Dynamic reorganization of functional networks underlying audiovisual interactions

Abstract

Crossmodal interactions involve crosstalk between different cortical areas and dynamic recruitment of regions, which is crucial for integrating sensory information into a coherent percept. Despite their significance, the dynamic cortical networks underlying the crossmodal influence of auditory information on visual motion processing—particularly in terms of temporally resolved EEG connectivity—have yet to be comprehensively characterized. In the present study, we investigated frequency-specific networks underlying audiovisual interactions during motion and speed estimation. Functional networks were generated using directed transfer function (DTF) and adaptive DTF (ADTF) to estimate connectivity patterns of electroencephalogram (EEG) data. Network-based statistical analyses revealed frequency-specific networks in the theta and alpha bands, which supported long-range communication between occipital/parieto-occipital, parietal, and frontal regions during audiovisual interactions compared to unisensory visual motion processing. Graph theory analyses demonstrated a transition from localized and segregated processing to global integration, emphasizing cortical network reorganization according to the demands of sensory processing. Moreover, these analyses further revealed frequency-specific shifts in connectivity over time, with low-frequency oscillations exhibiting sustained connectivity increases, while high-frequency bands showed transient patterns, reflecting the temporal flexibility of neural networks. These findings illustrate how local and global network modulations reflect the brain’s dynamic reorganization, balancing integration and segregation during crossmodal influences.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-23390-4.

Introduction

The human brain is adapted to guide behavior in natural environments that provide information to different sensory organs. Therefore, the integration of information from different sensory modalities is of central importance for a coherent perception of the external world. Notably, the integration and binding of sensory information in the spatial and temporal domain, as well as crossmodal influences where one modality modulates perception in another, have been considered essential elements of perception^1–3. Numerous audiovisual paradigms have illustrated that such crossmodal influences can produce substantial changes in various aspects of perception. For instance, previous research has indicated that audiovisual interactions in the temporal domain can alter perception of different motion attributes, such as direction⁴, speed^5,6, sensitivity to coherent motion⁷, discrimination and categorization of motion^8,9. These findings highlight the multisensory nature of motion and provide important implications for perceptual dynamics in daily life situations^10,11.

Utilizing a speed judgment paradigm, Kaya and Kafaligonul¹² investigated the neural correlates of auditory-driven modulations in visual motion perception. In their study, the duration of time interval demarcated by brief auditory clicks significantly alters the perceived speed of apparent motion, such that a shorter auditory time interval is typically perceived to move faster than the one with a long time interval^5,6. Consistent with the fact that audition is dominant in the temporal domain, these audiovisual interactions have been described by “temporal ventriloquism”^13,14. That is to say, it has been described that static clicks alter the perceived time interval between motion frames (e.g., capturing the timing of visual motion frames), thereby leading to changes in the perceived speed of visual motion. Studying such perceptual illusions provides a perspective into how the brain binds asynchronous sensory signals. Using this approach, Kaya and Kafaligonul¹² revealed modulations in both early and late ERP components across multiple scalp regions (parieto-occipital, parietal, and prefrontal areas), suggesting that auditory temporal information exerts its influence on visual motion processing at multiple stages of neural processing (see also Kaya et al.,¹⁵). The timeline of neural modulations further pointed to a dynamic interplay between the identified cortical areas, emphasizing that the interactions between different areas play a key role in audiovisual processing and final motion perception. Despite these advances, our understanding of how large-scale neural networks and oscillatory dynamics support such crossmodal interactions remains limited.

In the present study, we investigated functional networks associated with auditory-driven modulation of motion perception by using the EEG (electroencephalogram) dataset of Kaya and Kafaligonul¹². While previous findings have provided valuable insights into the cortical dynamics involved in audiovisual processing, particularly from fMRI-based approaches, the temporally resolved reorganization of large-scale functional networks remains less understood, especially in the context of perceptual motion tasks that require integration of temporally asynchronous inputs. Recent work by Singh et al.¹⁶, for example, demonstrated that perceived audiovisual simultaneity is associated with increased local segregation and reduced global integration of brain networks, as measured by BOLD correlations. While such studies offer important spatial perspectives, they are limited in capturing the fast and frequency-specific interactions that EEG connectivity methods afford. Accordingly, we employed two leading multichannel estimators, directed transfer function¹⁷ (DTF) and adaptive DTF¹⁸ (ADTF), to reveal the flow of neural processing and the organization of brain networks across different frequency bands. Numerous studies have validated the application of DTF to sensor-level EEG data, highlighting its robustness to noise and insensitivity to volume conduction, as well as its capacity to provide reliable estimates of functional connectivity without the need for source reconstruction^19–21 We further applied network-based statistics²² and graph theory²³ to systematically examine key network features, such as clustering, efficiency, integration, and segregation, which are crucial for understanding the balance between local and global functional connectivity. This approach also allowed us to evaluate cortical self-organization and interaction among various cortical regions under different sensory stimulation profiles.

The rationale of the current study and our motivation to structure a data analysis pipeline based on oscillations, multichannel estimators, and graph theory were threefold. First, we aimed to understand frequency-resolved functional connectivity patterns underlying audiovisual interactions in the temporal domain. We specifically tested whether the brain exhibits different connectivity patterns for the processing of visual apparent motion in isolation and under the conditions in which audiovisual interactions became dominant. By doing so, we aimed to uncover distinct patterns and shared mechanisms within the neural pathways underlying crossmodal influences and multisensory integration. Second, we aimed to identify frequency-specific topological features of these networks associated with temporal dynamics of (auditory-driven changes in) motion perception using graph theory. While studies on audiovisual paradigms have started to reveal how frequency-specific network characteristics adapt dynamically for efficient crossmodal influence^24,25, the graph-theoretical representation of functional connections underlying perceptual shifts driven by fine-grained auditory timing—specifically, how subtle modulations in auditory intervals alter the perceived speed of visual motion—has not been systematically explored. Lastly, we aimed to understand the limitations of multichannel estimators, graph theory, and time-varying connectivity analysis in transient, event-related EEG recordings. Although some prior studies have applied graph-theoretical and connectivity-based approaches to time-sensitive paradigms^26–29, and a few recent studies have specifically focused on audiovisual processing^24,25,30, further investigation is warranted to determine how effectively these analyses capture event-related fluctuations in network organization of audiovisual integration, particularly at the sensor level. In this study, we specifically examined whether these approaches could resolve changes in functional connectivity linked to subtle differences in the auditory timing and its effects on perceived visual speed.

Materials and methods

Participants

We used the EEG dataset by Kaya and Kafaligonul¹². A total of 21 participants took part in the study, and the final dataset included recordings from 18 healthy volunteers (right-handed, age range 19–32 years) who completed all steps of the study according to the instructions. All participants had normal or corrected-to-normal visual acuity and normal hearing, and none had a history of neurological disorders by self-report. The entire protocol was carried out in accordance with international guidelines³¹ and approved by the local ethics committee at the Faculty of Medicine, Ankara University (Approval ID: 10.412.13). A written informed consent was obtained from each participant prior to enrollment in the study.

