Intrinsic functional architecture predicts remote motor cortical excitability changes induced by intermittent theta-burst stimulation

Summary

Repetitive transcranial magnetic stimulation (rTMS) modulates cortical excitability both locally and remotely through connected regions. However, how intrinsic functional architecture influences these remote effects remains unclear. Leveraging multi-site stimulation (targeting the left primary motor cortex [M1], dorsal premotor cortex, and caudal inferior parietal lobule) combined with resting-state functional magnetic resonance imaging, we investigate whether intrinsic functional architecture predicts rTMS-induced changes in contralateral M1 excitability. While group-level effects were absent, individual variability in excitability changes was significantly predicted by functional characteristics. When the engaged network of stimulated region is sensorimotor network, resting-state functional connectivity between the stimulated region and the right M1 significantly predicts excitability changes, moderated by within-network interactions. Otherwise, exploratory analysis found associations with network topological properties rather than direct coupling. These findings provide preliminary insights into rTMS neuromodulation and may inform future development of personalized treatments (e.g., for post-stroke motor rehabilitation), yet require further investigation in clinical populations.

Graphical abstract

Highlights

• •Intrinsic functional architecture predicts remote modulation effects of rTMS
• •Direct functional connectivity predicts remote effect of sensorimotor stimulation
• •Intra-network interactions of the sensorimotor network moderate the aforementioned prediction
• •Network interactions predict remote effect of non-sensorimotor stimulation

Neuroscience; Physiology; Systems neuroscience

Introduction

Repetitive transcranial magnetic stimulation (rTMS) is a non-invasive neuromodulation technique widely used in the treatment of neuropsychiatric disorders, including post-stroke motor recovery and major depressive disorder.¹ When applied to the motor cortex, rTMS can induce changes in cortical excitability that outlast the stimulation period, with aftereffects persisting for 30 min or longer.² Since motor-evoked potentials (MEPs) provide an objective and quantifiable measure of these changes, investigating rTMS-induced modulation of motor cortical excitability has been pivotal for both mechanistic understanding and clinical application.³ For example, studies have revealed a frequency-dependent pattern of rTMS effects: high-frequency rTMS (≥5 Hz) or intermittent theta burst stimulation (iTBS) typically increases motor cortex excitability,^4,5 while low-frequency rTMS (<5 Hz) or continuous theta burst stimulation (cTBS) typically decreases it.^5,6 These findings have advanced our understanding by suggesting that rTMS affects the brain through mechanisms analogous to long-term potentiation and long-term depression,⁷ thereby guiding clinical treatment protocols.¹

Beyond directly affecting the excitability of the motor cortex beneath the coil, changes in motor cortical excitability can also be induced by stimulating remotely connected regions, such as the contralateral motor cortex, dorsal premotor cortex (PMd), and posterior parietal cortex.⁸ Modulation of motor cortical excitability through connected regions also has important implications for rTMS protocols, particularly those aiming to promote motor recovery after stroke and other neurological conditions.^9,10,11 This modulation of remote regions is underpinned by inter-regional interactions within the brain. Consequently, variations in these inter-regional interactions may underlie the heterogeneous remote aftereffects of rTMS and give rise to the considerable inter-individual variability observed even in widely investigated protocols, such as those targeting the contralateral motor cortex.^{2,12,13,14,15,16}

The complex interactions between adjacent and noncontiguous brain areas depend on the brain’s intrinsic functional architecture.¹⁷ Specifically, the magnitude of immediate remote responses induced by single-pulse stimulation depends on the strength of resting-state functional connectivity (rsFC) between the stimulated region and remote regions.^18,19 Furthermore, beyond region-to-region rsFC, the topological architecture of functional brain networks has also been reported to influence remote responses.^20,21,22 Given that intrinsic functional architecture shapes immediate responses to single-pulse TMS, it may similarly influence the lasting effects induced by rTMS. However, it remains unclear whether individual intrinsic functional architecture contributes to the substantial variability observed in rTMS-induced changes in motor cortical excitability. Therefore, the present study aims to systematically investigate this question by integrating individual resting-state functional magnetic resonance imaging (rs-fMRI) with rTMS-induced remote effects assessed across multiple stimulation targets. As shown in Figure 1, we applied iTBS to the left primary motor cortex (M1), PMd, and the caudal part of the inferior parietal lobule (cIPL), and assessed the resulting changes in right M1 cortical excitability using MEPs. The selection of non-M1 targets was based on prior paired-pulse TMS evidence showing that conditioning stimulation of PMd and cIPL can modulate contralateral M1 excitability.⁸ Specifically, PMd was chosen as a non-M1 target because it is anatomically adjacent to M1, functionally highly associated with M1, and commonly used for modulating M1 cortical excitability.²³ In contrast, the cIPL was selected as a third target for its greater anatomical distance from M1 and functional separation, which is reflected in its primary engagement in higher order sensorimotor integration and attentional processes.²⁴ Crucially, it also produces physical discomfort comparable to that caused by M1 and PMd stimulation,²⁵ thereby minimizing the concern that differential subjective sensations might confound comparisons across targets. iTBS was selected due to its comparable effectiveness to conventional rTMS protocols within a shorter time frame,²⁶ and its growing prominence in clinical applications.²⁷ The results of this study may deepen our mechanistic understanding of how rTMS modulates motor cortical excitability via connected regions and could have implications for future research on network modulation.

Figure 1.

Experimental design and procedures

(A) Prior to TMS sessions, a T1-weighted structural image and rs-fMRI data were acquired for each participant to identify stimulation targets and assess individual intrinsic functional architecture. The representative T1 and rs-fMRI images shown on the left are from a single participant. In subsequent TMS sessions, iTBS was delivered to the left M1, PMd, and cIPL. MEPs were measured from the left first dorsal interosseous muscle.

(B) Timeline for each TMS session. MEPs were measured at baseline (pre), immediately after iTBS (post), and 30 min after iTBS (post-30).

