Complexity measures of brain wave dynamics

To understand the nature of brain dynamics as well as to develop novel methods for the diagnosis of brain pathologies, recently, a number of complexity measures from information theory, chaos theory, and random fractal theory have been applied to analyze the EEG data. These measures are crucial in quantifying the key notions of neurodynamics, including determinism, stochasticity, causation, and correlations. Finding and understanding the relations among these complexity measures is thus an important issue. However, this is a difficult task, since the foundations of information theory, chaos theory, and random fractal theory are very different. To gain significant insights into this issue, we carry out a comprehensive comparison study of major complexity measures for EEG signals. We find that the variations of commonly used complexity measures with time are either similar or reciprocal. While many of these relations are difficult to explain intuitively, all of them can be readily understood by relating these measures to the values of a multiscale complexity measure, the scale-dependent Lyapunov exponent, at specific scales. We further discuss how better indicators for epileptic seizures can be constructed.