{"paper_id":"0f3c7534-269f-4b35-9ff5-01d02558b28d","body_text":"1 \n \nFull title: A brain dynamic model based on graph neural network 1 \nreflect the inter-region interaction of cortical areas  2 \nShort title: brain dynamic model reflects the inter -region 3 \ninteraction 4 \n 5 \nShaoxian Li,1 Debin Zeng,2,3 Xiaoxi Dong,1 Yirong He,4 Tongtong Che,1 Jichang 6 \nZhang,1Zekun Yang,1Jie Jiang,1Lei Chu,5 Ying Han,6,7,8,9 Shuyu Li1* 7 \n 8 \n1State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, 9 \n100875, China 10 \n2Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, Shanghai, 11 \nChina 12 \n3Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence, Fudan University, 13 \nMinistry of Education, Shanghai, China 14 \n4Institute for Brain Research and Rehabilitation, South China Normal University, Guangzhou 510631, 15 \nChina 16 \n5Beijing Advanced Innovation Center for Biomedical Engineering, School of Biological Science & 17 \nMedical Engineering, Beihang University, Beijing 100083, China 18 \n6Department of Neurology, Xuanwu Hospital of Capital Medical University, Beijing 100053, China 19 \n7Biomedical Engineering Institute, Hainan University, Haikou 570228, China 20 \n8Center of Alzheimer’s Disease, Beijing Institute for Brain Disorders, Beijing 100050, China 21 \n9National Clinical Research Center for Geriatric Disorders, Beijing 100053, China 22 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n2 \n \n 23 \nAbstract 24 \nA central objective in neuroscience is to elucidate how the brain generates complex dynamic 25 \nactivity through the interactions of brain areas . In this study, we utilize d Interaction Network, a 26 \ngraph neural network model, to develop a computational framework  for predicting whole-brain 27 \ncortical blood oxygenation level dependent (BOLD) signals.  We derived an Inter -Regional 28 \nInteraction (IRI) metric to quantify information exchange among brain areas probing the underlying 29 \ndynamical mechanisms. In addition, the total IRI emitted from each brain region was calculated and 30 \ndefined as the IRI sent by region (RS-IRI). Our model predicted the following 10 time points BOLD 31 \nactivity from initial BOLD signals , and achieved a mean absolute error of 0.0 4. The predicted 32 \nfunctional connectivity (FC) achieves a correlation coefficient of 0.9 7 compared to the empirical 33 \nFC. The fluctuation amplitude of the IRI increases with the length of the connection and the largest 34 \nRS-IRI oscillation amplitude is observed in visual areas . The RS-IRI demonstrates a hierarchical 35 \norganization, characterized by more concentrated distributions in association regions and larger 36 \nfluctuation amplitudes in  unimodal regions. Applying our approach to Alzheimer’s disease (AD), 37 \nwe demonstrate that the frequency-specific amplitudes of IRI oscillations discriminate AD patients 38 \nfrom healthy controls and correlate with Mini-Mental State Examination scores. Together, this work 39 \npresents a deep learning–based framework for modeling brain dynamics as well a quantitative index 40 \nof inter-areal interactions, and offers a new perspective for disease characterization. 41 \nKeywords: Neurodynamic Modeling , Graph Neural Network (GNN), Brain Inter -regional 42 \nInteraction, Alzheimer's disease (AD) 43 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n3 \n \nAuthor Summary 44 \nThe human brain comprises distinct regions that interact through complex fiber tracts, forming 45 \nthe functional dynamics for diverse cognitive processes. We employed fMRI to assess functional 46 \nactivity and DTI to reconstruct fiber tract connectivity.  To elucidate how brain function emerges 47 \nfrom these inter -regional interactions, we developed a novel computational framework based on 48 \nGraph Neural Network (GNN) to model the brain’s interactive dynamics for its capacity to uncover 49 \nhidden and intricate patterns within data. From this model, we derived a quantitative metric termed 50 \nInter-Regional Interaction ( IRI), which characterized the fine -grained, dynamic fluctuations in 51 \ncommunication between brain areas. Our results suggest that this GNN-based model can accurately 52 \nsimulate brain functional activity and provide a quantitative description of neural interaction 53 \npatterns. Applying this model to a cohort of Alzheimer’s disease patients, we demonstrated that the 54 \nIRI metric not only effectively distinguish ed patients from healthy controls but also significantly 55 \ncorrelated with clinical cognitive performance (MMSE scores). This approach a dvances our 56 \nunderstanding of the fundamental principles of brain function and offers a promising tool for 57 \nidentifying the underlying mechanisms of neurological disorders. 58 \nIntroduction 59 \nThe human brain is a highly complex system comprising various types of n eurons and glial 60 \ncells. A central focus of brain research is understanding how the brain generates its intricate dynamic 61 \nactivities, which support a wide range of cognitive functions(1–3). Alterations in these dynamics 62 \ncan indicate systemic brain disorders (4) or transient pharmacological states (5). Many researchers 63 \nhave sought to describe brain dynamics from multiple perspectives, yielding insights  into 64 \nphenomena such as multistability(6 –8), metastability(9), co -occurring ripple oscillations (10), and 65 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n4 \n \ncriticality(11,12). A widely accepted consensus is that brain dynamics are markedly nonlinear(13), 66 \nwhich are presented at multiple levels, from individual neuron activity to the collective interactions 67 \nof neuronal populations. This pervasive nonlinearity contributes to the overall complexity of the 68 \nbrain as a system. While these studies analyze and characterize dynamic activities from various  69 \nperspectives, a pressing question remains: what factors, at both microscopic and macroscopic scales, 70 \ngive rise to these dynamic patterns? A broad proposition suggests that such nonlinear dynamics 71 \noriginate from both local intrinsic activity and inter-regional interactions(14). Crucially, these inter-72 \nregional interactions are constrained by the brain’s structural connectivity, which facilitates 73 \ninformation transmission between areas and integrates their activities into a globally cohesive yet 74 \nrichly interactive dynamic system, rather than an ensemble of isolated regional dynamics. To 75 \ninvestigate the mechanisms underlying these dynamics  more sophisticated, mechanism -oriented 76 \napproaches are needed to explore how these dynamics originate and are shaped. 77 \nDynamical models represent a vital approach for investigating brain dynamics, as their ability 78 \nto encapsulate complex activities within a single framework enab les both the elucidation of 79 \nunderlying mechanisms and the prediction of future states.  Since the introduction of the 80 \nfoundational Hodgkin-Huxley (H-H) model(15) and the Wilson-Cowan (W-C) model(16), extensive 81 \nresearch has expanded this neuronal framework to encompass larger systems (17). While thes e 82 \nstudies have successfully constructed dynamic models for individual neurons or specific brain 83 \nregions, a comprehensive understanding of brain activity mechanisms necessitates the development 84 \nof dynamic models for the entire brain.  Whole-brain dynamical models are typically constructed 85 \nusing network- based modeling, where brain regions are represented as nodes and structural 86 \nconnections between these regions serve as edges. For instance, dynamic causal modeling employs 87 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n5 \n \nmultivariate nonlinear equations to fit regional activity (18–21) and network-based modeling 88 \napproaches grounded in neural mass models or neural field models have been widely utilized(17,22–89 \n25). Several phenomenological models have also yielded significant results  in whole -brain 90 \nmodeling. For instance, the Hopf whole-brain model integrates structural connectivity (in the form 91 \nof adjacency matrices) with local dynamics such as noise and time delays in each brain region (26). 92 \nThis integration enables the analysis and prediction of functional connectivity (FC)  (26,27), 93 \nproviding dee per insights into the relationship between brain structure and function (28). 