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Individualised electrophysiological neural field models for the assessment of thalamocortical function in disorders of consciousness: A multicentre study

  • Lín Cóngyǔ ,

    Roles Conceptualization, Formal analysis, Investigation, Methodology, Software, Visualization, Writing – original draft

    congyu.lin@icm-institute.org (LC); pablo.nunez.novo@gmail.com (PN); jacobo.sitt@icm-institute.org (JDS)

    Affiliations Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, France, Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium

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  • Prejaas Tewarie,

    Roles Methodology, Software, Writing – review & editing

    Affiliation CERVO Brain Research Centre, Laval University, Québec, Canada

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  • Naji L. N. Alnagger,

    Roles Writing – review & editing

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium

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  • Iván Mindlin,

    Roles Writing – review & editing

    Affiliation Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, France

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  • Glenn J. M. Van der Lande,

    Roles Writing – review & editing

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium

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  • Laouen Belloli,

    Roles Data curation

    Affiliation Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, France

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  • Steven Laureys,

    Roles Resources

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, CERVO Brain Research Centre, Laval University, Québec, Canada, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium, International Consciousness Science Institute, Hangzhou Normal University, Hangzhou, China

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  • Lionel Naccache,

    Roles Writing – review & editing

    Affiliations Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, France, Département de Neurophysiologie, Assistance Publique—Hôpitaux de Paris, Groupe Hospitalier Pitié-Salpêtrière, Charles Foix, Sorbonne Université, Paris, France

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  • Benjamin Rohaut,

    Roles Writing – review & editing

    Affiliations Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, France, Département de Neurophysiologie, Assistance Publique—Hôpitaux de Paris, Groupe Hospitalier Pitié-Salpêtrière, Charles Foix, Sorbonne Université, Paris, France

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  • Aurore Thibaut,

    Roles Investigation, Writing – review & editing

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium

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  • Jitka Annen,

    Roles Conceptualization, Data curation, Funding acquisition, Writing – review & editing

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium, Department of Data Analysis, University of Ghent, Ghent, Belgium

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  • Olivia Gosseries,

    Roles Funding acquisition, Investigation, Project administration, Resources, Writing – review & editing

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium

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  • Pablo Núñez ,

    Contributed equally to this work with: Pablo Núñez, Jacobo D. Sitt

    Roles Conceptualization, Methodology, Software, Supervision, Validation, Visualization, Writing – original draft

    congyu.lin@icm-institute.org (LC); pablo.nunez.novo@gmail.com (PN); jacobo.sitt@icm-institute.org (JDS)

    Affiliations Coma Science Group, GIGA-Consciousness, GIGA Institute, University of Liège, Liège, Belgium, CERVO Brain Research Centre, Laval University, Québec, Canada, NeuroRehab & Consciousness Clinic, Neurology Department, University Hospital of Liège, Liège, Belgium, Biomedical Engineering Group, University of Valladolid, Valladolid, Spain, Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina, (CIBER-BBN), Madrid, Spain

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  • Jacobo D. Sitt

    Contributed equally to this work with: Pablo Núñez, Jacobo D. Sitt

    Roles Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Validation, Writing – review & editing

    congyu.lin@icm-institute.org (LC); pablo.nunez.novo@gmail.com (PN); jacobo.sitt@icm-institute.org (JDS)

    Affiliation Institut du Cerveau - Paris Brain Institute - ICM, Inserm, CNRS, Sorbonne Université, Paris, France

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This is an uncorrected proof.

Abstract

Understanding the neural mechanisms underlying disorders of consciousness (DoC) remains a major challenge, particularly in distinguishing limited awareness in minimally conscious state (MCS) and complete unawareness in unresponsive wakefulness syndrome, also coined vegetative state (UWS/VS). In this multicentre study, we fitted a biophysically informed corticothalamic neural field model to high-density EEG data from two large independent datasets, comprising 203 UWS patients, 270 MCS patients and 74 healthy controls. We then used the fitted parameters to simulate EEG time series on a per-subject basis and compared empirical and simulated complexity metrics. The model reliably captured the spectral features across different states of consciousness and revealed reduced corticothalamic integrity in DoC patients that was more pronounced in UWS than in MCS, supporting the mesocircuit hypothesis. Furthermore, the simulated EEG reproduced the complexity patterns of the empirical recordings, with permutation entropy emerging as a sensitive marker capable of distinguishing between MCS and UWS for both real and simulated time series.

Author summary

It is a major challenge in neuroscience and clinical care to understand why some patients show signs of minimal consciousness after severe brain injury, while others remain unaware. In this study, we used a physiologically informed corticothalamic model that describes how different neural populations fire and communicate to generate the electrical signals measured by EEG. By fitting the model to recordings of two large independent datasets of patients and healthy participants, we found that it could reliably reproduce the individual brain activity of different groups. The model parameters that describe the communication between the cortex and thalamus populations were found to be different between patient groups. Furthermore, the model was also able to reproduce important patterns of complexity of the real recordings, as the complexity measures obtained from the simulations were found to be highly correlated with the empirical ones and differed between patients who showed minimal consciousness and patients with unresponsive wakefulness. Together, these findings offer new insight into the brain mechanisms that support consciousness after injury and demonstrate the potential of biophysical modelling to create personalised models for future therapeutic applications.

Introduction

Disorders of consciousness (DoC) are a variety of clinical conditions in which patients who suffer from severe acquired brain injury experience impaired wakefulness and/or awareness [1]. Among them, coma refers to a state of complete absence of both awareness and wakefulness [2]. Usually within a month after injury, it can evolve into unresponsive wakefulness syndrome/vegetative state (UWS/VS), in which patients display signs of wakefulness such as eye-opening and reflexive movements, and/or the minimally conscious state (MCS), where patients additionally show minimal signs of awareness such as command following or visual pursuit [3,4]. The emergence from the MCS (eMCS), encompasses those individuals who regain functional communication or purposeful objects use, and they are no longer considered to be DoC [3].

