EEG microstate transition cost correlates with task demands

Giacomo Barzon; Ettore Ambrosini; Antonino Vallesi; Samir Suweis

doi:10.1371/journal.pcbi.1012521

. 2024 Oct 10;20(10):e1012521. doi: 10.1371/journal.pcbi.1012521

EEG microstate transition cost correlates with task demands

Giacomo Barzon ^1,^2,^*, Ettore Ambrosini ^1,³, Antonino Vallesi ^1,³, Samir Suweis ^1,⁴

Editor: Lyle J Graham⁵

PMCID: PMC11495555 PMID: 39388512

Abstract

The ability to solve complex tasks relies on the adaptive changes occurring in the spatio-temporal organization of brain activity under different conditions. Altered flexibility in these dynamics can lead to impaired cognitive performance, manifesting for instance as difficulties in attention regulation, distraction inhibition, and behavioral adaptation. Such impairments result in decreased efficiency and increased effort in accomplishing goal-directed tasks. Therefore, developing quantitative measures that can directly assess the effort involved in these transitions using neural data is of paramount importance. In this study, we propose a framework to associate cognitive effort during the performance of tasks with electroencephalography (EEG) activation patterns. The methodology relies on the identification of discrete dynamical states (EEG microstates) and optimal transport theory. To validate the effectiveness of this framework, we apply it to a dataset collected during a spatial version of the Stroop task, a cognitive test in which participants respond to one aspect of a stimulus while ignoring another, often conflicting, aspect. The Stroop task is a cognitive test where participants must respond to one aspect of a stimulus while ignoring another, often conflicting, aspect. Our findings reveal an increased cost linked to cognitive effort, thus confirming the framework’s effectiveness in capturing and quantifying cognitive transitions. By utilizing a fully data-driven method, this research opens up fresh perspectives for physiologically describing cognitive effort within the brain.

Author summary

In our daily lives, our brains manage various tasks with different mental demands. Yet, quantifying how much mental effort each task demands is not always straightforward. To tackle this challenge, we developed a way to measure how much cognitive effort our brains use during tasks directly from electroencephalography (EEG) data, which is one of the most used tools to non-invasively measure brain activity. Our approach involved the identification of distinct patterns of synchronized neural activity across the brain, named EEG microstates. By employing optimal transport theory, we established a framework to quantify the cost associated with cognitive transitions based on modifications in EEG microstates. This allowed us to link changes in brain activity patterns to the cognitive effort required for task performance. To validate our framework, we applied it to EEG data collected during a commonly employed cognitive task known as the Stroop task. This task is recognized for challenging us with varying levels of cognitive demand. Our analysis revealed that as the task became more demanding, there were discernible shifts in the EEG microstates. Importantly, these shifts in neural activity patterns corresponded to higher costs associated with cognitive transitions. Our approach offers a promising methodology to assess cognitive effort using neural data, contributing to our comprehension of how the brain manages and adapts to varying cognitive challenges.

Introduction

The complex activity patterns that support perception, cognition, and behavior in the healthy brain arise from the interactions of neuronal populations across various spatial and temporal scales [1]. At the macroscale, brain activity is characterized by spatially distributed groups of regions that exhibit temporally correlated activity and co-activate during behavioral tasks, thus acting as functional networks [2]. Recently, it has been shown that such functional networks may reflect the long-time average of rapidly switching metastable patterns (also called “metastable substates” or “dynamical states”), which are consistently observed with different imaging methods [3–7]. In the M/EEG literature, these patterns are termed “microstates” and are highly reproducible across studies and clustering techniques [8–10].

As our environment is constantly evolving, with new stimuli and challenges emerging regularly, our brain must remain flexible and adaptable to respond effectively to these changes. A crucial component that drives such reconfiguration is “executive functioning” or “cognitive control” [11–13]. This construct refers to the set of processes and mechanisms that enable goal-directed behavior in the face of changing circumstances [11,14–16]. When confronted with challenging situations, cognitive control allows the brain to regulate attention, inhibit irrelevant information, and shift cognitive resources to prioritize relevant tasks or goals [17].

Concurrently, it has been shown that the dynamical properties of the metastable substates during different active conditions are modulated compared with the resting state. Such adaptation has been demonstrated in a large variety of conditions such as cognitive loads [18], sleep-awake cycle [19], habituation of cognitive tasks [20], and is reflected in the overall reconfiguration of functional connectivity [21–23]. Importantly, alterations in the dynamic of brain states were found in psychiatric [8,24] and neurological disorders [25] and during normal aging [26]. Therefore, developing quantitative measures for quantifying the cost of such reconfiguration in the brain is crucial for explaining the impairments and guiding the possible effects of therapeutic interventions [27].

In recent years, much attention has been captured by the network controllability framework for measuring the brain transition cost [28,29]. Control theory based tools offer a mechanistic explanation for how the brain moves between cognitive states drawn from its network organization. In addition, control theory provides a quantitative way of computing the control cost as the amount of energy needed to steer a system along a desired trajectory. Despite its potential and broad spectrum of applications, it has some strong limitations [30,31]. For instance, it relies on the assumption of linearity in the dynamics. However, linear models fail to capture non-linear [32] and higher-order [33] phenomena ubiquitously encountered in brain dynamics. Moreover, stochasticity is not considered, but it is essential for accurately describing many aspects of brain function [34].

A promising approach for circumventing these limitations in quantifying the cost of control consists of reframing the task into a Schrödinger bridge problem [35,36]. More specifically, given an initial and a target probability distribution, representing, for instance, the distribution of metastable substates during resting and task conditions, the Schrödinger bridge problem asks for the most likely path or "bridge" that connects the two probability distributions given the spontaneous (resting) stochastic dynamics of the system. The transition cost is then estimated as the Kullback-Leibler divergence, which measures distances in the probability distribution space, between the baseline trajectory and the bridge. Intuitively, it measures the cost of “transporting” one distribution into another by a stochastic process that satisfies some given constraints. Indeed, the Schrödinger bridge problem has been proven to be formally equivalent to an (entropy-regularized) optimal transport problem [37,38].

Recently, such an approach was applied to an fMRI dataset of participants performing several cognitive tasks [39]. The authors show that the transition cost from the resting condition to the various tasks varies significantly, thus proposing this approach might be suitable for describing neurophysiological data. However, the tasks were qualitatively different and difficult to compare, thus there were no strong prior expectations of the task difficulty and the expected cognitive demand. Additionally, the reliability of individual differences in task-based fMRI activity is known to be quite poor [40], especially in the absence of long time series, as typically occurs in fMRI data, thus hindering the possibility of a subject-level analysis. Hence, in [39] time series data from individual subjects were combined to create a unified meta-subject dataset. Therefore, the analysis was exploratory and the reliability of such a metric remains limited. Moreover, in many contexts of cognitive interests, fMRI is not a suitable tool to measure neural correlates of behavior. For instance, one of its primary constraints is its inherent limitation to cognitive tasks that do not involve significant physical movement. This is a notable drawback, as many cognitive processes and behaviors inherently entail motor actions.