Design and procedure

The experimental design and procedures were covered by Kaya and Kafaligonul¹² in detail. Here, we briefly highlight the key features of stimulation and outline the critical steps of design. A two-frame apparent motion was used to generate visual motion. In each motion frame, a bar was flashed 3.4°above the fixation for 50 ms (Fig. 1a). The spatial displacement (i.e., horizontal center-to-center distance) was 1.3°. The inter-stimulus interval (visual ISI) between the motion frames and flashed bars was 100 ms. The auditory stimuli were a pair of static clicks and introduced binaurally with headphones. Each click was a rectangular windowed 480 Hz sine-wave carrier (sampled at 44.1 kHz with 8-bit quantization) and had a duration of 20 ms. The sound pressure level (SPL) was 75 dB.

Fig. 1.

(a) Schematic representation of the experimental design and the timeline of each trial. Each trial consisted of two consecutive presentations of a two-frame apparent motion with a 900 ms delay. These consecutive visual apparent motions were precisely the same, while the time interval between the concurrent auditory clicks (ISI_A) differed. Participants fixated centrally and judged which motion appeared faster. The auditory timings for low and high disparity levels are shown separately. Visual and auditory stimuli are represented by white bars and speaker icons, respectively. (b) Overview of the analysis pipeline. Top row: EEG signals were preprocessed, filtered into canonical frequency bands, and connectivity was computed using directed transfer function (DTF) and adaptive DTF. Bottom row: After thresholding and binarization, graph theory metrics (CC, LE, Q, GE) were extracted. Statistical comparisons were performed using network-based statistics (NBS) and graph-based analyses to evaluate condition-specific changes.

The design was based on comparing the speed of two consecutive apparent motions moving in the same direction (rightward or leftward). On each trial, the two-frame apparent motion was presented twice, and the temporal offset between each presentation (i.e., the offset of the first presentation and the onset of the second) was 900 ms (Fig. 1a). In the audiovisual (AV) conditions, a pair of clicks temporally centered with the presentation of each apparent motion was introduced. While each apparent motion was identical in terms of visual stimulation, the time interval defined by the pair of clicks (auditory ISI) was varied. For one of the apparent motion presentations, the time interval between static clicks was shorter than or equal to the visual time interval between the two motion frames (short condition). For the other one, the auditory time interval was longer than the visual time interval (long condition). In addition, the disparity level between short and long auditory intervals was varied, leading to low and high disparity levels. Specifically, the low disparity level involved a moderate difference between auditory intervals (100 ms vs. 160 ms), while the high disparity level involved a large difference (40 ms vs. 220 ms). Figure 1a illustrates the auditory timing conditions across disparity levels (short vs. long, low vs. high disparity level). Hence, the design included four audiovisual conditions with different auditory time intervals (low disparity level: 100 ms vs. 160 ms auditory ISI; high disparity level: 40 ms vs. 220 ms auditory ISI). At the end of each trial, the participants indicated which apparent motion (first or second) moved faster via keypress. The design also included unimodal conditions (visual-only, four corresponding auditory-only conditions). In these conditions, the timeline of events was exactly the same, but either apparent motions (visual-only) or pairs of clicks (auditory-only) were presented. Similar to the audiovisual conditions, the participants performed the speed comparison at the end of visual-only trials but only fixated and passively listened to clicks during the auditory-only conditions. Each participant completed four experimental sessions, with pseudorandomly intermixed conditions within each session, resulting in a total of 48 presentations per condition.

Data acquisition and preprocessing

The EEG data were acquired using a 64-channel MR-compatible system (Brain Products, GmbH, Gilching, Germany). The caps (BrainCap MR, Brain Products, GmbH) included 63 scalp electrodes and an additional electrocardiogram (ECG) electrode attached to the back of participants to control for cardioballistic artifacts. Two of the scalp electrodes (FCz and AFz) served as the reference and ground, respectively. The electrode impedances were consistently monitored and typically below 10 kΩ throughout an experimental session. The EEG signals were sampled at a rate of 1 kHz and underwent online band-pass filtering between 0.016 and 250 Hz. The neural signals, stimulus markers, and behavioral responses were recorded via Brain Vision Recorder Software (Brain Products, GmbH).

The preprocessing of EEG signals was carried out offline using Brain Vision Analyzer 2.0 software (Brain Products, GmbH). First, the data were down-sampled to 500 Hz, and the ECG signal was used to remove cardioballistic artifacts³². The data were then segmented into epochs ranging from −400 ms (before the onset of each apparent motion) to 1000 ms (after the onset of each apparent motion). A semi-automatic inspection was performed to identify and mark epochs with artifacts. Specifically, epochs showing voltage changes of less than 0.5 μV or more than 200 μV within a 100 ms window, as well as oscillations over 50 μV/ms, were marked as bad and subsequently rejected after manual screening. Independent component analysis (ICA) using the Infomax algorithm was applied to remove common EEG artifacts such as eye blinks. Topographic spline interpolation was used to correct bad channels³³. Following these standard preprocessing procedures, an average of 2.37% of trials per condition were rejected, and a total of 18 participants were retained for further analysis.

Frequency band isolation

Further processing steps were outlined in Fig. 1b and carried out with toolboxes and our own custom scripts written in MATLAB (The MathWorks, Natick, MA). In the speed judgment paradigm employed by Kaya and Kafaligonul¹², the participants performed a speed comparison on visual motion (primary task-relevant stimulus) and passively listened to concurrent clicks (secondary task-irrelevant stimulus). Therefore, the design emphasizes that the auditory signals originating from the secondary modality interfere and interact with the processing of visual motion. We applied the violation of the additive model to evaluate these audiovisual interactions³⁴ and identified nonlinear modulations by comparing (AV-A) waveforms with the activities elicited by visual apparent motion [(AV-A) vs. V]. This approach is also equivalent to comparing the audiovisual waveforms with the synthetic summation of unimodal signals [AV vs. (A + V)]. Accordingly, the neural responses to the auditory clicks (A) were subtracted from the corresponding AV conditions, yielding four distinct synthetic difference waveforms (AV-A) for each auditory time interval condition (i.e., AV-A₄₀, AV-A₁₀₀, AV-A_160, and AV-A₂₂₀). These bimodal differences (AV-A) were further used to reveal modulations varying with auditory timing. To study the effect of auditory timing on network-based measures, we specifically compared conditions within each disparity level. For the low disparity conditions, we compared AV-A₁₀₀ (short) vs. AV-A₁₆₀ (long), and for the high disparity conditions, we compared AV-A₄₀ (short) vs. AV-A₂₂₀ (long), as the observers performed speed comparisons during a trial.

Parameters for further analysis of waveforms were set according to the specifications provided by Aydın³⁵ and Aydın et al.³⁶. The (AV-A) waveform for each auditory time interval condition, along with the visual-only (V) data, were filtered using an Infinite-Impulse-Response (IIR) filter with a 35th-order and a 50 Hz notch filter to remove network noise. To isolate specific EEG frequency bands, five separate Finite-Impulse-Response (FIR) filters were applied, targeting delta (1–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz), and gamma (30–60 Hz) bands. The filter parameters were set featuring a 0 Hz transition band at both cutoff frequency edges, a pass-band ripple of 0.0575, a stop-band ripple of 0.001, and a density factor of 20. The optimal filter order for each frequency band was automatically determined using the Parks-McClellan equiripple FIR order estimator via MATLAB’s firpmord function in the Signal Processing Toolbox³⁷.

