A method for solving the inverse electrocardiogram problem based on neural networks

Abstract

This invention discloses a method for solving the inverse electrocardiogram (ECG) problem based on neural networks. The method includes the following steps: acquiring the three-dimensional geometric information of a cardiac source model and constructing an ECG dataset containing surface potentials and transmembrane potentials; dividing the dataset into training and test sets and preprocessing the data; constructing a neural network model using a bidirectional long short-term memory (BiLSTM) network and setting and optimizing the network parameters; training the constructed neural network model using the training set; performing simulation predictions on the trained model using the test set to achieve inverse reconstruction of cardiac potentials; evaluating and analyzing the results, and visualizing the results. This method effectively solves the ill-posedness problem in the inverse ECG problem through the deep learning capabilities of the neural network model, providing higher reconstruction accuracy and offering important technical support for the precise diagnosis and treatment of heart diseases.

Description

Technical Field

[0001] This disclosure relates to the field of cardiac electrophysiological imaging, specifically to a method for solving inverse cardiac electrophysiological problems based on neural networks. Background Technology

[0002] Cardiovascular disease has become a leading cause of death worldwide, especially in my country, where the incidence and mortality rates continue to rise. The electrical activity of the heart is closely related to its health, and cardiac potential reconstruction technology, by analyzing surface electrocardiogram signals, infers the spatial distribution of electrical activity within the heart, providing important evidence for the diagnosis and treatment of heart diseases.

[0003] In clinical practice, the traditional 12-lead electrocardiogram (ECG) is widely used for the diagnosis of cardiovascular diseases. By analyzing the electrical signal characteristics in the ECG, doctors can judge the patient's heart condition based on experience. However, ECG can only provide information on local electrical activity and is easily affected by noise in the body and sparse electrode distribution, which limits its diagnostic accuracy and scope.

[0004] To address this limitation, cardiac electrophysiological imaging (ECGI) has garnered significant attention. ECGI technology acquires omnidirectional surface potential signals by deploying multiple electrodes (typically more than 64) on the body surface and, combined with a geometric model of the heart and trunk, reconstructs the distribution of electrical activity within the heart. Compared to traditional electrocardiography (ECG), ECGI provides more detailed and accurate images of electrical activity, thus enabling better localization and diagnosis of complex cardiac diseases such as arrhythmias.

[0005] However, due to the complex structure of the heart, the inverse electrocardiogram problem exhibits significant ill-posedness. Traditional solution methods, such as direct regularization and iterative regularization, often require the introduction of additional constraints to improve the stability of the solution. However, these methods are extremely sensitive to parameter selection, have high computational complexity, and limited generalization ability, making them unsuitable for clinical applications.

[0006] With the development of artificial intelligence technology, machine learning and deep learning have demonstrated powerful capabilities in solving complex nonlinear problems. In recent years, researchers have attempted to apply deep learning to solve the inverse electrocardiogram (ECG) problem. By treating the ECG inverse problem as a nonlinear regression problem, they have used neural networks such as BiLSTM to build predictive models. Compared with traditional methods, deep learning methods can automatically extract complex features from data and exhibit stronger generalization ability and stability under large-scale data training, thus providing more accurate inverse reconstruction results. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this disclosure is to provide a neural network-based method for solving the inverse electrocardiogram (ECG) problem. This method effectively solves the ill-posedness of the ECG inverse problem by introducing a bidirectional long short-term memory (BiLSTM) network, achieving high-precision reconstruction of the internal electrical activity of the heart, and providing technical support for the diagnosis and treatment of heart diseases.

[0008] To achieve the above objectives, this disclosure provides the following technical solutions:

[0009] A method for solving the inverse electrocardiogram problem based on neural networks includes the following steps:

[0010] S100: Acquire the three-dimensional geometric information of the cardiac source model and the electrocardiogram data of a normal heart in one cycle;

[0011] S200: Construct an ECG dataset based on the ECG data, divide it into a training set and a test set, and process the data;

[0012] S300: Construct a neural network model and set network parameters;

[0013] S400: The neural network model is trained using a training set, and the model parameters are optimized during the training process to improve prediction accuracy;

[0014] S500: Uses a test set to simulate and predict the trained neural network model, achieving reverse reconstruction of cardiac potential;

[0015] S600: Evaluate the prediction results, generate a comparison chart of the reconstructed waveform of the heart node and the real waveform, and visualize the electrocardiogram signal.

