A method for reconstructing myocardial transmembrane potentials based on deep learning and extended Kalman filtering

Abstract

This invention discloses a method for reconstructing myocardial transmembrane potentials (TMPs) based on deep learning and extended Kalman filtering. It effectively combines and improves deep learning with extended Kalman filtering for TMP reconstruction. Taking into full account the dynamic activation process of cardiomyocytes and the generalization ability of neural networks, a pioneering method for TMP reconstruction is proposed. This is the first time that an extended Kalman filtering-based neural network has been used for TMP reconstruction. The introduction of a deep EKFNet for TMP reconstruction overcomes the limitations of traditional Kalman filtering and extended Kalman filtering techniques. By extending the static TMP recovery model to a dynamic space and incorporating the dynamic activation process of cardiomyocytes, physiological fidelity is improved. Unlike methods that require specifying regularization parameters or adding a forward transition matrix H, the proposed method has good adaptability, a feature that will have a positive impact on clinical practice.

Description

Technical Field

[0001] This invention belongs to the field of electrophysiological analysis technology, specifically relating to a method for reconstructing myocardial transmembrane potentials based on deep learning and extended Kalman filtering. Background Technology

[0002] The transmembrane potential of the heart is the potential difference between the inside and outside of the myocardial cell membrane caused by changes in the conductivity of the membrane. Body surface potential (BSP) is the potential distribution of cardiac electrical information conducted through the body trunk to the body surface. The action potential of a single myocardial transmembrane potential (TMP) corresponds precisely to the QRS wave in the body surface potential. A single TMP represents the periodic electrical activity of a single cell in the heart, and the final manifestation of the electrical activity of all cardiac cells conducted to the body surface is the clinically measured ECG. TMP recovery has significant clinical implications for the diagnosis and treatment of common heart diseases, such as myocardial infarction and ectopic pacing. Clinical treatment requires detailed information about the lesion, such as the location, shape, and area of ​​the infarct scar, and the number and location of ectopic pacemakers. For each myocardial cell, the point at which the TMP rises rapidly can be considered the pacing point of that cell, and the point at which the TMP amplitude is highest can be considered the point at which infarction or ischemia has occurred. When the TMP of all cardiac tissues is known, the detailed situation of infarction or ectopic pacing can be accurately determined.

[0003] Reconstructing cardiac electrical activity from body surface potentials (TMPs) is an ill-posed inverse problem. Recent studies have shown that using physiological model constraints can effectively regulate these inverse problems when parameters and regularization forms are predefined based on prior knowledge. In the absence of such prior knowledge, the common practice is to assume values ​​frequently used in the literature, but this introduces errors into the model, ultimately affecting the model's reconstruction accuracy and robustness. Furthermore, most methods for reconstructing TMPs are static mappings, neglecting the inherent dynamic activation processes of cardiomyocytes during the cardiac cycle. Summary of the Invention

[0004] In view of the above, the present invention provides a method for reconstructing myocardial transmembrane potential based on deep learning and extended Kalman filtering, which can automatically, quickly and accurately reconstruct myocardial transmembrane potential using multi-lead body surface potential data.

[0005] This invention is achieved through the following technical solution:

[0006] This invention discloses a method for reconstructing myocardial transmembrane potentials based on deep learning and extended Kalman filtering, comprising the following steps:

[0007] 1) Collect patients' electrophysiological data, and use this data to simulate myocardial transmembrane potential information under various conditions. Perform multiple simulations on different case files to obtain a large number of samples, and then divide all samples into training and testing sets. Each set of samples includes multi-lead surface electrocardiogram data and corresponding myocardial transmembrane potential information.

[0008] 2) Construct a network model based on deep learning and extended Kalman filtering, which consists of the state transition equation STNet, the measurement equation MENet, and the extended Kalman gain equation KGNet from input to output;

[0009] 3) Use the multi-lead body surface electrocardiogram data in the training set samples obtained in step 1) as the model input, and the corresponding myocardial transmembrane potential information as the ground truth label. Use the loss function to train the network model built in step 2) to obtain a model for predicting myocardial transmembrane potential.