The thalamus is a subcortical structure that serves as a central communication hub between the subcortical regions, the cerebellum, and the cortex. It not only acts as a first-order relay pathway between the sensory input and the primary sensory cortex, but also has higher-order nuclei, that facilitate corticocortical interactions, possibly contributing to the modulation of conscious states [5,6]. It has been suggested that the thalamus plays a crucial role in supporting conscious experience due to its ability to compress high-dimensional cortical activity patterns and then relay them back to the cortex as a lower-dimensional output. This efficient information compression mechanism is thought to support the unified, low-dimensional “essence” of conscious contents, i.e., how they are experienced as an integrated whole instead of disconnected features [5]. Notably, the central thalamus is critically involved in many cases of DoC, as shown by the fact that direct injury to this structure can by itself produce disturbances in consciousness [6,7]. Specific subnuclei are known to result in DoC after bilateral injuries [8], and corticothalamic integrity in acute DoC patients is associated with more favourable clinical outcomes [9]. These findings are consistent with the mesocircuit hypothesis, which posits that after severe brain injury, a widespread deafferentation of the striatum and thalamus leads to a breakdown in communication between the cortex, basal ganglia, and central thalamus [8]. Disruptions in the thalamocortical loops are common in many types of brain injury and are associated with a reduced ability to sustain cortical activity, impairing both arousal (via brainstem/basal forebrain) and awareness (via higher-order cortical areas) [5,7,8]. Indeed, interventions such as deep brain stimulation of the central thalamus have been shown to be effective in restoring both arousal and awareness in anesthetized non-human primates [10], and to increase cognitively mediated behaviours in MCS patients after traumatic brain injury [11–13]. Notable progress has also been made in thalamic low-intensity focused ultrasound intervention [14,15]. Case reports describe patients demonstrating clinically significant increases in behavioural responsiveness following each treatment, while maintaining stable blood pressure, heart rate, and blood oxygen saturation. Additionally, pharmacological interventions such as the dopaminergic agent amantadine were also associated with recovery in UWS and MCS patients [16]. According to the mesocircuit hypothesis, amantadine may be effective by promoting dopaminergic input to the striatum, and thus enhancing thalamocortical synaptic activity [8]. Characterizing patient-specific alterations in thalamocortical circuits is important for understanding the neurophysiological mechanisms underlying impaired awareness in DoC. In the long run, such mechanistic knowledge may also inform translational efforts aimed at identifying biomarkers or guiding interventions that target corticothalamic dynamics.

Assessing consciousness is inherently challenging because it is not a unitary construct and lacks a universally agreed-upon definition. In scientific investigations, however, it is often operationalized via two dimensions: arousal (the level of wakefulness) and awareness (the content of experience). These dimensions provide a practical framework for evaluating and classifying states of consciousness and related disorders [17]. Moreover, since subjective experience cannot be directly measured, assessment of the states of consciousness relies on observable features. These include behaviour, assessed via standardized scales such as Coma Recovery Scale-Revised (CRS-R) [18], as well as neuroimaging evidence derived from techniques like magnetic resonance imaging (MRI), positron emission tomography (PET), and electroencephalography (EEG) [19]. EEG stands as a powerful tool for the study of consciousness, given its high temporal resolution, non-invasiveness, and feature-rich spectral content [20–22]. Its diagnostic significance is highlighted by the European Academy of Neurology's recommendation to incorporate quantitative analysis of high-density EEG into multimodal assessments to distinguish between UWS and MCS [19,23].

While obtaining direct measures of thalamocortical activity is not possible with non-invasive EEG, models based on neural field theory (NFT), which model the non-linear dynamics of a large population of neurons [24], have been successfully used to predict the power spectrum of EEG. In particular, Robinson and colleagues [25–27] developed a physiologically informed NFT model that has repeatedly demonstrated its ability to accurately replicate empirically observable phenomena through corticothalamic populations and their interactions. Among others, they have modelled sleep and wake states [28], evoked response potentials [29], sleep spindles [30], seizures [31], and age-related EEG changes [32]. Furthermore, the model parameters can be fitted to empirical spectra to determine biophysical properties of the thalamocortical loops, as they relate directly to the physiological system. Previous research has attempted to use the model to distinguish between conscious and unconscious states through the model parameters after fitting to the subject’s power spectrum, including wake and Rapid eye movement (REM) states, as well as UWS, MCS and eMCS [33]. While they were successful in differentiating between conscious and unconscious states, namely wakefulness versus REM versus N3 sleep, and healthy participants versus patients with DoC, the parameter space could not distinguish between brain injury subgroups.

Numerous studies have shown that the complexity of brain signals is tightly linked with conscious experience, indicating that for a system to be able to support consciousness, it must be able to both integrate and differentiate information efficiently [34]. Therefore, to validate the capacity of the corticothalamic model to reconstruct the neural dynamics underlying consciousness, we proposed to test its outputs against established neural complexity measures. Lempel-Ziv complexity (LZC), an algorithm that determines the compressibility of a signal by measuring diversity in signal activity patterns, has been successfully used on spontaneous EEG to show a sharp decline in differentiation during anaesthesia in humans [35] and in animal EEG and electrocorticography [36]. Moreover, by measuring the LZC of the response of the cortex to transcranial magnetic stimulation (TMS), researchers have used the perturbational complexity index (PCI) to distinguish between conscious and unconscious states reliably [37]. Additionally, permutation entropy (PE), a measure of signal complexity that quantifies signal irregularity and complexity by calculating the entropy of the frequency of each possible permutation of symbolic sequences for a specific embedding dimension [38], and spectral entropy (SE), a measure of the predictability or uncertainty of the power spectrum distribution [39,40], have been successfully used to differentiate between UWS and MCS patients, further supporting EEG complexity as a key index of consciousness [20]. Based on this body of evidence, we hypothesized that a valid model should produce simulations mirroring these empirical findings.

In the present study, our primary goal is not to propose an immediately applicable clinical biomarker or therapeutic tool. Rather, we aim to assess whether this modelling framework can provide a biologically interpretable account of altered corticothalamic dynamics in DoC. We aim to leverage two large independent high-density EEG datasets of healthy controls and patients with DoC (namely UWS and MCS) to determine the features of the model’s parameter space that would reliably distinguish between DoC subgroups, i.e., MCS and UWS, in addition to differentiating between healthy controls and DoC patients. We also investigated how the model’s performance is influenced by inter-patient variability, such as CRS-R index [41] and time since onset (TSO). Additionally, we examined the frontal and parietal cortex in addition to the averaged whole brain activity, as the Global Neuronal Workspace (GNW) hypothesis suggests a fronto-parietal network plays a crucial role in making information accessible for conscious experience [42,43]. In contrast, the Integrated Information Theory (IIT) suggests that the content of consciousness is maintained by neural activity within a temporo-parietal-occipital “hot zone,” while the prefrontal cortex is more involved in conscious access [44, 45]. This ongoing debate highlights the need for further investigation into the distinct functional contributions of different brain regions to consciousness [46–49]. Furthermore, we evaluated the model’s ability to reproduce not only the spectral features of the empirical EEG, but also their complexity profiles, demonstrating the model’s robustness in capturing multiple dimensions of the data.

The key objectives we addressed were the following: (i) we successfully fitted a corticothalamic neural field model to the EEG power spectra of UWS, MCS, and healthy controls from two independent datasets; (ii) the model revealed distinct patterns of impaired corticothalamic circuits in patients with DoC, highlighting differences between MCS and UWS, in addition to comparing brain activity between patients and healthy controls; and (iii) we evaluated the model’s ability to simulate and recreate the brain complexity of the empirical recordings based on the biophysically-informed fitting of the parameters. These results demonstrate that the model captures both frequency-domain and dynamic characteristics of brain activity, providing a valuable framework for interpreting the underlying neurophysiological mechanisms of consciousness.