[0016] Preferably, in step S100, the electrocardiogram data is clinical data collected by the research team of Thomas Berger at the Medical University of Innsbruck, Austria, obtained through the official website of the ECGSIM software.

[0017] Furthermore, the electrocardiogram data includes body surface potentials (BSP) and transmembrane potentials (TMP).

[0018] A normal heart cycle lasts 505ms, and the simulation step size is 1ms. Among them, BSP is an electrical signal measured on the human body surface through 64 electrode patches, and TMP reflects the difference in potential between the inside and outside of the myocardial cell membrane at 257 nodes in the heart.

[0019] Preferably, the ECG dataset is constructed by changing the waveform of the cardiac source signal and using different surface lead signals generated by ECGSIM, expanding to a dataset containing BSP (64×3030) and TMP (257×3030) in 6 groups.

[0020] Preferably, in step S200, the dataset is divided by sampling electrical activity information at 1ms intervals. Specifically, a test set is formed by taking 1ms of sample data every 4ms, totaling 606ms, and a training set is formed by taking the remaining 4ms of sample data, totaling 2424ms. Furthermore, the divided data is normalized and scaled to the range [0,1] for better training and prediction.

[0021] Preferably, in step S300, the neural network model is built based on BiLSTM, and the specific construction process and parameter setting process are as follows:

[0022] S301: Establish an input layer to receive preprocessed BSP data; establish a bidirectional LSTM layer to handle bidirectional dependencies in time series data; add a ReLU activation layer to introduce nonlinearity, helping the network capture complex patterns in the data while avoiding the vanishing gradient problem; establish a fully connected layer to map features to the output space; establish a regression layer to handle regression tasks and calculate the network's loss.

[0023] S302: Set training options, using the Adam optimizer for gradient descent; to prevent overfitting, use the Dropout function to randomly drop a certain percentage of neurons during training, with a dropout rate set to 0.5; to prevent gradient explosion, set the gradient threshold to 1, specify an initial learning rate of 0.001, and use a segmented learning rate adjustment strategy, reducing the learning rate by multiplying by a factor of 0.5 after 300 training iterations; use a validation set to help monitor model performance during training, performing validation every 50 iterations; add data shuffling to reduce the model's tendency to learn patterns between batches and improve the model's generalization ability.

[0024] Preferably, in step S600, the evaluation of the prediction results includes using the coefficient of determination (R²) and the mean absolute error (MAE).

[0025] Preferably, the coefficient of determination (R²) for the evaluation index is defined as follows:

[0026] ,

[0027] In the formula, This represents the true value of the cardiac transmembrane potential. This represents the average transmembrane potential of the heart. This is a predicted value for cardiac transmembrane potential.

[0028] Preferably, the mean absolute error (MAE) is defined as follows:

[0029]

[0030] In the formula, This represents the true value of the cardiac transmembrane potential. This is a predicted value for cardiac transmembrane potential.

[0031] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0032] The method described in this disclosure can accurately solve the inverse problem of electrocardiography based on neural networks. It has significant advantages in terms of the accuracy of solving the inverse problem, the generalization ability of the model, and the processing of complex electrical signals, providing a strong guarantee for the accurate diagnosis and treatment of heart diseases.

