CN114638908B - A method for reconstructing magnetoacoustic magnetic particle concentration images under saturation magnetization state - Google Patents

Abstract

The present invention discloses a method for reconstructing a magnetoacoustic magnetic particle concentration image under a saturated magnetization state, the method comprising: based on a simulation model, obtaining sound pressure data at an ultrasonic transducer and gradient magnetic field data at a reconstruction area; constructing a sound pressure matrix using the sound pressure data obtained at each ultrasonic transducer, and constructing a system matrix using the gradient magnetic field data at the reconstruction area, the system matrix being used to describe the direct correspondence between the sound pressure and the concentration partial derivative of magnetic nanoparticles; and then using the LSQR method to obtain the concentration partial derivative distribution of magnetic nanoparticles, the concentration distribution of magnetic nanoparticles can be obtained. The present invention uses the LSQR-trapezoidal formula method to quickly, stably, and with high quality reconstruct the concentration distribution, with clear image boundaries, and has good application prospects.

Description

A method for reconstructing magnetoacoustic magnetic particle concentration images under saturation magnetization state

Technical Field

The present invention belongs to the technical field of concentration distribution image reconstruction, and in particular relates to a method for reconstructing magnetoacoustic magnetic particle concentration images under a saturated magnetization state based on a least squares QR decomposition method-trapezoidal formula method.

Background Art

Magnetic nanoparticles (MNPs) are widely used in the biomedical field due to their low toxicity, good biocompatibility, magnetic responsiveness, and controllability under an external magnetic field, including magnetic hyperthermia, drug delivery, targeted therapy, gene therapy, etc. Magnetic Particle Imaging (MPI) is the earliest imaging method to apply magnetic nanoparticles to medical diagnosis. In 2005, Gleich B et al. first reported the MPI imaging method in Nature. However, its spatial resolution is affected by theoretical and equipment factors and is currently 1-5 mm. In order to further improve the spatial resolution, in 2020, Shi Xiaoyu et al. first proposed Magneto-Acoustic Concentration Tomography with Magnetic Induction MACT-MI. This method naturally overcomes the electromagnetic interference problem between the drive coil and the detection coil, combines the advantages of electromagnetic technology and ultrasonic technology, and has the advantages of non-invasiveness, good contrast, high sensitivity, and high spatial resolution.

Regarding the study of the inverse problem of MACT-MI, on December 25, 2019, Xu Zhengyang et al. applied for "A magnetoacoustic coupled magnetic nanoparticle concentration image reconstruction method" (patent number: 201911020966.0), which disclosed a magnetoacoustic coupled magnetic nanoparticle concentration image reconstruction method. The time inversion method is used for sound source reconstruction, which involves the sound pressure derivative process, amplifies the influence of data noise on the reconstruction result, and the algorithm stability is poor, and the reconstruction result has boundary singularities. In 2021, Hu Yu et al. proposed a magnetoacoustic magnetic particle concentration imaging method based on TSVD (truncated singular value decomposition). This method has a good imaging effect when the coefficient matrix is a small sparse matrix, but the imaging effect is not ideal for large sparse coefficient matrices, and its theoretical formula is only applicable to solving the case of uniform concentration distribution, and the scope of application is narrow, so the inverse problem reconstruction of MACT-MI needs further research.

Summary of the invention

The technical problem to be solved by the present invention is to provide a method for reconstructing the concentration image of magnetoacoustic magnetic particles under saturated magnetization state in view of the above-mentioned deficiencies of the prior art. The preparation method uses the LSQR-trapezoidal formula method, which can quickly, stably and high-quality reconstruct the concentration distribution, with clear image boundaries, and has good application prospects.

