Abstract
Models of cardiac tissue span a wide range of complexity, from minimal models to biophysically detailed models. It is often assumed that minimal models accurately capture the core behaviors of propagating action potentials in biophysically detailed models. However, it remains unclear whether additional physiological detail introduces qualitatively new behaviors. Dispersion relations quantify the existence, stability, and bifurcations of traveling waves, but their computation for biophysically detailed models has been limited by system complexity and computational cost. To overcome these challenges, we develop Traveling Wave Investigation Software Tool (TWIST), a numerical framework for the systematic computation of traveling wave solutions and their spectra. Using TWIST, we compute and compare dispersion relations in the FitzHugh–Nagumo, Beeler–Reuter, and nine-variable ten Tusscher–Panfilov models. Our analysis shows that increasing physiological detail can introduce substantial additional structure in dispersion relations. In particular, the interaction of multiple activation processes in the ten Tusscher–Panfilov model gives rise to additional solution branches, including families of slow waves that are absent in minimal models and may play important roles in abnormal wave dynamics. Our comparisons across models of increasing complexity distinguish robust features of wave propagation from those arising specifically from detailed ionic interactions and represent a step toward validating that the observed behaviors reflect genuine cardiac phenomena rather than artifacts of specific model formulations.