94 \nFurthermore, they facilitate the simulation of whole- brain activity, allowing researchers to 95 \nunderstand various brain states and predict how different regions may respond to  external 96 \ndisturbances, serve as valuable tools in pathology and pharmacology research, aiding in the 97 \nexploration of how brain dynamics react to disruptions or interventions (27). However, these 98 \napproaches rely heavily on a priori expert knowledge and intuition. We aim to employ a data-driven 99 \nframework that enables researchers to extract richer insights directly from the intrinsic structure of 100 \nthe data. 101 \nIn recent years, deep learning has garnered significant attention in neuroscience due to its 102 \nsuccess in capturing hidden and complex patterns within data. Various convolutional neural 103 \nnetworks and recurrent neural networks have proven effective in modeling structural or functio nal 104 \nsignals (29,30). Motivated by the recognition that the brain can naturally be represented as a graph, 105 \nthere has been growing interest in applying graph neural networks (GNN) (31–33). GNN are 106 \nspecifically designed to treat the brain as a directed graph, where nodes represent anatomical brain 107 \nregions and edges denote morphological, functional, or structural connectivity between pairwise 108 \nnodes(34). Regarding node-edge processing paradigms, GNN can be categorized into three primary 109 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n6 \n \nclasses(35): (1) those that aggregate features of neighboring nodes using a learnable filter, as seen 110 \nin graph convolutional networks ; (2) those based on a self -attention algorithm that identifies the 111 \nmost significant neighbors for aggregation, as in graph attention networks; and (3) those employing 112 \na message -passing mechanism, where features of both the node are in consideration and its 113 \nneighboring nodes are combined to learn the local graph representation.  In recent years, some 114 \napproaches have also employed ordinary differential equations as update rules(36,37). Among these 115 \napproaches, message-passing-based interactive network (IN) enable the prediction of not only the 116 \ndynamic signal but also the inter -node interactions. In physics, IN have been successfully applied 117 \nto simulate diverse phenomena(38) and model Newton's Second Law (39), demonstrating their 118 \neffectiveness in modeling interaction patterns within complex networks while generating 119 \ninterpretable representations of node interactions. 120 \nTo achieve a more accurate fitting of whole- brain neural dynamics, this study developed a 121 \ncomputational model based on IN to predict BOLD signals across the entire cortical surface. The 122 \nmodel calculated interaction information between different brain regions constrained by structural 123 \nconnectivity and predicted dynamic changes in regions through their inter-regional interactions. We 124 \ntrained the model and evaluated its performance on a test set by calculating the Mean Absolute Error 125 \n(MAE) of the predictions and their correlation with actual FC as the metric of the method's 126 \neffectiveness in simulating dynamic variations of cortical signals.  We analyzed prediction errors 127 \nacross different regions and investigated its relationship with neural volatility and molecular 128 \nbiological maps to uncover the underlying causes of the spatial distribution in prediction accuracy. 129 \nLeveraging the model, we extracted inter -regional interaction information at the individual level. 130 \nBy applying this approach to fMRI from Alzheimer’s disease (AD) patients, we found that the model 131 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n7 \n \nsuccessfully captured oscillatory patterns in inter-regional interactions that differentiate AD patients 132 \nfrom normal controls (NC). The constructed model offers a novel approach for analyzing brain 133 \ndynamics, and the derived interaction metrics provide valuable insights for disease research. 134 \nResults 135 \nWorkflow 136 \nThis study constructed  an IN model based on a message -passing mechanism. By fitting and 137 \ntraining on BOLD signals, the model generated interaction messages between different brain regions, 138 \nenabling the simulation of whole -brain dynamics. The model was trained and validated using the 139 \nresting state fMRI (rs -fMRI) from the Human Connectome Project (HCP) dataset, and the inter -140 \nregion interactions (IRI) produced by the model were subsequently analyzed. The cortex was 141 \nsegmented into regions according to the MMP360 atlas(40). The mean BOLD signal of each region 142 \nwas calculated as a proxy for the dynamic neural activity within that region ( Figure 1 A). The 143 \nspecific training strategy is detailed in the Methods section. The trained model was then applied to 144 \nthe test set, and prediction errors  were analyzed across different regions ( Figure 1B). These error 145 \ndistributions underwent correlation analyses with other brain maps to investigate the sources of 146 \nregional heterogeneity in prediction accuracy. Subsequently, dynamic interaction messages between 147 \nregions were extracted, and the information fluctuation maps emitted by different regions were 148 \ncomputed ( Figure 1C). Finally, we applied our method to data collected from AD patients and 149 \ncontrol subjects at Xuanwu Hospital ( Figure 1D). We compared IRI between the AD and control 150 \ngroups and examined the association between the oscillation patterns of inter -regional interactions 151 \nand Mini-Mental State Examination (MMSE) scores.  152 \nModel Validation and Prediction Accuracy Analysis 153 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n8 \n \nTo validate the effectiveness of the methods employed in this study, we constructed 154 \nindividualized cortical neural activity prediction models based on IN for each subject, with data 155 \npartitioned into training and test sets chronologically, assigning the earlier time points to the training 156 \nset and the latter time points to the test . Model performance was evaluated using two metrics on the 157 \ntest set: the MAE between predicted and actual signals, and the correlation between FC matrices derived 158 \nfrom the predicted and actual signals. The raw BOLD signals were z-scored and the average whole-brain 159 \nMAE for the predicted data was 0.04. These results indicate that the model can accurately predict 160 \ndynamic fluctuations across the entire brain. Since each prediction sequence spans 10 TRs, we computed 161 \nthe functional connectivity of the predicted signals using two approaches: a segmented prediction method 162 \nand a continuous prediction method. The segmented method assesses the model’s ability to reproduce 163 \nFC over short timescales, while the continuous method evaluates performance in long -term prediction 164 \nscenarios, where error accumulation may occur (see Methods for details) . Both approaches partially 165 \nrecapitulated the structure of the actual functional connectivity (see Figure 2 B, Figure  S1). The 166 \ncorrelation coefficient between the FC derived from segmented predictions and the true FC is 0.9745 ± 167 \n0.0067, while the correlation for the continuous prediction method is lower at 0.4957 ± 0.0897.  168 \nWe found that predictive accuracy (MAE) varies across brain regions (Figure 2A). The frontal 169 \nlobe yields the best  predictions and the  visual area yields the poorest. We hypothesized that 170 \ndifferential prediction performance across brain regions reflects their distinct neural variability. To 171 \ntest this, we examined the relationship between predicted MAE and neural variability . We defined 172 \nneural variability as the standard deviation (SD) of regional signals(41). Our analysis revealed that, 173 \nat both the individual and regional levels, the model-predicted MAE was positively correlated with 174 \nneural variability, supporting the hypothesis that a higher MAE reflects more complex and flexible 175 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n9 \n \nregional activity (Figure 2C, D), therefore, harder to predict. 176 \nTo further investigate the underlying factors affecting prediction accuracy across brain regions, 177 \nwe correlated the MAE distribution with a diverse set of cortical maps . We hypothesized that 178 \nregional activity could be influenced by both the region's microstructure and mesoscopic functional 179 \nproperties. Therefore, we conducted correlation analyses between the region -wise average MAE 180 \nmaps derived from our model and various maps from neuromaps(42), including functional gradients, 181 \ncoarse-grained structural features, microstructural receptor distributions, and finer -grained gene 182 \ngradients. All correlations were assessed using permutation tests and corrected for multiple 183 \ncomparisons using the false discovery rate (FDR).  Notably, we found a statistically significant but 184 \nmodest negative association between model- predicted regional MAE and the mean distribution of 185 \nnorepinephrine transporters (NET) (Figure 2 E), as observed with Methylreboxetine targets (43). 186 \nThese receptors modulate presynaptic sodium uptake, thereby terminating neural signaling(44) . 187 \nThis finding may suggest that regions with a higher norepinephrine transporters  density leads to 188 \ngreater inhibition of noradrenergic signal transmission , which give rise to more stable signals and 189 \nenabling more accurate predictions by the model. 