The rhythmic stability of cardiac cells is governed by their phase dynamics, yet traditional analysis often relies on exhaustive time-series simulations to predict how a cell responds to external stimuli. While the concept of an isochron - a manifold representing all states that converge to a limit cycle in phase with each other -provides a rigorous framework for phase response, its application has been largely limited to simple 2D models. In this study, we compute isochronal structures in the eight-dimensional Beeler-Reuter (BR) ventricular cell model via a recently developed numerical-continuation approach, demonstrating its scalabiliity and interpretive power.
The approach reduces the complexity of the 8D state space into a plane composed of one-dimensional "isochron slices." Each slice is generated by systematically varying the stimulus amplitude and the cycle phase of a fixed-duration pulse. The set of slices provides a comprehensive overview of the cell's phase-resetting behavior, capturing intricate features of the BR model's recovery and plateau phases that are otherwise difficult to visualize.
By representing the cell's response as a function of phase and amplitude, we transform high-dimensional cardiac dynamics into a clear, planar geometry. This method allows for a precise characterization of the "vulnerable window" and phase-sensitivity, offering a robust computational handle for studying how pharmacological or pathological changes shift the fundamental timing of the cardiac cycle.