Brain dynamics reflecting an intra-network brain state is associated with increased posttraumatic stress symptoms in the early aftermath of trauma

This study examines the association between brain dynamic functional network connectivity (dFNC) and current/future posttraumatic stress (PTS) symptom severity, and the impact of sex on this relationship. By analyzing 275 participants’ dFNC data obtained ~2 weeks after trauma exposure, we noted that brain dynamics of an inter-network brain state link negatively with current (r=−0.179, pcorrected= 0.021) and future (r=−0.166, pcorrected= 0.029) PTS symptom severity. Also, dynamics of an intra-network brain state correlated with future symptom intensity (r = 0.192, pcorrected = 0.021). We additionally observed that the association between the network dynamics of the inter-network brain state with symptom severity is more pronounced in females (r=−0.244, pcorrected = 0.014). Our findings highlight a potential link between brain network dynamics in the aftermath of trauma with current and future PTSD outcomes, with a stronger protective effect of inter-network brain states against symptom severity in females, underscoring the importance of sex differences.

Wood Johnson Foundation, the Kaiser Family Foundation, the Harvard Center on the Developing Child, Stanley Center for Psychiatric Research at the Broad Institute of MIT and Harvard, the National Institutes of Health, One Mind, the Anonymous Foundation, and Cohen Veterans Bioscience.She has been a paid consultant for Baker Hostetler, Discovery Vitality, and the Department of Justice.She has been a paid external reviewer for the Chan Zuckerberg Foundation, the University of Cape Town, and Capita Ireland.She has had paid speaking engagements in the last three years with the American Psychological Association, European Central Bank.Sigmund Freud University -Milan, Cambridge Health Alliance, and Coverys.She receives royalties from Guilford Press and Oxford University Press.Dr. McLean has served as a consultant for Walter Reed Army Institute for Research, Arbor Medical Innovations, and BioXcel Therapeutics, Inc.Dr. Ressler has performed scienti c consultation for Bioxcel, Bionomics, Acer, and Jazz Pharma; serves on Scienti c Advisory Boards for Sage, Boehringer Ingelheim, Senseye, and the Brain Research Foundation, and he has received sponsored research support from Alto Neuroscience.

