Complexity synchronization analysis of neurophysiological data: Theory and methods

Ioannis Schizas¹Sabrina Sullivan¹Scott Kerick¹Korosh Mahmoodi^1*J. Cortney Bradford¹David L Boothe¹Piotr J Franaszczuk²Paolo Grigolini³Bruce J. West⁴

• ¹Combat Capabilities Development Command United States Army, Natick, Massachusetts, United States
• ²Johns Hopkins University, Baltimore, Maryland, United States
• ³University of North Texas, Denton, United States
• ⁴North Carolina State University, Raleigh, North Carolina, United States

We present a theoretical foundation based on the spontaneous self-organized temporal criticality (SOTC) and multifractal dimensionality µ to model complex neurophysiological and behavioral systems to infer the optimal empirical transfer of information among them. We hypothesize that heterogeneous time series characterizing the brain, heart, and lung organ-networks (ONs) are necessarily multifractal, whose level of complexity and, therefore, their information content is measured by their multifractal dimensions. We apply modified diffusion entropy analysis (MDEA) to assess multifractal dimensions of ON time series (ONTS), and complexity synchronization (CS) analysis to infer information transfer among ONs that are part of a network-of-organ-networks (NoONs). An automated parameter selection process is proposed that relies on the Kolmogorov-Smirnov statistic to properly choose stripe sizes which are crucial in the MDEA analysis using synthetic duration times derived from the Mittag-Leffler map, shows the strength of KS-based stripe size selection to track changes in the IPL parameter µ. The purpose of this paper is to advance the validation, standardization, and reconstruct-ability of MDEA and CS analysis of heterogeneous neurophysiological time series data. Results from processing these datasets show that the complexity of brain, heart, and lung ONTS co-vary over time during cognitive task performance in 44% of subjects, while complexity of brain-heart interactions significantly co-vary in 85% of subjects. We conclude that certain principles, guidelines, and strategies for the application of MDEA analysis need further consideration. We conclude with a summary of the MDEA's limitations and future research directions.