Electrode position optimization method for magnetic nanoparticle concentration magneto-acoustic-electric imaging

Abstract

The invention discloses an electrode position optimization method for magnetic nanoparticle concentration magneto-acoustic-electric imaging, which comprises the following steps of: presetting a plurality of groups of electrode number candidate values at the boundary of a biological tissue, and evaluating reconstructed image results under different electrode numbers to determine the optimal electrode number; taking the center position of the electrode as an optimization variable, and constructing an electrode position optimization index based on a sensitivity matrix; a deep learning model based on a deep neural network is constructed, and the model takes the electrode position optimization index as input and takes the electrode position parameter as output; and training the deep learning model, inputting an electrode position optimization index target value to the model after training is completed, and outputting a corresponding electrode position coordinate. According to the method, the precision and stability of the reconstructed image can be improved, the repeated simulation and trial-and-error cost is reduced, and the electrode optimization efficiency is improved.

Description

Technical Field

[0001] This invention belongs to the field of electrode detection technology, specifically relating to an electrode position optimization method for magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging. Background Technology

[0002] Electrode-detected magnetoacoustic-electroelectric imaging (MAET-ED) is a novel imaging method for magnetic nanoparticles. This method typically applies ultrasonic excitation to the measured medium under static magnetic field conditions, causing the magnetic nanoparticles to generate voltage signals related to their concentration distribution under multi-physics coupling. These voltage signals are then acquired by electrodes placed at the medium's boundary, enabling the imaging and reconstruction of the magnetic nanoparticle distribution. Compared to traditional magnetic nanoparticle imaging techniques, MAET-ED offers advantages in reducing electromagnetic excitation power consumption and overcoming particle size limitations. [Hou X, Yan X, Chen W, et al. Magneto-Acousto-Electrical Tomography of Magnetic Nanoparticles With Electrode Detection[J].IEEE Transactions on Instrumentation and Measurement,2025.]

[0003] Currently, in magnetic nanoparticle concentration magnetoacoustic-electroelectric imaging technology, single-channel electrodes are often arranged at the relative boundary positions of the measured medium to acquire voltage signals. However, the number of measurement signal channels obtained by a single-channel electrode is limited, and the measurement information lacks discriminativeness, severely affecting the accuracy and stability of the reconstructed image results.

[0004] Furthermore, the relative position of the electrode and the area to be imaged will affect the accuracy and stability of the MAET-ED reconstructed image; improving the measurement accuracy of MAET-ED is an urgent problem to be solved to bring this method closer to practical applications. Summary of the Invention

[0005] Based on the shortcomings of the prior art, the technical problem solved by the present invention is to provide an electrode position optimization method for magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging, which can improve the distinguishability of measurement data, improve the accuracy and stability of reconstructed images under different imaging conditions, and enhance the reliability of reconstructed images.

[0006] This invention proposes a method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging, comprising the following steps: S1. Place E electrodes at the boundary of the biological tissue and set the center position of the electrodes (x). i ,y i ) are optimization variables; S2. Construct an optimization index for the optimal electrode position based on the sensitivity matrix; S3. Construct a deep learning model based on a deep neural network, which includes an input layer, multiple hidden layers, and an output layer; S4. Train a deep learning model based on a deep neural network, and input the target value of the optimization index to obtain the corresponding electrode position coordinates.

[0007] Optionally, in step S1, the number of electrodes is determined as follows:

[0008] Several candidate values ​​for the number of electrodes are preset at the boundary of biological tissue. Each candidate value corresponds to the number of electrodes placed at equal intervals at the boundary of biological tissue. For each candidate value, electrodes are placed at equal intervals at the boundary of biological tissue according to the corresponding number. The coordinates of the center position of each electrode are determined, and a voltage signal is obtained based on the electrode position. The concentration distribution of magnetic nanoparticles is reconstructed using the obtained voltage signal to obtain the corresponding reconstructed image result. The reconstructed image results corresponding to different candidate values ​​of the number of electrodes are compared, and the final number of electrodes E is determined according to the preset evaluation index.