Introduction
Post-traumatic stress disorder (PTSD) may develop in individuals who have experienced or witnessed a traumatic event, such as military warfare, sexual or physical assault, accidents, or natural disasters 1 .Symptoms of PTSD include distressing thoughts, ashbacks, avoidance of reminders, changes in mood and cognition, and increased arousal, which can signi cantly impact an individuals' life 2 .Biological markers or biomarkers may be able to identify those who are more likely to develop PTSD following a traumatic incident 3,4 .Early identi cation of such individuals might allow for prompt treatment and preventive measures, potentially minimizing the severity and duration of PTSD symptoms.Furthermore, these markers may help in the development of tailored treatment methods, the optimization of therapeutic treatments, and the long-term monitoring of therapy response 5 .
In recent years, there has been a signi cant increase in the exploration and advancement of neuroimaging-based markers for identifying vulnerability to PTSD 6,7 .This emerging eld shows great potential in the rapid development of tools for early identi cation and intervention 8 .Studies utilizing neuroimaging techniques have uncovered notable alterations in brain function among individuals with PTSD.These alterations are marked by atypical functional network connectivity (FNC) patterns, as observed in resting-state functional magnetic resonance imaging (fMRI) studies [9][10][11] .Speci cally, these patterns are seen in various brain regions, including the hippocampus 12 , amygdala 13 , visual network 14 , and prefrontal cortex 13 in individuals with PTSD.This underscores the extensive in uence of trauma on brain networks.Furthermore, several studies have successfully utilized resting-state fMRI functional connectivity to predict the severity of PTSD symptoms [15][16][17][18] .Additionally, two recent studies revealed the ability to predict future symptom severity in participants with PTSD by analyzing resting-state fMRI data obtained after the trauma had occurred 19,20 .
It has been assumed that brain FNC remains quasi-static or invariant over long periods of time, leading many previous studies to focus solely on static FNC (sFNC) while ignoring the brain dynamics during rest.However, challenging this assumption, a relatively new concept called dynamic FNC (dFNC) has emerged [21][22][23][24][25] .A dynamic approach recognizes that FNC during the relatively short length of resting-state fMRI scans can exhibit temporal variations, thereby highlighting the importance of studying the dynamic aspects of FNC 26 .Unlike sFNC, dFNC offers greater sensitivity in capturing the spontaneous adaptations that occur in response to various cognitive and mental conditions 27 .By considering the spontaneously uctuating nature of neural signals across different temporal scales, dFNC allows for a more sophisticated evaluation of brain activity 28 .
Considering the dynamic nature of FNC in resting-state fMRI, several studies have explored dFNC in the context of PTSD in recent years [29][30][31][32] .However, none of these studies have examined the capability of dFNC to predict future PTSD symptom severity.In addition, previous research indicates that women are two to three times more likely than men to develop PTSD 33 .Despite this, there has been a notable absence of studies that examine the potential effects of sex on the relationship between dFNC features and the severity of current or future PTSD symptoms.
In the present study, we aim to build upon previous research on dFNC in the context of PTSD.Speci cally, we investigated the predictive capability of dFNC features for future PTSD symptom severity.Additionally, we explored the potential effects of sex on the association between dFNC features and both current and future symptom severity.As past studies have demonstrated, biological sex is not the primary determinant of the various neurophenotypes associated with adverse post-traumatic outcomes.Instead, a range of other factors such as low socioeconomic status or SES, including income 34,35 , housing quality 36 , and broader socioeconomic conditions, area deprivation index or ADI 37 also signi cantly in uence the risk and severity of PTSD.To address the contribution of these factors, we also included them as covariates in our analysis.
To accomplish these goals, we utilized the dataset from the Advancing Understanding of Recovery after Trauma (AURORA) project 38 .In the AURORA study, understanding whether dFNC features derived from resting-state fMRI early after a trauma can predict future PTSD symptom severity is crucial.This is especially true since neuroimaging was conducted approximately two weeks after the traumatic event, at a time when acute stress disorder may be assessed, but before the diagnosis of PTSD can be made.This timing allows us to investigate the potential of dFNC features as early biomarkers for PTSD and evaluate their predictive capability for the severity of PTSD symptoms at a later stage.

