Phase gradient modulation of spiral waves in cortical circuits using the complex Ginzburg-Landau equation

Disinhibited brain networks exhibit various forms of spatiotemporal waves, including complex spiral waves that evolve around a fixed spatial locus. In experiments, spiral waves are observed to alter their direction of rotation over time, for instance producing a series of waves with clockwise cycles before switching to waves rotating counterclockwise, or vice-versa. To capture this effect, we developed a model based on the Complex Ginzburg-Landau equation (CGLE). By introducing a modulation in the phase gradient of the complex field that reflects global, time-dependent fluctuations in the surrounding environment, the model produced waves that alternated in their direction of rotation. The rate of alternations was directly proportional to the amplitude of phase modulation. Conditions were explored for the emergence of quasi-stationary frozen waves and noise-induced quenching of spiral waves. Overall, the modified CGLE model provides a candidate mechanism for the emergence of spiral waves where rotational directions are dynamically altered, yielding rich forms of activity that account for the spatiotemporal patterns observed in disinhibited brain circuits.