#### Basis Function Based Data Driven Learning for the Inverse Problem of Electrocardiography

##### Tommy Peng, Avinash Malik, Laura Bear, Mark L. Trew

Objective: This paper proposes an neural network approach for predicting heart surface potentials (HSPs) from body surface potentials (BSPs), which reframes the traditional inverse problem of electrocardiography into a regression problem through the use of Gaussian 3D (G3D) basis function decomposition. Methods: HSPs were generated using G3D basis functions and passed through a boundary element forward model to obtain corresponding BSPs. The generated BSPs (input) and HSPs (output) were used to train a neural network, which was then used to predict a variety of synthesized and decomposed real-world HSPs. Results: Fitted G3D basis function parameters can accurately reconstruct the real-world left ventricular paced recording with percent root mean squared error (RMSE) of $1.34 \pm 1.30$%. The basis data trained neural network was able to predict G3D basis function synthesized data with RMSE of $8.46 \pm 1.55$%, and G3D representation of real-world data with RMSE of $18.5 \pm 5.25$%. Activation map produced from the predicted time series had a RMSE of 17.0% and mean absolute difference of $10.3 \pm 10.8$ms when compared to that produced from the actual left ventricular paced recording. Conclusion: A Gaussian basis function based data driven model for re-framing the inverse problem of electrocardiography as a regression problem is successful and produces promising time series and activation map predictions of real-world recordings even when only trained using Guassian data. Significance: The HSPs predicted by the neural network can be used to create activation maps to identify cardiac dysfunctions during clinical assessment.

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