In this work, we bridge this gap by generalizing the above method to electroencephalography (EEG) signals, which moreover measure neural activity more directly than fMRI. Specifically, we analyze an EEG dataset on participants performing a spatial Stroop task. The Stroop task is a standard experimental paradigm in cognitive psychology that investigates different aspects of cognitive control and executive functions, including selective attention, response inhibition, and interference resolution, by assessing the interference effect from conflicting stimulus features [41]. In its spatial variant [42–44], participants are typically presented with arrows pointing in different directions (e.g., top left or bottom right) and are asked to indicate the direction of the arrow through a spatially compatible button press. However, the pointing direction may conflict with its spatial location. For example, an arrow pointing to the top left corner might appear on the bottom right side of the screen. Typically, participants are slower and less accurate in incongruent conditions (i.e., when the spatial location of the arrow conflicts with the direction it is pointing to) than in congruent conditions (i.e., when spatial location and pointing direction coincide). This interference effect, referred to as the “Stroop effect”, is believed to reflect the difficulty in suppressing the automatic processing of the spatial location of the stimulus in favor of the task-relevant information (the arrow direction), with the consequent activation of a wrong response code that then needs to be suppressed. Commonly, it is computed as the difference in the response time (RT) between incongruent and congruent trials. Cognitive control demands can be further manipulated by varying the proportion of congruency (PC), namely the proportion of congruent trials in a given task block [45–47]. Indeed, in high-PC blocks, conflict is less likely, and cognitive control demands are lower, whereas, in low-PC blocks, trials are mostly incongruent, and cognitive control is more required [45,48]. Therefore, due to our well-defined quantitative prior expectation of cognitive demands, this dataset is ideally suited for assessing the effectiveness of the proposed framework to estimate brain transition costs.

Here, we first characterize the dynamics with a microstate analysis, which reveals that different conditions modulate the distribution of microstates. Next, we calculate the transition cost for each participant from the resting state to the various conditions. We observe a higher cost for incongruent stimuli. Importantly, this cost is significantly influenced by the level of cognitive control. Moreover, we find a correlation between variations in the cost and RTs, showing that a reduced cost is associated with improved task performance. Overall, these results highlight the value of characterizing brain dynamics and transition costs in understanding cognitive processes and offer insights into the relationship between neural activity patterns, cognitive effort, and behavioral performance.

Results

Framework for computing the control cost

In this work, we analyzed an EEG dataset recently collected (see “Dataset” section; Fig 1A). This dataset encompasses EEG recordings collected from a cohort of 44 participants during both a 5-min eyes-open resting-state session and a task-oriented sessions. Specifically, the task involved a spatial Stroop task designed with blocks featuring three distinct PC values (25%, 50%, and 75%) to systematically manipulate different levels of cognitive control engagement (high, medium, and low, respectively). Consequently, this setup provided multiple pre-established levels of cognitive demand expectation.

EEG activity was characterized utilizing a microstate analysis (see “EEG microstate-based analysis” section; Fig 1B). After identifying the most reliable templates for group maps, we proceeded to assess their distributions (also called “coverage” in the microstate literature) and transitions in each participant during both the resting and task conditions.

Utilizing their dynamics, we derived an estimation of the control cost employing the Schrödinger bridge framework (see “Brain transition cost” section, Fig 1C). In essence, this cost was calculated as the disparity between the spontaneous microstate dynamics during the resting phase and the bridge, which corresponds to the most likely pathway linking the distributions of microstates observed during resting and task-oriented conditions.

Microstate reconfiguration during task

The group-level clustering revealed seven optimal microstate classes, which explained almost 80% of the variance of the dataset (S1 Fig). These group maps resembled the usual microstates template ubiquitously found in the literature [49], and we labeled them accordingly (from A to G).

Before entering into applying the control cost framework, we needed to verify whether microstate distributions during the task were modulated with respect to the baseline (Fig 2). To achieve this, we first compared the microstates distribution at rest to the chance probability reflecting a uniform distribution across the seven microstates (i.e., 1/7 = .1429; see “Statistical Analysis” section). We found that microstate D was significantly more expressed at rest (M = 0.158, SE = 0.003, t(43) = 4.53, p < .0001, d = 0.68), while microstate E was significantly less expressed at rest (M = 0.121, SE = 0.003, t(43) = -7.54, p < .0001, d = -1.14). Next, we performed a linear mixed effects model for each microstate, incorporating congruency, PC level, and their interaction as predictors (See “Statistical Analysis” section). As a dependent variable, we computed the change in the probability distributions across different conditions compared to the resting state. Consequently, the intercept denoted an overall modulation from the resting state to task execution. The results of these analyses are reported in S1 Table. We found that microstates A and E were significantly suppressed during the execution of the task (intercept effect: b = -0.018 and -0.012, SE = 0.004 and 0.003, respectively). Moreover, their expression was significantly modulated by congruency, with a stronger suppression for incongruent compared to congruent trials (b = 0.003 and 0.003, SE = 0.001 and 0.001, respectively), as well as by the congruency by PC interaction (b = 0.005 and 0.004, SE = 0.002 and 0.002, respectively). These interaction effects were explained by the fact that the expression of both microstates was modulated by the PC level in opposite ways, being it less suppressed in congruent trials and more suppressed in incongruent trials as the PC level increased, resulting in an increase of the Stroop effect (i.e., the difference between incongruent and congruent trials) at higher PC levels, that is, when the cognitive control demands were lower. A similar pattern was observed for microstate B, with significant effects of congruency and the congruency by PC interaction (b = 0.005 and 0.005, SE = 0.001 and 0.002, respectively), despite the intercept effect did not survive the correction for multiple tests (b = -0.006, SE = 0.003). Microstate C also showed a significant effect of congruency, with a more suppressed expression in incongruent compared to congruent trials (b = -0.005, SE = 0.001), and was generally suppressed compared to rest (b = 0.013, SE = 0.002). By contrast, microstate G showed the opposite pattern of results compared to microstates A and E, being its expression significantly enhanced during task execution (b = 0.021, SE = 0.002) and significantly modulated by both congruency, with a stronger enhancement for incongruent compared to congruent trials (b = -0.010, SE = 0.001), and the congruency by PC interaction (b = -0.006, SE = 0.003), with positive and negative PC effects for incongruent and congruent trials, respectively. Finally, microstate F was significantly enhanced in incongruent compared to congruent trials (b = 0.005, SE = 0.001), microstate D was significantly more expressed overall compared to rest (b = 0.010, SE = 0.003). The remaining effects were not significant after correction for multiple tests (see S1 Table).

Fig 2 — The boxplots show the microstate distributions at rest (white boxplot) and during the experimental conditions. The saturation of the blue (orange) scale represents the PC level (and, thus, the level of control demands).

Transportation cost matrix

A key quantity, that we inferred from the EEG time series and their microstates, was the transportation cost matrix (Fig 3A). Such a matrix, in an optimal transport problem, provides information about the costs associated with transporting goods or resources from one location to another. In our framework, it defines the cost associated with increasing or decreasing the probability of one microstate from the source to the target distribution, and it has a clear intuition: the transportation cost is minimized along the more favorable transitions (i.e., more probable) during rest.