Participants
Data for the current analyses were collected as part of the multisite emergency department (ED) AURORA study.The AURORA study represents a signi cant research effort aimed at enhancing our understanding, prevention, and recovery strategies for individuals who have undergone a traumatic event.In AURORA study, trauma-exposed civilians brought to one of 29 participating EDs across the United States were recruited for this large, longitudinal study (details in 38 ).This study involved more than 4000 participants from the AURORA project, who provided clinical data at various intervals: 2 weeks (WK2), 4 weeks (WK4), 3 months (M3), 6 months (M6), and 12 months (M12) as illustrated in Fig. 1A.Additionally, neuroimaging data from ~ 400 participants were collected at WK2 from ve different scanning locations, which include Atlanta (Georgia), Belmont (Massachusetts), Philadelphia (Pennsylvania), St. Louis (Missouri), and Detroit (Michigan).The recruitment for this study took place between September 2017 and December 2020 (Final freeze 4 Psychometric release).We excluded those with low-quality resting-state fMRI and missing clinical information at the imaging acquisition date.This process resulted in 275 participants (181 females) being included in this analysis.Table 1 summarizes the demographic characteristics of the participants included in this study.Overall, our analysis suggests that state 2 and state 3 exhibit characteristics of inter-network states, evidenced by the increased connectivity across the seven networks.In contrast, state 1 is indicative of an intra-network state, as it demonstrates predominantly within-network connectivity patterns.
Dynamic FNC occupancy rates link with PCL-5 scores.
By utilizing the three identi ed brain states for the entire group and the state vector, estimated for each individual, which represents the state of the brain network at any given time point, we calculated three occupancy rates (OCRs) for each participant.The OCR of each state represents the proportion of time each participant spends in that state (see Method Section and Supplementary Fig. 1). Figure 3A shows the correlation between OCRs and PCL-5 scores at various time points.The associations were computed using General Linear Model (GLM) accounting for age, sex, years of education, scanning site, income, marital status, employment status, and percentile ADI, and the resulting t-statistics were transformed to correlation (r).A positive signi cant association was found between the OCR of state 1 and the PCL-5 scores at M3 (r = 0.192, β = 0.0039, SE = 0.0012, 95% CI: 0.0015 ~ 0.0062, p corrected = 0.021, N = 226 after excluding sample with missing scores, see Table 1).These results indicate that the participants with higher PTSD symptom severity spend more time in state 1, which is indicative of an intera-network brain state.
Sex modulates the relationship between OCRs and PCL-5 scores.
To examine the in uence of sex on the relationship between OCRs and PCL-5 scores, we conducted GLM analyses for males (N = 94) and females (N = 181), separately.In these analyses, we included age, years of education, scanning site, income, marital status, employment status, and ADI as covariates.The correlation results between OCRs and PCL-5 scores for females and males are presented in Fig. 3B and Fig. 3C, respectively.While no signi cant association was found between OCRs and PCL-5 scores in the male group, we did observe signi cant associations between the OCR of state 1 and state 3 with PCL-5 scores at WK2 and M3.Notably, only the association between OCR of state 3 and PCL-5 at WK2 remained signi cant after applying FDR correction (r=-0.244,β= -0.0030, SE = 0.0011, 95% CI: -0.0048~-0.0010,p corrected = 0.014, N = 181).We also observed a positive link between state 1 OCR and WK2 PCL-5 (r = To verify that the strong correlation in females is not due to their larger sample size compared to males, we tested the correlations between state 3 OCR and WK2 PCL-5 scores in both groups.Using Fisher's ztransformation and calculating standard errors, we found a signi cant difference in the correlations between females and males (|Z-test statistic| = 1.734, p = 0.041), suggesting that the relationship between OCRs and PCL-5 scores at WK2 differs signi cantly between sexes.

Both posttraumatic stress (PTS) and non-PTS group generate similar dFNC states
We categorized participants into posttraumatic stress or PTS (N = 124) and non-PTS (N = 151) groups based on their WK 2 PCL-5 scores, with a cutoff point of 31.Those scoring above 31 were classi ed as PTS, while those below were considered non-PTS 39 .We used the term PTS instead of PTSD because the classi cation was based on PCL-5 scores at the time of imaging (i.e., WK2), before an o cial PTSD diagnosis till WK8.We then examined state pattern differences between the two groups by performing separate k-means clustering analyses on their dFNC data.

