of the target magnetic field, the number of compensation coils can be effectively reduced, the eddy current effect is reduced, the current efficiency of the array coil is improved, and the scheme of magnetic field compensation is optimized; the method can adapt to various types of target to-be-compensated magnetic field distribution, and achieves the purpose of dynamic magnetic field compensation.)

1. A magnetic field compensation method based on array coils is characterized by comprising the following steps:

1) selecting a corresponding magnetic field decomposition method according to the type of the magnetic field to be compensated to obtain a decomposition result of the target magnetic field;

2) selecting a current distribution curved surface, establishing a current density function in each coil in the array coil, and selecting a corresponding current density decomposition method to decompose the current density function;

3) establishing a relation between each basis function in the current function of the current density and a basis function obtained by decomposing a target magnetic field according to the Biao-Saval law;

4) establishing a target magnetic field distribution optimization function;

5) and obtaining a parameter optimization result of the array coil of the target magnetic field according to the obtained optimization function, thereby determining the flow function distribution and the coil structure.

2. The array coil-based magnetic field compensation method according to claim 1, wherein the optimization results of the parameters of the array coil include the optimization results of the shape and number of the array coil and the current in the array coil.

3. The array coil-based magnetic field compensation method according to claim 1, wherein the decomposition method of the target magnetic field is a harmonic function orthogonal basis decomposition, or other decomposition method based on a hilbert space basis function, or other decomposition method capable of maintaining an initial state of the magnetic field superposition.

4. The array coil-based magnetic field compensation method according to claim 1, wherein the decomposition method of the current density is decomposition using fourier series or other decomposition method based on hilbert space basis function.

5. The array coil-based magnetic field compensation method according to claim 1, wherein the magnetic field to be compensated is a Halbach magnet magnetic field having a cylindrical magnet structure, and the magnetic field compensation method for the magnetic field comprises the following steps:

1) and expanding the target magnetic field into a harmonic function expression by using a harmonic function orthogonal basis:

wherein n and m are the degree and order of harmonic function, r, theta and phi are polar coordinate variables α_n,m、b_n,mFor harmonic quadrature fundamental amplitude values of the respective order n, m, P^m _nIs the associated Legendre formula;

2) cylindrical surface is selected as current-carrying curved surface to simplify current density into angular componentAnd axial component J_zTarget magnetic field (B)_x，B_y，B_z) Expressed as:

wherein, mu₀Represents magnetic permeability; r represents the vector distance of the source point from the origin; r is^′Representing the vector distance of the target field point from the origin;

for a Q x K array coil distribution, the current density function within each coil element is expressed using a fourier series expansion as:

wherein, V ∈ [1, V ]],h∈[1,H]，

Wherein V represents the number of stages of axial Fourier expansion; h represents the number of Fourier expansion stages in the angular direction; r represents the radius of the target field point; z_qRepresenting the qth unit axial coordinate; l represents the axial half height of the current-carrying curved surface:representing the amplitude of the (v, h) -th Fourier expansion corresponding to the k-th row and q-column element coils;representing the angular coordinate representing the kth element;representing the angular component of the k-th cell,is the angular component after rotation;

3) obtaining a distribution rule of corresponding magnetic field components which can be generated on a target magnetic field by each basis function in the flow function of each current density according to the Biot-Saval law, and thus establishing a relation between each basis function in the flow function of the current density and a basis function obtained by decomposing the target magnetic field; the magnitude of the basis functions in each flow function can be achieved by solving the following system of linear equations:

wherein the content of the first and second substances,a current value of the (k, q) th coil corresponding to the (n, m) th target magnetic field; a. the_kqTo correspond to(n, m) a target magnetic field, (k, q) a coefficient matrix of the coil;is the target magnetic field amplitude.

4) Establishing an optimization function from the flow function to the target magnetic field distribution;

5) and acquiring a parameter optimization result of the array coil providing the target magnetic field according to the obtained optimization function.

6. The array coil-based magnetic field compensation method according to claim 1, wherein in step 4), the optimization parameters selected when establishing the optimization function include one or more of energy storage, energy consumption, inductance, magnetic field accuracy, and current efficiency.

7. An array coil based magnetic field compensation device, characterized in that it performs magnetic field compensation using the method according to any of claims 1-6.