For each participant, the transportation cost was obtained from the joint probability distribution of co-occurrence for two consecutive steps during resting. As shown in Fig 3B, we found that such distribution is asymmetric, indicating a preference or bias in transitioning from one state to another with respect to the opposite direction. Moreover, the self-transition probabilities are quite large, indicating that the system tends to persist in its current state over time, thereby confirming the metastable nature of the microstates.

Transition cost reflects task demand

Subsequently, we investigated for each participant the costs associated with transitioning from a resting state to different conditions within the Stroop task. To quantify these costs, we utilized the Schrödinger bridge framework and calculated the associated Kullback-Leibler divergence (Fig 4A). We again performed a linear mixed effect model with the interaction between Congruency and PC on the computed transition costs (see “Statistical Analysis” section). This analysis revealed the significant effects of congruency, with lower costs for congruent than incongruent trials (b = -0.007, SE = 0.001, t = -5.04, p < .0001, d = -0.76), and the congruency by PC interaction (b = -0.009, SE = 0.002, t = -3.74, p = .0001, d = -0.42), with positive and negative PC effects for incongruent and congruent trials, respectively.

Fig 4 — (a) The boxplots show the distribution of transition costs as a function of both the stimulus congruency, that is congruent (C) vs. incongruent (I) and the PC level (PC25, PC50, PC75;), as indicated by their significant interaction in the linear mixed effects analysis. (b) The plot shows the participants’ Stroop effects in transition costs (i.e., the difference in transition costs between incongruent and congruent trials: Δ Cost) as a function of their Stroop effects in response times (Δ RT), as indicated by the random effects revealed by the linear mixed effects model (see main text).

To examine the potential relationship between transition costs and task performance of each participant, we performed a linear mixed effects model on the computed costs including response times as predictors after having calculated the difference in costs and response times between incongruent and congruent conditions (i.e., the Stroop effects), considering each level of control (see “Statistical Analysis” section; see also Figs 4B and S2). Our results revealed that higher Stroop effects in transition costs were associated with higher Stroop effects in response times and potentially indicative of performance (b = 0.054, SE = 0.015, t = 3.69, p = .0003, d = 0.45).

We performed the same analyses on the Kullback-Leibler divergence between the microstates distributions during the task and resting conditions instead of transition costs (see S3 Fig). These analyses failed to find the significant effect of congruency (t = -1.74, p = .0833, d = -0.26) and the congruency by PC interaction (t = -1.33, p = .1841, d = -0.20) on Kullback-Leibler divergence, and the Stroop effects in Kullback-Leibler divergence values were not significantly associated with participants’ performance, as assessed by their Stroop effects in response times (t = 0.19, p = .8467, d = 0.03).

Discussion

In this study we have employed a stochastic control framework to measure the brain transition cost in an existing EEG dataset. Through our investigation, we have confirmed a correlation between cost and cognitive demand observed during a spatial Stroop task. To our current knowledge, this is the first application of such a framework to EEG data, thus providing a computational pipeline to quantify cognitive demand in EEG experiments.

To estimate brain transition costs from the Schrödinger bridge framework, we used a probabilistic approach that resorts to a reduction of dimensionality. A growing body of literature suggests that brain activity, across different scales, exhibits organization within a low-dimensional manifold. The trajectories of neural activity can thus be described as discrete transitions between a few metastable attractors, which capture a significant portion of the overall activity variance. In particular, the analysis of EEG activity is increasingly conducted using the microstates approach. This method reduces the recorded electrical signal into non-overlapping and distinct topographies [8,9]. Although individual topographies have been associated with partial activations or deactivations of canonical resting-state networks [49,50] and specific spectral bands [51,52], the functional and cognitive role of the microstates has not yet been fully established [10].

Specifically within our dataset, we observed distinct distributions of microstates across different conditions. Notably, certain microstates differentiated between tasks and resting states, while others were specific to incongruent stimuli and modulated by the level of cognitive demand. Specifically, microstate C was suppressed during the tasks, possibly representing posterior dominant resting state (alpha) rhythms. Also microstates A and E were suppressed during the task, with larger suppression for a larger level of cognitive demand. As a tentative speculation, they might be related to alpha suppression or the deactivation of the default mode network. However, this interpretation is in contrast with existing literature, since microstate A is commonly attributed to resting condition [8,50], but it should be noted that we used an eyes-open resting state, which likely reduced the power in the alpha band. Instead, microstates D, F, and G were more prominent during tasks. Microstate F was more prevalent during incongruent stimuli compared to congruent stimuli, while microstate G was more present in blocks with higher expected levels of control. Consequently, they may be linked to specific brain regions involved in inhibitory control and conflict resolution [53,54].

Moreover, a global modulation can be assessed by computing the Kullback-Leibler (KL) divergence between the task and resting conditions [18]. We observed that the KL divergence tends to be larger for more demanding task conditions, which is consistent with the idea that cognitive load influences the divergence between microstate distributions. However, despite this trend, our analyses failed to find significant effects. This suggests that while KL divergence is a useful measure for capturing global shifts between task and resting states, it may lack the sensitivity required to detect more nuanced effects related to cognitive cost when compared to the Schrödinger bridge method. The latter, by accounting for the transition paths between distributions, appears to capture additional information about cognitive load that is not reflected in KL divergence alone.

This modulation of certain microstates could be associated with the dynamic reorganization of specific functional networks, as previously observed [55,56]. Confirmation of these hypotheses and further investigation into the microstates can be achieved through source localization, which will be explored in future works. Overall, a higher cost may be related to a larger network reconfiguration. Indeed, a larger cognitive demand induces a more global alteration in brain activity, which is needed to make functional networks transiently adopt a more efficient but less economical configuration [21]. However, the specific mechanisms governing these shifts between states of the brain remain unclear [57,58]. Moreover, whether such cognitive cost may represent an increase in metabolic consumption is still to be investigated [59]. It is important to mention that in a stochastic linear setting, the Schrödinger bridge control cost is formally equivalent to the “classical” control cost (i.e., the expectation of the time integral of squared control signal) [37,39,60], which has a clear physical interpretation.

Our approach integrates into the current literature on the brain’s neural control [28–31,34,57,58,61–63]. The core foundation of all these models involves a metric that quantifies the amount of effort required for a dynamical system to traverse its state space across diverse conditions. The existing methodologies typically rely on the full knowledge of the underlying structural connectome and an explicit representation of the dynamics. Under the assumption of linear dynamics, it is possible to estimate this metric efficiently by utilizing an explicit analytical formula [28,64]. However, these approaches overlook the intricate nonlinear characteristics of brain dynamics, and may not be computationally feasible for large networks [30]. On the contrary, to extend this framework to biophysically detailed dynamical models, extensive numerical simulations become a necessary recourse [19]. Instead, our approach offers the advantage of estimating the reconfiguration cost directly from neurophysiological recordings. Additionally, its flexibility allows for versatile application across various imaging techniques [39]. However, its applicability to EEG data holds particular importance due to its widespread usability, cost-effectiveness compared to techniques such as fMRI or MEG, and non-invasiveness compared to intracranial recordings.