Results

Responses to iTBS at all three stimulation targets

No adverse events or side effects were reported during or after the experimental procedures. The cortical stimulation targets for each participant are visualized in Figure 2A. The Shapiro-Wilk tests confirmed that the paired differences in area under the curve (AUC) were normally distributed for both the immediate post-iTBS effects (left M1: W = 0.923, p = 0.147; PMd: W = 0.902, p = 0.050; and cIPL: W = 0.926, p = 0.166) and the 30-min post-iTBS effects (left M1: W = 0.916, p = 0.129; PMd: W = 0.982, p = 0.962; and cIPL: W = 0.925, p = 0.140). Paired t tests revealed no significant iTBS-induced changes in AUC at the group level when stimulating any of the three targets, either immediately post-iTBS (left M1: t[17] = −0.028, p = 0.978; PMd: t[18] = 0.349, p = 0.731; and cIPL: t[17] = −0.778, p = 0.447; Figure 2B) or 30 min post-iTBS (left M1: t[16] = −0.578, p = 0.572; PMd: t[18] = 0.051, p = 0.960; and cIPL: t[18] = −1.523, p = 0.145; Figure 2C). The absence of significant group-level effects highlights the substantial inter-individual variability in response to iTBS. Further analysis revealed that AUC changes measured 30 min post-iTBS were positively correlated with changes measured immediately post-iTBS (Figure 2D) following stimulation of PMd (r = 0.72 and p < 0.001) and cIPL (r = 0.53 and p = 0.023). For M1 stimulation, a similar positive trend was observed, though it did not reach statistical significance (r = 0.32 and p = 0.213). These correlational analyses suggest that although the iTBS-induced changes exhibited substantial inter-individual variability, individual response profiles exhibited moderate relative temporal stability up to 30 min post-iTBS. Two-sample t tests showed no significant differences between M1 and PMd stimulation either immediately post-iTBS (t[35] = 0.113 and p = 0.911) or at 30 min (t[34] = 0.616 and p = 0.542). Similarly, M1 and cIPL stimulation produced comparable effects both immediately (t[34] = −0.411 and p = 0.684) and at 30 min (t[34] = −0.318 and p = 0.753). No significant effects of sex or age on AUC changes were observed (all p > 0.05).

Figure 2.

Inter-individual variability in iTBS-induced excitability changes

(A) Individual cortical targets for M1, PMd, and cIPL stimulation.

(B) AUC values derived from MEP input-output (I/O) curves at baseline (pre) and immediately post-iTBS (post).

(C) AUC values at baseline (pre) and 30 min post-iTBS (post-30). Individual data are shown as connected points.

(D) Correlations between iTBS-induced AUC changes measured at post and post-30.

Lines and shaded areas represent linear regression fits and 95% confidence intervals, respectively. Markers represent individual participant data (circles = M1; squares = PMd; and hexagons = cIPL). In (A)–(C), the top row represents M1 stimulation (n = 18 participants), the middle row represents PMd stimulation (n = 19 participants), and the bottom row represents cIPL stimulation (n = 18 participants).

rsFC predicts changes in contralateral motor cortical excitability induced by M1 iTBS

Given the substantial inter-individual variability in iTBS-induced effects, we investigated the E-field weighted rsFC, calculated by weighting the connectivity strength between the stimulated region and the contralateral M1 with the simulated electric field strength within the stimulated region.²⁸ The analysis revealed that E-field weighted rsFC between the stimulated region and right M1 significantly predicted AUC changes measured immediately post-iTBS when targeting the left M1 (β = −0.47, standard error [SE] = 0.21, and 95% credible interval [CrI] = [−0.87, −0.05]; Figure 3A; Table 1). Sensitivity analyses confirmed the robustness of this relationship across different electric field thresholds used to define the regions, and independent of whether electric field weighting was applied (Figure S2). After removing all covariates from the Bayesian model, the result remained significant (β = −0.51, SE = 0.20, and 95% CrI = [−0.89, −0.09]). In contrast to M1 stimulation, E-field weighted rsFC did not significantly predict AUC changes when iTBS was applied to either left PMd or cIPL (Figures 3B and 3C; Table 1). At 30 min post-iTBS, E-field weighted rsFC showed a similar negative predictive trend for AUC changes when targeting left M1 (Figure 3D), although this did not reach statistical significance (β = −0.36, SE = 0.22, and 95% CrI = [−0.78, 0.09]).

Figure 3.

Predictive relationship between rsFC and iTBS-induced changes in contralateral motor cortical excitability

(A–F) Predictive relationships are shown for (A–C) immediately after iTBS and for (D–F) 30 min after iTBS, targeting left M1 (A and D; n = 18 participants), PMd (B and E; n = 19 participants), and cIPL (C and F; n = 18 participants). Lines and shaded areas represent linear regression fits and 95% credible intervals (CrIs) after controlling for covariates. Dots represent individual participants’ raw data. This format applies to all subsequent covariate-adjusted regression figures.

Table 1.

Bayesian linear regression models predicting iTBS-induced changes in contralateral motor cortical excitability

Factors	Model estimates
	AUC changes (post/pre)			AUC changes (post-30/pre)
	β	SE	95% CrI	β	SE	95% CrI
Left M1 stimulation
E-field weighted rsFC	−0.47	0.21	[−0.87 −0.05]a	−0.36	0.22	[−0.78 0.09]
Baseline AUC	−0.11	0.21	[−0.52 0.32]	−0.04	0.24	[−0.52 0.44]
Caffeine use	−0.35	0.46	[−1.24 0.57]	−0.21	0.45	[−1.10 0.68]
Coil placement difference	0.09	0.20	[−0.31 0.49]	0.27	0.24	[−0.20 0.73]
Left PMd stimulation
E-field weighted rsFC	−0.19	0.23	[−0.64 0.27]	−0.09	0.22	[−0.51 0.34]
Baseline AUC	−0.32	0.21	[−0.72 0.11]	−0.23	0.23	[−0.68 0.23]
Caffeine use	−0.39	0.37	[−1.10 0.36]	−0.38	0.38	[−1.13 0.38]
Coil placement difference	0.33	0.23	[−0.14 0.77]	0.32	0.24	[−0.17 0.78]
Left cIPL stimulation
E-field weighted rsFC	−0.05	0.26	[−0.56 0.47]	0.13	0.24	[−0.34 0.59]
Baseline AUC	0.01	0.26	[−0.51 0.51]	−0.12	0.23	[−0.56 0.33]
Caffeine use	0.02	0.36	[−0.69 0.72]	−0.33	0.37	[−1.02 0.43]
Coil placement difference	0.17	0.26	[−0.34 0.68]	−0.01	0.23	[−0.47 0.44]

Abbreviations: β, standardized regression coefficient; SE, standard error; CrI, Bayesian 95% credible interval.

^aindicates that the 95% Bayesian credible interval excludes zero (Bayesian linear models).