In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for reconstructing magnetoacoustic magnetic particle concentration images under saturated magnetization state, characterized in that the method comprises the following steps:

Step 1, setting the initial simulation conditions of the magnetoacoustic magnetic particles in the saturated magnetization state, and obtaining the sound pressure data at the ultrasonic transducer and the gradient magnetic field data at the reconstruction area based on the preset simulation model; the reconstruction area is a Wmm×Wmm area centered on the magnetic nanoparticle group, and the reconstruction area is divided into M×M grids by finite element; the gradient magnetic field data at the reconstruction area includes the gradient magnetic field data at each grid;

Step 2: constructing a sound pressure matrix using the sound pressure data obtained at each ultrasonic transducer, and constructing a system matrix using the gradient magnetic field data at the reconstruction area, wherein the system matrix is used to describe the direct correspondence between the sound pressure and the concentration partial derivative of the magnetic nanoparticles;

Step 3, using the sound pressure matrix and system matrix constructed in step 2 to obtain the concentration partial derivative distribution of the magnetic nanoparticles using the LSQR method;

Step 4: Use the partial derivative distribution of the magnetic nanoparticle concentration to obtain the magnetic nanoparticle concentration distribution, thereby obtaining a magnetoacoustic magnetic particle concentration reconstructed image under the saturated magnetization state.

Preferably, in step 1, the simulation initial conditions of the magnetoacoustic magnetic particles in the saturated magnetization state are set, and based on the preset simulation model, the sound pressure data at the ultrasonic transducer and the gradient magnetic field data at the reconstruction area are obtained; a Wmm×Wmm area is selected as the reconstruction area with the magnetic nanoparticle group as the center, and the reconstruction area is divided into M×M grids by finite element; the gradient magnetic field data at the reconstruction area includes the gradient magnetic field data at each grid; including:

Initialize the simulation conditions of magnetic nanoparticle parameters, Helmholtz coil and Maxwell coil current, select model EMG308 as magnetic nanoparticles, place the magnetic nanoparticle group at the center of the coil, and pass current into the Helmholtz coil and Maxwell coil respectively. The Helmholtz coil provides a static magnetic field B _sat to make the magnetic nanoparticles reach a saturated state, and the Maxwell coil provides a uniform gradient magnetic field B _g . Draw a circle with a fixed scanning radius with the magnetic nanoparticle group as the center, and discretely set multiple ultrasonic transducers on the circle to obtain the sound pressure data of multiple time points received by each ultrasonic transducer, and obtain the original sound field p(r, t) at each ultrasonic transducer.

Preferably, a circle is drawn with a fixed scanning radius with the magnetic nanoparticle group as the center, 165 ultrasonic transducers are discretely set on the circle, and the sound pressure data of 470 time points received by each ultrasonic transducer are obtained; a 50mm×50mm area is selected as the reconstruction area with the magnetic nanoparticle group as the center, and the reconstruction area is divided into 250×250 grids by finite element method.

Preferably, the sound pressure matrix is constructed using the sound pressure data obtained at each ultrasonic transducer, and the system matrix is constructed using the gradient magnetic field data at the reconstruction area. The system matrix is used to describe the direct correspondence between the sound pressure and the concentration partial derivative of the magnetic nanoparticles, including:

The magnetic force on the magnetic nanoparticles is expressed as

In formula (1), f(r′,t) is the magnetic force on the magnetic nanoparticles at time t; r′ is the position of the sound source point to be determined, and t is the time; N(r′) is the concentration of the magnetic nanoparticles; m represents the magnetic moment of the magnetic nanoparticles; is the magnitude of the gradient magnetic field at the sound source point at time t; e _z represents the unit vector in the z direction;

The relationship between sound source and sound pressure is as follows:

In formula (2), p(r,t) is the sound pressure at any point at time t, in Pa; r is the position of any point; _cs is the speed of sound in biological tissue, in m/s; is the sound source term; t is the time; r′ is the location of the desired sound source point, R = |rr′|; Ω is the entire study area;

Due to the unidirectionality of magnetic force, the sound source term can be expressed as

Substituting formula (3) into formula (2), we get

Because when calculating the instantaneous spatial distribution problem, It can be treated as a constant, so we can get

From the above formula, we can see that there is a direct correspondence between the sound pressure and the concentration partial derivative. By describing this correspondence through the system matrix A, we can abstract the matrix relationship:

Ax＝b(6)

Where A is the system matrix, x is the concentration partial derivative, b is the sound pressure matrix, and the sound pressure data in the sound pressure matrix b corresponds to p(r, t); according to equations (5) and (6) and combined with the gradient magnetic field data, the system matrix A is obtained.

