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.
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)
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.
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)
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.
![](data:image/png;base64,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)
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)).
![](data:image/png;base64,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)
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.