A brain dynamic model based on graph neural network reflect the inter-region interaction of cortical areas

24 A central objective in neuroscience is to elucidate how the brain generates complex dynamic 25 activity through the interactions of brain areas . In this study, we utilize d Interaction Network, a 26 graph neural network model, to develop a computational framework for predicting whole-brain 27 cortical blood oxygenation level dependent (BOLD) signals. We derived an Inter -Regional 28 Interaction (IRI) metric to quantify information exchange among brain areas probing the underlying 29 dynamical mechanisms. In addition, the total IRI emitted from each brain region was calculated and 30 defined as the IRI sent by region (RS-IRI). Our model predicted the following 10 time points BOLD 31 activity from initial BOLD signals , and achieved a mean absolute error of 0.0 4. The predicted 32 functional connectivity (FC) achieves a correlation coefficient of 0.9 7 compared to the empirical 33 FC. The fluctuation amplitude of the IRI increases with the length of the connection and the largest 34 RS-IRI oscillation amplitude is observed in visual areas . The RS-IRI demonstrates a hierarchical 35 organization, characterized by more concentrated distributions in association regions and larger 36 fluctuation amplitudes in unimodal regions. Applying our approach to Alzheimer’s disease (AD), 37 we demonstrate that the frequency-specific amplitudes of IRI oscillations discriminate AD patients 38 from healthy controls and correlate with Mini-Mental State Examination scores. Together, this work 39 presents a deep learning–based framework for modeling brain dynamics as well a quantitative index 40 of inter-areal interactions, and offers a new perspective for disease characterization. 41

Neurodynamic Modeling , Graph Neural Network (GNN), Brain Inter -regional 42 Interaction, Alzheimer's disease (AD) 43 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 3 Author Summary 44 The human brain comprises distinct regions that interact through complex fiber tracts, forming 45 the functional dynamics for diverse cognitive processes. We employed fMRI to assess functional 46 activity and DTI to reconstruct fiber tract connectivity. To elucidate how brain function emerges 47 from these inter -regional interactions, we developed a novel computational framework based on 48 Graph Neural Network (GNN) to model the brain’s interactive dynamics for its capacity to uncover 49 hidden and intricate patterns within data. From this model, we derived a quantitative metric termed 50 Inter-Regional Interaction ( IRI), which characterized the fine -grained, dynamic fluctuations in 51 communication between brain areas. Our results suggest that this GNN-based model can accurately 52 simulate brain functional activity and provide a quantitative description of neural interaction 53 patterns. Applying this model to a cohort of Alzheimer’s disease patients, we demonstrated that the 54 IRI metric not only effectively distinguish ed patients from healthy controls but also significantly 55 correlated with clinical cognitive performance (MMSE scores). This approach a dvances our 56 understanding of the fundamental principles of brain function and offers a promising tool for 57 identifying the underlying mechanisms of neurological disorders. 58

59 The human brain is a highly complex system comprising various types of n eurons and glial 60 cells. A central focus of brain research is understanding how the brain generates its intricate dynamic 61 activities, which support a wide range of cognitive functions(1–3). Alterations in these dynamics 62 can indicate systemic brain disorders (4) or transient pharmacological states (5). Many researchers 63 have sought to describe brain dynamics from multiple perspectives, yielding insights into 64 phenomena such as multistability(6 –8), metastability(9), co -occurring ripple oscillations (10), and 65 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 4 criticality(11,12). A widely accepted consensus is that brain dynamics are markedly nonlinear(13), 66 which are presented at multiple levels, from individual neuron activity to the collective interactions 67 of neuronal populations. This pervasive nonlinearity contributes to the overall complexity of the 68 brain as a system. While these studies analyze and characterize dynamic activities from various 69 perspectives, a pressing question remains: what factors, at both microscopic and macroscopic scales, 70 give rise to these dynamic patterns? A broad proposition suggests that such nonlinear dynamics 71 originate from both local intrinsic activity and inter-regional interactions(14). Crucially, these inter-72 regional interactions are constrained by the brain’s structural connectivity, which facilitates 73 information transmission between areas and integrates their activities into a globally cohesive yet 74 richly interactive dynamic system, rather than an ensemble of isolated regional dynamics. To 75 investigate the mechanisms underlying these dynamics more sophisticated, mechanism -oriented 76 approaches are needed to explore how these dynamics originate and are shaped. 77 Dynamical models represent a vital approach for investigating brain dynamics, as their ability 78 to encapsulate complex activities within a single framework enab les both the elucidation of 79 underlying mechanisms and the prediction of future states. Since the introduction of the 80 foundational Hodgkin-Huxley (H-H) model(15) and the Wilson-Cowan (W-C) model(16), extensive 81 research has expanded this neuronal framework to encompass larger systems (17). While thes e 82 studies have successfully constructed dynamic models for individual neurons or specific brain 83 regions, a comprehensive understanding of brain activity mechanisms necessitates the development 84 of dynamic models for the entire brain. Whole-brain dynamical models are typically constructed 85 using network- based modeling, where brain regions are represented as nodes and structural 86 connections between these regions serve as edges. For instance, dynamic causal modeling employs 87 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 5 multivariate nonlinear equations to fit regional activity (18–21) and network-based modeling 88 approaches grounded in neural mass models or neural field models have been widely utilized(17,22–89 25). Several phenomenological models have also yielded significant results in whole -brain 90 modeling. For instance, the Hopf whole-brain model integrates structural connectivity (in the form 91 of adjacency matrices) with local dynamics such as noise and time delays in each brain region (26). 92 This integration enables the analysis and prediction of functional connectivity (FC) (26,27), 93 providing dee per insights into the relationship between brain structure and function (28). 94 Furthermore, they facilitate the simulation of whole- brain activity, allowing researchers to 95 understand various brain states and predict how different regions may respond to external 96 disturbances, serve as valuable tools in pathology and pharmacology research, aiding in the 97 exploration of how brain dynamics react to disruptions or interventions (27). However, these 98 approaches rely heavily on a priori expert knowledge and intuition. We aim to employ a data-driven 99 framework that enables researchers to extract richer insights directly from the intrinsic structure of 100 the data. 101 In recent years, deep learning has garnered significant attention in neuroscience due to its 102 success in capturing hidden and complex patterns within data. Various convolutional neural 103 networks and recurrent neural networks have proven effective in modeling structural or functio nal 104 signals (29,30). Motivated by the recognition that the brain can naturally be represented as a graph, 105 there has been growing interest in applying graph neural networks (GNN) (31–33). GNN are 106 specifically designed to treat the brain as a directed graph, where nodes represent anatomical brain 107 regions and edges denote morphological, functional, or structural connectivity between pairwise 108 nodes(34). Regarding node-edge processing paradigms, GNN can be categorized into three primary 109 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 6 classes(35): (1) those that aggregate features of neighboring nodes using a learnable filter, as seen 110 in graph convolutional networks ; (2) those based on a self -attention algorithm that identifies the 111 most significant neighbors for aggregation, as in graph attention networks; and (3) those employing 112 a message -passing mechanism, where features of both the node are in consideration and its 113 neighboring nodes are combined to learn the local graph representation. In recent years, some 114 approaches have also employed ordinary differential equations as update rules(36,37). Among these 115 approaches, message-passing-based interactive network (IN) enable the prediction of not only the 116 dynamic signal but also the inter -node interactions. In physics, IN have been successfully applied 117 to simulate diverse phenomena(38) and model Newton's Second Law (39), demonstrating their 118 effectiveness in modeling interaction patterns within complex networks while generating 119 interpretable representations of node interactions. 