A design method for a magnet array for unilateral magnetic resonance soil detection

Abstract

The present invention belongs to the technical field of unilateral nuclear magnetic resonance detection, and relates to a design method of a magnet array for unilateral magnetic resonance soil detection, including: initializing the parameters of each magnet in the magnet array, fixing a circular radio frequency coil under the magnet array, and passing an alternating current of a CPMG sequence into the radio frequency coil to generate a periodically oscillating excitation magnetic field; the receiving coil receives the induced electromotive force generated by the electromagnetic wave released by the magnetization vector during the relaxation process, and calculates the inclination angle and the bend angle of the magnetization vector after pulse excitation through the induced electromotive force; taking the inclination angle and the bend angle as the optimization target, a quadratic programming method is used to adjust the optimal magnet array design parameters for the radio frequency coil of fixed size, and the design parameters include: the position, rotation angle and size of each magnet. The problem of shallow depth and small area of ​​the detection sensitive area is solved. The obtained magnet array parameters can obtain a measurement signal of the transverse relaxation time with low distortion in the target area.

Description

Technical Field

[0001] The invention belongs to the technical field of unilateral nuclear magnetic resonance detection, and in particular relates to a design method of a magnet array for unilateral magnetic resonance soil detection. Background Art

[0002] The cultivation of agricultural products is closely related to the soil environment. Soil is the basis for the growth of crops. Soil moisture, pore structure and organic matter content are key factors affecting crop growth. Compared with the traditional soil sampling magnetic resonance detection method, unilateral magnetic resonance detection technology has potential advantages in soil moisture and pore structure detection due to its non-invasive, portable and fully open characteristics. Conventional unilateral portable magnet arrays such as Halbach magnets, U-type magnets and C-type magnets all have problems with small detection sensitivity areas and shallow detection depths, making it difficult to detect soil areas with high spatial resolution.

[0003] The Chinese patent publication number CN111948587A discloses a high temperature stable magnetic resonance magnet structure. The magnet structure uses four main magnets that are cubic main magnets with exactly the same geometric size and central symmetry. The four magnets are distributed in a U shape to generate a static gradient magnetic field in the sensitive area of ​​the magnetic base. This method mainly focuses on reducing the impact of ambient temperature changes on the static magnetic field strength, and the detection depth is relatively shallow.

[0004] China Patent Publication No. CN114062412A discloses a handheld unilateral non-destructive testing magnetic resonance sensor structure. The sensor structure includes four magnets, and the magnetization direction is along the axial direction of the magnet, thereby generating a gradient magnetic field. However, the gradient magnetic field area of ​​the magnet structure of the sensor structure is only located 0.5mm above the magnet, and the detection depth is relatively shallow.

[0005] Chinese patent publication number CN109030532A discloses a unilateral magnetic resonance three-dimensional imaging system. The static magnetic field of the system is provided by a magnet mechanism and a scanning module. The magnet mechanism includes a semi-elliptical magnet and a U-shaped magnet inside the semi-elliptical magnet. The magnet mechanism provides a relatively uniform static main magnetic field in the first plane, and the scanning module generates an additional magnetic field superimposed on the static main magnetic field to form a uniform static magnetic field in the sensitive area. However, the depth of its detection sensitive area is 2 cm, and the sensitive area is small. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a design method of a magnet array for unilateral magnetic resonance soil detection. The designed magnet array solves the problems of shallow depth and small area of ​​the detection sensitive area.

[0007] The present invention is achieved in this way.

[0008] A design method for a magnet array for unilateral magnetic resonance soil detection, the design method comprising:

[0009] Initializing the parameters of each magnet in the magnet array, the parameters including size, position and rotation angle, calculating the static magnetic field generated by the magnet array under the parameters according to the Biot-Savart law, and hydrogen protons generate a macroscopic magnetization vector under the action of the static magnetic field;

[0010] A circular radio frequency coil is fixed under the magnet array, and an alternating current of a CPMG (Carr-Purcell-Meiboom-Gill) sequence is passed through the radio frequency coil to generate a periodically oscillating excitation magnetic field; the parameters of the CPMG sequence include alternating current intensity, excitation frequency, 90° pulse excitation time, echo time, and the number of excitation pulses;

[0011] The receiving coil receives the induced electromotive force generated by the electromagnetic wave released by the magnetization vector during the relaxation process, and calculates the inclination angle and the tilt angle of the magnetization vector after the pulse excitation through the induced electromotive force;

[0012] Taking the tilt angle and the bevel angle as optimization targets, a quadratic programming method is used to adjust the optimal magnet array design parameters for a fixed-size radio frequency coil, wherein the design parameters include: the position, rotation angle and size of each magnet.

