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Real world data do not always obey the statistical restraints imposed upon them by sophisticated analysis techniques. In spectral analysis for instance, an ergodic process – the interchangeability of temporal for spatial averaging – is assumed for a repeat-trial design. Many evolutionary scenarios, such as learning and motor consolidation, do not conform to such linear behaviour and should be approached from a more flexible perspective. To this end we previously introduced the method of optimal spectral tracking (OST) in the study of trial-varying parameters. In this extension to our work we modify the OST routines to provide an adaptive implementation capable of reacting to dynamic transitions in the underlying system state. In so doing, we generalise our approach to characterise both slow-varying and rapid fluctuations in time-series, simultaneously providing a metric of system stability. The approach is first applied to a surrogate dataset and compared to both our original non-adaptive solution and spectrogram approaches. The adaptive OST is seen to display fast convergence and desirable statistical properties. All three approaches are then applied to a neurophysiological recording obtained during a study on anaesthetic monitoring. Local field potentials acquired from the posterior hypothalamic region of a deep brain stimulation patient undergoing anaesthesia were analysed. The characterisation of features such as response delay, time-to-peak and modulation brevity are considered.

A novel method of optimal spectral tracking is presented which permits the characterisation of trial-varying parameters. Many experimental studies suffer from the limitations of available analysis methodologies, which often impose a condition of stationarity. This severely limits our ability to track slow varying or dynamic responses with any statistical certainty. Presented is a complete framework for the non-stationary analysis of trial-varying data. Theory is introduced and developed in the characterisation of speed dependent neural modulation of the locomotor drive to tibialis anterior (TA) during healthy treadmill locomotion. The approach adopts adaptive filter theory while retaining a spectral focus, thus remaining compatible with much of the current literature. Spectral tracking procedures are evaluated using both surrogate and neurophysiological time-series. Confidence intervals are derived in both empiric and numerical form. Analysis of the pre-synaptic drive to TA under the modulation of treadmill belt speed follows, with results demonstrating clear speed dependent influences on the spectral content of TA, suggesting dynamic neural modulation of the locomotor drive. Findings include speed-modulated components at 7-12 Hz (early swing) and 15-20 Hz (pre-stance). Speed invariant components were identified at 8-15 and 15-20 Hz during early and late swing, in agreement with previous studies. Modification to the method permits a sub-optimal alternative, encouraging the exploration of short epoched data.