Measures of whole-brain functional networks

For each participant, we obtained five distinct frequency bands (delta, theta, alpha, beta, gamma) for the visual-only (V) and four audiovisual difference waveforms (AV-A₄₀, AV-A₁₀₀, AV-A_160, and AV-A₂₂₀), resulting in a total of 25 subsets of data (5 experimental conditions × 5 frequency bands). Connectivity matrices for each subset were constructed using all electrodes based on estimates from the DTF¹⁷ and adaptive DTF (ADTF)¹⁸. We based DTF parameters on previous studies^35,36,38. Similarly, for the ADTF analysis, we followed the methodology described in Xi et al.²⁴ and Xi et al.²⁵. These parameters were first optimized and validated using a separate dataset of audiovisual interactions (Kaya & Kafaligonul³⁹) before being applied to the current dataset.

Directed transfer function

The directed transfer function (DTF) was introduced by Kaminski and Blinowska¹⁷ to characterize information flow between neural populations. It is widely used to construct frequency-specific networks and to capture neural information transfer while minimizing the impact of spurious interactions caused by volume conduction¹⁹. Recent developments have reinforced the validity of applying multivariate autoregressive (MVAR) models at the sensor level, enabling reliable estimation of directional and causal interactions directly from multichannel EEG recordings⁴⁰. Techniques derived from MVAR modeling, such as DTF, offer a reliable alternative to bivariate autoregressive methods by effectively characterizing spectral relationships in complex neural systems⁴¹. It has been extensively applied to sensor-level EEG data, producing stable estimates of functional connectivity without requiring source reconstruction^19,20. In line with established methodological guidance, we did not apply preprocessing steps that could distort the correlation structure of the multichannel data (e.g., common average referencing or surface Laplacian). Prior work has emphasized that “DTF is insensitive to volume conduction and very robust in respect to noise”¹⁹ and that “projections on the cortex surface are not needed and may disturb the phase relations between channels”²⁰. While some recent studies have raised theoretical concerns about volume conduction effects, subsequent analyses concluded that “in practice this influence does not distort substantially the estimates”²¹. Following this literature, we applied preprocessing steps consistent with recommended practices for applying DTF to sensor-level EEG data, and source reconstruction was not included in our analysis pipeline. DTF was calculated based on the following formula⁴²:

1

This formula describes the influence of channel-j on channel-i at a particular frequency f. k is the number of channels, and H is the transfer matrix of the system calculated based on the MVAR modeling. It estimates only one MVAR model from all time points within the epochs^42,43. Therefore, while DTF could be selected according to the frequency range of interest, it could not provide time-varying connectivity estimations. The result of this equation lies in the range of [0, 1], where a value closer to 0 indicates weak or no influence, and a value closer to 1 indicates a strong influence between the channels. We calculated DTF connectivity matrices (C_63x63) for each frequency band of an experimental condition using the electrophysiological Connectome (e-Connectome-2-full) software toolbox⁴⁴. An integrated ARfit package⁴⁵ was used to estimate the multivariate autoregressive (AR) models necessary for DTF calculation.

Adaptive directed transfer function

Similar to DTF, ADTF is a frequency-domain estimator of interactions between channels based on multivariate autoregressive (MVAR) modeling. However, its adaptive nature enables it to capture time-varying connectivity relationships between cortical areas. We included ADTF in our analysis to systematically investigate network dynamics over time and to compare two widely used connectivity estimates of DTF and ADTF on the same dataset. Similar to DTF, ADTF has been shown to be robust to volume conduction; therefore, we applied the same preprocessing strategy as described above. The time-varying coefficient matrices of the adaptive MVAR model were calculated by using the Kalman filter algorithm⁴⁶, resulting in a time-varying transfer matrix H(f,t). Accordingly, ADTF was calculated as a function of both frequency and time based on the following formula⁴⁴:

2

This formula describes the influence of channel j on channel i at a particular frequency f and time t. Here, k represents the number of channels in the network. High values of ADTF indicate a strong influence between channel j and channel i, implying that high information flow occurs between these channels at the specified frequency and time. Conversely, low ADTF values suggest weak or no influence between the channels [see also Wilke et al.¹⁸ and He et al.⁴⁴]. In our analysis, we calculated ADTF connectivity matrices (C_63x63) for each frequency band sampled at 2 ms time steps (i.e., 500 Hz) using the electrophysiological Connectome (e-Connectome-2-full) software toolbox⁴⁴. This approach allowed us to capture the dynamic changes in connectivity patterns over time, providing a more detailed understanding of the temporal evolution of brain network interactions during an experimental condition.

Graph theoretical analysis

Functional connections between brain regions can be analyzed by modeling as complex networks through graph theory, which allows for the identification and understanding of subnetworks that may differ across experimental conditions. As mentioned above, we first used DTF and ADTF to generate connectivity strength values for each channel pair within the constructed matrices for each frequency band. These connectivity matrices were then converted into undirected binary matrices (i.e., adjacency matrices) by applying thresholding based on network sparsity (Fig. 1b). The sparsity threshold was defined as the ratio of existing edges to the maximum possible number of edges in the network, preserving a proportion (0 < t < 1) of the strongest weights from the connectivity matrix⁴⁷. For subsequent analyses, sparsity thresholds ranged from 0.1 to 0.5 in intervals of 0.1⁴⁸. In the adjacency matrices, rows and columns correspond to the nodes in the network, representing the EEG electrodes, while the entries indicate the links or edges filled with cortical dependency estimates. Various characteristic network parameters were then calculated using these adjacency matrices to investigate the topological performance of neural interactions in unisensory and multisensory conditions. These parameters included global efficiency, local efficiency, clustering coefficient, and modularity, encompassing both segregation and integration characteristics of the brain. Although segregation and integration are opposing demands in networks, they both serve as major organizational principles and are essential for the dynamic functional organization of brain networks. Segregation allows for specialized processing within local clusters of neurons, enabling efficient and focused responses to specific tasks. Integration, on the other hand, facilitates the coordination and communication between these specialized regions, ensuring that the brain can generate coherent and adaptive responses to complex stimuli. Together, these principles underpin the brain’s ability to balance localized, specialized functions with broader, coordinated activities, which is crucial for maintaining optimal cognitive and perceptual performance⁴⁹. The modeling and extraction of topological features using graph theory were performed using the Brain Connectivity Toolbox, as introduced by Rubinov and Sporns²³. The following subsections provide a brief overview of the specific network measures used in this study.

Network segregation

Network segregation refers to the formation of densely interconnected clusters or neighbors, in terms of topological distance, that are specialized in certain processing tasks. These local communities are segregated from each other, with most edges linking nodes within the same modules and only a few connections between different modules⁴⁹. The clustering coefficient (CC) and local efficiency (LE) are essential measures of network segregation, depending on the number of triangles present in the network. The clustering coefficient quantifies the level of local segregation by measuring the density of connections between a node and its neighbors. It is determined by calculating the proportion of triangles around a node that are formed by connected neighbors. When a node is surrounded by a highly interconnected cluster, this arrangement is vital for the operational functionality of local clusters within the graph³⁵. Local efficiency measures the effectiveness of information transfer among the remaining nodes after one node is removed from its local cluster, thereby reflecting the network’s robustness and fault tolerance at a local level⁵⁰. High local efficiency indicates that the network can maintain efficient communication even if some nodes are disrupted, underscoring the resilience of the brain’s local networks. CC and LE are mathematically calculated based on the following formulas^51,52:

3

where C_i is the clustering coefficient of node i (C_i = 0 for k_i < 2), k_i is the degree of node i, and t_i is the number of triangles around node i. A high CC indicates that nodes have a high tendency to form closely connected groups, reflecting local interconnectedness within the network. The CC ranges between 0 and 1, where 0 signifies no clustering (nodes are not connected to each other), and 1 indicates maximum clustering (each node’s neighbors are fully interconnected).