Preferably, in step 3, the concentration partial derivative distribution of the magnetic nanoparticles is obtained by using the sound pressure matrix and the system matrix constructed in step 2 using the LSQR method, including:

The LSQR method is introduced to solve the system matrix as a large sparse coefficient matrix, and finally the concentration partial derivative distribution is obtained;

The solution process includes:

Let the standard orthogonal matrix U _k = [u ₁ ,u ₂ ,…,u _k ] (u _j ∈ R ^mi ) and The bidiagonal matrix is

Among them (α ₁ ,α ₂ ,…,α _k ∈R; β ₂ ,β ₃ ,…,β _k+1 ∈R).

The iterative process is as follows: The iterative process is as follows:

Step 301, conditional initialization

β ₁ =||b||; α ₁ =||A ^T u ₁ || ₂ ; β ₁ u ₁ =b;

Step 302, diagonalize the coefficient matrix

β _j+1 =||Av _j -α _j u _j || ₂ ; α _j+1 =||A ^T u _j+1 -β _j+1 v _j || ₂ ;

(j＝1,2,...,k).

Step 303, calculate the QR decomposition intermediate variable

Step 304: Update the values of x and the intermediate variable w

Step 305: Determine the iteration condition

If ||Ax _k -b||≤ε is satisfied, the iteration is terminated, where ε is the allowable error, and ε is set to 0.01;

Repeat steps 302 to 305 for j=1, 2, ..., k.

Preferably, in step 4, obtaining the concentration distribution of magnetic nanoparticles by using the partial derivative distribution of the concentration of magnetic nanoparticles, thereby obtaining a magnetoacoustic magnetic particle concentration reconstruction image, comprises:

It is known that the relationship between the partial derivative of concentration and the concentration distribution satisfies the following relationship:

Assuming that the side length of the grid is l, l = 0.2 mm, the concentration partial derivative x can be expressed as:

The concentration distribution N(r') can be expressed as

By introducing the trapezoidal formula method with simple calculation and high accuracy, we can get

Among them, 0≤c≤249,1≤d≤250, combined with the x(c,d) boundary condition, the concentration distribution can be obtained.

Compared with the prior art, the present invention has the following advantages:

1. The present invention aims to solve the problems of slow reconstruction speed, poor reconstruction quality and boundary singularity in the existing magnetoacoustic magnetic particle concentration imaging methods. The present invention solves the magnetoacoustic magnetic particle concentration distribution based on the LSQR-trapezoidal formula method, and can reconstruct the concentration distribution with high quality, fast and stable, with clear image boundaries and no singularity.

2. The present invention divides the calculation area into grids specified by the finite element method, discretizes the sound field data and the magnetic field data, constructs a system matrix reflecting the relationship between the sound pressure and the concentration partial derivatives, reconstructs the concentration partial derivative distribution using the LSQR method, and reconstructs the concentration distribution image using the trapezoidal formula method.

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

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of a method for reconstructing magnetoacoustic and magnetic particle concentration images under saturation magnetization state based on the least squares QR decomposition method-trapezoidal formula method of the present invention.

Figure 2 shows the simulation model.

Figure 3 shows the Helmholtz coil current.

FIG4 is a schematic diagram showing the principle of obtaining sound pressure data and magnetic field data.

Figure 5 shows the gradient concentration model.

Figure 6a is a diagram of the simulation results.

Figure 6b is a graph of target concentrations.