[0010] 4) Input the multi-lead body surface electrocardiogram data from the test set sample obtained in step 1) into the model trained in step 3) for predicting myocardial transmembrane potential, and the myocardial transmembrane potential can be directly predicted and output.

[0011] As a further improvement, the sample data in the experiment described in this invention is based on a personalized heart-trunk model of a real patient in ECGSIM software. By modifying the pacing time of the myocardial transmembrane potential, the amplitude and duration of the action potential, and the location, size and degree of the infarction area, different numbers of ectopic pacemakers at different locations and different degrees of infarction are simulated. At the same time, the corresponding body surface potential is obtained through the transformation matrix obtained by the boundary finite element method.

[0012] As a further improvement, the STNet described in this invention consists of three recurrent neural networks (GRUs) and a three-layer multilayer perceptron (MLP). The MENet consists of three n*n convolutional blocks and a three-layer MLP, where each convolutional block contains a convolutional layer, a batch normalization layer, and a ReLU activation layer. The KGNet consists of a concatenation operation and a three-layer MLP. The state transition equation is replaced by a recurrent neural network that performs well in time series modeling tasks, and the measurement equation is replaced by a convolutional neural network that performs well in high-dimensional space feature extraction tasks. The Jacobian matrix of the last few fully connected layers of STNet and MENet is calculated, and then concatenated with the observation φt and input together into the extended Kalman gain network to obtain the extended Kalman gain coefficient.

[0013] As a further improvement, the process of training the network model in step 3) of the present invention is as follows: First, initialize the model parameters, including the bias vector and weight matrix of each layer, the learning rate, and the optimizer; second, input the electrocardiogram data of the body surface in the training set samples into the model, the model forward propagates and outputs the corresponding prediction result, and calculate the loss function L between the prediction result and the label; finally, based on the loss function L, use the optimizer to iteratively update the model parameters using the gradient descent method until the loss function L converges, and the training is completed.

[0014] As a further improvement, when the network model is applied to reconstruct myocardial transmembrane potential function, the expression for the loss function L is as follows:

[0015]

[0016] x t This represents the true value of the cardiac transmembrane potential at time t. This represents the output of the STNet network. This represents the posterior estimate at time t, which is the final output of the network.

[0017] The beneficial effects of this invention are as follows:

[0018] This invention proposes a groundbreaking method for reconstructing transient myocardial cell (TMP) by addressing the dynamic activation process of cardiomyocytes and enhancing model generalization. The proposed EKF-based deep learning framework differs significantly from traditional methods, marking the first application of EKF neural networks for TMP reconstruction. This invention extends the static TMP recovery model to a dynamic space and incorporates the dynamic activation process of cardiomyocytes, improving physiological fidelity. Furthermore, this method's unique advantage lies in its broad applicability across diverse patient populations. Unlike methods that require specifying regularization parameters or incorporating a forward transition matrix H, the proposed method exhibits superior adaptability. This characteristic will have a positive impact on clinical practice, as evidenced by various real-world applications.

[0019] This invention proposes a Deep Extended Kalman Filter Network (EKFNet) to replace the traditional EKF method for TMP reconstruction. It extends the existing static TMP recovery model to a dynamic space and establishes a physiological model by further modeling the dynamic activation process of cardiomyocytes. Compared to other methods limited to individual cases, this method does not require setting regularization parameters or introducing a positive transfer matrix H, exhibiting high generalization and applicability to a wide range of patients. Therefore, this method demonstrates greater universality in clinical practice, providing effective treatment options or solutions for a wider range of patients. This advantage is expected to be reflected in multiple practical application scenarios. Simultaneously, this method better reflects the actual situation of TMP reconstruction, which is a nonlinear and ill-posed problem. Most current methods assume TMP reconstruction as a linear and ill-posed problem, using neural networks to fit the nonlinear state transition equations and measurement equations, achieving better experimental results. Finally, it provides a potential clinical tool for TMP recovery. Simulation and real-world experiments demonstrate that, compared to existing methods, this tool can achieve more accurate TMP recovery in a time-saving, stable, and low-cost manner. Attached Figure Description

