CN106556813A - The linear hybrid optimization method of active shimming coils in a kind of magnetic resonance system - Google Patents

Abstract

The invention discloses in a kind of magnetic resonance system active shimming coils linear hybrid optimization method, convergence difficulties have been solved by linear programming, obtain globally optimal solution, and matrix operationss mode is adopted to magnetic field, harmonic wave, calculating speed and design efficiency are greatly improved, in overcoming existing shimming technique, restrains that relatively difficult, solution efficiency is low, cannot meet the shortcoming of globally optimal solution.

Description

The linear hybrid optimization method of active shimming coils in a kind of magnetic resonance system

Technical field

The present invention is a kind of linear hybrid optimization method of active shimming coils in magnetic resonance system, belongs to nuclear magnetic resonance The design field of system unit.

Background technology

Magnetic resonance system is broadly divided into nuclear magnetic resonance (Magnetic Resonance Imaging) and nuclear magnetic resoance spectrum Instrument (Nuclear Magnetic Resonance) two big class.MRI system has become medical industry as clinical diagnosises instrument Indispensable medical instruments and equipment, compared with the equipment such as traditional X-ray, CT scanner, ultrasonic imaging device, with hurtless measure, The advantages of low radiation dose, high-resolution and any direction tomoscan, through the development of more than 30 years, its application was extensive Popularization.NMR system is then widely used in the field of scientific studies such as biomedicine, investigation of materials.

Used as the core component of magnetic resonance system, main magnet is used for the background magnetic for providing certain magnetic field intensity, high evenness .Magnetic field intensity is one of important indicator of magnetic resonance system, and magnetic field intensity is higher, then the imaging time of magnetic resonance system is got over Short, the resolution and definition of imaging is also higher.Uniformity of magnetic field is also the important indicator for affecting magnetic resonance system image quality, General medicine whole body imaging magnetic resonance system requires that uniformity of magnetic field is in 5ppm (5 × 10 in the imaging ball body of 40～50cm^-6) Within, the uniformity of magnetic field requirement of functional imaging magnet system is then higher.

Due in main magnet in coil winding, assembling process, inevitably by coiling error, magnet skeleton The impact of the factor such as cold events and rigging error, the true field uniformity of main magnet decline than the uniformity of magnetic field of design 1～2 magnitude.Therefore special shimming technique is needed to correct come the magnetic field in the imaging region to magnetic resonance system.

Shimming technique is divided into two kinds of passive shimming and active shimming.Wherein active shimming (Active shimming) is general In high uniform magnet system, by designing several groups of annulars or saddle coil, different electric currents are passed to, by producing particular space The magnetic field superposition of distribution is corresponded on the main magnetic field, respectively and offsets uneven component therein, so as to the magnetic field for improving main magnet is equal Evenness, this technology are referred to as active shimming technique.

Active shimming technique has been widely used in some High-Fields, the magnetic resonance system of high evenness and nuclear magnetic resonance spectrometer In, have become one of important indicator of decision magnetic resonance system equipment final performance.

Active shimming coils are divided into two kinds of superconducting coil and room-temperature coils.Superconduction shim coil is together put with main magnet coil Put under liquid helium environment, in superconducting state, larger electric current can be loaded, its Main Function in shimming.Room temperature shim coil one As be arranged on room temperature hole in, to compensate remaining Magnetic field inhomogeneity degree.

Traditional active method for shimming is analytic process, is carried out by the Distribution of Magnetic Field or harmonic component that produce to electrified wire Analysis, so that it is determined that the location parameter of wire, which has the disadvantage that some coils cannot meet requirement because axial dimension is long, and Multiturn coil can take certain space position, cause magnetic field precise decreasing.On this basis, in recent years numerical method is introduced The design of shim coil, such as genetic algorithm (GA), SQP etc., its ultimate principle is：

1) by the spherical harmonics coefficient decomposition analysis to magnetic field, N*M point, construction are selected in imaging sphere or ellipsoid Particular harmonic in Distribution of Magnetic Field, as the magnetic field of the goal with design；

2) number and location parameter of coil are preset, as the initial solution of optimization；

3) magnetic field at the specified point is solved, is obtained with the maximum field deviation of magnetic field of the goal as constraints；

4) other constraintss, such as the axial length constraint of coil, not overlay requirements of coil etc. are added；

5) using superconducting line consumption as goal condition；

6) result is obtained by the nonlinear optimization means such as genetic algorithm or SQP.

