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As another critical implementation of moving frames for partial differentialequations, this paper proposes a novel numerical scheme by aligning one ofthree orthogonal unit vectors at each grid point along the direction of a wavepropagation to construct an organized set of frames, called a connection. Thisconnection characterizes the geometry of wave propagation depending on (1) theinitial point, (2) type of wave, and (3) shape of the domain with conductionproperties. The constructed connection is differentiated again to derive theRiemann curvature tensor of orthonormal bases corresponding to importantphysical and biological meanings in wave propagation. As a practicalapplication, the proposed scheme is applied to diffusion-reaction equations toobtain the Atlas, or a geometric map with connections, of an atrium withcardiac fibers, for the quantitative and qualitative analysis of cardiac actionpotential propagation, which could contribute to the clinical and surgicalplanning of atrial fibrillation.

PDE-induced connection of moving frames for the Atlas of the cardiac electric propagation on 2D atrium