We also found that the probability of transitioning from one microstate to another is asymmetric. Such asymmetric transitions indicate potential fluxes and net flows within the system, which in turn can contribute to the overall production of entropy at a macroscopic level [65]. Therefore, our results hint at a macroscopic entropy production of the brain, even at rest. A promising future direction could involve quantifying entropy production across various task conditions as a measure of cognitive load [66]. This would involve investigating changes during tasks and determining if the control cost can explain the variation in energy the brain needs to supply for differing cognitive demands. Several other metrics have already been proposed to quantify the cognitive loads from microstate analysis, such as the entropy rate or the Hurst exponents [67,68]. However, these measures lack a clear interpretation regarding transition costs, as they do not account for dynamics. Our method, in contrast, estimates not the cognitive load during a single condition but the cost of transitioning between different conditions.

It would be further interesting to explore whether pathological conditions could influence the control cost. For instance, in the case of stroke, there have been documented changes in the microstates [69,70] and, more generally, in the dynamics of metastable states [25]. Additionally, the functional repertoire of macroscopic brain dynamics has been found to be reduced in Amyotrophic Lateral Sclerosis [71] and Parkinson’s disease [72]. Therefore, it is intriguing to consider whether this altered flexibility is associated with an increase in control costs, which our framework could estimate. Furthermore, different conditions may affect distinct regions of the brain, resulting in alterations across various domains [73]. Consequently, it is reasonable to assume that the cognitive cost will be particularly higher for tasks impaired due to specific neural alterations. Therefore, investigating individual differences in microstate transition cost in different groups (e.g., strokes), or applying it to tasks where the evaluation of cognitive demands is not known, are all interesting avenues to pursue in future research.

Materials and methods

Dataset

We re-analyzed the continuous EEG data collected in a recent study from our lab [74]. In that study, we aimed to investigate the neural correlates of cognitive control in resolving the interference between competing responses. To this aim, EEG signals were recorded from 44 participants during a 4-min resting state session and while they performed a spatial Stroop task requiring mouse responses and comprising blocks with three PC values (25%, 50%, and 75%) to manipulate different levels of cognitive control engagement (Fig 1A; see[74] for details about the task and procedure). Briefly, the data were recorded at 500 Hz with 64 electrodes mounted according to the 10–10 system. All electrodes were references to FCz during the recording. A standard ICA-based preprocessing was performed to correct for eye movements, blinks, and muscular activity based on scalp topography, dipole location, evoked time course, and the power spectrum of the components [74].

EEG microstate-based analysis

Preprocessed EEG data were further bandpass filtered (1–40 Hz) and downsampled at 250 Hz.

Microstate analysis was performed using the open-source package “Pycrostates” [75]. Microstate analyses followed the modified k-means clustering algorithm [76,77]. First, a subject-level analysis was performed by extracting local maximal values (peaks) of the global field power (GFP) from each EEG recording. GFP was calculated as the standard deviation of the amplitude across all channels at each time point. EEG maps at GFP peaks are reliable representations of the topographic maps because of their high signal-to-noise ratio [78].

For each participant, we randomly extracted the same number (10000) of GFP peaks, that were subjected to clustering. Then, the individual topographies are used in the group-level analysis to fit a second clustering algorithm. The optimal number of clusters (K* = 7) was determined using the cross-validation criterion, which minimizes the variance of the residual noise (see S1 Text). The centroids of the K* clusters identify the group-specific microstate templates (Fig 1B). Both the individual and group maps are reported in the online repository.

The group templates were then fitted back to the preprocessed EEG recordings. The EEG map at each time point was labeled according to the map with minimum Euclidean distance, equivalent to the highest absolute spatial correlation. Thereafter, EEG maps were converted into microstate sequences (k_t). For each EEG recording, we characterized the probability distribution of the microstates (π) under each condition. As the order of presentation of congruent and incongruent trials within each block was randomized, the microstate distribution for the task conditions was calculated from the pooled trials, excluding inter-trial intervals and boundary microstates. In contrast, the resting distribution was estimated during the initial resting phase. To ensure consistency, the resting phase was also divided into 2-second windows (i.e., the duration of a single trial). In addition, we compute the joint probability distribution Q_ij for two consecutive steps i and j during the resting period (i.e., $Q_{i j} = P r o b [k_{t - 1} = i; k_{t} = j]$ ).

Brain transition cost

To quantify the cost of transitioning from resting to task, we applied the Schrödinger bridge problem [36,39,60,79] (Fig 1C). We assumed that the brain dynamic unfolds over time along trajectories of discrete states (i.e., the microstates), namely K₀^T = (k₀, k_1,…, k_T). Similarly to [39], we denoted by q(K₀^T) = q(k₀, k_1,…, k_T) the probability distribution of the trajectories at resting. The resting condition is also characterized by the (marginal) probability distribution of microstates π⁰. To accommodate task demands, the brain has to modulate the probability distribution of the microstates, which we defined as π^T for the target (task) probability distribution. The trajectory linking the resting to the task condition can be similarly characterized by the probability distribution p(K₀^T). The control cost can thus be defined as the Kullback-Leibler (KL) divergence between the modulated p(K₀^T) and spontaneous q(K₀^T) trajectory distributions. This transition cost reflects how different the modulated trajectories are from the resting ones. Since estimating the probability distributions over the trajectories is infeasible, we can still infer the most probable trajectory as the Schrödinger bridge [39]. The Schrödinger bridge problem finds the most likely path linking the initial and target distribution given the prior stochastic evolution of the system by minimizing the Kullback-Leibler divergence between the two distributions.

In mathematical terms, the transition cost can be thus computed as

$C o s t = {m i n}_{P_{i j} \in U} D_{K L} (P_{i j}, Q_{i j}) = {m i n}_{P_{i j} \in U} - \sum_{i j} P_{i j} l o g Q_{i j} + \sum_{i j} P_{i j} l o g P_{i j} = {m i n}_{P_{i j} \in U} \sum_{i j} C_{i j} P_{i j} - H (P_{i j})$ , where Q_ij is the joint probability distribution for two consecutive timesteps at rest, $H (P_{i j}) = - \sum_{i j} P_{i j} l o g P_{i j}$ is the information entropy, and the minimization is constrained over the matrix spaces ${U = {P}_{i j} > 0 & \sum_{i j} P_{i j} = 1 | \sum_{j} P_{i j} = π_{i}^{0} & \sum_{i} P_{i j} = π_{j}^{T}}$ (see [39,60] for the detailed mathematical derivation).

Interestingly, $C_{i j} = - l o g Q_{i j}$ plays the role of a transportation cost matrix, while each P_ij that satisfies the constraints in U corresponds to a feasible trajectory linking the resting to the task condition. Indeed, the Schrödinger bridge problem can be recast as an (entropy-regularized) optimal transport problem [60]. Intuitively, to supply the needed cognitive demand, the brain has to modulate its dynamics, which results in a modulation of microstate distribution. In other words, the distribution of some microstates would be enhanced, while others would be suppressed. Thus, the brain has to “transport” some mass (i.e., microstate probability distribution) into another. How much mass is moved from each supply (i.e., resting) location to each demand (i.e., task) location is defined as the “transportation plan” and is encoded in the matrix P_ij. The transportation cost matrix C then represents the cost of transporting one unit of mass along each supply-demand pair. Solving the optimal transport problem means finding the transportation plan P_ij that minimizes the total cost (with an entropic regularization term) while satisfying constraints like the given initial, supply, and final, demand distributions and non-negativity constraints (i.e., ensuring that negative values are not allowed in the transportation plan).