Network-specific predictive power of rsFC for iTBS-induced changes in contralateral motor cortical excitability

To further investigate how the topological architecture of functional brain networks predicts iTBS-induced changes in contralateral motor cortical excitability, we identified individual-specific functional networks using the InfoMap community detection algorithm. For each stimulation, the “primary engaged network” was identified as the network showing the highest Spearman’s correlation with the whole-brain connectivity pattern of the stimulated region (Figure 4A). The primary engaged network was the sensorimotor network (SMN) for all M1 stimulations (n = 18 participants), which was also the primary engaged network of right M1. In contrast, PMd and cIPL stimulations exhibited heterogeneous network engagement due to inter-individual variability in brain anatomy and functional organization (Figure S3). Specifically, the primary engaged network for PMd stimulations was the SMN (n = 6 participants), frontoparietal network (FPN) (n = 7 participants), or default mode network (DMN) (n = 3 participants), while for cIPL stimulations it was the FPN (n = 7 participants) or DMN (n = 8 participants) (Figure 4B). To ensure robustness, we excluded six sessions where the primary engaged network assignment was unstable across adjacent electric field strength thresholds used to define the stimulated region (i.e., 90% and 99% of the maximum electric field strength).

Figure 4.

The predictive power of rsFC depends on the intrinsic functional network organization

(A) Representative example showing how the engaged network was identified for one participant. The upper heatmap shows the whole-brain rsFC matrix, and the lower heatmap shows the rsFC between the stimulated region and the whole brain.

(B) Primary engaged networks for each stimulation target (M1, PMd, and cIPL). Donut charts show the proportion of sites for which the primary engaged network was the SMN (blue), FPN (yellow), or DMN (red) (M1, n = 18; PMd, n = 16; cIPL, n = 15 sessions; six sessions with unstable primary-network assignment across adjacent E-field thresholds were excluded).

(C) Top: individualized cortical targets for iTBS stimulation color-coded by region (blue for M1, yellow for PMd, red for cIPL), grouped by the engaged network (SMN, FPN, or DMN). Bottom: relationship between E-field weighted rsFC and post-iTBS AUC changes. Symbols denote stimulation target: circles for M1, squares for PMd, and hexagons for cIPL. Sample sizes per network: SMN, n = 24 sessions; FPN, n = 14 sessions; DMN, n = 11 sessions.

Given the heterogeneity in network engagement, we examined whether the predictive power of rsFC depended on the identity of the engaged network. We categorized the data into SMN, FPN, and DMN groups based on the primary engaged network of each stimulation. We then tested whether rsFC predicted AUC changes measured immediately post-iTBS within each group (Figure 4C). Bayesian linear mixed model results revealed that, when pooling all SMN stimulations, E-field weighted rsFC significantly predicted iTBS-induced effects (β = −0.48, SE = 0.19, and 95% CrI = [−0.84, −0.09]). After removing all covariates from the Bayesian model, the result remained significant (β = −0.52, SE = 0.18, and 95% CrI = [−0.88, −0.15]). Conversely, for FPN or DMN stimulations, E-field weighted rsFC showed no significant predictive power. Furthermore, to assess potential general inter-network effects, pooling data from FPN and DMN stimulations also yielded non-significant results (β = −0.12, SE = 0.22, and 95% CrI = [−0.54, 0.32]). Across all analyses, no significant interaction was found between E-field weighted rsFC and either the stimulation target or the engaged network identity. Regarding AUC changes measured 30 min post-iTBS, E-field weighted rsFC showed a negative but non-significant predictive effect on changes induced by SMN stimulation (β = −0.30, SE = 0.21, and 95% CrI = [−0.70, 0.11]), and no predictive power for other networks (Table S1).

Topological properties of functional brain networks play a dual role in predicting motor cortical excitability changes

We further investigated the influence of the topological properties of functional brain networks on the prediction of iTBS-induced remote effects. Functional brain networks support neural information processing through two complementary mechanisms: segregation (specialized processing within dense modules) and integration (information flow between modules).^29,30 We calculated the mean within-module degree and participation coefficient at two levels. First, at the primary engaged network level to capture network-specific topology,²² and second, at the whole-brain level to capture global network organization³¹ (Figures 5A and 5B). Given that the predictive power of rsFC differed between intra-network and inter-network effects (as shown previously), we examined these two categories separately.

Figure 5.

Topological properties moderate rsFC prediction for intra-network effects and predict inter-network effects

(A and B) Schematics showing (A) the within-module degree (WMD) of the primary engaged network and (B) the participation coefficient (PC) of the whole brain.

(C) Interaction between rsFC and the WMD of SMN in predicting AUC changes at post (n = 24 sessions).

(D–F) (D) Interaction between rsFC and the whole-brain PC in predicting AUC changes at post-30 (n = 23 sessions). (E) and (F) present simple slope tests based on raw data. Participants were divided into high and low groups based on median splits of the WMD and PC, respectively. Due to insufficient sample sizes for Bayesian mixed-effects modeling after grouping, these plots display raw data points with regression lines and confidence intervals derived from simple linear regression for illustrative purposes. In (E), the high-WMD subgroup contains n = 13 sessions and the low-WMD subgroup contains n = 11 sessions; in (F), the high-PC subgroup contains n = 12 sessions and the low-PC subgroup contains n = 11 sessions.

(G) The WMD of the primary engaged network negatively predicts AUC changes post-iTBS (n = 24 sessions).

(H) The whole-brain PC negatively predicts AUC changes post-iTBS (n = 25 sessions).

In (E) to (H), symbols denote stimulation conditions: blue circles for M1 stimulation, blue squares for PMd stimulation with the SMN as the primary engaged network, yellow squares for PMd stimulation with the FPN as the primary engaged network, yellow hexagons for cIPL stimulation with the FPN as the primary engaged network, red squares for PMd stimulation with the DMN as the primary engaged network, and red hexagons for cIPL stimulation with the DMN as the primary engaged network.

First, for intra-network effects, which were significantly predicted by rsFC, we examined whether topological properties moderated the predictive power of rsFC. Results revealed that the mean within-module degree of the SMN significantly moderated the predictive power of E-field weighted rsFC (β = −0.39, SE = 0.14, and 95% CrI = [−0.67, −0.11]), whereas the mean participation coefficient did not (β = 0.14, SE = 0.20, and 95% CrI = [−0.26, 0.54]). After removing all covariates from the Bayesian model, the interaction remained significant (β = −0.38, SE = 0.14, and 95% CrI = [−0.65, −0.10]). Simple slope tests indicated that E-field weighted rsFC negatively predicted post-iTBS AUC changes when the within-module degree was high (Figure 5C). In contrast, neither the mean whole-brain within-module degree (β = −0.38, SE = 0.20, and 95% CrI = [−0.77, 0.02]) nor the participation coefficient (β = −0.32, SE = 0.20, and 95% CrI = [−0.69, 0.10]) significantly moderated the predictive utility of rsFC. Furthermore, regarding AUC changes at 30 min post-iTBS, although no significant results were found in the primary analyses (Table S1), we observed a marginally significant interaction between E-field weighted rsFC and the mean whole-brain participation coefficient (β = 0.37, SE = 0.20, and 95% CrI = [−0.03, 0.75]). Simple slope tests revealed that rsFC showed a negative predictive trend for delayed excitability changes when the participation coefficient was low (Figure 5D).