120 To achieve a more accurate fitting of whole- brain neural dynamics, this study developed a 121 computational model based on IN to predict BOLD signals across the entire cortical surface. The 122 model calculated interaction information between different brain regions constrained by structural 123 connectivity and predicted dynamic changes in regions through their inter-regional interactions. We 124 trained the model and evaluated its performance on a test set by calculating the Mean Absolute Error 125 (MAE) of the predictions and their correlation with actual FC as the metric of the method's 126 effectiveness in simulating dynamic variations of cortical signals. We analyzed prediction errors 127 across different regions and investigated its relationship with neural volatility and molecular 128 biological maps to uncover the underlying causes of the spatial distribution in prediction accuracy. 129 Leveraging the model, we extracted inter -regional interaction information at the individual level. 130 By applying this approach to fMRI from Alzheimer’s disease (AD) patients, we found that the model 131 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 7 successfully captured oscillatory patterns in inter-regional interactions that differentiate AD patients 132 from normal controls (NC). The constructed model offers a novel approach for analyzing brain 133 dynamics, and the derived interaction metrics provide valuable insights for disease research. 134

135 Workflow 136 This study constructed an IN model based on a message -passing mechanism. By fitting and 137 training on BOLD signals, the model generated interaction messages between different brain regions, 138 enabling the simulation of whole -brain dynamics. The model was trained and validated using the 139 resting state fMRI (rs -fMRI) from the Human Connectome Project (HCP) dataset, and the inter -140 region interactions (IRI) produced by the model were subsequently analyzed. The cortex was 141 segmented into regions according to the MMP360 atlas(40). The mean BOLD signal of each region 142 was calculated as a proxy for the dynamic neural activity within that region ( Figure 1 A). The 143 specific training strategy is detailed in the Methods section. The trained model was then applied to 144 the test set, and prediction errors were analyzed across different regions ( Figure 1B). These error 145 distributions underwent correlation analyses with other brain maps to investigate the sources of 146 regional heterogeneity in prediction accuracy. Subsequently, dynamic interaction messages between 147 regions were extracted, and the information fluctuation maps emitted by different regions were 148 computed ( Figure 1C). Finally, we applied our method to data collected from AD patients and 149 control subjects at Xuanwu Hospital ( Figure 1D). We compared IRI between the AD and control 150 groups and examined the association between the oscillation patterns of inter -regional interactions 151 and Mini-Mental State Examination (MMSE) scores. 152 Model Validation and Prediction Accuracy Analysis 153 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 8 To validate the effectiveness of the methods employed in this study, we constructed 154 individualized cortical neural activity prediction models based on IN for each subject, with data 155 partitioned into training and test sets chronologically, assigning the earlier time points to the training 156 set and the latter time points to the test . Model performance was evaluated using two metrics on the 157 test set: the MAE between predicted and actual signals, and the correlation between FC matrices derived 158 from the predicted and actual signals. The raw BOLD signals were z-scored and the average whole-brain 159 MAE for the predicted data was 0.04. These results indicate that the model can accurately predict 160 dynamic fluctuations across the entire brain. Since each prediction sequence spans 10 TRs, we computed 161 the functional connectivity of the predicted signals using two approaches: a segmented prediction method 162 and a continuous prediction method. The segmented method assesses the model’s ability to reproduce 163 FC over short timescales, while the continuous method evaluates performance in long -term prediction 164 scenarios, where error accumulation may occur (see Methods for details) . Both approaches partially 165 recapitulated the structure of the actual functional connectivity (see Figure 2 B, Figure S1). The 166 correlation coefficient between the FC derived from segmented predictions and the true FC is 0.9745 ± 167 0.0067, while the correlation for the continuous prediction method is lower at 0.4957 ± 0.0897. 168 We found that predictive accuracy (MAE) varies across brain regions (Figure 2A). The frontal 169 lobe yields the best predictions and the visual area yields the poorest. We hypothesized that 170 differential prediction performance across brain regions reflects their distinct neural variability. To 171 test this, we examined the relationship between predicted MAE and neural variability . We defined 172 neural variability as the standard deviation (SD) of regional signals(41). Our analysis revealed that, 173 at both the individual and regional levels, the model-predicted MAE was positively correlated with 174 neural variability, supporting the hypothesis that a higher MAE reflects more complex and flexible 175 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 9 regional activity (Figure 2C, D), therefore, harder to predict. 176 To further investigate the underlying factors affecting prediction accuracy across brain regions, 177 we correlated the MAE distribution with a diverse set of cortical maps . We hypothesized that 178 regional activity could be influenced by both the region's microstructure and mesoscopic functional 179 properties. Therefore, we conducted correlation analyses between the region -wise average MAE 180 maps derived from our model and various maps from neuromaps(42), including functional gradients, 181 coarse-grained structural features, microstructural receptor distributions, and finer -grained gene 182 gradients. All correlations were assessed using permutation tests and corrected for multiple 183 comparisons using the false discovery rate (FDR). Notably, we found a statistically significant but 184 modest negative association between model- predicted regional MAE and the mean distribution of 185 norepinephrine transporters (NET) (Figure 2 E), as observed with Methylreboxetine targets (43). 186 These receptors modulate presynaptic sodium uptake, thereby terminating neural signaling(44) . 187 This finding may suggest that regions with a higher norepinephrine transporters density leads to 188 greater inhibition of noradrenergic signal transmission , which give rise to more stable signals and 189 enabling more accurate predictions by the model. 190 191 Inter-regional interaction information and its characteristics 192 The advantage of IN model is the ability to capture information transfer between distinct brain 193 regions. In this study, we derived the IRI from functional signals, utilizing the extraction method 194 described in the Methods section. To address the 30-dimensional interaction messages, we reduced 195 the data by selecting the first principal component as the IRI (Figure S2), resulting in a time-varying 196 IRI sequence for each inter -regional connection ( Figure 3A). Also, we aggregated the interaction 197 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 10 messages originating from each region and similarly selected the first principal component of this 198 sum as the IRI sent by region (RS-IRI). We used the SD of the IRI as a measure of the flexibility of 199 information transfer between brain regions. A positive correlation was observed between this 200 flexibility and the length of the inter -regional connection (Figure 3B), suggesting that long -range 201 connections may exhibit a greater capacity for adaptive information transfer. This increased capacity 202 may be due to their exposure to more dynamic transmission conte xts, the involvement of more 203 complex signals, and the need for larger signal fluctuations to ensure accurate transmission. 