Study of chaotic behavior of tremor of some Parkinsonians under deep brain stimulation

Deep Brain Stimulation, functional neurosurgery for Parkinson's disease treatment, has three parameters: frequency, pulse width, and voltage. They should be selected appropriately to achieve an effective treatment. In this research, we studied some nonlinear dynamics of Parkinsonian tremor under Deep Brain Stimulation. We recorded finger tremor signals of 8 patients at different voltages as data. To study tremor behavior variation at different voltages, we extracted some nonlinear dynamic features of the data. These features were: embedding space, correlation dimension, largest Lyapunov exponent, entropy and variance of embedding space along x, and y axes. We found that the largest Lyapunov exponents were positive and correlation dimensions of data were not integer, and also all embedding spaces at different voltages had attractors. These observations show that the tremor signal has chaotic behaviors. Also, embedding space variance along x, and y axes in all cases and entropy in the most of them had minimum values at highest voltages in comparison with other voltages. We plotted bar graphs of embedding space variances along x, and y axes at every patient's recorded voltages. A reduction procedure was seen after a threshold in all graphs. As a result, all the chaotic features change with the voltage variation. In the future, it could be possible to select the optimum stimulation voltages by using chaotic features of tremor.