This is a strongly convex optimization problem, therefore the existence and uniqueness of the optimal solution are guaranteed. Such an optimal solution can be iteratively determined in an efficient way using the Sinkhorn algorithm [80].

Statistical analysis

The statistical analyses were performed in Matlab using ad-hoc scripts.

First, to identify the microstates that were specifically more (or less) expressed at rest, we performed for each microstate a two-tailed one-sample t-test against .1429 (i.e., the chance probability reflecting a uniform distribution across the seven microstates, corresponding to 1/7) on the participants’ probabilities of observing each microstate at rest.

Next, to investigate the task-dependent reconfiguration of microstate probability, we performed a linear mixed effects model for each microstate, including in the fixed part of the model the predictors for the stimulus congruency (incongruent vs, congruent trials, coded as -.5 and .5, respectively), the PC level (PC25, PC50, and PC75, coded as -.5, 0, and .5, respectively), and their interaction. Consequently, the intercept effect denoted an overall modulation from the resting state to task execution. It is important here to note that we expected the PC level to have a linear, graded impact on the analyzed measures, in line with recent findings from our lab[46,47]. The same predictors were also included in the random part of the model along with the participants’ random intercepts (i.e., we used a full random model). As a dependent variable, we computed the change in the probability distributions in the six different conditions (derived from the combination of the Congruency and PC levels) with respect to the resting state. We report the estimated coefficient (b), as well as the corresponding standard errors (SE) and t and p values for each fixed effect. We calculated the p values by using Satterthwaite’s approximation of degrees of freedom, which was also used to compute the corresponding effect size estimates (expressed as Cohen’s d). The obtained results were then corrected for multiple tests (n = 28) by using the false discovery rate correction. After having fitted such a model, we performed a residual analysis, which verified the assumptions of homoscedasticity and normality of the residuals and did not reveal relevant signs of stress in model fitting.

The same analytical approach was used to investigate whether transition costs were modulated by task demands, by performing a similar full-random linear mixed effects model on the participants’ transition costs, with the congruency by PC interaction in both the fixed and random part. Moreover, in order to investigate whether transition costs were related to task performance, we first computed the difference between transition costs in incongruent and congruent trials, corresponding to the Stroop effect in transition costs, and analyzed them with a linear mixed effects model with participants’ Stroop effects in response times as a continuous predictor, which was also included in the random part of the model as participants’ random slopes, along with the participants’ random intercepts. It is important here to note that the Stroop effect is the standard measure of the interference resolution ability in the cognitive control literature.

Supporting information

S1 Fig. Selection of the best number of microstates using the cross-validation criterion.

(left) Fraction of total variance (GEV) explained by the microstates. (center) Residual noise. (right) Cross-validation (CV) as a function of the number of microstates (N states).

(PDF)

pcbi.1012521.s001.pdf^{(146.1KB, pdf)}

S2 Fig. Behavioural results of the spatial Stroop task.

Distribution of response times (RT) for the 44 participants during each task condition.

(PDF)

pcbi.1012521.s002.pdf^{(115.4KB, pdf)}

S3 Fig. Global modulation of microstate distributions during the spatial Stroop task.

Distribution of Kullback-Leibler divergence (D_KL) between the task (π_task) and resting (π_rest) for the 44 participants.

(PDF)

pcbi.1012521.s003.pdf^{(158.8KB, pdf)}

S1 Table. LMM results for microstate occurrences.

For each microstate, a linear mixed model was implemented to test whether the change in the probability distribution during task execution compared to the resting state is modulated by the stimulus congruency, the PC level, and their interaction.

(PDF)

pcbi.1012521.s004.pdf^{(94.9KB, pdf)}

S1 Text. Modified k-means clustering.

Mathematical details on the modified k-means clustering algorithm.

(PDF)

pcbi.1012521.s005.pdf^{(97KB, pdf)}

Data Availability

The preprocessed data and the code that support the findings of this study are available at https://github.com/gbarzon/brain_control_cost and were deposited on Zenodo (https://doi.org/10.5281/zenodo.13709700).

Funding Statement

Work by A.V and S.S. is supported by #NEXTGENERATIONEU (NGEU) and funded by the Ministry of University and Research (MUR), National Recovery and Resilience Plan (NRRP), project MNESYS (PE0000006) – A Multiscale integrated approach to the study of the nervous system in health and disease (DN. 1553 11.10.2022). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1012521.r001

Decision Letter 0

Lyle J Graham, Christoph Strauch

22 Feb 2024

Dear Mr Barzon,

Thank you very much for submitting your manuscript "EEG microstate transition cost correlates with task demands" for consideration at PLOS Computational Biology.

As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. In light of the reviews (below this email), we would like to invite the resubmission of a significantly-revised version that takes into account the reviewers' comments.

Three expert reviewers have provided thorough reviews on your manuscript. While they are all interested in your study, more serious concerns are voiced regarding methods and analyses, but also for the interpretation of findings. In sum, a strong revision will be needed to address these concerns adequately.

We cannot make any decision about publication until we have seen the revised manuscript and your response to the reviewers' comments. Your revised manuscript is also likely to be sent to reviewers for further evaluation.

When you are ready to resubmit, please upload the following:

[1] A letter containing a detailed list of your responses to the review comments and a description of the changes you have made in the manuscript. Please note while forming your response, if your article is accepted, you may have the opportunity to make the peer review history publicly available. The record will include editor decision letters (with reviews) and your responses to reviewer comments. If eligible, we will contact you to opt in or out.

[2] Two versions of the revised manuscript: one with either highlights or tracked changes denoting where the text has been changed; the other a clean version (uploaded as the manuscript file).

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Please prepare and submit your revised manuscript within 60 days. If you anticipate any delay, please let us know the expected resubmission date by replying to this email. Please note that revised manuscripts received after the 60-day due date may require evaluation and peer review similar to newly submitted manuscripts.

Thank you again for your submission. We hope that our editorial process has been constructive so far, and we welcome your feedback at any time. Please don't hesitate to contact us if you have any questions or comments.

Sincerely,

Christoph Strauch

Academic Editor

PLOS Computational Biology

Lyle Graham

Section Editor

PLOS Computational Biology

***********************

Reviewer's Responses to Questions

Comments to the Authors:

Please note here if the review is uploaded as an attachment.

Reviewer #1: Barzon et al. describe a new approach to develop a quantitative measure of "cognitive effort" using EEG microstates. The method is tested on a previously published dataset in which healthy participants perform a spatial Stroop task at three different levels of cognitive control demand.

They find:

- different microstate occurrences for different tasks

- transport cost depends on stimulus type, cognitive control level, and their interaction

- transport cost differences (Delta cost) correlates positively with reaction time (RT)

Strengths:

- The authors address a relevant question, i.e. how to estimate cognitive effort from neurophysiological data.

- They present a novel and innovative method. Transport theory has not been applied to EEG microstate data.

- The method is well described and reproducible.

- Microstate methodology follows standard procedures including an estimation of the optimum number of clusters (CV criterion).

