Identifying Phase-Amplitude Coupling in Cyclic Alternating Pattern using Masking Signals

Judiciously classifying phase-A subtypes in cyclic alternating pattern (CAP) is critical for investigating sleep dynamics. Phase-amplitude coupling (PAC), one of the representative forms of neural rhythmic interaction, is defined as the amplitude of high-frequency activities modulated by the phase of low-frequency oscillations. To examine PACs under more or less synchronized conditions, we propose a nonlinear approach, named the masking phase-amplitude coupling (MPAC), to quantify physiological interactions between high (α/lowβ) and low (δ) frequency bands. The results reveal that the coupling intensity is generally the highest in subtype A1 and lowest in A3. MPACs among various physiological conditions/disorders (p < 0.0001) and sleep stages (p < 0.0001 except S4) are tested. MPACs are found significantly stronger in light sleep than deep sleep (p < 0.0001). Physiological conditions/disorders show similar order in MPACs. Phase-amplitude dependence between δ and α/lowβ oscillations are examined as well. δ phase tent to phase-locked to α/lowβ amplitude in subtype A1 more than the rest. These results suggest that an elevated δ-α/lowβ MPACs can reflect some synchronization in CAP. Therefore, MPAC can be a potential tool to investigate neural interactions between different time scales, and δ-α/lowβ MPAC can serve as a feasible biomarker for sleep microstructure.

corresponds to an intermittent lower level of activation, recovers background activity and separates the phase-As. A complete CAP cycle is initiated from an phase-A and a phase-B close behind. Both the two kinds of phases can last from 2 to 60 seconds. At least two consecutive CAP cycles are required to compose a CAP sequence. Non-CAP episode is thus defined as the remaining NREM sleep which is not occupied by CAP sequences.
The three phase-A subtypes of CAP are classified according to their spectral assessments. A1 is dominated by high-voltage  waves (0.5-4Hz), and A2 appears when rapid activities occur for 20-50% of the total activation time, whereas A3 is characterized by rapid activities, especially in  activity (15-30Hz), which can occupy more than the half of the total phase-A duration 1 . Alterations of phase-A subtypes have been reported on several sleep disorders, such as sleep apnea 2 , insomnia 3 , narcolepsy 4 as well as nocturnal frontal lobe epilepsy 5 .

Empirical Mode Decomposition
Empirical Mode Decomposition (EMD) is a pre-processing method of Hilbert-Huang transform (HHT) 6 . EMD can decompose an inter-and intra-wave modulated time series into its intrinsic mode functions (IMFs), which are designed to obtain interested components based on the instantaneous spectra of IMFs. Due to its nature in maintaining the original shape of the signal, it is thus an adaptive and reliable tool in analyzing the physiological signals that may be nonlinear and nonstationary.
We design a synthetic signal to demonstrate the ability of EMD in handling with nonstationary composition.
Two nonstationary components with frequencies range within 25~35Hz and 55~65Hz are designed (Supplementary Table S3). As shown in Supplementary Fig. S1, the extracted IMFs almost reproduce the designed components. Supplementary Fig. S2 shows the algorithm of EMD in steps. For a given signal x , (1) Generating local mean curve: the algorithm begins with identifying all the local maxima and minima. The upper envelope u e is generated by connecting all the local maxima using a cubic spline curve. Likewise, all the local minima are connected to create the lower envelope l e . Then we compute the mean m of these two envelopes.
(2) Sifting process: the first component is obtained by subtracting (1) m from x , a qualified IMF should free of riding wave with its local mean curve close to zero at any point. The sifting process should perform again on (1) h since (1) h still possess multiple extrema between zero crossings. After recursively applying this step on () l h , the sifting process will stop on the condition that the shortest period component of the signal (here we take the first IMF 1 c as an example) is obtained. Then we separate c1(t) from the data and obtain the residue r1(t).
(3) Generating IMFs: If the residue r1(t) still contains larger scales information, it is treated as a new input and repeated the sifting process again. This process should be repeated on all the subsequent residues. Finally, the EMD produce IMFs with a residue signal.
Not until the residue r(t) should either constant, or a monotonic slope, or a function with only one extremum that the whole procedure is terminated.