Reconstruction of data inside myocardium from spatial measurements with neural networks

Myocardium is a muscle tissue of the heart that causes the strongest electrophysiological activity in the human body. Signals from the myocardium are recorded by many experimental and medical devices. These signals are used in cardiac surgery, biomedical engineering, and pharmacology. Here we propose a method for reconstruction of the signals inside the myocardium from measurements in a fixed set of points on the myocardial surface. Signals of transmembrane and extracellular potential from the myocardium have a notable pattern that repeats across all mediums with some time shifts and minor variations. It is possible to approximate the function that map coordinates inside the myocardium to expected signals. A multi-layer perceptron can do this task if some reformulation of the mathematical statement reduces the Lipschitz constant of the target function.