CN106556813B - Linear mixed optimization method of active shimming coil in magnetic resonance system - Google Patents
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Abstract
The invention discloses a linear mixed optimization method of an active shimming coil in a magnetic resonance system, which solves the problem of difficult convergence through linear programming to obtain a global optimal solution, adopts a matrix operation mode for a magnetic field and harmonic waves, greatly improves the calculation speed and the design efficiency, and overcomes the defects of difficult convergence, low solution efficiency and incapability of meeting the global optimal solution in the shimming technology in the prior art.
Description
Technical Field
The invention discloses a linear mixed optimization method of an active shimming coil in a magnetic resonance system, and belongs to the technical field of design of components of the magnetic resonance imaging system.
Background
Magnetic Resonance systems are mainly classified into two major categories, Magnetic Resonance Imaging (Magnetic Resonance Imaging) and Nuclear Magnetic Resonance spectroscopy (Nuclear Magnetic Resonance). The MRI system has become an indispensable medical instrument device in the medical industry as a clinical diagnosis tool, and compared with the traditional X-ray, CT scanner, ultrasonic imager and other devices, the MRI system has the advantages of no trauma, low radiation dose, high resolution, tomography in any direction and the like, and after more than 30 years of development, the application thereof has been popularized in a large scale. NMR systems are widely used in scientific research fields such as biomedicine and material research.
As a core component of a magnetic resonance system, a main magnet is used to provide a background magnetic field with a certain magnetic field strength and high uniformity. The magnetic field intensity is one of the important indexes of the magnetic resonance system, and the higher the magnetic field intensity is, the shorter the imaging time of the magnetic resonance system is, and the higher the resolution and definition of the imaging are. The magnetic field uniformity is also an important index influencing the imaging quality of a magnetic resonance system, the general medical whole-body imaging magnetic resonance system requires an imaging sphere of 40-50 cm, and the magnetic field uniformity is 5ppm (5 multiplied by 10)-6) Within, the magnetic field uniformity requirements for functional imaging magnet systems are higher.
Because the main magnet is in the coil winding, the assembly in-process, can receive the influence of factors such as coiling error, the cold shrink of magnet skeleton and assembly error inevitably, the actual magnetic field homogeneity of main magnet falls 1 ~ 2 orders of magnitude than the magnetic field homogeneity of design. Special shimming techniques are therefore required to correct the magnetic field in the imaging region of the magnetic resonance system.
The shimming technology is divided into passive shimming and active shimming. Active shimming (Active shimming) is generally performed in a high-homogeneity magnet system, by designing a plurality of groups of annular or saddle-shaped coils, passing different currents, and generating a magnetic field with specific spatial distribution to be superposed on a main magnetic field, so as to respectively and correspondingly offset inhomogeneous components in the main magnetic field, thereby improving the magnetic field uniformity of the main magnet, and the technology is called as an Active shimming technology.
The active shimming technology has been widely applied to some high-field and high-uniformity magnetic resonance systems and nuclear magnetic resonance spectrometers, and has become one of the important indexes for determining the final performance of the magnetic resonance system equipment.
The active shimming coil is divided into a superconducting coil and a room temperature coil. The superconducting shimming coil is placed in a liquid helium environment along with the main magnet coil, is in a superconducting state, can load larger current and plays a main role in shimming. Room temperature shim coils are typically mounted within the room temperature bore to compensate for residual magnetic field inhomogeneities.
The traditional active shimming method is an analysis method, and the position parameters of the conducting wire are determined by analyzing the magnetic field distribution or harmonic components generated by the electrified conducting wire. On the basis, in recent years, a numerical method is introduced to the design of the shim coils, such as a Genetic Algorithm (GA), a sequence quadratic programming and the like, and the basic principle is as follows:
1) through the analysis of the spherical harmonic coefficient of the magnetic field, selecting N M points on the imaging spherical surface or the elliptical surface, and constructing the magnetic field distribution of specific harmonics as a designed target magnetic field;
2) presetting the number and position parameters of coils as an initial solution of optimization;
3) solving the magnetic field at a specific point to obtain the maximum magnetic field deviation from the target magnetic field as a constraint condition;
4) adding other constraint conditions, such as axial length constraint of coils, non-overlapping requirement of coils and the like;
5) using the amount of the superconducting wire as a target condition;
6) and obtaining a result by a genetic algorithm or a nonlinear optimization means such as sequence quadratic programming.