190 \n 191 \nInter-regional interaction information and its characteristics 192 \nThe advantage of IN model is the ability to capture information transfer between distinct brain 193 \nregions. In this study, we derived the IRI from functional signals, utilizing the extraction method 194 \ndescribed in the Methods section. To address the 30-dimensional interaction messages, we reduced 195 \nthe data by selecting the first principal component as the IRI (Figure S2), resulting in a time-varying 196 \nIRI sequence for each inter -regional connection ( Figure 3A). Also, we aggregated the interaction 197 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n10 \n \nmessages originating from each region and similarly selected the first principal component of this 198 \nsum as the IRI sent by region (RS-IRI). We used the SD of the IRI as a measure of the flexibility of 199 \ninformation transfer between brain regions. A positive correlation was observed between this 200 \nflexibility and the length of the inter -regional connection (Figure 3B), suggesting that long -range 201 \nconnections may exhibit a greater capacity for adaptive information transfer. This increased capacity 202 \nmay be due to their exposure to more dynamic transmission conte xts, the involvement of more 203 \ncomplex signals, and the need for larger signal fluctuations to ensure accurate transmission. 204 \nTo investigate whether different functional sub- networks send information with distinct 205 \nstrengths, we plotted boxplots of emission strength across sub-networks (Figure 3C). We found that 206 \nas hierarchical level increases, the distribution of emitted information strength exhibits lower 207 \nvariance. This centralization may arise from higher-order regions, such as the default mode network 208 \n(DMN), exhibiting a relatively lower excitation–inhibition ratio, which leads to stronger inhibitory 209 \nsignals and consequently more stable information emission (45,46). Finally, we quantified the 210 \nvariance of RS-IRI across brain regions, finding that visual regions exhibited the greatest flexibility 211 \nin emitting interaction information ( Figure 3D). This may reflect the highly diverse information 212 \ngenerated and output by these regions. 213 \nApplication in Alzheimer's diseases  214 \nTo investigate whether neurodegenerative pathology induces alterations in the dynamic interactions 215 \namong cortical regions, we applied our computational model to data from AD patients. Our analyses 216 \nrevealed differences in the mean predict ed MAE between the AD and NC groups  but did not show 217 \nsignificant group differences (Figure 4A), likely due to the limited sample size. Before computing the 218 \nIRI, we compared the SD of interaction messages across each dimension between the AD and NC groups, 219 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n11 \n \nwhich we used as a proxy for the amount of information carried by the IRI . We found that, in most 220 \ndimensions, the between-group differences were significant, while non-significant dimensions tended to 221 \nhave lower SD, suggesting that these dimensions may carry less informational content (Figure 4B). The 222 \nSD of interaction messages in the NC group was significantly higher than in the AD group, indicating 223 \ngreater flexibility in inter-regional interactions for the NC group. This may refle ct that the AD patients 224 \nexperience dysfunction in inter-regional information transfer with less informative content. 225 \nWe computed the IRI for each subject in both the AD and NC groups. Our results indicated that the 226 \nAD and NC groups differ in their IRIs, wi th the AD group showing more high -frequency components 227 \n(Figure 4C). To examine whether the spectral content of the IRI could distinguish AD patients from 228 \ncontrols, we performed Fast Fourier Transform (FFT) on the IRI signals for each edge, obtaining their 229 \nspectral profiles. We then conducted t- tests on the amplitude at each frequency band, applying FDR 230 \ncorrection, the results see supplementary table. Results confirmed our hypothesis, revealing significant 231 \ndifferences in IRI predominantly in the high-frequency range, where the AD group exhibited markedly 232 \nincreased IRI on connecting edges ( Figure 4 D). This attenuation of high -frequency inter -regional 233 \ninformation exchange suggests that cognitive deficits in AD may be associated with increased high-234 \nfrequency noise contamination in neural interactions. We analyzed the connections showing significant 235 \ndifferences in IRI across different frequency bands and found that the majority of IRI with significant 236 \ndifferences were located in the information flows of intra- or inter- higher-order regions, particularly 237 \ninvolving the frontoparietal network and the ventral attention network (Figure 4D).  238 \nWe further investigated the relationship between IRI across different frequency bands and cognitive 239 \nimpairment in AD patients, we correlated the amplitude values of each edge within each frequency band 240 \nwith the MMSE scores in the AD group. Significance was evaluated using permutation testing with FDR 241 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n12 \n \ncorrection. Ultimately, we identified six edges where amplitude of communication in specific frequency 242 \nbands significantly correlated with MMSE scores , predominantly distributed in the medial and lateral 243 \nprefrontal cortices and the c ingulate cortex (Figure 5). All these regions are situated within the fronto -244 \nparietal network, default mode network, and ventral attention network, indicating that IRI within and 245 \nbetween these networks may reflect cognitive performance as measured by the MMSE in AD patients.  246 \nDiscussion 247 \nOur study developed a computational model based on IN to predict BOLD signals across the entire 248 \ncortical surface. This model computes interregional interaction information constrained by structural 249 \nconnectivity and predicts dynamic BOLD changes in brain regions through their inter -regional 250 \ninteractions. Validation using MAE  and FC correlation demonstrated that this approach effectively 251 \nsimulates dynamic variations in cortical signals. By extracting inter -regional interaction information at 252 \nthe individual level from the model and applying it to a dataset of AD patients, we found that the model 253 \ncaptures distinct oscillatory interaction patterns between brain regions in AD patients compared to NC. 254 \nThe constructed model offers a novel method for analyzing brain dynamics, and the derived interaction 255 \nmetrics provide new perspectives for disease research. 256 \nThe rationale for using GNN in brain dynamical modeling 257 \nGNN represent a deep learning framework adept at analyzing network -structured data. They are 258 \nextensively applied across various domains, including power grids(47), transportation networks(48), and 259 \nfinancial systems (49). Recently, some researchers have begun employing GNN for modeling neural 260 \nsystems(50,51) due to their superior capacity for processing and analyzing network-structured data. Most 261 \nGNN utilize graph convolution modules(52–54), while others use message-passing mechanisms, which, 262 \nalthough computationally intensive, can capture interactions between pairs of nodes, such as gravitational 263 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n13 \n \ninteractions among planets (39) and forces between high -energy particles (55). This message -passing 264 \napproach emphasizes connections but requires greater computational capacity. To enhance the reliability 265 \nof interaction information and minimize interference from multiple computational modules, this study 266 \nadopts a streamlined model construction approach: both the interaction information generation module 267 \nand the node state generation module are constructed using simple multilayer perceptron (MLP), without 268 \nintegrating additional computational components. 269 \nInspired by these studies, we developed an IN model capable of predicting cortical BOLD signals 270 \nby leveraging dynamic interregional interactions. The model achieved an average MAE of 0.04 in 271 \npredicting overall fMRI signals. This results represent an improvement over the diffusion convolution 272 \nrecurrent neural network (DCRNN) and graph WaveNet (GWN) used in prior research (53), 273 \ndemonstrating the model’s effectiveness in capturing dynamic fluctuations in cortical BOLD signals. 