The HEURECA method: Tracking multiple phase coupling dynamics on a single trial basis

Highlights

• The HEURECA method is introduced.

• HEURECA detects time segments of quasi-stable EEG phase coupling patterns.

• HEURECA enables the detection of complex, multivariate phase associations.

• HEURECA determines synchrostates, i.e. recurring EEG phase coupling topographies.

• HEURECA works on a single trial basis.

Abstract

Background

Although acquisition techniques have improved tremendously, the neuroscientific understanding of complex cognitive phenomena is still incomplete. One of the reasons for this shortcoming may be the lack of sophisticated signal processing methods. Complex cognitive phenomena usually involve various mental subprocesses whose temporal occurrence varies from trial to trial. Mostly, these mental subprocesses require large-scale integration processes between multiple brain areas that are most likely mediated by complex, non-linear phase coupling mechanisms. Consequently, a spatiotemporal analysis of complex, multivariate phase synchronization patterns on a single trial basis is necessary.

New method

This paper introduces the HEURECA method (How to Evaluate and Uncover Recurring EEG Coupling Arrangements) that enables the dynamic detection of distinguishable multivariate functional connectivity states in the electroencephalogram. HEURECA adaptively divides a trial into segments of quasi-stable phase coupling topographies and assigns similar topographies to the same synchrostate cluster.

Results

HEURECA is evaluated by means of simulated data. The results show that it reliably reconstructs a time series of recurring phase coupling topographies and successfully gathers them into clusters of interpretable neural synchrostates. The advantages and unique features of HEURECA are further illustrated by investigating the popular complex cognitive phenomenon insight.

Comparison with existing methods

Unlike existing methods, HEURECA detects complex phase relationships between more than two signals and is applicable to single trials.

Conclusions

Since HEURECA is applicable to all kinds of circular data, it not only provides new insights into insight, but also into a variety of other phenomena in neuroscience, physics or other scientific fields.

Introduction

In recent years, neuroscientific acquisition techniques have improved tremendously and new experimental paradigms have been developed that enable even the recording of complex cognitive phenomena like, for instance, learning, problem solving or creative ideation. Despite these recent advances, the neuroscientific understanding of complex cognitive phenomena is still incomplete. According to Cohen (2014) this shortcoming might be the result of a lack of sophisticated signal processing methods. Complex cognitive phenomena usually involve various mental subprocesses whose temporal occurrence varies from trial to trial. Thus, a dynamic analysis of single trials is necessary. Even superimpositions of several subprocesses are plausible. Most likely, each mental subprocess involves a distinctive set of brain areas that are not necessarily close to each other but that nevertheless exchange and integrate information. Current research suggests that such large-scale integration processes are mediated by phase synchronization or phase coupling mechanisms (cf. Fries, 2015, Uhlhaas et al., 2010, Fell and Axmacher, 2011). Considering the sophisticated nature of the brain, these phase coupling mechanisms are probably non-linear and more complex than simple phase shifts. Consequently, a complex multivariate phase synchronization measure is required in order to successfully study the neurophysiological correlates of complex cognitive phenomena. Since several brain areas are involved whose functional roles vary over time an appropriate methodology further needs to take the spatiotemporal characteristics of the phase couplings into account. Several authors already stressed the relevance of multivariate synchronization measures (cf., e.g. Jalili et al., 2014, Jalili et al., 2007, Pauen and Ivanova, 2013, Knyazeva et al., 2010), the benefits of including the spatial aspects of of electroencephalographic signals into analysis (cf., e.g. Michel et al., 2009, Khanna et al., 2015, Knyazeva et al., 2010, Jalili et al., 2007), the advantage of single trial analyses that avoid the massive loss of information and the smearing that arises from averaging (cf., e.g. Tzovara et al., 2012, De Lucia et al., 2007) as well as the importance of single subject analyses when, for instance, studying individual patients with specific sensory-cognitive impairments (cf., e.g. Tzovara et al., 2012, De Lucia et al., 2007). Nevertheless, so far, no method exists that allows a spatiotemporal analysis of complex multivariate phase synchronization patterns on a single trial basis. To close this gap, an according method is presented in the present paper.

