  Simulation of the monodomain equation, crucial for modeling the heart's
electrical activity, faces scalability limits when traditional numerical
methods only parallelize in space. To optimize the use of large multi-processor
computers by distributing the computational load more effectively, time
parallelization is essential. We introduce a high-order parallel-in-time method
addressing the substantial computational challenges posed by the stiff,
multiscale, and nonlinear nature of cardiac dynamics. Our method combines the
semi-implicit and exponential spectral deferred correction methods, yielding a
hybrid method that is extended to parallel-in-time employing the PFASST
framework. We thoroughly evaluate the stability, accuracy, and robustness of
the proposed parallel-in-time method through extensive numerical experiments,
using practical ionic models such as the ten-Tusscher-Panfilov. The results
underscore the method's potential to significantly enhance real-time and
high-fidelity simulations in biomedical research and clinical applications.