Results

We utilized two large, independent high-density EEG datasets, combining resting-state and local-global (LG) recordings, which included a total of 277 UWS, 340 MCS, and 74 controls. We aimed to identify specific alterations in corticothalamic circuits that distinguish between the brain states of healthy individuals and patients, as well as between awareness and unawareness. Following preprocessing, we computed the power spectrum for the average of all 183 electrodes, as well as separately for the average values of Fz and Pz, along with 8 immediately surrounding electrodes, respectively, and used a Markov chain random walk to fit the model parameters. These parameters are related to neural firing and connectivity, see Fig 1B and Methods section for detail. Afterwards, the complexity of the empirical and simulated time series was estimated over the epochs by means of the LZC algorithm [50], the SE [39] and the PE in the theta band [38]. The PE was computed in the theta band () and with an embedding dimension of 3, due to previous literature indicating it is particularly effective at discriminating between UWS and MCS patients [22,20], see [40] for the specific implementation. Finally, the correlation between empirical and simulated measures was estimated by means of Spearman’s coefficient. Fig 1A shows a schematic description of the main steps of the study.

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Fig 1. A Protocol of the study.

High-density EEG recordings from patients with prolonged DoC were used to estimate the parameters of a corticothalamic neural field model. To this end, the average power spectrum of 183 scalp channels, as well as the average from electrodes Fz, Pz and surrounding electrodes, were obtained. After fitting the model, time series were simulated for all subjects using the parameters obtained from the three power spectra. The Lempel-Ziv complexity of the empirical and simulated time series was obtained, their correlation was computed and their capacity to replicate group differences was assessed. B Corticothalamic neural field model. The cortex component consists of an excitatory population (e) and an inhibitory population (i); the thalamus component consists of a reticular population (r) and a relay population (s). The relay population receives external inputs denoted by n. The non-zero gains between each two populations are denoted by . Inhibitory connections are shown in dashed lines. There is no time delay between populations within the same anatomical part, but a loop delay of exists for any connection between cortex and thalamus.

https://doi.org/10.1371/journal.pcbi.1014905.g001

Group differences in model parameters

Examples of power spectrum fitting for a representative subject from each group are shown in Fig 2A. The model successfully fit the spectra across all groups with low chi-square error, and no significant differences in fitting error were observed between groups, as shown in Fig 2B. Table A in S1 Text lists the spectral features of the empirical and fitted power spectra. Alpha and beta peak frequencies were quantified only in the healthy control group because distinct spectral peaks in these ranges were not consistently identifiable in the patient groups. Peak-frequency analyses were therefore restricted to cases where a meaningful local spectral maximum could be defined, whereas relative band-power analyses were performed for all groups. Across delta, theta, alpha, beta and gamma bands, the relative power was well replicated with minimal deviation from the empirical data, as supported by evidence for the null hypothesis in the Bayesian analysis and showing high correlations at individual level, as shown in Table A in S1 Text. Additionally, Pearson correlation analysis confirmed that the simulated spectra accurately predicted empirical subject-level variations across most features.

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Fig 2. A Power spectra for one representative subject from each group.

The power spectra were plotted on a log-log scale over 1-40 Hz. The green line represents the empirical data used as input to the model, the yellow line shows the model’s output, and the purple line displays the power spectrum of a simulated time series based on the model’s parameter settings. This illustrates how well the model captures the key spectral features of the recorded data across groups. B Chi-squared error between the empirical and simulated power spectra. The fitting errors are consistently low across all subject groups and datasets (Liège and Paris), and no statistically significant difference in error was found between groups.

https://doi.org/10.1371/journal.pcbi.1014905.g002

The Kruskal-Wallis tests revealed global interactions between the three groups for both the Liège and Paris datasets in model parameters, specifically between the control and patient groups. No significant differences were found between the frontal and parietal channels, so the subregional analyses were not presented in the main results but can be found in Tables B-C in S1 Text, and Figs A-B in S1 Text. No significant correlation was found between the model’s parameters and the TSO or CRS-R index (Table D-E in S1 Text). The parameters that exhibited significant group effects in both datasets were the following (see Fig 3; the statistics and p-values can be found in Tables 1 and 2 for the Liège and Paris datasets, respectively 1) , excitatory corticothalamic loop gain, which was lower in patients; 2), the inhibitory corticothalamic loop gain, which was higher in patients; 3) , the intrathalamic loop gain, which was higher in patients; 4) , the delay between cortical and thalamic populations, which was higher in patients; and 5) , the electromyogram (EMG) component, which was higher in patients.

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Table 1. Statistical comparisons of the group (Kruskal-Wallis test) and pairwise (Mann-Whitney U-test) interactions between groups (UWS, MCS, HC) of the model parameters in the Liège dataset. FDR corrected for the number of comparisons. UWS: unresponsive wakefulness syndrome. MCS: minimally conscious state. HC: healthy controls.

https://doi.org/10.1371/journal.pcbi.1014905.t001

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Table 2. Statistical comparisons of the group (Kruskal-Wallis test) and pairwise (Mann-Whitney U-test) interactions between groups (UWS, MCS, HC) of the model parameters in the Paris dataset. FDR corrected for the number of comparisons. UWS: unresponsive wakefulness syndrome. MCS: minimally conscious state. HC: healthy controls.

https://doi.org/10.1371/journal.pcbi.1014905.t002

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Fig 3. Comparisons of the model parameters for the three subject groups in two datasets.

Significant differences were found between HC and DoC patients in both datasets in the following parameters: 1) , the gain of the excitatory corticothalamic loop was lower in DoC patients; 2) , the gain of the inhibitory corticothalamic loop is higher in DoC patients; 3) , the gain of the intrathalamic loop was higher in DoC patients; 4) , the delay between cortical and thalamic regions was longer in DoC patients; 5) the EMG component amplitude was larger in DoC patients. Moreover, two parameters differed between MCS and UWS patient groups in the Paris dataset only: 1) was larger in the MCS group than in UWS group; 2) was larger in MCS group than in the UWS group. Blue lines indicate a significance level of p < 0.05.

https://doi.org/10.1371/journal.pcbi.1014905.g003

Subsequent pairwise comparisons confirmed that these differences were statistically significant between the Healthy Control (HC) and both patient groups individually for both datasets (MCS and UWS, p < 0.001, Mann-Whitney U test; see Tables 1 and 2 for the test statistics and p-values for the Liège and Paris datasets, respectively). Moreover, in the Liège dataset, , the gain between cortical excitatory populations, was lower in the control group than in the MCS group (p = 0.012); and , the EMG component, was higher in patients than in the MCS and UWS group, with both p-values < 0.001.

Mann-Whitney U-tests revealed significant differences between the MCS and UWS groups in the Paris dataset. The gain of the excitatory corticothalamic loop () was higher in the MCS group than in the UWS group (p = 0.043). Similarly, the corticothalamic delay ( was longer in the MCS group, with a p-value of 0.043. No difference was found between the MCS and UWS groups in Liège dataset. Nevertheless, the median value for was higher in the MCS group, consistent with the Paris result. The trend of was not consistent across datasets.