[0020] Figure 1 This is a visualization analysis diagram of the simulation experiment of the ectopic pacing localization task of the present invention;

[0021] Figure 2 This is a visualization analysis diagram of the simulation experiment of myocardial infarction detection task according to the present invention;

[0022] Figure 3 This is a visualization analysis diagram of the ablation experiment results of the present invention;

[0023] Figure 4 This is a schematic flowchart of the myocardial transmembrane potential reconstruction method of the present invention;

[0024] Figure 5 This is a schematic diagram of the network model structure constructed in this invention;

[0025] Figure 6 This is a schematic diagram showing the details of each module in the model of this invention. Detailed Implementation

[0026] This invention discloses a method for reconstructing myocardial transmembrane potentials based on deep learning and extended Kalman filtering, comprising the following steps:

[0027] 1) Collect patients' electrophysiological data, simulate myocardial transmembrane potential information of patients under various conditions using this physiological data, and perform multiple simulations on different case files to obtain a large number of samples. Each sample includes multi-lead body surface electrocardiogram data and corresponding myocardial transmembrane potential information, and then divide all samples into training set and test set.

[0028] 2) Construct a network model based on deep learning and extended Kalman filtering, which consists of a state transition equation (STNet), a measurement equation (MENet), and an extended Kalman gain equation (KGNet) from input to output;

[0029] 3) Use the multi-lead body surface electrocardiogram data of the training set obtained in step 1) as the model input, and the corresponding myocardial transmembrane potential as the ground truth label. Use the loss function to train the network model built in step 2 to obtain a model for predicting myocardial transmembrane potential.

[0030] 4) Input the multi-lead body surface electrocardiogram data of the test set obtained in step 1) into the model trained in step 3, and the output myocardial transmembrane potential can be directly predicted.

[0031] The specific implementation process of step 1) is as follows: The simulation data in the experiment is based on a personalized heart-trunk model of a real patient in ECGSIM software. By modifying the pacing time of the myocardial transmembrane potential, the amplitude and duration of the action potential, and the location, size, and degree of the infarct area, different numbers of ectopic pacemakers at different locations and different degrees of infarction are simulated. At the same time, the corresponding body surface potential can be obtained through the transformation matrix obtained by the boundary finite element method. A total of 2000 sets of data were simulated, including 600 cases of ectopic pacing and 1400 cases of myocardial infarction. In the ectopic pacing localization task, 500 cases were used for model training and 100 cases were used for model testing. In each set of data, the size of BSP is (64, 530) and the size of TMP is (697, 530), where 64 represents the corresponding 64 leads of somatic cells, 697 represents the total 697 nodes on the heart, and 530 represents the sequence length in the time dimension within one cycle. Simultaneously, it was ensured that the ectopic pacing sites were not duplicated in all cases, and the fully activated TMP was set to 15mv, and the resting TMP was set to -85mv. In the myocardial infarction detection task, 1200 cases were used for model training, and 200 cases were used for model testing.

[0032] The specific implementation process of step 2) is as follows: STNet consists of three recurrent neural networks (GRUs) and a three-layer multilayer perceptron (MLP). MENet consists of three 3*3 convolutional blocks and a three-layer MLP, where each convolutional block contains a convolutional layer, a batch normalization layer, and a ReLU activation layer. KGNet consists of a concatenation operation and a three-layer MLP. Recurrent neural networks, which perform well in temporal modeling tasks, are used to replace the state transition equation, and convolutional neural networks, which perform well in high-dimensional feature extraction tasks, are used to replace the measurement equation. According to the extended Kalman update equation, the extended Kalman gain coefficient is related not only to the observation φt of frame t, but also to the first-order partial derivatives of the state transition equation and the measurement equation. First, the Jacobian matrix of the last few fully connected layers of STNet and MENet is calculated, and then concatenated with the observation φt and input into the extended Kalman gain network to obtain the extended Kalman gain coefficient.