274 \nThe segmented prediction approach facilitated partial reproduction of FC structures (see Figure 2C, 275 \nD), with a correlation coefficient of 0.9745 to actual FC , slightly higher than the 0.95 reported for 276 \nDCRNN(53). However, due to different  computational methodologies, these values are not directly 277 \ncomparable. Consequently, the correlation between sequentially predicted FC and true FC, affected by 278 \naccumulated errors, was lower at 0.4957. This result, like other data -driven models (30), is modest 279 \ncompared to most traditional dynamical models, which typically begin with empirical equatio ns and 280 \nstructured networks and iteratively tune parameters to enhance the similarity between generated and 281 \nactual FC(27,56,57). Improving FC correlation in generated sequences is plausible since these sequences 282 \nneed only replicate certain structural aspects of FC rather than its full range of features. Our method 283 \noptimized the model by fitting it to real sequences, minimizing the discrepancy between generated and 284 \nactual data via the loss function. Despite the model's underwhelming performance in  continuous FC 285 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n14 \n \nprediction, which indicates a deficiency in capturing long -range temporal dependencies,  it enables 286 \nderived inter-regional interactions to inform subsequent predictions of cortical dynamics. Ideally, if the 287 \nmodel could perfectly simulate whole -brain dynamics, the generated sequences should exhibit a 288 \ncomplete FC structure. Unfortunately, the current model appears focused primarily on input and target 289 \n10 TR data, aligning with our design objectives, while neglecting long-range influences. This limitation 290 \nis understandable, as such constraints were not explicitly incorporated into the model. Prior studies have 291 \nsuggested that long-range BOLD signal simulations driven by data depend on noise(30). Since our model 292 \nexcluded noise, long-range predictions tend to converge toward attractors over time. We believe, however, 293 \nthat introducing noise could undermine the reliability of the IRI metrics, leading us to incorporate only 294 \nregularization-based noise introduction, avoiding explicit noise-driven modeling. 295 \nUnderstanding and application of IRI  296 \nUsing our model, we extracted IRI and related it to the concept of information flow. Historically, 297 \ninformation flow has  been described as the directionality and strength of information transfer among 298 \ndifferent brain regions(58,59). This definition, in conjunction with effective connectivity, bears similarity 299 \nto approaches such as dynamic causal modeling(60) . Recent advancements in DTI have provided a 300 \nstructural basis for information flow(61,62). However, characterizing information transfer directionality 301 \nin a purely static manner is insufficient. To fully under stand information processing in the brain , 302 \nincluding perception, transduction, coordination, storage, and generation, an analysis of dynamic 303 \nfluctuations is imperative, as these processes reflect continuous changes in the brain's underlying states, 304 \neven under constant environmental conditions(63,64). These dynamics evolve over time and are rooted 305 \nin the brain’s structural connectivity(65) . Therefore, when constructing a comprehensive bra in 306 \ncommunication model, these factors must be duly considered(66,67) . In this study, the whole -brain 307 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n15 \n \ndynamical model based on GNN gener ates dynamic interregional information transfer by integrating 308 \nBOLD signals from different regions and their structural connectivity, representing these processes as a 309 \ntemporal sequence. This sequence is akin to edge Time Series (eTS), originally defined as a co -310 \nfluctuation time series, the pointwise product of z -scored signals from two brain regions at successive 311 \ntime points(68). It provides a mechanism for deconstructing FC into temporal sequences. A connection-312 \ncentric measure called edge functional connectivity (edge FC or eFC) captures the dynamic expression 313 \nof brain functional systems through fine -scale edge time series analysis (69,70). However, unlike eTS, 314 \nthe IRI produced from the IN model is not reconstructed from static FC, thereby avoiding concerns 315 \nregarding its \"dynamic\" nature (71–73). Crucially, the IRI is grounded in the underlying structural 316 \nconnectivity derived from DTI, rather than being inferred solely from functional signals. Essentially, IRI 317 \noffers a method for deriving fluctuations in connection edges directly from dynamic variations in fMRI 318 \nsignals, and these fluctuations are both structure-based and biologically grounded. 319 \nWe observed a positive correlation between the variability of IRI and the length of connections. 320 \nLong-range connections are known to play a crucial role in brain activity (74). Although some studies 321 \nsuggest that brain geometry alone can reconstruct functional connectivity(75), other research , both 322 \nexperimental and clinical, demonstrates that sparse long-range connections are vital for the complexity 323 \nof brain functional dynamics (76–78). Our findings support this notion, indicating that long- range 324 \nconnections are essential in whole -brain modeling, with their significance increasing with connection 325 \nlength. A dditionally, some studies report that distant projections are more strongly influenced by 326 \nelectrical stimulation(79), which may explain our results: greater IRI variability could correspond to a 327 \nhigher information -carrying capacity, suggesting that long -range connections transmit more potent 328 \nelectrical stimuli. The average strength of IRI emitted by different brain regions exhibits a gradient 329 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n16 \n \ndistribution across various functional subnetworks, indicating that higher -order brain regions generate 330 \nthe strongest IRI during resting-state conditions. This suggests that these regions are more likely to play 331 \na dominant role in resting-state activity.  332 \nIn the analysis of AD patients, we noticed that the IRI in the AD group contained more high -333 \nfrequency components, yet the standard deviation (SD) of the interaction messages was significantly 334 \nlower. This suggests diminished flexibility in information transmission coupled with increased erroneous 335 \nnoise, which reduced the proportion of meaningful content within the transmitted signals.  We observed 336 \nsignificant differences in the IRI within the 0.4– 0.5 Hz frequency band compared to NC. These 337 \noscillatory pattern variations have been documented in EEG studies (80). Unlike previous research that 338 \nfocused on signals from individual brain regions, our study employs IRI; since IRI is inherently related 339 \nto the underlying regional signals, the findings align with earlier research indicating abnormal neuronal 340 \nfiring activity in the theta frequency band in AD patients(81). Due to the limited temporal resolution of 341 \nfMRI data, we cannot capture information in higher frequency ranges. Nevertheless, leveraging the high 342 \nspatial resolution of fMRI allows us to analyze how oscillatory interaction frequencies between brain 343 \nregions relate to cognitive scores and to identify specific connection sites involved. We identified six 344 \nconnections where IRI significantly correlates with M MSE scores in AD patients, predominantly 345 \ndistributed in the medial and lateral prefrontal cortices and the cingulate cortex . Notably, four of these 346 \nlinks connect the DMN to other networks. These findings support prior research on functional 347 \nconnectivity alterations in AD patients (82), reinforcing the notion that the DMN exhibits pathological 348 \nchanges in AD, subsequently affecting other regions involved in higher cognitive functions via 349 \ninterregional interactions. 350 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n17 \n \nLimitations 351 \nFirst, this study employs GNN to predict discretized fMRI signals . However, it does not construct 352 \ncontinuous dynamic models akin to differential equations. Future research incorporating mechanistic 353 \napproaches from machine learning (83) could facilitate the development of brain dynamics models 354 \ncapable of continuous prediction.  Second, the structural connectivity in this study was based on data 355 \nobtained through DTI tractography for model construction. However, DTI imaging may have accuracy 356 \nlimitations and often overlooks non -long-range synaptic transmissions between brain regions (e.g., 357 \nadjacency ef fects). The brain’s dynamic behavior may not solely depend on network -like structural 358 \nconnectivity(84); some studies suggest that brain dynamics could also arise from geometric 359 \nmorphology(75). Integrating approaches such as geodesic distance (85) and cellular architecture 360 \nsimilarity networks (86) can complement these various connection s. Employing heterogeneous GNN 361 \nmethods(87) may aid in constructing such multifaceted models. Third, current models are primarily data-362 \ndriven at a macroscopic scale and neglect microstructural elements such as neurons. They also do not 363 \nincorporate task-driven models at the phenotypic cognitive level. Future work should aim to integrate 364 \ntask-based approaches, developing multimodal, multiscale models based on microscopic priors, aligning 365 \nwith the goal of multiscale brain modeling(88). 