Heart conductivity inversion optimization algorithm based on supervised full-connection neural network

Abstract

The invention provides a heart conductivity inversion optimization algorithm of a supervised full-connection neural network, and belongs to the field of medical electrical impedance imaging algorithms. The method comprises the following steps: constructing a human thoracic cavity heart section initial image and carrying out finite element subdivision on a to-be-detected region; establishing a forward modeling objective function and an inversion objective function; conductivity distribution and corresponding potential difference value data models are generated in batches through the forward model, and a training set is constructed; a full-connection neural network of an encoder-decoder structure is constructed, the input is a potential difference value vector, the output is a conductivity variable quantity, and feature transmission is optimized through bottleneck layer compression and residual connection; introducing a forward modeling consistency regularization item into the loss function; a dynamic learning rate strategy and a gradient cutting technology are adopted. The method does not need to depend on clinical data acquisition equipment, high-precision conductivity inversion is achieved through a pure algorithm, the nonlinear mapping relation between the electrical impedance imaging input quantity and the electrical impedance imaging output quantity is represented, and efficient algorithm support is provided for non-invasive diagnosis of heart diseases.

Description

Technical Field

[0001] The present invention relates to the field of medical electrical impedance tomography algorithms, and particularly to an optimized algorithm for cardiac conductivity inversion based on a supervised fully connected neural network, which is applicable to the rapid and high-precision reconstruction of the dynamic conductivity distribution of the heart. Background Art

[0002] At present, there are various forms of cardiac function detection methods, but it is difficult to perform dynamic and rapid detection imaging of the heart and the sensitivity for the examination of lesion points is insufficient. Electrical Impedance Tomography (EIT), as a non-invasive and real-time monitoring technology, measures the surface voltage response through a multi-electrode system on the chest and reconstructs the conductivity distribution image, showing broad application potential in the field of biomedicine, especially in cardiac function monitoring. For example, in the early stage of myocardial infarction, the imbalance of ion concentrations inside and outside myocardial cells causes cell edema and abnormal electrical conduction, resulting in obvious changes in the electrical impedance of local myocardium, and the cause can be detected and treated in advance by the EIT method.

[0003] In recent years, electrical impedance tomography algorithms have been continuously updated, from traditional methods of solving mathematical non-linear ill-posed problems to neural network prediction in machine learning and unsupervised electrical impedance image reconstruction methods, etc. The existing problems are as follows: the cost of potential difference acquisition equipment is high and the noise interference is large, and traditional algorithms have a high dependence on data; the iterative inversion algorithm has a long calculation time and low real-time performance; the performance of the neural network model will significantly decline when migrated to different imaging scenarios. This patent discloses an optimized algorithm for cardiac conductivity inversion based on a supervised fully connected neural network, focusing on the conductivity distribution in a relatively stable state, for the anatomical structure image at a single time point, and having high sensitivity for the detection of abnormal changes in cardiac myocardial impedance. Summary of the Invention

[0004] Aiming at the problems of low calculation efficiency, insufficient resolution and poor robustness existing in the traditional cardiac electrical impedance tomography (EIT) inversion method, the present invention proposes an optimized algorithm for cardiac conductivity inversion based on a supervised fully connected neural network. By deeply integrating the supervised learning strategy and the physical constraint optimization mechanism, this algorithm constructs an end-to-end conductivity inversion model to achieve a high-precision non-linear mapping between the potential difference and the conductivity update amount, significantly improving the imaging resolution and algorithm stability.

[0005] To solve the above problems, the present invention provides the following technical solutions:

[0006] An optimized algorithm for cardiac conductivity inversion based on a supervised fully connected neural network, comprising the following steps:

[0007] Step 1: Construct multiple groups of thoracic heart finite element model datasets in the field domain, generate potential difference characteristic data through forward solution, and establish an inversion optimization objective function for thoracic heart imaging.

[0008] Step 2: Preprocess the potential difference and conductivity difference characteristic data and input them into a supervised fully connected neural network to obtain the model conductivity update amount. According to the updated potential difference difference, continuously iterate and update the fully connected network parameters to obtain an optimized supervised fully connected neural network.