- The experimental design has a tunable parameter PC (proportion of congruency) that gives a clear hypothesis about the actual cognitive demand.

- The results are well documented, quantified and statistically evaluated.

- The dataset has a good sample size, n=44.

While the overall approach and the presented results promise a valuable and insightful publication, there is a number of open issues, listed below.

- Existing strategies to estimate cognitive load should be discussed in more detail. Previously used methods include spectral analyses but also EEG microstate analyses, in particular Jia et al., https://doi.org/10.1038/s41598-021-03577-1. To validate their new method, the authors should compare their results with at least one previously published approach (e.g. entropy rate, Hurst exponent).

- The proposed transition cost measure has an interesting interpretation in terms of brain state switches. Whether these transition dynamics (Q_ij) are really relevant could be tested by comparing with a simpler approach that looks at the shape

of the microstate distribution only. For example, does the entropy of the microstate distribution alone (in each condition) perform worse than the proposed measure that takes into account Q_ij?

- p.4, Fig. 1: "found in the literature [Michel et al. 2018], and we labeled them accordingly (from A to E)". Microstate class E (ms-E) shown in Fig. 1b is very different from ms-E in Michel et al., NeuroImage, 2018, or in Custo et al., 2017. The authors should discuss this and consider using a different label for this map.

- p.8, microstate backfitting: "The EEG map at each time point was labeled according to the map...". Does this imply that maps were back-fitted at each time point without any temporal smoothing (interpolation, parametric smoothing, minimum duration etc.)? If yes, this should be made explicit as smoothing is very common in the microstate community.

- The authors use the term "occurrence" throughout the manuscript. While it becomes clear what they are referring to, I would suggest to switch to "coverage" or "distribution" as occurrence is a commonly used but different microstate parameter that refers to the frequency with which a given microstate class occurs and therefore has units of frequency (1/s). This could easily confuse readers used to the 'standard' terminology.

- The authors identify ms-A as indicative of the resting condition (e.g. Fig. 2). This is very unusual, ms-A is commonly associated with task performance and rest is often associated with ms-C (ms-D), probably representing posterior dominant

resting state rhythms (alpha). This must be discussed and further assessed. Is this attributable to the relatively large number of clusters (K=9)? Does the finding persist in the case K=4?

- Please provide more quantitative information about the analysed trials. Apparently, microstate distributions were obtained for each presented stimulus. How long were these trials on average and how many microstates were found during one stimulus/response trial? From Tafuro et al., I understand that participants had 750 ms to initiate movement, 2000 ms to complete, and 1500 ms blank post-stimulus. Let's say an average trial lasts about 2000 ms (assuming that participants

complete in much less than the given 2000 ms) and the average microstate duration is 100 ms. This gives only 20 microstates per trial and as little as 2 samples/histogram bin for K=9 microstates. Please provide the actual number of samples that went into the estimated microstate distributions. Within a block (high, medium, low), were the microstate distributions for all

C- (or I-) trials pooled? Were microstates at trial boundaries excluded?

- p.4: "In essence, this cost was calculated as the disparity between the spontaneous microstate dynamics during the resting phase and the bridge".

This is where my most serious doubt lies. While the approach is clear and meaningful in general, this does not seem to reflect the experimental reality of the dataset. From Fig. 1a, I understand that the resting phase occupied the first 4 minutes,

followed by the task phase that switches between high/medium/low blocks and C/I stimuli within each block. This means that the actual brain state transitions occurred between different task conditions (e.g. C-M and I-M, or between high and medium), but not between rest and task.

Is the bridge calculation rest-task meaningful in this context?

Does the approach still work when you calculate transition costs between the different tasks as they occurred during the actual experiment?

Do the authors assume that subjects return to the resting state between consecutive stimuli? If yes, can this be justified from the literature?

- p.5 "our results hint at a macroscopic entropy production..." - consider moving this to the Discussion section.

- "stimulus type" is only used twice on page 6. As it is an important part of the results, please introduce the term in the Methods section.

- Fig. 4a: The bracket on the right (single asterisk) seems to compare C-low and I-low. Is this a mistake and should the bracket indicate the comparison I-high and I-low instead? Please clarify.

- Fig. 4b: The correlation is not very clear from the plot. "revealed a significant positive correlation within this distribution" -

does this refer to the whole data cloud shown in Fig. 4B? Can the authors please add a line indicating the correlation?

- The Discussion section is extremely short regarding the neurobiological interpretation and the potential practical value of the results.

Points that should be addressed include:

a) Why does ms-A appear as an indicator of the resting state (and not ms-C, as reported in the literature)?

b) Fig. 4a, why are transition cost differences more pronounced for the easier stimulus type C (congruent)? Shouldn't the transition cost differences be larger for the more demanding incongruent (I) type?

c) Fig. S4 shows that RT is large for I-low and C-high. Doesn't this mean that RT is an inconsistent measure of cognitive demand?

d) Given the variance, is the effect size observed for incongruent stimuli shown in Fig. 4a relevant for practical use at all? There seems to be (almost) no change in transition cost although the PC varies between 75% and 25%.

e) Although statistically significant, is the correlation shown in Fig. 4b of any practical value? How large is the correlation coefficient? I hypothesize that the correlation is significant only due to the congruent trials. The cost for incongruent tasks looks constant in Fig. 4a, so the difference congruent-incongruent follows the congruent data. Why did the authors assess the difference values, are they of any biological relevance (are they used in the literature?).

Overall, as the authors promise "fresh perspectives for physiologically describing cognitive effort", the results require a more critical evaluation. There are some positive correlations for congruent trials but the discrepancy between congruent and incongruent tasks makes the results much less convincing (unless explained further).

Minor points:

---------------

- The greek letter pi occurs as both upper and lower case letters throughout the manuscript and Figures, please use one form only.

- The term in Fig. 1c is "min D_KL", on p. 9 it's "min KL"

- Fig. S2: See above, "occurrence" can be confusing as most microstate papers define occurrence differently and a unit of 1/s is expected.

Reviewer #2: This manuscript tries to link the construct of cognitive effort to the transition cost between multiple brain states. This research question is answered by using electrophysiological indexes for those quasi-stable brain states, i.e. micro-states, in the context of a cognitive control demanding task, a spatial Stroop task. The authors use the difference in microstates occurrence between a resting-state and the three different cognitive control level conditions of the task to show evidence for the link between cognitive effort, task conditions and ultimately behavior. In this paper, the proxy used for cognitive control is the transition cost between the different states that is estimated through a novel method for EEG.

At the general level, the paper presents an interesting approach, namely, how to assess cognitive effort through the estimation of transition costs among quasi-stable brain states. The paper, however, presents a strong lack of details in the methods but also the reported results. This lack impacts not only the replicability of the method to other contexts but also simply the understanding of most analysis in the paper. I come back to this issue among the several major points that I think need to be addressed. Parallel to this lack of methodological aspects, or maybe related, it looks like the statistical analysis chosen by the authors doesn't allow to tell whether the data supports the conclusion of the authors.

Because of these problems my main comments on this manuscript are on the methodological side rather than on the research questions per se. In the following, I detail my main concerns for each section of the results.

