Brain functional network after intervention with rTMS in OCD individuals is pushed to a more unstable state to decrease obsessive behaviors

doi:10.21203/rs.3.rs-4196746/v1

Repetitive Transcranial Magnetic Stimulation (rTMS) is an FDA-approved treatment for Obsessive-Compulsive Disorder (OCD). Nevertheless, understanding a global mechanism of the changes in the brain functional network could lead us to optimize the effectiveness of this method. Therefore, reorganization of the brain functional network after intervention with rTMS was investigated in this study based on the structural balance theory. We hypothesized that functional plasticity after the intervention is imposed on the brain functional network by changes in the topology of triadic associations in the network and leading the network to a higher balance energy level (less stable). Consequently, brain functional networks of OCDs were calculated based on the phase lag indexes of their resting state EEGs before and after intervention in a frequency specific manner. Subsequently, global network parameters including number of positive and negative links, types of triadic interactions (balanced or unbalanced triads), tendency of negative/positive links to make hub, and balance energy level were compared between pre and post-intervention. Our findings revealed a significant decrease in weak-balanced and an increase in strong-unbalanced triads, particularly in the Beta І frequency band. In addition, significant decrease was observed in tendency of negative links to make hubs across certain frequency bands. These changes after intervention increase the network balanced energy level toward a less stable state. We hope these findings pave the way for refining the strategy of rTMS interventions by reorganizing the brain functional network.

Obsessive-Compulsive Disorder (OCD) is widely acknowledged as a profoundly debilitating psychiatric condition. It is characterized by two main criteria: obsessions and compulsions. Obsessions involve distressing and extreme thoughts that induce anxiety. This leads individuals to engage in repetitive behaviors (compulsions) as a means of alleviating this anxiety¹. The lifetime prevalence of OCD in the general population has been estimated to be around 2–3%, with an equal distribution between genders².

Individuals with OCD face challenges that extend beyond behavioral aspects. These challenges encompass cognitive functions, which are intricately connected to observable structural and functional alterations in the brain^3,4. Anatomical maps reveal changes in specific regions of the frontostriatal system and its interconnected distant areas⁵. These alterations, along with dysfunctions in cortico-striatal circuits, including the orbitofrontal cortex (OFC)⁶, default-mode network (DMN)⁷, and frontal-parietal areas⁸ are associated with the clinical and cognitive profile observed in OCD individuals.

Existing treatments have not fully addressed the challenges encountered by individuals with OCD⁹. As a result, transcranial magnetic stimulation (TMS) has gained attention as an alternative intervention in recent years¹⁰. In the realm of TMS utilization, there are diverse needs for refining protocols to achieve enhanced effects¹¹. Therefore, gaining a deeper understanding of the mechanisms driving changes induced by TMS in OCD individuals is crucial. This understanding encompasses alterations in brain functions. It holds the potential to significantly improve our ability to address these requirements.

In this regard, despite commendable efforts involving diverse neuroimaging techniques, the utilization of EEG remains restricted. Consequently, a notable gap persists in our understanding. This gap gains more significance given the potential insights this technique could offer regarding changes in neural oscillations¹². The undeniable importance of neural oscillations in diverse cognitive tasks is noteworthy, particularly in OCD. For instance, abnormal alpha-beta oscillations impede cognitive flexibility, a crucial aspect for individuals with OCD¹³. Furthermore, it has been suggested that slow rhythms signify the suppression of thalamocortical loops in action selection. Consequently, abnormalities in low-frequency activity may denote the pathological (repetitive) nature of action selection characteristic of OCD^14,15.

The potential insights gained from EEG analysis of OCD individuals undergoing repetitive TMS (rTMS) intervention extend to exploring modifications in neural networks. However, the application of these analyses in this context has been limited. This perspective aligns with the recent emphasis on viewing the brain as a cohesive unit, where the extent of brain damage is considered more crucial than its specific location¹⁶. Consequently, employing certain theories can significantly propel advancements in this area. Graph theory-based techniques are among such theories, offering both advantages and drawbacks. This approach is adept at identifying changes in brain pathologies. It delivers both local and global characterizations of brain connections. Consequently, it offers valuable insights into intricate brain networks¹⁷.

