Objective: To develop, train and test neural networks for predicting heart surface potentials (HSPs) from body surface potentials (BSPs). The method re-frames traditional inverse problems of electrocardiography into regression problems, constraining the solution space by decomposing signals with multidimensional Gaussian impulse basis functions. Methods: 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. Results: 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 of $9.1\pm 1.4$ %. 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% 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. Activation times calculated from predicted HSPs for left-ventricular pacing had a mean absolute error of $10.4\pm 11.4$ 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. Significance: 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.

中文翻译：

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心电图逆问题的脉冲数据模型

目的：开发、训练和测试用于从体表电位 (BSP) 预测心脏表面电位 (HSP) 的神经网络。该方法将传统的心电图逆问题重新构建为回归问题，通过使用多维高斯脉冲基函数分解信号来限制解空间。方法：在离散的心脏表面位置使用单高斯基函数生成脉冲 HSP，并使用体积导体躯干模型投影到相应的 BSP。BSP（输入）和 HSP（输出）都映射到常规的 2D 表面网格并用于训练神经网络。网络的预测能力用看不见的合成和实验数据进行了测试。结果：训练了一个密集的全连接单隐藏层神经网络，将体表脉冲映射到心脏表面高斯基函数，以重建 HSP。从神经网络预测穿过心脏表面的合成脉冲，均方根误差为$9.1\下午 1.4$ %。预测的信号对高达 20 dB 的噪声具有鲁棒性，并且由于躯干内心脏的位移和旋转导致的误差是有限且可预测的。心脏向脊柱移动 40 毫米导致信号特征定位误差增加 4%。训练脉冲函数数据集可以减少，预测误差保持有界。使用时空高斯基函数可靠地分解来自体外猪心脏的记录的 HSP。根据预测的左心室起搏 HSP 计算的激活时间的平均绝对误差为$10.4\pm 11.4$小姐。其他起搏场景的分析也取得了类似的成功。结论：来自高斯基函数的脉冲可能是一种有效且稳健的方法来训练简单的神经网络数据模型，以从分解的 BSP 中重建 HSP。意义：神经网络预测的 HSP 可用于生成激活图，无创识别心电功能障碍的特征，并指导后续治疗方案。