[0013] Furthermore, taking the tilt angle and the bevel angle as the optimization targets, the quadratic programming method is used to adjust the optimal magnet array design parameters for the fixed-size RF coil, including:

[0014] Calculate the root mean square error of the inclination angle and 0° and the flip angle and 90° in the target area;

[0015] The loss function is set as: ,in, is the fitness value of the loss function, is the inclination angle, It's the bevel angle. For depth, Measure the depth of the target, is the root mean square error function, expressed as: ,in, is the true value, is an estimated value, is the sample size;

[0016] The size, position and rotation angle of the magnet array are used as nonlinear constraints. for:

[0017] = ,

[0018] in, Indicates The length, width and height of a magnet; Indicates The spatial position of the center of the magnet, is the X-axis coordinate, for Axis coordinates, in order to maintain the symmetry of each magnet in the magnet array, the center of each magnet is fixed at In the plane, the coordinates of the Y axis are the same; Indicates A magnet with a point is the rotation center, the counterclockwise rotation angle of the initial position toward the z direction; Indicates no Same magnet number;

[0019] Will Combine them into matrix P in order:

[0020] P= ;

[0021] in, is a sub-element of the matrix P;

[0022] The Lagrangian equation with nonlinear constraints is expressed as: ,in, is the Lagrangian function, is the Lagrange multiplier, Represents the fitness value of the loss function.

[0023] Furthermore, the Newton iteration method is used to solve the design parameters of the optimal magnet array for a fixed-size RF coil:

[0024] Newton's iteration method is used to solve , expand The first two terms of the Taylor series are expressed as: + ,in, is the gradient symbol, is the step size matrix, is the iteration ordinal;

[0025] Known for The initial value of , the iteration formula is: in, represents the Hessian matrix, express The inverse of the Hessian matrix; when it satisfies: , is the threshold, or the maximum number of iterations is reached When , the iteration stops and all the parameters of the magnet array are obtained.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] Compared with the existing single-sided magnetic resonance magnet array design method, the design method of the present invention optimizes the magnet array design parameters in combination with the magnetization vector calculation parameters inclination angle and bevel angle that affect the signal quality and the target measurement depth. The obtained magnet array parameters can obtain a low-distortion transverse relaxation time measurement signal in the target area. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of a design method of a magnet array for unilateral magnetic resonance soil detection provided by the method of the present invention;

[0029] Figure 2 1 is a diagram of a magnet array structure of an embodiment of the method of the present invention, (a) a diagram of a unilateral magnetic resonance magnet array structure, (b) a schematic diagram of a magnetization direction;

[0030] Figure 3 The detection results of the method embodiment of the present invention for a 5 cm×5 cm sensitive area with a depth of 10 cm are as follows: (a) the distribution of the dip angle, and (b) the distribution of the flip angle;

[0031] Figure 4 It is the detection result of the sensitive area of ​​5cm×5cm with a depth of 10cm in the embodiment of the method of the present invention, (a) the acquisition signal, and (b) the peak fitting result of the transverse relaxation time. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0033] See also Figure 1 As shown, a design method of a magnet array for unilateral magnetic resonance soil detection, the method comprising:

[0034] Radio frequency coils are placed on the surface to generate pulse sequences to excite hydrogen protons in the soil to make quantum transitions;

[0035] Initialize the parameters of each magnet in the magnet array, the parameters including size, position and rotation angle, calculate the static magnetic field generated by the magnet array under the parameters according to the Biot-Savart law, and hydrogen protons generate a macroscopic magnetization vector under the action of the static magnetic field; the magnet here is a permanent magnet.