204 To investigate whether different functional sub- networks send information with distinct 205 strengths, we plotted boxplots of emission strength across sub-networks (Figure 3C). We found that 206 as hierarchical level increases, the distribution of emitted information strength exhibits lower 207 variance. This centralization may arise from higher-order regions, such as the default mode network 208 (DMN), exhibiting a relatively lower excitation–inhibition ratio, which leads to stronger inhibitory 209 signals and consequently more stable information emission (45,46). Finally, we quantified the 210 variance of RS-IRI across brain regions, finding that visual regions exhibited the greatest flexibility 211 in emitting interaction information ( Figure 3D). This may reflect the highly diverse information 212 generated and output by these regions. 213 Application in Alzheimer's diseases 214 To investigate whether neurodegenerative pathology induces alterations in the dynamic interactions 215 among cortical regions, we applied our computational model to data from AD patients. Our analyses 216 revealed differences in the mean predict ed MAE between the AD and NC groups but did not show 217 significant group differences (Figure 4A), likely due to the limited sample size. Before computing the 218 IRI, we compared the SD of interaction messages across each dimension between the AD and NC groups, 219 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 11 which we used as a proxy for the amount of information carried by the IRI . We found that, in most 220 dimensions, the between-group differences were significant, while non-significant dimensions tended to 221 have lower SD, suggesting that these dimensions may carry less informational content (Figure 4B). The 222 SD of interaction messages in the NC group was significantly higher than in the AD group, indicating 223 greater flexibility in inter-regional interactions for the NC group. This may refle ct that the AD patients 224 experience dysfunction in inter-regional information transfer with less informative content. 225 We computed the IRI for each subject in both the AD and NC groups. Our results indicated that the 226 AD and NC groups differ in their IRIs, wi th the AD group showing more high -frequency components 227 (Figure 4C). To examine whether the spectral content of the IRI could distinguish AD patients from 228 controls, we performed Fast Fourier Transform (FFT) on the IRI signals for each edge, obtaining their 229 spectral profiles. We then conducted t- tests on the amplitude at each frequency band, applying FDR 230 correction, the results see supplementary table. Results confirmed our hypothesis, revealing significant 231 differences in IRI predominantly in the high-frequency range, where the AD group exhibited markedly 232 increased IRI on connecting edges ( Figure 4 D). This attenuation of high -frequency inter -regional 233 information exchange suggests that cognitive deficits in AD may be associated with increased high-234 frequency noise contamination in neural interactions. We analyzed the connections showing significant 235 differences in IRI across different frequency bands and found that the majority of IRI with significant 236 differences were located in the information flows of intra- or inter- higher-order regions, particularly 237 involving the frontoparietal network and the ventral attention network (Figure 4D). 238 We further investigated the relationship between IRI across different frequency bands and cognitive 239 impairment in AD patients, we correlated the amplitude values of each edge within each frequency band 240 with the MMSE scores in the AD group. Significance was evaluated using permutation testing with FDR 241 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 12 correction. Ultimately, we identified six edges where amplitude of communication in specific frequency 242 bands significantly correlated with MMSE scores , predominantly distributed in the medial and lateral 243 prefrontal cortices and the c ingulate cortex (Figure 5). All these regions are situated within the fronto -244 parietal network, default mode network, and ventral attention network, indicating that IRI within and 245 between these networks may reflect cognitive performance as measured by the MMSE in AD patients. 246

247 Our study developed a computational model based on IN to predict BOLD signals across the entire 248 cortical surface. This model computes interregional interaction information constrained by structural 249 connectivity and predicts dynamic BOLD changes in brain regions through their inter -regional 250 interactions. Validation using MAE and FC correlation demonstrated that this approach effectively 251 simulates dynamic variations in cortical signals. By extracting inter -regional interaction information at 252 the individual level from the model and applying it to a dataset of AD patients, we found that the model 253 captures distinct oscillatory interaction patterns between brain regions in AD patients compared to NC. 254 The constructed model offers a novel method for analyzing brain dynamics, and the derived interaction 255 metrics provide new perspectives for disease research. 256 The rationale for using GNN in brain dynamical modeling 257 GNN represent a deep learning framework adept at analyzing network -structured data. They are 258 extensively applied across various domains, including power grids(47), transportation networks(48), and 259 financial systems (49). Recently, some researchers have begun employing GNN for modeling neural 260 systems(50,51) due to their superior capacity for processing and analyzing network-structured data. Most 261 GNN utilize graph convolution modules(52–54), while others use message-passing mechanisms, which, 262 although computationally intensive, can capture interactions between pairs of nodes, such as gravitational 263 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 13 interactions among planets (39) and forces between high -energy particles (55). This message -passing 264 approach emphasizes connections but requires greater computational capacity. To enhance the reliability 265 of interaction information and minimize interference from multiple computational modules, this study 266 adopts a streamlined model construction approach: both the interaction information generation module 267 and the node state generation module are constructed using simple multilayer perceptron (MLP), without 268 integrating additional computational components. 269 Inspired by these studies, we developed an IN model capable of predicting cortical BOLD signals 270 by leveraging dynamic interregional interactions. The model achieved an average MAE of 0.04 in 271 predicting overall fMRI signals. This results represent an improvement over the diffusion convolution 272 recurrent neural network (DCRNN) and graph WaveNet (GWN) used in prior research (53), 273 demonstrating the model’s effectiveness in capturing dynamic fluctuations in cortical BOLD signals. 274 The segmented prediction approach facilitated partial reproduction of FC structures (see Figure 2C, 275 D), with a correlation coefficient of 0.9745 to actual FC , slightly higher than the 0.95 reported for 276 DCRNN(53). However, due to different computational methodologies, these values are not directly 277 comparable. Consequently, the correlation between sequentially predicted FC and true FC, affected by 278 accumulated errors, was lower at 0.4957. This result, like other data -driven models (30), is modest 279 compared to most traditional dynamical models, which typically begin with empirical equatio ns and 280 structured networks and iteratively tune parameters to enhance the similarity between generated and 281 actual FC(27,56,57). Improving FC correlation in generated sequences is plausible since these sequences 282 need only replicate certain structural aspects of FC rather than its full range of features. Our method 283 optimized the model by fitting it to real sequences, minimizing the discrepancy between generated and 284 actual data via the loss function. Despite the model's underwhelming performance in continuous FC 285 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 14 prediction, which indicates a deficiency in capturing long -range temporal dependencies, it enables 286 derived inter-regional interactions to inform subsequent predictions of cortical dynamics. Ideally, if the 287 model could perfectly simulate whole -brain dynamics, the generated sequences should exhibit a 288 complete FC structure. Unfortunately, the current model appears focused primarily on input and target 289 10 TR data, aligning with our design objectives, while neglecting long-range influences. This limitation 290 is understandable, as such constraints were not explicitly incorporated into the model. Prior studies have 291 suggested that long-range BOLD signal simulations driven by data depend on noise(30). Since our model 292 excluded noise, long-range predictions tend to converge toward attractors over time. We believe, however, 293 that introducing noise could undermine the reliability of the IRI metrics, leading us to incorporate only 294 regularization-based noise introduction, avoiding explicit noise-driven modeling. 