Dynamical systems for non-invasive control of neural activity

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Many neurological disorders, including Parkinson's disease (PD), are characterized by abnormally strong oscillations in brain activity. At a cellular level, these oscillations lead to synchronous activity: Neurons fire in lockstep with each other, so that they are unable to perform their normal roles in controlling movements, interpreting sensory input, and planning future behaviours. The prevalence of these pathological oscillations has led to a search for interventions that can control them.Outside the field of neuroscience, oscillations have been observed in many other systems, at scales ranging from subatomic particles to power grids. In studying these systems, mathematicians have identified a phenomenon known as "asynchronous quenching". This results when an oscillating system is perturbed by an external input that oscillates at a slightly different frequency and with a slightly different amplitude. This simple intervention can drastically reduce the strength of the unwanted oscillation.Mathematically, asynchronous quenching is a universal behaviour of a certain class of oscillating systems that includes the brain. Nevertheless, it has not to our knowledge been used in any previous neuroscience study. This is likely due to the daunting complexity of interacting oscillators, which can produce a wide range of unpredictable behaviours. We therefore propose a tightly integrated experimental and mathematical approach to test the validity of asynchronous quenching as a means of controlling brain oscillations.Our overarching goal will be to reduce the pathological oscillations seen in PD, using non-invasive brain stimulation. In Aim 1, we will simulate models of brain function that produce normal oscillations and search for stimulation parameters that reduce them. We will then validate these mathematical results in animal experiments, involving electrophysiological recordings from populations of neurons. In Aim 2, we will use pharmacological methods to generate brain oscillations that resemble those in PD. We will update the model to capture these oscillations and then identify stimulation parameters that restore normal function. In Aim 3, we will determine empirically whether these interventions can restore behavioural functions that are lost in PD. Together, these Aims will lead to a new understanding of brain oscillations, which will improve outcomes for the large number of PD patients who are ineligible for standard surgical treatments.