A population model of deep brain stimulation in movement disorders from circuits to cells

Copyright © 2020 Yousif, Bain, Nandi and Borisyuk.For more than 30 years, deep brain stimulation (DBS) has been used to target the symptoms of a number of neurological disorders and in particular movement disorders such as Parkinson's disease (PD) and essential tremor (ET). It is known that the loss of dopaminergic neurons in the substantia nigra leads to PD, while the exact impact of this on the brain dynamics is not fully understood, the presence of beta-band oscillatory activity is thought to be pathological. The cause of ET, however, remains uncertain, however pathological oscillations in the thalamocortical-cerebellar network have been linked to tremor. Both of these movement disorders are treated with DBS, which entails the surgical implantation of electrodes into a patient's brain. While DBS leads to an improvement in symptoms for many patients, the mechanisms underlying this improvement is not clearly understood, and computational modeling has been used extensively to improve this. Many of the models used to study DBS and its effect on the human brain have mainly utilized single neuron and single axon biophysical models. We have previously shown in separate models however, that the use of population models can shed much light on the mechanisms of the underlying pathological neural activity in PD and ET in turn, and on the mechanisms underlying DBS. Together, this work suggested that the dynamics of the cerebellar-basal ganglia thalamocortical network support oscillations at frequency range relevant to movement disorders. Here, we propose a new combined model of this network and present new results that demonstrate that both Parkinsonian oscillations in the beta band and oscillations in the tremor frequency range arise from the dynamics of such a network. We find regions in the parameter space demonstrating the different dynamics and go on to examine the transition from one oscillatory regime to another as well as the impact of DBS on these different types of pathological activity. This work will allow us to better understand the changes in brain activity induced by DBS, and allow us to optimize this clinical therapy, particularly in terms of target selection and parameter setting.Peer reviewe

Stability of Circular Orbits in General Relativity: A Phase Space Analysis

Phase space method provides a novel way for deducing qualitative features of nonlinear differential equations without actually solving them. The method is applied here for analyzing stability of circular orbits of test particles in various physically interesting environments. The approach is shown to work in a revealing way in Schwarzschild spacetime. All relevant conclusions about circular orbits in the Schwarzschild-de Sitter spacetime are shown to be remarkably encoded in a single parameter. The analysis in the rotating Kerr black hole readily exposes information as to how stability depends on the ratio of source rotation to particle angular momentum. As a wider application, it is exemplified how the analysis reveals useful information when applied to motion in a refractive medium, for instance, that of optical black holes.Comment: 20 pages. Accepted for publication in Int. J. theor. Phy