295 Understanding and application of IRI 296 Using our model, we extracted IRI and related it to the concept of information flow. Historically, 297 information flow has been described as the directionality and strength of information transfer among 298 different brain regions(58,59). This definition, in conjunction with effective connectivity, bears similarity 299 to approaches such as dynamic causal modeling(60) . Recent advancements in DTI have provided a 300 structural basis for information flow(61,62). However, characterizing information transfer directionality 301 in a purely static manner is insufficient. To fully under stand information processing in the brain , 302 including perception, transduction, coordination, storage, and generation, an analysis of dynamic 303 fluctuations is imperative, as these processes reflect continuous changes in the brain's underlying states, 304 even under constant environmental conditions(63,64). These dynamics evolve over time and are rooted 305 in the brain’s structural connectivity(65) . Therefore, when constructing a comprehensive bra in 306 communication model, these factors must be duly considered(66,67) . In this study, the whole -brain 307 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 15 dynamical model based on GNN gener ates dynamic interregional information transfer by integrating 308 BOLD signals from different regions and their structural connectivity, representing these processes as a 309 temporal sequence. This sequence is akin to edge Time Series (eTS), originally defined as a co -310 fluctuation time series, the pointwise product of z -scored signals from two brain regions at successive 311 time points(68). It provides a mechanism for deconstructing FC into temporal sequences. A connection-312 centric measure called edge functional connectivity (edge FC or eFC) captures the dynamic expression 313 of brain functional systems through fine -scale edge time series analysis (69,70). However, unlike eTS, 314 the IRI produced from the IN model is not reconstructed from static FC, thereby avoiding concerns 315 regarding its "dynamic" nature (71–73). Crucially, the IRI is grounded in the underlying structural 316 connectivity derived from DTI, rather than being inferred solely from functional signals. Essentially, IRI 317 offers a method for deriving fluctuations in connection edges directly from dynamic variations in fMRI 318 signals, and these fluctuations are both structure-based and biologically grounded. 319 We observed a positive correlation between the variability of IRI and the length of connections. 320 Long-range connections are known to play a crucial role in brain activity (74). Although some studies 321 suggest that brain geometry alone can reconstruct functional connectivity(75), other research , both 322 experimental and clinical, demonstrates that sparse long-range connections are vital for the complexity 323 of brain functional dynamics (76–78). Our findings support this notion, indicating that long- range 324 connections are essential in whole -brain modeling, with their significance increasing with connection 325 length. A dditionally, some studies report that distant projections are more strongly influenced by 326 electrical stimulation(79), which may explain our results: greater IRI variability could correspond to a 327 higher information -carrying capacity, suggesting that long -range connections transmit more potent 328 electrical stimuli. The average strength of IRI emitted by different brain regions exhibits a gradient 329 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 16 distribution across various functional subnetworks, indicating that higher -order brain regions generate 330 the strongest IRI during resting-state conditions. This suggests that these regions are more likely to play 331 a dominant role in resting-state activity. 332 In the analysis of AD patients, we noticed that the IRI in the AD group contained more high -333 frequency components, yet the standard deviation (SD) of the interaction messages was significantly 334 lower. This suggests diminished flexibility in information transmission coupled with increased erroneous 335 noise, which reduced the proportion of meaningful content within the transmitted signals. We observed 336 significant differences in the IRI within the 0.4– 0.5 Hz frequency band compared to NC. These 337 oscillatory pattern variations have been documented in EEG studies (80). Unlike previous research that 338 focused on signals from individual brain regions, our study employs IRI; since IRI is inherently related 339 to the underlying regional signals, the findings align with earlier research indicating abnormal neuronal 340 firing activity in the theta frequency band in AD patients(81). Due to the limited temporal resolution of 341 fMRI data, we cannot capture information in higher frequency ranges. Nevertheless, leveraging the high 342 spatial resolution of fMRI allows us to analyze how oscillatory interaction frequencies between brain 343 regions relate to cognitive scores and to identify specific connection sites involved. We identified six 344 connections where IRI significantly correlates with M MSE scores in AD patients, predominantly 345 distributed in the medial and lateral prefrontal cortices and the cingulate cortex . Notably, four of these 346 links connect the DMN to other networks. These findings support prior research on functional 347 connectivity alterations in AD patients (82), reinforcing the notion that the DMN exhibits pathological 348 changes in AD, subsequently affecting other regions involved in higher cognitive functions via 349 interregional interactions. 350 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 17

351 First, this study employs GNN to predict discretized fMRI signals . However, it does not construct 352 continuous dynamic models akin to differential equations. Future research incorporating mechanistic 353 approaches from machine learning (83) could facilitate the development of brain dynamics models 354 capable of continuous prediction. Second, the structural connectivity in this study was based on data 355 obtained through DTI tractography for model construction. However, DTI imaging may have accuracy 356

and often overlooks non -long-range synaptic transmissions between brain regions (e.g., 357 adjacency ef fects). The brain’s dynamic behavior may not solely depend on network -like structural 358 connectivity(84); some studies suggest that brain dynamics could also arise from geometric 359 morphology(75). Integrating approaches such as geodesic distance (85) and cellular architecture 360 similarity networks (86) can complement these various connection s. Employing heterogeneous GNN 361 methods(87) may aid in constructing such multifaceted models. Third, current models are primarily data-362 driven at a macroscopic scale and neglect microstructural elements such as neurons. They also do not 363 incorporate task-driven models at the phenotypic cognitive level. Future work should aim to integrate 364 task-based approaches, developing multimodal, multiscale models based on microscopic priors, aligning 365 with the goal of multiscale brain modeling(88). 366 367