8. The array coil based magnetic field compensation apparatus of claim 1, comprising: the system comprises array coil equipment, a central controller, a PID controller, an amplifier, a current detector, a probe and a power supply;

the central controller is used for controlling the PID controller, the power supply and the amplifier, and modulates the waveform of the current by controlling the PID controller;

the power supply reaches the required current amplitude value through the amplifier and is connected into the array coil equipment;

the current detector detects the actual current value in the array coil equipment and feeds the actual current value back to the central controller;

the probe detects the magnetic field of a target area and feeds the magnetic field back to the central controller.

9. The array coil based magnetic field compensation device according to claim 1, wherein the array coil device comprises an array coil body, a multi-channel power supply capable of independently powering each coil in the array coil body through a connection wire, and a current limiting resistor disposed on the connection wire.

10. The array coil based magnetic field compensation device according to claim 1, wherein the current detector is a current detection resistor, and the probe is a magnetic field measurement device based on a hall element or a magnetic resonance principle.

Technical Field

The invention relates to the technical field of magnetic field compensation, in particular to a magnetic field compensation method and device based on an array coil.

Background

The conventional magnetic field compensation equipment generally decomposes a magnetic field into a plurality of groups (theoretically, infinite groups) of orthogonal bases based on spherical harmonic analysis, then designs a group of coil equipment for each group of orthogonal bases, and combines a plurality of groups of coils to realize the compensation of a target magnetic field in application. The multiple groups of orthogonal coils have the problem of mutual interference, and in addition, the eddy current effect is also obvious.

The array coil shimming technology utilizes a group of coil arrays, can directly generate target magnetic field distribution, does not generate an additional pollution field, has the advantages of small inductance, small eddy current effect and the like, and has great development potential in the occasions needing magnetic field compensation application, such as magnetic resonance shimming, gradient, radio frequency and the like. The conventional array coil magnetic field compensation equipment generally adopts a regular and uniformly distributed unit distribution coil structure to realize direct magnetic field compensation, and the non-optimized and universal array coil equipment has the problems of low current efficiency and poor pertinence, so that the application is limited.

Disclosure of Invention

The present invention provides a magnetic field compensation method and apparatus based on array coils, aiming at the above-mentioned deficiencies in the prior art. According to the distribution of a target magnetic field to be shimmed (possibly superposition of harmonic orthogonal base magnetic field components of several orders), performance parameters of equipment in the array coil are calculated according to all target spherical harmonic function components, and the optimal array coil equipment under the target magnetic field is obtained according to the established target parameters in an optimized mode.

The technical scheme adopted by the invention is as follows: the magnetic field compensation method based on the array coil comprises the following steps:

1) selecting a corresponding magnetic field decomposition method according to the type of the magnetic field to be compensated to obtain a decomposition result of the target magnetic field;

2) selecting a current distribution curved surface, establishing a current density function in each coil in the array coil, and selecting a corresponding current density decomposition method to decompose the current density function;

3) establishing a relation between each basis function in the current function of the current density and a basis function obtained by decomposing a target magnetic field according to the Biao-Saval law;

4) establishing a target magnetic field distribution optimization function;

5) and obtaining a parameter optimization result of the array coil of the target magnetic field according to the obtained optimization function, thereby determining the flow function distribution and the coil structure.

Preferably, the optimization results of the parameters of the array coils include optimization results of the shape, number and current in the array coils.

Preferably, the decomposition method of the target magnetic field is harmonic function orthogonal basis decomposition, or other decomposition method based on Hilbert space basis function, or other decomposition method capable of maintaining the initial state of the magnetic field superposition.

Preferably, the decomposition method of the current density is decomposition using a fourier series, or other decomposition methods based on hilbert space basis functions.

Preferably, the magnetic field to be compensated is a Halbach magnet magnetic field having a cylindrical magnet structure, and the magnetic field compensation method for the magnetic field includes the following steps:

1) and expanding the target magnetic field into a harmonic function expression by using a harmonic function orthogonal basis:

wherein n and m are the degree and order of harmonic function, r, theta and phi are polar coordinate variables α_n,m、b_n,mFor harmonic quadrature fundamental amplitude values of the respective order n, m, P^m _nIs the associated Legendre formula;

