Heart electrophysiological imaging reconstruction method based on learnable descent algorithm

Abstract

The invention discloses a heart electrophysiological imaging reconstruction method based on a learnable descent algorithm, which can realize reconstruction from a body surface potential (BSP) to a myocardial transmembrane potential (TMP), and has a better regularization effect and can learn prior information in measured data compared with a traditional regularization method of an image level. In addition, compared with a method of directly replacing a regular term with a neural network, the method is higher in interpretability and has less parameter quantity, so that the method is very suitable for clinical application and higher in credibility. By performing myocardial transmembrane potential reconstruction on myocardial ischemia and ectopic pacing diseases, the superiority of the method is proved according to various evaluation indexes, and compared with other methods, the method is closer to a true value in the experiment process, and the reconstruction effect is more accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of electrocardiogram image reconstruction, and in particular relates to a cardiac electrophysiological imaging reconstruction method based on a learnable descent algorithm. Background Art

[0002] Heart disease is a common disease with high morbidity and mortality. Obtaining cardiac electrophysiological signals is very important for the diagnosis and treatment of heart disease. At present, modern clinical medicine can diagnose heart disease mainly in two ways: non-invasive and invasive. Invasive diagnosis can accurately diagnose the type of heart disease and locate the lesions of heart disease, but this invasive diagnostic method must place the instrument into the human body, which is harmful to the patient's health and has certain safety risks.

[0003] With the advancement of medicine, non-invasive electrocardiographic imaging (ECGI) technology has been developed. The ECG signal measured on the body surface is used as a direct mapping of the heart surface potential. The heart surface electrical signal is obtained by inverse reconstruction of multi-lead ECG signals and the heart trunk geometric model. Compared with invasive diagnosis, non-invasive ECG imaging has great clinical significance for improving the diagnosis and treatment of patients. The cardiac electrical signal obtained by ECGI is the myocardial transmembrane potential (TMP), which refers to the potential difference between the inside and outside of the heart cell membrane. The voltage measured on the body surface through the heart chest conductor model is the body surface potential (BSP), such as the standard 12-lead electrocardiographic (ECG) we are familiar with. Based on the 12-lead ECG observation, the doctor can preliminarily determine the type and location of the patient's cardiovascular disease. However, this judgment is based on the doctor's experience and knowledge and is not very accurate. Moreover, BSP is only an indirect measurement of the heart electrical signal and can only make a rough assessment of the heart state. TMP can show the infarct area and pacing location based on the voltage amplitude. Compared with TMP reconstruction imaging, TMP has more advantages in disease diagnosis.

[0004] Reverse reconstruction of the heart surface potential TMP through the body surface potential BSP belongs to the ECG inverse problem, but the number of nodes on the heart surface is much larger than the number of leads of the body surface potential. There will be infinite solutions, so it is an ill-conditioned inverse problem. When compressing TMP from high dimensions to low dimensions for reverse solution, information will inevitably be lost. More prior information needs to be introduced for solution. In solving the ECG inverse problem, common method frameworks are divided into three categories: 1. Based on traditional iterative optimization methods; 2. Data-driven deep learning methods; 3. Deep learning methods based on mathematical models.

[0005] The Tikhonov method is one of the most classic traditional regularization methods, which can obtain a rough solution. However, since it does not utilize the correlation between the frames of the myocardial transmembrane potential time series, the results obtained are usually too smooth and the information loss is too large, which is not conducive to the diagnosis of diseases. Variational Autoencoders (VAE) is a generative model that can learn the potential data distribution from a large number of data features, but lacks physiological model constraints and has high requirements for data quality and quantity. Summary of the invention

[0006] In view of the above, the present invention discloses a cardiac electrophysiological imaging reconstruction method based on a learnable descent algorithm (LDA), which can realize the reconstruction from body surface potential BSP to myocardial transmembrane potential TMP. Compared with the traditional image-level regularization method, the present invention has a better regularization effect and can learn the prior information in the measurement data. In addition, compared with the method of directly replacing the regularization term with a neural network, the present invention is more interpretable and has fewer parameters, so it is very suitable for clinical applications and has higher credibility.

