Deep 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, provided a number of conditions are satisfied. For such patients, we predict that 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 closed-loop strategies found in the literature, namely phase-locked and adaptive DBS.
Essential tremor manifests predominantly as a tremor of the upper limbs. One therapy option is high-frequency deep brain stimulation, which continuously delivers electrical stimulation to the ventral intermediate nucleus of the thalamus at about 130 Hz. Constant stimulation can lead to side effects, it is therefore desirable to find ways to stimulate less while maintaining clinical efficacy. One strategy, phase-locked deep brain stimulation, consists of stimulating according to the phase of the tremor. To advance methods to optimise deep brain stimulation while providing insights into tremor circuits, we ask the question: can the effects of phase-locked stimulation be accounted for by a canonical Wilson-Cowan model? We first analyse patient data, and identify in half of the datasets significant dependence of the effects of stimulation on the phase at which stimulation is provided. The full nonlinear Wilson-Cowan model is fitted to datasets identified as statistically significant, and we show that in each case the model can fit to the dynamics of patient tremor as well as to the phase response curve. The vast majority of top fits are stable foci. The model provides satisfactory prediction of how patient tremor will react to phase-locked stimulation by predicting patient amplitude response curves although they were not explicitly fitted. We also approximate response curves of the significant datasets by providing analytical results for the linearisation of a stable focus model, a simplification of the Wilson-Cowan model in the stable focus regime. We report that the nonlinear Wilson-Cowan model is able to describe response to stimulation more precisely than the linearisation.
Deep 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 Introduction 1 Symptoms of several neurological disorders are thought to arise from overly synchronous 2 activity within neural populations. The severity of clinical impairment in Parkinson's 3 disease (PD) is known to be correlated with an increase in the beta (13-35 Hz) 4 oscillations in the local field potential (LFP) and in the activity of individual neurons in 5October 16, 2018 2/34 the basal ganglia [1, 2]. The tremor symptoms associated with essential tremor (ET) are 6 thought to arise from synchronous activity in a network of brain areas including the 7 thalamus [3]. In both PD and ET the muscle activity driving the tremor is coherent 8 with local field potentials in the thalamus [4] and bursts of spikes produced by 9 individual thalamic neurons [5]. 10 Deep brain stimulation (DBS) is a well-established treatment option for PD and ET 11 which involves delivering stimulation via electrodes implanted into the brain. The 12 present generation of the technology involves manually tuning the parameters of 13 stimulation, such as the pulse width, frequency and intensity in an attempt to achieve 14 the best treatment. In particular, the choice of frequency is known to be crucial for 15 efficacy, and high frequency DBS (120-180 Hz) has been found to be effective for PD 16 and ET patients [6]. High frequency DBS is known to suppress the pathological 17 oscillations occurring in PD [7], but despite its long history, the underlying mechanisms 18 causing this suppression remain unclear, and several distinct theories have been 19 proposed [8-10]. One influential theory suggests that high frequency DBS activates 20 target neurons to such an extent that their synaptic transmission becomes saturated 21 and they are no longer able to transmit pathological oscillations [11]. Since high 22 frequency DBS can cause side-effects such as speech-impairments [12] and gambling 23 tendencies [13], improvements to this treatment approach are desi...
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