[0036] A circular radio frequency coil is fixed under the magnet array, and an alternating current in a CPMG (Carr-Purcell-Meiboom-Gill) sequence is passed through the radio frequency coil to generate a periodically oscillating excitation magnetic field; the parameters of the CPMG sequence include alternating current intensity, excitation frequency, 90° pulse excitation time, echo time, and the number of excitation pulses;

[0037] In this embodiment, a radio frequency coil with a radius of 20 cm is placed on the ground, and an ideal 20A pulse alternating current is passed through it. The pulse excitation frequency is 309kHz, and a CPMG pulse excitation sequence is used. The 90° pulse excitation time is 130 , the echo time is 40ms, and a total of 25 180° excitation pulses are generated;

[0038] The number of optimized magnet arrays is 5. In this embodiment, the parameters of the Halbach magnet array are used as the initial values ​​of the magnet array. The length, width and height of each magnet in the Halbach magnet array are the same, with a length of 2 cm, a width of 10 cm and a height of 2 cm. The X-axis and Z-axis coordinates of the center coordinate position of each magnet are: [7,1], [4.9,5.9], [0,8], [-4.9,5.9], [-7,1] cm, and the corresponding rotation angles are 0°, 45°, 90°, 135°, and 180°, respectively.

[0039] The shell of the magnet array is fixed by white resin material. The magnet material of the magnet array is N52 type neodymium iron boron and is nickel-plated to prevent corrosion.

[0040] The target detection depth of the target area is 10cm, and the sensitive area of ​​the target area is , the number of finite elements in the target area is 121;

[0041] During the pulse excitation process, hydrogen protons undergo quantum transitions, and the magnetization vector nutates around the effective radio frequency magnetic field. The induced electromotive force generated by the electromagnetic waves released by the magnetization vector received by the receiving coil during the relaxation process is used to solve the Bloch equation by the rotation matrix method to obtain the inclination angle and flip angle of the magnetization vector after pulse excitation. The Bloch equation is a differential equation that describes the spin behavior in the nuclear magnetic resonance system. The process of obtaining the inclination angle and flip angle of the magnetization vector after pulse excitation is a conventional technology in the field and will not be repeated here.

[0042] When calculating the inclination angle and the flip angle, the continuous target area is divided into multiple finite elements, and the inclination angle and the flip angle of the finite elements are calculated to obtain the inclination angle and the flip angle of the entire target area.

[0043] Taking the tilt angle and bevel angle as optimization targets, the quadratic programming method is used to adjust the optimal magnet array design parameters for a fixed-size RF coil. The design parameters include: the position, rotation angle and size of each magnet. Including:

[0044] Calculate the root mean square error of the inclination angle and 0° and the flip angle and 90° in the target area;

[0045] The loss function is expressed as: ,in, is the fitness value of the loss function, is the inclination angle, It's the bevel angle. For depth, Measure the depth of the target, is the root mean square error function, expressed as: in, is the true value, is an estimated value, is the number of samples; based on the size, position and rotation angle constraints of the magnet array, a nonlinear constraint formula is introduced:

[0046] = ,

[0047] in, Indicates The length, width and height of a magnet; Indicates The spatial position of the center of the magnet, for Axis coordinates, is the Z-axis coordinate. In order to maintain the symmetry of each magnet in the magnet array, the center of each magnet is fixed at In the plane, this makes the Y-axis coordinate zero; Indicates A magnet with a point is the rotation center, the counterclockwise rotation angle of the initial position toward the Z direction; Indicates no Same magnet number;

[0048] Will Combine them into matrix P in order:

[0049] P= ;

[0050] in, is a sub-element of the matrix P;

[0051] Combining the inclination angle and flip angle formula, a new Lagrangian equation with nonlinear constraints is formed as follows: in, is the Lagrangian function, is the Lagrange multiplier.

[0052] Newton's iteration method is further used to solve , expand The first two terms of the Taylor series are expressed as: + in, is the gradient symbol, is the step size matrix, q is the iteration number;

[0053] Known for The initial value of , the iteration formula is: in, represents the Hessian matrix, express The inverse of the Hessian matrix; when it satisfies: , is the threshold, or the maximum number of iterations is reached When , the iteration stops.

[0054] In this embodiment, the maximum number of iterations is set to 50 times. ;

[0055] All parameters of the magnet array are obtained through iterative calculation.