But due to having preset coil number and location parameter, there is certain limitation in optimization, it is impossible to ensure global optimum Change result.And the coil number and location parameter of initial setting up are both become dependent upon, if arranging bad, convergence rate is very Slowly, or even without solution.

Sharon E.Ungersma and Hao Xu of Stanford universities of the U.S. et al. propose that a kind of linear programming is used for setting Room temperature shim coil is counted, the ultimate principle of the method is：

1) the three-dimensional continuous net lattice point of division on the skeleton of shim coil, the electric current of each mesh point have 8 optional directions, Between can have electric current to pass through, and meet Kirchhoff's current law (KCL)；

2) magnetic field configuration according to needed for each rank shimming, sets magnetic field deviation constraint condition, and with minimum heating power is Object function, designs the controllable space three-dimensional current path figure of magnetic field deviation.

The result that the method is obtained is separate winding structure, is only applicable to room temperature shim coil, and with minimum heating power For object function, it is impossible to obtain with line cost minimization scheme；As which arranges grid in three dimensions, each mesh point has 8 Degree of freedom, each degree of freedom are both needed to meet Kirchhoff's law and Distribution of Magnetic Field bit-type, therefore solving model scale is greatly, solves Efficiency is very low.Therefore this method does not obtain practical application.

The content of the invention

The purpose of the present invention is the defect for overcoming prior art, there is provided the line of active shimming coils in a kind of magnetic resonance system Property method for mixing and optimizing, has solved convergence difficulties by linear programming, has obtained globally optimal solution, and adopted square to magnetic field, harmonic wave Battle array computing mode, greatly improves calculating speed and design efficiency, and relatively difficult, solution effect is restrained in overcoming existing shimming technique Rate is low, cannot meet the shortcoming of globally optimal solution.

The technical scheme for realizing above-mentioned purpose is：The linear hybrid optimization side of active shimming coils in a kind of magnetic resonance system Method, comprises the following steps：

Step S1, active shimming coils require input：Determine the design requirement of active shimming coils, the design requirement includes The size of imaging region, the spatial dimension of arrangement coil, the intensity of shim coil and deviation allowable value, using these requirements as setting The input of meter active shimming coils；

Step S2, arranges net region, sets up linear programming model, specifically include following operation：

S21, axial magnetic field Bz in the imaging region of magnetic resonance system resolve into each expansion to harmonic constant：

Which is launched under rectangular coordinate system, is obtained：

Wherein, Anm and Bnm is every harmonic constant, constant term A₀₀As central magnetic field Bz0, eliminates n>The items of 1 rank it Uniform magnetic field is obtained afterwards；

S22, the imaging region surface required in step S1 choose m1, m2 target field correspondingly according to direction of warp and weft Point, chooses altogether M target site, calculates magnetic field of the goal B by formula (2)_tar；

S23, in the spatial dimension of the arrangement coil required in step S1, the spatial dimension is the space with square-section Scope, divides n1, n2 grid correspondingly in radial and axial direction, divides altogether N number of grid, and each grid is equivalent to The electric current circular arc of the electric current loop or certain radian of square-section, the magnetic field of the M point that unitary current i is chosen on imaging region surface Contribution B_MNCan be calculated with simple integral method, wherein M is target site, and N is grid number, M=m1*m2, N=n1*n2；All nets The harmonic contribution matrix of the corresponding electric current loop of lattice or electric current circular arc is H；The harmonic wave of unitary current i is H_KN, wherein K is the humorous of calculating Ripple item, N are grid number；All calculating adopt matrix operationss, and it is I=[I to define the corresponding current matrix of all grids₁,I₂,…, I_N], then all electric current loops or electric current circular arc are as follows to the contribution harmonic difference in magnetic field：

S24, if the current density, J of each grid is identical, then the cumulative volume V of corresponding electric current loop or electric current circular arc is：

In formula (4),For electric current loopOr the ring radian of electric current circular arc；

S25, requires to set up linear programming model for shimming, with minimum line amount as object function, magnetic field deviation or humorous Used as constraints, the electric current of each grid is optimized variable to ripple deviation, and linear programming model is as follows：

In formula (5), eps B are the magnetic field deviation of requirement, and epsH is the harmonic wave deviation of requirement, H_tarFor the shimming line for requiring Harmonic wave corresponding to circle intensity, I max are the corresponding maximum current of each grid, if with maximum current density Jmax to limit bar Part, then I max=J max*Agrid, wherein Agrid are the corresponding sectional area of each grid；

