Inverse Problem of Electrocardiography: Estimating the Location of Cardiac Ischemia in a 3D Realistic Geometry

Deep learning formulation of electrocardiographic imaging integrating image and signal information with data-driven regularization

AIMS

Electrocardiographic imaging (ECGI) is a promising tool to map the electrical activity of the heart non-invasively using body surface potentials (BSP). However, it is still challenging due to the mathematically ill-posed nature of the inverse problem to solve. Novel approaches leveraging progress in artificial intelligence could alleviate these difficulties.

METHODS AND RESULTS

We propose a deep learning (DL) formulation of ECGI in order to learn the statistical relation between BSP and cardiac activation. The presented method is based on Conditional Variational AutoEncoders using deep generative neural networks. To quantify the accuracy of this method, we simulated activation maps and BSP data on six cardiac anatomies.We evaluated our model by training it on five different cardiac anatomies (5000 activation maps) and by testing it on a new patient anatomy over 200 activation maps. Due to the probabilistic property of our method, we predicted 10 distinct activation maps for each BSP data. The proposed method is able to generate volumetric activation maps with a good accuracy on the simulated data: the mean absolute error is 9.40 ms with 2.16 ms standard deviation on this testing set.

CONCLUSION

The proposed formulation of ECGI enables to naturally include imaging information in the estimation of cardiac electrical activity from BSP. It naturally takes into account all the spatio-temporal correlations present in the data. We believe these features can help improve ECGI results.

Using parametric model order reduction for inverse analysis of large nonlinear cardiac simulations

Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization. We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.