[0007] The present invention is achieved through the following technical solutions:

[0008] The present invention discloses a cardiac electrophysiological imaging reconstruction method based on a learnable descent algorithm, comprising the following steps:

[0009] 1) Obtain data pairs of myocardial transmembrane potential TMP and body surface potential BSP for training and divide them into training set and test set;

[0010] 2) Based on the mathematical model of cardiac electrophysiological imaging, a convolutional neural network is used to design regularization terms and transform the reconstruction problem into an optimization problem with regularization terms;

[0011] 3) Construct a learnable gradient descent LDA network model to solve the above optimization problem with regularization terms;

[0012] 4) Inputting the training set into the learnable gradient descent LDA network model and designing a loss function to train the learnable gradient descent LDA network model;

[0013] 5) Input the test set into the trained learnable gradient descent LDA network model to reconstruct the output and obtain the corresponding TMP potential image.

[0014] As a further improvement, the myocardial transmembrane potential TMP and body surface potential BSP data pairs obtained in step 1) of the present invention have a total of 400 groups of TMP sequences with different pacing sites, different infarction sites, and different infarction areas, and the size of each group of data is 697×500, where 697 is the number of heart nodes and 500 is the sequence length; the corresponding 64-lead BSP sequence, the size of each group of data is 64×500.

[0015] As a further improvement, the mathematical model expression of cardiac electrophysiological imaging in step 2) of the present invention is as follows:

[0016] Φ = Hu;

[0017] Where u represents the distribution of myocardial transmembrane potential TMP on the heart, Φ represents the body surface potential record BSP, and H is the conversion matrix.

[0018] As a further improvement, in step 2) of the present invention, the optimization problem expression with regularization term is as follows:

[0019]

[0020] The first term is the data fidelity term, and the second term r(u;θ) is a regularization term with a learnable parameter θ.

[0021] As a further improvement, the regular term expression in step 2) of the present invention is as follows:

[0022]

[0023] Where g is the feature extraction module, || || 2,1 represents the L2,1 norm, g i,θ (u) represents the i-th feature extraction vector containing parameter θ in the feature information of the myocardial transmembrane potential u.

[0024] As a further improvement, the feature extraction module g of the present invention is expressed as follows:

[0025] g(u)=w4*σ(w3*σ(w2*σ(w1*u)));

[0026] Where σ is the activation function, represents the convolution weight and * represents the convolution operation.

[0027] As a further improvement, the learnable gradient descent LDA network model in step 3) of the present invention is composed of a plurality of cascaded computing modules, each of which includes a data fidelity term gradient descent and a regular term gradient descent, and the specific expression is as follows:

[0028]

[0029] where z k+1 represents the output result of the gradient descent of the data fidelity term in the k+1th computation module, u k+1 and u k They represent the output results of the regularization gradient descent in the k+1th and kth calculation modules, respectively, and α k Represents the step size of the gradient descent in the kth computation module.

[0030] As a further improvement, in step 4) of the present invention, the training set is input into the learnable gradient descent LDA network model and the loss function is designed to train the learnable gradient descent LDA network model as follows:

[0031] 8.1 Initialize model parameters, including the bias vector and weight matrix of each layer, learning rate and optimizer;

[0032] 8.2 Input the body surface potential BSP in the training set samples into the learnable gradient descent LDA network model, forward propagate the model output to obtain the corresponding prediction result, i.e., myocardial transmembrane potential TMP, and calculate the loss function;

[0033] 8.3 Based on the loss function, use the optimizer to iteratively update the model parameters through the gradient descent method until the loss function converges and the training is completed.