[0009] Step 3: Use the final supervised fully connected neural network model to solve the conductivity distribution sequence of the object to be measured and perform image reconstruction according to the sequence.

[0010] Preferably, in Step 1, a two-dimensional circular model is used for the field domain, triangular element meshing (6402 triangular elements) is performed, and multiple groups of heart finite element benchmark models with different conductivity distributions are established. The boundary electrode potential difference data is calculated through the forward algorithm. At the same time, an initial conductivity uniform distribution model (σ0 = 1 S / m) is set, and its potential difference is calculated as a reference benchmark. Finally, the conductivity difference (Δσ) between the benchmark model and the initial model is used as the supervised learning target, and the potential difference difference (ΔV) is used as the network input to generate training sample pairs for the end-to-end inversion task.

[0011] The construction of the inversion optimization objective function for thoracic heart imaging in Step 1 is specifically as follows:

[0012]

[0013]

[0014] In the above formula, Δm is the difference between the resistivity of the prediction model and the true resistivity; Δd is the difference between the prediction model and the true potential difference, aiming to minimize the difference between the resistivity difference at each iteration and the voltage difference under the R constraint. Introduce a new variable R into the above formula, and the objective function is obtained by the Lagrange multiplier method:

[0015]

[0016] Preferably, in Step 2, the preprocessing of the characteristic data is specifically as follows:

[0017] Subtract the potential difference and conductivity under the initialized target model conductivity from the characteristic data described in Step 1, and perform hyperbolic tangent normalization to obtain the training set; according to the training set, use the method of convergence monitoring to train the model of the supervised neural network and update the training set to obtain the optimal solution of the network training parameters.

[0018] In Step 2, only local information is updated during each iteration. However, the variable R described in Step 1 includes global information, which will consume a large amount of computing resources during the iteration process. Therefore, the objective function is divided into two parts:

[0019] Training phase:

[0020]

[0021] The model error rms M is:

[0022]

[0023] Prediction phase:

[0024] S pr (Δm) = ||Δm - RΔd|| 2

[0025] In each iteration, it is necessary to check the data error. Define the data error rms D as:

[0026]

[0027] The data error can be used to check whether the model in the current stage matches the inversion data. When rms D diverges in the first few steps at the start of the prediction phase, the prediction should be stopped, which may indicate that the prediction model is completely different from the training model. If the data error of the currently predicted model is greater than the data error of the previous step, then the prediction phase should be stopped at this time, and the final prediction model should be the prediction model when the data error is the smallest.

[0028] Preferably, the supervised fully connected neural network in Step 2 includes: an input layer, a processing module, and an output layer.

[0029] The input layer of the supervised fully connected neural network in Step 2 is the difference Δd (dimension 1×208) between the boundary electric potential differences of the true model obtained from the finite element solution of the forward problem described in Step 1 and the initialized model.

[0030] The processing module of the supervised fully connected neural network in Step 2 is an improved multi-layer fully connected network.

[0031] Preferably, the improved deep learning model in step 2 achieves high-precision conductivity inversion through a multi-layer fully connected network structure and an adaptive training strategy: the model adopts a multi-layer fully connected architecture. The first layer maps the input potential difference difference to a high-dimensional feature space. The middle layer mines non-linear associations through the LeakyReLU activation function (α = 0.2). The last layer outputs the normalized conductivity update amount after batch normalization and Tanh activation, and ensures that the output value is within the preset range [-1, 1]. Dropout with a dropout rate of 0.3 is introduced in the middle layer of the network to suppress overfitting, and batch normalization is used to accelerate convergence. During training, the Adam optimizer with an initial learning rate of 0.0001 and a weight decay of 0.0001 is adopted, combined with a stepped learning rate decay strategy that decays by half every 4 epochs, to dynamically balance the convergence speed and accuracy. The smooth L1 loss is selected as the loss function, and the piecewise function (square loss when the error < 1, otherwise linear loss) is used to balance the robustness to outliers and the sensitivity to small errors, ultimately achieving highly stable and highly generalized conductivity inversion. Through this structural design and the combined application of technologies, the model can effectively learn the complex patterns of the input data, thus achieving better performance in processing high-dimensional data and complex pattern recognition.