DETAILED DESCRIPTION

Example 1

Magnetoacoustic magnetic particle concentration imaging method

As shown in Figure 1, the calculation area is divided into grids of a prescribed grid according to the finite element method, the acoustic field data and the magnetic field data are discretized, a system matrix reflecting the connection between the acoustic pressure and the concentration partial derivative is constructed, the concentration partial derivative distribution is reconstructed using the LSQR method, and the concentration distribution image is reconstructed using the trapezoidal formula method. As shown in Figure 1, the present invention is implemented by the following technical scheme: The present invention provides a method for reconstructing the concentration image of magnetoacoustic magnetic particles under saturated magnetization state based on the LSQR-trapezoidal formula method, which specifically includes the following steps:

S1. Setting the initial conditions for the simulation of the magnetoacoustic magnetic particles in the saturated magnetization state, and obtaining the sound pressure data at the ultrasonic transducer and the gradient magnetic field data at the reconstruction area based on the preset simulation model;

Furthermore, the simulation model of the magnetoacoustic magnetic particles in the saturated magnetization state is constructed as follows: a two-dimensional axisymmetric model is established with the help of COMSOL Multiphysics 5.6 for simulation research. As shown in FIG2 , the coil material is copper, and the coil is placed with the z-axis as the center axis. The coil radius is r=150 mm, the origin is the coil center, and the middle cylindrical area is the research area.

1. Simulation conditions

(1) Parameters of magnetic nanoparticles

Taken from EMG 308 (Ferrotec (USA) Corporation), its specifications are shown in Table 1.

Table 1 EMG 308 Specifications

(2) Excitation current

A constant current of 50A in the counterclockwise direction is simultaneously passed through the upper and lower coils of the Helmholtz coil, and the magnetic field strength generated is about 1.93×10 ⁵ A/m, which is greater than the saturation magnetic field strength of EMG308, and the magnetic nanoparticles reach a saturated state. A counterclockwise current is passed through the upper coil of the Maxwell coil, and a clockwise current of the same magnitude is passed through the lower coil. The currents with time characteristics shown in Figure 3 are passed through both coils.

Specifically, the simulation conditions of magnetic nanoparticle parameters, Helmholtz coil and Maxwell coil current are initialized, model EMG308 is selected as magnetic nanoparticles, the magnetic nanoparticle group is placed at the center of the coil, current is respectively passed through the Helmholtz coil and the Maxwell coil, the Helmholtz coil provides a static magnetic field B _sat to make the magnetic nanoparticles reach a saturated state, and the Maxwell coil provides a uniform gradient magnetic field B _g ; as shown in Figure 4, a circle is drawn with a fixed scanning radius with the magnetic nanoparticle group as the center, 165 ultrasonic transducers are discretely set on the circle, the sound pressure data of 470 time points received by each ultrasonic transducer are obtained, and the original sound field p(r, t) at each ultrasonic transducer is obtained; a 50mm×50mm area is selected as the reconstruction area with the magnetic nanoparticle group as the center, and the reconstruction area is divided into 250×250 grids by finite element method, and the gradient magnetic field data at each grid is extracted.

S2, constructing an acoustic pressure matrix using the acoustic pressure data obtained at each ultrasonic transducer, and constructing a system matrix using the gradient magnetic field data at the reconstruction area, wherein the system matrix is used to describe a direct correspondence between the acoustic pressure and the concentration partial derivative of the magnetic nanoparticles;

The acoustic pressure matrix is constructed using the acoustic pressure data obtained at each ultrasonic transducer, and the system matrix is constructed using the gradient magnetic field data at the reconstruction area. The system matrix is used to describe the direct correspondence between the acoustic pressure and the concentration partial derivative of the magnetic nanoparticles, including:

The magnetic force on the magnetic nanoparticles is expressed as

In formula (1), f(r′,t) is the magnetic force on the magnetic nanoparticles at time t; r′ is the position of the sound source point to be determined, and t is the time; N(r′) is the concentration of the magnetic nanoparticles; m represents the magnetic moment of the magnetic nanoparticles; is the magnitude of the gradient magnetic field at the sound source point at time t; e _z represents the unit vector in the z direction;

The relationship between sound source and sound pressure is as follows:

In formula (2), p(r,t) is the sound pressure at any point at time t, in Pa; r is the position of any point; _cs is the speed of sound in biological tissue, in m/s; is the sound source term; t is the time; r′ is the location of the desired sound source point, R = |rr′|; Ω is the entire study area;