366 \n 367 \nMethods 368 \nParticipants 369 \nThis study utilizes two batches of data, obtained from the Human Connectome Project (HCP) by 370 \nthe National Institutes of Health (NIH) (89) and from the Neurology Department at Xuanwu Hospital, 371 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n18 \n \nCapital Medical University in China.  Following quality control procedures based on head motion and 372 \nthe length of the remaining time series, a total of 148 participants from the HCP dataset were retained, 373 \nincluding 72 males and 76 females, aged between 22 and 35 years.  In addition, we enrolled 41 patients 374 \ndiagnosed with Alzheimer's disease (AD) from the memory clinic of the Neurology Department at 375 \nXuanwu Hospital, Capital Medical University (CMU) in China. We also recruited 42 healthy individuals 376 \nas normal controls from  local communities in Beijing, China. This study obtained approval from the 377 \nMedical Research Ethics Committee at Xuanwu Hospital, and all participants provided written informed 378 \nconsent. Standard clinical assessments were conducted on all participants, whic h included a thorough 379 \nmedical history investigation, neurological examination, and neuropsychological tests. The cognitive 380 \ntests administered encompassed the Montreal Cognitive Assessment (MoCA, Beijing version) (90), 381 \nAuditory Verbal Learning Test (A VLT), Clinical Dementia Rating (CDR) (91), Mini -Mental State 382 \nExamination (MMSE), Hamilton Depression Rating Scale (HAMD), Activities of Daily Living (ADL) 383 \nscale, Hachinski Ischemic Scale, and the Center for Epidemiologic Studies Depression scale (92). The 384 \npatients with AD were diagnosed based on the criteria of the National Institute of Aging -Alzheimer’s 385 \nAssociation (NIA -AA) for clinically probable AD (93). After data preprocessing, the final sample 386 \ncomprised 34 healthy control individuals and 23 AD patients. The age range of the participants was 387 \nbetween 53 and 81 years. Among the AD group, there were 14 males and 9 females, while the contr ol 388 \ngroup consisted of 21 males and 13 females. 389 \nData acquisition 390 \nThe HCP dataset comprises resting -state functional magnetic resonance imaging (rs -fMRI) and 391 \ndiffusion magnetic resonance imaging (dMRI) data. Each participant in the HCP dataset underwent two 392 \n15-minute resting-state fMRI scans at different time points, acquired from two directions. This resulted 393 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n19 \n \nin a total of 60 minutes of rs -fMRI data, comprising 4800 repetitions with a Time Repetition (TR) of 394 \n720ms. The scans were performed on a Siemens Skyra  scanner with a 3T field strength. This study 395 \nutilizes two batches of data, obtained from the Human Connectome Project (HCP) by the National 396 \nInstitutes of Health (NIH)(89) and from the Neurology Department at Xuanwu Hospital, Capital Medical 397 \nUniversity in China. The HCP dataset comprises rs -fMRI and dMRI data. Each participant in the HCP 398 \ndataset underwent two 15-minute rs fMRI scans at different time points, acquired from two directions. 399 \nThis resulted in a total of 60 minutes of rs-fMRI data, comprising 4800 repetitions with a Time Repetition 400 \n(TR) of 720ms. The scans were performed on a Siemens Skyra scanner with a 3T field strength. 401 \nThe data from the Neurology Department at Xuanwu Hospital, Capital Medical University (CMU), 402 \ncomprises rs-fMRI and DTIdata. All images were acquired on 3.0 T Siemens system (Magnetom Trio 403 \nTim; Erlangen, Germany) at the Department of Radiology, Xuanwu Hospital, Capital Medical University, 404 \nBeijing, China. T1-weighted images were acquired using a magnetization prepared rapid gradient echo 405 \n(MPRAGE) sequence (TR = 1900 ms; TE = 2.2 ms; TI = 900 ms; flip angle = 9◦;FOV= 224 mm × 256 406 \nmm; matrix size = 448 × 512; number of slices = 176; slice thickness = 1 mm). Functional images were 407 \nacquired axially using a gradient-echo EPI sequence (TR = 2000 ms; TE = 40 ms; flip angle = 90◦ ;FOV= 408 \n240 mm × 240 mm; matrix size =64 × 64; number of sections = 28; section thickness = 4 mm; voxel size 409 \n= 3.75 × 3.75 × 4mm3;gap= 1 mm; volume number = 239). DTI images were collected axially by using 410 \na single-shot echo-planar sequence (repetition time (msec)/echo time (msec), 11000/98; flip angle, 90◦; 411 \nfield of view, 256 × 232 mm2; 128 × 116 matrix; 60 sections; section thickness, 2 mm; voxel size, 2 × 2 412 \n× 2 mm3; 30 gradient directions with b value of 1000 sec/mm2 and one image with a b value of 0 413 \nsec/mm2; and three averages). 414 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n20 \n \nData preprocessing 415 \nFor the HCP dataset , an affine transformation was initially applied to register individual dMRI 416 \nimages with the T1-weighted image. Then, the structural image of each individual was registered to the 417 \nICBM152 template(94), yielding an inverse warping transformation from the standard space to the dMRI 418 \nspace. The HCP MMP 1.0 atlas (40) was then mapped onto the sample space using this inverse 419 \ntransformation. This division divided the entire brain into 360 brain regions, with 180 regions per 420 \nhemisphere. Fiber tractography was subsequently performed using DSI -Studio(95). By calculating the 421 \neigenvalues and eigenvectors of water molecules in three directions, fiber tracts wer e traced. Two 422 \nweighted matrices, the connection density matrix and the connection length matrix, were constructed 423 \nbased on the fiber tracts between two nodes.  424 \nRegarding fMRI data processing, the HCP -pipeline was initially applied for minimal 425 \npreprocessing(96). Subsequently, a high-pass filter with FWHM greater than 2000s was applied to the 426 \nfMRI signals and the ICA-FIX(97,98) method was then employed to remove noise components from the 427 \nfMRI signals, followed by regression of the data using the global signal as a regressor. Finally, a bandpass 428 \nfilter ranging from 0.009 to 0.08 Hz was applied to eliminate most of the noise. After post -processing, 429 \nthe entire cerebral cortex was segmented according to the HCP MMP 1.0 atlas( 40). The average fMRI 430 \nsignal within each brain region was calculated, obtaining fMRI signal values for the 360 brain regions. 431 \nIncomplete data were discarded, and subjects with head motion exceeding 0.25 were excluded. Among 432 \nthe remaining subjects, time points with head motion exceeding 0.25 were removed, and the data were 433 \ndivided into non-uniform intervals. Each interval overlapped by grouping them in sets of 20 time points, 434 \nwhere the first ten time points represented the input data, and the latter ten t ime points represented the 435 \ntrue values of the output data. If an interval contained fewer than 20 time points, it was discarded. The 436 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n21 \n \ndata from individuals with input-output groupings greater than 2000 were retained, resulting in a total of 437 \n148 participants, including 72 males and 76 females, with ages ranging from 22 to 35 years.  438 \nAs for t he data from the Neurology Department at Xuanwu Hospital we utilized the MRTrix 3.0 439 \npipeline(99) for DTI preprocessing. Firstly, an affine transformation was applied to register individual 440 \nDTI images with the T1 -weighted image. Subsequently, the structural images of each individual were 441 \nregistered to the ICBM152 template(94) . Computing the eigenvalues and eigenvectors of water 442 \nmolecules in the brain along three directions to trace the fiber and obtained connection probabilities. The 443 \nconnection probabilities between two brain regions were summed based on the HCP MMP 1.0 atlas(40), 444 \nresulting in a connection probability-weighted structural connectivity matrix (SC). 445 \nWe utilized the fMRIPrep 20.0.7 pipeline (100) for the preprocessing of fMRI data. The 446 \npreprocessing steps for the T1- weighted images included intensity non- uniformity correction, skull 447 \nstripping, spatial normalization to the standard space (MNI152NLin6Asym), brain tissue segmentation, 448 \nand cortical surface reconstruction. The preprocessing steps for the rs-fMRI data involved removing the 449 \nfirst five time points, motion correction, slice-timing correction, and co-registration to the corresponding 450 \nT1-weighted images using boundary-based registration. Subsequently, we employed spatial smoothing 451 \nusing an isotropic Gaussian kernel with a full width at half maximum (FWHM) of 6 mm. In the denoising 452 \nphase, we performed automatic removal of motion artifacts using ICA -based Automatic Removal Of 453 \nMotion Artifacts (AROMA)(101), a 24-parameter model, and linear regression, which included signals 454 \nfrom the mean white matter and cerebral spinal fluid (102). This was followed by the application of a 455 \nhigh-pass filter using a discrete cosine filter with a cutoff period of 128 s. After processing, the whole-456 \nbrain cortex was parcellated according to the HCP MMP 1.0 atlas(40) and the average fMRI signal within 457 \neach brain region was calculated to obtain signal values for 360 brain regions. After excluding the images 458 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n22 \n \nwith significant head motion (head motion exceeding 0.5), the final sample comprised 34 healthy control 459 \nindividuals and 23 AD patients. The age range of the participants was between 53 and 81 years. Among 460 \nthe AD group, there were 14 males and 9 females, while the control group consisted of 21 males and 13 461 \nfemales. 