2) cylindrical surface is selected as current-carrying curved surface to simplify current density into angular componentAnd axial component J_zTarget magnetic field (B)_x，B_y，B_z) Expressed as:

wherein, mu₀Represents magnetic permeability; r represents the vector distance of the source point from the origin; r' represents the vector distance of the target field point from the origin;

for a Q x K array coil distribution, the current density function within each coil element is expressed using a fourier series expansion as:

wherein, V ∈ [1, V ]],h∈[1,H]，

Wherein V represents the number of stages of axial Fourier expansion; h represents the number of Fourier expansion stages in the angular direction; r represents the radius of the target field point; z_qRepresenting the qth unit axial coordinate; l represents the axial half height of the current-carrying curved surface:representing the amplitude of the (v, h) -th Fourier expansion corresponding to the k-th row and q-column element coils;representing the angular coordinate representing the kth element;representing the angular component of the k-th cell,is the angular component after rotation;

3) obtaining a distribution rule of corresponding magnetic field components which can be generated on a target magnetic field by each basis function in the flow function of each current density according to the Biot-Saval law, and thus establishing a relation between each basis function in the flow function of the current density and a basis function obtained by decomposing the target magnetic field; the magnitude of the basis functions in each flow function can be achieved by solving the following system of linear equations:

wherein the content of the first and second substances,a current value of the (k, q) th coil corresponding to the (n, m) th target magnetic field; a. the_kqA matrix of coefficients for the (k, q) coil for the corresponding (n, m) target magnetic field;is the target magnetic field amplitude.

4) Establishing an optimization function from the flow function to the target magnetic field distribution;

5) and acquiring a parameter optimization result of the array coil providing the target magnetic field according to the obtained optimization function.

Preferably, in step 4), the optimization parameters selected when establishing the optimization function include one or more of energy storage, energy consumption, inductance, magnetic field accuracy, and current efficiency.

The invention also provides magnetic field compensation equipment based on the array coil, which adopts the method for magnetic field compensation.

Preferably, the array coil-based magnetic field compensation apparatus includes: the system comprises array coil equipment, a central controller, a PID controller, an amplifier, a current detector, a probe and a power supply;

the central controller is used for controlling the PID controller, the power supply and the amplifier, and modulates the waveform of the current by controlling the PID controller;

the power supply reaches the required current amplitude value through the amplifier and is connected into the array coil equipment;

the current detector detects the actual current value in the array coil equipment and feeds the actual current value back to the central controller;

the probe detects the magnetic field of a target area and feeds the magnetic field back to the central controller.

Preferably, the array coil device comprises an array coil body, a multi-channel power supply capable of independently supplying power to each coil in the array coil body through a connecting lead and a current limiting resistor arranged on the connecting lead.

Preferably, the current detector is a current detection resistor, and the probe is a magnetic field measuring device based on a hall element or a magnetic resonance principle.

The invention has the beneficial effects that: according to the magnetic field compensation method and the magnetic field compensation equipment based on the array coil, the optimal design combined with the distribution characteristics of the target magnetic field can effectively reduce the number of exciting coils, reduce the eddy current effect, improve the current efficiency of the array coil and optimize the magnetic field compensation scheme; the method can adapt to various types of target to-be-compensated magnetic field distribution, and achieves the purpose of dynamic magnetic field compensation.

Drawings

Fig. 1 an array coil device of magnetic field distribution B (1, -1/0/1) in embodiment 1 of the present invention;

FIG. 2 is a graph comparing the performance of example 1 of the present invention with a conventional array coil apparatus;

FIG. 3 is an array coil apparatus with a magnetic field distribution of B (3, -3/-2/-1/0/1/2/3) according to an embodiment of the present invention;

FIG. 4 is an array coil apparatus with magnetic field distribution B (2, -2/-1/0) & B (3, -2/-1/0) according to an embodiment of the present invention;

fig. 5 is a schematic structural view of an array coil device in embodiment 2 of the present invention;

fig. 6 is a schematic structural diagram of magnetic field compensation in embodiment 2 of the present invention.

Detailed Description

The present invention is further described in detail below with reference to examples so that those skilled in the art can practice the invention with reference to the description.

It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.