However, due to the fact that the number and the position parameters of the coils are preset, optimization has certain limitation, and a global optimization result cannot be guaranteed. And both depend on the number of coils and position parameters of initial setting, and if the setting is not good, the convergence speed is very slow, even no solution exists.
Sharon e.ungersma and Hao Xu et al, Stanford university, usa, propose a linear programming for designing room temperature shim coils, the basic principle of which is:
1) three-dimensional continuous grid points are divided on a framework of the shimming coil, the current of each grid point has 8 selectable directions, and the current can pass through the grid points and meets the kirchhoff current law;
2) setting a magnetic field deviation constraint condition according to the magnetic field configuration required by shimming of each order, and designing a space three-dimensional current path diagram with controllable magnetic field deviation by taking the minimum heating power as a target function.
The result obtained by the method is a separated coil structure, is only suitable for room-temperature shimming coils, and cannot obtain a scheme with the minimum cost by taking the minimum heating power as a target function; because the grids are arranged in the three-dimensional space, each grid point has 8 degrees of freedom, and each degree of freedom needs to satisfy kirchhoff's law and magnetic field distribution position, the size of the solving model is extremely large, and the solving efficiency is very low. Therefore, this method has not been put to practical use.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a linear mixed optimization method of an active shimming coil in a magnetic resonance system, solves the problem of difficult convergence through linear programming, obtains a global optimal solution, adopts a matrix operation mode for a magnetic field and harmonic waves, greatly improves the calculation speed and the design efficiency, and overcomes the defects that the convergence is difficult, the solution efficiency is low and the global optimal solution cannot be met in the shimming technology in the prior art.
The technical scheme for realizing the purpose is as follows: a linear hybrid optimization method for active shimming coils in a magnetic resonance system comprises the following steps:
step S1, the active shim coil requires input: determining design requirements of the active shimming coil, wherein the design requirements comprise the size of an imaging region, the space range for arranging the coil, the strength of the shimming coil and deviation allowance values, and the requirements are used as input for designing the active shimming coil;
step S2, setting a grid area, and establishing a linear programming model, which specifically comprises the following procedures:
s21, the axial magnetic field Bz in the imaging region of the magnetic resonance system is decomposed into an expansion of the harmonic coefficients:
and expanding the obtained object under a rectangular coordinate system to obtain:
wherein Anm and Bnm are harmonic coefficients, and constant term A00I.e. the central magnetic field Bz0, eliminating n>1 order of each item can obtain a uniform magnetic field;
s22, selecting M1 and M2 target field points in one-to-one correspondence according to the longitude and latitude directions on the surface of the imaging area required by the step S1, selecting M target field points in total, and calculating a target magnetic field B by the formula (2)tar；
S23, in the space range of arranging coil required by the step S1, the space range is a space range with rectangular section, N1 and N2 grids are divided in the radial direction and the axial direction in one-to-one correspondence, N grids are divided in total, each grid is equivalent to a current ring with rectangular section or a current arc with certain radian, and the unit is current arcMagnetic field contribution B of current i at M points selected on the surface of the imaging areaMNCan be calculated by a single integral method, wherein M is a target field point, N is a grid number, M is M1M 2, N is N1N 2; the harmonic contribution matrix of the current loop or current arc corresponding to all grids is H; harmonic of unit current i being HKNWherein K is the calculated harmonic term and N is the number of grids; all the calculations adopt matrix operation, and the current matrix corresponding to all the grids is defined as I ═ I1,I2,…,IN]The contributions and harmonics of all current loops or current arcs to the magnetic field are as follows:
s24, assuming that the current density J of each grid is the same, the total volume V of the corresponding current loop or current arc is:
in the formula (4), the reaction mixture is,
is a current loop