462 \nIN models construction 463 \nThe model can be considered a hidden function 𝐹𝐹(𝑥𝑥), denoted as 𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎(𝑥𝑥), and its overall operation 464 \nprocess can be represented by an equation. 465 \n�𝑋𝑋1, 𝑋𝑋2, … , 𝑋𝑋𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜� = 𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎��𝑋𝑋1, 𝑋𝑋2, … , 𝑋𝑋𝑇𝑇𝑖𝑖𝑖𝑖�; 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺ℎ� (1) 466 \nIn which 𝑋𝑋𝑜𝑜𝑜𝑜𝑜𝑜 represents the predicted fMRI signal, expressed as a 360 -dimensional vector, with 467 \nthe subscript number indicating the number of time points. This study uses fMRI signals from 10 time 468 \npoints as input, hence 𝑇𝑇= 10. 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺ℎ denotes the whole-brain network, which is represented using a 469 \nstructural connectivity matrix derived from dMRI tracking. 470 \nThe process of information interaction includes two parts: the transmission and reception of 471 \ninformation. Based on this idea, 𝐹𝐹(𝑥𝑥)can be decomposed into two functions: the information interaction 472 \nfunction, 𝐼𝐼(𝑥𝑥), and the state change function, 𝑅𝑅(𝑥𝑥). This model can be simplified to the level of brain 473 \nregions. Information is transmitted between brain regions through the interaction function 𝐼𝐼(𝑥𝑥) , as 474 \nshown in equation (2). 475 \n𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗= 𝐼𝐼��𝑥𝑥𝑖𝑖\n1, 𝑥𝑥𝑖𝑖\n2, … , 𝑥𝑥𝑖𝑖\n𝑇𝑇𝑖𝑖𝑖𝑖�, �𝑥𝑥𝑗𝑗\n1, 𝑥𝑥𝑗𝑗\n2, … , 𝑥𝑥𝑗𝑗\n𝑇𝑇𝑖𝑖𝑖𝑖�,𝐶𝐶𝑖𝑖𝑗𝑗� (2) 476 \n𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗  represents the interaction between brain region 𝑖𝑖  and brain region 𝑗𝑗 , with 𝐶𝐶𝑖𝑖𝑗𝑗  being the 477 \ncharacteristic of the connection between brain region 𝑖𝑖  and brain region 𝑗𝑗 , which is estimated with 478 \nstructural connectivity matrices generated from structural connectivity (SC) and global parameter 𝐺𝐺, 479 \ndefined as 𝐶𝐶𝑖𝑖𝑗𝑗= 𝑆𝑆 𝐶𝐶𝑖𝑖𝑗𝑗× 𝐺𝐺 . 𝑥𝑥𝑖𝑖\n1, 𝑥𝑥𝑖𝑖\n2, … , 𝑥𝑥𝑖𝑖\n𝑇𝑇𝑖𝑖𝑖𝑖  represents the input fMRI signal from region 𝑖𝑖  in time 480 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n23 \n \n𝑇𝑇𝑖𝑖𝑖𝑖= 10. Assuming that the information transfer between brain regions is additive , meaning that for 481 \nbrain region 𝑖𝑖, the influences from different brain regions are directly summated, then the change in state 482 \nof a brain region can also be expressed in a simplified form through a state change function, equation (3). 483 \n𝕏𝕏𝑖𝑖= 𝑁𝑁 ��𝑥𝑥𝑖𝑖\n1, 𝑥𝑥𝑖𝑖\n2, … , 𝑥𝑥𝑖𝑖\n𝑇𝑇𝑖𝑖𝑖𝑖�, � 𝐼𝐼 𝑅𝑅 𝐼𝐼𝐼𝐼𝑖𝑖,𝑗𝑗\n𝑗𝑗\n� (3) 484 \nIn which 𝕏𝕏𝑖𝑖= [𝑥𝑥𝑖𝑖\n1, 𝑥𝑥𝑖𝑖\n2, … , 𝑥𝑥𝑖𝑖\n𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜]  represents the predicted fMRI signal from region 𝑖𝑖  in time 485 \n𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜= 10. To minimize the complexity of the model and enhance its interpretability, this study utilizes 486 \nthe MLP to construct functions 𝐼𝐼(𝑥𝑥) and 𝑅𝑅(𝑥𝑥), that is, by using simple linear layers and activation 487 \nfunctions for construction. The method of constructing 𝐼𝐼(𝑥𝑥) involves multiplying the characteristics of 488 \nthe connecting edges directly by the output of the multilayer perceptron, allowing the characteristics of 489 \nthe connecting edges to influence the information interaction between brain regions, which can be 490 \nrepresented by the equation (4) 491 \n𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗= 𝐼𝐼𝑚𝑚𝑚𝑚��𝑥𝑥𝑖𝑖\n1, 𝑥𝑥𝑖𝑖\n2, … , 𝑥𝑥𝑖𝑖\n𝑇𝑇𝑖𝑖𝑖𝑖�, �𝑥𝑥𝑗𝑗\n1, 𝑥𝑥𝑗𝑗\n2, … , 𝑥𝑥𝑗𝑗\n𝑇𝑇𝑖𝑖𝑖𝑖�� × 𝐶𝐶𝑖𝑖𝑗𝑗 (4) 492 \nIn which 𝐼𝐼𝑚𝑚𝑚𝑚 represents the MLP for 𝐼𝐼(𝑥𝑥). 493 \nThe model inputs are the values of whole -brain fMRI signals for 10 time points, with the output 494 \nbeing the predicted values of whole -brain fMRI signals for the next 10 time points. For each sequence 495 \nof an individual's scan, input values are constructed as 𝑖𝑖𝑛𝑛 𝐺𝐺𝑛𝑛𝑛𝑛= 𝕏𝕏𝑖𝑖𝑖𝑖,𝑘𝑘 𝑓𝑓𝑓𝑓 𝐺𝐺  𝑘𝑘= [0,1,2, … , 𝑘𝑘𝑚𝑚𝑎𝑎𝑚𝑚], and 496 \ntruth values as 𝑛𝑛 𝐺𝐺𝑛𝑛𝑛𝑛ℎ = 𝕏𝕏𝑜𝑜𝑡𝑡 𝑜𝑜𝑡𝑡, 𝑘𝑘  𝑓𝑓𝑓𝑓 𝐺𝐺  𝑘𝑘= [10,11,12 , … , 𝑘𝑘𝑚𝑚𝑎𝑎𝑚𝑚]. 𝕏𝕏𝑘𝑘 represente the input fMRI signal in 497 \n10 time points, which means a 10×360 dimension vector. Therefore, the number of time points for both 498 \ninput and truth values remain the same, equal to the number of input-output pairs 𝑘𝑘𝑚𝑚𝑎𝑎𝑚𝑚. Data from each 499 \nindividual's four fMRI scan sequences are constructed in this manner, forming a dataset for each 500 \nindividual. 501 \nT\no illustrate the model’s prediction of whole -brain states, we used a three- node system as an 502 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n24 \n \nexample (Figure 6 ). For each pair of nodes  (brain regions), the model takes as input the 10- TR 503 \nfMRI time series from both regions and their s tructural connectivity, computing the interaction 504 \ninformation via 𝐼𝐼(𝑥𝑥). Using this interaction information and the original node states, the predicted 505 \nstate for the next time point in each region is computed with 𝑅𝑅(𝑥𝑥). The predicted states are then 506 \ncompared to the actual fMRI values for the subsequent 10 TRs using the Huber loss, which is 507 \nbackpropagated to update the model parameters.  508 \nThe dataset is split into training, validation, and test sets in an 8:1:1 ratio, with the initial 90% of 509 \nthe data serving as the training and validation sets and the final 10% designated as the test set. During 510 \ntraining, the data for both the training and validation sets are randomly shuffled and re-partitioned at each 511 \nepoch. We use torch_geometric to realize the model and  load train data and the optimizer employed is 512 \nAdam. The loss function utilizes Huber Loss (103) incorporating L1 regularization, which is a loss 513 \nfunction that performs well across a variety of fitting tasks(104). The weight of regularization is 1e-4.The 514 \ndataset is split into training, validation, and test sets in an 8:1:1 ratio, with the initial 90% of the data 515 \nserving as the training and validation sets and the final 10% designated as the test set. During training, 516 \nthe data for both the training and validation sets are randomly shuffled and re-partitioned at each epoch. 517 \nWe use torch_geometric to realize the model and load train data and the optimizer employed is Adam. 518 \nThe loss function utilizes Huber Loss(103) incorporating L1 regularization, which is a loss function that 519 \nperforms well across a variety of fitting tasks(104). The weight of regularization is 1e-4. 520 \nBefore training, we first randomly select a single individual for model hyperparameter optimization, 521 \nand this individual does not participate in subse quent training and analysis. During the hyperparameter 522 \ntuning process, global parameters are set based on previous research experience, with a value of 𝐺𝐺=523 \n0.6 . Grid search is used to optimize model parameters, including the dimension of information 524 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n25 \n \ntransferred between two brain regions, the output dimension of 𝐼𝐼(𝑥𝑥) , 𝐼𝐼 𝑖𝑖𝐷𝐷𝐼𝐼𝐼𝐼𝐼𝐼∈ [20,30,50,200] , the 525 \nnumber of layers in 𝐼𝐼(𝑥𝑥), 𝐿𝐿𝐼𝐼∈ [2,3,4,5,6], the number of layers in 𝑅𝑅(𝑥𝑥), 𝐿𝐿𝐼𝐼∈ [2,3,4,5,6], learning 526 \nrate 𝐿𝐿 𝐺𝐺∈ [1 × 10−3, 5 × 10−4, 1 × 10−4, 5 × 10−5] , weight decay 𝑊𝑊𝑊𝑊∈ [1 × 10−6, 1 × 10−7, 1 ×527 \n10−8], and total training epochs 𝑒𝑒𝐺𝐺𝑓𝑓𝑒𝑒ℎ𝑠𝑠 ∈[50 ,100,300,400,1000,2000]. The model is selected based 528 \non the mean absolute error on the test set, with the final hyperparameters set as 𝐼𝐼 𝑖𝑖𝐷𝐷𝐼𝐼𝐼𝐼𝐼𝐼= 30, 𝐿𝐿𝐼𝐼= 5, 529 \n𝐿𝐿𝐼𝐼= 5 , 𝐿𝐿𝐺𝐺= 1 × 10−4 ， 𝑊𝑊𝑊𝑊= 1 × 10−8 . Taking both training effectiveness and time into 530 \nconsideration, the number of epochs is set to 100. 531 \nModel Validation 532 \nMean absolute error 533 \nThe mean absolute error (MAE) serves as a direct measure of the dis similarity between predicted 534 \nvalues and true values. Let the predicted value at time 𝑇𝑇 be denoted as 𝑋𝑋𝑇𝑇, and the true value as 𝑌𝑌𝑇𝑇, 535 \nthen 𝑋𝑋𝑇𝑇= [𝑥𝑥𝑇𝑇,1, 𝑥𝑥𝑇𝑇,2, … , 𝑥𝑥𝑇𝑇,𝑁𝑁] and 𝑌𝑌𝑇𝑇= [𝑦𝑦𝑇𝑇,1, 𝑦𝑦𝑇𝑇,2, … , 𝑦𝑦𝑇𝑇,𝑁𝑁], where 𝑁𝑁= 360 is the total number of 536 \nbrain regions, 𝑥𝑥𝑇𝑇,𝑖𝑖 represents the predicted fMRI signal value for brain region 𝑖𝑖 at time 𝑇𝑇 and 𝑦𝑦𝑇𝑇,𝑖𝑖 537 \nrepresents the true fMRI signal value for brain region 𝑖𝑖 at time 𝑇𝑇. The MAE is calculated by computing 538 \nthe absolute error across different brain regions and then taking the average of these absolute errors. The 539 \nspecific calculation process is defined by the following equation: 540 \n𝑀𝑀𝑀𝑀𝑀𝑀= 1\n10 � 1\n𝑁𝑁�� 𝑥𝑥𝑇𝑇,𝑖𝑖− 𝑦𝑦𝑇𝑇,𝑖𝑖�\n𝑁𝑁\n𝑖𝑖=1\n10\n𝑇𝑇=1\n(5) 541 \nThe above expression  represents the MAE for a single prediction result. To ensure more reliable 542 \noutcomes, we repeated the process 20 times on the test set, carrying out a total of 200 time points of 543 \nfMRI signal prediction tasks, and calculated the average MAE to evaluate the model's predictive 544 \nperformance, as showed in equation (6). 