Discussion
Our current research aimed to investigate the signi cance of temporal changes in brain connectivity, measured by dynamic functional network connectivity (dFNC), in indicating the presence and severity of PTSD symptoms.Additionally, we examined the in uence of sex-speci c differences on the predictive ability of these connectivity measures.Our results indicate that the amount of time spent in an internetwork brain state serves as a protective factor against PTSD, whereas time spent in an intera-network brain state is linked to a higher PTSD symptom severity.Furthermore, we observed that the negative association between the duration spent in an inter-network brain state and PCL-5 is more pronounced in the female group.
Dynamic FNC offers an enhanced predictive power compared to static FNC (sFNC), supplying an additional layer of information about the severity of symptoms in brain disorders over time, a level of detail not attainable by its static counterparts [40][41][42] .For instance, a recent study demonstrated that a classi cation model relying on dFNC features surpassed the performance of other classi cation models in patients diagnosed with multiple sclerosis 42 .In another study involving participants with PTSD, the temporal variability, as captured by dFNC, demonstrated a higher classi cation accuracy than the model obtained only by sFNC features 41 .Our study demonstrates that dFNC features associate not only with current traumatic stress symptoms, but predict future symptoms of PTSD and may reveal important sex differences.
In our study sample, comprising participants exposed to traumatic events, we analyzed dFNC and differentiated three distinct brain network states.Two out of the three states (i.e., state 2&3) exhibited a higher degree of integration in the sensory network, while state 1 demonstrated a more disconnected sensory network.State 3 manifested the strongest connectivity within the CCN, within the CBN, and between the CBN and the SCN.Moreover, we found that state 1 was characterized by intera-network connectivity, while the other two states exhibited inter-network connections with both strong negative and positive connectivity among brain networks.These observations collectively highlight that brain networks display substantial dynamism, a characteristic they maintain even without the presence of external stimuli as has been observed in other brain disorders [21][22][23][24][25]29,40 . Additonally, we investigated whether the dynamics of brain networks in participants with PTS differed from those in the non-PTS group.Upon separately analyzing data from both groups of participants, we observed that each group generated similar dFNC states, as expected and observed in other disorders 43 .This suggests that the dynamic nature of brain networks persists irrespective of PTS, highlighting the potential complexities and resilience of the brain's network dynamics in the face of trauma and related disorders.
A prior study, employing the same population as the current research, demonstrated that the static functional connectivity between the left dorsolateral prefrontal cortex (DLPFC) and the arousal network (AN), as well as between the right inferior temporal gyrus (ITG) and the default mode network (DMN), could predict both WK2 and M3 PCL-5 scores 20 .In the current study, we found that the whole-brain OCRs estimated from dFNC predict the PCL-5 at the time of neuroimaging data collection (referred to as WK2), as well as the PCL-5 scores 10 weeks post-data collection (referred to as month 3 or M3).Our new analyses contribute to a deeper understanding of the neurobiological mechanisms underlying PTSD by looking at brain network dynamics.
Speci cally, we found that participants with higher PCL-5 scores tend to spend more time in an interanetwork brain state, referred to as state 1.Importantly, the amount of time spent in this state was found to predict future symptom severity at M3 (Fig. 3A).State 1 is characterized by reduced connectivity among sensory networks, including visual, auditory, and sensory motor networks.Furthermore, our results con rmed that spending more time in an inter-network brain state (state 3) is negatively correlated with PCL-5 scores at WK2 and M3 (Fig. 3A).State 3 is characterized by increased connectivity among sensory networks, suggesting enhanced information exchange and integration between these networks.Previous studies have consistently reported impairments in visual processing, as well as auditory processing, in individuals with PTSD 44,45 .Multiple neuroimaging studies have demonstrated alterations in the functioning of the visual, auditory, and motor cortex among participants with PTSD [45][46][47] .Notably, abnormal activation in the visual cortex during picture viewing tasks has been observed in these individuals 45 .Furthermore, signi cant alterations in visual processing have been identi ed within the ventral visual stream, which is responsible for processing object properties 45 .This suggests that PTSD affects the speci c components of the visual system involved in object recognition and perception, as previous ndings highlight a role for structural integrity of the ventral visual stream in the development of PTSD 48,49 .Our current ndings, in conjunction with previous reports of subtle de cits in sensory networks, particularly the visual sensory system in PTSD, provide compelling evidence that disruptions in information integration among sensory networks are closely linked to the severity of PTSD symptoms 48- 51 .Enhancing the connectivity and integration within these networks could potentially serve as a therapeutic target for mitigating symptom severity and improving outcomes in individuals with PTSD 52 .