Or the circumferential radian of the current arc;
s25, establishing a linear programming model aiming at the shimming requirement, taking the minimum linear quantity as an objective function, taking the magnetic field deviation or harmonic deviation as a constraint condition, taking the current of each grid as an optimization variable, wherein the linear programming model is as follows:
in the formula (5), epsB is a desired magnetic field deviation, epsH is a desired harmonic deviation, HtarImax is the maximum current for each grid for the harmonic corresponding to the required shim coil strengthIf the maximum current density Jmax is taken as a limiting condition, Imax is Jmax × Agrid, wherein Agrid is a cross-sectional area corresponding to each grid;
step S3, performing linear optimization to obtain theoretical coil distribution: after the linear programming model of the formula (5) is solved, the theoretical current distribution of the coils can be obtained, the number and the positions of the coils can be obtained according to the theoretical current distribution of the coils, and the position of each coil is determined by the inner radius r1, the outer radius r2 and the axial coordinates z1 and z 2;
step S4, establishing a nonlinear programming model for nonlinear optimization;
the model for nonlinear programming is as follows:
formula (6), epsB is the desired magnetic field bias; epsH is the required harmonic deviation; z is a radical of1,iThe axial left end coordinate of the ith coil is obtained; z is a radical of2,iThe axial right-end coordinate of the ith coil is shown; z is a radical of1lb、z1ub is the upper and lower limits of the coil size obtained according to linear programming, and the size of ub can be properly controlled within the required space range; bcal and Hcal are calculated values of magnetic fields and harmonic waves in one-to-one correspondence; nz (i) the number of turns per coil, tz the width of the wire used; the used conducting wires are ensured to be integral turns through constraint conditions, and each coil is not overlapped;
the nonlinear programming model of the formula (6) realizes nonlinear optimization through an inner product point method, sequential quadratic programming or other numerical optimization algorithms; knowing the size of the used lead, and obtaining coil structure parameters which accord with the reality through a nonlinear programming model;
step S5, judging whether the coil structure parameters obtained by the nonlinear programming meet the engineering requirements, if so, performing the step S6, and if not, returning to the step S4;
and step S6, outputting the structural parameters of the active shimming coil.
In the above linear hybrid optimization method for the active shimming coil in the magnetic resonance system, in step S1, the spatial range for arranging the coil is determined by the minimum inner radius Rmin, the maximum outer radius Rmax, the minimum axial coordinate Zmin and the maximum axial coordinate Zmax of the coil.
In the above linear hybrid optimization method for the active shimming coil in the magnetic resonance system, in S22, the selection of the target field point is linear selection or a gaussian integration point is adopted, so that the harmonic wave can be directly obtained through the magnetic field for calibration.
In the linear hybrid optimization method for the active shimming coil in the magnetic resonance system, in the formula (5), the magnetic field deviation constraint or the harmonic constraint is selected according to requirements in constraint conditions; the harmonic wave constraint is smaller than the magnetic field deviation constraint, the optimization scale is smaller, the solving speed is high, and when the magnetic field deviation requirement is known, the magnetic field deviation needs to be converted into the harmonic wave deviation.
In the linear hybrid optimization method for the active shimming coil in the magnetic resonance system, one of the magnetic field constraint and the harmonic constraint in the formula (6) can be selected according to requirements.
The number of layers of the single-order shimming coil is generally 1-4, the radial size of each coil can be directly determined through a linear programming structure, the degree of freedom of a nonlinear model is reduced, and the convergence speed is accelerated. In the multi-order coil optimization, if eight groups of coils within the second order are required to be designed, the method and the program for calculating the magnetic field contribution or the harmonic contribution are general, the magnetic field contribution or the harmonic contribution of the coils of different orders can be obtained only by changing the types of the coils, the design of multiple groups of coils is rapidly realized, and the design efficiency is improved.
