Time map method for spatiotemporal simulation of cardiac and neural signal propagation

We propose a novel computational scheme that utilizes a time map, a scalar field representing excitation arrival time, to spatialize the time-dependent dynamics of cardiac and neural signal propagation in multidimensional spaces. The time map can be derived from sequential action potential imaging data, the eikonal equation, or numerical solutions of reaction–diffusion equations governing biological signal propagation. Once computed, the time map can be stored and modified to reflect changes in geometry and domain conductivity. The time map can be used for rapid multidimensional propagation simulations by serving as an instantaneous impulse in systems of ordinary differential equations. Furthermore, a modified time map can be reconstructed from the baseline time map in one- and two-dimensional domains. Numerical experiments and computational simulations are presented to demonstrate the numerical efficiency and effectiveness of the proposed scheme. Practical applications are also explored, such as fast multidimensional simulation with the modified time map and conductivity reconstruction from altered time maps.