However, there are specific challenges that Graph Theory may not effectively tackle. This leaves a noticeable gap in the current literature. For instance, the interaction between two regions and their influence on each other can be affected by a third region with which both have interactions. To illustrate, if we designate x, y, and z as distinct regions, examining the interaction between x and y necessitates accounting for the effects of xz and yz interactions on its weight and sign. This phenomenon, identified as triadic interactions, can be explored through the long-term Structural Balance Theory (SBT).

Applying this theory across diverse domains has occurred over the past two decades. It spans from politics to biological and social networks¹⁸. In fact, identifying specific patterns not only enhances the likelihood of structural balance being a prevalent occurrence in signed networks but also justifies the crucial role of triadic interactions in the stability of these networks¹⁹. Moreover, the application of this theory contributes to a deeper understanding of how the inclination to minimize overall stress influences the organization of signed networks. It achieves this by delineating four types of triads, each varying in the level of energy and balance. These types consist of strongly balanced T3: (+++), weakly balanced T1: (+−−), strongly unbalanced (frustrated) T2: (++−), and weakly unbalanced (frustrated) T0: (−−−). These symbols, "+" and "−", denote the sign of functional connectivity values between regions.

While a limited number of studies exist, this approach has revealed that individuals with Autism Spectrum Disorder (ASD) exhibit lower balance energy compared to typical pairs. This finding is possibly linked to challenges in demonstrating flexible behavior²⁰. Furthermore, Saberi and colleagues (2021)²¹ introduced a global measure named 'tendency to make hub.' This measure emphasizes the significance of the arrangement of negative links in the balance (stability) of the resting-state brain network. Following in their footsteps, other researchers¹² aimed to investigate how the arrangement of positive and negative links influences the stability of the brain's functional network in individuals with OCD compared to healthy controls. Their findings suggest that a decreased number of unbalanced triads and an increased number of strongly balanced triads contribute to reduced balance energy. This indicates a more stable state within the brain's functional network. Consequently, they hypothesized that brain stimulation interventions, such as TMS, should exert their effects by injecting energy into the brain through alterations in triads. Such a process could enhance the plasticity of the OCD brain, thus facilitating a change in its state. Ultimately, it may lead to disrupting the looping thoughts that are repeated extensively in the brains of individuals with OCD. However, this assertion has not undergone scrutiny until now. To address this gap, we conducted an investigation employing an analysis of triadic interactions utilizing the SBT. Our focus was on comparing the stability and triadic structures of signed weighted networks in both post and pre-intervention conditions. Furthermore, we conducted a comprehensive global-scale analysis of hubness for the networks in both conditions. The aim was to discern topological distinctions between the signed weighted networks associated with these two conditions.

We hypothesized that the strong unbalanced state is more prone to exhibit a significant increase, thereby contributing to an elevated total energy post-intervention. This phenomenon, building upon the findings of Saberi et al. (2021)²¹, is potentially linked to a diminished inclination towards making negative or positive hubs. Consequently, this manifests as a reduction in balanced triads and a simultaneous rise in unbalanced triads.

2.1. Behavioral results

Results from the Wilcoxon Signed Rank Test for nonparametric data showed a significant impact of the intervention on both Y-BOCS scores (p = 0.0009, Standardized Test Statistic = 3.30064) and the obsessive subscale (p = 0.0014, Standardized Test Statistic = 3.18466). Similarly, a significant reduction in participants' compulsive symptoms post-intervention was observed, as indicated by the parametric Paired-Samples T-test (p = 0.0134, t = -2.8573) (Refer to Table 1).