The linear mixed optimization method of the active shimming coil in the magnetic resonance system has the following beneficial effects:
(1) the linear programming model is adopted for optimization, so that the problems of difficult convergence and low efficiency of the conventional method are solved, and meanwhile, the global optimal result can be obtained;
(2) the invention can select magnetic field deviation optimization or harmonic optimization according to requirements, thereby improving the convenience and efficiency of design;
(3) according to the invention, each grid is equivalent to a current loop or a current arc with a rectangular cross section, so that the calculation precision is improved, and the calculation speed and the design efficiency are improved by adopting a matrix operation mode during magnetic field calculation or harmonic calculation.
Drawings
Fig. 1 is a flow chart of a method for linear hybrid optimization of active shim coils in a magnetic resonance system in accordance with the present invention;
FIG. 2 is a current distribution diagram obtained by linear optimization of the coil Z2 in the first embodiment;
FIG. 3 is a spatial distribution diagram of the coil Z2 after optimization according to the first embodiment;
FIG. 4 is a diagram illustrating current distribution after the length of the shimming skeleton is changed to 200mm or the mutual inductance contribution matrix is increased;
fig. 5 is a spatial distribution diagram of the X-coil after optimization in the second embodiment.
Detailed Description
In order that those skilled in the art will better understand the technical solution of the present invention, the following detailed description is given with reference to the accompanying drawings:
referring to fig. 1 to 5, taking design Z2, an X coil as an example, an imaging region is a spherical region with a diameter of 25mm, a shimming skeleton with a radius Rmin of 130.5mm and a length L of 400mm, and a superconducting wire with a diameter of 0.436mm is selected. The coil strength of Z2 is required to be more than or equal to 25mT/m2/A, and the coil strength of X is required to be more than or equal to 1.5 mT/m/A.
The first embodiment is as follows:
a Z2 coil is designed, and a linear mixed optimization method of an active shimming coil in a magnetic resonance system comprises the following steps:
step S1, the active shim coil requires input: the imaging region is a spherical region with the diameter of 25mm, the radius of a shimming framework is 130.5mm, the length L is 400mm, and a superconducting wire with the diameter of 0.436mm is selected. The coil strength of Z2 is required to be more than or equal to 25mT/m 2/A;
step S2, setting a grid area, and establishing a linear programming model: for the Z2 coil, the corresponding harmonic coefficient is A21The value is the intensity of the Z2 coil. In the range of the space region (Rmin, Rmax, -L/2, L/2), 1 grid is radially divided, 1000 grids are axially divided, and the maximum current is Imax-1A. According to the characteristics of the Z2 coil, only the first 8 harmonic wave is restrained, and the characteristics are obtainedAnd (3) a linear planning model:
wherein HKNAs harmonic matrices of the K-th order, i.e. HKN＝AKAnd r is the harmonic radius of the imaging area of 12.5 mm. N is the total number of meshes divided, J is the maximum current density allowed (i.e. the ratio of the maximum current to the cross-sectional area of the wire), and Agrid is the cross-sectional area of each mesh. The odd order constraint for the Z2 coil is 0 to ensure symmetry of the Z2 coil and the even order constraint is a small offset to ensure that the magnetic field offset of the Z2 coil is slight.
Step S3, performing linear optimization to obtain theoretical coil distribution: the theoretical current distribution of the coils can be obtained according to the linear programming model of the formula (7), the number and the positions of the coils can be obtained according to the theoretical current distribution of the coils, and referring to fig. 2, the current distribution obtained through linear optimization in the design of the Z2 coil can be clearly seen, and 4 coils and the positions thereof are provided;
step S4, establishing a nonlinear programming model for nonlinear optimization;
the model for nonlinear programming is as follows:
formula (6), epsB is the desired magnetic field bias; epsH is the required harmonic deviation; z is a radical of1,iThe axial left end coordinate of the ith coil is obtained; z is a radical of2,iThe axial right-end coordinate of the ith coil is shown; z is a radical of1lb、z1ub is the upper and lower limits of the coil size obtained according to linear programming, and the size of ub can be properly controlled within the required space range; bcal and Hcal are calculated values of magnetic fields and harmonic waves in one-to-one correspondence; nz (i) the number of turns per coil, tz the width of the wire used;
the coil of step Z2 is non-linearly optimized according to equation (6) to obtain the coil structure parameters meeting the engineering requirements, and table 1 is the structure parameters after Z2 coil optimization:
| inner radius (mm) | Outer radius (mm) | Left end coordinate (mm) | Right coordinates (mm) | Number of turns | 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 optimized Z2 coil strength is 25.22mT/m2/A, and the maximum magnetic field deviation is 0.28 per thousand. Referring to fig. 3, the spatial distribution of the optimized Z2 coil is shown.