[0034] The beneficial effects of the present invention are as follows:

[0035] The present invention proposes to perform L 2,1 Norm calculation to construct the regularization term and L 2,1 The norm is smoothed, so that the explicit gradient solution of the regularization term can be directly obtained. Compared with the traditional image-level regularization method, the present invention has a better regularization effect and can learn the prior information in the measurement data. In addition, compared with the method of directly replacing the regularization term with a neural network, the present invention is more interpretable and has fewer parameters, so it is very suitable for clinical applications and has higher credibility.

[0036] The learnable gradient descent algorithm used in the present invention is used to reconstruct myocardial transmembrane potential for myocardial ischemia and ectopic pacing diseases during the experiment. The superiority of the present invention is demonstrated based on various evaluation indicators. Compared with other methods, the present invention is closer to the true value during the experiment and the reconstruction effect is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic diagram of the structure of the cardiac electrophysiological imaging reconstruction model based on the learnable descent algorithm of the present invention;

[0038] Figure 2The TMP waveform reconstruction results of each method for patients with myocardial infarction;

[0039] Figure 3 The results of TMP three-dimensional image reconstruction of patients with myocardial infarction by each method;

[0040] Figure 4 The TMP waveform reconstruction results of each method for patients with ectopic pacing;

[0041] Figure 5 The three-dimensional image reconstruction results of TMP for patients with ectopic pacing using various methods. DETAILED DESCRIPTION

[0042] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0043] The present invention discloses a cardiac electrophysiological imaging reconstruction method based on a learnable descent algorithm. Figure 1 The present invention is a schematic diagram of the structure of a cardiac electrophysiological imaging reconstruction model based on a learnable descent algorithm, which includes the following steps:

[0044] 1) Obtain data pairs of myocardial transmembrane potential TMP and body surface potential BSP for training and divide them into training set and test set;

[0045] 2) Based on the mathematical model of cardiac electrophysiological imaging, a convolutional neural network is used to design regularization terms and transform the reconstruction problem into an optimization problem with regularization terms;

[0046] 3) Construct a learnable gradient descent LDA network model to solve the above optimization problem with regularization terms;

[0047] 4) Inputting the training set into the learnable gradient descent LDA network model and designing a loss function to train the learnable gradient descent LDA network model;

[0048] 5) Input the test set into the trained learnable gradient descent LDA network model to reconstruct the output and obtain the corresponding TMP potential image.

[0049] The specific steps include:

[0050] (1) Prepare data.

[0051] A personalized heart-trunk geometry model was selected in ECGSim to simulate ectopic pacing and myocardial infarction data. The transfer matrix H was obtained by finite element method through heart-trunk modeling. The simulation data included 400 sets of TMP sequences with different pacing sites, different infarction sites, and different infarction areas. The size of each set of data was (697, 500), where 697 was the number of cardiac nodes and 500 was the sequence length; the corresponding 64-lead BSP sequence, the size of each set of data was (64, 500). The data set was divided into training set and test set in a ratio of 8:1.

[0052] (2) Model building

[0053] In order to obtain the cardiac surface potential information, it is necessary to first determine the forward model of electrical signal propagation. The bivariate diffusion (Aliev-Panfilov, AP) model is used to describe the dynamic activation model of myocardial transmembrane potential:

[0054]

[0055] Where u is the myocardial transmembrane potential (TMP), v is the reconstruction current, and D is the diffusion tensor. The meshless method is used to discretize the three-dimensional space of the heart:

[0056]

[0057] According to the quasi-static approximation of Maxwell's equations, the Poisson equation of the myocardial transmembrane potential can be expressed as:

[0058]

[0059] where σ i , σ e is the anisotropic conductivity tensor. The difference between the intracellular potential and the extracellular potential Represents the myocardial transmembrane potential TMP. By adding appropriate boundary conditions, the equation can be solved to obtain the relationship between the transmembrane potential and the body surface potential. By solving, the ECG forward problem can be expressed by the following linear equation:

[0060] Φ=Hu

[0061] Where u represents the distribution of myocardial transmembrane potential TMP on the heart, Φ represents the body surface potential record BSP, H is the conversion matrix, and the inverse ECG problem is to reconstruct the heart surface potential TMP inversely through the body surface potential BSP. In order to solve the ill-posed inverse problem of reconstructing TMP using the BSP and transfer matrix H obtained from body surface measurements, the reconstruction problem is transformed into an optimization problem with regularization terms:

[0062]

[0063] The first term is the data fidelity term, and the second term r(u;θ) is a regularization term with a learnable parameter θ.

