Adaptation of dynamical properties of time series data and its applications in deep brain stimulation

The chaotic nature of the brain can be observed by electroencephalogram signals. This chaotic behavior can be affected by the progressive nature of neurodegenerative disorders like Parkinson disease. The gradual changes in dynamical behavior of brain can be tracked to facilitate effective and timely treatment. Deep brain stimulation (DBS) is used in therapy when the medication stops working. We investigate the use of chaotic signal as stimulus in DBS. We stimulate a simulated model of isolated neuron with different types of stimuli to see if periodicity in neuronal spiking can be disrupted and show that neuron, when stimulated with chaotic signal, does fire up in non-periodic/chaotic manner. Furthermore, as a step toward the development of our system for estimation of chaotic behavior of brain, we investigate the use of recurrent neural networks to adapt the chaotic characteristics of a chaotic time series in this research work. We explore two different setups of long short-term memory (LSTM). In first setup, we define three unique topologies of LSTM network and analyze those for chaotic parameter estimation in seven different test cases for shallow and deep networks. We show that the deep LSTM networks are capable of modeling the chaotic behavior of a wide range of parameters and that the network performs the best when the architecture is driven by chaotic attributes of the time series data. In second setup, we use LSTM network in a traditional configuration to predict the chaotic time series data and demonstrate that the LSTM network can make prediction over a range of chaotic parameters with adequate accuracy. This provides the basis for the generation of chaotic stimulation signals when required.