Step S5, judging whether the coil structure parameters obtained by the nonlinear programming meet the engineering requirements, if so, performing the step S6, and if not, returning to the step S4; in the embodiment, the strength requirement of the coil Z2 is more than or equal to 25mT/m2/A, the strength of the optimized coil Z2 is 25.22mT/m2/A, the engineering requirement is met, and the step S6 is carried out;
in step S6, structural parameters of the Z2 coil are output.
Referring to fig. 4, it is shown that the Z2 coil current distribution obtained when the backbone length is changed to 200mm or when the mutual inductance matrix constraint with the main magnet coils is added, the 5 coils and their positions can be clearly seen. In other optimization methods, because the number of coils and the initial position are set, multiple manual attempts are needed to obtain the result. It is worth pointing out that the global optimal solution of the number and initial position of different coils is obtained quickly according to different space and strength requirements, which is the advantage of the present invention that is different from other optimization algorithms.
In addition, the optimization method can also be used for active shimming design required by a plurality of arrangement space ranges, so that certain coils can be positioned on the framework of the main magnet coils, and the internal space of the main magnet is saved.
Example two:
an X coil is designed, and a linear mixed optimization method of an active shimming coil in a magnetic resonance system comprises the following steps:
step S1, the active shim coil requires input: the imaging region is a spherical region with the diameter of 25mm, the radius of a shimming framework is 130.5mm, the length L is 400mm, and a superconducting wire with the diameter of 0.436mm is selected. The strength requirement of the X coil is more than or equal to 1.5 mT/m/A;
step S2, setting a grid area, and establishing a linear programming model: the X-coil is located on the upper surface of the Z2 coil and can be optimized for harmonic bias or magnetic field bias constraints, here magnetic field bias. The X-coils are saddle-shaped coil structures and analysis shows that each of the X-coils has a radian measure of 2 pi/3 and is antisymmetric about the XY plane, and that the harmonics have only a low order term of a31 term and a11 term when symmetric about the YZ plane. And removing M points on the surface of the imaging area as described above, calculating a target magnetic field matrix Btar corresponding to the required intensity of the X coil, and dividing N grids in the space range of the X coil, wherein each grid is equivalent to a pair of current circular arcs with a rectangular section, the radians of the current circular arcs are 2 pi/3, and the current circular arcs are in positive symmetry with respect to the YZ plane. The linear programming model is as follows:
wherein B isMNAnd generating magnetic field contribution matrixes at M points for the current arcs corresponding to the N grids. I. J, Agrid has the meaning previously described, onesNIs a row vector with 1 element value and N elements. Therefore, the sum of the currents of all grids is ensured to be 0 so as to meet the condition that the loop current of the saddle-shaped coil is 0, a plurality of areas can be divided into a space range, and each area is divided into grids so as to obtain an asymmetric X-shaped coil design.
Step S3, performing linear optimization to obtain theoretical coil distribution: theoretical current distribution of the coils can be obtained according to the linear programming model of the formula (8), and the number and the positions of the coils can be obtained according to the theoretical current distribution of the coils;
step S4, establishing a nonlinear programming model for nonlinear optimization;
the model for nonlinear programming is as follows:
formula (6), epsB is the desired magnetic field bias; epsH is the required harmonic deviation; z is a radical of1,iThe axial left end coordinate of the ith coil is obtained; z is a radical of2,iThe axial right-end coordinate of the ith coil is shown; z is a radical of1lb、z1ub is the upper and lower limits of the coil size obtained according to linear programming, and the size of ub can be properly controlled within the required space range; bcal and Hcal are calculated values of magnetic fields and harmonic waves in one-to-one correspondence; nz (i) the number of turns per coil, tz the width of the wire used;
and (3) performing nonlinear optimization on the coil in the step Z2 according to the formula (6) to obtain a coil structure parameter meeting the engineering requirement, wherein the coil structure parameter after the X coil is optimized is shown in the table 2:
TABLE 2
The strength of the optimized X coil is 1.501mT/m2/A, and the maximum magnetic field deviation is 0.55 per thousand.