2.2. EEG data results

The comparisons between post and pre-conditions, conducted for each of the nine frequency bands separately, revealed significant differences in the Beta І frequency band for both |T1| and |T2|. However, an examination of the results for |T1| (p =0.0470, t-value =-2.1945, Cohen’s d =-0.5865) and |T2| (p =0.0264, t-value =2.5036, Cohen’s d =0.6691) indicates a lack of conformity in their patterns of increase or decrease. A significant difference in Beta frequency bands was also evident in the total network energy (Un), with a notable increase in Beta ІІІ (p =0.0315, t-value =2.4104, Cohen’s d =0.6442).

Despite the absence of statistically significant differences between post and pre-conditions in positive (P) and negative (N) links across all frequency bands, a consistent pattern emerged, revealing an increase in positive links and a decrease in negative links observed in almost all frequency bands. Notably, in Beta І, the effect size for both positive (Cohen’s d (P) =0.5686) and negative (Cohen’s d (N) =-0.5686) links surpassed that of other frequency bands, falling within the medium range. Nevertheless, the statistical significance in link topology became apparent through noticeable variations in the Alpha ІІ and Beta І frequency bands, indicating a global tendency in the network to make negative hubs (TMH_n). This observation is supported by the results for Alpha ІІ (p =0.0469, t-value =-2.1954, Cohen’s d =-0.5867) and Beta І (p =0.0309, t-value =-2.4199, Cohen’s d =-0.6467) (Table 2 displays the acquired results for each measure, while Figure 1 provides a visual representation for enhanced comprehension).

Table 2. The paired t-test results compare post- vs. pre-measures employed for each of the nine measures, including the count of negative/positive links (|N|/|P|), the total energy of triads (Un), the tendency to form hubs with negative/positive links (TMH_n/TMH_p), and the number of triads (|Ti|).popoood

		Delta	Theta	Alpha І	Alpha ІІ	Beta І	Beta ІІ	Beta ІІІ	Beta IV	Gamma
	p-value	0.1556	0.6591	0.3865	0.1528	0.0531	0.3141	0.1039	0.2032	0.9504
	t-value	-1.5074	-0.4515	0.8962	-1.5185	-2.1276	-1.0471	-1.7487	-1.3399	-0.0634
	p-value	0.1556	0.6591	0.3865	0.1528	0.0531	0.3141	0.1039	0.2032	0.9504
	t-value	1.5074	0.4515	-0.8962	1.5185	2.1276	1.0471	1.7487	1.3399	0.0634
	p-value	0.2427	0.8385	0.4215	0.2254	0.1777	0.2393	0.3363	0.1761	0.2871
	t-value	-1.2238	0.2079	0.8300	-1.2726	-1.4251	-1.2333	-0.9984	-1.4309	-1.1100
	p-value	0.1679	0.7724	0.5019	0.1584	0.0470	0.2820	0.0598	0.5396	0.7362
	t-value	-1.4605	-0.2954	0.6907	-1.4964	-2.1945	-1.1223	-2.0616	-0.6299	0.3443
	p-value	0.5159	0.6314	0.3301	0.1427	0.0264	0.1265	0.1721	0.6485	0.7256
	t-value	0.6679	-0.4913	-1.0118	1.5603	2.5036	1.6329	1.4450	-0.4666	-0.3586
	p-value	0.1680	0.4408	0.5349	0.1963	0.1298	0.5860	0.2476	0.1838	0.9460
	t-value	1.4601	0.7952	-0.6374	1.3621	1.6173	0.5584	1.2105	1.4039	0.0691
	p-value	0.8635	0.2145	0.2160	0.1595	0.0813	0.5040	0.0315	0.7802	0.7477
	t-value	0.1753	-1.3051	-1.3004	1.4924	1.8896	0.6872	2.4104	-0.2850	-0.3285
TMH_n	p-value	0.1295	0.7966	0.3196	0.0469	0.0309	0.1925	0.0681	0.0873	0.9383
TMH_n	t-value	-1.6190	0.2631	1.0349	-2.1954	-2.4199	-1.3746	-1.9896	-1.8494	0.0789
TMH_p	p-value	0.5732	0.0821	0.4154	0.7105	0.6342	0.6597	0.1742	0.9203	0.5904
TMH_p	t-value	0.5779	1.8839	0.8413	-0.3794	-0.4872	0.4506	-1.4375	0.1020	0.5518

