Journal of Clinical & Experimental Pharmacology

Abstract

Spectral and Higher-Order-Spectral Analysis of Tremor Time Series

Malenka Mader, Juliane Klatt, Florian Amtage, Bernhard Hellwig, Wolfgang Mader, Linda Sommerlade and Björn Schelter

Objectives: The aim of this study was to investigate linear and nonlinear properties of tremor time series. To this end, we applied linear (second order) and nonlinear (higher order) spectral and cross-spectral analysis to 58 Electroencephalographic (EEG) and Electromyographic (EMG) tremor recordings of seven essential and five Parkinsonian Tremor patients. Methods: Second and third order spectral analysis was performed on two types of data. First, data was simulated from a model mimicking the nonlinear properties of the tremor time series. Limitations of linear second order spectral analysis are illustrated in those simulations. Those limitations can be overcome by nonlinear third order spectral analysis. Second, tremor recordings from the trembling hand and contralateral motor area of the brain of the tremor patients were analyzed both by second and third order spectral analysis. Results: Linear spectral analysis suggested nonlinearity of dynamics and interactions of processes measured by EEG and EMG. Applying bispectral analysis those nonlinearities were investigated. We found that a measure for nonlinearity based on bispectra was significant for most EMG recordings, as well as for the interaction of EEG and EMG. Conclusions: Linear spectral analysis is a powerful tool when assessing spectral properties of time series. However, linear techniques fail to reveal nonlinear couplings. In the application of nonlinear spectral analysis to tremor time series, we showed that the dynamics of the hand muscle as well as the interaction of hand muscle and brain are governed by nonlinearities.