title: Estimation of the phase response curve from Parkinsonian tremor.
abstract: Phase response curves (PRCs), characterizing the response of an oscillator to weak external perturbation, have been estimated from a broad range of biological oscillators, including single neurons in vivo. PRC estimates, in turn, provide an intuitive insight into how oscillatory systems become entrained and how they can be desynchronized. Here, we explore the application of PRC theory to the case of Parkinsonian tremor. Initial attempts to establish a causal effect of subthreshold transcranial magnetic stimulation applied to primary motor cortex on the filtered tremor phase were unsuccessful. We explored the possible explanations of this and demonstrate that assumptions made when estimating the PRC in a traditional setting, such as a single neuron, are not arbitrary when applied to the case of tremor PRC estimation. We go on to extract the PRC of Parkinsonian tremor using an iterative method that requires varying the definition of the tremor cycle and estimating the PRC at multiple peristimulus time samples. Justification for this method is supported by estimates of PRC from simulated single neuron data. We provide an approach to estimating confidence limits for tremor PRC and discuss the interpretational caveats introduced by tremor harmonics and the intrinsic variability of the tremor's period.
authors.affiliation: Sobell Department of Motor Neuroscience and Movement Disorders, University College London Institute of Neurology, London, United Kingdom;
authors.forename: Tabish A
authors.initials: TA
authors.lastname: Saifee
authors.affiliation: Sobell Department of Motor Neuroscience and Movement Disorders, University College London Institute of Neurology, London, United Kingdom;
authors.forename: Mark J
authors.initials: MJ
authors.lastname: Edwards
authors.affiliation: Sobell Department of Motor Neuroscience and Movement Disorders, University College London Institute of Neurology, London, United Kingdom;
authors.forename: Panagiotis
authors.initials: P
authors.lastname: Kassavetis
authors.affiliation: Division of Neuroscience, Medical Research Institute, University of Dundee, Dundee, United Kingdom; and Department of Neurology, Ninewells Hospital Dundee, Dundee, United Kingdom thomasgilbertson@nhs.net.
authors.forename: Tom
authors.initials: T
authors.lastname: Gilbertson
mesh_terms: D000200:Action Potentials; D000368:Aged; D001683:Biological Clocks; D005260:Female; D006801:Humans; D008297:Male; D008959:Models, Neurological; D009044:Motor Cortex / Q000503:physiopathology*; D018482:Muscle, Skeletal / Q000294:innervation / Q000503:physiopathology; D009474:Neurons / Q000502:physiology*; D020734:Parkinsonian Disorders / Q000150:complications*; D012815:Signal Processing, Computer-Assisted; D050781:Transcranial Magnetic Stimulation; D014202:Tremor / Q000209:etiology / Q000503:physiopathology*
keywords: Morris-Lecar neuron; Parkinson's disease; phase response curve; transcranial magnetic stimulation; tremor