A Consistent Definition of Phase Resetting Using Hilbert Transform.

Sorinel A Oprisan

doi:10.1155/2017/5865101

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.

Highlights

Oscillatory activities over a wide range of spatial scales, from single neural cells to whole brain regions, are believed to be relevant for brain activities from sensory information processing to consciousness [1]
The first step in extracting the phase resetting curve (PRC) from experimental data is performing a Hilbert Transform (HT) on the original voltage time series using (2)
The instantaneous amplitude is the amplitude of the complex HT and the instantaneous frequency is the rate of change of the instantaneous phase angle (see (4))

Summary

A Consistent Definition of Phase Resetting Using Hilbert Transform

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. 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 found that the phase shift of HT amplitude between the pre- and poststimulus cycles gives an accurate estimate of the PRC. 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

Background

Model and Method

Results

Conclusions