Referring to fig. 5, the spatial distribution of the X-coils is optimized.
Step S5, judging whether the coil structure parameters obtained by the nonlinear programming meet the engineering requirements, if so, performing the step S6, and if not, returning to the step S4; in the embodiment, the strength requirement of the X coil is more than or equal to 1.5mT/m/A, the strength of the optimized Z2 coil is 1.501mT/m2/A, the maximum magnetic field deviation is 0.55 per thousand, the engineering requirement is met, and the step S6 is carried out;
in step S6, the structural parameters of the X coil are output.
Other-order coils can quickly obtain the global optimal solution by a similar method.
The invention adopts a linear mixing algorithm to design the active shimming coil, grids are divided in a single or a plurality of space regions, each grid is equivalent to a current ring or a current arc with a rectangular section, and the grids can also be current rings or current arcs with other various sections.
The invention adopts a linear mixing algorithm to design the active shimming coil, including but not limited to solving the result by restricting the magnetic field deviation or harmonic deviation, such as the current loop is restricted by 0 or inductance matrix.
The invention adopts a linear mixing algorithm to design the active shimming coil, adopts linear optimization to obtain a theoretical global optimal solution, and further obtains a scheme meeting engineering requirements through nonlinear optimization, wherein the optimization algorithms which can be adopted by the nonlinear part include but are not limited to an inner product point method and a sequence quadratic programming method, and also can be other algorithms such as a simulated annealing algorithm, a genetic algorithm and the like.
The invention adopts a linear mixing algorithm to design the active shimming coil, and reduces the scale of a linear optimization model in a linear optimization part, including but not limited to a symmetry decomposition space requirement range or a preset grid current direction, thereby accelerating the optimization speed of optimization.
The invention adopts a linear mixing algorithm to design the active shimming coil, and can also be used for designing coils with other similar characteristics.
In summary, the linear hybrid optimization method for the active shimming coil in the magnetic resonance system of the invention solves the problem of difficult convergence through linear programming to obtain the global optimal solution, and adopts a matrix operation mode for the magnetic field and the harmonic wave, thereby greatly improving the calculation speed and the design efficiency, and overcoming the defects of difficult convergence, low solution efficiency and incapability of meeting the global optimal solution in the shimming technology in the prior art.
It should be understood by those skilled in the art that the above embodiments are only for illustrating the present invention and are not to be used as a limitation of the present invention, and that changes and modifications to the above described embodiments are within the scope of the claims of the present invention as long as they are within the spirit and scope of the present invention.
