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%DIFDELCMD < \pm %%% 1.30\%. The basis data trained neural network was able to predict G3D basis function synthesized data with RMSE of 8.46%DIFDELCMD < \pm %%% 1.55\%, and G3D representation of real-world data with RMSE of 18.5%DIFDELCMD < \pm %%% 5.25\%. Activation map produced from the predicted time series had a RMSE of 17.0\% and mean absolute difference of 10.3%DIFDELCMD < \pm %%% 10.8ms 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.\pm1\\%DIF > increase in signal feature localization error. The set of training impulse function data could be reduced and prediction error remained bounded. Recorded HSPs from in-vitro pig hearts were reliably decomposed using space-time Gaussian basis functions. Predicted HSPs for left-ventricular pacing had a mean absolute error of 10.4\pm11.4 ms. Other pacing scenarios were analyzed with similar success. Conclusion: Impulses from Gaussian basis functions are potentially an effective and robust way to train simple neural network data models for reconstructing HSPs from decomposed BSPs. The HSPs predicted by the neural network can be used to generate activation maps that non-invasively identify features of cardiac electrical dysfunction and can guide subsequent treatment options.
The proposed method re-frames traditional inverse problems of electrocardiography into regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions. Impulse HSPs were generated with single Gaussian basis functions at discrete heart surface locations and projected to corresponding BSPs using a volume conductor torso model. Both BSP (inputs) and HSP (outputs) were mapped to regular 2D surface meshes and used to train a neural network . Predictive capabilities of the network were tested with unseen synthetic and experimental data. A dense full connected single hidden layer neural network was trained to map body surface impulses to heart surface Gaussian basis functions for reconstructing HSP. Synthetic pulses moving across the heart surface were predicted from the neural network with root mean squared error %DIFDELCMD < \pm %%% %DIFDELCMD < \pm %%% %DIFDELCMD < \pm %%% %DIFDELCMD < \pm %%% of 9.1\pm1.4\%. Predicted signals were robust to noise up to 20 dB and errors due to displacement and rotation of the heart within the torso were bounded and predictable. A shift of the heart 40 mm toward the spine resulted in a 4\\%DIF > increase in signal feature localization error. The set of training impulse function data could be reduced and prediction error remained bounded. Recorded HSPs from in-vitro pig hearts were reliably decomposed using space-time Gaussian basis functions. Predicted HSPs for left-ventricular pacing had a mean absolute error of 10.4\pm11.4 ms. Other pacing scenarios were analyzed with similar success. Conclusion: Impulses from Gaussian basis functions are potentially an effective and robust way to train simple neural network data models for reconstructing HSPs from decomposed BSPs. The HSPs predicted by the neural network can be used to generate activation maps that non-invasively identify features of cardiac electrical dysfunction and can guide subsequent treatment options.
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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
The proposed method re-frames traditional inverse problems
R
a regression problem through the use of Gaussian 3D (G3D) basis function decomposition. Methods:
regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions. Impulse
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using G3D basis functions and passed through a boundary element forward model to obtain corresponding BSPs . The generated BSPs (input) and HSPs (output) were
with single Gaussian basis functions at discrete heart surface locations and projected to corresponding BSPs using a volume conductor torso model. Both BSP (inputs) and HSP (outputs) were mapped to regular 2D surface meshes and
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, 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
. Predictive capabilities of the network were tested with unseen synthetic and experimental data. A dense full connected single hidden layer neural network was trained to map body surface impulses to heart surface Gaussian basis functions for reconstructing HSP. Synthetic pulses moving across the heart surface were predicted from the neural network with
D
(RMSE) of 1.34
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1.30\%. The basis data trained neural network was able to predict G3D basis function synthesized data with RMSE of 8.46
D
1.55\%, and G3D representation of real-world data with RMSE of 18.5
D
5.25\%. Activation map produced from the predicted time series had a RMSE of 17.0\% and mean absolute difference of 10.3
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10.8ms 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.
of 9.1
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.4\%. Predicted signals were robust to noise up to 20 dB and errors due to displacement and rotation of the heart within the torso were bounded and predictable. A shift of the heart 40 mm toward the spine resulted in a 4