[0032] The output layer of the supervised fully connected neural network in step 2 is the conductivity difference update amount Δm (dimension 1×6402).

[0033] Preferably, in step 2, according to the updated potential difference difference, the parameters of the fully connected network are continuously iteratively updated, and the specific implementation is as follows: in the training stage of step 1, when the maximum number of iterations is reached or when rms M is small enough or no longer decreases, the training stage ends, and R1 to R obtained in the training stage k are stored.

[0034] Preferably, in step 3, using the final supervised fully connected neural network model, the conductivity distribution sequence of the object to be measured is solved. The specific implementation includes: preparing the forward potential difference data of a true model; then initializing a conductivity model with all 1s, and calculating its potential difference data through forward calculation in step 1; taking the difference between the potential difference data of the true model and the initialized model to obtain Δd1, which is used as the input data of the supervised fully connected network in step 2. An output data Δm1 of a conductivity update amount is obtained through the neural network parameters of R1, and added to the previous conductivity m1. The update formula is:

[0035] m i+1 = m i + Δm i , i = 1, 2,..., k - 1

[0036] Then, forward calculation of the potential difference and the potential difference difference is performed again as the new input data Δdprior , the neural network parameters entering R2 until finally passing through R k The conductivity update amount Δm obtained by predicting the neural network parameters prior , perform the last conductivity update to obtain the final predicted model conductivity sequence, and obtain the reconstructed image of the model by the imaging algorithm.

[0037] Through the above technical processing, the beneficial effects of the present invention are mainly manifested in:

[0038] 1. After meshing the area to be measured, the forward problem is discretized for triangular element analysis, the element stiffness matrix is calculated, and then the overall stiffness matrix is assembled for overall solution. Here, the finite element method is used to replace the partial differential equation in EIT, which can accurately and quickly approximate the true solution.

[0039] 2. Using the difference between the true chest model and the initial model conductivity as the supervision signal, the neural network model parameters are optimized through backpropagation, so as to achieve an accurate mapping from the potential difference to the conductivity update amount.

[0040] 3. An adaptive training strategy is adopted to effectively improve the accuracy of conductivity inversion. By learning the complex relationships in the high-dimensional feature space, the resolution and accuracy of the inversion results are improved, and the calculation time is greatly reduced.

[0041] 4. The present invention uses batch normalization to accelerate convergence and stabilize training, combines the LeakyReLU and Tanh double activation functions to enhance the nonlinear mapping ability, and at the same time introduces Dropout regularization to prevent overfitting and improve the generalization ability of the model. The smooth L1 loss function is used to balance the sensitivity to small errors and the robustness to outliers, further enhancing the stability and adaptability of the model. Description of the Drawings

[0042] Figure 1 It is a schematic flow chart of the heart conductivity inversion optimization algorithm based on a supervised fully connected neural network of the present invention.

[0043] Figure 2 It is a schematic diagram of the finite element mesh division of the present invention. Detailed Embodiments

[0044] The following further elaborates on the present invention in conjunction with the drawings and embodiments, but does not limit the present invention.

[0045] In order to more clearly elaborate the objectives, technical solutions and advantages of the present invention, the following will further describe the present invention in detail through specific embodiments in conjunction with the drawings.

[0046] Such as Figure 1As shown, the heart conductivity inversion optimization algorithm based on a supervised fully connected neural network provided by an embodiment of the present invention includes the following steps:

[0047] Step 1: Construct multiple groups of thoracic heart finite element model datasets in the field domain, generate potential difference feature data through forward solution, and establish an inversion optimization objective function for thoracic heart imaging.

[0048] Step 2: Preprocess the potential difference and conductivity difference feature data and input them into a supervised fully connected neural network to obtain the model conductivity update amount. According to the updated potential difference difference, continuously iterate and update the fully connected network parameters to obtain an optimized supervised fully connected neural network.