[0009] Further, in step S1, the reconstruction of the magnetic nanoparticle concentration distribution based on the acquired voltage signal includes: constructing a voltage matrix using the voltage data acquired at each electrode pair; and constructing a sensitivity matrix using the acoustic field vibration velocity and reciprocal current density data at the imaging area. This sensitivity matrix describes the correspondence between voltage and magnetic nanoparticle concentration, including:

[0010] The voltage signal measured by the detection electrode is represented as follows:

[0011] In the formula, r is the source point of the magnetic particle region, α0 is the free magnetic permeability, m is the magnetic moment of the magnetic nanoparticle, L(α) is the Langevin function, J(r) is the reciprocal current density, and v(r,t) is the sound field vibration velocity. By discretizing using the method of moments, the voltage measured by any electrode under arbitrary excitation is expressed as:

[0012] In the formula, Ω i The region to be imaged can be represented by a matrix equation as follows:

[0013] In the formula, U is the voltage signal measured by the multi-channel electrode, A is the sensitivity matrix, and N is the magnetic nanoparticle concentration; the number of pixels in the imaging area is denoted as m×n=M, where m represents the number of segments in the x-direction and n represents the number of segments in the y-direction. Assuming the sampling time is taken at p time points, the matrix equation is expressed as:

[0014] In the formula, the sensitivity matrix A is an Ip×M matrix, U is an Ip×1 matrix, N is an M×1 matrix, and I represents the number of measurement modes for any electrode pair under arbitrary ultrasonic excitation. Solving the matrix equation constructed from the electrical signal U and the sensitivity matrix A yields the concentration distribution N of the magnetic nanoparticles.

[0015] Optionally, in step S2, the optimal electrode position optimization index includes:

[0016] The condition number K of the Hessian matrix of the sensitive field constructed from the sensitivity matrix A is expressed as:

[0017] In the formula, λ max λ is the largest eigenvalue. min Let A be the minimum eigenvalue and A be the sensitivity matrix.

[0018] The relative error β of the reconstructed image is expressed as:

[0019] In the formula, N represents the concentration distribution of the target magnetic nanoparticles. * The concentration of the reconstructed magnetic nanoparticles;

[0020] Optionally, in step S3, the deep learning model based on a deep neural network includes:

[0021] The input layer is used to input data consisting of electrode position optimization indices corresponding to multiple electrode layouts, represented as:

[0022] In the formula, e represents the number of electrode placements; the hidden layer, consisting of three fully connected layers, is used to map the input multidimensional feature vector to the electrode position parameter feature space; the output layer is used to output the corresponding electrode positions, expressed as:

[0023] Optionally, in step S4, the training method for the deep learning model based on a deep neural network includes:

[0024] A magnetoacoustic-electric simulation model was constructed using finite element simulation software to obtain sound field vibration velocity and reciprocal current density data. Based on the data, the electrode position optimization index corresponding to different electrode layouts was calculated. The electrode position optimization index vector was preprocessed, including logarithmic transformation of the condition number and normalization of the input samples and output labels.

[0025] A deep learning model is trained using an optimized index vector as input and an electrode position coordinate vector as output. The deep neural network model employs supervised learning, and the training process utilizes a conjugate gradient optimization algorithm, iteratively updating network weights and thresholds through backpropagation. The training process uses mean squared error as the loss function, and an L2 regularization term is introduced into the loss function. The output layer of the deep neural network uses a saturated linear activation function.

[0026] After the optimization model training is completed, the target value vector x=[K,β] of the optimal electrode position optimization index is input into the deep learning model. T This yields the corresponding electrode position coordinate vector.