[0033] The features and advantages of this invention can be specifically reflected in the following three aspects:

[0034] (1) This invention is based on neural network technology, especially Bidirectional Long Short-Term Memory (BiLSTM) network, which effectively extracts spatial and temporal features from cardiac electrical signals by training a large amount of ECG data. Compared with traditional regularization methods (such as Tikhonov regularization and L-curve regularization), BiLSTM has stronger nonlinear fitting ability and temporal dependence characteristics, and can more accurately infer the distribution of electrical activity inside the heart when dealing with the inverse ECG problem. Traditional regularization methods often rely on the selection of regularization parameters by adding regularization terms to the objective function. Their performance varies on different datasets, the computational complexity is high, and they may have insufficient generalization ability when dealing with noise. However, through deep learning, especially BiLSTM network, key features can be automatically extracted from the complex mapping relationship between body surface potential and epicardial potential, reducing the dependence on manually set parameters, significantly improving the solution accuracy of the inverse ECG problem, and the performance is particularly significant on large-scale datasets.

[0035] (2) Traditional methods are prone to performance degradation when processing complex cardiac electrical signals due to lack of definiteness. This invention, by employing a deep learning model, especially the bidirectional information processing mechanism of BiLSTM, can maintain high generalization ability when facing different pathological conditions, ensuring stability and accuracy in clinical applications.

[0036] (3) After solving the inverse electrocardiogram problem, this invention combines a three-dimensional geometric model and uses visualization technology to intuitively present the spatial distribution and changes in cardiac electrical activity. This visualization function not only helps researchers better understand the mechanism of cardiac electrical activity, but also provides clinicians with an intuitive auxiliary diagnostic tool, improving the accuracy and efficiency of diagnosis. Attached Figure Description

[0037] Figure 1 This is a flowchart of a method for solving the inverse electrocardiogram problem based on a neural network, provided in one embodiment of this disclosure;

[0038] Figure 2 This is a panel schematic diagram of obtaining a cardiac source geometric model and electrocardiogram dataset using ECGSIM software according to another embodiment of this disclosure;

[0039] Figure 3 This is a waveform diagram of the potential of lead 30 and the transmembrane potential of the heart node 30 in a summary electrocardiogram data table provided in another embodiment of this disclosure;

[0040] Figure 4 This is a schematic diagram of the Bidirectional Long Short-Term Memory (BiLSTM) network structure provided in another embodiment of this disclosure;

[0041] Figure 5 This is a comparison diagram of the reconstructed waveform of the 150th node of the heart and the actual waveform provided in another embodiment of this disclosure;

[0042] Figure 6 This is a three-dimensional visualization of the reconstructed cardiac transmembrane potentials at different test time points provided by Map3D in another embodiment of this disclosure. Detailed Implementation

[0043] The following will refer to the appendix. Figures 1 to 6 Specific embodiments of this disclosure are described in detail. While specific embodiments of this disclosure are shown in the accompanying drawings, it should be understood that this disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of this disclosure to those skilled in the art.

[0044] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out this disclosure; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of this disclosure. The scope of protection of this disclosure is determined by the appended claims.

[0045] To facilitate understanding of the embodiments of this disclosure, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of this disclosure.

[0046] This disclosure provides a method for solving the inverse electrocardiogram (ECG) problem based on neural networks. The method uses ECGSIM to obtain a clinical data set as input and then solves the ECG inverse problem based on a BILSTM neural network.

[0047] In one embodiment, such as Figure 1 As shown, a method for solving the inverse electrocardiogram problem based on neural networks includes the following steps:

[0048] S100: Acquires three-dimensional geometric information of the cardiac source model and body surface potential (BSP) and transmembrane potential (TMP) data of a normal heart in one cycle using ECGSIM software;

[0049] S200: Construct an ECG dataset based on the acquired BSP and TMP data, divide the data into training and test sets, and normalize the data by scaling it to [0,1] for better training and prediction.

[0050] S300: A neural network model is constructed based on a bidirectional long short-term memory network (BiLSTM), and the network parameters are set.