[0049] Step 3: Use the final supervised fully connected neural network model to solve the conductivity distribution sequence of the object to be measured and perform image reconstruction according to the sequence.

[0050] Preferably, in Step 1, a two-dimensional circular model is used in the field domain, and triangular element meshing (6,402 triangular elements) is performed to obtain the [[ID=##]] Figure 2 shown mesh diagram, establish multiple groups of heart finite element benchmark models with different conductivity distributions, and calculate the boundary electrode potential difference data through the forward algorithm. At the same time, set an initial conductivity uniform distribution model (σ0 = 1 S / m), calculate its potential difference as a reference benchmark; finally, use the conductivity difference (Δσ) between the benchmark model and the initial model as the supervised learning target, and the potential difference difference (ΔV) as the network input to generate training sample pairs for the end-to-end inversion task.

[0051] The construction of the inversion optimization objective function for thoracic heart imaging in Step 1 is specifically:

[0052] min Δm,R ||Δm - RΔd|| 2

[0053]

[0054] In the above formula, Δm is the difference between the predicted model resistivity and the true resistivity; Δd is the difference between the predicted model and the true potential difference, aiming to minimize the difference between the resistivity difference at each iteration and the voltage difference under the R constraint. Introduce a new variable R into the above formula, and obtain the objective function by the Lagrange multiplier method:

[0055]

[0056] Preferably, in Step 2, the preprocessing of the feature data is specifically:

[0057] Subtract the characteristic data described in step 1 from the potential difference and conductivity at the initialized target model conductivity, and perform hyperbolic tangent normalization to obtain the training set; according to the training set, use the method of convergence monitoring to train the model of the supervised neural network and update the training set to obtain the optimal solution of the network training parameters.

[0058] In step 2, only local information is updated in each iteration process, while the variable R described in step 1 includes global information, which will consume a large amount of computing resources during the iteration process. Therefore, the objective function is divided into two parts:

[0059] Training stage:

[0060]

[0061] Model error rms M is:

[0062]

[0063] Prediction stage:

[0064] S pr (Δm) = ||Δm - RΔd|| 2

[0065] In each iteration, it is necessary to check the data error. Define the data error rms D as:

[0066]

[0067] The data error can be used to check whether the model in the current stage matches the inversion data. When rms D diverges in the first few steps at the start of the prediction stage, the prediction should be stopped, which may be the case where the prediction model is completely different from the training model. If the data error of the currently predicted model is greater than the data error of the previous step, then the prediction stage should stop at this time, and the final prediction model should be the prediction model when the data error is the smallest.

[0068] Preferably, the supervised fully connected neural network in step 2 includes: an input layer, a processing module, and an output layer.

[0069] The input layer of the supervised fully connected neural network described in step 2 is the difference Δd (dimension 1×208) between the boundary potential differences of the true model and the initialized model obtained by solving the forward problem of the finite element in step 1.

[0070] The processing module of the supervised fully connected neural network described in step 2 is an improved multi-layer fully connected network.

[0071] Preferably, the improved deep learning model in step 2 achieves high-precision conductivity inversion through a multi-layer fully connected network structure and an adaptive training strategy: The model adopts a multi-layer fully connected architecture. The first layer maps the input potential difference difference to a high-dimensional feature space. The middle layer mines non-linear associations through the LeakyReLU activation function (α = 0.2). The last layer outputs the normalized conductivity update amount after batch normalization and Tanh activation, and ensures that the output value is within the preset range [-1, 1]. Dropout with a dropout rate of 0.3 is introduced in the middle layer of the network to suppress overfitting, and batch normalization is used to accelerate convergence. During training, the Adam optimizer with an initial learning rate of 0.0001 and a weight decay of 0.0001 is adopted, combined with a stepped learning rate decay strategy that decays by half every 4 epochs, to dynamically balance the convergence speed and accuracy. The smooth L1 loss is selected as the loss function, and the piecewise function (quadratic loss when the error < 1, otherwise linear loss) is used to balance the robustness to outliers and the sensitivity to small errors, finally achieving high-stability and high-generalization conductivity inversion. Through this structural design and the combined application of technologies, the model can effectively learn the complex patterns of the input data, thus achieving better performance in processing high-dimensional data and complex pattern recognition.

