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Stochastic modeling of the neuronal activity in the subthalamic nucleus and model parameter identification from Parkinson patient data

Biological Cybernetics volume 103, pages 273–283 (2010)Cite this article

Abstract

Several stochastic models, with various degrees of complexity, have been proposed to model the neuronal activity from different parts of the human brain. In this article, we use a simple Ornstein–Uhlenbeck process (OUP) to model the spike activity recorded from the subthalamic nucleus of patients suffering from Parkinson’s disease at the time of implantation of the electrodes for deep brain stimulation. From the recorded data, which contains information about the spike times of a single neuron, we identify and extract the model parameters of the OUP. We then use these parameters to numerically simulate the inter-spike intervals and the voltage across the neuron membrane. We finally assess how well the proposed mathematical model fits to the measured data and compare it with other commonly adopted stochastic models. We show an excellent agreement between the computer-generated data according to the OUP model and the measured one, as well as the superiority of the OUP model when compared to the Poisson process model and the random walk model; thus, establishing the validity of the OUP as a simple yet biologically plausible model of the neuronal activity recorded from the subthalamic nucleus of Parkinson’s disease patients.

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Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Chicago, 851 S Morgan Street, M/C 154, Chicago, IL, USA

    Ishita Basu, Daniel Graupe & Daniela Tuninetti

  2. Department of Neurosurgery, University of Illinois at Chicago, 912 S Wood Street, M/C 799, Chicago, IL, USA

    Konstantin V. Slavin

Authors
  1. Ishita Basu
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  2. Daniel Graupe
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  3. Daniela Tuninetti
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  4. Konstantin V. Slavin
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Correspondence to Ishita Basu.

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Basu, I., Graupe, D., Tuninetti, D. et al. Stochastic modeling of the neuronal activity in the subthalamic nucleus and model parameter identification from Parkinson patient data. Biol Cybern 103, 273–283 (2010). https://doi.org/10.1007/s00422-010-0397-3

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  • DOI: https://doi.org/10.1007/s00422-010-0397-3

Keywords

  • Ornstein–Uhlenbeck process
  • Stochastic modeling
  • Inter-spike interval
  • Parkinson’s disease
  • Subthalamic nucleus
  • Parameter identification