Reconstruction of retrospective cardiac activity--numerical study in a single cell and in a linear strand

Although computational modeling of the prospective electrical activity in the cardiac tissue is well established and robust, the retrospective extrapolation of this activity has not been explored to date. Here, we establish an algorithm for the backward-in-time extrapolation of electrical activity from measurements taken in the present. Using minimal human cardiac kinetic models and a modified Newton-Raphson algorithm, we demonstrate the feasibility of past activity reconstruction in a single cell and in a linear strand. In a single cell, reconstruction of state variables' shape, the action potential morphology, and the time of stimulation was successful for up to 1300 ms poststimulation and for data with signal-to-noise ratio levels higher than 40 dB. For linear strands, the action potential morphology was reconstructed for 500 ms poststimulation, and the reconstructed conduction velocity remained unaffected for signal-to-noise ratio levels higher than 50 dB. Moreover, tissue restitution properties due to various pacing rates were successfully reconstructed by the backward-in-time algorithm. These preliminary results demonstrate that past cardiac activity may be reconstructed from measurements in the present. We envision that this methodology could be implemented in future clinical applications, for example to trace the location and timing of ectopic foci during ablation procedures.