[0072] The output layer of the supervised fully connected neural network in step 2 is the conductivity difference update amount Δm (dimension 1×6402).

[0073] Preferably, in step 2, according to the updated potential difference difference, the parameters of the fully connected network are continuously iteratively updated, and the specific implementation is as follows: In the training stage of step 1, when the maximum number of iterations is reached or when rms M is small enough or no longer decreases, the training stage ends, and R1 to R obtained in the training stage k are stored.

[0074] Preferably, in step 3, using the final supervised fully connected neural network model, the conductivity distribution sequence of the object to be measured is solved. The specific implementation includes: preparing the forward calculation potential difference data of a real model; then initializing a conductivity model of all 1s, and calculating its potential difference data through forward calculation in step 1; taking the difference between the potential difference data of the real model and the initialized model to obtain Δd1, which is used as the input data of the supervised fully connected network in step 2, and obtaining an output data Δm1 of the conductivity update amount through the neural network parameters of R1, and adding it to the previous conductivity m1. The update formula is:

[0075] m i+1 = m i + Δm i , i = 1, 2,..., k - 1

[0076] Then, forward calculation of the potential difference and the potential difference difference is performed again as the new input data Δdprior , the neural network parameters entering R2, until finally passing through R k , the conductivity update amount Δm obtained by predicting the neural network parameters prior , perform the last conductivity update to obtain the final predicted model conductivity sequence, and obtain the reconstructed image of the model by the imaging algorithm.

[0077] The present invention adopts an adaptive training strategy to effectively improve the accuracy of conductivity inversion, improves the resolution and accuracy of the inversion result by learning the complex relationships in the high-dimensional feature space, and greatly reduces the calculation time.