P-value < 0.05

In brief, we examined changes in weighted signed networks and explored topological alterations following rTMS intervention in individuals with OCD. In other words, we explored Heider's balance theory to elucidate how rTMS intervention influences the stability state of the brain functional network in OCD individuals. In this context, our objective was to investigate the pattern of changes in hub interactions, forming triads, following the intervention. Due to the scarcity of research on the influence of rTMS on neural networks in OCDs and an identified gap in the network neuroscience literature, as emphasized by Ciotti and colleagues (2015)²². In this analysis, we extracted positive and negative subnetworks, exploring each in/dependently. Our study, as far as we know, presents the initial empirical evidence for applying balance theory utilizing EEG to investigate the effects of rTMS intervention.

The comparison of post and pre-conditions revealed a significant decrease and increase in weak-balanced and strong-unbalanced triads, respectively, particularly within the Beta І frequency band. Additionally, this significance within the beta bands manifested in Beta ІІІ, with a notable increase in the total energy of triads post-intervention. However, from a topological standpoint, the intervention's effects were significantly evident only in a decrease in the tendency to make negative hubs in both Alpha ІІ and Beta І bands. Since Beta I also reflects the observed changes after various interventions^23-25, these findings strengthen the possibility of considering Beta frequency as an important potential indicator. The bursts of low beta activity are considered a key element in the dynamics of frontal task-related brain activity^23,²⁶. This activity contributes to cortical excitability and attention disturbances²⁷. Additionally, excessive Beta I activity has been associated with intrusive thoughts, distinguishing between individuals who engage in rumination and those who do not²⁸. Concurrently, abnormal alpha synchrony has been suggested as a contributing factor to the diminished energy levels in the OCD network. Ultimately, this results in a more stable state for individuals with OCD¹². While the evolving pattern generally aligns with previous research²¹^,²⁹, consensus remains elusive on some specifics. In line with the findings presented by some other previous works¹², an anticipated increase in after intervention was expected. This observed disparity, especially concerning frequencies associated with beta bands, is not a recent concern. While certain studies have documented increased beta activity linked to OCD³⁰, others have presented an opposing viewpoint³¹. A portion of this inconsistency may be attributed to variations among OCD subgroups. Not all OCDs manifest the same brain activity patterns. For instance, research indicates that OCD subgroups, distinguished by differences in cognitive task performance, such as the Trail-Making Test, display distinct oscillation patterns³².

Furthermore, individuals with OCD exhibit heightened levels of obsessions, leading to increased power in Beta I. Interestingly, this characteristic is not observed in subgroups with higher scores in compulsions. Such variation is associated with differences in mental activity between these two subgroups³³.

Given the significant change values observed in the and triads, it seems that the network post-intervention follows a pattern of transitioning from to and ultimately converting to (Figure 2 illustrates this pattern of change).

Given that the observed pattern shows a reduction in balanced triads and, conversely, an increase in strong unbalanced ones after intervention, we can infer from previous works that the network has changed toward having higher total energy levels²¹. In other words, the intervention has acted as a factor for conveying external energy, consequently changing the stability state of the network toward a less stable state¹². These discussions align with our other findings, which revealed an increase in energy levels post-intervention across most frequency bands.

It seems that the stable state, characterized by lower energy levels, serves as the groundwork for the expression of obsessive and compulsive traits in OCD individuals. This, consequently, impedes state changes in the OCD brain, resulting in a reduction in neuroplasticity. From this standpoint, it can be posited that the synchronization among diverse brain regions in individuals with OCD might underlie the persistence of the observed symptoms¹². Indeed, OCD not only results in heightened functional differentiation within neural networks but also disrupts the flexibility of connections among different brain regions. In this regard, isolated networks have been identified as a neural marker for OCD and a focus for innovative interventions³⁴. This rigidity mirrors the inability to change thought patterns related to obsessive symptoms³⁵, thereby contributing to anxiety as one of the characteristic features of OCD³⁶.