Step S3, carries out linear optimization, obtains theoretical coil distribution：After the completion of the linear programming model of formula (5) is solved, i.e., The theoretical current distribution of coil is obtained, number and the position of coil are obtained according to the distribution of the theoretical current of coil, each Coil position is determined by inside radius r1, outer radius r2 and axial coordinate z1, z2；

Step S4, sets up Nonlinear programming Model, carries out nonlinear optimization；

The model of Non-Linear Programming is as follows：

Formula (6), eps B are the magnetic field deviation of requirement；Eps H are the harmonic wave deviation of requirement；z_1,iFor the axle of i-th coil Mark is sat up straight to the left；z_2,iFor the axial right-hand member coordinate of i-th coil；z₁lb、z₁Ub is the coil dimension obtained according to linear programming Bound, its size can do suitable control in the spatial dimension for requiring；Bcal and Hcal are harmonious for magnetic field correspondingly The value of calculation of ripple；Nz (i) is the number of turn of each coil, and tz is the width using wire；Ensure that what is used leads by constraints Line is whole numbers of turns, and each coil is not overlapped；

The model of the Non-Linear Programming of formula (6) is by interior plot point method, SQP or other numerical optimisation algorithms realities Existing nonlinear optimization；The size of known use wire, obtains meeting actual loop structure by Nonlinear programming Model；

Step S5, judges whether the loop structure that Non-Linear Programming is obtained meets engine request, if meet being walked Rapid S6, if being unsatisfactory for return to step S4；

Step S6, exports the structural parameters of active shimming coils.

The linear hybrid optimization method of active shimming coils in a kind of above-mentioned magnetic resonance system, in step S1, deployment line The spatial dimension of circle is sat by coil minimum inside radius Rmin, maximum outer radius Rmax, minimum axial direction coordinate Zmin and maximum axial Mark Zmax is determined.

The linear hybrid optimization method of active shimming coils in a kind of above-mentioned magnetic resonance system, in S22, the target field Gauss integration point is chosen or adopted to the selection of point for linear, convenient directly to try to achieve harmonic wave by magnetic field and checked.

The linear hybrid optimization method of active shimming coils in a kind of above-mentioned magnetic resonance system, in formula (5), in constraint bar In part, magnetic field deviation constraint or harmonic wave constraint are selected as requested；Harmonic wave constraint relative to magnetic field deviation constraint, optimization scale compared with Little, solving speed is fast, in known magnetic field deviation requirement, needs for magnetic field deviation to be converted to harmonic wave deviation.

The linear hybrid optimization method of active shimming coils in a kind of above-mentioned magnetic resonance system, the magnetic field in formula (6) is about The constraint of beam harmonic selects one as requested.

Generally 1～4 layer of the number of plies of single-order shim coil, can directly by the footpath of each coil of linear programming structure determination To size, while reducing the degree of freedom of nonlinear model, accelerate convergence rate.In the optimization of multistage coil, if desired for design The methods and procedures of eight groups of coils within second order, calculating magnetic field contribution or harmonic contribution is general, it is only necessary to change coil Type can try to achieve the field contribution or harmonic contribution of not same order coil, quickly realize the design of multigroup coil, improve design Efficiency.

In the magnetic resonance system of the present invention, the linear hybrid optimization method of active shimming coils, has the advantages that：

(1) linear programming model optimization is employed, solves the problems, such as that conventional method convergence difficulties and efficiency are too low, while Global optimum's result can be obtained；

(2) present invention can select magnetic field deviation optimization or harmonic wave optimization as requested, improve the convenience and efficiency of design；

(3) each grid is equivalent to the present invention electric current loop or electric current circular arc of square-section, improves computational accuracy, and Matrix operationss mode is adopted in magnetic field calculation or Harmonics Calculation, calculating speed and design efficiency is improve.

Description of the drawings

Fig. 1 is the flow chart of the linear hybrid optimization method of active shimming coils in magnetic resonance system of the invention；

Fig. 2 is the current distributing figure that obtains to Z2 coil linear optimizations in embodiment one；

Fig. 3 is the Z2 coil space scattergrams after optimizing in embodiment one；

Fig. 4 is that one shimming backbone length of embodiment is changed into 200mm or increases the electric current after mutual inductance contribution matrix restraint Scattergram；

Spatial distribution maps of the Fig. 5 for the x-ray circle after optimizing in embodiment two.

