A waveform-independent measure of recurrent neural activity

Rhythmic neural activity, so called oscillations, play a key role for neural information transmission, processing and storage. Neural oscillations in distinct frequency bands are central to physiological brain function and alterations thereof have been associated with several neurological and psychiatric disorders. The most common methods to analyse neural oscillations, e.g. short-term Fourier transform or wavelet analysis, assume that measured neural activity is composed of a series of symmetric prototypical waveforms, e.g. sinusoids. However, usually the models generating the signal, including waveform shapes of experimentally measured neural activity are unknown. Decomposing asymmetric waveforms of nonlinear origin using these classic methods may result in spurious harmonics visible in the estimated frequency spectra. Here, we introduce a new method for capturing rhythmic brain activity based on recurrences of similar states in phase-space. This method allows for a time-resolved estimation of amplitude fluctuations of recurrent activity irrespective of or specific to waveform-shapes. The algorithm is derived from the well-established field of recurrence analysis, which has rarely been adopted in neuroscience. In this paper, we show its advantages and limitations in comparison to short-time Fourier transform and wavelet convolution using periodic signals of different waveform shapes. Further, we demonstrate its application using experimental data, i.e. intracranial electrophysiological recordings from the human motor cortex of one epilepsy patient.