In addition to the sensory networks, our ndings reveal that state 1 is characterized by relatively lower within-CBN connectivity and between CBN and SCN connectivity (i.e., CBN/SCN) compared to the other two states.This observation aligns with previous structural neuroimaging studies that have reported reduced cerebellar volumes in individuals with PTSD 53,54 .Furthermore, functional neuroimaging studies have provided corresponding evidence by demonstrating alterations in neural activity and functional connectivity of the cerebellum in PTSD 55 .Our new nding, that participants with higher PCL-5 scores preferentially spent more time in the state characterized by lower CBN, adds another layer of information to the understanding of temporal network patterns associated with CBN in PTSD.This suggests that alterations in cerebellar connectivity patterns may play a role in modulating symptom severity and could serve as potential markers for the disorder.
In the subsequent analysis, we investigated the in uence of sex on the relationship between brain network dynamics and symptom severity.We observed that the association between OCRs, and PCL-5 scores was more prominent in females.Speci cally, the correlation between state 3 OCR and WK2 PCL-5 was statistically signi cant within the female group, and the strength of this correlation was notably higher among females compared to males (Fig. 3B and C).It is worth noting that previous studies have extensively explored the role of sex in the development of PTSD, with emerging evidence suggesting differences in symptomatology and underlying neurobiology between males and females 33,[56][57][58][59][60] .In line with these ndings, our results further support the notion that the identi ed dFNC biomarkers, particularly when correlating with symptom severity, are stronger in females; this could potentially re ect the higher prevalence of PTS/PTSD in this demographic.
Recent large-scale genomic studies show that women of European and African ancestry may have higher heritability for PTSD than men, suggesting that genetic factors may also play a signi cant role in the disorder's development, particularly in interaction with sex differences 61,62 .However, it's important to note that biological sex is not the primary determinant of the various neurophenotypes associated with adverse post-traumatic outcomes; other factors such as low socioeconomic status also play a signi cant role 34,35 .To avoid a narrow focus on sex alone, our analysis took into consideration all available socioeconomic and demographic factors from the dataset.This approach allowed us to conduct a comprehensive analysis of the connection between OCRs and PTSD symptom severity, speci cally considering the sex effect.Additionally, women's risk for PTSD is partially determined by the fact that they experience sexual traumas more frequently.For example, a study shows that women exhibit almost twice the PTSD symptoms in sexual assault survivors 63 .However, in the AURORA dataset, the type of trauma does not play a major role in driving sex differences.The traumas are primarily motor vehicle collisions (MVCs) for both women and men, yet sex differences in dFNC link with PTSD sympthom severity are still observed.
Several limitations should be acknowledged while interpreting the present ndings.The overall sample size was relatively modest, and the sample sizes amongst the comparison groups (male vs. female) were not the same.Furthermore, participants who completed all scans and had more complete datasets may differ from those who did not complete all scans, making it unclear if the results apply to dropouts who may be at higher risk for PTSD after trauma.In this study, we examined dFNC in individuals with PTS and a non-PTS group, both of whom were exposed to trauma.To gain a comprehensive understanding, further research is required to directly compare the dFNC features among the PTSD group, a group of healthy individuals exposed to a traumatic event, and a group of healthy individuals who have not undergone any traumatic experiences.However, we assume that healthy individuals exposed to trauma could serve as a more suitable control group for those with PTSD, facilitating our understanding of the underlying neural processes of PTSD.Additionally, in this study, we investigated the relationship between dFNC features and the severity of PTSD symptoms at various time points.However, to enhance our understanding, future research should compare dFNC features among groups exhibiting different PTSD trajectories during a one-year assessment.In our study, we utilized the initial neuroimaging data available from the AURORA study, which was collected two weeks post-trauma, before any PTSD diagnosis at week 8.Given that the AURORA study also gathered neuroimaging data at six months post-trauma, future research would bene t from examining the dFNC patterns using the resting-state fMRI data from this later time point.Such analysis could yield more profound insights into the evolving brain dynamics associated with PTSD.