4

where E_loc,i is the local efficiency of node i, and d_jh(N_i) is the length of the shortest path between j and h, that contains only neighbors of i. a_ij is the connection status between i and j: a_ij = 1 if a link exists between i and j (i.e., they are neighbors), and a_ij = 0 otherwise. A high LE indicates that nodes have efficient communication pathways with their direct neighbors, even if one node is removed. LE ranges between 0 and 1, where 0 signifies no local efficiency (poor communication within local clusters) and 1 indicates maximum local efficiency (optimal communication within local clusters).

Network modularity

The modular structure, or modularity, of a network is a sophisticated measure of segregation that reflects the local connectivity structure of the graph^23,49. In complex networks, modules represent the balance between the density of connections within a module and those between different modules^53,54. When modules display high levels of internal clustering and fewer interconnections with other modules, this indicates a high level of modularity, where each module specializes in specific functional tasks. The modularity measure, Q, quantifies the network’s tendency to form these segregated clusters. It is calculated using the following formula⁵⁴:

5

In the formula, l denotes the number of edges in the network. The term m_i represents the module to which node-i belongs. If node-i and node-j are in the same module (m_i = m_j), then δ(m_i, m_j) equals 1; otherwise, it equals 0. Modularity increases when nodes within the same module have denser connections (more functional edges) with each other compared to sparser connections between modules. This measure is closely related to the functional organization of brain regions, providing flexibility and adaptability under changing conditions⁵⁰. Clustering and modularity both capture similar aspects of the connectivity structure since highly modular networks often consist of densely clustered communities. However, high clustering alone does not necessarily indicate the presence of modules or communities⁴⁹. Thus, each measure of local connectivity provides unique information about the locally embedded nodes and the community structure.

Network integration

While clustering, local efficiency, and modularity assess local connectivity and the segregation of nodes into communities, other measures capture the network’s capacity for engaging in global interactions and network-wide integration⁴⁹. Integration refers to the ability of distributed cortical regions to effectively combine and share information, relying on path lengths and distances between nodes²³. In functional networks, the paths connecting pairs of brain regions represent the routes of information flow. These paths are calculated by the number of distinct edges in binary graphs, providing insights into the efficiency of global integration. A short path length indicates that each node can, on average, be reached from any other node via a path with only a few edges, suggesting higher potential for communication and stronger integration among functionally dependent regions. In the current study, global efficiency (GE) is used as a measure of integration in brain networks. GE was calculated using the average inverse distance matrix using the following formula⁵¹:

6

In the formula, d_ij represents the distance between node-i and node-j. The highest possible GE value is found in a network where every node is directly connected to every other node by a single edge, resulting in all distances between nodes (i.e., all d_ij) equal one. Conversely, the lowest global efficiency is observed in completely disconnected networks, where the distances between nodes are infinite. Networks with shorter path lengths have higher global efficiency, meaning that, on average, nodes can communicate with each other through a minimal number of steps, enhancing the efficiency of information transfer.

Network-based statistics of connectivity matrices

To determine significant differences in connectivity patterns and sub-networks between unisensory and multisensory conditions, as well as among various auditory timing conditions, we analyzed the (thresholded and non-binarized) whole-brain connectivity matrices using Network-Based Statistics (NBS)²⁰. NBS is a nonparametric method for mass univariate significance testing of each network connection, designed to control for the multiple comparison problem (MCP). Compared to other statistical procedures that correct p-values for each connection individually, NBS offers greater statistical power in managing the family-wise error (FWE) rate in complex networks. This method has been previously employed to explore the neurological basis of various psychotic disorders^48,55,56. Accordingly, we utilized NBS to examine different connected components of brain functional networks under specific unisensory and multisensory conditions in healthy participants.

In the NBS analysis, we compared unisensory (V) with multisensory (AV-A) conditions, as well as different auditory timing conditions (high vs. low disparity). First, we focused on the effects elicited by audiovisual interactions at the network level, regardless of auditory timing. Thus, contrasts were defined as “unisensory > multisensory” and “unisensory < multisensory,” combining all audiovisual conditions (AV-A) across different auditory timing conditions. We used DTF in this stage of our analysis. Then, we examined the time-varying changes in network dynamics through the NBS analysis of ADTF. Using the ADTF measure, we further tested the contrasts between short and long auditory time intervals within each disparity level (i.e., “short < long” and “short > long”), in addition to the comparisons between unisensory and multisensory conditions. Additionally, we assessed the functional connections that either increased or decreased over time for each condition. The FWER in NBS analysis was controlled at the cluster level, with an alpha (ɑ) threshold value of 0.01 applied to the p-values associated with each connection. We performed 5000 permutations, and the test statistics threshold was set as T < 3.0. Significant subnetworks were visualized using BrainNet Viewer⁵⁷.

Statistical analysis of network indices

Further statistical tests were carried out to understand how network indices change under different conditions. We performed two-way repeated-measures ANOVA with factors of frequency band and stimulation (V, AV-A₄₀, AV-A₁₀₀, AV-A_160, and AV-A₂₂₀) on each graph theory index derived from DTF. Follow-up paired comparisons were performed to compare network properties of audiovisual conditions and to examine the effects of audiovisual interactions in time.

We applied a similar approach to the graph theory indices derived from ADTF. We incorporated cluster-based permutation tests, encompassing all time points from −100 to 800 ms. Considering the temporal dimension ADTF approach, paired comparisons on GT indices also included a correction in the time domain to overcome Type I error. This approach aims to test all neighboring and continuous time points of each GT index (i.e., network metrics of CC, LE, Q, GE) that are significantly different among specific conditions while addressing the problem of multiple statistical comparisons and preserving the temporal neighbor relationships objectively⁵⁸. In the initial step, the GT metrics from all participants were combined irrespective of the condition and then randomly split into two groups. This shuffling procedure was used to create surrogate data and was repeated 1000 times to generate a null distribution. Under the null hypothesis, which assumes no difference between specific conditions, the difference in averaged GT values between two particular conditions was computed for both the real data and the corresponding shuffled surrogates. The difference in GT values between specific conditions was transformed into a z-score by subtracting the mean of the null distribution from the actual GT difference and then dividing by the standard deviation of the null distribution⁵⁹. This z-score was converted to a p-value using a cumulative distribution function, yielding a time series of p-values. To account for multiple comparisons, cluster-based statistics were used to control false alarms at the map-level threshold, employing the supra-threshold cluster size test with an ɑ threshold value of 0.01, applied to the p-values associated with each time point⁶⁰. After thresholding all statistical maps generated under the null hypothesis, we obtained a distribution of the largest supra-threshold clusters expected under the null hypothesis. In the distribution of the largest clusters expected under the null hypothesis, clusters containing less than 99% (two-tailed) were removed. Finally, all neighboring and continuous time points of a significant cluster were highlighted on GT plots, indicating continuous significance at two-tailed p < 0.01. Since this test can only compare two conditions at a time, we performed the comparisons as outlined above.

