Isolated wave segments in a neural tissue model with volume transmission: discreteness matters

Isolated wave segments are a type of spatiotemporal activity that has been repeatedly reported in experimental studies of spreading depolarization on the cerebral cortex and retina of laboratory animals. However, it has been theoretically shown that such a pattern cannot be stable in a continuous excitable medium. In our work, we address this problem using the model of a discrete–continuous medium. We present the targeted numerical study of isolated wave segments, including scenarios of their emergence and an estimation of their stability to various deformations. We show that an isolated wave segment can exhibit the properties of a space-time attractor by cyclically changing its shape and approaching it from different initial conditions. Such a wave segment is not necessarily small, although small segments may occur more easily and are, therefore, more likely. Finally, we show that the behavior we found persists also under conditions of a heterogeneous propagation medium, which indicates the applicability of our findings to the analysis of spatiotemporal patterns in real nervous tissue.