[0033] The process of training the network model in step (3) is as follows: First, initialize the model parameters, including the bias vector and weight matrix of each layer, the learning rate and the optimizer; second, input the electrocardiogram data of the body surface in the training set samples into the model, the model forward propagates and outputs the corresponding prediction result, and calculate the loss function L between the prediction result and the label; finally, according to the loss function L, use the optimizer to iteratively update the model parameters through gradient descent until the loss function L converges, and the training is completed.

[0034] When the network model is applied to reconstruct myocardial transmembrane potential function, the expression for the loss function L is as follows:

[0035]

[0036] x t This represents the true value of the cardiac transmembrane potential at time t. This represents the output of the STNet network. This represents the posterior estimate at time t, which is the final output of the network.

[0037] To more clearly describe the present invention, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0038] like Figure 1 As shown, the myocardial transmembrane potential reconstruction method based on deep learning and extended Kalman filtering of this invention includes the following steps:

[0039] S1. Import the physiological data of the case patients and use modeling and simulation software to obtain simulation data.

[0040] Patient case files constructed using the finite element method were imported into the cardiac modeling and simulation software ECGSIM. The location of the simulated ventricular activation source point was selected by clicking with the mouse. Simultaneously, the activation time, action potential amplitude, excitation duration, and resting potential value of the transmembrane potential at each node of the heart were adjusted to simulate various arrhythmias. Simulated multi-lead ECG data and corresponding myocardial transmembrane potentials were obtained using MATLAB software. A total of 2000 sets of data were simulated, including 600 cases of ectopic pacing and 1400 cases of myocardial infarction, in .mat format. In the ectopic pacing localization task, 500 cases were used for model training, and 100 cases were used for model testing. In each set of data, the BSP size was (64, 530), and the TMP size was (697, 530), where 64 represents the corresponding 64 somatic leads, 697 represents the total 697 nodes on the heart, and 530 represents the sequence length in the time dimension within one cycle. Simultaneously, it was ensured that the ectopic pacing sites were not duplicated in all cases, and the fully activated TMP was set to 15mv, and the resting TMP was set to -85mv. In the myocardial infarction detection task, 1200 cases were used for model training, and 200 cases were used for model testing.

[0041] S2. Build a network model based on deep learning and extended Kalman filtering.

[0042] Similar to KF, EKF also consists of five formulas, but its state transition model and observation model are nonlinear, which is consistent with the actual situation of the TMP reconstruction problem. Its formula is:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] Where f and h are the nonlinear state transition equation and measurement equation, respectively, where A t and H t Q' and R' are the first-order partial derivatives of the functions f and h with respect to the state variables, expressed in the form of Jacobian matrices. Q' and R' are the process noise covariance matrix and the observation noise covariance matrix, respectively.

[0049] According to physiological modeling, both the state transition equation and the measurement equation are nonlinear and cannot be locally linearized. Due to the strong nonlinear mapping capability of neural networks, they are innovatively used to replace the equations. The structure of the EKFNet network is shown in the figure. EKFNet mainly consists of the state transition equation (STNet), the measurement equation (MENet), and the Kalman gain equation (KGNet), as shown in the figure. Specifically, STNet consists of three GRUs and a three-layer multilayer perceptron (MLP). MENet consists of three 3*3 convolutional blocks with residual union and a three-layer MLP, where each convolutional block contains a convolutional layer, a batch normalization layer, and a real activation layer. KGNet consists of connection operations and a three-layer MLP. Since the state transition equation is highly correlated with the dynamic activation process of cardiomyocytes, the gate recurrent unit (GRU), which performs well in time modeling tasks, is used to replace the state transition equation.

[0050] In contrast, the measurement equation is primarily related to a high-dimensional spatial mapping of cardiac potentials and body surface potentials. Therefore, a CNN, which performs well in high-dimensional feature extraction tasks, was used instead of the measurement equation. As can be seen from the Kalman update equation, the Kalman gain coefficient is not only related to the observation value z in frame t... t This is related to the first-order partial derivatives of the state transition equation and the measurement equation. Therefore, we first calculate the Jacobian matrices of the last few fully connected layers of STNet and MENet, and then combine them with the concatenated observation z. t The Kalman gain coefficients are obtained by inputting them into the Kalman gain network.