In this context, as outlined by Saberi et al. (2021)²¹, Figure 3 schematically elucidates how our observed pattern explains the process of transitioning the signed network into a less stable state.

Alternatively, from another perspective, it appears that even a single session of rTMS has the potential to enhance the metastability and intrinsic ignition of the brain. Consequently, this leads to increased overall brain activity²⁹^,³⁷. Intrinsic ignition quantifies the brain's dynamics, capturing its capacity to transition between stability states. This phenomenon is grounded in two connectivity tendencies: coupling, where regions form robust connections, and independence, where regions uphold distinctive activity patterns³⁸.

Simultaneously, metastability signifies the continuous evolution of functional connectivity patterns. Attaining maximal metastability indicates the brain's peak for network switching³⁹. Healthy neural dynamics occur within a metastable regime, fostering correlated cognitive performance, such as cognitive flexibility and information processing⁴⁰. These functions are impaired in individuals with OCD⁴¹. Derived from our results, it is plausible to assert that rTMS intervention plays a role in reducing OCD symptoms by enhancing metastability, flexibility, and total energy within the brain. This enhancement, in turn, seems to facilitate improvements in cognitive functions, particularly cognitive flexibility. However, substantiating this hypothesis necessitates further investigations in the future, with a specific focus on exploring alterations in both impaired cognitive functions and the dynamics of the brain in individuals with OCD following rTMS intervention. In this context, we think that directing rTMS interventions towards strategically designed approaches to reorganize OCD functional networks into a normalized form can enhance the effectiveness of these interventions.

Furthermore, the results obtained from the comparisons between the normal and pre-intervention groups, outlined in Supplementary Table S1 and depicted in Supplementary Fig. S1, indicate a significantly lower number of triads in the normal groups across five frequency bands. While a similar pattern was observed in the comparison between the normal and post-intervention groups, as indicated in Supplementary Table S2, the number of frequency bands in which we observed a significantly lower number of triads decreased to only two frequency bands (for a clearer visualization, see Supplementary Fig. S2). The same trend was observed in the number of triads. However, in these triads, only the Beta І frequency band did not exhibit a significant difference after intervention with the normal group. A similar finding was reported in a previous study¹², where the OCD group exhibited a lower number of triads compared to the control one, with significant differences observed in the Beta І frequency band.

Being the first study to explore topological changes following rTMS intervention using SBT and TMH concepts, our research lacks specific studies for direct comparison. Validating our findings necessitates additional studies with a larger number of subjects. In addition, we positioned our channels according to the 10–20 system to effectively encompass brain regions. However, the requirement to conduct our experiment in clinics equipped with EEG devices featuring 19 channels for patient accessibility imposed specific limitations. As a result, exploring the sensitivity of the topology findings in this study to the number of channels emerges as a compelling subject for future research.

4.1. Participants

Out of the initial group of 214 individuals diagnosed with OCD and meeting the specified criteria, who underwent rTMS intervention at the Neuroscience Clinic in Tehran, Iran from 2019 to 2022, only 45 individuals adhered to the assigned intervention with precise parameters. Following the steps illustrated in Figure 4, fourteen participants (7 females, 50.00%; mean age, 32.57 years; SD, 9.8270; range, 20-45) were selected for inclusion in this study. The diagnostic process involved a two-step approval process, with two licensed psychiatrists initially confirming their OCD diagnosis through a Structured Clinical Interview based on DSM-5 criteria. Following this, individuals with a score of 16 or higher on the Yale-Brown Obsessive-Compulsive Scale (Y-BOCS) were considered eligible. To ensure control over medication effects on the results, inclusion criteria also required maintaining a stable medication regimen for at least 6 weeks before and throughout the study. Exclusion criteria included a history of substance abuse, expressed concerns about undergoing rTMS intervention based on a safety screening questionnaire⁴², concurrent use of alternative treatments, documented instances of seizures, head trauma, brain surgery, intellectual disability, neurological disorders, or recent receipt of electroconvulsive therapy within the last month. Table 3 presents a concise overview of participant demographics and statistics.