[0027] The advantages of this invention are as follows: 1. An electrode position optimization method for magnetic nanoparticle concentration magnetoacoustic-electroelectric imaging improves the distinguishability of measurement data, reduces the ill-conditioned nature of reconstructed images, thereby improving the accuracy and stability of reconstructed images and enhancing the reliability of imaging results. 2. An electrode position optimization method for magnetic nanoparticle concentration magnetoacoustic-electroelectric imaging uses a deep learning model to learn the nonlinear relationship between electrode position and optimization index, thereby determining the optimal electrode position, reducing the large amount of repetitive simulation and reconstruction calculations in traditional trial-and-error optimization, and improving optimization efficiency.

[0028] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of the present invention more apparent and understandable, the following detailed description is provided in conjunction with preferred embodiments and accompanying drawings. Attached Figure Description

[0029] 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:

[0030] Figure 1 A flowchart of an electrode position optimization method for magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging;

[0031] Figure 2 A schematic diagram illustrating the acquisition of acoustic field vibration velocity data;

[0032] Figure 3 This is a schematic diagram of the electrode placement structure;

[0033] Figure 4 A deep neural network optimized for electrode placement;

[0034] Figure 5 Image of the target magnetic nanoparticles;

[0035] Figure 6 This is a schematic diagram of the reconstruction results for a single-channel electrode.

[0036] Figure 7 A schematic diagram illustrating the reconstruction results for optimizing the electrodes. Detailed Implementation

[0037] The features and exemplary embodiments of various aspects of this application will be described in detail below. To make the objectives, technical solutions, and advantages of this application clearer, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain this application and not to limit it. For those skilled in the art, this application can be implemented without some of these specific details. The following description of the embodiments is merely to provide a better understanding of this application by illustrating examples.

[0038] In this embodiment, there are two sets of evaluation indicators: the correlation coefficient CC and the relative error RE are used to compare the reconstruction results of different candidate values ​​of electrode number and to compare the reconstruction image results of the optimal electrode and the single-channel electrode; the Hessian matrix condition number K and the relative error β of the reconstructed image are used to construct the optimal electrode position optimization index.

[0039] This invention provides a method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging, comprising the following steps:

[0040] refer to Figure 1 A method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic imaging includes the following steps: S1. Place E electrodes at the boundary of the biological tissue and set the center position of the electrodes (x). i ,y i ) are optimization variables; S2. Construct an optimization index for the optimal electrode position based on the sensitivity matrix; S3. Construct a deep learning model based on a deep neural network, which includes an input layer, multiple hidden layers, and an output layer; S4. Train a deep learning model based on a deep neural network, and input the target value of the optimization index to obtain the corresponding electrode position coordinates.

[0041] The specific implementation process is as follows:

[0042] S1. Place E electrodes at the boundary of the biological tissue and set the center position of the electrodes (x). i ,y i ) for optimization variables

[0043] Five candidate values ​​were pre-set at the biological tissue boundary, with electrode numbers of 4, 6, 8, 10, and 12 respectively. Electrodes of different numbers were placed at equal intervals along the biological tissue boundary, and the coordinates of the center positions of each electrode were determined. A two-dimensional model based on the MAET-ED principle was built using COMSOL Multiphysics 6.3 for simulation. Voltage signals were obtained through the electrode center position coordinates, and the matrix equations were solved using the Tikhonov regularized reconstruction method to obtain reconstructed image results for different electrode numbers. Correlation coefficient CC and relative error RE were introduced to compare the target concentration distribution with the reconstructed concentration distribution, expressed as: (8) (9)

[0044] In the formula N n The target magnetic nanoparticle concentration value, N n,r To reconstruct the magnetic nanoparticle concentration value, The average concentration of the target magnetic nanoparticles. To reconstruct the average concentration of magnetic nanoparticles, the final number of electrodes E is determined based on the comparison results of the correlation coefficient CC and the relative error RE. This number of electrodes is then used as the fixed number of electrodes for subsequent electrode position optimization and deep learning training.