545 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n26 \n \n𝑀𝑀𝑀𝑀𝑀𝑀𝑎𝑎𝑎𝑎𝑎𝑎= 1\n𝐺𝐺� 1\n10 � 1\n𝑁𝑁�� 𝑥𝑥𝑇𝑇,𝑖𝑖− 𝑦𝑦𝑇𝑇,𝑖𝑖�\n𝑁𝑁\n𝑖𝑖=1\n10\n𝑇𝑇=1\n(6) 546 \nIn the above equation, 𝐺𝐺= 20  de notes the number of times the computation is repeated. To 547 \ncompare the differences in the fitting effects across various brain regions, this study calculated the 548 \naverage MAE for different brain regions, as shown in equation (7). 549 \n𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖= 1\n𝐺𝐺� 1\n10 �� 𝑥𝑥𝑇𝑇,𝑖𝑖− 𝑦𝑦𝑇𝑇,𝑖𝑖�\n10\n𝑇𝑇=1\n(7) 550 \nIn equation (7), 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖 represents the average MAE for the i-th brain region. 551 \nContinuous /segmented function connectivity 552 \nIn this study, functional connectivity (FC) is obtained by calculating the Pearson Correlation 553 \nCoefficient, whose formula is as follows: 554 \n𝐺𝐺𝑖𝑖,𝑗𝑗=\n∑ �𝑥𝑥𝑖𝑖, 𝑜𝑜− 𝑥𝑥𝚤𝚤� ��𝑥𝑥𝑗𝑗, 𝑜𝑜− 𝑥𝑥𝚥𝚥� �𝑖𝑖\n𝑜𝑜=1\n� ∑ �𝑥𝑥𝑖𝑖, 𝑜𝑜− 𝑥𝑥̅�\n2𝑖𝑖\n𝑜𝑜=1 � ∑ �𝑥𝑥𝑗𝑗, 𝑜𝑜− 𝑥𝑥𝚥𝚥� �\n2𝑖𝑖\n𝑜𝑜\n=1\n(8) 555 \nThe term 𝐺𝐺𝑖𝑖,𝑗𝑗 represents the correlation between the fMRI signal generated by brain region 𝑖𝑖 and 556 \nthat by brain region 𝑗𝑗, where 𝑥𝑥𝑖𝑖, 𝑜𝑜 denotes the fMRI signal value produced by brain region 𝑖𝑖 at time 557 \npoint 𝑛𝑛 ,  and 𝑥𝑥𝑗𝑗, 𝑜𝑜  denotes the fMRI signal value produced by brain region 𝑗𝑗  at time point 𝑛𝑛 .  The 558 \nvariable n represents the total number of time points used for the calculation. By performing the 559 \naforementioned operation between each pair of defined brain regions, the functional connectivity matrix 560 \nbetween the brain regions can be obtained. 561 \nTo obtain FC, this study employed two methods for generating the predicted sequences: continuous 562 \nprediction and segmented prediction. Continuous prediction refers to inputting a 10 TR (time resolution) 563 \nwindow, using the output as the next input to obtain the prediction result for the following time window, 564 \nand then connecting these predictions to form a complete fMRI sequence. Let 𝜒𝜒𝑖𝑖 represent the input 565 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n27 \n \nsequence, 𝜒𝜒𝑜𝑜𝑘𝑘  denote the output obtained from the k -th iteration, and 𝑆𝑆 𝑒𝑒𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝  signify the output 566 \nsequence; this process can be expressed by equation (9): 567 \n�\n𝜒𝜒𝑜𝑜1 = 𝐹𝐹(𝜒𝜒𝑖𝑖; 𝐺𝐺)\n𝜒𝜒𝑜𝑜𝑘𝑘+1= 𝐹𝐹�𝜒𝜒𝑜𝑜𝑘𝑘; 𝐺𝐺�   𝑓𝑓𝑓𝑓 𝐺𝐺  1 < 𝑘𝑘< 𝑇𝑇 −1\n𝑆𝑆\n𝑒𝑒𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝= 𝑒𝑒𝑓𝑓 𝑛𝑛𝑒𝑒𝐺𝐺𝑛𝑛𝑒𝑒𝑛𝑛𝐺𝐺𝑛𝑛𝑒𝑒� 𝜒𝜒𝑜𝑜𝑘𝑘   𝑓𝑓𝑓𝑓 𝐺𝐺  1 < 𝑘𝑘< 𝑇𝑇�  \n(9) 568 \nIn equation (9), 𝐹𝐹(𝑥𝑥) is the predictive model, 𝐺𝐺 is the brain network, 𝑇𝑇 is the number of cycles 569 \nset, which is 10 in this study, and concatenate is a function that joins sequences. For functional 570 \nconnectivity validation, 𝜒𝜒𝑖𝑖 is set to the first 10 TR time window from the test set. 571 \nSegmented prediction refers to dividing a continuous time series into small intervals of 10 TR time 572 \nwindows, inputting each interval into the model to obtain the corresponding prediction, and connecting 573 \nthe different interval predictions chronologically to form a complete fMRI predicted sequence. Let the 574 \nk-th interval be represented as 𝜒𝜒𝑖𝑖𝑘𝑘, then 𝜒𝜒𝑖𝑖𝑘𝑘= [𝑋𝑋10𝑘𝑘−9, 𝑋𝑋10𝑘𝑘−8, … , 𝑋𝑋10𝑘𝑘], where 𝑋𝑋𝑖𝑖 denotes the fMRI 575 \nsignal values for all brain regions corresponding to the i -th TR of the continuous time series. The 576 \nprediction process is specifically shown in equation (10): 577 \n�\n𝜒𝜒𝑜𝑜𝑘𝑘= 𝐹𝐹�𝜒𝜒𝑖𝑖𝑘𝑘; 𝐺𝐺�   𝑓𝑓𝑓𝑓 𝐺𝐺   1 < 𝑘𝑘< 𝑇𝑇\n𝑆𝑆\n𝑒𝑒𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝= 𝑒𝑒𝑓𝑓 𝑛𝑛𝑒𝑒𝐺𝐺𝑛𝑛𝑒𝑒𝑛𝑛𝐺𝐺𝑛𝑛𝑒𝑒� 𝜒𝜒𝑜𝑜𝑘𝑘   𝑓𝑓𝑓𝑓 𝐺𝐺  1 < 𝑘𝑘< 𝑇𝑇�\n(10) 578 \nFor this research, the chosen input is the continuous sequence before splitting the series that 579 \neliminates time points with head motion greater than 0.25. Starting from the 90th percentile position, a 580 \ntotal of 100 TRs of the fMRI sequence is selected, and it is split into 10 groups with every 10 TRs as one 581 \ngroup. The full sequence is thereby divided into 10 intervals, T=10. 582 \nThe predicted sequences obtained from the two methods mentioned above both utilize the Pearson 583 \ncorrelation method as outlined in equation (8) to calculate FC, which is then compared to the actual 584 \nfunctional connectivity matrix. The actual sequence used for calculating the true FC is the one 585 \ncorresponding to the prediction input values; that is, in continuous prediction, the actual sequence starts 586 \nfrom the 10 TR fMRI signal used as input and continues for a total of 100 TRs of fMRI sequence values, 587 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n28 \n \nwhereas in segmented prediction), the actual sequence is composed of the actual values corresponding 588 \nto each segment's output values. After obtaining the true FC and the predicted FC, the Pearson correlation 589 \ncoefficient is used to determine their correlation. The predicted FC is defined as 𝐹𝐹 𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝 and the actual 590 \nFC as 𝐹𝐹 𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ. For 𝑘𝑘 ∈[𝐺𝐺 𝐺𝐺𝑒𝑒𝑊𝑊, 𝑛𝑛 𝐺𝐺𝑛𝑛𝑛𝑛ℎ],  𝐹𝐹 𝐶𝐶𝑖𝑖,𝑗𝑗\n𝑘𝑘 denotes the element in the i-th row and j-th column of the 591 \nFC matrix, representing the functional connectivity of the fMRI signal between the i -th and j- th brain 592 \nregions. The PCCs (Pearson correlation coefficients) between the predicted and actual FC can  then be 593 \ndetermined by equation (11). 594 \n𝑃𝑃𝐶𝐶 𝐶𝐶𝑠𝑠=\n∑ �\n𝐹𝐹\n𝐶𝐶𝑖𝑖,𝑗𝑗\n𝑚𝑚\n𝑡𝑡𝑡𝑡\n𝑝𝑝− 𝐹𝐹𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝�����������𝐹𝐹𝐶𝐶𝑖𝑖,𝑗𝑗\n𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜ℎ − 𝐹𝐹𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜ℎ�����������𝑖𝑖, 𝑖𝑖\n𝑖𝑖=1,\n𝑗𝑗=1\n� ∑ �𝐹𝐹 𝐶𝐶𝑖𝑖,𝑗𝑗\n𝑚𝑚\n𝑡𝑡𝑡𝑡\n𝑝𝑝− 𝐹𝐹𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝����������\n2𝑖𝑖, 𝑖𝑖\n𝑖𝑖=1,\n𝑗𝑗=1 � ∑ �𝐹𝐹𝐶𝐶𝑖𝑖,𝑗𝑗\n𝑜𝑜𝑡𝑡𝑜𝑜\n𝑜𝑜ℎ − 𝐹𝐹𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ�����������\n2𝑖𝑖\n𝑖𝑖=1\n(11) 595 \nThe equation (11) specifies that 𝐹𝐹 𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝��������� and 𝐹𝐹 𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ���������� represent the global average values of the 596 \npredicted and actual FC matrices, respectively. 597 \nModel Analysis 598 \nInter-regional interaction information (IRI) 599 \nFollowing model training, initial input data for the testing set were used to generate t he model 600 \noutputs. As described in the Methods -Models section, input data segmented every 10 tr yield a 30-601 \ndimensional message. By employing overlapping segmentation, a total of 200 such segments (each 602 \ncomprising 10 tr) were inputted, resulting in message data with dimensions of 30 × 200 × 𝑁𝑁𝑠𝑠𝑜𝑜𝑠𝑠, 𝑡𝑡𝑝𝑝𝑎𝑎𝑡𝑡, 603 \nwhere 𝑁𝑁𝑠𝑠𝑜𝑜𝑠𝑠, 𝑡𝑡𝑝𝑝𝑎𝑎𝑡𝑡 indicates the total number of connectivity edges across subjects. PCA was applied to 604 \nreduce the dimensionality of the obtained data's first component, producing IRI data with dimensions of 605 \n𝑁𝑁𝑚𝑚𝑝𝑝 × 200 × 𝑁𝑁𝑠𝑠𝑜𝑜𝑠𝑠, 𝑡𝑡𝑝𝑝𝑎𝑎𝑡𝑡, where 𝑁𝑁𝑝𝑝𝑚𝑚 is the number of selected components. In this experiment, most 606 \nsubjects' first principal component (PC1) explained nearly 90% of the variance, so all IRI analyses were 607 \nbased on the dimensionality reduction to PC1, which means 𝑁𝑁𝑚𝑚𝑝𝑝= 1. 608 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n29 \n \nIRI sent by region 609 \nFor the IRI sent by region (RS‑IRI), we first summed, for each region, the message data across all 610 \nedges connected to that region along the corresponding dimensions. We then performed PCA on these 611 \nregion‑level message vectors to derive the RS‑IRI with dimensions of 𝑁𝑁𝑚𝑚𝑝𝑝 × 200 × 𝑁𝑁𝑡𝑡𝑡𝑡𝑎𝑎𝑖𝑖𝑜𝑜𝑖𝑖. We used 612 \nthe MMP360 atlas so 𝑁𝑁𝑡𝑡𝑡𝑡𝑎𝑎𝑖𝑖𝑜𝑜𝑖𝑖= 360. The PC1 accounted for nearly 90% of the total variance, so we 613 \nadopted PC1 as the RS‑IRI, which means 𝑁𝑁𝑚𝑚𝑝𝑝= 1. 614 \nModel Application 615 \nFast Fourier Transform (FFT) 616 \nTo characterize the oscillatory patterns underlying dynamic inter -regional brain interactions, we 617 \napplied Fast Fourier Transform (FFT) to the inter-regional information measures to obtain their spectral 618 \nrepresentations. Specifically, for each individual an d each structural connection, the temporal inter -619 \nregional interaction measure 𝐼𝐼 𝑅𝑅 𝐼𝐼(𝑛𝑛) w as subjected to the Fourier transform as specified in Equation 620 \n(12), yielding the frequency domain distribution 𝐼𝐼 𝑅𝑅 𝐼𝐼(𝑘𝑘): 621 \n𝐼𝐼𝑅𝑅𝐼𝐼(𝑘𝑘) = � 𝐼𝐼 𝑅𝑅 𝐼𝐼(𝑛𝑛)𝑒𝑒−𝑗𝑗2𝜋𝜋𝑘𝑘 𝑜𝑜\n𝑇𝑇\n𝑇𝑇−1\n𝑜𝑜=0\n, 𝑘𝑘= 0,1,2, … , 𝑇𝑇 −1 (12) 622 \nwhere 𝑇𝑇 represents the total number of time points. In this study, the analysis was performed on 623 \n𝐼𝐼𝑅𝑅𝐼𝐼(𝑛𝑛) da ta aggregated over 100 TRs, thus 𝑇𝑇= 100. Due to the inherently low sampling rate of the 624 \ndata, spectral analysis was confined to the frequency band of 0.005–0.5 Hz. 625 \nGroup-level comparison between AD patients and controls. 626 \nFor all subjects, we first identified and extracted the common inter-region brain connections present 627 \nacross the entire cohort. The FFT was applied to the time series of these connections for each individual. 