4.2. Experimental procedure

The study conducted at a Neuroscience Clinic in Tehran, Iran, under the supervision of Shahid Beheshti University, adhered to the 1964 Helsinki Federation principles and received approval from the ethical review board (IR.SBU.REC.1401.028). After selecting participants based on inclusion and exclusion criteria, informed consent was obtained from all participants after fully explaining the procedure. Pre- and post-tests, including 19-channel EEG and Y-BOCS assessments, were conducted before and after the rTMS intervention. These steps are illustrated in Figure 5.

4.3. rTMS treatment parameters

Both a Magstim Rapid 2 rTMS device (Magstim, UK) and a 70-mm figure-of-8-shaped coil (air film coil) were utilized. The sessions commenced with determining the active motor threshold (AMT) through visual recognition, defined as the lowest TMS intensity eliciting a liminal motor-evoked response during maximum voluntary contraction of the abductor policies brevis muscle (APB). The TMS coil was positioned on the left and right DLPFC following the 10–20 EEG system. Each participant received a personalized white cap, marked at both target locations during the initial session. Sessions encompassed both targets, allocating approximately 20 minutes to the right DLPFC and 18:26 minutes to the left DLPFC, totaling around 40 minutes per session. The right DLPFC protocol incorporated a stimulation frequency of 1 Hz at 120% AMT, comprising 2 stimulation trains lasting 600 s each, with 60 s intervals between trains. This yielded a total of 1,200 pulses per session and 24,000 pulses throughout the entire intervention. The protocol has been modified to employ a frequency of 10 Hz for the left DLPFC at 120% AMT. This includes 75 stimulation trains, each lasting 4 seconds, with 11-second intervals between trains, totaling 3,000 pulses per session and 60,000 pulses overall⁴³.

4.4. Clinical assessments

4.4.1. Y-BOCS

The Y-BOCS served as a tool for evaluating OCD symptoms and assessing changes post-intervention, offering numerous advantages⁴⁴. Primarily, it quantifies the severity of obsessive-compulsive symptoms and comprehensively explores major obsessions and compulsions, thereby offering essential qualitative insights⁴⁵. This involves rating symptom severity from 0 to 4 for each of the 5 allocated items in both subscales. Its high sensitivity to treatment responses has established it as a frequently used semi-structured interview instrument⁴⁶. Additionally, its capability to screen individuals with OCD makes it a valuable choice for various research endeavors. Notably, the Y-BOCS has been translated into diverse languages, with a reported reliability of 0.98 and a Cronbach's Coefficient Alpha exceeding 0.7 for the Persian version⁴⁷.

4.4.2. EEG recording

EEG recordings were conducted using the Mitsar EEG system and EEG Studio software, in conjunction with a 19 Ag/AgCl ElectroCap. Participants were seated comfortably in a shielded room to minimize external noises. They were instructed to first close their eyes for approximately 4 minutes and then focus on a predetermined dot 1.5 meters away to capture their eye-open condition for the same time. Channels were arranged according to the 10–20 EEG system, with electrodes on FP1/FP2, F3/F4, C3/C4, P3/P4, O1/O2, F7/F8, T3/T4, T5/T6, Fz, Cz, Pz. Figure 6 precisely represents these arrangements⁴⁸. As depicted, the electrodes encompass the five widely recognized lobes of the brain. A1 and A2 electrodes served as references, maintaining electrode impedance below 5 kΩ, and a sampling frequency of 500 Hz was utilized.