[0051] S400: The neural network model is trained using the training set. During training, various optimization strategies are used to continuously adjust the model parameters to improve prediction accuracy. In the initial training phase, the model structure is simple, using default parameters (SGD optimizer, fixed learning rate 0.01, batch size 32, no Dropout layer, no gradient threshold). At this point, the model's mean absolute error (MAE) is 2.76 ± 0.69 mV, and the coefficient of determination (R²) is 93.6 ± 1.37%. The model can perform basic reconstruction of cardiac potentials, but its ability to capture complex temporal features is weak. Through optimization strategies, the optimizer is switched to the Adam optimizer, the initial learning rate is set to 0.001, and a piecewise learning rate adjustment strategy is adopted (decreasing by 50% every 300 epochs). Furthermore, to prevent gradient explosion, a gradient threshold of 1 is set. The batch size is adjusted to 20, and the Dropout function is introduced with a dropout rate of 0.5. After optimization, the mean absolute error (MAE) of the model decreased to 0.79 ± 0.139 mV, and the coefficient of determination (R²) increased to 99.91 ± 0.05%. During the optimization process, performance was monitored on the validation set every 50 iterations to ensure the model maintained high prediction accuracy across different datasets.

[0052] S500: Uses a test set to simulate and predict the trained neural network model, achieving reverse reconstruction of cardiac potential;

[0053] S600: The prediction results are evaluated using the coefficient of determination (R²) and mean absolute error (MAE), a comparison chart of the reconstructed waveform of the heart node and the real waveform is generated, and the ECG signal is visualized using Map3D software.

[0054] The above embodiments constitute the complete technical solution of this disclosure. The method described in this embodiment can quickly and effectively solve the electrocardiogram inverse problem and reconstruct the internal electrical activity of the heart through a bidirectional long short-term memory network. It has significant advantages in terms of accuracy and stability, providing a more reliable technical means for the diagnosis and treatment of cardiovascular diseases.

[0055] In another embodiment, clinical data collected by Thomas Berger's research team at the Medical University of Innsbruck, Austria, was obtained through the ECGSIM software website. ECGSIM is based on an equivalent surface source model, which posits that the potential generated by the heart on the body surface is entirely determined by the transmembrane potential of the myocardium. Figure 2 As shown, using ECGSIM software, the three-dimensional geometric information of the cardiac source model and the BSP (64*505) and TMP (257*505) data of a normal heart in one cycle (505ms, simulation step size 1ms) were successfully acquired. BSP is the electrical signal measured on the human body surface using 64 electrode patches, while TMP reflects the difference in potential across the myocardial cell membrane at 257 nodes in the heart. To further enrich the dataset, different surface lead signals were generated by changing the waveform of the cardiac source signal using ECGSIM, and then merged and extended to 3030ms, constructing an ECG dataset containing BSP (64×3030) and TMP (257×3030). The waveforms of the potential of lead 30 and the transmembrane potential of the 30th node in the heart, as shown in the table below, are also included. Figure 3 As shown.

[0056] In another embodiment, the dataset is divided, and electrical activity information is sampled at 1ms intervals. A test set is formed by taking 1ms of sample data every 4ms (606ms total), and a training set is formed by taking the remaining 4ms (2424ms total). The divided data is then normalized and scaled to the range [0,1] for better training and prediction.

[0057] It should be noted that the normalization operation is implemented through the following program, an example of which is shown below:

[0058] %% Data normalization

[0059] [p_train, ps_input] = mapminmax(P_train, 0, 1); % Normalize the input training set, scaling it to the [0, 1] interval.

[0060] p_test = mapminmax('apply', P_test, ps_input); % Normalize the input test set using the same normalization parameters as the training set.

[0061] [t_train, ps_output] = mapminmax(T_train, 0, 1); % Normalizes the output training set, scaling the output data to the [0, 1] interval.

[0062] t_test = mapminmax('apply', T_test, ps_output); % Normalize the output test set using the same normalization parameters as the training set.

[0063] In another embodiment, a BiLSTM neural network model is constructed, and the network structure is as follows: Figure 4 As shown, the setup process and parameter setting process are as follows:

[0064] An input layer is built to receive preprocessed BSP data; a bidirectional LSTM layer is built to handle the bidirectional dependencies of the time series; a ReLU activation layer is added to introduce nonlinearity, helping the network capture complex patterns in the data while avoiding the gradient vanishing problem; a fully connected layer is built to map features to the output space; and a regression layer is built to handle regression tasks and calculate the network's loss.