Due to the unidirectionality of magnetic force, the sound source term can be expressed as

Substituting formula (3) into formula (2), we get

Because when calculating the instantaneous spatial distribution problem, It can be treated as a constant, so we can get

From the above formula, we can see that there is a direct correspondence between the sound pressure and the concentration partial derivative. By describing this correspondence through the system matrix A, we can abstract the matrix relationship:

Ax＝b(6)

Where A is the system matrix, x is the concentration partial derivative, b is the sound pressure matrix, and the sound pressure data in the sound pressure matrix b comes from p(r, t).

According to equations (5) and (6) and combined with the gradient magnetic field data, the system matrix A is obtained, and the size of the system matrix is 77550×62500. The sound pressure matrix b is constructed using the sound pressure data at the ultrasonic transducer, and the size of the matrix is 77550×1.

S3, using the sound pressure matrix and system matrix constructed in step 2 to obtain the concentration partial derivative distribution of the magnetic nanoparticles using the LSQR method;

Further, obtaining the concentration partial derivative distribution of the magnetic nanoparticles includes:

The LSQR method is introduced to solve the system matrix as a large sparse coefficient matrix, and finally the concentration partial derivative distribution is obtained;

The solution process includes:

Let the standard orthogonal matrix U _k = [u ₁ ,u ₂ ,…,u _k ] (u _j ∈ R ^mi ) and The bidiagonal matrix is

Among them (α ₁ ,α ₂ ,…,α _k ∈R; β ₂ ,β ₃ ,…,β _k+1 ∈R).

The iterative process is as follows: The iterative process is as follows:

Step 301, conditional initialization

β ₁ =||b||; α ₁ =||A ^T u ₁ || ₂ ; β ₁ u ₁ =b;

Step 302, diagonalize the coefficient matrix

β _j+1 =||Av _j -α _j u _j || ₂ ; α _j+1 =||A ^T u _j+1 -β _j+1 v _j || ₂ ;

(j＝1,2,...,k).

Step 303, calculate the QR decomposition intermediate variable

Step 304: Update the values of x and the intermediate variable w

Step 305: Determine the iteration condition

If ||Ax _k -b||≤ε is satisfied, the iteration is terminated, where ε is the allowable error, and ε is set to 0.01;

Repeat steps 302 to 305 for j=1, 2, ..., k.

S4. Utilize the partial derivative distribution of magnetic nanoparticle concentration to obtain the magnetic nanoparticle concentration distribution, thereby obtaining a magnetoacoustic magnetic particle concentration reconstruction image under the saturated magnetization state.

Furthermore, the concentration distribution of magnetic nanoparticles is obtained by using the partial derivative distribution of the concentration of magnetic nanoparticles, so as to obtain a magnetoacoustic magnetic particle concentration reconstruction image under the saturated magnetization state, including:

It is known that the relationship between the partial derivative of concentration and the concentration distribution satisfies the following relationship:

Assuming that the side length of the grid is l, l = 0.2 mm, the concentration partial derivative x can be expressed as:

The concentration distribution N(r') can be expressed as

By introducing the trapezoidal formula method with simple calculation and high accuracy, we can get

Among them, 0≤c≤249,1≤d≤250, combined with the x(c,d) boundary condition, the concentration distribution can be obtained.

The above steps can reconstruct the concentration distribution. Considering that MNPs are diffuse and gradually change in biological tissues, a concentration gradient model is established. As shown in FIG5 , the outer circular area is the biological area, and the inner area is the MNPs area. EMG 308 is selected for MNPs. The reconstruction results and the concentration reconstruction target are shown in FIG6a and FIG6b . The method proposed in the present invention can reconstruct the concentration distribution with high quality without singularity. In order to further evaluate the applicability of the present invention, the correlation coefficient CC and the relative error RE are introduced to compare the target concentration distribution with the reconstructed concentration distribution. The specific method adopts the following formula:

Where _Nn is the target nanoparticle concentration value, Nn _,r is the reconstructed nanoparticle concentration value, is the average concentration of target nanoparticles, is the average concentration of target nanoparticles.

