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AbstractDeep brain stimulation (DBS) is known to be an effective treatment for a variety of neurological disorders, including Parkinson’s disease and essential tremor (ET). At present, it involves administering a train of pulses with constant frequency via electrodes implanted into the brain. New ‘closed-loop’ approaches involve delivering stimulation according to the ongoing symptoms or brain activity and have the potential to provide improvements in terms of efficiency, efficacy and reduction of side effects. The success of closed-loop DBS depends on being able to devise a stimulation strategy that minimizes oscillations in neural activity associated with symptoms of motor disorders. A useful stepping stone towards this is to construct a mathematical model, which can describe how the brain oscillations should change when stimulation is applied at a particular state of the system. Our work focuses on the use of coupled oscillators to represent neurons in areas generating pathological oscillations. Using a reduced form of the Kuramoto model, we analyse how a patient should respond to stimulation when neural oscillations have a given phase and amplitude. We predict that, provided certain conditions are satisfied, the best stimulation strategy should be phase specific but also that stimulation should have a greater effect if applied when the amplitude of brain oscillations is lower. We compare this surprising prediction with data obtained from ET patients. In light of our predictions, we also propose a new hybrid strategy which effectively combines two of the strategies found in the literature, namely phase-locked and adaptive DBS.Author summaryDeep brain stimulation (DBS) involves delivering electrical impulses to target sites within the brain and is a proven therapy for a variety of neurological disorders. Closed loop DBS is a promising new approach where stimulation is applied according to the state of a patient. Crucial to the success of this approach is being able to predict how a patient should respond to stimulation. Our work focusses on DBS as applied to patients with essential tremor (ET). On the basis of a theoretical model, which describes neurons as oscillators that respond to stimulation and have a certain tendency to synchronize, we provide predictions for how a patient should respond when stimulation is applied at a particular phase and amplitude of the ongoing tremor oscillations. Previous experimental studies of closed loop DBS provided stimulation either on the basis of ongoing phase or amplitude of pathological oscillations. Our study suggests how both of these measurements can be used to control stimulation. As part of this work, we also look for evidence for our theories in experimental data and find our predictions to be satisfied in one patient. The insights obtained from this work should lead to a better understanding of how to optimise closed loop DBS strategies.

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