Correlation of complexity features between empirical and simulated data

We computed LZC, SE, and for both the empirical and simulated data and evaluated the correlation between the two parameter sets within each group. We first examined the difference of complexity measures between frontal and parietal channels across subject groups but found no significant effect (Table F in S1 Text). Therefore, we report only the results using the 183-channel recordings, with the full statistics results in Table G in S1 Text.

As shown in Fig 4, in the Liège empirical dataset, no significant group difference in LZC was found, but the Paris empirical dataset showed a significant group effect (p < 0.001), with post hoc tests revealing that LZC of HC was significantly higher than that of MCS (p < 0.001) and UWS (p < 0.001). Similarly, in Liège simulated time series, we found that the LZC of the HC group was higher than the MCS group (p < 0.001), and that the LZC of UWS was higher than MCS (p = 0.008). In the simulation for the Paris dataset, we found that the LZC of the HC group was higher than the MCS (p < 0.001) and UWS (p < 0.001). Additionally, we found significant correlation between the LZC of empirical and simulated data, as visualized in Fig 5. In the Paris dataset, the correlation coefficients were 0.655 (p < 0.001) for HC, 0.449 (p < 0.001) for MCS, and 0.254 (p < 0.001) for UWS. In the Liège dataset, the correlations were 0.717 (p < 0.001) for HC, 0.542 (p < 0.001) for MCS, and 0.378 (p = 0.027) for UWS. For all combined data in two datasets the correlation coefficient was 0.458 (p < 0.001). Statistical results are shown in Table 3.

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Table 3. Statistical comparisons of the group and pairwise interactions between groups (UWS, MCS, HC) of the Lempel-Ziv Complexity (LZC) of the real and simulated time series in two datasets. Global interactions were evaluated with Kruskal-Wallis tests, while pairwise interactions were evaluated with Mann-Whitney U-tests.

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Fig 4. Comparison of complexity measures of real and simulated time series across subject groups in two datasets.

In the Liège dataset, the SE and PE of the time series were significantly higher in the HC group than in the two patient groups in both real and simulated data. In the Paris dataset, the LZC, SE and PE of the time series were significantly higher in the HC group than in the two patient groups in both real and simulated data; in addition, the PE was found to be significantly higher in the MCS group than in the UWS group. The simulated time series reproduced this overall pattern, with one exception: in the Liège dataset, the LZC of the MCS group was lower than that of both the HC and UWS groups. Blue lines indicate a significance level of p < 0.05.

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Fig 5. Correlation of the complexity measures between empirical and simulated data in the two datasets.

Panel A and B show separately the correlation plots for the Liège and Paris datasets, including Lempel-Ziv complexity (LZC), spectral entropy (SE), and theta-band permutation entropy (). In general, showed the strongest correspondence between real and simulated data, and correlations were consistently higher in the healthy control group compared to patient groups.

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SE was also computed for both empirical and simulated data and the results are shown in Fig 4. In both the Liège and Paris datasets, SE differed significantly across subject groups (Liège: p < 0.001; Paris: p < 0.001). Post-hoc comparisons showed that SE was significantly higher in the HC group than in both patient groups in both datasets (both datasets p < 0.001). The same pattern was observed in the simulated data: in Liège, SE was higher in HC compared to MCS (p < 0.001) and UWS (p = 0.003); in Paris, HC also showed higher SE than MCS (p < 0.001) and UWS (p < 0.001). However, no significant difference was found between the MCS and UWS groups in either dataset. We also found a moderate to high correlation between the SE of real and simulated data in both datasets (Fig 5): ρ = 0.698 for HC, ρ = 0.583 for MCS and ρ = 0.436 for UWS in the Paris dataset (all p < 0.001); in the Liège dataset the correlations were ρ = 0.561 (p < 0.001) for HC, ρ = 0.602 (p < 0.001) for MCS and ρ = 0.470 (p = 0.005) for UWS. For all combined data in two datasets the correlation coefficient was 0.613 (p < 0.001). Statistical results can be found in Table 4.

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Table 4. Statistical comparisons of the group and pairwise interactions between groups (UWS, MCS, HC) of the Spectral Entropy (SE) of the real and simulated time series in two datasets. Global interactions were evaluated with Kruskal-Wallis tests, while pairwise interactions were evaluated with Mann-Whitney U-tests.

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Finally, we examined the theta band of the time series (Fig 4). In both datasets, Mann-Whitney U tests revealed that the was significantly higher in healthy controls than in the patients (Paris: p < 0.001; Liège: p < 0.001; all pairwise control vs. patient group tests with p < 0.001). Notably, in the Paris dataset, the of the MCS group was higher than that of the UWS group (p < 0.001). Simulated data mirrored these results, with significant group effects in both datasets (Paris: p < 0.001; Liège: p < 0.001), and post-hoc comparisons confirmed higher values in HC than in the patient groups (all p < 0.001). In the Paris simulated data, the MCS group had higher than the UWS group (p = 0.018). A high correlation was found between the of real and simulated data in Paris dataset (Fig 5): 0.847 for HC, 0.700 for MCS and 0.630 for UWS, (all p < 0.001); In the Liège dataset, the correlation of of real and simulated data was high for HC (ρ = 0.927, p < 0.001) and MCS (ρ = 0.857, p < 0.001), and lower for UWS (ρ = 0.372, p = 0.030). For all combined data in the two datasets the correlation coefficient was 0.803 (p < 0.001). Detailed statistics results are provided in Table 5.

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Table 5. Statistical comparisons of the group and pairwise interactions between groups (UWS, MCS, HC) of the Permutation Entropy (PE) of the real and simulated time series in two datasets. Global interactions were evaluated with Kruskal-Wallis tests, while pairwise interactions were evaluated with Mann-Whitney U-tests.

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See supplementary material Figs C-D in S1 Text for the comparisons between frontal and parietal channels, as well as the correlation analyses for the full data in Table H in S1 Text. We found that the complexity was higher in the TSO > 1 group than in the TSO < 1 group, which is significantly shown in all three measures in the Paris dataset and the PE in the Liège dataset (Fig E in S1 Text and Table I in S1 Text). Low correlation was found between the CRS-R index and SE and PE values in the Paris dataset (Table J in S1 Text).

Discussion

Corticothalamic parameters and the role of thalamocortical loops

The results demonstrated that the corticothalamic model accurately captured key spectral features across groups. It was able to reproduce the frequency of the alpha and beta peak in the HC subjects, the prominent theta band activity in the MCS patients, and the delta-dominated power spectrum in UWS patients. Previous studies showed its ability to simulate healthy resting-state activity, sleep spindles [30] and periodic spikes during epileptic seizures [31]. It has been observed that, in the case of complete thalamocortical deafferentation, spectral peaks can be absent altogether [51], which was the case in some UWS patients, and the model was able to reliably replicate the absence of periodic components in the spectrum. Our findings further validate the model’s applicability in a variety of scenarios by showing its ability to simulate brain states of healthy individuals and brain-injured patients in two independent datasets (Liège and Paris), where the latter was able to distinguish between UWS and MCS, extending previous findings [33]. We thus confirmed the model’s ability to fit and simulate the comparatively smoother power spectral density (PSD) curve of DoC patients. The model's high goodness of fit across all groups further supports its suitability for estimating the connectivity between the neuronal populations it incorporates, as reflected in its parameter values.

