A magnetoacoustic electromagnetic particle image reconstruction method based on time reversal method

Abstract

This invention discloses a method for reconstructing magnetoacoustic electromagnetic particle images based on time-reversal. This method utilizes the method of moments discretization, combining the voltage-time inversion formula with the theory of the magnetoacoustic electromotive force problem for magnetic particles. It reconstructs the spatiotemporal discrete signals of the first and second derivatives of the voltage acquired by the electrodes into an equivalent field source distribution within the imaging region. A unit current is injected across the electrodes, and the potential distribution is obtained by solving the reciprocal potential Poisson equation. Combining the field source and the reciprocal potential distribution, the discrete divergence field of the magnetic nanoparticle concentration can be calculated, and then expressed as a five-point difference form of the Poisson equation. Finally, the Gauss-Seidel iterative method is used to solve this equation to obtain an image of the magnetic nanoparticle concentration distribution. This invention effectively reduces computational complexity and storage requirements, significantly improves imaging speed, and expands the application potential of this technology in the field of medical imaging.

Description

Technical Field

[0001] This invention belongs to the technical field of concentration distribution image reconstruction, and particularly relates to a magnetoacoustic electromagnetic particle image reconstruction method based on time inversion. Background Technology

[0002] Xiaoheng Yan's application for "An Electrode-Detection Magnetoacoustic Electromagnetic Particle Imaging Device and Method" (application number: 202410008351.0), filed on January 4, 2024, first proposed the Electrode-Detection Magnetoacoustic Electromagnetic Particle Concentration Imaging Method (MAET-ED). This method is a novel non-invasive biomedical magnetic particle imaging technique based on Langevin theory and the magnetoacoustic-electroelectric effect. It utilizes ultrasonic excitation instead of electromagnetic excitation, effectively solving the problem of excessive electromagnetic excitation in existing magnetic particle imaging methods. Regarding magnetoacoustic electromagnetic particle image reconstruction methods, only Xiaohan Hou et al. proposed an Electrode-Detection Magnetoacoustic Electromagnetic Particle Image Reconstruction Method based on Projected Gradient Descent-Least Squares (PGD-LSMR) in 2025. This method focuses on using the PGD-LSMR algorithm to solve the virtual wave source matrix equation for concentration image reconstruction. While achieving high reconstruction accuracy, it requires large amounts of data storage and numerous iterations, resulting in high computational complexity and making it difficult to use for real-time imaging. Therefore, further research is needed to address the speed issue of MAET-ED image reconstruction.

[0003] This paper proposes a magnetoacoustic electromagnetic particle image reconstruction method based on time inversion. For the first time, it combines the forward problem theory of magnetoacoustic electromagnetic particles with the voltage time inversion formula to derive the theory and algorithm for magnetoacoustic electromagnetic particle image reconstruction. It can reconstruct magnetoacoustic electromagnetic particle images based solely on the first and second derivative data of voltage measured at the boundary, reducing the amount of data stored and thus improving the imaging speed. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a time-reversal-based image reconstruction method for magnetoacoustic electromagnetic particles. By combining the time-reversal method with the forward problem theory of magnetoacoustic electromagnetic particles, and employing a method of moments (MoM) discretization (finite element method sampling), selecting impulse basis functions as local basis functions, and determining weight functions through point matching, a time-reversal-based image reconstruction method for magnetoacoustic electromagnetic particles is established. This method relies solely on boundary measurement voltage signals for image reconstruction, improving both reconstruction time and efficiency.

[0005] To address the aforementioned technical problems, this invention provides a magnetoacoustic electromagnetic particle image reconstruction method based on time-reversal, comprising the following steps: Step 1: Discretization of the voltage signal, the first derivative signal of the voltage, and the second derivative signal of the voltage; Step 2: Obtaining the source distribution of the voltage-like fluctuation field within the imaging region; Step 3: Obtaining the concentration of magnetic nanoparticles within the image region. and Gradient distribution in the direction; Step 4: Obtain the reconstructed image of magnetic nanoparticle concentration.

[0006] Optionally, in step 1, select An ultrasonic transducer is used for ultrasonic excitation, and data is collected. Electrode voltage signal under position excitation Voltage first derivative signal and voltage second derivative signal ,in, By setting different sampling times, the continuous signal is discretized to obtain the magnetoacoustic signal distribution at different scanning positions.