In contrast to the intra-network findings, for inter-network effects, which were not predictable by rsFC, we found no evidence that topological properties at either the engaged network level or the global brain level moderated this relationship. We therefore explored whether these topological properties could serve as predictors of inter-network remote effects. Results showed that both the mean within-module degree of the engaged network (β = −0.40, SE = 0.19, and 95% CrI = [−0.77, −0.01]; Figure 5E) and the mean whole-brain participation coefficient (β = −0.43, SE = 0.20, and 95% CrI = [−0.81, −0.03]; Figure 5F) were significant predictors. After removing all covariates from the Bayesian model, these two predictors were not significant (within-module degree: β = −0.36, SE = 0.21, and 95% CrI = [−0.77, 0.07]; participation coefficient: β = −0.26, SE = 0.21, and 95% CrI = [−0.66, 0.18]). Conversely, the participation coefficient of the engaged network (β = 0.01, SE = 0.26, and 95% CrI = [−0.50, 0.52]) and the whole-brain within-module degree (β = −0.24, SE = 0.22, and 95% CrI = [−0.67, 0.22]) were not. Notably, the two significant predictors (the engaged network’s within-module degree and the whole-brain participation coefficient) were not collinear (r = 0.12, and p = 0.566). Therefore, we employed Bayesian model comparison based on leave-one-out cross-validation to assess whether combining these two topological properties, or even accounting for their interaction, would improve predictive accuracy. Results indicated that the combined model showed superior predictive accuracy compared to either single-variable model (vs. within-module degree only: expected log predictive density difference [elpd diff] = 3.3 and SE = 2.4; vs. participation coefficient only: elpd diff = 5.3 and SE = 2.4), although this advantage did not reach strong statistical significance (Figure S4). For AUC changes measured 30 min post-iTBS, none of the topological properties reached statistical significance as predictors (Table S1).

Finally, across all analyses, we found no significant interactions between topological properties and stimulation targets or engaged network identity. The moderating roles of the mean within-module degree of the engaged network remained robust to the choice of threshold used for defining rsFC matrices, and the predictive roles of the mean within-module degree of the engaged network and whole-brain participation coefficient became more pronounced at higher thresholds (Figure S5). In a complementary analysis, given that PMd and cIPL are often considered nodes within the FPN, we also examined whether the topological properties of the FPN could predict the effects induced by stimulating these targets, yielding no significant results (Table S2). Furthermore, we examined the predictive capacity of the engaged network’s within-module degree and the whole-brain participation coefficient on AUC changes specifically for FPN or DMN stimulations. We observed that both FPN stimulations (within-module degree: β = −0.24, SE = 0.30, and 95% CrI = [−0.81, 0.38]; participation coefficient: β = −0.39, SE = 0.28, and 95% CrI = [−0.93, 0.20]) and DMN stimulations (within-module degree: β = −0.47, SE = 0.21, and 95% CrI = [−0.86, −0.02]; participation coefficient: β = −0.30, SE = 0.27, and 95% CrI = [−0.80, 0.26]) exhibited consistent negative predictive relationships. Finally, considering the potential for clinical translation, we conducted supplementary exploratory receiver operating characteristic (ROC) analyses for both intra-network and inter-network effects. As illustrated in Figure S6; Table S3, compared to the baseline classification models that included only covariates (intra-network effects: AUC = 0.75, 95% confidence interval [CI] = [0.298, 0.955]; inter-network effects: AUC = 0.771, 95% CI = [0.460, 0.938]), the full models incorporating rsFC and network topology demonstrated superior classification performance (intra-network effects: AUC = 0.898, 95% CI = [0.622, 1]; inter-network effects: AUC = 0.924, 95% CI = [0.643, 1]).

Discussion

By integrating a multi-site stimulation paradigm with a 32-min rs-fMRI, this study provides evidence that individual functional architecture predicts iTBS-induced changes in motor cortical excitability when targeting remote connected regions. Although iTBS did not produce significant group-level effects on contralateral M1 excitability across all three stimulation sites, our findings show that beyond the functional connectivity strength between the stimulated region and motor cortex, the topological organization of functional networks also plays a critical role in predicting iTBS-induced excitability changes. These predictive relationships serve to explain the substantial inter-individual variability in responses, rather than reflecting a reliable physiological effect of iTBS at the group level. These findings advance our understanding of how intrinsic functional architecture influences rTMS remote effects and may serve as a valuable reference for future research on personalized neuromodulation strategies in clinical applications such as post-stroke motor rehabilitation.

rsFC reflects the temporal correlation of spontaneous activity, representing the pattern of intrinsic information exchange between brain regions. This notion is supported by electrical stimulation¹⁷ and single-pulse TMS^18,19,20 studies, which show that stimulation evokes stronger immediate responses in remote regions with higher rsFC. Consistently, we found that rsFC significantly and negatively predicted iTBS-induced changes in contralateral M1 excitability following left M1 stimulation: stronger rsFC predicted greater inhibition. This negative relationship is in line with the well-established interhemispheric inhibition (IHI) theory.^13,32 Notably, when incorporating data from PMd stimulations for which the primary engaged network was also the SMN, the negative relationship remained robust with narrower CrI (Figures 2A and S3C). However, whether this predictive relationship could extend to other SMN nodes or whether contralateral SMN stimulation is primarily driven by IHI mechanisms requires further investigation. This predictive power appears to be constrained by network organization. Our findings indicated that when the engaged network was no longer the SMN, rsFC failed to predict changes in contralateral M1 excitability. This dissociation implies that the principles governing rTMS remote effects may fundamentally differ between intra-network and inter-network contexts. For intra-network effects (where the stimulated and remote regions share the same primary engaged network), the strength of direct functional connectivity serves as a primary predictor of these remote changes; whereas for inter-network effects (where the stimulated and remote regions have different primary engaged networks), these remote changes may be more closely associated with broader network-level interactions rather than direct coupling.