The variation in model parameters across groups partially aligns with the findings of Assadzadeh et al. [33]. Although we did not replicate the group effect on synaptic rise or decay rates, we observed similar variance in corticothalamic loop parameters. The physiological interpretation of these parameter changes is consistent with the mesocircuit hypothesis mechanisms in the context of DoC. Specifically, in the patient group, we noted a lower absolute value for the gain of the corticothalamic excitatory and inhibitory loop, along with a longer delay between cortical and thalamic populations. This finding supports the mesocircuit hypothesis, which posits that disrupted EEG patterns in DoC patients are due to impairments in corticothalamic connectivity [8]. This hypothesis has been substantiated by various studies employing different methodologies, including MRI [52], PET [53], EEG [21], and spectral dynamic causal modelling on MRI data [54]. The results are also in agreement with those observed using the same model on the EEG of patients experiencing acute coma within the first 48 hours after cardiac arrest, in which patients with poor outcome showed increased corticothalamic inhibition, and higher delay compared to those with good outcome [55]. This represents an important extension of previous EEG-based analyses of DoC. Although the corticothalamic parameters in the model should not be understood as direct measurements of thalamic activity, their group-level variation offers a physiologically grounded account of how altered corticothalamic interactions may contribute to impaired consciousness. In this sense, our study supports the use of biophysically informed EEG modelling as a mechanistic approach for probing circuit-level dysfunction in DoC.

Beyond the differences observed between patients and healthy controls, the model also revealed a subtler, yet meaningful distinction between MCS and UWS patients in the Paris dataset, which was not previously reported by Assadzadeh et al. [33]. Specifically, in the Paris dataset, we found that the gain of the excitatory corticothalamic loop was lower in UWS compared to MCS. This finding aligns with previous studies. For example, Magrassi et al. [56] reported increased activity of medial thalamic neurons and stronger phase coupling between thalamic discharges and cortical EEG signals in MCS patients compared to those with UWS, based on microelectrode recordings. Similarly, MRI studies have shown that thalamocortical pathways connecting the thalamus with the dorsal and posterior regions of the posteromedial cortex exhibit less white matter integrity in UWS patients than in MCS patients [57,58]. We thus propose that the higher corticothalamic gain in the model may reflect a more preserved thalamocortical interaction in MCS. Considering the proven accuracy of the model in replicating spectral features after fitting, this finding would be in line with a previous study, which showed that a higher corticothalamic integrity, corresponding to certain EEG spectral features such as theta and beta peaks, is also indicative of an increased likelihood of recovery of consciousness in acute DoC patients [9].

Interestingly, we found that corticothalamic delay was shorter in UWS than in MCS. One possible interpretation is that shorter delays in UWS may reflect a breakdown of refined thalamocortical processing, leading to fast, asynaptic, and hyperexcitable physiological activity that is incapable of supporting consciousness. This aligns with evidence showing UWS patients have lower PCI associated with stereotypical responses to TMS-EEG [37], altered fMRI signal propagation [59], and an increase in thalamic hemodynamic response found in UWS patients [60]. In contrast, the longer delay in MCS could indicate a partially preserved though potentially slowed thalamocortical circuit, which would allow for some conscious processing in the MCS patients, but the structural damage, such as axonal injury or demyelination [17,61], could lead to slowed signal transmission along thalamocortical fibers, thereby increasing effective delays. When interpreting these findings, the difference in the experimental conditions in two datasets should be factored in. The Paris dataset was acquired during the LG paradigm, which is explicitly designed to probe conscious auditory processing. The fact that the model effectively captures network differences under an active probing paradigm suggests that engaging the network may help unmask the different brain dynamics and conscious states between MCS and UWS patients. This task-dependent performance of the model should also be treated with caution when interpreting the complexity measures discussed in the following section.

In addition to the main findings, we observed that the EMG component was consistently larger in patients across the Liège dataset; Since the EMG component is introduced to account for non-neural, high-frequency noise, this pattern could reflect increased movement artifacts associated with patients’ physiological states. However, this interpretation should be approached with caution. The EMG term primarily serves as a mathematical ‘patch’, compensating for spectral features that are not well captured by the neural field model. Therefore, its variation may simply reflect a model mismatch in fitting the high-frequency range, rather than a meaningful physiological distinction between groups.

Contrary to our initial hypothesis, we found no significant differences between frontal and parietal regions across all the measures examined, including model parameters and signal complexity. This might be due to the fact that the corticothalamic model addressed different aspects of the EEG data. For instance, several investigations have suggested that parietal regions may be more sensitive than frontal areas in distinguishing MCS from UWS, particularly through time-varying gamma phase synchronization, mutual information, participation coefficient, and clustering coefficient [40,62,63]. However, these metrics primarily emphasize functional connectivity and network-level integration, whereas our modelling approach focuses on reproducing the spectral power of EEG signals. As such, the lack of observed regional differences in our results may reflect a mismatch between the targeted neural features: power spectrum fitting may not be sufficiently sensitive to capture the dynamic inter-regional interactions that characterize conscious state differentiation.

EEG complexity analyses

Having established that the model’s parameter space can distinguish clinical groups, we further analyzed the signal complexity of the real and simulated data, providing the link between the abstract parameters and measurable neurophysiological output. The simulated time series did not reproduce all spectral features with the same precision as the fitted spectra, which indicates that the conversion from spectral-domain fitted parameters to time-domain simulation parameters may introduce some loss of precision. Importantly, however, the simulated signals retained the main dynamical features needed for the present analysis. This provides an independent validation of the modelling approach: the model was not fitted to LZC, PE or SE, but the positive results suggest that the fitted parameters capture underlying signal dynamics beyond the power spectrum alone. We found that the permutation entropy in the theta band more effectively discriminates between groups compared to LZC and SE, both in real and simulated data. In the Paris dataset, the was significantly lower in the UWS patient group than the MCS patient group, consistently in the real and simulated EEG. While this result is in agreement with Sitt et al. [20], where it was demonstrated that lower-frequency band complexity is a more robust and sensitive marker for distinguishing levels of consciousness in DoC patients, our study extends this by showing that a biophysical model fitted to EEG spectra can for the most part reproduce condition-specific complexity profiles.