[0007] Optionally, in step 2, the voltage-type wave equations can be solved using the time-reversal method to obtain the field source of the voltage-type wave equations for magnetic nanoparticles. The expression is: (1)

[0008] In the formula, Let be the speed of sound propagating in the medium. The closed surface on which the ultrasonic transducer is located. This refers to the source location of the ultrasonic transducer. The location of the field point where the imaging region is located. The time delay from the source point to the field point. This represents the gradient of the magnetic nanoparticles at the field point where the imaging region is located. The reciprocal current density at the field point where the imaging region is located. The magnetic moment of the magnetic nanoparticles. The permeability of free space, The density of the medium within the imaging region, curved surface exist The normal vector of the position, and for The first and second derivatives of the magnetoacoustic signal at time t; after discretization using the method of moments, formula (1) can be reduced to: (2)

[0009] In the formula, For the first in the imaging region The position vectors of each field point For ultrasonic transducers The position vectors of the source points To determine the number of scans for the ultrasonic transducer, the first and second derivative data matrices of the voltage signal obtained in the first step are substituted into equation (3). The Hilbert transform of the right side of equation (3) is then used to extract the amplitude information. Combined with the boundary polarity information and time, the field source in the voltage-like fluctuation field can be reconstructed. distributed.

[0010] Optionally, in step 3, the direction of the static magnetic field is specified. The axis, the direction of ultrasonic excitation is in axis, reciprocal current density The direction is The field source in a voltage-type fluctuation field can be simplified as follows: (3)

[0011] Equation (3) combined with the source distribution obtained in step 2 and the reciprocal potential gradient obtained by solving the reciprocal potential Poisson equation, yields the concentration. exist The derivative of the direction. Rotate the electrode 90° clockwise and repeat the above steps; similarly, the concentration can be obtained. exist The derivative of the direction.

[0012] Optionally, in step 4, the boundary magnetic particle concentration is initially assumed. The following is combined with step 3 and Find the concentration divergence field: (4)

[0013] The discretized divergence field is written in the form of a five-point difference Poisson equation. The Poisson equation is solved using the Gauss-Seidel iterative method. The update formula for the Gauss-Seidel iterative method is as follows: (5)

[0014] In the formula, The square of the grid step size. For the first The current concentration iteration value of the grid. For the first The current concentration iteration value of the grid. For the first The concentration iteration value in the previous round of the grid, For the first The current concentration iteration value of the grid. For the first The concentration iteration value in the previous round of the grid, For the first The concentration divergence value of the current grid iteration can be used to obtain the concentration distribution of magnetic nanoparticles by solving the iterative formula. The number of iterations can be set. In the updated formula (5) Until the following convergence condition is met: (6)

[0015] In the formula, For the first The concentration iteration value in the previous round of the grid, For tolerance, the current round concentration iteration value that satisfies the tolerance convergence condition of equation (6) This is the desired concentration distribution of magnetic nanoparticles. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings of the embodiments will be briefly described below: Figure 1 This is a flowchart of the present invention; Figure 2 This is a schematic diagram of the principle of electrode-detection magnetic particle magnetoacoustic-electric imaging. Figure 3 This is a map showing the concentration of magnetic particles. Figure 4 Concentration of magnetic nanoparticles based on this method Oriented gradient reconstruction map and concentration reconstruction map. Detailed Implementation

[0017] The following will provide a more detailed description of the magnetoacoustic electromagnetic particle image reconstruction method based on time reversal proposed in this invention, with reference to the accompanying drawings in the embodiments of this invention.

[0018] In a preferred embodiment, such as Figure 1 As shown, the simulation sampling time is set, and the acquired voltage signal is discretized using the method of moments. The computational domain is divided into a specified grid using the finite element method. The impulse basis function is selected as the local basis function, and the original voltage signal and its first and second derivative signals are processed. , and Discretize the data into a specified voltage data matrix, and determine the weighting function using a point-matching method. Using the Dirac function and derived through the time-reversal method, the original first and second derivative signals of the voltage are reconstructed into the field source in the voltage-like fluctuation field. Distribution; based on the discretization solution of the magnetoacoustic-electroelectric reciprocity process of magnetic particles with an injection current of 1A and only a pair of electrodes A and B, the reciprocal current density in the imaging region can be obtained by combining it with the specific MAET-ED model. Distribution; the concentration is obtained by combining the field sources in the voltage-like fluctuation field of the acquired imaging region with the reciprocal current density. exist and The concentration of magnetic nanoparticles in the imaging region can be obtained by solving the concentration Poisson equation using the Gauss-Seidel iterative method based on the directional derivative distribution. Distribution image.

[0019] This invention discloses a magnetoacoustic electromagnetic particle image reconstruction method based on time reversal. Figure 2 Based on the MAET-ED principle, a simulation model was constructed in a Cartesian coordinate system. A 15mm square represents biological tissue, and a 10mm radius circle represents the MNP region, with a concentration of [missing information]. Superparamagnetic nanoparticles EMG707 were used to apply ultrasonic excitation to tissue using a point sound source with a radius of 3 mm. The ultrasonic excitation consisted of a three-cycle Hanning window modulated signal with a center frequency of 1 MHz. This was achieved through the following technical solution.

