Estimation of the phase response curve from Parkinsonian tremor

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.