[0051] Finally, the network can be represented by the following three equations:

[0052]

[0053] K = KGNet(A, H,)

[0054]

[0055] To ensure the accuracy of the state transition equations and the final reconstruction results, a constraint loss function is set. The loss function is designed as the superposition of these two partial loss functions:

[0056]

[0057] x t This represents the true value of the cardiac transmembrane potential at time t. This represents the output of the STNet network. This represents the posterior estimate at time t, which is the final output of the network.

[0058] S3. Train the network model.

[0059] First, initialize the model parameters, including the bias vector and weight matrix of each layer, the learning rate, and the optimizer. Second, input the surface electrocardiogram data from the training set samples into the model, and the model outputs the corresponding prediction result through forward propagation. Calculate the loss function L between the prediction result and the label. Finally, based on the loss function L, use the optimizer to iteratively update the model parameters using gradient descent until the loss function L converges, and the training is complete.

[0060] S4. Input the signal to be tested, and obtain the myocardial transmembrane potential through the model.

[0061] The prediction results of this invention are measured by three evaluation metrics: 1) Correlation coefficient (CC): It describes the degree of linear correlation between the true value and the prediction result; 2) Structural similarity (SSIM): It evaluates the structural similarity between the real image and the reconstructed image, i.e. the real ectopic pacing image and the reconstructed ectopic pacing image; 3) Location error (LE): It evaluates the location accuracy of ectopic pacing by calculating the Euclidean distance.

[0062] Table 1 and Figure 1 Quantitative and visual analysis of ectopic pacing simulation experiments: Table 1 shows the quantitative analysis of five methods in ectopic pacing cases. It can be seen from the table that the reconstruction results of Tikhonov, TV, and VAEnet are inferior to EKFNet. Notably, compared to KFNet, EKFNet has higher CC, SSIM, and lower LE, while KFNet introduces a system transfer matrix during training, which EKFNet does not. Qualitative three-dimensional spatial reconstruction visualization analysis is shown in [link to table]. Figure 1 As shown in the figure, red indicates high potentials, and the red areas represent the earliest activated parts, which can be considered ectopic pacemakers, while the blue areas represent areas that are not yet activated. The figure shows that EKFNet is closest to the true value in terms of activation location, activated tissue, and boundary details, which is very helpful in clinical diagnosis requiring more accurate information about ectopic pacemakers. Cases 1 and 2 show that neither the Tikhonov nor TV methods can clearly reconstruct the wavefront conduction region, losing much detail at the boundaries and exhibiting artifacts in other non-activated areas. The color depth indicates that the TV method incorrectly captures the activation time of the earliest node, while the VAE method performs better, but the wavefront shape is still not close enough to the true value. KFNet's reconstruction is very close to the true value, but its edge details and activation time capture are still inferior to EKFNet.

[0063]

[0064] Table 1

[0065] Table 2 and Figure 2 Quantitative and visualization analysis of a simulation experiment for myocardial infarction detection: This experiment mainly verifies the reconstruction effect of the algorithm proposed in this chapter on infarct scars of different degrees and locations. The three-dimensional spatial reconstruction of TMP can reveal low-pressure areas on the heart. When abnormally low-pressure areas appear during cardiac electrical activity conduction, it can be preliminarily identified as ischemic infarct tissue. Five different methods were used to reconstruct infarct scars of two different locations and degrees. The visualization results are as follows: Figure 2 As shown, the regularization terms used in the Tikhonov and TV methods do not fully adapt to the prior information of the TMP spatiotemporal distribution, resulting in significant discrepancies between the reconstructed infarct scar and the ground truth. In cases 3 and 4, the infarct area is not clearly defined using the Tikhonov method, and the reconstruction is not smooth enough. The TV method does not closely match the ground truth in terms of infarct scar area and shape, leading to an overly large and downward-shifted infarct area in cases 3 and 4. The VAE and KF methods outperform traditional methods, but both suffer from inaccurate infarct scar shape. The proposed EKF method, however, exhibits good noise adaptability, clearly reconstructing the infarct core location, infarct scar, and ischemic region.