[0020] Step 1: Set the number of stimuli to 38, and collect data from each. Electrode voltage signal under position excitation Voltage first derivative signal and voltage second derivative signal ,in, Set the sampling time to By setting 801 sampling points, the continuous signal was discretized to obtain the voltage signal, the first derivative signal, and the second derivative signal distribution at different scanning positions.

[0021] Step 2: Solving the voltage-type wave equations using the time-reversal method yields the field source of the voltage-type wave equations for magnetic nanoparticles. The expression is: (1)

[0022] In the formula, Let be the speed of sound propagating in the medium. The closed surface on which the ultrasonic transducer is located. This refers to the source location of the ultrasonic transducer. The location of the field point where the imaging region is located. The time delay from the source point to the field point. This represents the gradient of the magnetic nanoparticles at the field point where the imaging region is located. The reciprocal current density at the field point where the imaging region is located. The magnetic moment of the magnetic nanoparticles. The permeability of free space, The density of the medium within the imaging region, curved surface exist The normal vector of the position, and for The first and second derivatives of the voltage signal at time t.

[0023] Following the discretization method based on the method of moments, and employing the finite element mesh generation method, a set of... Each grid cell is used to select the pulse basis function. Define local basis functions and specify weight functions according to point matching. To use the Dirac function, we can discretize equation (1): (2)

[0024] We will obtain data from different ultrasonic excitation locations, and different... First-order magnetoacoustic-electric derivative data at time 1 and magnetoacoustic-electric second derivative signal Substituting this into equation (2), and taking the Hilbert transform of the right side of equation (2) to extract amplitude information, and then combining it with the polarity information of the imaging region, the field source... It can be simplified to: (3)

[0025] In the formula and Using the Hilbert transform operator and polarity extraction operator, in the positive problem of the experimental example in this study, the magnetoacoustic-electric signal of magnetic particles can also be derived as: (4)

[0026] In the formula, The conductivity in the imaging region, For constant coefficient terms, for Directional vibration velocity, For the polarization intensity, equation (4) can be finally simplified to: (5)

[0027] In the formula, For concentration exist The derivative of the direction, sound pressure In time The integral over. Equation (5) yields the relationship between the magnetoacoustic signal and the initial excitation sound pressure at the concentration change boundary. In time The integral over the wave is proportional to the wave shape; by comparing the waveforms, the concentration gradient can be obtained. The polarity information is combined with equation (3) to reconstruct the field source in the voltage-type fluctuation field. distributed.

[0028] Step 3: Construct the magnetoacoustic-electroreciprocal process of magnetic particles. A 1A current is uniformly injected onto two detection electrodes on a biological tissue with a side length of 15mm. The reciprocal potential is then... The Poisson equation that is satisfied is: (6)

[0029] In the formula, For the entire solution domain, For the boundary of the entire solution domain, For the boundary outward normal direction, and To determine the location of the detection electrode, the imaging area can be obtained by solving equation (6). The reciprocal current density matrix and reciprocal potential matrix of each grid cell.

[0030] In this preferred embodiment, the direction of the static magnetic field is defined as follows: The axis, the direction of ultrasonic excitation is in axis, reciprocal current density The direction is The field source in a voltage-type fluctuation field can be simplified as follows: (7)

[0031] Using the field source distribution from step 2, the concentration can be obtained. exist The derivative of the direction. Rotate the electrode 90° clockwise and repeat the above steps; similarly, the concentration can be obtained. exist The derivative of the direction.

[0032] In step 4, the boundary conditions are combined with those in step 3. and Find the concentration divergence field: (8)

[0033] The discretized divergence field is written in the form of a five-point difference Poisson equation. The Poisson equation is solved using the Gauss-Seidel iterative method. The update formula for the Gauss-Seidel iterative method is as follows: (9)

[0034] In the formula, The square of the grid step size. For the first The current concentration iteration value of the grid. For the first The current concentration iteration value of the grid. For the first The concentration iteration value in the previous round of the grid, For the first The current concentration iteration value of the grid. For the first The concentration iteration value in the previous round of the grid, For the first The concentration divergence value of the current grid iteration can be used to obtain the concentration distribution of magnetic nanoparticles by solving the iterative formula. The number of iterations can be set. In the updated formula (9) Until the following convergence condition is met: (10)

[0035] In the formula, For the first The concentration iteration value in the previous round of the grid, For tolerance, the current round concentration iteration value that satisfies the tolerance convergence condition of equation (10) This is the desired concentration distribution of magnetic nanoparticles.