4.5. EEG analysis

4.5.1. Preprocessing

Initially, meticulous selection was undertaken to identify segments of approximately one-minute EEG signals with minimal artifacts. Throughout the recording process, vigilant supervision was maintained to avoid bad channels and mitigate other disruptive factors, thereby ensuring the overall quality of the collected data. A bandpass filtering approach was implemented using a basic finite impulse response (FIR) filter, with low and high cutoff frequencies set at 0.5 Hz and 45 Hz, respectively. Subsequently, the independent component analysis (ICA) technique, complemented by visual inspection, was employed to eliminate artifacts such as eye blinks and eye movements. For comprehensive analysis, nine frequency bands were chosen: Delta (0.5–4 Hz), Theta (4–8 Hz), Alpha I (8–10 Hz), Alpha II (10–12 Hz), Beta I (12–15 Hz), Beta II (15–18 Hz), Beta III (18–25 Hz), Beta IV (25–30 Hz), and Gamma (30–40 Hz).

4.5.2. Functional connectivity calculation

Over recent years, there has been an increased focus on exploring functional connectivity (FC), necessitating the use of appropriate measures to assess the coupling among brain regions and aiming to analyze communication patterns among time series. To assess the topological impact of positive and negative links in the brain and triadic interactions, the FC matrix serves as a valuable tool. To fulfill this aim in the study, the FC matrix was applied individually to each of the six segments within one minute of preprocessed data for each subject, each spanning nine seconds. Subsequently, the six FC matrices were averaged to derive the ultimate FC matrix. The computation of the FC matrix involved a two-step process utilizing topographical profile similarity-based high-order FC (tHOFC) ⁴⁹. In the initial step, a representation of the low-order FC (LOFC) profile for each electrode was obtained by calculating the FC vector. This was achieved through computing the FC between every pair of electrodes. Subsequently, to gain a more comprehensive insight into the LOFC, tHOFC was computed to represent the similarity of LOFC profiles between every pair of electrodes⁵⁰. In other words, whereas LOFC concentrates on processing domain-specific information, tHOFC combines information from various domains based on the functional hierarchy⁴⁹.

The initial step involved considering the weighted phase lag index (wPLI), an extension of the PLI. This choice was made due to its advantages over other functional connectivity measures, including lower sensitivity to noise, capability to mitigate the impact of changes in the coherency phase⁵¹, and long-term test-retest reliability⁵². WPLI, as determined by equation (1)¹², quantifies phase synchronization between distinct brain regions. It specifically concentrates on the phase relationship in signals, incorporating the weighting of each phase discrepancy based on lag magnitude. By specifically considering phase differences around zero for calculation, wPLI minimizes the occurrence of identifying erroneous "false positive" connectivity in phase synchronization⁵².

In Equation (1), the absolute value is represented by |.|, the sign function is denoted as sgn, and the imaginary part is indicated by imag, with t representing the time index and n the total number of time points.

In the subsequent step, the utilization of Pearson correlation was implemented to derive the ultimate FC matrix. This step was essential to incorporate both negative and positive values for examining triadic interactions. Considering that Structural Balance Theory (SBT) has the capability to offer valuable insights into how the presence of a third electrode within a triadic structure can significantly impact the connection between two others²⁰. The practicality of conducting this examination was therefore facilitated by the application of SBT. Similar to certain previous studies¹²^,²⁰, this research also employs four types of triads within this framework to gain insights into the stability of a network in both pre-and post-conditions. Within this context, two types of balanced triads emerge strongly balanced T3 (+ + +) and weakly balanced T1 (+ − −). Conversely, two types of unbalanced triads are identified: strongly unbalanced T2 (+ + −) and weakly unbalanced T0 (− − −) (Figure 3). The symbols "−" and "+" denote asynchrony and phase synchrony, clarifying the sign of functional connectivity (FC) weights between the electrodes. Unbalanced triads inherently seek to transition towards a balanced state due to their instability. This inclination aligns with the minimum energy principle, as systems tend to minimize energy levels for increased stability⁵³. The concept of stability further clarifies disparities between weak and strong states in both balanced and unbalanced conditions. For instance, T2 is considered stronger than T0 because it is more unstable and exhibits a greater tendency to shift towards states with lower energy and heightened stability. Similarly, T3 is stronger and more balanced than T1, given its greater stability²¹. In this context, the balanced or stable state can be defined as the minimum energy level where there is no dynamic need to alter link signs owing to instability¹⁹^,²¹. As depicted in Figure 7, when interactions are unbalanced, the multiplication of their edges yields a negative value. Conversely, in interactions characterized as balanced, this product remains negative.