[0045] Further, in step S1, the reconstruction of the magnetic nanoparticle concentration distribution based on the acquired voltage signal includes: constructing a voltage matrix using the voltage data acquired at each electrode pair, and constructing a sensitivity matrix using the acoustic field vibration velocity and reciprocal current density data at the imaging area. This sensitivity matrix is ​​used to describe the correspondence between voltage and magnetic nanoparticle concentration, including:

[0046] The voltage signal measured by the detection electrode is represented as follows: (10)

[0047] In the formula, r is the source point of the magnetic particle region, α0 is the free magnetic permeability, m is the magnetic moment of the magnetic nanoparticle, L(α) is the Langevin function, J(r) is the reciprocal current density, and v(r,t) is the sound field vibration velocity. By discretizing using the method of moments, the voltage measured by any electrode under arbitrary excitation is expressed as: (11)

[0048] In the formula, Ω iThe region to be imaged can be represented by a matrix equation as follows: (12)

[0049] In the formula, U is the voltage signal measured by the multi-channel electrode, A is the sensitivity matrix, and N is the concentration of magnetic nanoparticles.

[0050] In this embodiment, the number of segments in the x-direction is m=301, the number of segments in the y-direction is n=301, the number of pixels in the area to be imaged is denoted as M=90601, and the sampling time is set to 1401 time points. The matrix equation is expressed as: (13)

[0051] Solving the matrix equation constructed from the electrical signal U and the sensitivity matrix A yields the concentration distribution N of the magnetic nanoparticles.

[0052] S2. Constructing an optimal electrode position index based on the sensitivity matrix

[0053] The condition number K of the Hessian matrix of the sensitive field constructed from the sensitivity matrix A is expressed as: (14)

[0054] In the formula, λ max λ is the largest eigenvalue. min Let A be the minimum eigenvalue and A be the sensitivity matrix.

[0055] The relative error β of the reconstructed image is expressed as: (15)

[0056] In the formula, N represents the concentration distribution of the target magnetic nanoparticles. * To determine the reconstructed magnetic nanoparticle concentration, the Hessian matrix condition number K of the sensitive field calculated for different electrode layouts and the relative error β of the reconstructed image were used to construct the deep learning input data.

[0057] S3. Construct a deep learning model based on a deep neural network, which includes an input layer, multiple hidden layers, and an output layer.

[0058] refer to Figure 4 The deep learning model based on deep neural networks includes:

[0059] The input layer consists of input data comprised of electrode position optimization indices corresponding to multiple electrode layouts. The input data comprises the calculated Hessian condition number K for different electrode layouts and the relative error β of the reconstructed image, expressed as: (16)

[0060] The deep learning model has three hidden layers; the output layer represents the electrode positions, as shown below: (17)

[0061] S4. Train a deep learning model based on a deep neural network, and input the target value of the optimization index to obtain the corresponding electrode position coordinates.

[0062] A magnetoacoustic-electric simulation model was constructed using finite element simulation software to obtain data on sound field vibration velocity and reciprocal current density, and the electrode position optimization index corresponding to different electrode layouts was calculated based on the data.

[0063] refer to Figure 2 and Figure 3 The acoustic field vibration velocity and reciprocal current density data of the area to be imaged are calculated using finite element simulation software. The specific steps are as follows:

[0064] The initial conditions for the simulation of magnetoacoustic-electromagnetic imaging of magnetic nanoparticle concentration under saturated magnetization were set, and the acoustic field vibration velocity data and reciprocal current density data of biological tissue regions were obtained based on the preset simulation model.

[0065] Specifically, the simulation model for magnetoacoustic-electromagnetic imaging of magnetic nanoparticle concentration under saturated magnetization is constructed as follows: a two-dimensional model is established using COMSOL Multiphysics 6.3 for simulation research. The imaging area is a square region, the biological tissue size is 60×60mm, and the magnetic nanoparticle region is a circle with a radius of 4mm and a concentration of 1.8×10⁻⁶. 22 / mL, with the position reference being the center.