[0064] (3) The Learnable Descent Algorithm (LDA) extracts the sparse features of u by learning a smooth nonlinear mapping g and applying l 2,1 The norm enhances robustness and sparsity:

[0065]

[0066] g(u)=w4*σ(w3*σ(w2*σ(w1*u)))

[0067] Where σ is the activation function, represents the convolution weight and * represents the convolution operation.

[0068] In order to further solve the non-convex and non-smooth problem of the regularization term r(u), Nesterov's smoothing strategy is used to smooth r(u), which can be expressed as:

[0069]

[0070] Where y is the dual variable, represents the dual space. For any ε>0, the smooth approximation can be expressed as:

[0071]

[0072] The solution goal can be expressed as:

[0073]

[0074] Further closed solution

[0075]

[0076] The optimization objective can be further written as:

[0077]

[0078] The learnable gradient descent algorithm is used to solve the explicit solution of the cardiac transmembrane potential and construct a network. The proposed learnable gradient descent network is expanded into several modules. Each calculation module contains data fidelity gradient descent and regularization gradient descent. The data fidelity gradient descent is:

[0079]

[0080] Where: subscript k+1 represents the k+1th module, Z k+1Represents the intermediate result after gradient descent, α k is the step size of the likelihood gradient descent.

[0081] The regularization gradient descent is:

[0082]

[0083] in is the proximal gradient operator.

[0084] To obtain the solution in proximal form, we approximate

[0085]

[0086] Can get

[0087]

[0088] where α k , β k All are parameters.

[0089] To ensure the convergence of the algorithm, calculate

[0090]

[0091] Two explicit solutions w obtained by gradient descent of the regularization term k+1 and v k+1 Compare them, calculate the size of their objective functions respectively, and select the one with the smaller objective function as the output u of the current module k+1 , the output of the last module is the reconstructed image obtained by the network, which can be expressed as:

[0092]

[0093] (4) First, the model is initialized, where the approximate parameters are initialized to 0.001, a 4-layer convolutional neural network is used, and the number of network features is 64. Then the body surface potential BSP in the training sample is input into the learnable gradient descent LDA network model, and the output result of the last module is obtained by forward propagation. The network parameters are updated using gradient descent, and the optimizer uses the Adam optimization method. When the optimization target converges or the number of training times reaches the maximum number of iterations, the training is completed.

[0094] (5) The body surface potential BSP of the test set is input into the trained network, and the reconstructed myocardial transmembrane potential TMP is output.

[0095] Below we verify the effectiveness of the present invention based on simulation experiments. The experiment uses TMP and BSP data pairs generated by ECGSIM simulation software. There are 400 groups of TMP sequences with different pacing sites, different infarction sites, and different infarction areas. The size of each group of data is 697×500, where 697 is the number of heart nodes and 500 is the sequence length; the corresponding 64-lead BSP sequence, the size of each group of data is 64×500. The training set and test set are divided into 8:1 ratios, and the Adam optimizer is used. The initial learning rate is 0.0001, the batch size is 64, and each approximate parameter is initialized to 0.001. First, the training is performed for the number of iterations K=3.