Previous studies indicate that the intrinsic functional network architecture constrains the propagation pathways of single-pulse TMS-evoked responses.²¹ In addition, the within-network connectivity strength of the network engaged by the stimulated region, along with whole-brain modularity, has been shown to predict average network responses.²² This highlights the critical role of network-level interactions in TMS-induced remote effects. Building on this, we examined how functional network topological properties predict changes in contralateral M1 excitability. Our results suggest two distinct patterns through which these topological properties relate to the remote effects of rTMS. For intra-network effects, we found that the within-network connectivity strength of the SMN moderated the predictive utility of rsFC. Specifically, a negative predictive relationship between rsFC and contralateral M1 excitability changes emerged exclusively when within-network connectivity strength was strong. This suggests that the remote effects of rTMS are associated not only with the functional coupling between the stimulated and remote sites but also with the broader interactions within the engaged network. This aligns with findings from combined TMS-electroencephalogram (EEG) and whole-brain computational modeling studies, which demonstrate that signal propagation relies on reverberant re-entrant network activity.³³

While direct rsFC was not predictive of inter-network effects, network-level metrics emerged as potential predictors, which offer preliminary evidence that inter-network effects are likely more closely associated with complex network-level interactions than with direct region-to-region connections. Specifically, rTMS effects on remote regions appear to be linked to both whole-brain inter-network integration and the internal cohesion of the engaged network. Direct electrical stimulation studies support this from a temporal perspective, showing that evoked responses propagate within the engaged network before spreading to other networks.³⁴ This implies that intra-network propagation dynamics may influence subsequent inter-network effects. This notion is supported by our supplementary analysis (Figure S4), which showed that combining these topological properties improved predictive accuracy and identified a marginally significant interaction between the engaged network’s within-module degree and the whole-brain participation coefficient. Given the complexity of the statistical models, we employed a Bayesian approach to mitigate the risk of overfitting and conducted rigorous sensitivity analyses to evaluate the stability of our findings. These analyses revealed that our core findings regarding intra-network effects are highly robust. This underscores the statistical reliability of functional characteristics as predictors of the remote intra-network effects of rTMS. Conversely, the predictive models for inter-network effects exhibited greater sensitivity. Although such sensitivity is theoretically expected given the relatively small sample size and high heterogeneity introduced by pooling data across diverse engaged networks, findings pertaining to inter-network effects should still be cautiously interpreted as preliminary associations that warrant further validation in larger, independent cohorts.

Another notable finding is that the predictive utility of baseline intrinsic functional architecture for iTBS-induced remote effects exhibited marked temporal dependence: it showed significant predictive power for immediate effects but diminished at 30 min post-iTBS. While our data cannot identify the mechanisms underlying this temporal shift, several potential contributing factors warrant consideration. First, immediate post-iTBS effects primarily reflect rapid changes in corticospinal excitability, related to the initial propagation of stimulation-induced activity along the baseline intrinsic functional architecture and early changes in synaptic efficacy. Second, as time progresses to 30 min, the effects may involve more complex synaptic consolidation processes³⁵ and may be modulated by homeostatic plasticity.³⁶ The efficiency and time course of consolidation and homeostatic control might vary considerably across individuals. Thus, the predictive power of baseline features naturally weakens at 30 min. Finally, within 30 min post-iTBS, brain networks may undergo dynamic reorganization,³⁷ which may in turn reduce the predictive power of baseline features for longer term effects. Identifying the potential mechanisms underlying temporal dependence will require future research, but this finding already suggests the necessity of acquiring fMRI measurements at multiple time points across multiple iTBS sessions. Furthermore, although the present study primarily focuses on stable intrinsic functional features measured at rest, growing evidence indicates that responsiveness to non-invasive brain stimulation likely emerges from complex interactions between the intrinsic functional architecture and state-dependent fluctuations in brain activity. For instance, trial-by-trial fluctuations in pre-stimulus alpha power have been shown to significantly impact TMS-evoked hemodynamic activations throughout the cortico-subcortical motor system.³⁸ From this perspective, stable intrinsic functional features such as those examined here and transient brain states may represent complementary dimensions that jointly contribute to inter-individual and inter-session variability in iTBS responses. Disentangling their relative contributions was beyond the scope of the present study, and future work integrating individualized functional network mapping with real-time state monitoring (e.g., EEG) represents a promising avenue for understanding how dynamic brain states and relatively stable intrinsic functional architecture jointly shape the modulatory effects of iTBS.

An important finding of this study is that iTBS to all three target sites did not produce significant group-level changes in contralateral M1 cortical excitability. This null effect aligns with the heterogeneous findings regarding remote iTBS effects: some studies have reported significant group-level changes,^2,13 whereas others have observed null results.^39,40,41 The absence of group-level effects fundamentally constrains our inference about the intervention’s overall efficacy: we cannot assume that iTBS to these remote sites produces consistent, directional modulation at the population level. As such, without a universal group-level response, interpreting how intrinsic functional architecture predicts iTBS remote effects must rely on established frameworks from previous literature, such as IHI theory. Nevertheless, our analyses revealed that baseline rsFC and network topology predicted substantial variance in individual response (Figures 4 and 5), suggesting that heterogeneity in intrinsic functional architecture may contribute to the null group effect. Crucially, this systematic predictability suggests that the observed excitability changes represent structured, biologically meaningful modulation rather than random noise. Di Lazzaro et al.¹² provide relevant evidence. They also found no group-level remote effects overall when targeting contralateral M1, but age-stratified analyses revealed significant inhibitory effects in middle-aged adults (41–60 years old) that were masked in the full sample. This also indicates how individual characteristics could obscure patterns even when systematic effects exist within subgroups. Because our study sample consisted exclusively of young adults, the potential relationship between the age-stratification effect observed by Di Lazzaro et al. and intrinsic functional architecture remains to be explored in future studies. Other factors may also have contributed to the null group-level effect. The stimulation intensity (70% resting motor threshold [RMT]) was selected based on established parameters for healthy participants,^12,42 but may have induced relatively small remote effects compared to higher intensities used in clinical studies.²⁶ Whether higher intensities would produce detectable group-level effects, and whether architecture-based predictions would hold at higher intensities, represent important questions for future research.