To explore potential links between large-scale brain network dynamics and perceptual performance, we performed exploratory correlation analyses between graph theory metrics and behavioral data. For each participant, behavioral performance was quantified as the percentage of trials in which the short auditory interval condition was perceived as faster than the long auditory interval. Corresponding graph metrics (e.g., global efficiency, modularity) were computed as the difference between short and long auditory intervals, separately for each disparity level, using values derived from significant time clusters identified in the graph theory analysis. Simple linear regression models were then applied to assess the association between behavioral scores and graph differences, using subject-level data. Both slope and intercept coefficients were estimated, and the results were interpreted cautiously due to the modest sample size and absence of statistically significant correlations (p > 0.05 for all tests).

Results

Summary of behavioral findings

We replotted the behavioral data to summarize the findings of Kaya and Kafaligonul¹². To quantify the effect of auditory time intervals on perceived speed, we calculated the percentage of trials in which the apparent motion with a short auditory time interval was perceived as faster than the one with a long auditory interval. Figure 2 displays the distribution of these percentage values under low and high disparity conditions. For both conditions, the participants perceived the apparent motion with a short auditory time interval as faster in over 60% of the trials. As reported by Kaya and Kafaligonul¹², the percentage values significantly exceeded the 50% chance level (Bonferroni corrected two-tailed t-tests, all p < 0.001). Along with other studies (e.g., Duyar et al.⁶¹; Yilmaz & Kafaligonul⁶²), these results highlight significant audiovisual interactions in the temporal domain. More importantly, the percentage value of high disparity was significantly higher than that of low disparity condition (t₁₇ = 7.95, p < 0.001, Cohen’s d = 1.87), indicating a significant effect of temporal disparity on the observed audiovisual interactions. The findings overall demonstrate robust effects of auditory timing on motion and speed estimation.

Fig. 2.

Behavioral results (n = 18). The percentage of trials in which the apparent motion with a short auditory interval was perceived as faster than the one with a long interval is shown for low and high temporal disparity levels. Individual participant data are represented by connected points, while group-averaged data are shown as boxplots.

Directed transfer function and derived graph theory indices

We first identified the nonlinear interactions between the neural representations of visual apparent motion and auditory clicks by comparing the activity of visual apparent motion (V) with the difference waveforms (AV-A). That is to say, in the initial stage of our analyses, we aimed to determine changes in functional networks associated with audiovisual interactions. Accordingly, we compared the functional connectivity estimates of DTF across V and combined audiovisual (AV-A) conditions by applying network-based statistics. Importantly, the application of sparsity thresholding and cluster-level permutation testing in NBS minimizes potential influences stemming from condition-related power differences, particularly those that might arise from subtraction-based waveform derivations. Additionally, DTF (and ADTF) offers resilience against amplitude-related distortions, providing conservative yet reliable estimates of functional connectivity, even at the sensor level. To further guard against power-related confounds, we applied binarization prior to computing graph theory indices. Collectively, these steps strengthen the validity of the extracted connectivity patterns by ensuring that the observed effects are rooted in network topology rather than fluctuations in signal amplitude.

The functional connectivity patterns in theta (p = 0.0034) and alpha (p = 0.0018) bands were significantly increased in the difference waveforms compared to the visual-only condition (Fig. 3a vs. b). The increased connections predominantly involved long-range connectivity patterns between the parietal/parieto-occipital and frontal regions, highlighting the interactions across sensory representations/neural activities over distant cortical areas (Fig. 3b). In the theta and alpha bands, audiovisual interactions exhibited extensive intra-hemispheric and interhemispheric connections, suggesting robust facilitation at the network level. On the other hand, we identified robust increases in functional connections during unisensory processing of motion (visual-only) across all frequency bands but with distinct characteristics (delta p = 0.0086; theta p < 0.001; alpha p = 0.0017; beta p < 0.001; gamma p < 0.001). The strengthening of functional connections occurred through densely connected neighboring subgroups within narrower occipital and parietal regions, suggesting more localized processing during visual-only processing (Fig. 3a). The pattern of connectivity increase was most prominent in the theta, alpha, and beta bands but relatively sparse in the delta and gamma bands. These findings suggest that unisensory processing of visual stimuli relies more on localized networks, while audiovisual interactions engage broader, more integrative networks specific to the alpha and theta frequency bands. We also compared the visual-only waveforms with those of individual auditory timing conditions. These comparisons overall indicated similar changes at the network level (Figures S1-S4).

Fig. 3.

Functional connectivity differences between unisensory visual (V) and audiovisual difference (AV-A) waveforms (n = 18). Significant connections identified by network-based statistics are displayed across sagittal (left and right), axial, and coronal brain views. Representations were obtained with the BrainNet Viewer Toolbox⁵⁷. Results are presented for five frequency bands (delta, theta, alpha, beta, and gamma), with corresponding p-values indicated for each frequency band. (a) Functional connectivity was significantly stronger during unisensory processing of visual motion. Blue edges represent the regions with higher DTF connectivity in the unisensory condition, primarily concentrated in occipital and parieto-occipital clusters. (b) Long-range connections became stronger for the audiovisual interactions. Red edges highlight regions with higher DTF connectivity, pronounced between frontal and parietal/parieto-occipital regions, especially in the theta and alpha bands.

The alterations in functional networks were further examined across different conditions by analyzing the topological parameters (CC, LE, Q, and GE) based on graph theory. Given that network parameters from different sparsity thresholds showed similar statistical results, we presented the topological parameters at the conservative 0.1 sparsity threshold, consistent with previous literature^24,48,63. Figure 4 displays the alterations in topological parameters across distinct frequency bands and sensory conditions (V, AV-A₄₀, AV-A₁₀₀, AV-A_160, and AV-A₂₂₀). A repeated-measures ANOVA on these measures revealed significant main effects of modality/sensory stimulation, frequency band, and a two-way interaction (Table 1). Pairwise comparisons between sensory conditions revealed that network characteristics, including CC, LE, and Q, were significantly higher during visual-only processing compared to difference waveforms of all time interval and disparity conditions and frequency bands (FDR-corrected, all p < 0.0001). Interestingly, for the CC and LE measures based on the alpha band, there were significant differences across auditory time intervals (short vs. long) in the high disparity and marginally significant in the low disparity level. Conversely, GE was significantly higher in all audiovisual conditions compared to the visual-only (FDR-corrected, all p < 0.0001; see also Table S1). These comparisons suggest that the significant main effects of modality, frequency, and the observed pairwise interactions were primarily driven by differences in the processing of visual-only (V) and audiovisual interaction (AV-A) across distinct frequency bands. There were no robust and consistent differences across auditory timing conditions.

Fig. 4.

The averaged network values for CC, LE, Q, and GE derived from DTF were presented for each frequency band and condition. Error bars represent the standard error (± SEM) across subjects (n = 18).

Table 1.

Repeated-measures ANOVA on graph theory indices derived from DTF (n = 18). Statistical results are presented for the clustering coefficient (CC), local efficiency (LE), modularity (Q), and global efficiency (GE).

