Extrapolation of Ventricular Activation Times From Sparse Electroanatomical Data Using Graph Convolutional Neural Networks

Abstract

Electroanatomic mapping is the gold standard for the assessment of ventricular tachycardia. Acquiring high resolution electroanatomic maps is technically challenging and may require interpolation methods to obtain dense measurements. These methods, however, cannot recover activation times in the entire biventricular domain. This work investigates the use of graph convolutional neural networks to estimate biventricular activation times from sparse measurements. Our method is trained on more than 15,000 synthetic examples of realistic ventricular depolarization patterns generated by a computational electrophysiology model. Using geometries sampled from a statistical shape model of biventricular anatomy, diverse wave dynamics are induced by randomly sampling scar and border zone distributions, locations of initial activation, and tissue conduction velocities. Once trained, the method accurately reconstructs biventricular activation times in left-out synthetic simulations with a mean absolute error of 3.9 ms ± 4.2 ms at a sampling density of one measurement sample per cm². The total activation time is matched with a mean error of 1.4 ms ± 1.4 ms. A significant decrease in errors is observed in all heart zones with an increased number of samples. Without re-training, the network is further evaluated on two datasets: (1) an in-house dataset comprising four ischemic porcine hearts with dense endocardial activation maps; (2) the CRT-EPIGGY19 challenge data comprising endo- and epicardial measurements of 5 infarcted and 6 non-infarcted swines. In both setups the neural network recovers biventricular activation times with a mean absolute error of less than 10 ms even when providing only a subset of endocardial measurements as input. Furthermore, we present a simple approach to suggest new measurement locations in real-time based on the estimated uncertainty of the graph network predictions. The model-guided selection of measurement locations allows to reduce by 40% the number of measurements required in a random sampling strategy, while achieving the same prediction error. In all the tested scenarios, the proposed approach estimates biventricular activation times with comparable or better performance than a personalized computational model and significant runtime advantages.

Keywords: cardiac computational modeling; deep learning; electroanatomic mapping; graph convolutional networks; sparse measurements.

Figure 1

Illustration of the proposed deep learning based pipeline to estimate biventricular local activation times. In a first step the cardiac anatomy including scar (red area) and border zone distribution (blue area) is segmented from MR images and discretized by a tetrahedral mesh. The sparse measurement cloud of endocardial activation times (colored spheres) is manually registered and mapped to the mesh. A graph convolutional neural network is using the mesh and vertex-wise features to estimate the local activation times in the entire biventricular domain.

Figure 2

Illustration of the incorporated vertex-wise features: (A) Positional encoding of vertex positions in a cylindrical coordinate system. (B) Additional relative positional encodings. (C) Categorical features denoting vertices belonging to the left or right endocardium (pink, orange), scar (red), or border zone (blue). (D) The projected electroanatomical measurements. (E) Fourteen features extracted from the 12-lead ECG traces.

Figure 3

Illustration of the proposed graph convolutional network architecture. Input is a tetrahedral mesh representing the biventricular anatomy. Per vertex, 24 geometric and electrophysiological features are extracted. First, a series of 20 GraphSAGE convolutional layers with 32 units and leaky rectified linear activation are applied to extract local features over an increasing receptive field. The output of each layer as well the input features are concatenated. The concatenated feature vector is further processed by a global feature extractor, which applies three fully connected layers of increasing size and a final global max pooling. The pooled feature vector is appended to the concatenated feature vector. Local activation times in the entire biventricular geometry are estimated by processing the combined feature vectors with three non-linear fully connected layers and a final linear transformation.

Figure 4

Visualization of the swine torso template with ECG lead placement (green markers), which were used for the computation of synthetic ECGs.

Figure 5

Mean absolute error for different subsampling ratios on our in-house cohort comprising four swine datasets with high-resolution endocardial EAMs. Comparison of the graph convolutional network (GCN), the personalized computational model (DEP), and a naive nearest neighbor projection (NN). The red bar denotes the mean, the black bar denotes the 15–95 percentiles.

Figure 6

Illustration of the prediction results for the graph convolutional neural network (GCN), the personalized computational model (DEP), and the nearest neighbor projection method (NN) for different sampling ratios. Provided samples are highlighted by pink spheres.

Figure 7

Visual comparison of the ground truth 12-lead ECG (black) taken from one case of the in-house dataset and the synthetic ECG (blue) simulated from the graph convolutional neural network prediction given the full electroanatomical map. Please note that lead I is missing because of a hardware failure.

Figure 8

Mean absolute error distributions (mean: red; 15–95 percentile: black) on the left ventricular endocardium (A) and the epicardium (B) of the graph convolutional predictions on cohort #2 comprising eleven swine datasets with high-resolution endocardial EAMs.

Figure 9

Illustration of the prediction results for the pig “Neus” from the CRT-EPIGGY19 challenge when providing 100% of the endocardial measurements to the graph convolutional neural network (GCN) and the personalized computational model (DEP). The neural network is able to retain the information on the endocardium and provide a coarse approximation of the left epicardial activation time. The computational model fails to accurately match the endocardial information and over-estimates the late activation on the left epicardium.

Figure 10

Illustration of the results of the ablation study applied to the in-house dataset. Mean absolute endocardial reconstruction errors are compared for different graph convolutional networks trained on subsets of all features (ALL): no ECG features (NoECG), only QRS duration (QRS), QRS duration with vertical positivities (QRS + Vert), and QRS duration with electrical axis (QRS + EA). The results suggest that ECG information, particularly the QRS duration, is necessary for the accurate estimation of activation maps. The small differences between the networks with ECG features suggest that the networks do not rely solely on ECG features to estimate the endocardial activation maps.

Figure 11

Illustration of the prediction results for the graph convolutional neural network using the proposed active sampling strategy and the random sampling strategy after selecting 10% of septal vertices. Provided samples are highlighted by black dots. The segmented border zone mask is overlayed in pink and located antero-septal in this swine model of myocardial infarction. Compared to the random sampling strategy, the active sampling approach better captures important details of the ground truth, such as the location of earliest activation and deceleration zones associated with the slow conductive border zone.