Through the evaluation of the present invention, it can be found that the correlation coefficient and relative error of the present invention are 0.9816 and 0.2761 respectively, and the reconstruction accuracy is relatively high.

The above is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent change made to the above embodiment according to the technical essence of the invention still falls within the protection scope of the technical solution of the present invention.

Claims (6)

1. The method for reconstructing the magnetoacoustic magnetic particle concentration image in the saturated magnetization state is characterized by comprising the following steps of:

Step one, setting a simulation initial condition of magnetoacoustic magnetic particles in a saturated magnetization state, and acquiring sound pressure data at an ultrasonic transducer and gradient magnetic field data at a reconstruction region based on a preset simulation model; the reconstruction region is formed by taking a region with the length of Wmm multiplied by Wmm as a center of a magnetic nanoparticle group as a reconstruction region, and carrying out finite element division on the reconstruction region to divide the reconstruction region into M multiplied by M grids; the gradient magnetic field data at the reconstruction region includes gradient magnetic field data at each grid;

constructing a sound pressure matrix by utilizing sound pressure data acquired by each ultrasonic transducer, and constructing a system matrix by utilizing gradient magnetic field data at the reconstruction area, wherein the system matrix is used for describing that a direct corresponding relation exists between sound pressure and the concentration partial derivative of the magnetic nano particles;

thirdly, acquiring concentration partial derivative distribution of the magnetic nano particles by using the sound pressure matrix and the system matrix constructed in the second step through an LSQR method;

And step four, acquiring magnetic nanoparticle concentration distribution by utilizing magnetic nanoparticle concentration partial derivative distribution, so as to acquire a magnetoacoustic magnetic particle concentration reconstruction image in a saturated magnetization state.

2. The method for reconstructing a magnetoacoustic magnetic particle concentration image in a saturated magnetization state according to claim 1, wherein in the first step, a simulation initial condition of magnetoacoustic magnetic particles in a saturated magnetization state is set, and sound pressure data at an ultrasonic transducer and gradient magnetic field data at a reconstruction region are obtained based on a preset simulation model; selecting an Nmm multiplied by Nmm region as a reconstruction region by taking a magnetic nanoparticle group as a center, and carrying out finite element division on the reconstruction region to divide the reconstruction region into M multiplied by M grids; the gradient magnetic field data at the reconstruction region includes gradient magnetic field data at each grid; comprising the following steps:

Initializing magnetic nanoparticle parameters, simulating conditions of a Helmholtz coil and a Maxwell coil current, selecting an EMG308 model as a magnetic nanoparticle, placing a magnetic nanoparticle group at the center of the coil, respectively introducing current into the Helmholtz coil and the Maxwell coil, providing a static magnetic field B _sat by the Helmholtz coil to enable the magnetic nanoparticle to reach a saturated state, and providing a uniform gradient magnetic field B _g by the Maxwell coil; and drawing a circle with a fixed scanning radius by taking the magnetic nanoparticle group as the center, discretely arranging a plurality of ultrasonic transducers on the circle, acquiring sound pressure data of a plurality of time points received by each ultrasonic transducer, and acquiring an original sound field p (r, t) at each ultrasonic transducer.

3. The method for reconstructing the magnetic acoustic magnetic particle concentration image in the saturated magnetization state according to claim 1, wherein a circle is drawn with a fixed scanning radius by taking a magnetic nanoparticle group as a center, 165 ultrasonic transducers are discretely arranged on the circle, and sound pressure data of 470 time points received by each ultrasonic transducer are obtained; selecting a 50mm multiplied by 50mm area as a reconstruction area by taking the magnetic nanoparticle group as the center, and carrying out finite element division on the reconstruction area to divide the reconstruction area into 250 multiplied by 250 grids.