[0065] In this example, training options are set, using the Adam optimizer for gradient descent; to prevent overfitting, the Dropout function is used to randomly drop a certain percentage of neurons during training, with a dropout rate set to 0.5; to prevent gradient explosion, the gradient threshold is set to 1, the initial learning rate is specified as 0.001, and a segmented learning rate adjustment strategy is used, reducing the learning rate by multiplying by a factor of 0.5 after 300 training iterations; a validation set is used during training to help monitor the model's performance, with validation performed every 50 iterations; data shuffling is added to reduce the model's tendency to learn patterns across batches, improving the model's generalization ability.

[0066] It should be noted that the BiLSTM neural network is built using the following program, an example of which is shown below:

[0067] %% Create Model

[0068] layers = [

[0069] sequenceInputLayer(inputSize) % Input layer

[0070] bilstmLayer(500, 'OutputMode', 'sequence') % BiLSTM layer

[0071] dropoutLayer(0.5) % Dropout layer

[0072] reluLayer % ReLU activation layer

[0073] fullyConnectedLayer(outputSize) % Fully connected layer

[0074] regressionLayer]; % Regression layer

[0075] %% Parameter Settings

[0076] options = trainingOptions('adam', ... % Adam optimizer)

[0077] 'MaxEpochs', 900, ... % Maximum number of iterations

[0078] 'InitialLearnRate', 0.001, ... % Initial learning rate adjusted to 0.001

[0079] 'LearnRateSchedule', 'piecewise', ... % Segmented learning rate adjustment

[0080] 'LearnRateDropFactor', 0.5, ... % Learning rate decrease factor

[0081] 'LearnRateDropPeriod', 300, ... % Learning rate drop period

[0082] 'ValidationData', {p_test, t_test}, ...% Validation dataset

[0083] 'ValidationFrequency', 50, ... % Validation frequency

[0084] 'MiniBatchSize', 20, ... % Mini-batch size

[0085] 'GradientThreshold', 1, ... % Gradient threshold

[0086] 'Shuffle', 'every-epoch', ... % Shuffle the data after each epoch.

[0087] 'Plots', 'training-progress', ... % Plot the training progress curves.

[0088] 'Verbose', false); % Suppress verbose output

[0089] In another embodiment, a BiLSTM network architecture is trained using a predefined network structure and training options based on a training set. This is achieved using the `trainNetwork` function in MATLAB, specifically designed for training deep learning networks. After training, the trained neural network model `net` is simulated and predicted using a test set to achieve inverse reconstruction of cardiac potentials. After the simulation prediction is completed, the prediction results are denormalized to ensure that the model's output has the same scale and range as the actual data, facilitating practical applications or further analysis.

[0090] It should be noted that the BiLSTM neural network achieves model training, simulation prediction, and data inverse normalization through the following procedure, as shown in the example below:

[0091] %% Training Model

[0092] net = trainNetwork(p_train, t_train, layers, options);

[0093] %% Simulation Prediction

[0094] t_sim1 = predict(net, p_train);

[0095] t_sim2 = predict(net, p_test );

[0096] %% Data denormalization

[0097] T_sim1 = mapminmax('reverse', t_sim1, ps_output);

[0098] T_sim2 = mapminmax('reverse', t_sim2, ps_output);

[0099] In another embodiment, the model reconstruction results are evaluated and analyzed. The evaluation metrics, coefficient of determination (R²) and mean absolute error (MAE), are defined as follows:

[0100]

[0101]

[0102] In the formula, This represents the true value of the cardiac transmembrane potential. This represents the average transmembrane potential of the heart. This represents the predicted transmembrane potential for the heart. The determination coefficient of BiLSTM is used for the entire heart. The value is 99.91 ± 0.05%, close to 1, with a mean absolute error. The value is 0.79±0.139mV, which is close to 0, indicating that the BiLSTM algorithm effectively realizes the reverse reconstruction of cardiac potential.