Our findings in healthy individuals may have implications for the clinical application of rTMS. In post-stroke motor rehabilitation, stimulating the contralesional M1 to modulate network reorganization represents an important therapeutic approach.^1,43 Although this study focused on the remote modulatory effects of iTBS on M1 excitability, these remote effects may reflect broader, large-scale brain network reorganization processes rather than purely localized effects. Thus, the predictors identified in this study may provide preliminary clues for predicting therapeutic responsiveness in clinical populations. Beyond continuous regression analysis, we also explored whether these predictors could classify categorical responders (i.e., those showing iTBS-induced suppression of contralateral M1 cortical excitability). While intrinsic functional architecture showed limited discriminative ability on its own, integrating it with covariates (such as baseline motor cortical excitability) yielded highly significant classification performance (AUC >0.89 for both intra- and inter-network effects). This suggests that rather than acting as a standalone biomarker, intrinsic functional architecture might serve as a complementary predictor that could potentially help refine prognosis. However, given the relatively small sample size and the absence of independent validation, the high AUC values should be interpreted with caution. These classification findings should be regarded as preliminary and require replication in larger, independent cohorts, as well as further validation in clinical populations using clinically relevant outcome measures. In current TMS clinical practice, modulating ipsilesional M1 through stimulating remotely functionally connected non-M1 regions (such as PMd or cIPL) is less commonly emphasized than stimulating the contralesional M1. This study compared the modulatory effects of PMd and cIPL stimulation on contralateral M1 excitability with those of M1 stimulation. As reported in the results section, we found no significant differences between M1 and non-M1 targets. While these null findings should be interpreted cautiously, they suggest that non-M1 targets warrant further investigation as potential therapeutic approaches. The potential efficacy of non-M1 targets in specific patient populations is supported by emerging clinical evidence. For example, PMd stimulation has shown promise in patients with insufficient M1 structural reserve,⁴⁴ and cIPL stimulation has potential efficacy in patients with deficits in motor-related higher order cognitive functions such as hemispatial neglect.⁴⁵ However, whether these findings imply that non-M1 stimulation has therapeutic efficacy comparable to M1 stimulation in stroke patients requires further investigation. Furthermore, given the substantial functional heterogeneity of regions such as PMd and cIPL, and our finding that rTMS remote effects depend on the functional characteristics of the stimulated region, future studies should employ individualized fMRI-guided targeting for precise localization rather than relying on scalp-based methods. Finally, our study provides preliminary insights into how intrinsic functional architecture may influence rTMS remote effects. Extending beyond single-pulse TMS literature,^20,21,22 our findings suggest that rsFC within the SMN network shows relatively robust predictive power for rTMS remote effects, while inter-network topological effects remain preliminary. These findings may serve as a reference for future connectivity-based rTMS targeting research.^46,47

Limitations of the study

Our study offers new perspectives on the neural mechanisms underlying rTMS remote effects and identifies several key directions for future research. Crucially, although we provide preliminary validation of how intrinsic functional architecture influences iTBS-induced changes in contralateral motor cortex excitability in healthy individuals, it is essential to extend these findings to clinical populations. Future work should focus on patients, such as those with stroke, to evaluate the clinical utility of these predictors for individualized treatment. Furthermore, the limited sample size constrained our ability to systematically examine variations when engaging different brain networks or regions. Studies with larger samples are needed to address this limitation. Since this study focused solely on iTBS, future research should investigate whether the predictive role of functional architecture applies to other protocols, such as cTBS or conventional high/low-frequency stimulation. Additionally, an important avenue for future research is integrating structural connectivity measures alongside functional network topology. We acknowledge that anatomical connectivity, particularly the integrity of the corpus callosum, plays a critical role alongside functional connectivity. Multimodal studies combining resting-state fMRI and diffusion MRI would help clarify how anatomical constraints interact with functional architecture in shaping remote excitability changes, potentially revealing whether structural and functional connectivity provide complementary predictive information. Finally, by characterizing the role of functional architecture in mediating rTMS remote effects, this study opens new avenues for exploring its impact on the broader motor circuit and, ultimately, on motor function. Extending these neurophysiological insights to behavioral outcomes represents a necessary next step toward translating the findings in this study into optimized TMS targeting strategies for clinical practice.

Resource availability

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact Chaozhe Zhu (czzhu@bnu.edu.cn).

Materials availability

This study did not generate new unique reagents.

Data and code availability

• •All data reported in this paper are available from the lead contact upon request.
• •This paper does not report original code.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (82071999 and 61431002). We thank Lijiang Wei and Yilong Xu for their assistance in conducting the experiments.

Author contributions

Conceptualization, methodology, formal analysis, investigation, writing – original draft, writing – review and editing, and visualization, Y.C.; conceptualization, methodology, data curation, formal analysis, and investigation, Z.Z.; conceptualization and data curation, F.L.; data curation, H.C.; data curation, T.C.; data curation, S.L.; writing – review and editing, Z.L.; conceptualization, funding acquisition, investigation, project administration, resources, and writing – review and editing, C.Z.

Declaration of interests

The authors declare no competing interests.

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used generative AI in order to improve the readability and language of the manuscript. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
fMRI data	This paper	N/A
MEP data	This paper	N/A
Software and algorithms
MATLAB R2020b	MathWorks, Natick, Massachusetts, USA	https://www.mathworks.com/
DPABI V8.2 software	Chao-Gan Yan’s team et al.48	https://rfmri.org/DPABI
Brain Connectivity Toolbox	Rubinov M & Sporns O’s team et al.49	https://sites.google.com/site/bctnet
R studio V4.3.0	R studio	https://posit.co/download/rstudio-desktop/

Experimental model and study participant details

Twenty-four healthy Chinese volunteers (15 male, 9 female; mean age ± SD = 24.29 ± 2.37 years) participated in this study. All participants were right-handed,⁵⁰ and reported no history of neurological or psychiatric disorders. They were not taking any medications affecting the central nervous system, and had no contraindications to TMS (e.g., pregnancy or metal implants), in accordance with standard safety guidelines.⁵¹ The study protocol was approved by the Ethics Committee of the State Key Laboratory of Cognitive Neuroscience and Learning at Beijing Normal University (IRB-A-035-2023001), and written informed consent was obtained from all participants prior to participation.

Method details

MRI data acquisition

MRI data were acquired using a 3T Siemens Magnetom Prisma scanner equipped with a 64-channel head coil. High-resolution T1-weighted structural images were obtained using a magnetization-prepared rapid gradient-echo (MPRAGE) sequence with the following parameters: repetition time (TR) = 2530 ms; echo time (TE) = 2 ms; field-of-view (FOV) = 230 mm; flip angle = 7°; 208 sagittal slices; slice thickness = 0.9 mm; voxel size = 0.9 × 0.9 × 0.9 mm³. rs-fMRI data were acquired using a gradient-echo echo-planar imaging (EPI) sequence. Data were collected in four 8-minute runs across two days (two runs per day). During scanning, participants were instructed to keep their eyes open and fixate on a central cross. The acquisition parameters were: TR = 2000 ms; TE = 30 ms; FOV = 216 mm; flip angle = 90°; slice thickness = 1.8 mm; voxel size = 1.8 × 1.8 × 1.8 mm³. One participant was excluded due to incomplete scanning.