368 Participants 369 This study utilizes two batches of data, obtained from the Human Connectome Project (HCP) by 370 the National Institutes of Health (NIH) (89) and from the Neurology Department at Xuanwu Hospital, 371 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 18 Capital Medical University in China. Following quality control procedures based on head motion and 372 the length of the remaining time series, a total of 148 participants from the HCP dataset were retained, 373 including 72 males and 76 females, aged between 22 and 35 years. In addition, we enrolled 41 patients 374 diagnosed with Alzheimer's disease (AD) from the memory clinic of the Neurology Department at 375 Xuanwu Hospital, Capital Medical University (CMU) in China. We also recruited 42 healthy individuals 376 as normal controls from local communities in Beijing, China. This study obtained approval from the 377 Medical Research Ethics Committee at Xuanwu Hospital, and all participants provided written informed 378 consent. Standard clinical assessments were conducted on all participants, whic h included a thorough 379 medical history investigation, neurological examination, and neuropsychological tests. The cognitive 380 tests administered encompassed the Montreal Cognitive Assessment (MoCA, Beijing version) (90), 381 Auditory Verbal Learning Test (A VLT), Clinical Dementia Rating (CDR) (91), Mini -Mental State 382 Examination (MMSE), Hamilton Depression Rating Scale (HAMD), Activities of Daily Living (ADL) 383 scale, Hachinski Ischemic Scale, and the Center for Epidemiologic Studies Depression scale (92). The 384 patients with AD were diagnosed based on the criteria of the National Institute of Aging -Alzheimer’s 385 Association (NIA -AA) for clinically probable AD (93). After data preprocessing, the final sample 386 comprised 34 healthy control individuals and 23 AD patients. The age range of the participants was 387 between 53 and 81 years. Among the AD group, there were 14 males and 9 females, while the contr ol 388 group consisted of 21 males and 13 females. 389 Data acquisition 390 The HCP dataset comprises resting -state functional magnetic resonance imaging (rs -fMRI) and 391 diffusion magnetic resonance imaging (dMRI) data. Each participant in the HCP dataset underwent two 392 15-minute resting-state fMRI scans at different time points, acquired from two directions. This resulted 393 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 19 in a total of 60 minutes of rs -fMRI data, comprising 4800 repetitions with a Time Repetition (TR) of 394 720ms. The scans were performed on a Siemens Skyra scanner with a 3T field strength. This study 395 utilizes two batches of data, obtained from the Human Connectome Project (HCP) by the National 396 Institutes of Health (NIH)(89) and from the Neurology Department at Xuanwu Hospital, Capital Medical 397 University in China. The HCP dataset comprises rs -fMRI and dMRI data. Each participant in the HCP 398 dataset underwent two 15-minute rs fMRI scans at different time points, acquired from two directions. 399 This resulted in a total of 60 minutes of rs-fMRI data, comprising 4800 repetitions with a Time Repetition 400 (TR) of 720ms. The scans were performed on a Siemens Skyra scanner with a 3T field strength. 401 The data from the Neurology Department at Xuanwu Hospital, Capital Medical University (CMU), 402 comprises rs-fMRI and DTIdata. All images were acquired on 3.0 T Siemens system (Magnetom Trio 403 Tim; Erlangen, Germany) at the Department of Radiology, Xuanwu Hospital, Capital Medical University, 404 Beijing, China. T1-weighted images were acquired using a magnetization prepared rapid gradient echo 405 (MPRAGE) sequence (TR = 1900 ms; TE = 2.2 ms; TI = 900 ms; flip angle = 9◦;FOV= 224 mm × 256 406 mm; matrix size = 448 × 512; number of slices = 176; slice thickness = 1 mm). Functional images were 407 acquired axially using a gradient-echo EPI sequence (TR = 2000 ms; TE = 40 ms; flip angle = 90◦ ;FOV= 408 240 mm × 240 mm; matrix size =64 × 64; number of sections = 28; section thickness = 4 mm; voxel size 409 = 3.75 × 3.75 × 4mm3;gap= 1 mm; volume number = 239). DTI images were collected axially by using 410 a single-shot echo-planar sequence (repetition time (msec)/echo time (msec), 11000/98; flip angle, 90◦; 411 field of view, 256 × 232 mm2; 128 × 116 matrix; 60 sections; section thickness, 2 mm; voxel size, 2 × 2 412 × 2 mm3; 30 gradient directions with b value of 1000 sec/mm2 and one image with a b value of 0 413 sec/mm2; and three averages). 414 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 20 Data preprocessing 415 For the HCP dataset , an affine transformation was initially applied to register individual dMRI 416 images with the T1-weighted image. Then, the structural image of each individual was registered to the 417 ICBM152 template(94), yielding an inverse warping transformation from the standard space to the dMRI 418 space. The HCP MMP 1.0 atlas (40) was then mapped onto the sample space using this inverse 419 transformation. This division divided the entire brain into 360 brain regions, with 180 regions per 420 hemisphere. Fiber tractography was subsequently performed using DSI -Studio(95). By calculating the 421 eigenvalues and eigenvectors of water molecules in three directions, fiber tracts wer e traced. Two 422 weighted matrices, the connection density matrix and the connection length matrix, were constructed 423 based on the fiber tracts between two nodes. 424 Regarding fMRI data processing, the HCP -pipeline was initially applied for minimal 425 preprocessing(96). Subsequently, a high-pass filter with FWHM greater than 2000s was applied to the 426 fMRI signals and the ICA-FIX(97,98) method was then employed to remove noise components from the 427 fMRI signals, followed by regression of the data using the global signal as a regressor. Finally, a bandpass 428 filter ranging from 0.009 to 0.08 Hz was applied to eliminate most of the noise. After post -processing, 429 the entire cerebral cortex was segmented according to the HCP MMP 1.0 atlas( 40). The average fMRI 430 signal within each brain region was calculated, obtaining fMRI signal values for the 360 brain regions. 431 Incomplete data were discarded, and subjects with head motion exceeding 0.25 were excluded. Among 432 the remaining subjects, time points with head motion exceeding 0.25 were removed, and the data were 433 divided into non-uniform intervals. Each interval overlapped by grouping them in sets of 20 time points, 434 where the first ten time points represented the input data, and the latter ten t ime points represented the 435 true values of the output data. If an interval contained fewer than 20 time points, it was discarded. The 436 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 21 data from individuals with input-output groupings greater than 2000 were retained, resulting in a total of 437 148 participants, including 72 males and 76 females, with ages ranging from 22 to 35 years. 438 As for t he data from the Neurology Department at Xuanwu Hospital we utilized the MRTrix 3.0 439 pipeline(99) for DTI preprocessing. Firstly, an affine transformation was applied to register individual 440 DTI images with the T1 -weighted image. Subsequently, the structural images of each individual were 441 registered to the ICBM152 template(94) . Computing the eigenvalues and eigenvectors of water 442 molecules in the brain along three directions to trace the fiber and obtained connection probabilities. The 443 connection probabilities between two brain regions were summed based on the HCP MMP 1.0 atlas(40), 444 resulting in a connection probability-weighted structural connectivity matrix (SC). 445 We utilized the fMRIPrep 20.0.7 pipeline (100) for the preprocessing of fMRI data. The 446 preprocessing steps for the T1- weighted images included intensity non- uniformity correction, skull 447 stripping, spatial normalization to the standard space (MNI152NLin6Asym), brain tissue segmentation, 448 and cortical surface reconstruction. The preprocessing steps for the rs-fMRI data involved removing the 449 first five time points, motion correction, slice-timing correction, and co-registration to the corresponding 450 T1-weighted images using boundary-based registration. Subsequently, we employed spatial smoothing 451 using an isotropic Gaussian kernel with a full width at half maximum (FWHM) of 6 mm. In the denoising 452 phase, we performed automatic removal of motion artifacts using ICA -based Automatic Removal Of 453 Motion Artifacts (AROMA)(101), a 24-parameter model, and linear regression, which included signals 454 from the mean white matter and cerebral spinal fluid (102). This was followed by the application of a 455 high-pass filter using a discrete cosine filter with a cutoff period of 128 s. After processing, the whole-456 brain cortex was parcellated according to the HCP MMP 1.0 atlas(40) and the average fMRI signal within 457 each brain region was calculated to obtain signal values for 360 brain regions. After excluding the images 458 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 22 with significant head motion (head motion exceeding 0.5), the final sample comprised 34 healthy control 459 individuals and 23 AD patients. The age range of the participants was between 53 and 81 years. Among 460 the AD group, there were 14 males and 9 females, while the control group consisted of 21 males and 13 461 females. 462 IN models construction 463 The model can be considered a hidden function 𝐹𝐹(𝑥𝑥), denoted as 𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎(𝑥𝑥), and its overall operation 464 process can be represented by an equation. 