4. The method for reconstructing a magnetic-acoustic-magnetic particle concentration image in a saturated magnetization state according to claim 2, wherein constructing a sound pressure matrix from sound pressure data acquired at each ultrasonic transducer, constructing a system matrix from gradient magnetic field data at the reconstruction region, the system matrix describing a direct correspondence between sound pressure and a concentration partial derivative of magnetic nanoparticles, comprises:

the magnetic force to which the magnetic nanoparticles are subjected is expressed as

In the formula (1), f (r', t) is the magnetic force received by the magnetic nano particles at the moment t; r' is the position of the sound source point, and t is time; n (r') is the concentration of the magnetic nanoparticles; m represents the magnetic moment of the magnetic nanoparticle; The magnitude of the gradient magnetic field at the position of the sound source point at the moment t; e _z denotes a unit vector in the z direction;

The sound source and sound pressure relationship is as follows:

In the formula (2), p (r, t) is the sound pressure at any point at the time t, and the unit is Pa; r is any point position; c _s is the speed of sound in the biological tissue in m/s; f (r, t) is the sound source term; t is time; r 'is the position of the source point, r= |r-R' |; omega is the entire study area;

due to the unidirectional nature of the magnetic force, the sound source term can be expressed as

Bringing formula (3) into formula (2) to obtain

Since in calculating the problem of temporal spatial distribution,Can be processed according to constant, so that

The above equation can be used to obtain a direct correspondence between sound pressure and partial concentration derivative, and describing the correspondence through the system matrix a can be abstracted to obtain a matrix relation:

Ax＝b (6)

wherein A is a system matrix, x is a concentration partial derivative, b is a sound pressure matrix, and sound pressure data in the sound pressure matrix corresponds to p (r, t); and combining gradient magnetic field data according to the formula (5) and the formula (6), thereby obtaining a system matrix A.

5. The method for reconstructing a magnetic acoustic magnetic particle concentration image in a saturated magnetization state according to claim 2, wherein in the third step, the concentration partial derivative distribution of the magnetic nanoparticles is obtained by using the sound pressure matrix and the system matrix constructed in the second step by using the LSQR method, and the method comprises the following steps:

introducing an LSQR method, solving a system matrix serving as a large sparse coefficient matrix, and finally obtaining concentration partial derivative distribution;

The solving process comprises the following steps:

Let orthonormal matrix U _k＝[u₁,u₂,…,u_k](u_j∈R^mi) and Double diagonal matrix of

Wherein (α ₁,α₂,…,α_k∈R;β₂,β₃,…,β_k+1 ε R);

the iterative process is as follows: the iterative process is as follows:

Step 301, condition initialization

β₁＝||b||;α₁＝||A^Tu₁||₂;β₁u₁＝b；

α₁v₁＝A^Tu₁;w₁＝v₁;x₀＝0；

Step 302 diagonalizing a coefficient matrix

β_j+1＝||Av_j-α_ju_j||₂;α_j+1＝||A^Tu_j+1-β_j+1v_j||₂;

(j＝1,2,...,k)；

Step 303, calculating QR decomposition intermediate variables

Step 304, updating the values of x and intermediate variable w

Step 305, judging iteration conditions

If ||ax _k -b||ε is satisfied, the iteration is terminated, where epsilon is the allowable error, epsilon=0.01 is set;

for j=1, 2..k, steps 302-305 are repeated.

6. A method for reconstructing a magnetoacoustic magnetic particle concentration image in a saturated magnetization state according to claim 3, wherein in step four, the magnetic nanoparticle concentration distribution is obtained by using the magnetic nanoparticle concentration partial derivative distribution, thereby obtaining a magnetoacoustic magnetic particle concentration reconstructed image, comprising:

The concentration partial derivative is known to satisfy the following relationship with the concentration distribution:

Assuming the side length of the grid is l, l=0.2 mm, the concentration partial derivative x can be expressed as:

The concentration profile N (r') can be expressed as

The trapezoidal formula method with simple calculation and higher precision is introduced for solving, and the method can be obtained

Wherein, c is more than or equal to 0 and less than or equal to 249,1 and d is more than or equal to 250, and the concentration distribution can be obtained by combining the boundary conditions of x (c, d).