Complexity measures and self-similarity on spreading depression waves

Self-similarity has been considered to be present in most of the spatial pattern formation phenomena occurring in natural contexts. In the case of the spreading depression (SD), there are conjectures about the presence of self-similarity in the circular wave formations. Shiner–Davison–Landsberg (SDL) complexity measure framework has been used in several contexts, in order to understand and classify systems and behaviors that are supposed to be complex. Here, by using SDL measure over data collected on SD experiments, self-similarity conjecture is tested. The data came from chicken retina spreading depression experience by measuring two concomitant signals: the extra-cellular potential and the intrinsic optical signal, that were collected in two different spatial scales. The SDL complexity was calculated for the data and two main results appeared: all the studied substances present similar SDL dynamical behavior and, considering the same substance, optical signals present different SDL values for different spatial scales. Consequently, it is not possible to conclude that SD phenomenon presents self-similarity.