465 �𝑋𝑋1, 𝑋𝑋2, … , 𝑋𝑋𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜� = 𝐹𝐹𝑎𝑎𝑎𝑎𝑎𝑎��𝑋𝑋1, 𝑋𝑋2, … , 𝑋𝑋𝑇𝑇𝑖𝑖𝑖𝑖�; 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺ℎ� (1) 466 In which 𝑋𝑋𝑜𝑜𝑜𝑜𝑜𝑜 represents the predicted fMRI signal, expressed as a 360 -dimensional vector, with 467 the subscript number indicating the number of time points. This study uses fMRI signals from 10 time 468 points as input, hence 𝑇𝑇= 10. 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺ℎ denotes the whole-brain network, which is represented using a 469 structural connectivity matrix derived from dMRI tracking. 470 The process of information interaction includes two parts: the transmission and reception of 471 information. Based on this idea, 𝐹𝐹(𝑥𝑥)can be decomposed into two functions: the information interaction 472 function, 𝐼𝐼(𝑥𝑥), and the state change function, 𝑅𝑅(𝑥𝑥). This model can be simplified to the level of brain 473 regions. Information is transmitted between brain regions through the interaction function 𝐼𝐼(𝑥𝑥) , as 474 shown in equation (2). 475 𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗= 𝐼𝐼��𝑥𝑥𝑖𝑖 1, 𝑥𝑥𝑖𝑖 2, … , 𝑥𝑥𝑖𝑖 𝑇𝑇𝑖𝑖𝑖𝑖�, �𝑥𝑥𝑗𝑗 1, 𝑥𝑥𝑗𝑗 2, … , 𝑥𝑥𝑗𝑗 𝑇𝑇𝑖𝑖𝑖𝑖�,𝐶𝐶𝑖𝑖𝑗𝑗� (2) 476 𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗 represents the interaction between brain region 𝑖𝑖 and brain region 𝑗𝑗 , with 𝐶𝐶𝑖𝑖𝑗𝑗 being the 477 characteristic of the connection between brain region 𝑖𝑖 and brain region 𝑗𝑗 , which is estimated with 478 structural connectivity matrices generated from structural connectivity (SC) and global parameter 𝐺𝐺, 479 defined as 𝐶𝐶𝑖𝑖𝑗𝑗= 𝑆𝑆 𝐶𝐶𝑖𝑖𝑗𝑗× 𝐺𝐺 . 𝑥𝑥𝑖𝑖 1, 𝑥𝑥𝑖𝑖 2, … , 𝑥𝑥𝑖𝑖 𝑇𝑇𝑖𝑖𝑖𝑖 represents the input fMRI signal from region 𝑖𝑖 in time 480 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 23 𝑇𝑇𝑖𝑖𝑖𝑖= 10. Assuming that the information transfer between brain regions is additive , meaning that for 481 brain region 𝑖𝑖, the influences from different brain regions are directly summated, then the change in state 482 of a brain region can also be expressed in a simplified form through a state change function, equation (3). 483 𝕏𝕏𝑖𝑖= 𝑁𝑁 ��𝑥𝑥𝑖𝑖 1, 𝑥𝑥𝑖𝑖 2, … , 𝑥𝑥𝑖𝑖 𝑇𝑇𝑖𝑖𝑖𝑖�, � 𝐼𝐼 𝑅𝑅 𝐼𝐼𝐼𝐼𝑖𝑖,𝑗𝑗 𝑗𝑗 � (3) 484 In which 𝕏𝕏𝑖𝑖= [𝑥𝑥𝑖𝑖 1, 𝑥𝑥𝑖𝑖 2, … , 𝑥𝑥𝑖𝑖 𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜] represents the predicted fMRI signal from region 𝑖𝑖 in time 485 𝑇𝑇𝑜𝑜𝑜𝑜𝑜𝑜= 10. To minimize the complexity of the model and enhance its interpretability, this study utilizes 486 the MLP to construct functions 𝐼𝐼(𝑥𝑥) and 𝑅𝑅(𝑥𝑥), that is, by using simple linear layers and activation 487 functions for construction. The method of constructing 𝐼𝐼(𝑥𝑥) involves multiplying the characteristics of 488 the connecting edges directly by the output of the multilayer perceptron, allowing the characteristics of 489 the connecting edges to influence the information interaction between brain regions, which can be 490 represented by the equation (4) 491 𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗= 𝐼𝐼𝑚𝑚𝑚𝑚��𝑥𝑥𝑖𝑖 1, 𝑥𝑥𝑖𝑖 2, … , 𝑥𝑥𝑖𝑖 𝑇𝑇𝑖𝑖𝑖𝑖�, �𝑥𝑥𝑗𝑗 1, 𝑥𝑥𝑗𝑗 2, … , 𝑥𝑥𝑗𝑗 𝑇𝑇𝑖𝑖𝑖𝑖�� × 𝐶𝐶𝑖𝑖𝑗𝑗 (4) 492 In which 𝐼𝐼𝑚𝑚𝑚𝑚 represents the MLP for 𝐼𝐼(𝑥𝑥). 493 The model inputs are the values of whole -brain fMRI signals for 10 time points, with the output 494 being the predicted values of whole -brain fMRI signals for the next 10 time points. For each sequence 495 of an individual's scan, input values are constructed as 𝑖𝑖𝑛𝑛 𝐺𝐺𝑛𝑛𝑛𝑛= 𝕏𝕏𝑖𝑖𝑖𝑖,𝑘𝑘 𝑓𝑓𝑓𝑓 𝐺𝐺 𝑘𝑘= [0,1,2, … , 𝑘𝑘𝑚𝑚𝑎𝑎𝑚𝑚], and 496 truth values as 𝑛𝑛 𝐺𝐺𝑛𝑛𝑛𝑛ℎ = 𝕏𝕏𝑜𝑜𝑡𝑡 𝑜𝑜𝑡𝑡, 𝑘𝑘 𝑓𝑓𝑓𝑓 𝐺𝐺 𝑘𝑘= [10,11,12 , … , 𝑘𝑘𝑚𝑚𝑎𝑎𝑚𝑚]. 𝕏𝕏𝑘𝑘 represente the input fMRI signal in 497 10 time points, which means a 10×360 dimension vector. Therefore, the number of time points for both 498 input and truth values remain the same, equal to the number of input-output pairs 𝑘𝑘𝑚𝑚𝑎𝑎𝑚𝑚. Data from each 499 individual's four fMRI scan sequences are constructed in this manner, forming a dataset for each 500 individual. 501 T o illustrate the model’s prediction of whole -brain states, we used a three- node system as an 502 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 24 example (Figure 6 ). For each pair of nodes (brain regions), the model takes as input the 10- TR 503 fMRI time series from both regions and their s tructural connectivity, computing the interaction 504 information via 𝐼𝐼(𝑥𝑥). Using this interaction information and the original node states, the predicted 505 state for the next time point in each region is computed with 𝑅𝑅(𝑥𝑥). The predicted states are then 506 compared to the actual fMRI values for the subsequent 10 TRs using the Huber loss, which is 507 backpropagated to update the model parameters. 508 The dataset is split into training, validation, and test sets in an 8:1:1 ratio, with the initial 90% of 509 the data serving as the training and validation sets and the final 10% designated as the test set. During 510 training, the data for both the training and validation sets are randomly shuffled and re-partitioned at each 511 epoch. We use torch_geometric to realize the model and load train data and the optimizer employed is 512 Adam. The loss function utilizes Huber Loss (103) incorporating L1 regularization, which is a loss 513 function that performs well across a variety of fitting tasks(104). The weight of regularization is 1e-4.The 514 dataset is split into training, validation, and test sets in an 8:1:1 ratio, with the initial 90% of the data 515 serving as the training and validation sets and the final 10% designated as the test set. During training, 516 the data for both the training and validation sets are randomly shuffled and re-partitioned at each epoch. 517 We use torch_geometric to realize the model and load train data and the optimizer employed is Adam. 518 The loss function utilizes Huber Loss(103) incorporating L1 regularization, which is a loss function that 519 performs well across a variety of fitting tasks(104). The weight of regularization is 1e-4. 520 Before training, we first randomly select a single individual for model hyperparameter optimization, 521 and this individual does not participate in subse quent training and analysis. During the hyperparameter 522 tuning process, global parameters are set based on previous research experience, with a value of 𝐺𝐺=523 0.6 . Grid search is used to optimize model parameters, including the dimension of information 524 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 25 transferred between two brain regions, the output dimension of 𝐼𝐼(𝑥𝑥) , 𝐼𝐼 𝑖𝑖𝐷𝐷𝐼𝐼𝐼𝐼𝐼𝐼∈ [20,30,50,200] , the 525 number 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 rate 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 10−8], and total training epochs 𝑒𝑒𝐺𝐺𝑓𝑓𝑒𝑒ℎ𝑠𝑠 ∈[50 ,100,300,400,1000,2000]. The model is selected based 528 on the mean absolute error on the test set, with the final hyperparameters set as 𝐼𝐼 𝑖𝑖𝐷𝐷𝐼𝐼𝐼𝐼𝐼𝐼= 30, 𝐿𝐿𝐼𝐼= 5, 529 𝐿𝐿𝐼𝐼= 5 , 𝐿𝐿𝐺𝐺= 1 × 10−4 ， 𝑊𝑊𝑊𝑊= 1 × 10−8 . Taking both training effectiveness and time into 530 consideration, the number of epochs is set to 100. 531 Model Validation 532 Mean absolute error 533 The mean absolute error (MAE) serves as a direct measure of the dis similarity between predicted 534 values and true values. Let the predicted value at time 𝑇𝑇 be denoted as 𝑋𝑋𝑇𝑇, and the true value as 𝑌𝑌𝑇𝑇, 535 then 𝑋𝑋𝑇𝑇= [𝑥𝑥𝑇𝑇,1, 𝑥𝑥𝑇𝑇,2, … , 𝑥𝑥𝑇𝑇,𝑁𝑁] and 𝑌𝑌𝑇𝑇= [𝑦𝑦𝑇𝑇,1, 𝑦𝑦𝑇𝑇,2, … , 𝑦𝑦𝑇𝑇,𝑁𝑁], where 𝑁𝑁= 360 is the total number of 536 brain regions, 𝑥𝑥𝑇𝑇,𝑖𝑖 represents the predicted fMRI signal value for brain region 𝑖𝑖 at time 𝑇𝑇 and 𝑦𝑦𝑇𝑇,𝑖𝑖 537 represents the true fMRI signal value for brain region 𝑖𝑖 at time 𝑇𝑇. The MAE is calculated by computing 538 the absolute error across different brain regions and then taking the average of these absolute errors. The 539 specific calculation process is defined by the following equation: 540 𝑀𝑀𝑀𝑀𝑀𝑀= 1 10 � 1 𝑁𝑁�� 𝑥𝑥𝑇𝑇,𝑖𝑖− 𝑦𝑦𝑇𝑇,𝑖𝑖� 𝑁𝑁 𝑖𝑖=1 10 𝑇𝑇=1 (5) 541 The above expression represents the MAE for a single prediction result. To ensure more reliable 542 outcomes, we repeated the process 20 times on the test set, carrying out a total of 200 time points of 543 fMRI signal prediction tasks, and calculated the average MAE to evaluate the model's predictive 544 performance, as showed in equation (6). 545 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 26 𝑀𝑀𝑀𝑀𝑀𝑀𝑎𝑎𝑎𝑎𝑎𝑎= 1 𝐺𝐺� 1 10 � 1 𝑁𝑁�� 𝑥𝑥𝑇𝑇,𝑖𝑖− 𝑦𝑦𝑇𝑇,𝑖𝑖� 𝑁𝑁 𝑖𝑖=1 10 𝑇𝑇=1 (6) 546 In the above equation, 𝐺𝐺= 20 de notes the number of times the computation is repeated. To 547 compare the differences in the fitting effects across various brain regions, this study calculated the 548 average MAE for different brain regions, as shown in equation (7). 