On modeling the neuronal activity in movement disorder patients by using the Ornstein Uhlenbeck Process

Abstract

Abstract-Mathematical models of the neuronal activity in the affected brain regions of Essential Tremor (ET) and Parkinson's Disease (PD) patients could shed light into the underlying pathophysiology of these diseases, which in turn could help develop personalized treatments including adaptive Deep Brain Stimulation (DBS). In this paper, we use an Ornstein Uhlenbeck Process (OUP) to model the neuronal spiking activity recorded from the brain of ET and PD patients during DBS stereotactic surgery. The parameters of the OUP are estimated based on Inter Spike Interval (ISI) measurements, i.e., the time interval between two consecutive neuronal firings, by means of the Fortet Integral Equation (FIE). The OUP model parameters identified with the FIE method (OUP-FIE) are then used to simulate the ISI distribution resulting from the OUP. Other widely used neuronal activity models, such as the Poisson Process (PP), the Brownian Motion (BM), and the OUP whose parameters are extracted by matching the first two moments of the ISI (OUP-MOM), are also considered. To quantify how close the simulated ISI distribution is to the measured ISI distribution, the Integral Square Error (ISE) criterion is adopted. Amongst all considered stochastic processes, the ISI distribution generated by the OUP-FIE method is shown to produce the least ISE. Finally, a directional Wilcoxon signed rank test is used to show statistically significant reduction in the ISE value obtained from the OUP-FIE compared to the other stochastic processes.

Modeling sequence and quasi-uniform assumption in computational neurostimulation

“…Developing computational neurostimulation models requires the right balance of detailed multiscale model with appropriate reductionism (Douglas et al, 2015;Frohlich et al, 2015;Holt and Netoff, 2014;Karamintziou et al, 2014;Mina et al, 2013;Modolo et al, 2011;Shukla et al, 2014). This review attempts to present the modeling process as tractable, even when dealing with unknowns, including serializing modeling steps and applying the quasi-uniform assumption where relevant.…”

SPA: Stochastic Probability Adjustment for System Balance of Unsupervised SNNs

“…Our system can be used in a wide range of unsupervised SNN frameworks and improve their classification performance. The transmitter's movement is modeled as a Brownian-like stochastic process, and the establishment of synapses is similar to the Ornstein Uhlenbeck Process (OUP) [13]. Through the constraints of the stochastic process, the overall competition of SNNs is reduced, thus improving image classification accuracy.…”