To study multivariate phase synchronization processes in the brain, several methods have already been proposed (cf. Allefeld et al., 2007, Canolty et al., 2012, Haig et al., 2000, Mutlu and Aviyente, 2011, Osorio and Lai, 2011, Rudrauf et al., 2006, Schelter et al., 2006, Vejmelka et al., 2009, Pauen and Ivanova, 2013, Allefeld and Kurths, 2004, Pascual-Marqui, 2007, Evans and Aviyente, 2008). Other authors included the temporal as well as the spatial aspects of synchronization into analysis and determined so-called synchrostates, i.e. distinct EEG connectivity maps that reoccur over time (Ito et al., 2004, Ito et al., 2007, Chu-Shore et al., 2012, Betzel et al., 2012, Jamal et al., 2015b, Jamal et al., 2015a). For instance, Ito et al., 2004, Ito et al., 2007 investigate the temporal characteristics of recurrent spatial phase patterns in the resting EEG. The authors determine distinguishable spatial phase patterns that are stable across subjects but that fluctuate dramatically over time. Similarly, Chu-Shore et al. (2012) evaluate the temporal stability of functional connectivity networks in the spontaneous EEG and find that stable network templates emerge after as little as ∼100 s of recording. For shorter time segments, the authors cannot report any consistent structure. Thus, their results already indicate that EEG connectivity patterns can change within seconds or less and that, at the same time, some characteristics remain stable over time. These findings are complemented by the work of Betzel et al. (2012) that provide evidence for a limited repertoire of fast changing connectivity states in the resting state EEG with quasi-stable epochs of about 100 ms. A similar time scale is reported by Jamal et al., 2015b, Jamal et al., 2015a who detect a small set of distinctive synchrostates during a face perception task. They usually find three up to five synchrostates that recur over time, remain stable for approximately 100 ms and are connected via rapid transitions from one to another. Furthermore, they find differences between these synchrostates for children with Autism Spectrum Disorder, children diagnosed with low anxiety, children diagnosed with high anxiety and typically developed children (Jamal et al., 2015a). Mheich et al. (2015) pursue a similar approach and apply their method to high density EEGs recorded from six subjects during a picture recognition and naming task. They examine a time segment of 620 ms after the presentation of a picture and find six distinct phase coupling networks that last between 37 ms and 164 ms.

The research summarized above demonstrates the great potential that the spatiotemporal analysis of distinctive connectivity patterns holds for the understanding of large-scale synchronization and the dynamics of functional connectivities in the brain. However, the introduced methodological approaches were designed for different purposes and are, therefore, not ideal for the objective described above. The first limitation arises from the connectivity measures that are utilized. Chu-Shore et al. (2012) as well as Betzel et al. (2012) use measures that are, at least partly, based on amplitude information. Thus, they are not designed to detect phase couplings regardless of existing amplitude associations. All other methods consider instantaneous phase differences that are independent of the signal amplitude. Yet, these approaches utilize bivariate connectivity measures (cf. Jamal et al., 2015b, Jamal et al., 2015a, Mheich et al., 2015, Ito et al., 2004, Ito et al., 2007). Thus, more complex, multivariate dependencies cannot be captured. Another restriction is given by the temporal dynamics that are detected by the different methodologies. For instance, Jamal et al., 2015b, Jamal et al., 2015a and Mheich et al. (2015) perform multi trial analyses, i.e. they focus on phase relations that are stable across trials. All the other authors perform single trial analyses. Chu-Shore et al. (2012) use fixed and non-overlapping time windows of one second. With this, they specialize on slower dynamics in the range of seconds. Unlike Chu-Shore et al. (2012), Betzel et al. (2012) obtain a connectivity estimate for every sampling point. However, this connectivity estimate is also based on an entire time window due to the utilized embedding operation. Hence, the time resolution is still restricted. Similarly, Ito et al. (2004) calculate their phase measures within time windows of 600 ms, whereas they avoid the use of time windows in their study from 2007. Instead, they compare the instantaneous phase difference between the reference electrode and each other electrode for two consecutive time points. With this, the approach has the highest temporal resolution. However, it only discovers differences in the global deviations from the reference phase rather than uncovering differences regarding inter-phase-relationships. Table 1 provides an overview of the most important features of the introduced spatiotemporal methods that can be utilized to detect distinctive EEG connectivity states. As can be seen, if complex phase coupling topographies shall be detected that include phase associations between more than two signals, and if their temporal dynamics are supposed to be tracked with a high precision on a single subject or even single trial basis, a new method is required.