Table of Contents
International Scholarly Research Notices
Volume 2017 (2017), Article ID 5865101, 10 pages
https://doi.org/10.1155/2017/5865101
Research Article

A Consistent Definition of Phase Resetting Using Hilbert Transform

Department of Physics and Astronomy, College of Charleston, 66 George Street, Charleston, SC 29424, USA

Correspondence should be addressed to Sorinel A. Oprisan

Received 13 December 2016; Accepted 9 April 2017; Published 3 May 2017

Academic Editor: Tibor Toth

Copyright © 2017 Sorinel A. Oprisan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A phase resetting curve (PRC) measures the transient change in the phase of a neural oscillator subject to an external perturbation. The PRC encapsulates the dynamical response of a neural oscillator and, as a result, it is often used for predicting phase-locked modes in neural networks. While phase is a fundamental concept, it has multiple definitions that may lead to contradictory results. We used the Hilbert Transform (HT) to define the phase of the membrane potential oscillations and HT amplitude to estimate the PRC of a single neural oscillator. We found that HT’s amplitude and its corresponding instantaneous frequency are very sensitive to membrane potential perturbations. We also found that the phase shift of HT amplitude between the pre- and poststimulus cycles gives an accurate estimate of the PRC. Moreover, HT phase does not suffer from the shortcomings of voltage threshold or isochrone methods and, as a result, gives accurate and reliable estimations of phase resetting.