549 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖= 1 𝐺𝐺� 1 10 �� 𝑥𝑥𝑇𝑇,𝑖𝑖− 𝑦𝑦𝑇𝑇,𝑖𝑖� 10 𝑇𝑇=1 (7) 550 In equation (7), 𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖 represents the average MAE for the i-th brain region. 551 Continuous /segmented function connectivity 552 In this study, functional connectivity (FC) is obtained by calculating the Pearson Correlation 553 Coefficient, whose formula is as follows: 554 𝐺𝐺𝑖𝑖,𝑗𝑗= ∑ �𝑥𝑥𝑖𝑖, 𝑜𝑜− 𝑥𝑥𝚤𝚤� ��𝑥𝑥𝑗𝑗, 𝑜𝑜− 𝑥𝑥𝚥𝚥� �𝑖𝑖 𝑜𝑜=1 � ∑ �𝑥𝑥𝑖𝑖, 𝑜𝑜− 𝑥𝑥̅� 2𝑖𝑖 𝑜𝑜=1 � ∑ �𝑥𝑥𝑗𝑗, 𝑜𝑜− 𝑥𝑥𝚥𝚥� � 2𝑖𝑖 𝑜𝑜 =1 (8) 555 The term 𝐺𝐺𝑖𝑖,𝑗𝑗 represents the correlation between the fMRI signal generated by brain region 𝑖𝑖 and 556 that by brain region 𝑗𝑗, where 𝑥𝑥𝑖𝑖, 𝑜𝑜 denotes the fMRI signal value produced by brain region 𝑖𝑖 at time 557 point 𝑛𝑛 , and 𝑥𝑥𝑗𝑗, 𝑜𝑜 denotes the fMRI signal value produced by brain region 𝑗𝑗 at time point 𝑛𝑛 . The 558 variable n represents the total number of time points used for the calculation. By performing the 559 aforementioned operation between each pair of defined brain regions, the functional connectivity matrix 560 between the brain regions can be obtained. 561 To obtain FC, this study employed two methods for generating the predicted sequences: continuous 562 prediction and segmented prediction. Continuous prediction refers to inputting a 10 TR (time resolution) 563 window, using the output as the next input to obtain the prediction result for the following time window, 564 and then connecting these predictions to form a complete fMRI sequence. Let 𝜒𝜒𝑖𝑖 represent the input 565 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 27 sequence, 𝜒𝜒𝑜𝑜𝑘𝑘 denote the output obtained from the k -th iteration, and 𝑆𝑆 𝑒𝑒𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝 signify the output 566 sequence; this process can be expressed by equation (9): 567 � 𝜒𝜒𝑜𝑜1 = 𝐹𝐹(𝜒𝜒𝑖𝑖; 𝐺𝐺) 𝜒𝜒𝑜𝑜𝑘𝑘+1= 𝐹𝐹�𝜒𝜒𝑜𝑜𝑘𝑘; 𝐺𝐺� 𝑓𝑓𝑓𝑓 𝐺𝐺 1 < 𝑘𝑘< 𝑇𝑇 −1 𝑆𝑆 𝑒𝑒𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝= 𝑒𝑒𝑓𝑓 𝑛𝑛𝑒𝑒𝐺𝐺𝑛𝑛𝑒𝑒𝑛𝑛𝐺𝐺𝑛𝑛𝑒𝑒� 𝜒𝜒𝑜𝑜𝑘𝑘 𝑓𝑓𝑓𝑓 𝐺𝐺 1 < 𝑘𝑘< 𝑇𝑇� (9) 568 In equation (9), 𝐹𝐹(𝑥𝑥) is the predictive model, 𝐺𝐺 is the brain network, 𝑇𝑇 is the number of cycles 569 set, which is 10 in this study, and concatenate is a function that joins sequences. For functional 570 connectivity validation, 𝜒𝜒𝑖𝑖 is set to the first 10 TR time window from the test set. 571 Segmented prediction refers to dividing a continuous time series into small intervals of 10 TR time 572 windows, inputting each interval into the model to obtain the corresponding prediction, and connecting 573 the different interval predictions chronologically to form a complete fMRI predicted sequence. Let the 574 k-th interval be represented as 𝜒𝜒𝑖𝑖𝑘𝑘, then 𝜒𝜒𝑖𝑖𝑘𝑘= [𝑋𝑋10𝑘𝑘−9, 𝑋𝑋10𝑘𝑘−8, … , 𝑋𝑋10𝑘𝑘], where 𝑋𝑋𝑖𝑖 denotes the fMRI 575 signal values for all brain regions corresponding to the i -th TR of the continuous time series. The 576 prediction process is specifically shown in equation (10): 577 � 𝜒𝜒𝑜𝑜𝑘𝑘= 𝐹𝐹�𝜒𝜒𝑖𝑖𝑘𝑘; 𝐺𝐺� 𝑓𝑓𝑓𝑓 𝐺𝐺 1 < 𝑘𝑘< 𝑇𝑇 𝑆𝑆 𝑒𝑒𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝= 𝑒𝑒𝑓𝑓 𝑛𝑛𝑒𝑒𝐺𝐺𝑛𝑛𝑒𝑒𝑛𝑛𝐺𝐺𝑛𝑛𝑒𝑒� 𝜒𝜒𝑜𝑜𝑘𝑘 𝑓𝑓𝑓𝑓 𝐺𝐺 1 < 𝑘𝑘< 𝑇𝑇� (10) 578 For this research, the chosen input is the continuous sequence before splitting the series that 579 eliminates time points with head motion greater than 0.25. Starting from the 90th percentile position, a 580 total of 100 TRs of the fMRI sequence is selected, and it is split into 10 groups with every 10 TRs as one 581 group. The full sequence is thereby divided into 10 intervals, T=10. 582 The predicted sequences obtained from the two methods mentioned above both utilize the Pearson 583 correlation method as outlined in equation (8) to calculate FC, which is then compared to the actual 584 functional connectivity matrix. The actual sequence used for calculating the true FC is the one 585 corresponding to the prediction input values; that is, in continuous prediction, the actual sequence starts 586 from the 10 TR fMRI signal used as input and continues for a total of 100 TRs of fMRI sequence values, 587 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 28 whereas in segmented prediction), the actual sequence is composed of the actual values corresponding 588 to each segment's output values. After obtaining the true FC and the predicted FC, the Pearson correlation 589 coefficient is used to determine their correlation. The predicted FC is defined as 𝐹𝐹 𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝 and the actual 590 FC as 𝐹𝐹 𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ. For 𝑘𝑘 ∈[𝐺𝐺 𝐺𝐺𝑒𝑒𝑊𝑊, 𝑛𝑛 𝐺𝐺𝑛𝑛𝑛𝑛ℎ], 𝐹𝐹 𝐶𝐶𝑖𝑖,𝑗𝑗 𝑘𝑘 denotes the element in the i-th row and j-th column of the 591 FC matrix, representing the functional connectivity of the fMRI signal between the i -th and j- th brain 592 regions. The PCCs (Pearson correlation coefficients) between the predicted and actual FC can then be 593 determined by equation (11). 594 𝑃𝑃𝐶𝐶 𝐶𝐶𝑠𝑠= ∑ � 𝐹𝐹 𝐶𝐶𝑖𝑖,𝑗𝑗 𝑚𝑚 𝑡𝑡𝑡𝑡 𝑝𝑝− 𝐹𝐹𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝�����������𝐹𝐹𝐶𝐶𝑖𝑖,𝑗𝑗 𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜ℎ − 𝐹𝐹𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜𝑜𝑜ℎ�����������𝑖𝑖, 𝑖𝑖 𝑖𝑖=1, 𝑗𝑗=1 � ∑ �𝐹𝐹 𝐶𝐶𝑖𝑖,𝑗𝑗 𝑚𝑚 𝑡𝑡𝑡𝑡 𝑝𝑝− 𝐹𝐹𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝���������� 2𝑖𝑖, 𝑖𝑖 𝑖𝑖=1, 𝑗𝑗=1 � ∑ �𝐹𝐹𝐶𝐶𝑖𝑖,𝑗𝑗 𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ − 𝐹𝐹𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ����������� 2𝑖𝑖 𝑖𝑖=1 (11) 595 The equation (11) specifies that 𝐹𝐹 𝐶𝐶𝑚𝑚𝑡𝑡𝑡𝑡𝑝𝑝��������� and 𝐹𝐹 𝐶𝐶𝑜𝑜𝑡𝑡𝑜𝑜 𝑜𝑜ℎ���������� represent the global average values of the 596 predicted and actual FC matrices, respectively. 597 Model Analysis 598 Inter-regional interaction information (IRI) 599 Following model training, initial input data for the testing set were used to generate t he model 600 outputs. As described in the Methods -Models section, input data segmented every 10 tr yield a 30-601 dimensional message. By employing overlapping segmentation, a total of 200 such segments (each 602 comprising 10 tr) were inputted, resulting in message data with dimensions of 30 × 200 × 𝑁𝑁𝑠𝑠𝑜𝑜𝑠𝑠, 𝑡𝑡𝑝𝑝𝑎𝑎𝑡𝑡, 603 where 𝑁𝑁𝑠𝑠𝑜𝑜𝑠𝑠, 𝑡𝑡𝑝𝑝𝑎𝑎𝑡𝑡 indicates the total number of connectivity edges across subjects. PCA was applied to 604 reduce the dimensionality of the obtained data's first component, producing IRI data with dimensions of 605 𝑁𝑁𝑚𝑚𝑝𝑝 × 200 × 𝑁𝑁𝑠𝑠𝑜𝑜𝑠𝑠, 𝑡𝑡𝑝𝑝𝑎𝑎𝑡𝑡, where 𝑁𝑁𝑝𝑝𝑚𝑚 is the number of selected components. In this experiment, most 606 subjects' first principal component (PC1) explained nearly 90% of the variance, so all IRI analyses were 607 based on the dimensionality reduction to PC1, which means 𝑁𝑁𝑚𝑚𝑝𝑝= 1. 608 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 29 IRI sent by region 609 For the IRI sent by region (RS‑IRI), we first summed, for each region, the message data across all 610 edges connected to that region along the corresponding dimensions. We then performed PCA on these 611 region‑level message vectors to derive the RS‑IRI with dimensions of 𝑁𝑁𝑚𝑚𝑝𝑝 × 200 × 𝑁𝑁𝑡𝑡𝑡𝑡𝑎𝑎𝑖𝑖𝑜𝑜𝑖𝑖. We used 612 the MMP360 atlas so 𝑁𝑁𝑡𝑡𝑡𝑡𝑎𝑎𝑖𝑖𝑜𝑜𝑖𝑖= 360. The PC1 accounted for nearly 90% of the total variance, so we 613 adopted PC1 as the RS‑IRI, which means 𝑁𝑁𝑚𝑚𝑝𝑝= 1. 614 Model Application 615 Fast Fourier Transform (FFT) 616 To characterize the oscillatory patterns underlying dynamic inter -regional brain interactions, we 617 applied Fast Fourier Transform (FFT) to the inter-regional information measures to obtain their spectral 618 representations. Specifically, for each individual an d each structural connection, the temporal inter -619 regional interaction measure 𝐼𝐼 𝑅𝑅 𝐼𝐼(𝑛𝑛) w as subjected to the Fourier transform as specified in Equation 620 (12), yielding the frequency domain distribution 𝐼𝐼 𝑅𝑅 𝐼𝐼(𝑘𝑘): 621 𝐼𝐼𝑅𝑅𝐼𝐼(𝑘𝑘) = � 𝐼𝐼 𝑅𝑅 𝐼𝐼(𝑛𝑛)𝑒𝑒−𝑗𝑗2𝜋𝜋𝑘𝑘 𝑜𝑜 𝑇𝑇 𝑇𝑇−1 𝑜𝑜=0 , 𝑘𝑘= 0,1,2, … , 𝑇𝑇 −1 (12) 622 where 𝑇𝑇 represents the total number of time points. In this study, the analysis was performed on 623 𝐼𝐼𝑅𝑅𝐼𝐼(𝑛𝑛) da ta aggregated over 100 TRs, thus 𝑇𝑇= 100. Due to the inherently low sampling rate of the 624 data, spectral analysis was confined to the frequency band of 0.005–0.5 Hz. 625 Group-level comparison between AD patients and controls. 626 For all subjects, we first identified and extracted the common inter-region brain connections present 627 across the entire cohort. The FFT was applied to the time series of these connections for each individual. 