Conclusions
In summary, our investigation into the dFNC of civilians recently exposed to trauma revealed distinct patterns in brain network dynamics.Our ndings indicate that the duration participants spent in certain brain network states can forecast both their current and subsequent PCL-5 scores.Speci cally, we identi ed that spending time in an intra-network brain state is associated with higher PCL-5 scores, while engagement in an inter-network brain state correlates with lower PCL-5 scores.Furthermore, our analysis highlighted the role of multiple brain networks encompassing the visual, auditory, sensory-motor, and cerebellar networks, in PTSD.We also observed a stronger association between brain dynamics and PCL-5 scores in females compared to the male group.By incorporating sex-speci c disparities, tailoring interventions and treatment strategies accordingly, we can potentially develop more effective and personalized approaches for PTSD.

Study population
The participants in this study are from the Advancing Understanding of Recovery after Trauma project (AURORA) (Freeze 4.0 dataset).AURORA is a multisite longitudinal study in which participants are enrolled within 72 hours of trauma exposure 38 .In this study, the participants who experienced incidents like a car accident, a high fall (> 10 feet), a physical assault, sexual violence, or mass casualty incident were considered to have experienced trauma.The inclusion criteria include: 1) aged between 18 and 65 years old, 2) being alert and oriented at the Emergency Department (ED), 3) having the ability to speak and write English uently, 4) having no cognitive impairment, 5) having the ability to use the smartphone for > 1-year post-enrollment.Exclusion criteria included solid organ damage, severe bleeding, a requirement for a chest tube, and the likelihood of being admitted for longer than 72 hours.A subset of participants underwent MRI either in the morning or the afternoon of the study visit, which occurred approximately two weeks after the traumatic event (i.e., WK2).After preprocessing and quality check, N = 275 participants' data were used in our study.

Clinical measures
The PTSD Checklist for DSM-5 (PCL-5) was administered to assess PTSD symptoms at multiple time points, including pre-trauma (PRE), week 2 (WK2), week 8 (WK8), month 3 (M3), month 6 (M6), and month 12 (M12), as depicted in Fig. 1A.It is important to emphasize that different time frames were considered for each of the time points: the 2-week (WK2) assessment re ected symptoms experienced over the past two weeks, while assessments from week 8 (WK8) onwards considered symptoms over the past 30 days.
This longitudinal assessment allows for a comprehensive understanding of the participants' PTSD symptomatology throughout the study duration.Table 1 summarizes the demographic and clinical characteristics of the participants included in this study.Additionally, to distinguish individuals with posttraumatic stress (PTS) from those without PTS in WK2 of the study, we employ a threshold for the PCL-5 at 31.Participants with a PCL-5 score greater than 31 are classi ed as having PTS, while those with a score less than 31 are considered non-PTS 39 .It is important to note that we refer to this group as having PTS and not PTSD, as the PTSD diagnosis was made in W8, while we used the WK2 PCL-5 scores to identify these two groups.

Imaging acquisition protocol
Participants a thorough screening process before undergoing scanning, which involved checking for any contraindications to magnetic resonance imaging (MRI) or other exclusion criteria.For female participants and those who could potentially be pregnant, a pregnancy test was administered prior to entering the MRI environment.MRI scans were conducted using 3T Siemens scanners at each site.While the scan sequences remained largely consistent across imaging sites, some variations in sequence parameters were present due to differences in hardware.The imaging protocol for each site is outlined in Supplementary Table 1.The resting-state imaging procedure lasted approximately 9 minutes, during which participants were instructed to keep their eyes open.They were asked to focus on the white cross displayed at the center of the screen and maintain a state of stillness throughout the imaging session 20 .