[0066]

[0067] Table 2

[0068] Table 3 and Figure 3 The ablation experiments of the method presented in this invention demonstrate that each module of the model has a positive impact on reconstruction accuracy. The ablation study compares EKF with STNet, and the comparison results are as follows... Figure 3 As shown in the figure, the network EKF with Kalman gain reconstructs the TMP signal faster and more accurately, indicating that Kalman gain is indispensable. Finally, the structural similarity (SSIM) and relative error (RE) between the results and the ground truth were calculated to quantitatively measure the reconstruction effect, as shown in Table 3. The results show that the Kalman gain coefficients learned by the network can improve the reconstruction accuracy of the TMP signal. This experiment verifies the effectiveness of the proposed method of improving TMP signal reconstruction by learning Kalman gain coefficients through the network.

[0069]

[0070] Table 3

[0071] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. Those skilled in the art can readily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for reconstructing myocardial transmembrane potentials based on deep learning and extended Kalman filtering, comprising the following steps: 1) Collect patients' electrophysiological data, and use this data to simulate myocardial transmembrane potential information under various conditions. Perform multiple simulations on different case files to obtain a large number of samples, and then divide all samples into training and testing sets. Each set of samples includes multi-lead surface electrocardiogram data and corresponding myocardial transmembrane potential information. 2) Construct a network model based on deep learning and extended Kalman filtering, which consists of the state transition equation STNet, the measurement equation MENet, and the extended Kalman gain equation KGNet from input to output; 3) Use the multi-lead body surface electrocardiogram data in the training set samples obtained in step 1) as the model input, and the corresponding myocardial transmembrane potential information as the ground truth label. Use the loss function to train the network model built in step 2) to obtain a model for predicting myocardial transmembrane potential. 4) Input the multi-lead electrocardiogram data from the test set sample obtained in step 1) into the model trained in step 3) for predicting myocardial transmembrane potential, and the myocardial transmembrane potential can be directly predicted and output.

2. The method for myocardial transmembrane potential reconstruction according to claim 1, characterized in that: The sample data in the experiment were based on personalized heart-truncation models of real patients in ECGSIM software. By modifying the pacing time of myocardial transmembrane potential, the amplitude and duration of action potential, and the location, size and degree of infarction area, different numbers of ectopic pacemakers in different locations and different degrees of infarction were simulated. At the same time, the corresponding body surface potentials were obtained through the transformation matrix obtained by the boundary finite element method.

3. The method for myocardial transmembrane potential reconstruction according to claim 1, characterized in that: The STNet consists of three recurrent neural networks (GRUs) and a three-layer multilayer perceptron (MLP). The MENet consists of three n*n convolutional blocks and a three-layer MLP, where each convolutional block contains a convolutional layer, a batch normalization layer, and a ReLU activation layer. The KGNet consists of a concatenation operation and a three-layer MLP. Recurrent neural networks, which perform well in time series modeling tasks, are used to replace the state transition equations, and convolutional neural networks, which perform well in high-dimensional space feature extraction tasks, are used to replace the measurement equations. The Jacobian matrix of the last few fully connected layers of STNet and MENet is calculated, and then concatenated with the observation φt and input together into the extended Kalman gain network to obtain the extended Kalman gain coefficients.

4. The method for myocardial transmembrane potential reconstruction according to claim 1, 2, or 3, characterized in that: The process of training the network model in step 3) is as follows: First, initialize the model parameters, including the bias vector and weight matrix of each layer, the learning rate, and the optimizer; second, input the electrocardiogram data of the body surface in the training set samples into the model, and the model outputs the corresponding prediction result through forward propagation, and calculate the loss function L between the prediction result and the label; finally, based on the loss function L, use the optimizer to iteratively update the model parameters using the gradient descent method until the loss function L converges, and the training is completed.

5. The method for myocardial transmembrane potential reconstruction according to claim 4, characterized in that: When the network model is applied to reconstruct myocardial transmembrane potential function, the expression for the loss function L is as follows: This represents the true value of the myocardial transmembrane potential at time t. This represents the output of the STNet network. This represents the posterior estimate at time t, which is the final output of the network.

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