628 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 30 For each edge (connection) and for each frequency band, the amplitude values were subjected to a two-629 sample t -test to compare the AD and NC group. The resulting p- values from these tests were then 630 corrected using the FDR. Finally, we counted the number of inter -regional brain connections that still 631 exhibited a significant group difference in each frequency band. These connections represent the 632 pathways where the information transfer between the corresponding brain regions shows a significant 633 group-wise difference between the AD and NC groups at that specific frequency band. 634 The association between oscillation amplitude and MMSE scores 635 First, inter-regional brain connections common to all subjects were identified. For each patient in 636 the AD group, the FFT was applied to the time series of these connections. We then calculated Pearson 637 correlation coefficients between the spectral amplitude of each edge within each frequency band and the 638 participants' MMSE scores. Statistical significance was assessed using a permutation test with 1,000 639 iterations. To control for multiple comparisons, p -values were adjusted using the FDR. Only results 640 retaining significance after FDR correction are visualized in the figure. 641 Acknowledgments 642 Funding: 643 National Natural Science Foundation of China 32271146 and 81972160 644 Startup Funds for Top-notch Talents at Beijing Normal University 645 China Postdoctoral Science Foundation (2025M772874) 646 Author contributions: 647 Conceptualization: SYL, DBZ, SXL 648 Methodology: SXL, DBZ, TTC 649 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 31 Investigation: SXL, DBZ 650 Visualization: SXL 651 Supervision: SYL 652 Writing— original draft: SXL, JCZ, ZKY, JJ 653 Writing—review & editing: SYL, SXL, DBZ, XXD, YRH, LC 654 Competing interests: 655 Authors declare that they have no competing interests. 656 Figures: 657 658 Figure 1 Overall Workflow. A) The IN construction based on neuroimaging data and inter-region interaction (IRI) 659 generation. The model was trained independently for each subject, inputting 10 TRs of BOLD signals, and outputting 660 the predicted 10 TRs of BOLD signals. During prediction, the model can calculate the information transmitted 661 between regions. B) Validation of the predicted fMRI signals, including MAE and FC correlation analysis. The 662 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 32 generated MAE map was further correlated with neural variability and receptor map. C) Analysis of IRIs. The 663 message exchanged between each pair of regions, as computed by the model, was reduced via PCA, with the first 664 principal component representing the IRI. The analysis included the IRI on each edge and the total IRI sent by region 665 (see Methods). D) Application of the model to AD patients. The IN model for each individual was computed within 666 the AD and control groups to obtain group- average prediction errors and individual IRIs. The IRIs were subjected 667 to fast Fourier transform (FFT) to reveal oscillation patterns in inter-regional interactions. The amplitudes in different 668 frequency bands were then correlated with MMSE scores. 669 670 671 Figure 2 Model validation results. A) The distribution across the whole brain of the group-averaged MAE (mean 672 absolute error) for model-predicted fMRI signals in each brain region. Drawn by BrainSpace(105). B) Comparisons 673 between FC derived from segmented prediction and continuous prediction with the tru e FC. The left panel shows 674 the distribution of correlation between the FC obtained from segmented prediction and the true FC. The right panel 675 shows the continuous prediction. The details of continuous and segmented prediction methods are provided in the 676 Methods. C) The relationship between MAE and global neural variability . One point denotes a subject. D) The 677 relationship between MAE and regional mean neural variability. E) The relationship between the distribution of 678 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 33 MAE and the distribution of the norepinephrine transporter. 679 680 Figure 3 Analysis of inter-regional interaction information (IRI). A) Flowchart for IRI derivation: Initially, 30-681 dimensional time series serve d as interaction messages for each connection. Dimensionality reduction was 682 performed to derive the IRI time series. IRI was quantified for each fiber tract, and the sum of IRI sent from each 683 brain region was termed IRI sent by region (RS -IRI). B) Correlation between IRI variance and fiber length. The 684 error bars for each point represent the standard deviation across subjects for the corresponding connection length 685 and IRI variance. C) D istribution of RS -IRI s trengths across different subnetworks. D) Distribution of RS -IRI 686 variability. 687 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 34 688 Figure 4 Group-level comparison between AD patients and controls. A) The group-averaged prediction MAE 689 maps on the cortical surface for the AD and NC groups. B) The between-group differences in the SD across each 690 dimension of the interaction messages for AD and NC groups, with asterisks indicating statistically significant 691 between-group differences at α = 0.05. C) The brief workflow for obtaining oscillation amplitudes across different 692 frequency bands of the IRI in the AD and NC groups. D) The between-group differences in the oscillation amplitudes 693 described in (A). For each frequency band, the IRI between-group differences are computed and subjected to FDR 694 correction. The top figure shows, at low -, mid -, and high- frequency ranges (0.135, 0.345 and 0.49Hz), the 695 connections exhibiting between-group differences in IRI oscillations and the corresponding brain regions, drawn by 696 BrainNet Viewer(106). The chosen frequency bands correspond to the deep purplish-red bands shown in the figure 697 below. The bottom figure presents the total number of connections between brain regions that show significant 698 between-group differences in oscillation amplitudes across different frequency bands for the IRI. 699 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 35 700 Figure 5 The association between oscillation amplitude across different IRI frequency bands and MMSE 701 scores in AD patients. In this figure, the connections and their connecting brain regions for which IRI is significantly 702 correlated with MMSE scores. A permutation test was used, with all results FDR -corrected. The plotted fit line 703 represents a linear (first -order) fit. The connections corresponding to the IRI oscillation amplitudes are projected 704 onto the brain, with the associated connections annotated at the top or on the right side. The numerical labels adjacent 705 to the brain correspond to the indices defined in the MMP atlas. Connected regions are separated by a hyphen (e.g., 706 'ID-ID'). For a complete list of MMP region IDs, see supplementary. 707 708 Figure 6 The overall operational process of the model. The information produced by interactions between brain 709 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 27, 2026. ; https://doi.org/10.64898/2026.01.26.701662doi: bioRxiv preprint 36 regions is estimated using the interaction operator 𝐼𝐼(𝑥𝑥), and the predicted values of the node state variables are 710 estimated using the region operator 𝑅𝑅(𝑥𝑥). Taking a three-node network as an example, for the red, yellow, and blue 711 ball representing the brain region nodes, each pair of connected nodes inputs into the interaction operator to obtain 712 the inter-region information (grey ball, 𝐼𝐼𝑅𝑅𝐼𝐼𝑖𝑖,𝑗𝑗), a 30-dimensional vector. For each node, the total sum of IRIs on all 713 the edges directly connected to it is computed as the total input information for that node (black ball). This total 714 input information, along with the node's own signal value, is entered into the region operator, yielding the predicted 715 values of the brain region's dynamic signals for the next 10 time points (concave ball). In the interaction operator, 716 the red and yellow balls represent the signal values of two different brain regions with a connection, and the white 717 ball is the output value of the multilayer perceptron. By multiplying this output with the connection weights (the 718 lines between the red and yellow spheres) and the global parameter, the information value for the interaction between 719 the two brain regions is obtained (grey sphere). In the region operator, the fMRI signal from the brain region itself, 720 along with the information input the region receives, is fed into a multilayer perceptron to compute the region’s 721 subsequent signals. 722 Data Availability Statement 723 The data used in this study are available through the Human Connectome Project (HCP; 724 https://www.humanconnectome.org/study/hcp-young-adult/document/extensively-processed-fmri-data-725 documentation), a publicly available repository. The code and other data used for the analyses will be 726 made publicly available on GitHub upon acceptance of the manuscript. 727

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