TMS procedures

Participants completed three TMS experiment sessions, each separated by an interval of 2–5 days, corresponding to the stimulation of three distinct targets: M1, PMd, and cIPL. Target order was counterbalanced across participants. The TMS experiment was performed using a Magstim Rapid² (Magstim Ltd., Dyfed, United Kingdom) with a D70 Air Film figure-of-eight coil. Surface electromyography (EMG) was recorded from the first dorsal interosseous (FDI) and abductor digiti minimi (ADM) muscles of both hands using bipolar surface electrodes connected to the Brainsight electromyography (EMG) Isolation Unit and Amplifier Pod (Rogue Research Inc., Montreal, Canada). The Brainsight neuronavigation system was also used to guide and record coil placement. Throughout the experiment, participants sat comfortably with muscles relaxed.

At the beginning of the first session, each participant’s motor hotspot and resting motor threshold (RMT) were determined. The hotspot was defined as the optimal coil position that consistently elicited the largest peak-to-peak MEP amplitude in the contralateral FDI muscle, with the coil held tangentially to the scalp and the handle pointing backward at approximately 45° to the midsagittal plane. To localize the hotspot, we first identified the omega-shaped area within the precentral gyrus on T1-weighted images as an anatomical landmark for the hand motor area, then conducted a systematic search around this region to identify the position producing maximal FDI responses. MEPs from the ADM muscle were recorded concurrently, and we verified that the identified hotspot elicited larger responses in FDI than ADM, confirming target muscle specificity. RMT was defined as the minimum stimulator intensity required to evoke an MEP of at least 50 μV peak-to-peak amplitude in the relaxed right FDI muscle in 5 out of 10 consecutive trials. Two participants were excluded due to the failure to elicit MEPs upon stimulation of the precentral gyrus. As shown in Figure 1, iTBS was applied to all three targets. The protocol consisted of 2-second trains of theta-burst stimulation (three-pulse bursts at 50 Hz, repeated at 5 Hz), separated by 8-second intervals, for a total of 600 pulses.³ Stimulation intensity was set to 70% of RMT, following established iTBS protocols that modulate motor cortical excitability through stimulation of contralateral M1 or functionally connected regions such as PMd.^12,42 The left M1 target was the motor hotspot identified previously. The left PMd target was located 2.5 cm anterior and 1 cm medial to the M1 hotspot,⁸ and the left cIPL target was identified at the P3⁸.

To mitigate the influence of circadian rhythms,⁵² three sessions for each participant were conducted at the same time of day (e.g., 9:00–12:00 or 14:00–17:00). Participants were instructed to maintain a regular sleep schedule before each session. Female participants were scheduled to avoid their menstrual period to minimize the effects of hormonal fluctuations.⁵³ To localize the bilateral motor hotspots, the omega-shaped area within the precentral gyrus, a reliable anatomical landmark for the hand motor area, was first identified on T1-weighted images to guide the subsequent search. The PMd and cIPL locations were first identified on each participant’s T1-weighted image⁵⁴ and then imported into the Brainsight system for neuronavigation. For all targets, the coil was held tangentially to the scalp, with the handle pointing backward at an approximately 45° angle to the midsagittal plane.

Quantification of remote effect

To mitigate potential biases arising from single-intensity MEP measurements,^55,56 changes in contralateral motor cortical excitability were quantified as the ratio of the area under the curve (AUC) for the post-intervention input-output (I/O) curve to the baseline AUC. For each measurement, I/O curves were constructed by delivering 10 stimuli per level across five intensity levels ranging from 80% to 160% of RMT in 20% increments^57,58 (Figure S1). Stimuli across intensity levels were presented in a pseudorandom order with an inter-trial interval of 4–6 seconds. MEPs were measured at baseline, immediately after iTBS, and 30 minutes post-iTBS. The 30-minute time point was chosen based on previous evidence that iTBS effects can persist for at least 30 minutes,^2,13,39 allowing us to examine both immediate and sustained effects of stimulation.

A four-parameter boltzmann sigmoid function was fitted to the I/O curve data:

$$MEP\left(I\right)={MEP}_{\mathit{min}}+\frac{{MEP}_{\mathit{max}}-{MEP}_{\mathit{min}}}{1+e^{\frac{I_{50}-I}{S}}}$$

where MEP_min and MEP_max are the minimum and maximum values of the curve; I₅₀ is the stimulus intensity required to elicit an MEP halfway between MEP_min and MEP_max; and S is the steepness of the curve at I₅₀.

To ensure data quality for curve fitting, EMG recordings from each trial were visually inspected by two independent operators. Trials were discarded if they showed pre-stimulus EMG activity exceeding 50 μV within 100 ms of the stimulus artifact⁵⁹ or were contaminated by noise. Additionally, MEPs exceeding 3 standard deviations from the mean at each stimulation intensity were discarded as outliers. All remaining MEP amplitudes were log10-transformed to better approximate a normal distribution.⁶⁰ After curve fitting, the resulting I/O curves were visually inspected again. Curves that failed to exhibit a sigmoidal pattern were excluded from further analysis.

MRI data preprocessing

rs-fMRI data were preprocessed with DPABI⁴⁸ in MATLAB R2020b. After discarding the initial ten volumes for signal stabilization, preprocessing included slice-timing correction, realignment, nuisance regression (removing signals from white matter, cerebrospinal fluid, and head-motion parameters), bandpass filtering (0.01–0.08 Hz), and spatial smoothing (3 mm FWHM Gaussian kernel). Head motion was confirmed to be within thresholds for all participants (maximum translation <3 mm and maximum rotation <3°).

