Minimum energy desynchronizing control for coupled neurons

Abstract

We employ optimal control theory to design an event-based, minimum energy, desynchronizing control stimulus for a network of pathologically synchronized, heterogeneously coupled neurons. This works by optimally driving the neurons to their phaseless sets, switching the control off, and letting the phases of the neurons randomize under intrinsic background noise. An event-based minimum energy input may be clinically desirable for deep brain stimulation treatment of neurological diseases, like Parkinson's disease. The event-based nature of the input results in its administration only when it is necessary, which, in general, amounts to fewer applications, and hence, less charge transfer to and from the tissue. The minimum energy nature of the input may also help prolong battery life for implanted stimulus generators. For the example considered, it is shown that the proposed control causes a considerable amount of randomization in the timing of each neuron's next spike, leading to desynchronization for the network.

Pulsatile desynchronizing delayed feedback for closed-loop deep brain stimulation

“…It would be interesting to compare the efficacy in suppressing pathological neuronal oscillations of the methods considered in this paper to other control methods, for instance, to those relying on event-based or phase-locked stimulation [66, 67, 101], where the stimuli are administered at a particular phase of the oscillation cycle. Vulnerable tremor phases were studied with non-invasive approaches [102, 103] as well as with thalamic DBS [104].…”

Neurocontrol: Methods, models and technologies for manipulating dynamics in the brain

“…For example, minimum time control [106], energy-optimal control [107]- [109], and both minimum energy and time control [110]. In [108], a procedure for finding an energyoptimal stimulus was proposed based on computation of Lyapunov exponents.…”

“…Conditions for desynchronizing two neurons were derived and were extended to large neural population by maximizing the phase distribution. Unlike other proposed methods in [106], [110], the procedure does not need the full model of the dynamics. Later, the methodology was moved closer towards experimentation (adapted for extracellular neural stimulation as is the case of DBS) in [111].…”

Locally optimal extracellular stimulation for chaotic desynchronization of neural populations

“…Theoretical work, e.g., Rosenblum and Pikovsky (2004) and Popovych et al (2005), show that desynchronization can be achieved with delayed feedback control to counter the effects of mean field coupling in a heterogeneous ensemble of oscillators. In Danzl et al (2009), a minimum time desynchronizing control based on phase resetting for a coupled neural network was established using a Hamilton-Jacobi-Bellman approach, which was later extended by Nabi et al (2013) to desynchronizeneurons using an energy-optimal criterion.…”

“…Unlike other proposed methods such as Danzl et al (2009), Nabi et al (2013), the procedure does not need the full model of the dynamics, and unlike Danzl et al (2010), only requires a single input. Furthermore, this procedure is highly adaptable, and has the potential to be applied to be applied to other models of neural activity, such as those with bursting limit cycles oscillators (see Sherwood and Guckenheimer (2010)) which are now thought to play a crucial role in Parkinson’s disease (Bevan et al 2006; Hahn et al 2008; Gale et al 2009; Ammari et al 2011; Tai et al 2011).…”