Additionally, the complexity measures of the simulated data showed a moderate to high correlation with those of real data: in all three measures, the correlations were higher for the healthy controls than for the patients. This discrepancy may reflect the larger inter-individual variability and spectral abnormalities found in pathological brain states, which challenged the model’s capacity to accurately capture their underlying dynamics. Among the metrics, the permutation entropy exhibited the strongest correspondence between modalities. This might also be due to the symbolic transformation used in this method, designed to enhance the signal-to-noise ratio of the metric and the relatively low within-group variance of this measure, further supporting its reliability as a measure of EEG signal complexity in consciousness studies. The previously reported high diagnostic accuracy in discriminating UWS and eMCS patients provided by in empirical recordings [20,22] is a key motivating factor in the potential use of the model in biomarker development. The present results should be interpreted primarily as mechanistic: they suggest that the model may help explain why condition-specific complexity differences emerge in EEG, rather than establishing the model itself as a clinical biomarker. Furthermore, the model allows estimation of how close a patient's brain dynamics are to criticality, a regime thought to support flexible, integrated information processing and consciousness [64]. Deviations from criticality are a commonly observed feature of the brain dynamics in DoC [65, 66], making it a valuable target for intervention. By identifying whether a patient’s brain is in a subcritical or supercritical state, the model may eventually help generate hypotheses for personalised therapeutic strategies, such as enhancing excitability in subcritical dynamics or stabilizing activity in supercritical ones.

In both the model parameter analysis and the time series complexity results, we observed that the difference between MCS and UWS patients was more pronounced in the Paris dataset than in the Liège dataset. It is essential to note that these datasets differ in their experimental design: the Liège dataset consists of resting-state recordings, whereas the Paris dataset utilizes data from a local–global auditory paradigm, which is treated here as a pseudo-resting state. Previous studies have demonstrated that the local-global paradigm can serve as a marker of conscious processing, with the global effect more frequently observed in MCS patients than in those with UWS [40,67]. One possible explanation for our results is that task-free, resting state recordings, may fail to detect subtle residual signs of consciousness. In contrast, the local-global paradigm actively engages hierarchical processing, which might allow for the detection of brain responses more directly linked to conscious awareness and cognition, thus providing greater sensitivity in distinguishing between states of consciousness.

Limitations and future directions

One limitation of this study is that we used scalp EEG recordings for the power spectrum fitting. The uncertainty of the original source of the activity recorded around the Fz and Pz electrodes might have hindered the detection of effects involving frontal and parietal areas that are central to dominant theories of consciousness, such as the GNW and the posterior “hot zone” IIT hypotheses [42,68]. These spatial constraints are especially relevant for paradigms like the LG task, where fronto-parietal dynamics play a critical role in conscious processing. In addition, we used a common average reference scheme, which, while commonly applied, can obscure localized neural activity by averaging signals across the entire scalp. More spatially specific referencing methods, such as current source density could potentially provide better differentiation between nearby cortical sources [69]. While source-reconstructed EEG could offer improved spatial mapping and better localization of underlying cortical sources, this was not feasible in the present study. Most patients lacked high-resolution T1-weighted MRI scans, and the substantial heterogeneity of brain lesions across individuals made it inappropriate to rely on standard anatomical templates, which could introduce significant spatial inaccuracies.

Beyond the constraints of the empirical data, the spatial resolution is also limited by our current use of a spatially averaged single-node neural field model. However, future extensions of the model can address this issue directly. Structural connectivity based on diffusion-weighted imaging (Deco 2008, Breakspear 2017) and multi-node thalamocortical architectures could be incorporated into the framework while maintaining parameter estimability from clinical EEG data. A first step in this direction could be simulating regionally specific EEG signals (e.g., at Fz and Pz) using a multi-node model where the excitatory populations of each node are connected to each other while one thalamic population is shared among nodes. Such an approach would allow cortico-cortical and cortico-thalamo-cortical interactions to be studied while preserving the physiological interpretability of the model.

Furthermore, the interpretation of model-derived parameters should be approached with caution. Although the model demonstrated good spectral fits across groups, some parameter estimates exhibited high standard deviation during the fitting process, indicating low parameter identifiability and suggesting the possibility that different combinations of parameters could yield similarly accurate fits to the data. This issue, common in complex biophysical modelling [70], highlights the need for caution when drawing mechanistic conclusions from individual parameter values. On the other hand, the low correlation of CRS-R index and the model parameter values and signal complexity measures indicates a key distinction between the neural information captured by the model and behavioural scales. The behavioural scoring might be too nuanced and influenced by too many factors (e.g., motor and sensory deficits, patient fluctuations) for a linear correlation with a specific neural parameter to emerge. The effect of TSO further illustrates this dissociation: while there is no effect on the model parameters themselves, it did influence dynamic output measures such as the signal complexity. Consequently, while the model robustly differentiates diagnostic categories, linking its parameters more closely to bedside clinical assessment remains a challenge requiring further investigation.

The model’s ability to preserve key features of signal complexity in its outputs could be a motivating factor for extending its application to simulating brain stimulation and pharmacological interventions in future studies. This direction has been supported by a recent study using an artificial intelligence framework to produce biologically realistic simulations of both conscious and DoC responses to brain stimulation, and generate predictions about the mechanisms of unconsciousness (Toker et al., 2026). As has been stated in the literature, any kind of perturbational analysis on a neural field model is only as valid as the model’s ability to capture relevant features of the brain dynamics [71]. Therefore, the strong capacity of the baseline biophysical model to capture relevant aspects of whole-brain dynamics makes the simulation of external interventions more feasible and potentially reliable. In neural field models, neural stimulation effects could be implemented as a controlled external input to specific neural populations, described by the waveform and time course of induced electric fields, combined with population-based neural dynamics, and plasticity rules [72, 73]. The individualized in silico simulations generated by the models would enable robust simulation of post-stimulation effects on EEG activity and thalamocortical loop parameters. Pharmacological interventions could also potentially be simulated in patient models using approaches similar to those used by Alnagger et al. and Mindlin et al. [71,74] on fMRI data, where parameter changes between placebo and drug conditions were used as modulating factors in the model to simulate treatment.

Conclusion

We demonstrated the feasibility of using neural field models to fit high-density EEG recordings from patients with DoC, and their ability to shed light on the specific thalamocortical circuits that contribute to aberrant power spectra. Moreover, we showed the capacity of the model to generate synthetic signals that closely mimic complexity features of the empirical recordings. The model’s ability to detect impaired communication between neuronal populations, combined with its capacity to simulate EEG time series, provides a promising mechanistic framework for studying individual impairments in DoC. In future work, the framework may also provide insight into estimation of proximity to criticality, and testing personalised treatment strategies aimed at restoring consciousness.

Materials and methods

Subjects

This retrospective study involved two independent datasets collected from the University and University Hospital of Liège, as well as the Pitié-Salpêtrière Hospital in Paris. Ethical approval for the study was granted by the Ethics Committees of both institutions, University Hospital and Faculty Ethics Committee of Liège and Ethical Committee of the French Society of Intensive Care Medicine – SRLF, in accordance with the Declaration of Helsinki. Written informed consent was obtained from the legal representatives of all patients and from the healthy control participants. Clinical evaluations were conducted using the CRS-R, with the final diagnosis determined by the highest CRS-R score obtained across multiple assessments (a minimum of five in the Liège dataset and a minimum of three in the Paris dataset [75]. All assessments were administered on separate days by experienced clinicians.