[0096] 500 epochs, and then increase the number of iterations by 2 rounds, and train 200 epochs each time, and so on, until K=13 and the training is completed. Table 1 shows the quantitative analysis results of the reconstructed myocardial transmembrane potential:

[0097] Table 1

[0098] Method Tikhonov TV ISTA-Net Proposed CC 0.552±0.144 0.580±0.304 0.663±0.262 0.668±0.157 SSIM 0.431±0.166 0.537±0.281 0.624±0.243 0.638±0.164 LE 44.669 35.844 21.423 18.502

[0099] The correlation coefficient (CC) is used to measure the correlation between the true value and the predicted result. The specific formula is:

[0100]

[0101] Structural Similarity (SSIM) evaluates the structural similarity between real images and images, that is, the similarity between the true TMP value and the TMP reconstruction result. The specific formula is:

[0102]

[0103] Among them, u and Represent the true value and reconstruction result of TMP respectively, Represents the covariance of the true value and the reconstruction result, Var(u) and Represent the variance of the true value and the reconstruction result, E(u) and Represent the mean of the true value and the reconstruction result respectively, c1 and c2 are used to avoid the denominator being 0 when calculating the structural similarity.

[0104] Location Error (LE): The Euclidean distance between ectopic pacemakers.

[0105] The table shows the quantitative result analysis of Tikhonov regularization, TV regularization, ISTA-Net and the present invention from left to right. It can be seen from the table that the mean values ​​of the evaluation indexes of the present invention are better than those of the other three methods, which proves the superiority of the present invention.

[0106] Figure 2 The figures are the reconstruction results of myocardial transmembrane potential waveforms of patients with myocardial infarction by various methods. The black waveform is the true image, and the red waveforms correspond to the reconstruction results of the present invention, ISTA-Net, Tikhonov algorithm and TV algorithm from top to bottom and from left to right. It can be seen that the traditional algorithm can hardly restore the waveform contour, and there is obvious jitter in the reconstruction of the waveform front end by ISTA-Net. The reconstruction result of the present invention is more stable and closer to the true image.

[0107] Figure 3 The three-dimensional image reconstruction results of myocardial transmembrane potential of patients with myocardial infarction by various methods, from top to bottom and from left to right, correspond to the reconstruction results of the true value, the present invention, ISTA-Net, Tikhonov algorithm and TV algorithm. It can be seen that the traditional algorithm cannot locate the myocardial infarction area, the positioning of ISTA-Net is not accurate enough, and the reconstruction effect of the present invention is closer to the true value.

[0108] Figure 4 The figures are the reconstruction results of the myocardial transmembrane potential waveform of patients with ectopic pacing by various methods. The black waveform is the true image, the red waveform is the true image, and the black waveform is the true image. From top to bottom and from left to right, they correspond to the reconstruction results of the present invention, ISTA-Net, Tikhonov algorithm and TV algorithm. It can be seen that the waveform contour reconstruction of the traditional algorithm is quite different from the true value, and the reconstruction effect of ISTA-Net has obvious jitter. It can be seen that the reconstruction result of the present invention is more stable and closer to the true image.

[0109] Figure 5 The three-dimensional image reconstruction results of myocardial transmembrane potential of patients with ectopic pacing by various methods, from top to bottom and from left to right, correspond to the reconstruction results of the true value, the present invention, ISTA-Net, Tikhonov algorithm and TV algorithm. It can be seen that the traditional algorithm cannot effectively locate the ectopic pacing area, the edge of the positioning area of ​​ISTA-Net is fuzzy, and the reconstructed edge of the present invention is clearer and closer to the true value.

[0110] The experimental results show that the myocardial transmembrane potential reconstruction method based on the learnable gradient descent algorithm of the present invention is effective, and the reconstruction from the body surface potential BSP to the myocardial transmembrane potential TMP is realized. Compared with the traditional image-level regularization method, the present invention has a better regularization effect and can learn the prior information in the measurement data. In addition, compared with the method of directly replacing the regularization term with a neural network, the present invention is more interpretable and has fewer parameters, so it is very suitable for clinical applications and has higher credibility. By reconstructing the myocardial transmembrane potential for myocardial ischemia and ectopic pacing diseases, the superiority of the present invention is proved according to various evaluation indicators. Compared with other methods, the present invention is closer to the true value during the experiment and the reconstruction effect is more accurate.

