Nonlinear analysis and selection of relevant parameters in assessing the treatment results of reducing tremor, using DBS procedure

The DBS (deep brain stimulation) is an invasive method of applying electrical stimulus to a sum of thalamic nucleus and represents a successful method for reducing the tremor. The aim of this research is to find a method to determine if there are abnormal responses to DBS for patients with Parkinson. DBS being an invasive method, it is indicated to determine if the method gives good results in a specific case before we pursuit with this neuro-surgical procedure. We computed the Lyapunov exponent, the fractal dimension and the self-correlation function to assess the relevance of nonlinear dynamic parameters in tremor analysis. To model a nonlinear process like Parkinsonian tremor we considered an iterated nonlinear function, which is easy to implement.