On the microstates occurrences:

- I am quite surprised by the lack of variance among the state occurrences. Based on Fig S2 (which would better sit in the main text given its importance) it does look like every state has a probability of roughly 1/9 (and 9 happens to be the number of microstates). This uniform distribution of state occurrences doesn't seem to be true in other microstates paper (e.g. Milz et al. 2016) and, to me, questions whether the microstates extracted are really task related. I would suggest that the authors explore ways of assessing whether their clustering is robust, e.g. resampling in the context of microstates https://pycrostates.readthedocs.io/en/latest/generated/auto_tutorials/cluster/10_subject_level_with_resampling.html

- On the linear mixed model. First I am surprised that the author chose a linear model and not a generalized linear model as the normality assumption of the residuals implied by a linear model cannot be respected in a change of probability of occurrence. That is, maybe this assumption is reasonable if those changes in occurrences are close to 0.5 but this is clearly not the case (Fig. S2). More importantly, the model description (also in the supplementary material) is insufficient to understand and evaluate the statistical model. What contrast coding was applied to the factors (e.g. reference/intercept is compatible condition? how were the three categories of control level coded?), what random structure was chosen? Moreover the post-hoc test applied could be avoided by having a better modelization. In this case, the Bonferroni correction will increase type II errors which might hide interesting results from this analysis.

Transportation cost matrix: I fail to understand the method. This might be due to my mathematical limitations and/or to an under-reporting of the method. In either case, this method being the core of the paper, it should be explained more thoroughly (e.g. what is P_{ij} in the equation on p. 9) and clearly (e.g. while I think I understand the parenthesis for Q_{ij}, I fail to see the link with the associated sentence).

transition cost reflects task demand:

- I don't understand why the authors choose a two-way ANOVA. It seems to me that the measures in this case are also repeated across participants. Hence at the minimum a repeated measure ANOVA needs to be conducted or, for more coherence with the microstate occurrence analysis, a linear mixed model. Without this control it is impossible to support this analysis, even more so in the absence of any index usually reported along with the p-values (i.e. no F statistic or degrees of freedom).

- For the link between reaction time and transition cost also the analysis is hard to understand because of the lack of reporting. The authors choose to compute correlations for each participant between RTs difference and cost. Is this between control levels? If so, I don't think a correlation is appropriate as 1) it is only for three points, 2) no guarantee exists on the linear link between RTs and cost difference across the three levels and 3) the second step analysis of the t-test ignores the uncertainty in the correlation. Assuming that point 2) is verified a better modelling approach would be to use again a linear mixed model and report the coefficient along the p-values. This would then resolve point 3) and, based on my understanding of what the authors did, be a proper test for the hypothesis laid out in this paragraph.

Minor:

- p.8 "To this aim, we recorded EEG in 44", implies that the data was recorded for this study

- p.5 last sentence of first paragraph, "Instead", poor wording?

- The terms High, medium and low to describe 25, 50 and 75 % of congruent trials is a conflict in itself. It would be easier to read if the proportion of incongruent trials was reported instead

- In p.2 I had difficulties following what exactly transition cost were defined as in relation to the research question, the Result section is however clearer. For the sake of readability, the authors may want to rewrite this section by explicitly relating to microstates in resting vs task.

- p. 6 last paragraph, "subjective performance" to describe RT seems surprising as RT doesn't usually qualify as a subjective measure.

- p. 8 Dataset section insufficiently describes the dataset, how many electrodes, what reference was used, the manuscript should be self-standing for such aspects

Sincerely,

Gabriel Weindel

New references:

Milz, P., Faber, P. L., Lehmann, D., Koenig, T., Kochi, K., & Pascual-Marqui, R. D. (2016). The functional significance of EEG microstates—Associations with modalities of thinking. _Neuroimage_, _125_, 643-656.

Reviewer #3: This research paper focuses on the dynamics of the brain, describe as microstates as observed in EEG, and their role with respect to cognitive processes. In particular, the authors investigate how brain activity correlates with the level of cognitive exertion during tasks by employing EEG data. These studies apply the principles of optimal transport theory and the Schrödinger bridge problem to examine the changes and dynamics in the brain as it responds to varying cognitive challenges.

I think this paper is sound, and I do not have strong objections to it. In particular, I thought it was interesting to note that employing optimal transport theory aids in comprehending the brain's dynamics and the cognitive effort required during tasks by transforming the Schrödinger bridge problem into an entropy-regularised optimal transport issue. This method facilitates the adjustment of brain dynamics to accommodate cognitive needs by altering the distribution of EEG microstates, intensifying some while diminishing others. By identifying the most cost-efficient transportation plan, which incorporates an entropic regularisation component, researchers can study the variations in EEG microstates throughout tasks, identifying greater costs linked to cognitive shifts. The transportation cost matrix represents the cost of moving mass between supply (resting) and demand (task) locations, offering insights into the brain's strategies for handling and adapting to different cognitive demands. This approach presents an innovative method for evaluating cognitive effort through brain data, underlining the connection between patterns of neural activity, cognitive strain, and behavioural outcomes.

At the end of the article, the whole scenario is clear, but at the level of the following sentence, I was confused. Hence, in my opinion, it would help to explain more clearly why it is possible to not use a mathematical modelling.

<<instead, advantage="" approach="" cost="" directly="" estimating="" from="" neurophysiological="" of="" offers="" our="" reconfiguration="" recordings="" the="">>

It would be interesting to also have the same analysis in a pathological context to explore whether pathological conditions could influence the control cost, because has been observed that in pathological conditions we have a reduced flexibility in brain dynamics linked to different sequences of patterns.

For future research, can be a good idea to focus more on brain dynamics and study the evolution of these microstates across EEG data, implementing a mathematical model which, starting from a realistic framework activity, can also implement the Schrödinger bridge problem to reproduce a similar analysis. In particular, some papers share of the motivations with these paper, and have explored complexity and flexibilithy in pathology, such as:

Cipriano, Lorenzo, et al. "Flexibility of brain dynamics is increased and predicts clinical impairment in Relapsing-Remitting but not in Secondary Progressive Multiple Sclerosis." medRxiv (2023): 2023-07; Polverino, Arianna, et al. "Flexibility of fast brain dynamics and disease severity in amyotrophic lateral sclerosis." Neurology 99.21 (2022): e2395-e2405; and Sorrentino, Pierpaolo, et al. "Flexible brain dynamics underpins complex behaviours as observed in Parkinson’s disease." Scientific reports 11.1 (2021): 4051. In my opinion, this is relevant literature in this context.

In the abstract, I would suggest describing in a very concise way what is the Stroop task to give immediately the main idea of the work.

In the introduction, after the following sentence, you can add a reference:

<< At the macroscale, brain activity is characterized by spatially distributed groups of regions that exhibit temporally correlated activity and co-activate during behavioral tasks, thus acting as functional networks>>.

The results and methods used are well described, clear and well explained. The statistical analysis done is sufficient.