[0036] The above description illustrates preferred embodiments of the present invention. It should be noted that this is not intended to limit the scope of the invention. Based on the principles of the present invention, any reasonable improvements and equivalent modifications that can be made by those skilled in the art without departing from the core concept of the invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing magnetoacoustic electromagnetic particle images based on time-reversal, characterized in that, Includes the following steps: Step 1: Discretize the original voltage signal, the first derivative signal of the voltage, and the second derivative signal of the voltage; Step 2: By combining the theoretical formula of the magnetoacoustic-electrodynamic problem of magnetic particles with the time inversion calculation formula of voltage signals, the field source distribution relationship in the voltage-like fluctuation field within the imaging area is established; Step 3: Obtain the concentration of magnetic nanoparticles at [specific value]. and Gradient distribution in the direction; Step 4: Solve the concentration Poisson equation using the Gauss-Seidel iterative method to obtain a reconstructed image of the magnetic nanoparticle concentration.

2. The magnetoacoustic electromagnetic particle image reconstruction method based on time reversal as described in claim 1, characterized in that, In step 1, select An ultrasonic transducer is used for ultrasonic excitation, and data is collected. Electrode voltage signal under position excitation Voltage first derivative signal and voltage second derivative signal ,in, By setting different sampling times, the continuous signal is discretized to obtain the voltage signal distribution at different scanning positions.

3. The magnetoacoustic electromagnetic particle image reconstruction method based on time reversal as described in claim 1, characterized in that, In step 2, the voltage-type wave equations can be solved by combining the time-reversal method to obtain the field source of the voltage-type wave equations for magnetic nanoparticles. The expression is: (1) In the formula, Let be the speed of sound propagating in the medium. The closed surface on which the ultrasonic transducer is located. This refers to the source location of the ultrasonic transducer. The location of the field point where the imaging region is located. The time delay from the source point to the field point. This represents the gradient of the magnetic nanoparticles at the field point where the imaging region is located. The reciprocal current density at the field point where the imaging region is located. The magnetic moment of the magnetic nanoparticles. The permeability of free space, The density of the medium within the imaging region, curved surface exist The normal vector of the position, and for The first and second derivatives of the magnetoacoustic signal at time t; After discretization using the method of moments, formula (1) can be reduced to: (2) In the formula, For the first in the imaging region The position vectors of each field point For ultrasonic transducers The position vectors of the source points To determine the number of scans for the ultrasonic transducer, the first and second derivative data matrices of the voltage signal obtained in the first step are substituted into equation (2). The Hilbert transform is then performed on the right side of equation (2) to extract the amplitude information. Combined with the polarity information of the imaging region and time, the field source in the voltage-like fluctuation field can be reconstructed. distributed.

4. The magnetoacoustic electromagnetic particle image reconstruction method based on time reversal as described in claim 1, characterized in that, In step 3, the direction of the static magnetic field is specified as follows: The axis, the direction of ultrasonic excitation is in axis, reciprocal current density The direction is The field source in a voltage-type fluctuation field can be simplified as follows: (3) Equation (3) combined with the source distribution obtained in step 2 and the reciprocal potential gradient obtained by solving the reciprocal potential Poisson equation, yields the concentration. exist The derivative of the direction; rotate the electrode 90° clockwise and repeat the above steps; similarly, the concentration can be obtained. exist The derivative of the direction.

5. The magnetoacoustic electromagnetic particle image reconstruction method based on time reversal as described in claim 1, characterized in that, In step 4, the boundary magnetic particle concentration is initially assumed. The following is combined with step 3 and Find the concentration divergence field: (4) The discretized divergence field is written in the form of a five-point difference Poisson equation. The Poisson equation is solved using the Gauss-Seidel iterative method. The update formula for the Gauss-Seidel iterative method is as follows: (5) In the formula, The square of the grid step size. For the first The current concentration iteration value of the grid. For the first The current concentration iteration value of the grid. For the first The concentration iteration value in the previous round of the grid, For the first The current concentration iteration value of the grid. For the first The concentration iteration value in the previous round of the grid, For the first The concentration divergence value of the current grid iteration can be used to obtain the concentration distribution of magnetic nanoparticles by solving the iterative formula; the number of iterations can be set. In the updated formula (5) Until the following convergence condition is met: (6) In the formula, For the first The concentration iteration value in the previous round of the grid, For tolerance, the current round concentration iteration value that satisfies the tolerance convergence condition of equation (6) This is the desired concentration distribution of magnetic nanoparticles.

Images