Preprocessing
We corrected the differences in image acquisition times between slices using the statistical parametric mapping (SPM12 @ https://www.l.ion.ucl.ac.uk/spm/) default slice timing routines.The slice acquired in the middle of the sequence was chosen as the reference slice.The subject's head movement was then corrected using a rigid body, and 3-dimensional brain translations and 3-dimensional rotations were estimated.Next, the imaging data were resampled to 3 × 3 × 3 mm 3 .and spatially normalized to the Montreal Neurological Institute (MNI) space using the echo-planar imaging (EPI) template and the SPM toolbox's default bounding box.The fMRI images were then smoothed using a Gaussian kernel with a full width at half maximum (FWHM) of 6 mm (Step1 in Fig. 1B).It should be emphasized that while participants in this study have also been featured in other AURORA analyses and resting-state studies 20,64 , the current analyses are distinct.Additionally, the preprocessing approach diverges from the standard protocols commonly employed in AURORA research in order to align with methodologies used in our other work.A similar preprocessing approach has been employed in several of our previous studies [23][24][25]43,65 .
Extracting independent components using Neuromark We applied a hybrid Neuromark framework to extract the meaningful networks for each subject.The Neuromark framework is based on the Neuromark template derived from two large datasets including the human connectome project (HCP: https://www.humanconnectome.org/study/hcp-youngadult/document/1200-subjects-data-release,823 subjects after the subject selection) and genomics superstruct project (GSP: https://dataverse.harvard.edu/dataverse/GSP,1005 subjects after the subject selection).This framework has been successfully implemented to many studies with a wide range of brain imaging markers identi ed across different brain diseases [23][24][25]43,65 . Detais of the construction of the templates can be found in our previous Neuromark paper 66 .
The Neuromark template consists 53 independent components (ICs), which were grouped into seven functional networks based on anatomic and functional prior knowledge (Fig. 1C).These networks included subcortical network (SCN), auditory network (ADN), sensorimotor network (SMN), visual network (VSN), cognitive control network (CCN), default-mode network (DMN), and cerebellar network (CBN) (Step2 in Fig. 1B) 67 .All 53 ICs and their coordination are shown in Supplementary Table 2.We used these priors (i.e., the Neuromark_fMRI_1.0 template, available in GIFT @ http://trendscenter.org/software/gift and on the TReNDS website @ http://trendscenter.org/data) to run a fully automated ICA analysis in GIFT 68 .We further: 1) detrended linear, quadratic, and cubic trends, 2) conducted multiple regression on the six realignment parameters and their temporal derivatives, 3) despiked detected outliers, and 4) applied a low-pass lter (cut-off frequency at 0.15Hz) to remove noise and artifacts.

Dynamic and static functional network
The dFNC of the whole brain was estimated via a sliding window approach, as shown in Fig. 2B (Step 3).We used a tapered window obtained by convolving a rectangle (window size = 20 TRs = 47.2 s) with a Gaussian (σ = 3) to localize the dataset at each time point.Prior research revealed that a window size between 30 and 60 s is a suitable option for capturing dFNC variation 69 .Thus, we assumed that a window size of 47.2 s is a reasonable choice.Next, within each window, we calculated the Pearson correlation between any pairs of ICs.We then concatenated the dFNCs of each participant to form a (C × C × T) array (where C = 53 denotes the number of ICs and T = 210), which represented the changes in brain connectivity between ICs as a function of time 67 .

Dynamic functional network connectivity clustering
We next concatenated the dFNC of all subjects, as shown in Step 4 of Fig. 1B, and applied the k-means clustering algorithm to the dFNC windows to partition the data into sets of distinct clusters representing transient connectivity "states" 70,71 .The optimal number of cluster order was estimated using the elbow criterion based on the ratio of within to between cluster distances.By sweeping the k-value from 2 to 9, we found that the optimal number of clusters was 3 24 .We used Euclidian distance as a distance metric in this k-means clustering algorithm with 1000 iterations (Step 4 in Fig. 1B).The k-means clustering analysis yielded three distinct states across all 275 participants and a state vector for each individual.

Figure 1 Data
Figure 1

Figure 2 Three
Figure 2

Figure 3 Dynamic
Figure 3

Table 1
demonstrates a notable similarity in brain states between the PTS and non-PTS groups, as anticipated.We quanti ed the similarity by calculating the Pearson correlation coe cient between corresponding states' FNC.The correlations between state 1 of the non-PTS group and state 1 of the PTS group, state 2 of the non-PTS group and state 2 of the PTS group, and state 3 of the non-PTS group and Additionally, our ndings that individuals with PTS tend to spend more time in state 1 compared to those without PTS corroborate our main nding that have established a connection between the heightened OCR of this state and PCL-5, hinting at the potential clinical relevance of this brain state in PTS.
zero in MATLAB, indicates a very small value, suggesting strong statistical signi cance and reinforcing the robustness of our ndings.Comparing the OCR of states in the non-PTS and PTS groups, we found a consistent pattern: state 1 consistently showed the highest OCR, while state 2 exhibited the lowest OCR in both groups (Fig.4C and 4D).These results suggest a consistent OCR pattern across states in both groups, indicating a high degree of similarity in identi ed brain states between the non-PTS and PTS groups.