[0111] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made to the present invention by those skilled in the art based on the disclosure of the present invention should be within the scope of protection of the present invention.

Claims

1. A cardiac electrophysiological imaging reconstruction method based on a learnable descent algorithm, comprising the following steps: 1) Obtain data pairs of myocardial transmembrane potential TMP and body surface potential BSP for training and divide them into training set and test set; 2) Based on the mathematical model of cardiac electrophysiological imaging, a convolutional neural network is used to design regularization terms and transform the reconstruction problem into an optimization problem with regularization terms; 3) Construct a learnable gradient descent LDA network model to solve the above optimization problem with regularization terms; 4) Inputting the training set into the learnable gradient descent LDA network model and designing a loss function to train the learnable gradient descent LDA network model; 5) Input the test set into the trained learnable gradient descent LDA network model to reconstruct the output and obtain the corresponding TMP potential image.

2. The cardiac electrophysiological imaging reconstruction method according to claim 1, characterized in that: The myocardial transmembrane potential TMP and body surface potential BSP data pairs obtained in the step 1) have a total of 400 groups of TMP sequences with different pacing sites, different infarction sites, and different infarction areas, and the size of each group of data is 697×500, where 697 is the number of cardiac nodes and 500 is the sequence length; the corresponding 64-lead BSP sequence, the size of each group of data is 64×500.

3. The cardiac electrophysiological imaging reconstruction method according to claim 1, characterized in that: The expression of the mathematical model of cardiac electrophysiological imaging in step 2) is as follows: Φ = Hu; Where u represents the distribution of myocardial transmembrane potential TMP on the heart, Φ represents the body surface potential record BSP, and H is the conversion matrix.

4. The cardiac electrophysiological imaging reconstruction method according to claim 1, characterized in that: In step 2), the optimization problem expression with regularization term is as follows: The first term is the data fidelity term, and the second term r(u;θ) is a regularization term with a learnable parameter θ.

5. The cardiac electrophysiological imaging reconstruction method according to claim 4, characterized in that: The regular term expression in step 2) is as follows: Where g is the feature extraction module, || || 2,1 represents the L2,1 norm, g i,θ (u) represents the i-th feature extraction vector containing parameter θ in the feature information of the myocardial transmembrane potential u.

6. The cardiac electrophysiological imaging reconstruction method according to claim 5, characterized in that: The feature extraction module g is expressed as follows: Where σ is the activation function, represents the convolution weight and * represents the convolution operation.

7. The cardiac electrophysiological imaging reconstruction method according to claim 1, characterized in that: The learnable gradient descent LDA network model in step 3) is composed of multiple cascaded computing modules, each of which contains data fidelity gradient descent and regularization gradient descent. The specific expressions are as follows: where z k+1 represents the output result of the gradient descent of the data fidelity term in the k+1th computation module, u k+1 and u k They represent the output results of the regularization gradient descent in the k+1th and kth calculation modules, respectively, and α k Represents the step size of the gradient descent in the kth computation module.

8. The cardiac electrophysiological imaging reconstruction method according to claim 1, characterized in that: in the step 4), the training set is input into the learnable gradient descent LDA network model and the loss function is designed to train the learnable gradient descent LDA network model as follows: 8.1 Initialize model parameters, including the bias vector and weight matrix of each layer, learning rate and optimizer; 8.2 Input the body surface potential BSP in the training set samples into the learnable gradient descent LDA network model, forward propagate the model output to obtain the corresponding prediction result, i.e., myocardial transmembrane potential TMP, and calculate the loss function; 8.3 Based on the loss function, use the optimizer to iteratively update the model parameters through the gradient descent method until the loss function converges and the training is completed.

Images