Specific embodiment

In order that those skilled in the art are better understood when technical scheme, it is right below in conjunction with the accompanying drawings Its specific embodiment is described in detail：

Fig. 1 to Fig. 5 is referred to, to design Z2, as a example by x-ray circle, ball domain of the imaging region for diameter 25mm, shimming skeleton half Footpath is Rmin=130.5mm, and length L is 400mm, from the superconducting line of 0.436mm.Z2 coil strengths are required as >=25mT/m2/ A, x-ray circle intensity requirement are >=1.5mT/m/A.

Embodiment one：

Design Z2 coils, the linear hybrid optimization method of active shimming coils in a kind of magnetic resonance system, including following step Suddenly：

Step S1, active shimming coils require input：Ball domain of the imaging region for diameter 25mm, shimming skeleton radius is Rmin=130.5mm, length L are 400mm, from the superconducting line of 0.436mm.Z2 coil strengths are required as >=25mT/m2/A；

Step S2, arranges net region, sets up linear programming model：For Z2 coils, its corresponding harmonic constant is A₂₁, Its value is the intensity of above-mentioned Z2 coils.In the range of area of space (Rmin, Rmax ,-L/2, L/2), radially divide 1 net Lattice, axially point 1000 grids, take maximum current for I max=1A.According to Z2 coil characteristics, it is only necessary to which front 8 order harmonicses are constrained, Obtain following linear programming model：

Wherein H_KNFor the harmonics matrix of K ranks, i.e. H_KN=A_K* r^K, r are imaging region harmonic wave radius 12.5mm.N is to draw Point total grid number, J is the maximum current density (i.e. the ratio of maximum current and wire cross-section area) allowed, Agrid is each The sectional area of grid.0 is constrained to the odd-order of Z2 coils, to ensure the symmetry of Z2 coils, dual numbers rank is constrained to one The deviation of very little, to ensure that the magnetic field deviation of Z2 coils is small.

Step S3, carries out linear optimization, obtains theoretical coil distribution：Line is obtained according to the linear programming model of formula (7) The theoretical current distribution of circle, is obtained number and the position of coil according to the distribution of the theoretical current of coil, refers to Fig. 2, The CURRENT DISTRIBUTION obtained through linear optimization in Z2 coil design, can be apparent from being seen that there is 4 coils and its position；

Step S4, sets up Nonlinear programming Model, carries out nonlinear optimization；

The model of Non-Linear Programming is as follows：

Formula (6), epsB are the magnetic field deviation of requirement；Eps H are the harmonic wave deviation of requirement；z_1,iFor the axial direction of i-th coil Left end coordinate；z_2,iFor the axial right-hand member coordinate of i-th coil；z₁lb、z₁Ub is the coil dimension obtained according to linear programming Bound, its size can do suitable control in the spatial dimension for requiring；Bcal and Hcal are magnetic field harmonic correspondingly Value of calculation；Nz (i) is the number of turn of each coil, and tz is the width using wire；

Nonlinear optimization is carried out to step Z2 coil according to formula (6), so as to the loop construction for being met engineering demand is joined Number, table 1 are the structural parameters after the optimization of Z2 coils：

Inside radius (mm)	Outer radius (mm)	Left end coordinate (mm)	Right-hand member coordinate (mm)	The number of turn	Electric current (A)
						130.5	130.936	-150.739	-118.911	73	1
130.5	130.936	-49.818	-37.174	29	-1
						130.5	130.936	37.174	49.818	29	-1
130.5	130.936	118.911	150.739	73	1

Table 1

The intensity of the Z2 coils of optimization is 25.22mT/m2/A, and maximum field deviation is 0.28 ‰.Fig. 3 is referred to, is optimized Z2 coils spatial distribution position.

Step S5, judges whether the loop structure that Non-Linear Programming is obtained meets engine request, if meet being walked Rapid S6, if being unsatisfactory for return to step S4；In the present embodiment, Z2 coil strengths require to be >=25mT/m2/A, the Z2 coils of optimization Intensity is 25.22mT/m2/A, meets engine request, carries out step S6；

Step S6, exports the structural parameters of Z2 coils.

