Revealing cross-frequency causal interactions during a mental arithmetic task through symbolic transfer entropy: a novel vector-quantization approach

Working memory (WM) is a distributed cognitive process that employs communication between prefrontal cortex and posterior brain regions in the form of cross-frequency coupling between theta (θ) and high-alpha (α2) brain waves. A novel method for deriving causal interactions between brain waves of different frequencies is essential for a better understanding of the neural dynamics of such complex cognitive process. Here, we proposed a novel method to estimate transfer entropy (TE) through a symbolization scheme, which is based on neural-gas algorithm (NG) and encodes a bivariate time series in the form of two symbolic sequences. Given the symbolic sequences, the delay symbolic transfer entropy (dSTENG) is defined. Our approach is akin to standard symbolic transfer entropy (STE) that incorporates the ordinal pattern (OP) symbolization technique. We assessed the proposed method in a WM-invoked paradigm that included a mental arithmetic task at various levels of difficulty. Effective interactions between Frontalθ (Fθ) and Parieto-Occipitalα2 (POα2) brain waves were detected in multichannel EEG recordings from 16 subjects. Compared with conventional methods, our technique was less sensitive to noise and demonstrated improved computational efficiency in quantifying the dominating direction of effective connectivity between brain waves of different spectral content. Moreover, we discovered an efferent Fθ connectivity pattern and an afferent POα2 one, in all the levels of the task. Further statistical analysis revealed an increasing dSTENG strength following the task's difficulty