Considering the crucial role of energy levels in various disorders¹²^,²⁰, we explored the total energy of a network (Un)⁵⁴ to gain deeper insights into understanding the extent of network balance. In alignment with the Hamiltonian perspective on physical energy⁵⁵, the computation of Un involved determining the negative of triads' products and dividing the resulting sums by the total number of ternary interactions (equation (2)). The obtained outcomes form a spectrum ranging from -1 to +1, where each end of the spectrum signifies fully strong conditions, with -1 indicating complete strength in balance and +1 representing full strength in unbalanced as well. Consequently, the minimization of Un results in enhanced stability for the network.

Here, 'w' signifies the edge weight of triad Ti, and 'x,' 'y,' and 'z' refer to the electrodes within triad Ti. Lastly, 'N' represents the overall count of triads in the network.

In addition, the utilization of the global hubness metric²¹ allows for the comparison of brain networks under pre and post-conditions, as well as the comparison of each of these conditions with the normal group, in terms of network topology. Hubs, representing electrodes with a substantial number of connections, are particularly influential in weighted networks where these connections carry significant weights. Given their role as local features, hubs play a pivotal role in shaping the overall topology of the brain network (equation (3)).

The negative and positive degrees of the ith electrode are represented by Di,n and Di,p, while M signifies the complete number of electrodes. Furthermore, wij,n, and wij,p refer to the negative and positive weights connecting the ith electrode with the rest of the electrodes.

Alternatively, for evaluating the potential alterations in TMHs and |Ti|s between pre and post-conditions, as well as between OCD and normal groups, we further examined the occurrence rate or the number of links related to |P| as positive links and |N| as negative ones across all nine frequency bands. This approach was taken even when there are no variations in the quantity of positive and negative links. In this context, Figure. 4 summarizes the steps that have been taken in this regard. In this context, Figure 8 summarizes the steps taken for EEG analysis.

4.6. Statistical analysis

The results obtained from the EEG analysis section were compared between post- and pre-conditions for all nine selected frequency bands separately. Before proceeding, the normality of the obtained results, encompassing both behavioral and EEG data, was assessed using the Shapiro–Wilk test⁵⁶. As the results confirmed the normality of EEG data, the Paired-Samples T-Test was employed to explore differences between post- and pre-conditions. However, given that all behavioral data did not exhibit normality, a Wilcoxon Signed Rank Test was employed for nonparametric analyses. A significance level of p<0.05 (Fisher permutation) was applied to detect statistically significant variations across all analyses.

Acknowledgment

We would like to thank all the participants for their generous help in this study. We also would like to thank Ms. Rodja Tahamtan for her cooperation in data recording.

Author contributions

R.Kh conceptualized the project. R.Kh and M.A. designed the experiment. A.T. and M.A. contributed to data analysis. M.A. and R.Kh wrote the manuscript. R.Kh, R.R., and A.R. supervised the project. R.Kh, R.R., A.T., and A.R. edited the manuscript.

Data availability statement

The datasets and codes used during the current study are available from the corresponding author upon request.

Ethics declaration

The experiment of the present study has been conducted according to the 1964 Helsinki Federation and the ethical review board of the Institute for Cognitive Science Studies approved the ethics of the experiment with reference number IR.SBU.REC.1401.028.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary Information Additional details regarding the data from the normal group and the results obtained from comparing their data with OCDs can be found in the supplementary material.

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No competing interests reported.

SupplementaryMaterial.docx

Brain functional network after intervention with rTMS in OCD individuals is pushed to a more unstable state to decrease obsessive behaviors

Status:

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Abstract

Figures

Introduction

Results

2.1. Behavioral results

Discussion

Methods

Declarations

References

Additional Declarations

Supplementary Files

Status:

Version 1