Refer to Fig. 4, it is shown that when backbone length is changed into 200mm or add and the mutual inductance square of main magnet coil During battle array constraint, 5 coils and its position can be clearly found out in the Z2 coil currents distribution for obtaining.And other optimization methods due to Coil number and initial position are set, needs repeatedly artificial trial just obtain result.It is worthy of note that, according to different Space and intensity requirement, quickly obtain the globally optimal solution of the number and initial position of different coils, this exactly present invention difference It is located in the advantage of other optimized algorithms.

Optimization method of the present invention can also be used for the active shimming design of multiple arrangement space area requirements in addition, so It is possible to some coils is located on the skeleton of main magnet coil, so as to save main magnet inner space.

Embodiment two：

X-ray circle is designed, the linear hybrid optimization method of active shimming coils in a kind of magnetic resonance system, including with Lower step：

Step S1, active shimming coils require input：Ball domain of the imaging region for diameter 25mm, shimming skeleton radius is Rmin=130.5mm, length L are 400mm, from the superconducting line of 0.436mm.X-ray circle intensity requirement is >=1.5mT/m/A；

Step S2, arranges net region, sets up linear programming model：X-ray circle is located at Z2 coil upper surfaces, can be by harmonic wave Deviation or magnetic field deviation constraint are optimized with magnetic field deviation here optimizing.X-ray circle be saddle coil structure, analysis shows x-ray circle In the radian of each coil be 2 π/3, and with regard to X/Y plane antisymmetry, during with regard to YZ plane symmetries, the lower term of its harmonic wave is only remaining A31 items and A11 items.M point is removed as previously described on imaging region surface, calculates the corresponding magnetic field of the goal of x-ray circle desired strength Matrix B tar, divides N number of grid in the range of x-ray cycle space, each grid be equivalent to radian for 2 π/3 and with regard to YZ planes just Symmetrical a pair have the electric current circular arc of square-section.Linear programming model is as follows：

Wherein B_MNFor the field contribution matrix that the corresponding electric current circular arc of N number of grid is produced in M point.The meaning of I, J, Agrid Justice is as it was previously stated, ones_NIt is the row vector that 1 element number is N for element value.So as to the electric current sum for ensureing all grids is 0, With the condition that the loop current for meeting saddle coil is 0, multiple regions, the subdivided net in each region can be divided to spatial dimension also Lattice, can obtain asymmetrical x-ray circle design.

Step S3, carries out linear optimization, obtains theoretical coil distribution：Line is obtained according to the linear programming model of formula (8) The theoretical current distribution of circle, is obtained number and the position of coil according to the distribution of the theoretical current of coil；

Step S4, sets up Nonlinear programming Model, carries out nonlinear optimization；

The model of Non-Linear Programming is as follows：

Formula (6), epsB are the magnetic field deviation of requirement；Eps H are the harmonic wave deviation of requirement；z_1,iFor the axial direction of i-th coil Left end coordinate；z_2,iFor the axial right-hand member coordinate of i-th coil；z₁lb、z₁Ub is the coil dimension obtained according to linear programming Bound, its size can do suitable control in the spatial dimension for requiring；Bcal and Hcal are magnetic field harmonic correspondingly Value of calculation；Nz (i) is the number of turn of each coil, and tz is the width using wire；

Nonlinear optimization is carried out to step Z2 coil according to formula (6), so as to the loop construction for being met engineering demand is joined Number, table 2 are the loop structure after the optimization of x-ray circle：

Table 2

The intensity of the x-ray circle that optimization is obtained is 1.501mT/m2/A, and maximum field deviation is 0.55 ‰.

Fig. 5 is referred to, the spatial distribution of x-ray circle after optimization.

Step S5, judges whether the loop structure that Non-Linear Programming is obtained meets engine request, if meet being walked Rapid S6, if being unsatisfactory for return to step S4；In the present embodiment, x-ray circle intensity requirement is >=1.5mT/m/A, the Z2 coils of optimization it is strong Spend for 1.501mT/m2/A, maximum field deviation is 0.55 ‰, meets engine request, carries out step S6；

Step S6, exports the structural parameters of x-ray circle.

Other rank coils can quickly obtain globally optimal solution by similar approach.

The present invention is designed to active shimming coils using linear hybrid algorithm, in single or multiple area of space divides net Lattice, each grid are equivalent to the electric current loop of square-section or electric current circular arc, or the electric current loop or electricity in other various sections Stream circular arc.