[0066] An acoustic source was set up outside the imaging region for excitation. Two excitation sources were set up, centered on a swarm of magnetic nanoparticles. The ultrasonic excitation consisted of a three-cycle Hanning window modulated signal with a center frequency of 1 MHz. Numerical simulation of the sound field was performed to obtain the time-varying sound field vibration velocity vector v at various spatial locations within the imaging region. x (r,t) and v y (r,t) is then stored discretely.

[0067] Based on preset electrode position coordinates, the reciprocal current density of 2000 different electrode layouts at the boundary of biological tissue was calculated using COMSOL Multiphysics 6.3 with MATLAB. A unit current was injected at the detection electrode, and the reciprocal current density J in the imaging region was calculated. x (r) and J y (r) is then stored discretely.

[0068] The aforementioned electrode position coordinates, based on preset parameters, are randomly sampled and generated under the following constraints: (18)

[0069] Using the discrete data of sound field vibration velocity and reciprocal current density obtained in the above steps, the Hessian condition number K and the relative error β of the reconstructed image are calculated as optimization indicators.

[0070] The electrode position optimization index vector is preprocessed, including performing a logarithmic transformation on the condition number and normalizing the input samples and output labels respectively.

[0071] A deep learning model is trained using 2000 sets of optimization index vectors as input and electrode position coordinate vectors as output. The deep neural network model adopts a supervised learning approach. During the training process, the conjugate gradient optimization algorithm is used, and the network weights and thresholds are iteratively updated through backpropagation. The mean squared error is used as the loss function during the training process, and an L2 regularization term is introduced into the loss function. The output layer of the deep neural network adopts a saturated linear activation function.

[0072] After the optimization model training is completed, the target value vector x=[1,0] of the optimal electrode position optimization index is input into the deep learning model. T This yields the corresponding electrode position coordinate vector.

[0073] The following is a comparison of the optimization metrics obtained by optimizing the electrode positions according to the above process:

[0074] The Hessian matrix condition number K for a single-channel electrode is 9.04 × 10⁻⁶. 6 The relative error β of the reconstructed image is 42.43%, indicating that the system is highly ill-conditioned and has a large reconstruction error under this layout; the condition number K of the optimized electrode layout obtained in this invention is 5.82 × 10⁻⁶. 6 The relative error β of the reconstructed image is 13.46%, which significantly reduces the ill-conditioned nature of the system and improves the reconstruction stability compared with the single-channel electrode layout.

[0075] To further evaluate the applicability of this invention, correlation coefficient CC and relative error RE are introduced to compare the target concentration distribution with the reconstructed concentration distribution.

[0076] Based on the evaluation of this invention, by Figure 5-7 As shown, the optimized electrode layout has better accuracy than the reconstructed image results of the single-channel electrode layout, with a correlation coefficient CC and a relative error RE of 0.9260 and 0.3852, respectively, indicating that the optimized electrode layout can improve the reconstruction accuracy.

[0077] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electroelectric imaging, characterized in that, The method includes the following steps: S1. Place E electrodes at the boundary of the biological tissue and set the center position of the electrodes (x). i ,y i ) are optimization variables; S2. Construct an optimization index for the optimal electrode position based on the sensitivity matrix; S3. Construct a deep learning model based on a deep neural network, which includes an input layer, multiple hidden layers, and an output layer; S4. Train a deep learning model based on a deep neural network, and input the target value of the optimization index to obtain the corresponding electrode position coordinates.

2. The method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging according to claim 1, characterized in that, In step S1, the number of electrodes is determined as follows: several sets of candidate values ​​for the number of electrodes are preset at the boundary of the biological tissue, and each set of candidate values ​​corresponds to the number of electrodes placed at equal intervals at the boundary of the biological tissue; for each set of candidate values ​​for the number of electrodes, electrodes are placed at equal intervals at the boundary of the biological tissue according to the corresponding number, the coordinates of the center position of each electrode are determined, and a voltage signal is obtained based on the electrode position; the concentration distribution of magnetic nanoparticles is reconstructed using the obtained voltage signal to obtain the corresponding reconstructed image result; the reconstructed image results corresponding to different candidate values ​​for the number of electrodes are compared, and the final number of electrodes E is determined according to the preset evaluation index.