Functional connectivity analysis

Seed-based analysis was performed to assess rsFC. First, electric field simulations were conducted using SimNIBS 4.1⁶¹ to individually define the regions of interest. These simulations integrated each participant’s T1-weighted image, along with the coil placement and stimulation intensity recorded by the neuronavigation system. Based on electric field simulations at the iTBS intervention sites and right motor hotspots, respectively, the stimulated region and the right motor cortical region were identified. These regions were defined as voxels where the electric field strength exceeded 95% of the maximum cortical field strength. This threshold was selected based on neurophysiological evidence from single-cell recordings in non-human primates, which showed that TMS-induced cortical activation corresponds to regions where the electric field exceeds 95% of maximum.⁶² We also investigated whether our main findings remained robust when using alternative thresholds (90% and 99% of maximum). Finally, the rsFC strength was calculated as the Fisher z-transformed Pearson correlation coefficient between the mean time series from the stimulated region and the right motor cortical region, which was then weighted by the mean electric field strength within the stimulated region.²⁸

Functional network mapping

For each participant, we constructed a functional connectivity matrix to identify large-scale brain networks. First, we transformed the Schaefer 1000 parcellation atlas⁶³ into the participant’s native rs-fMRI space. This parcellation-based approach enhances signal stability and reduces computational burden. We then generated a 1000 × 1000 adjacency matrix by calculating the Fisher z-transformed Pearson correlation between the mean time series of every pair of regions. The preprocessed connectivity matrices were binarized and used as input for the InfoMap community detection algorithm.⁶⁴ Each module was labeled according to the canonical network⁶³ with which it showed the highest Jaccard index, provided this index exceeded 0.1.

Prior to community detection, the connectivity matrix was preprocessed as follows. The connections between regions within 10 mm (Euclidean distance) were set to zero to mitigate potential artifacts from spatial smoothing.^65,66 Considering the low signal-to-noise ratio of the limbic network,^63,67 all connections involving limbic regions were excluded. The binarization threshold was set to retain the top 5% of connections. For four participants, this threshold was adjusted to 2% to separate the six canonical intrinsic functional networks,⁶⁷ consistent with a prior report.⁶⁶ To assess the reliability and specificity of this individualized functional network mapping, the procedure was performed twice for each participant using separate rs-fMRI runs acquired on two different days. The spatial similarity of the resulting networks was quantified using the Dice coefficient. This analysis confirmed that within-subject similarity was significantly higher than between-subject similarity across all six canonical networks (all p < 0.05, Bonferroni-corrected), demonstrating the robustness of our mapping procedure.

Graph-theoretical analysis

To better preserve topological information for graph-theoretical analysis, a separate weighted connectivity matrix was constructed by thresholding the preprocessed matrix to retain only the top 20% of positive connection strengths.³⁰ Graph-theoretical properties were computed using the Brain Connectivity Toolbox.⁴⁹ We focused on two key metrics: the participation coefficient,⁶⁸ which quantifies a node’s connections across different modules, and the within-module degree, which assesses a node’s intra-modular connectivity strength. Notably, we calculated a normalized within-module degree adjusted for module size rather than using the standard within-module degree z-score⁶⁹:

$$within-moduledegree\left(i\right)=\frac{1}{n}\sum _{j\in m}{W}_{ij}$$

where m denotes the module containing node i, j represents all other nodes within module m, W_ij is the weighted connection between node i and node j, and n is the total number of nodes in module m.

Quantification and statistical analysis

All statistical analyses were performed in R (version 4.3.0). Details of all statistical analyses—including test statistics (t, r, or W values), exact p-values or 95% credible intervals (CrIs), effect sizes, and sample sizes—are reported in the corresponding figure legends, main-text Results, and Tables, as detailed below. First, paired t-tests were used to analyze the pre- to post-intervention changes in the AUC for the I/O curves for each target (Figures 2B and 2C and the corresponding Results section). The normality of the paired differences was confirmed using the Shapiro–Wilk test. Pearson’s correlation coefficient (r) was computed to examine the association between the immediate post-intervention change in AUC and the change measured 30 min post-intervention (Figure 2D and Results). Statistical significance was defined as two-tailed p < 0.05 for all tests. Throughout the manuscript, “mean ± SD” denotes the sample mean and standard deviation when summarizing data, and denotes the mean and standard deviation of a Normal distribution when specifying Bayesian prior distributions.

Next, to investigate whether rsFC predicted iTBS-induced effects, we implemented Bayesian linear regression using the brms R package in Stan (Figures 3 and S2; Table 1, and Results). To reduce false positives and regularize the estimated associations, we employed weakly informative Normal priors (mean = 0, SD = 0.5) for all fixed-effect coefficients. All continuous variables were standardized before model fitting. Each model was run with four independent chains for 8000 iterations each, with the first 4000 iterations discarded as warm-up. Convergence was assessed by requiring Rhat <1.01 and effective sample sizes >1,000 for all parameters, and by visual inspection of trace plots.

The Bayesian linear regression model included three covariates related to participant state and experimental procedures to control for potential confounding factors. Baseline AUC was included, as baseline cortical excitability could influence iTBS-induced effects.^70,71 Caffeine use was coded as a covariate (0 = intake on test day consistent with daily habit, 1 = intake on test day over daily habit, -1 = intake on test day lower than daily habit), given that both chronic and acute caffeine consumption can affect TMS effectiveness.^72,73 Coil placement differences between pre- and post-iTBS MEP measurements were quantified as the ratio of the mean electric field strength in the contralateral M1 region (where MEPs were recorded) during the post-iTBS measurement to that during the pre-iTBS measurement. This covariate was included to control for potential confounding effects of measurement-related coil placement variability on observed motor cortical excitability changes.

For analyses pooling data across stimulation targets or engaged networks to investigate the predictive utility of topological properties for iTBS-induced effects, Bayesian linear mixed models were employed (Figures 4, 5, S4, and S5; Tables S1, S2, and S3 Table, and Results). Stimulation target and engaged network were included as independent fixed effects, while participant ID was modeled as a random intercept to account for inter-individual variability. For example, when examining how topological properties predicted inter-network effects, the model was specified as:

$$Effect\sim Predictor+Stimulationtarget+Engagednetwork+BaselineAUC+Caffeineuse+DifferenceofCoilPlacement+\left(1|ParticipantID\right)$$

Other model specifications, including priors, were identical to those described for the linear regression models. Given that the relatively small sample size and the number of predictors could lead to greater model complexity and a subsequent risk of overfitting, we also conducted statistical analyses using a simplified Bayesian model that excluded all covariates and retained only the predictors of interest. For all Bayesian analyses, we report the posterior mean (β), the posterior standard deviation (reported as SE), and the 95% credible interval (CrI) for each standardized regression coefficient. An effect was considered credible when the 95% CrI of the coefficient excluded zero. In Table 1, coefficients meeting this criterion are additionally marked with an asterisk (∗) for visual clarity; no asterisks are used in any figure.