101 Mathematical characterisation of the dynamics underlying rhythmic and non-rhythmic variants of delta activity

Abstract

Object: We applied a new test, nonlinear cross prediction (NLCP), to investigate whether or polymorphic delta activity (PDA) and frontal intermittent rhythmic delta activity (FIRDA) reflect linear or nonlinear brain dynamics. Furthermore realistic models were constructed to explain the dynamical properties of PDA and FIRDA. Methods: Forty-nine EEG time series with FIRDA and 40 time series with PDA were studied with the NLCP algorithm. This characterizes a time series in terms of its predictability, amplitude asymmetry, and time asymmetry, with the latter two measures reflecting nonlinearity. Parameters of an EEG model proposed by Lopes da Silva were adjusted to obtain time series resembling PDA and FIRDA. Results: FIRDA was more predictable than PDA. Most PDA segments could not be distinguished from linearly filtered noise. In contrast, FIRDA activity showed strong evidence of nonlinear dynamics. These dynamical properties of PDA and FIRDA could be reproduced by the Lopes da Silva model. PDA and FIRDA reflect a point attractor and a limit cycle attractor, respectively, perturbed by dynamical noise. Conclusion: Experimental analysis and modeling of the data suggest that PDA and FIRDA reflect fundamentally different types of brain dynamics. While PDA is filtered noise, reflecting low-level, random input to cortical networks, FIRDA may reflect limit-cycle oscillations due to increased excitation.