The present invention is designed to active shimming coils using linear hybrid algorithm, including but not limited to magnetic field deviation or harmonic wave Deviation is done constraint and tries to achieve result, and such as current loop is 0 constraint or inductance matrix constraint.

The present invention is designed to active shimming coils using linear hybrid algorithm, obtains theoretical global optimum using linear optimization Solution, is further met the scheme of engineering demand by nonlinear optimization, and the adoptable optimized algorithm of non-linear partial includes But it is not limited to interior plot point method, Sequential Quadratic Programming method, or the such as simulated annealing of other algorithms, genetic algorithm etc..

The present invention is designed to active shimming coils using linear hybrid algorithm, is divided in linear Optimization Dept., including but not limited to Using symmetry decomposition space claimed range or the predetermined cell sense of current, reduce the scale of linear optimization model, so as to add The optimal speed of fast optimization.

The present invention is designed to active shimming coils using linear hybrid algorithm, it is also possible to for the coil of other similar characteristics Design.

In sum, in magnetic resonance system of the invention active shimming coils linear hybrid optimization method, by linear Planning solves convergence difficulties, obtains globally optimal solution, and adopts matrix operationss mode to magnetic field, harmonic wave, greatly improves meter Speed and design efficiency are calculated, in overcoming existing shimming technique, restrains that relatively difficult, solution efficiency is low, cannot meet globally optimal solution Shortcoming.

Those of ordinary skill in the art it should be appreciated that the embodiment of the above be intended merely to explanation the present invention, And be not used as limitation of the invention, as long as in the spirit of the present invention, the change to embodiment described above Change, modification will all fall in the range of claims of the present invention.

Claims (5)

1. in a kind of magnetic resonance system active shimming coils linear hybrid optimization method, it is characterised in that comprise the following steps：

Step S1, active shimming coils require input：Determine the design requirement of active shimming coils, the design requirement includes imaging The size in region, the spatial dimension for arranging coil, the intensity of shim coil and deviation allowable value, using these requirements as design master The input of dynamic shim coil；

Step S2, arranges net region, sets up linear programming model, specifically include following operation：

S21, axial magnetic field Bz in the imaging region of magnetic resonance system resolve into each expansion to harmonic constant：

Which is launched under rectangular coordinate system, is obtained：

$Bz=A_{00}+{\mathrm{xA}}_{11}+{\mathrm{zA}}_{10}+B_{11}y+(3x^2-3y^2)A_{22}+\left(3xz\right)A_{21}+(-\frac{x^2}{2}-\frac{y^2}{2}+z^2)A_{20}+3B_{21}yz+...---\left(2\right)$

Wherein, A_nmAnd B_nmFor every harmonic constant, constant term A₀₀As central magnetic field Bz0, eliminates n>After the items of 1 rank i.e. Uniform magnetic field is obtained；

S22, the imaging region surface required in step S1 choose m1, m2 target site correspondingly according to direction of warp and weft, M target site is chosen altogether, magnetic field of the goal B is calculated by formula (2)_tar；

S23, in the spatial dimension of the arrangement coil required in step S1, the spatial dimension is the space model with square-section Enclosing, n1, n2 grid being divided correspondingly in radial and axial direction, divide altogether N number of grid, each grid is equivalent to square The electric current circular arc of the electric current loop or certain radian of tee section, the magnetic field tribute of the M point that unitary current i is chosen on imaging region surface Offer B_MNCan be calculated with simple integral method, wherein M is target site, and N is grid number, M=m1*m2, N=n1*n2；All grids The harmonic contribution matrix of corresponding electric current loop or electric current circular arc is H；The harmonic wave of unitary current i is H_KN, wherein K is the harmonic wave for calculating , N is grid number；All calculating adopt matrix operationss mode, and it is I=[I to define the corresponding current matrix of all grids₁, I₂,…,I_N], then all electric current loops or electric current circular arc are as follows to the contribution harmonic difference in magnetic field：

$\begin{array}{c}{B}_z=B_{MN}\·I\\ H=H_{KN}\·I\end{array}---\left(3\right);$

S24, if the current density, J of each grid is identical, then the cumulative volume V of corresponding electric current loop or electric current circular arc is：

In formula (4),For electric current loopOr the ring radian of electric current circular arc；

S25, requires to set up linear programming model for shimming, and with minimum line amount as object function, magnetic field deviation or harmonic wave are inclined Used as constraints, the electric current of each grid is optimized variable to difference, and linear programming model is as follows：

