Delayed global feedback in the genesis and stability of spatiotemporal patterns in paced biological excitable media

A multi-scale approach was used to investigate the roles of delayed global feedback (DGF) in the genesis and stability of spatiotemporal patterns in periodically-paced excitable media. Patterns that are temporal period-2 (P2) and spatially concordant (in-phase) or discordant (out-of-phase) were investigated. First, simulations were carried out using a generic spatiotemporal model composed of coupled FitzHugh-Nagumo units with DGF. When DGF is absent, concordant and discordant P2 patterns occur depending on initial conditions. The discordant P2 patterns are spatially random. When the DGF is negative, only concordant P2 patterns exist. When the DGF is positive, both concordant and discordant P2 patterns can occur. The discordant P2 patterns are still spatially random, but they satisfy that the global signal exhibits a temporal period-1 behavior. Second, to validate the spatiotemporal dynamics in a biological system, simulations were carried out using a 3-dimensional physiologically detailed ventricular myocyte model. This model can well capture the intracellular calcium release patterns widely observed in experiments. The properties of DGF were altered by changing ionic currents or clamping voltage. The spatiotemporal pattern dynamics of calcium release in this model match precisely with those of the generic model. Finally, theoretical analyses were carried out using a coupled map lattice model with DGF, which reveals the instabilities and bifurcations leading to the spatiotemporal dynamics and provides a general mechanistic understanding of the role of DGF in the genesis, selection, and stability of spatiotemporal patterns in paced excitable media. Author Summary Understanding the mechanisms of pattern formation in biological systems is of great importance. Here we investigate the dynamical mechanisms by which delayed global feedback affects pattern formation and stability in periodically-paced biological excitable media, such as cardiac or neural cells and tissue. We focus on the formation and stability of the temporal period-2 and spatially in-phase and out-of-phase patterns. Using a multi-scale modeling approach, we show that when the delayed global feedback is negative, only the spatially in-phase patterns are stable; when the feedback is positive, both spatially in-phase and out-of-phase patterns are stable. Also, under the positive feedback, the out-of-phase patterns are spatially random but satisfy that the global signals are temporal period-1 solutions.