Standard multiscale entropy reflects neural dynamics at mismatched temporal scales: What’s signal irregularity got to do with it?

Abstract

Multiscale Entropy (MSE) is used to characterize the temporal irregularity of neural time series patterns. Due to its' presumed sensitivity to non-linear signal characteristics, MSE is typically considered a complementary measure of brain dynamics to signal variance and spectral power. However, the divergence between these measures is often unclear in application. Furthermore, it is commonly assumed (yet sparingly verified) that entropy estimated at specific time scales reflects signal irregularity at those precise time scales of brain function. We argue that such assumptions are not tenable. Using simulated and empirical electroencephalogram (EEG) data from 47 younger and 52 older adults, we indicate strong and previously underappreciated associations between MSE and spectral power, and highlight how these links preclude traditional interpretations of MSE time scales. Specifically, we show that the typical definition of temporal patterns via "similarity bounds" biases coarse MSE scales-that are thought to reflect slow dynamics-by high-frequency dynamics. Moreover, we demonstrate that entropy at fine time scales-presumed to indicate fast dynamicsis highly sensitive to broadband spectral power, a measure dominated by low-frequency contributions. Jointly, these issues produce counterintuitive reflections of frequency-specific content on MSE time scales. We emphasize the resulting inferential problems in a conceptual replication of cross-sectional age differences at rest, in which scale-specific entropy age effects could be explained by spectral power differences at mismatched temporal scales. Furthermore, we demonstrate how such problems may be alleviated, resulting in the indication of scale-specific age differences in rhythmic irregularity. By controlling for narrowband contributions, we indicate that spontaneous alpha rhythms during eyes open rest transiently reduce broadband signal irregularity. Finally, we recommend best practices that may better permit a valid estimation and interpretation of neural signal irregularity at time scales of interest.

Spatiotemporal complexity patterns of resting‐state bioelectrical activity explain fluid intelligence: Sex matters

“…We obtained the mMSE vectors for each subject for frontal (F), frontal left (FL), frontal right (FR), central (C), parietal (P), parietal left (PL), parietal right (PR) and middle left (ML), middle right (MR) channel sets (Figure 1) separately, using the procedure outlined in Section 2.4 (see also Figure 3). In all of these cases, the mMSE vectors were stable and characterized by a skewed inverted‐U shape across time scales, which is typical for EEG and MEG signals (Costa et al, 2005; Courtiol et al, 2016; Grandy, Garrett, Schmiedek, & Werkle‐Bergner, 2016; Kosciessa et al, 2019; Kuntzelman, Jack Rhodes, Harrington, & Miskovic, 2018; see Figure 8). Indeed, this pattern also persists in other modalities, such as fMRI (e.g., Grandy et al, 2016; McDonough & Nashiro, 2014; McDonough & Siegel, 2018; Omidvarnia, Zalesky, Ville, Jackson, & Pedersen, 2019) or in simulation studies (e.g., Courtiol et al, 2016; Grandy et al, 2016; Kuntzelman et al, 2018).…”

“…According to the theory that we often refer to in the current work (Vakorin et al, 2011), fine or coarse scales represent local or global information processing, respectively. This concept has recently met some criticism (e.g., Kosciessa et al, 2019) and, therefore, should be treated with caution. Some methodological constraints of distinguishing fine and coarse timescales have also been pointed out (Omidvarnia et al, 2019).…”

“…Furthermore, coarse‐graining essentially acts as a moving average low pass filter, which obfuscates the frequency domain content of the signal, as it has little ability to separate frequency bands. This fact yields analysis of the relationship between mMSE and frequency content of the EEG signal difficult (Courtiol et al, 2016), although certain progress has been made recently in this area (Kosciessa et al, 2019). On a more positive note, limitations of the previously introduced approaches to the multivariate extension of the MSE regarding the choice of extension of composite delay vectors of multivariate signals has been successfully resolved (Looney et al, 2018; see also Ahmed & Mandic, 2011).…”

“…The vector‐valued complexity profiles of a signal obtainable using MSE or mMSE have been demonstrated to contain more information on the complexity of the underlying system than the SampEn measure alone. It should also be noted that complex dynamics typically involve structures across temporal scales, from fine‐scales to coarse‐scales (Ahmed & Mandic, 2011; Catarino, Churches, Baron‐Cohen, Andrade, & Ring, 2011; Costa, Goldberger, & Peng, 2002; Kosciessa, Kloosterman, & Garrett, 2019; Looney et al, 2018). Computational studies have shown the positive relationship between small‐world network organization and complexity on coarse‐scales (Nobukawa, Nishimura, & Yamanishi, 2019; Park et al, 2019).…”

Boosts in brain signal variability track liberal shifts in decision bias

“…Next, we investigated whether the entropy-behavior correlation could alternatively be explained by total signal variation (quantified via the signal SD), or spectral power. Specifically, the variance structure of a signal can influence entropy estimates through the pattern similarity (r) parameter (width of gray bars in Figure 2 ), even when this parameter is recomputed for each timescale after coarsening, as we did ( Kosciessa et al, 2020 ). In addition, E/MEG data is often quantified in terms of oscillatory spectral power in canonical delta (1–2 Hz), theta (3–7 Hz), alpha (8–12 Hz), beta (13–30 Hz) and gamma (60–100 Hz) bands, which might be able to explain the entropy results through a similar dependency.…”