Understanding dynamics of the system using Hilbert phases: An application to study neonatal and fetal brain signals

Abstract

The Hilbert phase φ(t) of a signal x(t) exhibits slips when the magnitude of their successive phase difference |φ(t i+1 ) − φ(t i )| exceeds π. By applying this approach to periodic, uncorrelated, and longrange correlated data, we show that the standard deviation of the time difference between the successive phase slips Δτ normalized by the percentage of slips in the data is characteristic of the correlation in the data. We consider a 50×50 square lattice and model each lattice point by a secondorder autoregressive (AR2) process. Further, we model a subregion of the lattice using a different set of AR2 parameters compared to the rest. By applying the proposed approach to the lattice model, we show that the two distinct parameter regions introduced in the lattice are clearly distinguishable. Finally, we demonstrate the application of this approach to spatiotemporal neonatal and fetal magnetoencephalography signals recorded using 151 superconducting quantum interference device sensors to identify the sensors containing the neonatal and fetal brain signals and discuss the improved performance of this approach over the traditionally used spectral approach.

Removal of interference from fetal MEG by frequency dependent subtraction

“…The fetal head position can be determined from ultrasound (Micheli et al, 2010), placement of a marker coil on the maternal abdomen (Micheli et al, 2010), or from phase slip analysis (Govindan et al, 2009). Then sensors in the vicinity of the fetal head (a reference exclusion zone) are removed from the potential reference channel list.…”

Decrement of uterine myometrial burst duration as a correlate to active labor: A Hilbert phase approach

“…Thus, spectral properties can be studied using Δ τ and this has been attempted in an earlier work [15] to study spectral content of the atmospheric variables. In the recent work we have localized the spontaneous fetal brain signals by studying the standard deviation of the inter-slip intervals ( σ (Δ τ ), where σ (·) denotes the standard deviation) [16]. …”

Detection of Discontinuous Patterns in Spontaneous Brain Activity of Neonates and Fetuses

“…The HP exhibits slips when the magnitude of their successive phase differences |ϕ( t i +1 ) − ϕ( t i | exceeds π. The time difference between the successive HP slips (Δτ) is characteristic of a system [9]. In the case of periodic signals, Δτ defines the signal's periodicity and standard deviation of Δτ, σ(Δτ), is zero in such cases.…”