[0103] In addition, a comparison diagram of the reconstructed waveform of the cardiac node and the real waveform is generated, such as... Figure 5 As shown, a comparison diagram of the reconstructed waveform and the true waveform of the 150th node of the heart is given. As can be seen from the figure, the resting potential of the reconstructed waveform is close to -80mV, and the peak value of the action potential of the reconstructed waveform is slightly less than 20mV, which is in line with the theoretical level. Moreover, the amplitude of the BiLSTM reconstructed potential basically coincides with the true value, indicating that the BiLSTM algorithm has a good reconstruction effect.

[0104] Simultaneously, combining the three-dimensional geometric information of the cardiac origin model with TMP predicted and actual values, Map3D software was used to visualize the electrocardiogram signals, such as... Figure 6 As shown, the transmembrane potentials of the heart at four time points—235ms, 260ms, 267ms, and 272ms—are visualized. The figure shows that the inverse reconstruction effect of the BiLSTM algorithm is very close to the real situation.

[0105] The foregoing general description of the invention and its specific embodiments should not be construed as a limitation on the technical solution of the invention. Those skilled in the art, based on the disclosure of this application, can add, reduce, or combine the disclosed technical features in the foregoing general description and / or specific embodiments (including examples) without departing from the constituent elements of the invention, to form other technical solutions within the scope of protection of this application.

Claims

1. A method for solving the inverse electrocardiogram problem based on neural networks, characterized in that, The method includes the following steps: S100: Acquire the three-dimensional geometric information of the cardiac source model and the electrocardiogram data of a normal heart in one cycle; S200: Construct an ECG dataset based on the ECG data, divide it into a training set and a test set, and process the data; S300: Construct a neural network model and set network parameters; S400: The neural network model is trained using a training set, and the model parameters are optimized during the training process to improve prediction accuracy; S500: Uses a test set to simulate and predict the trained neural network model, achieving reverse reconstruction of cardiac potential; S600: Evaluate the prediction results, generate a comparison chart of the reconstructed waveform of the heart node and the real waveform, and visualize the electrocardiogram signal; in, In step S100, the electrocardiogram data includes body surface potentials and transmembrane potentials; The body surface potential is an electrical signal measured on the human body surface using a 64-electrode patch. The transmembrane potential reflects the difference in potential across the membrane of myocardial cells at 257 nodes in the heart. In step S600, evaluating the prediction results includes using the coefficient of determination R. 2 and mean absolute error (MAE); Evaluation index coefficient of determination R 2 The definition is as follows: ； In the formula, This represents the true value of the cardiac transmembrane potential. This represents the average transmembrane potential of the heart. This is a predicted value for cardiac transmembrane potential. The Mean Absolute Error (MAE) is defined as follows: ； In the formula, This represents the true value of the cardiac transmembrane potential. This is a predicted value for cardiac transmembrane potential. The method is based on neural networks to accurately solve the inverse electrocardiogram problem; Bidirectional Long Short-Term Memory (BiLSTM) networks based on neural network technology can effectively extract spatial and temporal features from cardiac electrical signals by training a large amount of electrocardiogram data. After solving the inverse electrocardiogram problem, the spatial distribution and changes of cardiac electrical activity are visually presented through visualization technology, using a three-dimensional geometric model.

2. The method for solving the inverse electrocardiogram problem based on neural networks according to claim 1, characterized in that, In step S100, one cycle is 505ms.

3. The method for solving the inverse electrocardiogram problem based on neural networks according to claim 1, characterized in that, The ECG dataset is a dataset containing body surface potentials and transmembrane potentials, constructed by expanding the waveform of the cardiac source signal and using different body surface lead signals generated by ECGSIM to six groups.

4. The method for solving the inverse electrocardiogram problem based on neural networks according to claim 1, characterized in that, In step S200, the data set is divided so that electrical activity information is sampled at 1ms intervals.

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