	Modality			Frequency Band			Modality X Frequency Band
	F(4,17)	p		F(4,68)	p		F(16,272)	p
CC	527.7	< .001	0.969	14.1	< .001	0.454	41.4	< .001	0.709
LE	505.5	< .001	0.967	14.6	< .001	0.462	45.6	< .001	0.729
Q	480.8	< .001	0.966	15.8	< .001	0.481	20.4	< .001	0.546
GE	123.47	< .001	0.879	15.7	< .001	0.48	3.38	0.005	0.166

Adaptive directed transfer function and derived graph theory indices

The DTF analyses contributed to the understanding of functional connectivity changes in distinct frequency bands associated with audiovisual interactions in the temporal domain and the multisensory nature of motion perception. However, despite the original paradigm and behavioral data highlighting the strong effects of auditory timing, DTF analysis, and derived network measures were limited in detecting changes across different auditory timing conditions. To address this, we further applied an adaptive DTF (ADTF) algorithm that incorporates the temporal dimension of neural activities. The network characteristics of the CC, LE, Q, and GE were calculated based on the connectivity estimates derived from ADTF across five different frequency bands over time.

As indicated by different network measures (Figs. 5 and 6), the ADTF algorithm distinguished some of the auditory timing conditions. In the low-frequency bands (delta and theta, see also Table 2), the ADTF procedure revealed significant differences (all p < 0.01) between visual-only (V) and audiovisual conditions (AV-A₄₀, AV-A₁₀₀, AV-A_160, or AV-A₂₂₀). Particularly, these differences were dominant in the theta band and mainly indicated by CC, LE, and Q measures. Overall, the significant modulations in LE and CC were in similar time windows and experimental conditions (Fig. 5). This alignment is consistent with existing literature, suggesting that both measures reflect the network’s segregation capabilities. The overall trend of both measures showed a decline over time in theta and alpha bands, suggesting a weakening of local network connections in these low-frequency bands. The temporal dynamics of modularity (Q) showed a complex pattern (Fig. 6a). Compared to the visual-only, the modularity in the audiovisual conditions was higher and lower in the early and late identified time windows of the theta band, respectively. The significant modulations in global efficiency (GE) were dominant in the theta and beta frequency bands (Fig. 6b). The GE measures of theta band increased over time, suggesting an increase in the capacity for engaging in global interactions and network-wide integration. The alpha frequency band had a similar increase, but the paired comparisons of GE did not identify a significant time window. On the other hand, short and long auditory time intervals were notably distinguished for both disparity levels (AV-A₁₀₀ vs. AV-A₁₆₀; AV-A₄₀ vs. AV-A₂₂₀) in GE measures based on beta oscillations. The auditory timing was discriminated in local network measures (CC, Q) measures of alpha oscillations within some non-overlapping time windows.

Fig. 5.

Time-resolved dynamics of CC and LE derived from ADTF for each frequency band (n = 18). (a) CC values and (b) LE values are shown for visual-only (orange), short auditory time interval (blue), and long auditory time interval (dark blue) conditions, separated by low and high disparity levels. Significant time clusters (p < .01, cluster-corrected) are highlighted with bars and dashed lines.

Fig. 6.

Time-resolved dynamics of Q and GE derived from ADTF for each frequency band (n = 18). (a) Q values and (b) GE values are shown for visual-only (orange), short auditory time interval (blue), and long auditory time interval (dark blue) conditions, separated by low and high disparity levels. Significant time clusters (p < .01, cluster-corrected) are highlighted with bars and dashed lines.

Table 2.

Significant time windows (in milliseconds, p < .01) were identified by cluster-based permutation tests for graph theory indices—Clustering Coefficient (CC), Local Efficiency (LE), Modularity (Q), and Global Efficiency (GE)—derived from ADTF across auditory timing conditions (low and high disparity) and frequency bands (n = 18).

		CC		LE		Q		GE
		Low Disparity	High Disparity	Low Disparity	High Disparity	Low Disparity	High Disparity	Low Disparity	High Disparity
Delta	V–Short	500–670	520–680	530–670	520–690	NS	580–700	NS	NS
	V–Long	NS	550–630	NS	NS	NS	NS	NS	NS
	Short–Long	NS	NS	NS	NS	NS	NS	NS	NS
Theta	V–Short	400–440	520–600	400–440	520–600	230–310	200–310 550–650	230–330	240–330
	V–Long	400–440	540–630	400–440	540–600	250–300	250–310	230–330	NS
	Short–Long	690–740	NS	690–740	NS	NS	550–600	NS	NS
Alpha	V–Short	NS	NS	NS	NS	NS	NS	NS	NS
	V–Long	NS	NS	NS	NS	NS	NS	NS	160–240
	Short–Long	NS	170–220	NS	170–240	600–800	400–460	NS	NS
Beta	V–Short	NS	NS	NS	NS	NS	NS	NS	NS
	V–Long	NS	NS	NS	NS	NS	NS	NS	NS
	Short–Long	NS	420–490	NS	450–480	NS	NS	310–400	310–400
Gamma	V–Short	NS	NS	NS	NS	NS	NS	NS	NS
	V–Long	NS	NS	NS	NS	NS	NS	NS	NS
	Short–Long	NS	NS	NS	NS	NS	NS	NS	NS

Rows compare visual-only (V) with audiovisual short and long auditory timing conditions (V–Short; V–Long) and short versus long auditory conditions (Short–Long). NS corresponds to no significant differences.

Figures 5 and 6 demonstrated major overall modulations of network measures in the temporal domain. These temporal modulations were additionally reflected in raw connectivity matrices derived from the ADTF (Figs. S5-S9), providing an overview of connectivity pattern changes at each 100 ms time step. Using the network-based statistics to compare each matrix with the preceding time step, we observed that functional connections in lower frequency bands (delta, theta, and alpha) consistently increased over time, while those in higher frequency bands (beta and gamma) decreased. This indicates distinct patterns of cortical communication dynamics for different frequency bands (Figs. S10-S14, Table S2). These findings suggest that lower frequency oscillations play a stronger role in long-range cortical communication over time. Specifically, the increase in low-frequency connectivity persisted until ~ 400 ms, while high-frequency connectivity declined sharply within the first 100 ms. As high-frequency activity diminishes over time, the coordination across sensory modalities and audiovisual interaction relies increasingly on the sustained engagement of low-frequency oscillations. To complement our approach in previous analyses, we also compared individual audiovisual conditions with the visual-only, as well as auditory timing conditions with each other at each 100 ms time step. Significant alterations in functional connectivity patterns were observed in association with audiovisual interactions (Fig. 7, Table S3), and these significant changes were predominantly observed in the lower frequency bands (e.g., theta and alpha), consistent with the findings from the DTF analysis. Notably, these connections were particularly prominent in the early time windows, up to 200 ms, and similarly present across audiovisual conditions (Table S3). On the other hand, these additional analyses did not reveal any significant differences across auditory timing conditions.

Fig. 7.

Significant ADTF connectivity changes between unisensory visual (V) and audiovisual difference (AV-A) waveforms over time (n = 18). The significant connections identified by network-based statistics are displayed across axial and coronal brain views. Representations were obtained with the BrainNet Viewer Toolbox⁵⁷. Results are presented for significant frequency bands and time windows with corresponding p-values (Table S3). Red edges represent the regions with higher ADTF connectivity in the multisensory condition, primarily concentrated between frontal and parietal/parieto-occipital clusters.