EEG recordings in the Liège dataset were previously collected while participants were at rest [76]. In contrast, the Paris dataset included task-related EEG data obtained using the auditory LG paradigm [67], designed to explore both conscious and unconscious auditory processing. This paradigm presents sequences of five tones, with the final tone either matching the previous ones in pitch (local standard) or differing from them (local deviant). Additionally, a second level of regularity is introduced based on the overall frequency of the sequences, with 80% classified as global standards and 20% as global deviants.

We removed 1 MCS subject from the Liège dataset and 3 UWS subjects from the Paris dataset due to excessive signal noise. Eventually, the Liège dataset included 37 healthy controls and 120 patients with prolonged DoC (>28 days post-injury), comprising 33 UWS patients and 86 MCS patients. Portions of this dataset have been used in previous research [21,33,63,76]. The Paris dataset consisted of 354 prolonged DoC patients: 170 UWS, 184 MCS, and 37 healthy controls. This dataset has also been previously used [20, 22,77–79]. The demographic details of both datasets are summarized in Tables 6 and 7.

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Table 6. Socio-demographic and clinical data for the Liège dataset. Statistically significant between-group differences are marked with asterisks *p < 0.05 (Mann-Whitney U-test for age, chi-squared test for sex). m: mean; std: standard deviation; M: male; F: female; N/A: not applicable. CRS-R: Coma Recovery Scale – Revised.

https://doi.org/10.1371/journal.pcbi.1014905.t006

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Table 7. Socio-demographic and clinical data for the Paris dataset. Statistically significant between-group differences are marked with asterisks *p < 0.05 (Mann-Whitney U-test for age, chi-squared test for sex). m: mean; std: standard deviation; M: male; F: female; N/A: not applicable. CRS-R: Coma Recovery Scale – Revised.

https://doi.org/10.1371/journal.pcbi.1014905.t007

Electroencephalographic recordings

EEG recordings for both datasets were obtained using a 256-channel high-density EEG system (EGI, Electrical Geodesics Inc.) with a sampling rate of 250 Hz. During the recording sessions, subjects remained awake with their eyes open. Face and neck electrodes were removed, keeping a total of 183 channels.

In the Liège dataset, resting-state EEG was acquired for 20–30 minutes. The preprocessing pipeline included multiple steps. Initially, a 6th-order Butterworth high-pass filter at 0.5 Hz and an 8th-order IIR Butterworth low-pass filter at 100 Hz were applied, with notch filters at 50 and 100 Hz to remove power line interference. The EEG signal was then segmented into 2.2040-second epochs. Bad channels were identified through visual inspection of the raw time series, while noisy segments were detected by transforming the data into 20 principal components and visually inspecting them. Independent component analysis was performed to remove artifacts related to non-neural activity. Spherical interpolation was used to reconstruct rejected channels, and the final dataset was re-referenced to the average reference.

In the Paris dataset, EEG data were segmented into epochs ranging from -200 ms to 1336 ms relative to the onset of the first sound. Preprocessing was entirely automated. A band-pass filter with a bandwidth of 0.5 to 45 Hz was applied using a 6th- and 8th-order FFT-based Butterworth filter. Epoch lengths were set to 1.5 seconds. Adaptive outlier detection was then used to identify and exclude noisy epochs [80]. Finally, the data were re-referenced using an average reference, and baseline correction was performed. Although task-based and resting-state EEG capture evoked and spontaneous neural activity respectively, studies demonstrate that consciousness markers derived from task-based paradigms can generalize to the resting state [20,22]. This validates our approach of treating the LG paradigm data as a pseudo-resting state condition, incorporating all epochs of the recording regardless of the sequence.

Spectral features extraction

We extracted spectral features from the empirical EEG power spectra, the fitted analytical spectra generated by the model, and the spectra computed from simulated time series using the fitted parameters. For each subject and condition, we extracted relative power in the delta (1–4 Hz), theta (4–8 Hz), alpha (8–13 Hz), beta (13–30 Hz), and gamma bands (30–45 Hz), as well as alpha and beta peak frequency (for the HC only). Relative band power was calculated as the proportion of total power within the analyzed frequency range accounted for by each frequency band.

Neural field model

In a neural field model, the neural population activity is simulated by the mean firing rate of an afferent population within a node corresponding to a brain region. The model used in this study includes 4 interconnected populations within each node: cortical excitatory (), cortical inhibitory (), thalamic relay (), and thalamic reticular (), as shown in Fig 1B. Depending on the populations, the connections between them can be excitatory, zero (not connected), or inhibitory [27]. For each population , the mean firing rate , given a mean soma voltage , can be expressed with the nonlinear sigmoid function as in equation (1). The potential is computed from the firing activity in other connected populations as follows:

(1)(2)(3)

where denotes the potential of population A at position r and time t, is the threshold that the soma voltage needs to exceed to produce an action potential, is the maximum of the sigmoid function, and is the variance of the threshold. The synaptic connection to population from population is , where is the mean number of synapses from to , and is the time-integrated response to a unit input signal. is the mean firing arrival rate, allowing for a time delay due to anatomical separation between populations. This means is nonzero, equal to 1/2 of the corticothalamic propagation time (), only when and are cortical and thalamic populations respectively. and are the inverse rise and decay time of the cell-body potential produced by an impulse at a dendritic synapse. Thus equation (2) could be rewritten as a set of equations for each population separately, only taking into consideration the terms with nonzero parameters:

(4)(5)(6)(7)

where q is a constant noise input to the thalamus relay population.

The firing rate produced by a population need to travel to other populations over long range white matter tracts. This spreading activity obeys the damped wave equation:

(8)

where refers to the cortical damping rate; is the mean range.

These equations enable us to simulate the EEG-like time series. Since we are interested in the spectral features of the simulation, this could be done more efficiently by means of a transformation of the model into the frequency domain, as addressed in the original papers on the Robinson model [27,81]. By setting all the derivatives to 0 in (3) and (8), we can obtain spatially uniform steady states and solve the steady state firing rate of the excitatory population :

(9)

where denotes the inverse of the sigmoid function, is the steady state component of the input stimulus. We can further approximate the brain’s activity as linear, i.e., first order, perturbation relative to a steady state. By linearizing equation (1) and keeping only the first order term in the Taylor expansion equation, we get:

(10)(11)

Next, applying a Fourier transform on the differential operator in equation (2), (3) and (8) yields the transfer function of given a stimulus of wave vector k and angular frequency [29,81]:

(12)(13)(14)(15)

The gain denotes the differential response of population A per unit input from population B. And the gain loops are defined as: for the excitatory corticothalamic loop through the relay population, for the inhibitory corticothalamic loop through both relay and reticular populations, for the intrathalamic loop. The EEG power spectrum can be calculated by integrating the squared magnitude of achieved by integrating equation (9) over [27]:

(16)(17)

F(k) is a filter function that describes the volume conduction effect of the electrical activity of the cortex: the power in spatial modes with higher frequency (larger ) would be reduced due to the volume conduction of uncorrelated source activity. Here is the state-independent low-pass cutoff [82].