The magnetic field compensation method based on the array coil comprises the following steps:

1) selecting a corresponding magnetic field decomposition method according to the type of the magnetic field to be compensated to obtain a decomposition result of the target magnetic field;

2) selecting a current distribution curved surface, establishing a current density function in each coil in the array coil, and selecting a corresponding current density decomposition method to decompose the current density function;

3) establishing a relation between each basis function in the current function of the current density and a basis function obtained by decomposing a target magnetic field according to the Biao-Saval law;

4) establishing a target magnetic field distribution optimization function;

5) and obtaining a parameter optimization result of the array coil of the target magnetic field according to the obtained optimization function, thereby determining the flow function distribution and the coil structure.

The invention can be applied to shimming, ultra-low field and other application occasions needing space magnetic field compensation of the magnetic resonance equipment magnet. The magnetic field compensation function can comprise gradient in magnetic resonance, radio frequency function and magnetic field generation function with any shape.

Wherein the parameter optimization result of the array coil comprises the optimization results of the shape and the number of the array coil and the current in the array coil. The shape of the coil is optimally designed according to the distribution of the magnetic field to be compensated so as to adapt to the compensation application of various types of magnetic fields. The array coil may comprise a single coil, coil pair or multiple sets of coils, coil pairs. According to the invention, the current amplitude of the target magnetic field to be compensated is solved through the target array coil structure established by the parameter optimization result, and the driving array coil unit is controlled to work through an external circuit, so that the magnetic field compensation is realized.

The decomposition method of the target magnetic field is harmonic function orthogonal basis decomposition, or other decomposition methods based on Hilbert space basis function, or other decomposition methods capable of maintaining the initial state of magnetic field superposition.

The decomposition method of the current density is to use Fourier series to carry out decomposition, or other decomposition methods based on Hilbert space basis function.

In one embodiment, the magnetic field to be compensated is a Halbach magnet magnetic field having a cylindrical magnet structure, and the magnetic field compensation method for the magnetic field includes the following steps:

1) and expanding the target magnetic field into a harmonic function expression by using a harmonic function orthogonal basis:

wherein n and m are the degree and order of harmonic function, r, theta and phi are polar coordinate variables α_n,m、b_n,mFor harmonic quadrature fundamental amplitude values of the respective order n, m, P^m _nIs the associated Legendre formula;

2) cylindrical surface is selected as current-carrying curved surface to simplify current density into angular componentAnd axial component J_zTarget magnetic field (B)_x，B_y，B_z) Expressed as:

wherein, mu₀Represents magnetic permeability; r represents the vector distance of the source point from the origin; r' represents the vector distance of the target field point from the origin;

for a Q x K array coil distribution, the current density function within each coil element is expressed using a fourier series expansion as:

wherein, V ∈ [1, V ]],h∈[1,H]，

Wherein V represents the number of stages of axial Fourier expansion; h represents the number of Fourier expansion stages in the angular direction; r represents the radius of the target field point; z_qRepresenting the qth unit axial coordinate; l represents the axial half height of the current-carrying curved surface:representing the amplitude of the (v, h) -th Fourier expansion corresponding to the k-th row and q-column element coils;representing the angular coordinate representing the kth element;the angular component of the k-th cell is shown,is the angular component after rotation;

3) obtaining a distribution rule of corresponding magnetic field components which can be generated on a target magnetic field by each basis function in the flow function of each current density according to the Biot-Saval law, and thus establishing a relation between each basis function in the flow function of the current density and a basis function obtained by decomposing the target magnetic field; the magnitude of the basis functions in each flow function can be achieved by solving the following system of linear equations:

wherein the content of the first and second substances,a current value of the (k, q) th coil corresponding to the (n, m) th target magnetic field; a. the_kqA matrix of coefficients for the (k, q) coil for the corresponding (n, m) target magnetic field;is the target magnetic field amplitude.

4) Establishing an optimization function from the flow function to the target magnetic field distribution: on the basis, an array coil overall optimization function is established, and different optimization parameters such as energy storage, energy consumption, inductance, magnetic field accuracy, current efficiency and the like can be selected according to application scenes. Based on the model of the current density function, the relationship between the magnetic field and the current density Fourier series amplitude can be established, at the moment, according to the target magnetic field intensity to be compensated, the performance parameters aiming at each harmonic function orthogonal base can be obtained, and the optimal array coil distribution aiming at all the harmonic functions to be compensated can be obtained by utilizing the target function.

5) And acquiring a parameter optimization result of the array coil providing the target magnetic field according to the obtained optimization function.

A more specific example is provided below for further illustration.