To assess whether graph-theoretical differences were related to perceptual outcomes, we conducted exploratory correlation analyses between GT metrics and behavioral performance. None of these analyses revealed significant correlations between the behavioral performance and the differences (short-long) in any of the GT indices (p > 0.05), regardless of the disparity level (low or high).

Discussion

Multisensory processing involves the coordination and interaction of distributed cortical areas, emphasizing the dynamic and flexible recruitment of different brain regions^64–66. This aspect of sensory processing is particularly crucial for understanding cortical mechanisms and functional networks underlying perceptual dynamics. Using a dynamic audiovisual paradigm, we investigated cortical networks and oscillations associated with audiovisual interactions and the multisensory nature of motion and speed estimation. Utilizing network-based analyses and graph theory modeling, we investigated functional connectivity patterns in specific frequency bands, particularly in the theta and alpha bands, facilitating long-range communications between cortical regions during audiovisual interactions. These findings primarily associate these oscillations with the interaction/binding of auditory and visual inputs and reveal their important roles in global network coordination. We further observed significant modulations in local and global network measures, reflecting the dynamic reorganization of cortical networks to balance integration and segregation during audiovisual processing. The outcome of the network-based approach contributes to an evolving perspective on how the brain dynamically coordinates sensory information for a coherent multisensory percept. In light of our original aims, we discuss the implications of these findings for crossmodal influences, the multisensory integration underlying motion perception, and the limitations of network-based analyses in understanding temporal modulations.

Frequency-specific connectivity changes associated with audiovisual interactions and the multisensory nature of motion perception

Our findings revealed that audiovisual interactions are associated with distinct functional connectivity patterns compared to the processing of visual motion in isolation. For the unisensory processing of visual motion, cortical networks exhibited stronger localized connectivity, primarily in the theta, alpha, and beta bands, with significant increases predominantly confined to occipital and parieto-occipital regions, suggesting enhanced segregation of sensory information in the visual cortex. This aligns with previous research consistently showing activity in these regions closely linked to visual perception^67–75. Our results further validate the critical role of the occipital/parietal network in motion perception. More importantly, we found that audiovisual interactions engaged connectivity and crosstalk with other parietal and frontal scalp sites. These connections were primarily characterized by long-range pathways linking parieto-occipital regions to frontal areas, highlighting the involvement of distributed cortical networks in combining auditory and visual inputs. Previous studies have suggested that the interactions over frontal regions depend on the temporal properties of audiovisual stimulation^12,76. The neural activities over these regions are commonly associated with high-level sensory processing, with certain neurons demonstrating selectivity for the direction and speed of visual motion^77–79. For example, activations in areas such as the prefrontal cortex have been implicated in the comparison of sensory signals, playing a critical role in perceptual tasks that require the comparison of remembered and current stimuli. It is possible that the speed comparison task used by Kaya and Kafaligonul¹² might engage this region, as the task was performed within a two-interval forced-choice paradigm. Furthermore, specific subdivisions of the frontal regions, such as Brodmann area 8, are known to receive inputs from both the motion pathway and the auditory cortex⁸⁰ and have been proposed to contribute to audiovisual motion integration⁸¹.

Notably, the identified long-range communications between different regions were frequency-specific and carried out by alpha and theta oscillations. Modulations in the alpha band have been commonly reported by audiovisual studies^82–84, and alpha oscillations have been widely documented in facilitating crossmodal influences and inter-areal crosstalk between sensory regions⁸⁴. There is also strong evidence that the phase synchronization in the alpha band predicts whether successive stimuli are integrated or segregated in the temporal domain^86–90. By promoting long-range communication between frontal and posterior regions, alpha activity may reflect feedforward and/or top-down mechanisms crucial for coordinating crossmodal influences and perceptual binding, as well as maintaining ongoing perceptual states^91–93. This dynamic interplay combines local synchronization in the visual cortex with broader integration across occipital, parietal, and frontal areas⁹⁴, enabling flexible coordination of sensory and perceptual functions. While theta band is often associated with high-level cognitive functions^95–97, previous research on audiovisual paradigms also revealed that the modulations in the theta band reflect changes in multisensory perception⁸⁵. These studies utilized illusions based on the incongruence/mismatch between visual and auditory stimuli in the spatial or temporal domain^98,99. The findings illustrated that theta band oscillations may be an index of incongruity processing and reflect variations in the final illusory percept. Given that theta band oscillations have been implicated in the monitoring of response conflict¹⁰⁰ and are well suited for long-range information transfer across cortical regions¹⁰¹, they may serve as a neural mechanism for perceptual adjustment in multisensory profiles, where information might be temporally disparate and has to be integrated across different sensory regions.

While analyses based on DTF provided overall changes in network connectivity, the ADTF (adaptive DTF) analyses offered additional insights into how these connections evolved dynamically over time. Similarly, we found frequency-band-specific temporal shifts in connectivity patterns during the speed comparison task. Our results showed that low-frequency bands such as delta, theta, and alpha exhibited consistent increases in connectivity over time, highlighting their role in facilitating communication across different cortical regions. However, high-frequency bands, including beta and gamma, demonstrated transient connectivity patterns, reflecting localized processing demands that diminished rapidly over time. The processing of multisensory information requires flexible neural mechanisms that can rapidly adapt to the sensory changes in the environment⁶⁶. Such flexibility may be required for the integration of sensory inputs across cortical regions in different timescales. In accordance with this perspective, previous studies argued that neural oscillations provide time windows of varying durations to bind or segregate sensory information^71,102–105. These intrinsic neural timescales differ across different stages of cortical processing, with early sensory processing having relatively shorter timescales and higher-order areas demonstrating progressively longer timescales^106–108. Therefore, different timescales, reflected in distinct oscillatory frequency bands, have been proposed to route information through cortical networks, creating functional links between neural populations^109–111. That is to say, rapid processing demands in early sensory areas may rely on faster oscillations operating within shorter timescales, enabling the quick extraction and segregation of sensory features. On the other hand, the processing at later stages may depend on slower oscillations, facilitating the coordination and synthesis of information across distributed cortical regions to support relatively complex perceptual processing. Recent findings underscore the critical role of multi-timescale neural dynamics in shaping multisensory processing. Functional coupling across different frequency bands enables parallel processing of complementary information, enhancing system capacity through a process known as multiplexing^102,112,113. This dynamic interplay is particularly important for different stages of multisensory processing across different timescales, facilitating both rapid extraction of localized sensory features and the slower synthesis of distributed information required for higher-order processing. Our results align with this framework, demonstrating how fast oscillations reflect early sensory processing, while slower oscillations enable coordination across cortical regions for later stages, which might be important for effective integration and coherent perception. Our findings reflect the brain’s dynamic adaptability, demonstrating its capacity to rapidly transition between localized unisensory processing and broader integrative networks required for multisensory processing. Such flexibility allows neural networks to efficiently reconfigure within a short timeframe, optimizing both specialized and integrative functions to meet the varying demands of audiovisual interactions and binding.