3. The method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging according to claim 2, characterized in that, The reconstructed magnetic nanoparticle concentration distribution is achieved by constructing a voltage matrix using voltage data acquired at each electrode pair and a sensitivity matrix using acoustic field vibration velocity and reciprocal current density data at the imaging region. This sensitivity matrix describes the correspondence between voltage and magnetic nanoparticle concentration, including: The voltage signal measured by the detection electrode is represented as follows: In the formula, r is the source point of the magnetic particle region, α0 is the free magnetic permeability, m is the magnetic moment of the magnetic nanoparticle, L(α) is the Langevin function, J(r) is the reciprocal current density, and v(r,t) is the sound field vibration velocity; by discretizing using the method of moments, the voltage measured by any electrode under arbitrary excitation is expressed as: In the formula, Ω i The region to be imaged can be represented by a matrix equation as follows: In the formula, U is the voltage signal measured by the multi-channel electrode, A is the sensitivity matrix, and N is the magnetic nanoparticle concentration; the number of pixels in the imaging area is denoted as m×n=M, where m represents the number of segments in the x-direction and n represents the number of segments in the y-direction. Assuming the sampling time is taken at p time points, the matrix equation is expressed as: In the formula, the sensitivity matrix A is an Ip×M matrix, U is an Ip×1 matrix, N is an M×1 matrix, and I represents the number of measurement modes of any electrode pair under arbitrary ultrasonic excitation; by solving the matrix equation constructed by the electrical signal U and the sensitivity matrix A, the concentration distribution N of magnetic nanoparticles is obtained.

4. The method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging according to claim 1, characterized in that, In step S2, the optimal electrode position optimization index includes: The condition number K of the Hessian matrix of the sensitive field constructed from the sensitivity matrix A is expressed as: In the formula, λ max λ is the largest eigenvalue. min Let A be the minimum eigenvalue and A be the sensitivity matrix. The relative error β of the reconstructed image is expressed as: In the formula, N represents the concentration distribution of the target magnetic nanoparticles. * The concentration of the reconstructed magnetic nanoparticles.

5. The method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging according to claim 1, characterized in that, In step S3, the deep learning model based on a deep neural network includes: The input layer is used to input data consisting of electrode position optimization indices corresponding to multiple electrode layouts, represented as: In the formula, e represents the number of electrode placements; the hidden layer, consisting of three fully connected layers, is used to map the input multidimensional feature vector to the electrode position parameter feature space; the output layer is used to output the corresponding electrode positions, expressed as: In the formula, This is the center position of the electrode.

6. The method for optimizing electrode positions in magnetic nanoparticle concentration magnetoacoustic-electromagnetic imaging according to claim 1, characterized in that, In step S4, the training method of the deep learning model based on a deep neural network includes: constructing a magnetoacoustic-electroelectric simulation model using finite element simulation software, acquiring sound field vibration velocity and reciprocal current density data, and calculating electrode position optimization indices corresponding to different electrode layouts based on the data; preprocessing the electrode position optimization index vector, including performing a logarithmic transformation on the condition number and normalizing the input samples and output labels respectively; training the deep learning model with the optimization index vector as input and the electrode position coordinate vector as output; the deep neural network model adopts a supervised learning approach, employing a conjugate gradient optimization algorithm during training and iteratively updating network weights and thresholds through a backpropagation mechanism; using mean squared error as the loss function during training and introducing an L2 regularization term into the loss function; the output layer of the deep neural network adopts a saturated linear activation function; after the optimization model training is completed, inputting the target value vector x=[K,β] of the optimal electrode position optimization index into the deep learning model. T This yields the corresponding electrode position coordinate vector.

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