Volume 10 Supplement 1
Frequency control in neuronal oscillators using colored noise
© Galán; licensee BioMed Central Ltd. 2009
Published: 13 July 2009
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 . 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.
where σ2 is the variance of the colored noise, and the brackets denote averaging in time.
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.
This work has been supported by The Mount Sinai Health Care Foundation.
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