Insights from graph network modeling

The graph theoretical analysis based on DTF indicated a clear dominance of global integration during audiovisual interactions and, hence, multisensory processing, particularly reflected in heightened GE in all frequency bands. The increase in GE highlights the brain’s ability to enhance long-range connectivity to merge auditory and visual inputs into a cohesive percept and may reflect relatively higher-order processing demands due to crosstalk across distributed cortical regions⁴⁵. As Sporns¹¹⁴ noted, integrative processes can be viewed from the perspective of global communication efficiency and the network’s capacity to combine distributed information. This aligns with the idea that global efficiency reflects a workspace configuration characterized by long-range synchronization and reduced modularity, which emerges during demanding processes to facilitate information transfer in parallel¹¹⁵. Our findings also resonate with observations that greater cognitive effort elicits more globally efficient, less clustered, and less modular network configurations, enabling widespread synchronization across anatomically distant regions^94,116. On the other hand, the segregation was higher during unisensory processing of visual motion, as indicated by enhanced CC, LE, and Q values. These metrics reflect localized connectivity patterns confined primarily to occipital and parieto-occipital regions, emphasizing specialized visual processing within the sensory cortex. This pattern suggests that visual-only conditions rely more on specialized local processing hubs in occipital and parieto-occipital regions to handle visual motion perception efficiently. Regions with clustered interconnectivity often exhibit both spatial and topological proximity, contributing to low wiring costs and efficient resource allocation⁴⁹. Recent work by Singh et al.¹⁶ using fMRI-based graph analyses found that audiovisual binding was associated with increased local segregation and reduced global integration—a pattern that contrasts with the increased global efficiency and reduced modularity observed in our results. This apparent discrepancy may reflect differences in task demands (simultaneity judgment vs. speed estimation), neuroimaging modality (fMRI vs. EEG), and network construction. Their study¹⁶ captured relatively stable, spatially distributed correlations across the timescale of seconds, while our DTF/ADTF-based approach tracks rapid, frequency-specific, and directed interactions over hundreds of milliseconds. As emphasized by Fornito et al.⁵⁰, such methodological and temporal differences can lead to divergent patterns of network organization, even within the same cognitive domain. In addition, segregated and integrated network configurations are not mutually exclusive but may dominate under different cognitive conditions—segregated networks supporting fast, localized processing and integrated networks enabling deliberative, large-scale coordination. Taken together, our findings illustrate the dynamic balance between integration and segregation in network organization and suggest the brain’s remarkable adaptability to processing demands of diverse sensory profiles¹¹⁴. This dual mechanism allows the brain to flexibly respond to the unique demands of motion processing and audiovisual interactions. Our findings provide evidence for the dynamic and collaborative activity reflecting the flexible organization of neural networks underlying the multisensory nature of motion and speed estimation.

The time-varying graph theoretical analysis of ADTF provided suggestions about how cortical networks dynamically adapt to the demands of audiovisual processing. Our findings demonstrated distinct shifts in topological properties across low-frequency bands (delta, theta, and alpha), with CC and LE exhibiting a sharp decline around 200 ms post-stimulus, coinciding with a rise of Q and GE. Over the course of the 800 ms time window, the Q and GE stabilized after their initial increase, while CC and LE showed a partial rebound. However, the overall trend indicated a decrease in CC and LE and a sustained increase in Q and GE, emphasizing a gradual transition toward more integrative network configurations. This transition reflects a shift from localized connectivity to long-range communication and may be an indication of the brain’s ability to adapt and reconfigure connectivity patterns according to the changes in sensory processing demands. Similarly, previous studies suggest that functional networks can rapidly reorganize to meet specific demands of multisensory processing^117–119. Notably, in beta-band, all graph network indices, including measures associated with localized and specialized operations, demonstrated a marked increase over time, highlighting their relevance in task-related network reconfiguration^115,120. Interestingly, while beta-band GE steadily increased over time, this topological metric showed the most pronounced differentiation between short and long time intervals across both disparity levels, suggesting that beta-band networks might discriminate fine changes in auditory timing. However, we did not find any selectivity across disparity levels, and there was also no correlation with the behavioral changes.

Limitations and future directions

The present study further illustrates the limitations of network-based analyses and graph modeling in capturing sensory events and provides future directions for improving the temporal resolution of connectivity estimates. Our analyses revealed important changes in network dynamics and graph theoretical measures associated with audiovisual interactions within the context of motion and speed estimation. Since Kaya and Kafaligonul¹² identified significant effects of auditory timing (time interval and disparity level) in distinct ERP components, we further applied ADTF to examine the effects of auditory timing on connectivity and network measures. As mentioned earlier, these analyses captured overall/coarse changes at the network level. However, in terms of connectivity differences across auditory time intervals (short vs. long) and disparity levels (low vs. high), the analyses did not reveal consistent patterns of modulation—despite the behavioral results showing clear perceptual distinctions across these conditions. This likely reflects limitations in the temporal resolution of the employed connectivity approach, which may not capture short-lived or fine-grained fluctuations in connectivity that occur during rapidly changing stimulation. Moreover, previous work using this dataset¹² reported ERP modulations specifically related to auditory timing, suggesting that the effects of timing differences may be more locally expressed in early sensory responses, rather than in delayed large-scale network dynamics. These limitations highlight the need for analytical frameworks that are more sensitive to transient dynamics and localized activity differences. Future work employing higher-temporal-resolution connectivity measures with localized activity measures may better characterize how auditory timing modulates brain responses. It is also worth noting that the original dataset included a modest sample size and a limited number of trials per condition. While the sample size is within the typical range for EEG studies, it may not be optimal for ensuring the full stability of higher-order graph metrics. To mitigate these concerns, we employed conservative statistical strategies, including sparsity thresholding, binarization of connectivity matrices, and cluster-level permutation testing. However, these choices may also contribute to the absence of large-scale connectivity differences across audiovisual timing conditions. This null finding may reflect several possibilities: finer-grained or transient effects could exist but fall below the sensitivity threshold of our current analysis pipeline; or auditory timing may exert its influence on earlier perceptual stages (e.g., latency shifts or sensory gating), which are not readily captured by global graph metrics derived from DTF/ADTF. Future investigations with larger sample sizes will enable subgroup analyses to examine potential individual variability in response to crossmodal influences and provide a direct link between motion/speed estimation and functional alterations at the network level.

Conclusion

Taken together, our findings illustrate the dynamic interplay between local specialization and global communication in cortical networks during audiovisual interactions. We further identified the critical roles of theta and alpha oscillations for long-range connectivity and audiovisual interactions in the temporal domain. By employing time-sensitive adaptive analyses, we captured the brain’s remarkable adaptability in reorganizing functional networks to meet sensory processing demands. These results highlight how the brain leverages distinct frequency bands to balance segregation and integration, enabling efficient coordination of sensory inputs for the multisensory basis of motion and speed estimation. The findings overall provide important implications for understanding neural mechanisms underlying multisensory perception in daily life situations.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

I.A., S.A., and H.K. conceived of the study. I.A. and S.A. constructed and implemented the data analysis pipeline. I.A., S.A., and H.K. interpreted the results. I.A. wrote the first draft of the manuscript. I.A., S.A., and H.K. edited the manuscript and approved the final version.

Funding

This work was supported by the Scientific and Technological Research Council of Turkiye (BIDEB 2211-A) and the Turkish Academy of Sciences (TUBA-GEBIP Award).

Data availability

The dataset and analysis codes of the current study are available at https://osf.io/7p8as/?view_only=cce86ab3239842af9a07d1eb1e744b83.

Declarations

Competing interests

The authors declare no competing financial interests.