Claims (3)
1. A linear mixed optimization method for an active shimming coil in a magnetic resonance system is characterized by comprising the following steps:
step S1, the active shim coil requires input: determining design requirements of the active shimming coil, wherein the design requirements comprise the size of an imaging region, the space range for arranging the coil, the strength of the shimming coil and deviation allowance values, and the requirements are used as input for designing the active shimming coil;
step S2, setting a grid area, and establishing a linear programming model, which specifically comprises the following procedures:
s21, the axial magnetic field Bz in the imaging region of the magnetic resonance system is decomposed into an expansion of harmonic coefficients:
and expanding the obtained object under a rectangular coordinate system to obtain:
wherein A isnmAnd BnmIs a constant term A for each harmonic coefficient00Namely the harmonic coefficient of the central magnetic field Bz0, and eliminates n>1 order of each item can obtain a uniform magnetic field;
s22, selecting M1 and M2 target field points in one-to-one correspondence according to the longitude and latitude directions on the surface of the imaging area required by the step S1, selecting M target field points in total, and calculating a target magnetic field B by the formula (2)tar；
S23, in the space range of arranging the coil required by the step S1, the space range is a space range with a rectangular section, N1 and N2 grids are divided in the radial direction and the axial direction in a one-to-one correspondence mode, the total number of the grids is N, each grid is equivalent to a current ring with a rectangular section or a current arc with a certain radian, and the magnetic field contribution B of M points selected from the surface of an imaging area by unit current i isMNCan be calculated by a single integral method, wherein M is a target field point, N is a grid number, M is M1M 2, N is N1N 2; the harmonic contribution matrix of the current loop or current arc corresponding to all grids is H; harmonic of unit current i being HKNWherein K is the calculated harmonic term and N is the number of grids; all calculations are performed using a matrixCalculating mode, defining current matrix corresponding to all grids as I ═ I1,I2,…,IN]The contributions and harmonics of all current loops or current arcs to the magnetic field are as follows:
s24, assuming that the current density J of each grid is the same, the total volume V of the corresponding current loop or current arc is:
in the formula (4), the reaction mixture is,
the circular radian is the current ring or the circular arc of the current;
s25, establishing a linear programming model aiming at the shimming requirement, taking the minimum linear quantity as an objective function, taking the magnetic field deviation or harmonic deviation as a constraint condition, taking the current of each grid as an optimization variable, wherein the linear programming model is as follows:
in the formula (5), epsB is a desired magnetic field deviation, epsH is a desired harmonic deviation, HtarFor the harmonic corresponding to the required strength of the shimming coil, Imax is the maximum current corresponding to each grid, and if the maximum current density Jmax is taken as a limiting condition, Imax is Jmax × Agrid, wherein Agrid is the cross-sectional area corresponding to each grid;
in the formula (5), the magnetic field deviation constraint or the harmonic deviation constraint is selected as required in the constraint condition; compared with magnetic field deviation constraint, the harmonic deviation constraint has smaller optimization scale and high solving speed, and when the magnetic field deviation requirement is known, the magnetic field deviation needs to be converted into harmonic deviation;
step S3, performing linear optimization to obtain theoretical coil distribution: after the linear programming model of the formula (5) is solved, the theoretical current distribution of the coils can be obtained, the number and the positions of the coils can be obtained according to the theoretical current distribution of the coils, and the position of each coil is determined by the inner radius r1, the outer radius r2 and the axial coordinates z1 and z 2;
step S4, establishing a nonlinear programming model for nonlinear optimization;
the model for nonlinear programming is as follows:
formula (6), epsB is the desired magnetic field bias; epsH is the required harmonic deviation; z is a radical of1,iThe axial left end coordinate of the ith coil is obtained; z is a radical of2,iThe axial right-end coordinate of the ith coil is shown; z is a radical of1lb、z1ub is the upper and lower limits of coil size obtained from linear programming; bcal and Hcal are calculated values of magnetic fields and harmonic waves in one-to-one correspondence; nz (i) the number of turns per coil, tz the width of the wire used; the used conducting wires are ensured to be integral turns through constraint conditions, and each coil is not overlapped;
the nonlinear programming model of the formula (6) realizes nonlinear optimization through an inner product point method, sequential quadratic programming or other numerical optimization algorithms; knowing the size of the used lead, and obtaining coil structure parameters which accord with the reality through a nonlinear programming model;
selecting one item of the magnetic field constraint and the harmonic constraint in the formula (6) according to requirements;
step S5, judging whether the coil structure parameters obtained by the nonlinear programming meet the engineering requirements, if so, performing the step S6, and if not, returning to the step S4;
and step S6, outputting the structural parameters of the active shimming coil.
2. The linear hybrid optimization method for active shim coils in a magnetic resonance system according to claim 1, wherein in step S1, the spatial range for arranging the coils is determined by the minimum inner radius Rmin, the maximum outer radius Rmax, the minimum axial coordinate Zmin and the maximum axial coordinate Zmax of the coils.
3. The linear hybrid optimization method for the active shimming coil in the magnetic resonance system according to claim 1, wherein in S22, the selection of the target field point is linear or a gaussian integration point is adopted, so that the harmonic wave can be directly obtained through the magnetic field for calibration.
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