Claims

1. An optimized algorithm for cardiac conductivity inversion based on a supervised fully connected neural network, characterized in that, It includes the following steps: Step 1: Construct multiple sets of thoracic heart finite element model datasets in the field domain, generate potential difference characteristic data through forward solution, and establish an inversion optimization objective function for thoracic heart imaging. Step 2: Preprocess the potential difference and conductivity difference characteristic data and input them into a supervised fully connected neural network to obtain the updated amount of model conductivity. According to the updated potential difference difference, continuously iterate and update the parameters of the fully connected network to obtain an optimized supervised fully connected neural network. Step 3: Use the final supervised fully connected neural network model to solve the conductivity distribution sequence of the object under test and perform image reconstruction according to the sequence. Preferably, in Step 1, a two-dimensional circular model is used in the field domain, triangular element meshing (6402 triangular elements) is performed, multiple sets of heart finite element benchmark models with different conductivity distributions are established, and the boundary electrode potential difference data is calculated by the forward algorithm. At the same time, an initial conductivity uniform distribution model (σ0 = 1 S / m) is set, and its potential difference is calculated as a reference benchmark; finally, the conductivity difference (Δσ) between the benchmark model and the initial model is used as the supervised learning target, and the potential difference difference (ΔV) is used as the network input to generate training sample pairs for the end-to-end inversion task. The construction of the inversion optimization objective function for thoracic heart imaging in Step 1 is specifically as follows: min Δm,R ||Δm - RΔd|| 2 In the above formula, Δm is the difference between the predicted model resistivity and the true resistivity; Δd is the difference between the predicted model and the true potential difference, aiming to minimize the difference between the resistivity difference at each iteration and the voltage difference under the R constraint. A new variable R is introduced into the above formula, and the objective function is obtained by the Lagrange multiplier method: Preferably, in Step 2, the preprocessing of the characteristic data is specifically as follows: Subtract the potential difference and conductivity under the initialized target model conductivity from the characteristic data described in Step 1, and perform hyperbolic tangent normalization to obtain a training set; according to the training set, use the method of convergence monitoring to train the model of the supervised neural network and update the training set to obtain the optimal solution of the network training parameters. In Step 2, only local information is updated during each iteration process, while the variable R described in Step 1 includes global information, which will consume a large amount of computing resources during the iteration process. Therefore, the objective function is divided into two parts: Training stage: Model error rms M is as follows: Prediction stage: S pr (Δm) = ||Δm - RΔd|| 2 In each iteration, it is necessary to check the data error and define the root mean square (rms) of the data error D as follows: Data error can be used to check whether the model in the current stage matches the inversion data. When the rms D diverges in the first few steps at the start of the prediction stage, the prediction should be stopped, as there may be a situation where the prediction model is completely different from the training model. If the data error of the currently predicted model is greater than the data error of the previous step, then the prediction stage should be stopped at this time, and the final prediction model should be the prediction model when the data error is the smallest. Preferably, the supervised fully connected neural network in Step 2 includes: an input layer, a processing module, and an output layer. The input layer of the supervised fully connected neural network in Step 2 is the difference Δd (dimension 1×208) between the boundary potential differences of the true model and the initialized model obtained by solving the forward problem of the finite element in Step 1. The processing module of the supervised fully connected neural network in Step 2 is an improved multi-layer fully connected network. Preferably, the improved deep learning model in step 2 achieves high-precision conductivity inversion through a multi-layer fully connected network structure and an adaptive training strategy: the model adopts a multi-layer fully connected architecture. The first layer maps the input potential difference difference to a high-dimensional feature space. The middle layer mines non-linear associations through the LeakyReLU activation function (α = 0.2). The last layer outputs the normalized conductivity update amount after batch normalization and Tanh activation, and ensures that the output value is within the preset range [-1, 1]. Dropout with a dropout rate of 0.3 is introduced in the middle layer of the network to suppress overfitting, and batch normalization is used to accelerate convergence. During training, the Adam optimizer with an initial learning rate of 0.0001 and a weight decay of 0.0001 is adopted, combined with a stepped learning rate decay strategy that decays by half every 4 epochs to dynamically balance the convergence speed and accuracy. The smooth L1 loss is selected as the loss function, and the piecewise function (square loss when the error < 1, otherwise linear loss) is used to balance the robustness to outliers and the sensitivity to small errors, and finally achieve high-stability and high-generalization conductivity inversion. Through this structural design and the combined application of technologies, the model can effectively learn the complex patterns of the input data, thus achieving better performance in processing high-dimensional data and complex pattern recognition. The output layer of the supervised fully connected neural network in step 2 is the conductivity difference update amount Δm (dimension 1×6402). Preferably, in step 2, according to the updated potential difference difference, the fully connected network parameters are continuously iteratively updated, and the specific implementation is as follows: in the training phase of step 1, when the maximum number of iterations is reached or when rms M is small enough or no longer decreases, the training phase ends, and R1 to R k obtained in the training phase are stored. Preferably, in step 3, using the final supervised fully connected neural network model to solve the conductivity distribution sequence of the object under test, the specific implementation includes: preparing the forward potential difference data of a true model; then initializing a conductivity model with all 1s, and calculating its potential difference data through the forward calculation in step 1; taking the difference between the potential difference data of the true model and the initialized model to obtain Δd1, which is used as the input data of the supervised fully connected network in step 2, and obtaining an output data Δm1 of the conductivity update amount through the neural network parameters of R1, and adding it to the previous conductivity m1. The update formula is: m i+1 = m i + Δm i , i = 1, 2, ..., k - 1 Then, forward calculation is carried out to obtain the potential difference and the difference of potential differences as the new input data Δd prior , and the neural network parameters of R2 are input until the conductivity update amount Δm predicted by the neural network parameters of R k is obtained. Finally, the conductivity is updated for the last time to obtain the final predicted model conductivity sequence, and the reconstructed image of the model is obtained by the imaging algorithm. prior ​

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