Measuring the complexity of time series: An application to neurophysiological signals

Measures of signal complexity can be used to distinguish neurophysiological activation from noise in those neuroimaging techniques where we record var iations of brain activity with time, e.g., fMRI, EEG, ERP. In this paper we explore a recently developed approach to calculate a quantitative measure of deterministic signal complexity and information content: The Renyi numbe r. The Renyi number is by definition an entropy, i.e., a classically used m easure of disorder in physical systems, and is calculated in this paper ove r the basis of the time frequency representation (TFRs) of the measured sig nals. When calculated in this form, the Renyi entropy (RE) indirectly chara cterizes the complexity of a signal by providing an approximate counting of the number of separated elementary atoms that compose the time series in t he time frequency plane. In this sense, this measure conforms closely to ou r visual notion of complexity since low complexity values are obtained fur signals formed by a small number of "components". The most remarkable prope rties of this measure are twofold: 1) It dues not rely on assumptions about the time series such as stationarity or gaussianity and 2) No model of the neural process under study is required, e.g., no hemodynamic response mode l for fMRI. The method is illustrated in this pager using fMRI, intracrania l ERPs and intracranial potentials estimated from scalp recorded ERPs throu gh an inverse solution (ELECTRA). The main theoretical and practical drawba cks of this measure, especially its dependence of the selected TFR, are dis cussed. Also the capability of this approach to produce, with less restrict ive hypothesis, results comparable to those obtained with more standard met hods but is emphasized. Hum. Brain Mapping 11:46-57, 2000. (C) 2000 Wiley-L iss, Inc.