$s.t.\left\{\begin{array}{c}\left|B_{MN}\·I-B_{tar}\right|\≤\left|B_{tar}\right|epsB\\ \left|H_{KN}\·I-H_{tar}\right|\≤\left|H_{tar}\right|epsB\\ \left|I\right|\≤\mathrm{Im}ax\end{array}\right.---\left(5\right)$

In formula (5), eps B are the magnetic field deviation of requirement, and epsH is the harmonic wave deviation of requirement, H_tarShim coil to require is strong The corresponding harmonic wave of degree, I max are the corresponding maximum current of each grid, if with maximum current density Jmax as restrictive condition, Then I max=J max*Agrid, wherein Agrid are the corresponding sectional area of each grid；

Step S3, carries out linear optimization, obtains theoretical coil distribution：After the completion of the linear programming model of formula (5) is solved, you can Theoretical current to coil is distributed, and number and the position of coil, each coil is obtained according to the distribution of the theoretical current of coil Position is determined by inside radius r1, outer radius r2 and axial coordinate z1, z2；

Step S4, sets up Nonlinear programming Model, carries out nonlinear optimization；

The model of Non-Linear Programming is as follows：

$\begin{array}{cc}Objective:& \min V=\underset{i=1}{\overset{N}{\Σ}}{v}_i\end{array}$

$s.t.\left\{\begin{array}{c}\left|\frac{B_{cal}-B_{tar}}{B_{tar}}\right|\&le;epsB\\ \left|\frac{H_{cal}-H_{tar}}{H_{tar}}\right|\&le;epsB\\ z_{2,i}<z_{1,(i+1)},i=1,2,\mathrm{...},N-1\\ z_{1}lb<z_{1,i}<z_{1}ub,i=1,2,\mathrm{...},N\\ z_{2}lb<z_{2,i}<z_{2}ub,i=1,2,\mathrm{...},N\\ (z_{2,i}-z_{1,i})=N_z\left(i\right)\&CenterDot;tz,i=1,2,\mathrm{...},N\end{array}\right.---\left(6\right)$

Formula (6), epsB are the magnetic field deviation of requirement；Eps H are the harmonic wave deviation of requirement；z_1,iFor the axial left end of i-th coil Coordinate；z_2,iFor the axial right-hand member coordinate of i-th coil；z₁lb、z₁Ub is the upper and lower of the coil dimension that obtained according to linear programming Limit, its size can do suitable control in the spatial dimension for requiring；Bcal and Hcal meter correspondingly for magnetic field harmonic Calculation value；Nz (i) is the number of turn of each coil, and t z are the width using wire；Ensure that the wire for using is whole by constraints Circle is counted, and each coil is not overlapped；

The model of the Non-Linear Programming of formula (6) is realized non-by interior plot point method, SQP or other numerical optimisation algorithms Linear optimization；The size of known use wire, obtains meeting actual loop structure by Nonlinear programming Model；

Step S5, judges whether the loop structure that Non-Linear Programming is obtained meets engine request, if meet carrying out step S6, If being unsatisfactory for return to step S4；

Step S6, exports the structural parameters of active shimming coils.

2. in a kind of magnetic resonance system according to claim 1 active shimming coils linear hybrid optimization method, which is special Levy and be, in step S1, arrange the spatial dimension of coil by coil minimum inside radius Rmin, maximum outer radius Rmax, minimum axle Determine to coordinate Zmin and maximum axial coordinate Zmax.

3. in a kind of magnetic resonance system according to claim 1 active shimming coils linear hybrid optimization method, which is special Levy and be, in S22, Gauss integration point is chosen or adopted to the selection of the target site for linear, is conveniently directly asked by magnetic field Obtain harmonic wave to be checked.

4. in a kind of magnetic resonance system according to claim 1 active shimming coils linear hybrid optimization method, which is special Levy and be, in formula (5), in constraints, select magnetic field deviation constraint or harmonic wave constraint as requested；Harmonic wave constraint relative to Magnetic field deviation constraint, optimization scale are less, and solving speed is fast, in known magnetic field deviation requirement, need to change magnetic field deviation For harmonic wave deviation.

5. in a kind of magnetic resonance system according to claim 1 active shimming coils linear hybrid optimization method, which is special Levy and be, the magnetically confined harmonic constraint in formula (6) selects one as requested.