Another important component in simulating the power spectrum is the EMG component. The EMG signal is often observed at frequencies higher than 25 Hz in EEG recordings. It is caused by activity in pericranial muscles [83, 84]. Hence, an EMG component is included in the model power spectrum [85]:

(18)(19)

where and are the normalized EMG power and the characteristic EMG frequency, respectively. All the parameters and values can be found in Table 8 based on previous studies [26,27,30].

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Table 8. Model parameter ranges and fixed values. The fixed parameters and ranges are based on previous literature [26,27,30].

https://doi.org/10.1371/journal.pcbi.1014905.t008

The fitting process requires the “BrainTrak” library on MATLAB, which was developed as a method to analyze the sleep EEG signals and estimate corticothalamic model parameters for different brain activity in wake-sleep cycle [28,86]. The code is available on GitHub: https://github.com/BrainDynamicsUSYD/braintrak. The model optimization is estimated by minimizing the chi-squared () error between the simulated and empirical power spectrum:

(20)

where the error is weighted by for each frequency component to compensate for the large number of sampling points at high frequencies compared to low frequencies, which results from the logarithmic transformation of the signal frequencies. Thus, the likelihood of the parameters is estimated by:

(21)

so that the likelihood is maximized to 1 when the error is 0 and is minimized to 0 as the error increases. The fitting starts with a set of parameters gained from previous fittings of healthy subjects’ resting state data [28]. Then, a Markov Chain Monte Carlo sampling algorithm is used to characterize the posterior distribution of the parameters. At each step, a new random set of parameters is proposed by drawing a sample from a simple proposal distribution centered on the current parameter values. The new set of parameters is accepted if it yields a higher likelihood defined by equation (21). Otherwise, it is accepted with a probability equal to the ratio of the posterior probability of the new parameters to the posterior probability of the old parameters. This procedure will be repeated until there is no iterative change in the sampled probability distribution. The sequence of the accepted parameters in the random walk is referred to as the “chain”. After accepting 100 points on the chain, the parameter probability distribution is switched from an assumed one to the empirical one, which is then used to propose the subsequent step of the random walk. The first 5,000 points on the chain are discarded because they largely rely on the initial values. The total length of the preserved chain is 50,000 points. The final parameters are obtained by selecting the point on the chain that has the largest value of likelihood . The probability distribution of each parameter indicates whether a good fit is achievable with a narrow or wide choice of parameters.

After fitting the power spectrum, we used the “NFTsim” software package, written in C++ and bundled with MATLAB routines [73] to generate time series given the fitted parameters. The main idea is to inversely solve equation (21) to get the firing response for each population in the time domain. Afterwards, a neural field is created on a square domain with 144 grid cells in total, of which the spatially extended domain remains invariant throughout the simulation. The propagation process with time delay is constructed based on the physical length of the two dimensions in this field. The code for NFTsim is available on GitHub: https://github.com/BrainDynamicsUSYD/nftsim.

The power spectral density of the EEG signals used for model fitting was computed using the Welch method, with a segment length of 128 samples, an overlap of 100 samples, and a fast Fourier transform length of 4096. The PSD was computed for frequencies ranging from 1 to 40 Hz. We fitted 9 parameters for the spectrum fitting process: , , ,, , , , , , as indicated in equation (12) and (13), to be able to simulate the power spectrum. However, the process of simulating the time series requires the specific value of every gain between each pair of populations, which cannot be obtained directly from these 9 parameters, so we increased the fitted parameter number to 11: , , ,, , , , , , , . The simulated time series had a length of 60 seconds, with a step width of 0.0005 seconds.

Statistical analyses

The values of , , ,, , , , , and empirical and simulated LZC, PE and SE were compared among groups and electrodes by means of non-parametric statistical tests. Kruskal-Wallis tests were used to detect global interactions between the three groups (HC, MCS and UWS), and if interactions were found, Mann-Whitney U-tests were performed to determine between-group differences. To account for multiple comparisons, a false discovery rate (FDR) correction was applied [87]. The significance level was set at α = 0.05. The correlation strength was interpreted following conventional thresholds: high (), moderate () and low (). Bayes factors were used to quantify evidence for or against differences in spectral features between empirical and model-derived spectra. indicates evidence favoring the alternative hypothesis, whereas indicates evidence favoring the null hypothesis. Statistical analyses and signal processing were performed using MATLAB (version R2024b Mathworks, Natick, MA). Brain networks were visualized with BrainNet Viewer (http://www.nitrc.org/projects/bnv/) [88].

Supporting information

S1 Text. Table A.

Comparison of spectral features between empirical, fitted power and simulated time series spectra. Table B. Statistical comparisons of group effects (HC, MCS, UWS) on model parameters across both datasets. Table C. Statistical comparisons of the pairwise interactions between groups (UWS, MCS, HC) of the model parameters in two datasets (Mann-Whitney U-test). FDR corrected for the number of comparisons. Fig A. Comparison for the parameters fitted to the power spectrum for the three subject groups across channels of different regions in the Liège dataset. Fig B. Comparison for the parameters fitted to the power spectrum for the three subject groups across channels of different regions in the Paris dataset. Table D. Statistical comparison of model parameters between the Time Since Onset (TSO) more than 1 year and the TSO less than 1 year groups in both datasets. Table E. Correlation between model parameters and CRS-R scores. Table F. Comparison of the complexity measure for frontal and parietal channels across groups (Kruskal-wallis test). Table G. Pair comparison for complexity measures in frontal and parietal channels for real recordings and simulation of two datasets (Mann-Whitney U-test). Fig C. Group comparisons of complexity measures in real recordings and simulations from the Liège dataset. Fig D. Group comparison for complexity measures in real recording and simulation of Paris dataset. Table H. The correlation analyses (Spearman’s coefficient) for Fz and Pz channels of three complexity measures (LZC, SE and PE) in Liège and Paris datasets. Table I. Statistical comparison of complexity measures between the Time Since Onset (TSO) more than 1 year and the TSO less than 1 year groups in both datasets. Fig E. Comparison of complexity measure values between the Time Since Onset (TSO) more than 1 year and the TSO less than 1 year groups in both datasets. Table J. Correlation between three complexity measures and CRS-R scores in both datasets.

https://doi.org/10.1371/journal.pcbi.1014905.s001

(DOCX)

Acknowledgments

We thank the patients, their families and the control subjects for participating in our study. The authors extend their gratitude to the entire staff of the ICU and Nuclear Medicine and Radiodiagnostic departments at the University Hospital of Liège. We are especially thankful to the members of the Coma Science Group for their assistance with the clinical evaluations.

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