All in all, I find this is a sound piece of scientific work, and I congratulate the authors.</instead,>

**********

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PLoS Comput Biol. 2024 Oct 10;20(10):e1012521. doi: 10.1371/journal.pcbi.1012521.r002

Author response to Decision Letter 0

18 Jul 2024

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1012521.r003

Decision Letter 1

Lyle J Graham, Christoph Strauch

5 Sep 2024

Dear Mr Barzon,

Thank you very much for submitting your manuscript "EEG microstate transition cost correlates with task demands" for consideration at PLOS Computational Biology. As with all papers reviewed by the journal, your manuscript was reviewed by members of the editorial board and by several independent reviewers. The reviewers appreciated the attention to an important topic. Based on the reviews, we are likely to accept this manuscript for publication, providing that you modify the manuscript according to the review recommendations.

The reviewers and myself have found the manuscript to have much improved in the revision. There are a few comments left to address, but as these are fairly minor I don't think we have to bother the reviewers again, provided that these points are addressed properly in a minor revision. Congratulations on this very interesting manuscript!

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Reviewer #1: The revised version of Barzon et al. has answered most of my questions.

I still have a few comments and minor requests.

1) Re entropy rate:

I thank the authors for their additional analyses. The finding of a maximum entropy rate during rest is quite surprising, despite the literature cited by the authors. None of the three cited papers computes the entropy rate of a neurophysiological time series (EEG or BOLD). Escrichs et al. do not use entropy at all.

The entropy rate of a microstate sequence is expected to be lower in the resting state as the EEG becomes faster during cognition, as reported in Jia et al.

Together with the unusual finding of microstate-A dominance in the resting state, I wonder if the resting state was an eyes-open resting state or had low alpha power for some other reason ? I couldn't find information about eyes open/closed. Please add this.

I think the reader should be informed that the resting state in this study has these somewhat unusual features, to facilitate future comparisons. Please add

this to the Discussion.

2) Re KL-divergence:

The additional findings presented in Fig. S3 show that KL-divergence between the microstate distributions alone seems to perform quite well as an estimator of cognitive load. Re-iterating my request from the first review, could the authors please quantify which method is more effective in measuring cognitive cost? E.g. by comparing the effect size. I think this should also be added to the Discussion where Fig. S3 is just briefly mentioned. The reader should learn that it performs with a similar efficacy (or better than?) the more advanced Schroedinger bridge method although KL-divergence ignores the transition path. The simple method performs nicely and is closely related to the authors' approach. It shows that cognitive load is already encoded in the distance between the distributions, independent of the optimum path found between them.

3) Re entropy production:

Not sure if the author comment "However, to our knowledge, this measure has not yet been explored in the EEG field" was meant to say in the EEG microstate field?

Anyway, the technique has been used for non-human primate EEG data (https://doi.org/10.1093/cercor/bhac177) and has also been used to demonstrate

irreversibility and non-equilibrium dynamics in EEG microstate time series in Hermann et al. (https://doi.org/10.1007/s10548-023-01023-1).

These should be cited in the Discussion.

Minor:

The time axis in Fig R4 cannot be ms but thank you very much for clarifying the question.

Thanks for all the extra work that went into the revision. This is a very interesting approach and I'm looking forward to reading future research with it.

Reviewer #2: Congratulations to the authors for the improvement of the manuscript. I am now much more convinced by the results and the readability of the paper has greatly improved. I only have a few minor points left:

- The new sentence in the abstract could be merged with the previous one for something more concise but still informative on the nature of the task

- The results of the mixed models in section "Microstate reconfiguration during task" are now hard to follow, maybe the authors could only report coefficients and SE and report p values and cohen's d in a table). This would make these results clearer both for those who just want a quick summary and those who want to dig into the details and can look up the table.

- Bonini, Francesca, et al. "Action monitoring and medial frontal cortex: leading role of supplementary motor area." Science 343.6173 (2014): 888-891. Might be an interesting reference for the discussion for the modification of states G and F (3rd paragraph in the discussion)

Reviewer #3: I thank the authors for addressing my comments. I have no further remarks.

**********

Have the authors made all data and (if applicable) computational code underlying the findings in their manuscript fully available?

Reviewer #1: No: Raw data is not available, as far as I can see. Ok for me though.

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Reviewer #3: Yes

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PLoS Comput Biol. 2024 Oct 10;20(10):e1012521. doi: 10.1371/journal.pcbi.1012521.r004

Author response to Decision Letter 1

25 Sep 2024

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1012521.r005

Decision Letter 2

Lyle J Graham

28 Sep 2024

Dear Mr Barzon,

We are pleased to inform you that your manuscript 'EEG microstate transition cost correlates with task demands' has been provisionally accepted for publication in PLOS Computational Biology.

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PLoS Comput Biol. doi: 10.1371/journal.pcbi.1012521.r006

Acceptance letter

Lyle J Graham

3 Oct 2024

PCOMPBIOL-D-23-02005R2

EEG microstate transition cost correlates with task demands

Dear Dr Barzon,

I am pleased to inform you that your manuscript has been formally accepted for publication in PLOS Computational Biology. Your manuscript is now with our production department and you will be notified of the publication date in due course.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

S1 Fig. Selection of the best number of microstates using the cross-validation criterion.

(left) Fraction of total variance (GEV) explained by the microstates. (center) Residual noise. (right) Cross-validation (CV) as a function of the number of microstates (N states).

(PDF)

pcbi.1012521.s001.pdf^{(146.1KB, pdf)}

S2 Fig. Behavioural results of the spatial Stroop task.

Distribution of response times (RT) for the 44 participants during each task condition.

(PDF)

pcbi.1012521.s002.pdf^{(115.4KB, pdf)}

S3 Fig. Global modulation of microstate distributions during the spatial Stroop task.

Distribution of Kullback-Leibler divergence (D_KL) between the task (π_task) and resting (π_rest) for the 44 participants.

(PDF)

pcbi.1012521.s003.pdf^{(158.8KB, pdf)}

S1 Table. LMM results for microstate occurrences.

(PDF)

pcbi.1012521.s004.pdf^{(94.9KB, pdf)}

S1 Text. Modified k-means clustering.

Mathematical details on the modified k-means clustering algorithm.

(PDF)

pcbi.1012521.s005.pdf^{(97KB, pdf)}

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Data Availability Statement

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PERMALINK

EEG microstate transition cost correlates with task demands

Giacomo Barzon

Ettore Ambrosini

Antonino Vallesi

Samir Suweis

Roles

Abstract

Author summary

Introduction

Results

Framework for computing the control cost

Fig 1. Summary of the framework for the computation of the brain transition cost from EEG data.

Microstate reconfiguration during task

Fig 2. Microstate distributions distinguish tasks from resting.

Transportation cost matrix

Fig 3. Estimating the transportation cost matrix from microstate joint probability of consecutive timesteps at rest.

Transition cost reflects task demand

Fig 4. Brain transition cost correlates with task demand and performance.

Discussion

Materials and methods

Dataset

EEG microstate-based analysis

Brain transition cost

Statistical analysis

Supporting information

Data Availability

Funding Statement

References

Decision Letter 0

Lyle J Graham

Christoph Strauch

Roles

Author response to Decision Letter 0

Decision Letter 1

Lyle J Graham

Christoph Strauch

Roles

Author response to Decision Letter 1

Decision Letter 2

Lyle J Graham

Roles

Acceptance letter

Lyle J Graham

Roles

Associated Data

Supplementary Materials

Data Availability Statement

ACTIONS

PERMALINK

RESOURCES

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