[0056] Figure 2 A magnet array obtained by optimizing the embodiment, Figure 2 (a) is a diagram of the structure of a single-sided magnetic resonance magnet array, which includes a total of 5 magnets. Figure 2 (b) is the magnetization direction diagram of each magnet in the single-sided magnetic resonance array;

[0057] use Figure 2 The magnetic array in the target area is used to perform numerical simulation calculations;

[0058] In the simulation, the transverse relaxation time is set to 1 s and the longitudinal relaxation time is set to 5 s. Figure 3 and Figure 4 is a simulation result diagram of an embodiment of the present invention, Figure 3 (a) and Figure 3 (b) in the figure are respectively the simulation results of the inclination angle and the bevel angle of the magnet array designed by the method of the present invention in the target area, and the uniformity of the inclination angle and the bevel angle is high, and the deviation from the ideal value is small; Figure 4 (a) and Figure 4 (b) are the simulated echo signals of the magnetic array designed by the present invention and the results of peak fitting thereof, Figure 4The fitting curve obtained by single exponential curve fitting in the echo peak of (b) has a transverse relaxation time of 0.94s and a distortion degree of only 6%. The fitting formula used is expressed as: in, is the initial maximum amplitude, is the transverse relaxation time obtained by fitting, and V is the signal amplitude changing with time t.

[0059] The results show that the magnet array designed by the present invention has a high degree of fitting of the transverse magnetization vector in the target area.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing a magnet array for unilateral magnetic resonance soil detection, characterized in that: The design method comprises: Initializing the parameters of each magnet in the magnet array, the parameters including size, position and rotation angle, calculating the static magnetic field generated by the magnet array under the parameters according to the Biot-Savart law, and hydrogen protons generate a macroscopic magnetization vector under the action of the static magnetic field; A circular radio frequency coil is fixed under the magnet array, and an alternating current of a CPMG sequence is passed through the radio frequency coil to generate a periodically oscillating excitation magnetic field; the parameters of the CPMG sequence include alternating current intensity, excitation frequency, 90° pulse excitation time, echo time, and number of excitation pulses; The receiving coil receives the induced electromotive force generated by the electromagnetic wave released by the magnetization vector during the relaxation process, and calculates the inclination angle and the tilt angle of the magnetization vector after the pulse excitation through the induced electromotive force; Taking the tilt angle and the bevel angle as optimization targets, a quadratic programming method is used to adjust the optimal magnet array design parameters for a fixed-size radio frequency coil, wherein the design parameters include: the position, rotation angle and size of each magnet; Taking the tilt angle and bevel angle as optimization targets, the quadratic programming method is used to adjust the optimal magnet array design parameters for a fixed-size RF coil, including: Calculate the root mean square error of the inclination angle and 0° and the flip angle and 90° in the target area; The loss function is set as: ,in, is the fitness value of the loss function, is the inclination angle, It's the bevel angle. For depth, Measure the depth of the target, is the root mean square error function, expressed as: ,in, is the true value, is an estimated value, is the sample size; The size, position and rotation angle of the magnet array are used as nonlinear constraints. for: = ， in, Indicates The length, width and height of a magnet; Indicates The spatial position of the center of the magnet, is the X-axis coordinate, for Axis coordinates, in order to maintain the symmetry of each magnet in the magnet array, the center of each magnet is fixed at In-plane; Indicates A magnet with a point is the rotation center, the counterclockwise rotation angle of the initial position toward the Z direction; Indicates no Same magnet number; Will Combine them into matrix P in order: P= ； in, is a sub-element of the matrix P; The Lagrangian equation with nonlinear constraints is formed as follows: ,in, is the Lagrangian function, is the Lagrange multiplier; The Newton iteration method is used to solve the design parameters of the optimal magnet array for a fixed-size RF coil, including: Newton's iteration method is used to solve , expand The first two terms of the Taylor series are expressed as: + ,in, is the gradient symbol, is the step size matrix, is the iteration ordinal; Known for The initial value of , the iteration formula is: in, represents the Hessian matrix, express The inverse of the Hessian matrix; when it satisfies: , is the threshold, or the maximum number of iterations is reached When , the iteration stops and all the parameters of the magnet array are obtained.

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