628 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n30 \n \nFor each edge (connection) and for each frequency band, the amplitude values were subjected to a two-629 \nsample t -test to compare the AD and NC group. The resulting p- values from these tests were then 630 \ncorrected using the FDR. Finally, we counted the number of inter -regional brain connections that still 631 \nexhibited a significant group difference in each frequency band. These connections represent the 632 \npathways where the information transfer between the corresponding brain regions shows a significant 633 \ngroup-wise difference between the AD and NC groups at that specific frequency band.  634 \nThe association between oscillation amplitude and MMSE scores  635 \nFirst, inter-regional brain connections common to all subjects were identified. For each patient in 636 \nthe AD group, the FFT was applied to the time series of these connections. We then calculated Pearson 637 \ncorrelation coefficients between the spectral amplitude of each edge within each frequency band and the 638 \nparticipants' MMSE scores. Statistical significance was assessed using a permutation test with 1,000 639 \niterations. To control for multiple comparisons, p -values were adjusted using the FDR. Only results 640 \nretaining significance after FDR correction are visualized in the figure. 641 \nAcknowledgments 642 \nFunding: 643 \nNational Natural Science Foundation of China 32271146 and 81972160 644 \nStartup Funds for Top-notch Talents at Beijing Normal University 645 \nChina Postdoctoral Science Foundation (2025M772874) 646 \nAuthor contributions:  647 \n Conceptualization: SYL, DBZ, SXL 648 \n Methodology: SXL, DBZ, TTC 649 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n31 \n \n Investigation: SXL, DBZ 650 \n Visualization: SXL 651 \n Supervision: SYL 652 \n Writing— original draft: SXL, JCZ, ZKY, JJ 653 \n Writing—review & editing: SYL, SXL,  DBZ, XXD, YRH, LC 654 \nCompeting interests:  655 \nAuthors declare that they have no competing interests. 656 \nFigures: 657 \n 658 \nFigure 1 Overall Workflow. A) The IN construction based on neuroimaging data and inter-region interaction (IRI) 659 \ngeneration. The model was trained independently for each subject, inputting 10 TRs of BOLD signals, and outputting 660 \nthe predicted 10 TRs of BOLD signals. During prediction, the model can calculate the information transmitted 661 \nbetween regions. B) Validation of the predicted fMRI signals, including MAE and FC correlation analysis. The 662 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n32 \n \ngenerated MAE map was further correlated with neural variability and receptor map. C)  Analysis of IRIs.  The 663 \nmessage exchanged between each pair of regions, as computed by the model, was reduced via PCA, with the first 664 \nprincipal component representing the IRI. The analysis included the IRI on each edge and the total IRI sent by region 665 \n(see Methods). D) Application of the model to AD patients. The IN model for each individual was computed within 666 \nthe AD and control groups to obtain group- average prediction errors and individual IRIs. The IRIs were subjected 667 \nto fast Fourier transform (FFT) to reveal oscillation patterns in inter-regional interactions. The amplitudes in different 668 \nfrequency bands were then correlated with MMSE scores. 669 \n 670 \n671 \nFigure 2 Model validation results. A) The distribution across the whole brain of the group-averaged MAE (mean 672 \nabsolute error) for model-predicted fMRI signals in each brain region. Drawn by BrainSpace(105). B) Comparisons 673 \nbetween FC derived from segmented prediction and continuous prediction with the tru e FC. The left panel shows 674 \nthe distribution of correlation between the FC obtained from segmented prediction and the true FC. The right panel 675 \nshows the continuous prediction. The details of continuous and segmented prediction methods are provided in the 676 \nMethods. C) The relationship between MAE and global neural variability . One point denotes a subject.  D) The 677 \nrelationship between MAE and regional mean neural variability.  E) The relationship between the distribution of 678 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n33 \n \nMAE and the distribution of the norepinephrine transporter. 679 \n 680 \nFigure 3 Analysis of inter-regional interaction information (IRI). A) Flowchart for IRI derivation: Initially, 30-681 \ndimensional time series serve d as interaction messages for each connection. Dimensionality reduction was 682 \nperformed to derive the IRI time series. IRI was quantified for each fiber tract, and the sum of IRI sent from each 683 \nbrain region was  termed IRI sent by region (RS -IRI). B) Correlation between IRI variance and fiber length.  The 684 \nerror bars for each point represent the standard deviation across subjects for the corresponding connection length 685 \nand IRI variance.  C) D istribution of RS -IRI s trengths across different subnetworks.  D) Distribution of RS -IRI 686 \nvariability. 687 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n34 \n \n 688 \nFigure 4 Group-level comparison between AD patients and controls. A) The group-averaged prediction MAE 689 \nmaps on the cortical surface for the AD and NC groups.  B) The between-group differences in the SD across each 690 \ndimension of the interaction messages for AD and NC groups, with asterisks indicating statistically significant  691 \nbetween-group differences at α = 0.05. C) The brief workflow for obtaining oscillation amplitudes across different 692 \nfrequency bands of the IRI in the AD and NC groups. D) The between-group differences in the oscillation amplitudes 693 \ndescribed in (A). For each frequency band, the IRI between-group differences are computed and subjected to FDR 694 \ncorrection. The top figure shows, at low -, mid -, and high- frequency ranges (0.135, 0.345 and 0.49Hz), the 695 \nconnections exhibiting between-group differences in IRI oscillations and the corresponding brain regions, drawn by 696 \nBrainNet Viewer(106). The chosen frequency bands correspond to the deep purplish-red bands shown in the figure 697 \nbelow. The bottom figure presents the total number of connections between brain regions that show significant 698 \nbetween-group differences in oscillation amplitudes across different frequency bands for the IRI. 699 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n35 \n \n 700 \nFigure 5 The association between oscillation amplitude across different IRI frequency bands and MMSE 701 \nscores in AD patients. In this figure, the connections and their connecting brain regions for which IRI is significantly 702 \ncorrelated with MMSE scores. A permutation test was used, with  all results FDR -corrected. The plotted fit line 703 \nrepresents a linear (first -order) fit. The connections corresponding to the IRI oscillation amplitudes are projected 704 \nonto the brain, with the associated connections annotated at the top or on the right side. The numerical labels adjacent 705 \nto the brain correspond to the indices defined in the MMP atlas. Connected regions are separated by a hyphen (e.g., 706 \n'ID-ID'). For a complete list of MMP region IDs, see supplementary. 707 \n 708 \nFigure 6 The overall operational process of the model.  The information produced by interactions between brain 709 \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n36 \n \nregions is estimated using the interaction operator 𝐼𝐼(𝑥𝑥), and the predicted values of the node state variables are 710 \nestimated using the region operator 𝑅𝑅(𝑥𝑥). Taking a three-node network as an example, for the red, yellow, and blue 711 \nball representing the brain region nodes, each pair of connected nodes inputs into the interaction operator to obtain 712 \nthe inter-region information (grey ball, 𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗), a 30-dimensional vector. For each node, the total sum of IRIs on all 713 \nthe edges directly connected to it is computed as the total input information for that node (black ball). This total 714 \ninput information, along with the node's own signal value, is entered into the region operator, yielding the predicted 715 \nvalues of the brain region's dynamic signals for the next 10 time points (concave ball). In the interaction operator, 716 \nthe red and yellow balls represent the signal values of two different brain regions with a connection, and the white 717 \nball is the output value of the multilayer perceptron. By multiplying this output with the connection weights (the 718 \nlines between the red and yellow spheres) and the global parameter, the information value for the interaction between 719 \nthe two brain regions is obtained (grey sphere). 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It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint \n\n.CC-BY 4.0 International licenseperpetuity. 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