Predicting the effects of deep brain stimulation using a reduced coupled oscillator model

Abstract

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...

Phase dependence of response curves to stimulation and their relationship: from a Wilson-Cowan model to essential tremor patient data

“…In fact, the ARC is simply a scaled version of the opposite of the PRC derivative. A similar relationship has been first reported in a theoretical study in the context of an individual oscillator [36], and more recently in [14] in the context of population response curves of a Kuramoto model. It is noteworthy that a similar result is found for 2D focus models with slow decay, and in particular for the linearisation of the WC model, another popular neuroscience model very different in essence from coupled oscillator models.…”

“…However detailed knowledge of how ET comes about is missing, which makes simple, canonical models natural candidates to study ET. Recently, phaselocked DBS was studied using a Kuramoto oscillator model which conveniently captures phases, but does not model interacting neural populations with distinct properties [14]. In the present work, we focus on a neural mass model, the Wilson-Cowan (WC) model, whose architecture can be mapped onto the neural populations thought to be involved in the generation of ET, and allows for strong coupling between the populations.…”

Optimal Closed-loop Deep Brain Stimulation with Multi-Contact Electrodes

“…In this section, we consider how stimulation with a single electrode acts on a population of oscillators. Here we follow our previous paper [14], which the interested reader may refer to for a more detailed derivation of the results presented in this section. A list of frequently used notation is provided in Table 1 Our goal in this subsection is to show how the amplitude measured in feedback signals can be related to the synchrony of neural populations.…”

“…In our previous work [14], we provided a mathematical basis for the phase and amplitude dependence of DBS. Here, we extend these ideas and introduce adaptive coordinated reset (ACR), which proposes a closed-loop strategy especially suited to multi-contact systems.…”

“…Under the reasonable assumption that the time evolution of θ n is approximately monotonic, it can be shown that [14]…”