Aims: We want to compute QRS complexes from activation maps and a predefined shape for the transmembrane voltage V. In the context of ECGi, it would allow to directly reconstruct activation maps, without resorting to reconstruction and post-processing of cardiac electrical potentials. Here we compare two possible formulations to compute QRS complexes.
Model and method: Several methods exist to simulate an ECG. Assuming that the transmembrane voltage V is given, the electrical potential in the torso (extracardiac and cardiac extracellular) U may be retrieved following two approaches. Either it solves a Laplace equation with discontinuous conductivity coefficient (heart and torso) and ionic current as a source (source formulation); or the quasi-stationary electrical balance between the intra- and extracellular fields (balance formulation). Commonly, the potential U is computed from the balance formulation. Anyway, we may also use the source formulation. Note that both formulations coincide only if V solves the complete bidomain equations. We compute reference activation maps and QRS complexes with a bidomain code. Afterwards the electrical field U is also calculated from the activation maps and a predefined V (and ionic model), using the two different formulations.
Results: We compare the potential fields U and the QRS complexes obtained by these two methods to the reference ones. Preliminary results show some significant differences between the two methods, with a better accuracy for the most popular balance formulation, for a smoothed heaviside form of V.