- Poster presentation
- Open Access
Frequency control in neuronal oscillators using colored noise
- Roberto F Galán1Email author
https://doi.org/10.1186/1471-2202-10-S1-P252
© Galán; licensee BioMed Central Ltd. 2009
- Published: 13 July 2009
Keywords
- Deep Brain Stimulation
- Nonlinear Oscillator
- Firing Frequency
- Input Current
- Neuronal Excitability
Introduction
It is well-known that the natural frequency of nonlinear oscillators, like neurons, can be strongly affected when driven by a periodic force or when embedded in a network [1]. In contrast, the effects of stochastic forces on the frequency of nonlinear oscillators are incompletely understood. In this context, we have mathematically investigated how colored noise and its amplitude affect the firing frequency of neurons. Our result suggests that low-amplitude colored noise may be used in deep-brain stimulation protocols to control neuronal excitability efficiently.
Methods
where σ2 is the variance of the colored noise, and the brackets denote averaging in time.
Results
Note that the average frequency change is always negative, indicating that the colored noise lowers the natural frequency of the oscillator. In the white-noise limit (τ→0), the net frequency change goes to zero. In the limit of slowly varying inputs (τ→∞), the net frequency change is -σ2/(2ω0). Thus, by combining the amplitude and time constant of the noise, one obtains a wide range for frequency control. This may have important implications for deep brain stimulation, in particular, to efficiently decrease neuronal excitability in hyperactive areas (e.g., the focus of an epileptic seizure) with minimal current injection.
Declarations
Acknowledgements
This work has been supported by The Mount Sinai Health Care Foundation.
Authors’ Affiliations
References
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- Galán RF, Ermentrout GB, Urban NN: Efficient estimation ofphase-resetting curves in real neurons and its significance forneural-network modeling. Phys Rev Lett. 2005, 94: 158101-158105. 10.1103/PhysRevLett.94.158101.PubMed CentralPubMedView ArticleGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd.