Instantaneous Frequency: A New Functional Biomarker for Dynamic Brain Causal Networks

Abstract

Background:

This study introduces instantaneous frequency (IF) analysis as a novel method for characterizing dynamic brain causal networks from functional magnetic resonance imaging blood-oxygen-level-dependent signals.

Methods:

Effective connectivity, estimated using dynamic causal modeling, is analyzed to derive IF sequences, with the average IF across brain regions serving as a potential biomarker for global network oscillatory behavior.

Results:

Analysis of data from the Alzheimer’s Disease (AD) Neuroimaging Initiative, Open Access Series of Imaging Studies, and Human Connectome Project demonstrates the method’s efficacy in distinguishing between clinical and demographic groups, such as cognitive decline stages (e.g., normal control, early mild cognitive impairment [MCI], late MCI, and AD), sex differences, and sleep quality levels.

Conclusion:

Statistical analyses reveal significant group differences in IF metrics, highlighting its potential as a sensitive indicator for early diagnosis and monitoring of neurodegenerative and cognitive conditions.

Introduction

In computational neuroscience, brain biomarkers serve as essential quantifiable indicators of biological processes, aiding in detecting, characterizing, and monitoring brain pattern changes, progressing neurological conditions, and mechanisms underlying various clinical phenotypes. These biomarkers provide a window into complex brain dynamics, supporting precision in understanding disease development and individual variability across clinical states. Structural biomarkers, generally measuring stable brain anatomical features such as gray matter volume, cortical thickness, and white matter integrity, provide valuable insights into long-term and static neural integrity and structural abnormalities that accompany neurological conditions.^1,2 However, structural metrics, while informative, often fall short in capturing the dynamic and activity-driven aspects of brain function associated with complex cognitive and pathological states. Temporal neural interactions and adaptive responses offer insights into how brain regions coordinate over time, revealing mechanisms and compensatory functions crucial for studying mental and neurological disorders.^3–6 As a result, research has increasingly focused on functional biomarkers that capture dynamic changes in neural responses fluctuating with cognitive and pathological demands and provide a nuanced view of real-time interactions among different brain regions. By capturing temporal relevance and causative changes, functional biomarkers facilitate early diagnosis, reveal disease heterogeneity, and enable new insights into disease progression and cognitive variability.^7–9

Dynamic causality across brain regions is a critical component of brain functionality, encompassing the directional interactions between distinct brain regions and offering insights into how these interactions evolve and adapt over time.^7,10,11 This causal fluctuation is integral to understanding not only the basic mechanisms of brain connectivity but also its perturbations among different neurodegenerative stages, such as mild cognitive impairment (MCI) and Alzheimer’s Disease (AD).^12–14 These fluctuations reveal essential differences in the adaptability, resilience, and stability of brain networks under both healthy and pathological conditions. Despite advances in effective connectivity modeling, current studies primarily estimate static or slowly evolving causal interactions but do not explicitly quantify how these influences fluctuate dynamically over time. However, neural activity is inherently nonstationary and the brain continuously adapts its functional organization in response to both internal and external factors. A few prior studies have applied frequency analysis to higher temporal resolution neuroimaging modalities, such as Magnetoencephalography and high-density electroencephalograph (EEG), to capture transient oscillatory changes in brain dynamics.^15,16 Another major gap in current research is the lack of a biomarker that quantifies the temporal fluctuations of directional brain interactions, limiting our ability to detect subtle yet functionally significant changes in brain network dynamics. Such a biomarker is essential for understanding how brain connectivity varies across different disease stages and clinical phenotypes. In neurodegenerative diseases such as AD and MCI, disruptions in the temporal stability of brain networks may indicate underlying pathological changes. Similarly, in conditions such as sleep disorders and sex-related neural differences, alterations in dynamic brain connectivity may reflect variations in cognitive function, behavioral patterns, and overall brain health. By capturing these fluctuations, an effective biomarker could provide valuable insights into disease characterization and individual differences in brain function.

To address the gap in quantifying temporal fluctuations in directional brain interactions, we introduce a novel approach to derive functional biomarkers from dynamic effective networks by analyzing the rate of change in causal influences across brain regions. Specifically, leveraging effective connectivity constructed from blood oxygen level-dependent (BOLD) signals using dynamic causal modeling (DCM), we compute the instantaneous frequency (IF) of these effective connectomes to capture time-dependent fluctuations in effective connectivity. IF quantifies the rate at which causal influences between brain regions change over time, offering a high-resolution dynamic marker of functional brain connectivity. We then define the average IF across brain regions as our proposed biomarker. This biomarker reflects the oscillatory behavior of the entire network, offering insight into global brain dynamics. Our experimental results indicate that this biomarker exhibits significant differences across neurodegenerative stages, such as AD and MCI, as well as among other clinical phenotypes. To enhance the specificity of our findings, we conduct connectome-level analyses, pinpointing particular connectomes with significant clinical phenotype-related differences. This connectome-focused analysis allows us to identify targeted connections within the network that serve as precise markers of brain state changes underlying various clinical phenotypes and neuropsychiatric conditions.

Methods

Preliminaries

A brain effective network with $N$ nodes is a weighted directed graph $G=\left\{V,E\right\}=\left(A,X\right)$, where $V={\left\{v_i\right\}}_{i=1}^N$ is the set of graph nodes representing brain regions and $E=\left\{e_{i,j}\right\}$ is the directed edge set. $X\in R^{N\times c}$ is the node feature matrix where $x_i\in R^c$ is the $i\text{th}$ row of $X$, representing the node feature of $v_i$. $A\in R^{N\times N}$ is the adjacency matrix where $a_{i,j}\in R$ represents the weight of the edge between $v_i$ and $v_j$. As the brain effective network is an undirected graph, $a_{i,j}\ne a_{j,i}\in R$. The sign of $a_{i,j}$ indicates the direction of causal impact between $v_i$ and $v_j$, where $a_{i,j}>0$ signifies the causal effect on $v_j$ induced by $v_i$ and vice versa. Additionally, we denote the BOLD signal obtained from functional magnetic resonance imaging (fMRI) as $B\in R^{N\times b}$, where $b$ is the length of the signal.

Construction of dynamic brain effective network

We construct brain effective networks by utilizing BOLD signals obtained from fMRI with a DCM framework.^17,18 Each brain region is represented as an effective network node, while temporal changes in effective connectivity define the edges of the network. This temporal effective connectivity, represented by the dynamic adjacency matrix, $A\left(t\right)$ can be modeled as

$$\frac{dB\left(t\right)}{dt}=\alpha A\left(t\right)B\left(t\right)+Cu\left(t\right).$$

Here $Cu\left(t\right)$ accounts for external neuronal inputs, $u\left(t\right)$, that influence dynamic $A\left(t\right)$. For our purposes, $Cu\left(t\right)=0$ since we focus on resting-state fMRI, eliminating external influences. The parameter $\alpha$ is a constant modulating neuronal lag among brain nodes. Consequently, we can derive the expression of $A\left(t\right)$ as follow:

$$A\left(t\right)=\frac{1}{\alpha B\left(t\right)}\frac{dB\left(t\right)}{dt}$$

To discretize this continuous model, we define $A\left(t\right)$ in terms of BOLD signal change over discrete time intervals, resulting in:

$$A\left(t\right)=\frac{1}{\alpha B\left(t\right)}\frac{B\left(t+1\right)-B\left(t\right)}{\Delta t}=\frac{1}{\alpha }\left(\frac{B\left(t+1\right)}{B\left(t\right)}-1\right)$$

The effective connectivity between nodes $v_i^f$ and $v_j^f$ at time $t$ is defined as follow:

$$A_{i,j}\left(t\right)=\beta \left(\frac{B_j\left(t+1\right)}{B_i\left(t\right)}-1\right),$$

where $\beta =\frac{1}{\alpha }\in \left[0,1\right]$ and $B_i$ is the BOLD signal at node $v_i$.

This framework allows us to analyze effective connectivity dynamics in resting-state brain networks, providing insights into causal interactions across brain regions.

IF of effective connectomes

In the adjacency matrix, $A\left(t\right)\in R^{N\times N\times b}$, of the brain effective network, each element $A_{i,j}\left(t\right)\in R^b$ reflects the time-varying casual impact between node $v_i$ and $v_j$. We first perform Hilbert transform to each $A_{i,j}\left(t\right)$ to generate the phase matrix, and then we compute the IF matrix by utilizing the phase matrix.^19–21

Computation of instantaneous phase matrix.

Denote the instantaneous phase matrix as $P\left(t\right)\in R^{N\times N\times b}$, which provides the instantaneous phase of dynamic effective connectivity over time. The instantaneous phase signal for each dynamic effective connectivity can be computed as follow:

$$P_{i,j}\left(t\right)=\arg \left(\widetilde{A_{i,j}}\left(t\right)\right),$$

where $\widetilde{A_{i,j}}\left(t\right)$, representing the analytic signal of Hilbert transform $H\left[\cdot \right]$, can be computed as follow:

$$\widetilde{A_{i,j}}\left(t\right)=H\left[A_{i,j}\left(t\right)\right]=\frac{1}{\pi }{\int }_{-\infty }^{\infty }\frac{A_{i,j}\left(\pi \right)}{t-\tau }d\tau .$$

Computation of IF matrix.

To obtain the IF matrix $F\left(t\right)$, we compute the time derivative of each element in the phase matrix $P\left(t\right)$:

$$F_{i,j}\left(t\right)=\frac{d{P}_{i,j}\left(t\right)}{dt}.$$

This IF represents the rate of change in causal influence between nodes over time. It captures the fluctuation speed and frequency of causal relationships, indicating the dynamic regulatory properties of these effective connections. High IF indicates rapid changes in causality, implying a high level of flexibility or adaptability in brain networks under certain conditions. The workflow of computing IF matrix is presented in Figure 1.

Fig. 1.

Overview of the proposed IF-based biomarker framework. A dynamic brain effective network is represented as a weighted adjacency matrix $A\in R^{N\times N\times T}$, where $N$ is the number of brain regions (nodes) and $T$ is the number of time frames. The network evolves over time, capturing directional causal interactions between regions. Operator $H$ denotes the Hilbert transform, used to obtain the analytic signal from a time series, and operator $D$ denotes the time derivative. These are applied element-wise to the time-varying effective connectivity to compute the instantaneous phase and frequency for each directed edge. The resulting IF values are then averaged across all edges to produce a subject-level IF biomarker representing global dynamic network behavior. IF, instantaneous frequency.

Computation of functional biomarker.

To compute the functional biomarker, $\Omega \left(t\right)$, of the global effective network, we average the node-level IF sequence:

$$\Omega \left(t\right)=\frac{1}{N\left(N-1\right)}{\sum }_{i=1}^N{\sum }_{j=1,j\ne i}^N{F}_{i,j}\left(t\right)$$

Statistical method for group difference analysis

Since the functional biomarkers $\Omega \in R^b$ are time-series data, we use the dynamic time warping (DTW) distance^22–24 to assess the similarity between each pair of sequences. DTW is a time-series alignment algorithm that enables comparison between sequences that may vary in speed or timing. It finds an optimal nonlinear alignment between two time series by minimizing the cumulative distance, allowing for temporal misalignments between signals. In this study, DTW is used to compare variations in IF time series across subjects or conditions. For two distinct groups of biomarkers, we calculate intragroup DTW distances within each group and a cross-group DTW distance between them. To evaluate statistical significance, we apply two Mann–Whitney U tests^25,26 comparing each intragroup distance against the cross-group distance. If both tests indicate significant differences, we consider the two groups of biomarkers to be significantly different.

Data Description and Preprocessing

This study employs three independent brain imaging datasets. The first dataset is from Alzheimer’s Disease Neuroimaging Initiative (ADNI).²⁷ The ADNI was launched in 2003 as a public–private partnership, led by principal investigator Michael W. Weiner. The original goal of ADNI was to test whether serial MRI, positron emission tomography (PET), other biological markers, and clinical and neuropsychological assessment can be combined to measure the progression of MCI and early AD. The current goals include validating biomarkers for clinical trials, improving the generalizability of ADNI data by increasing diversity in the participant cohort, and to provide data concerning the diagnosis and progression of AD to the scientific community. For up-to-date information, see (http://adni.loni.usc.edu). Our ADNI data includes 154 normal control (NC) subjects (mean age = 77.46 – 5.98, 59 males), 70 early MCI (EMCI) subjects (mean age = 73.75 – 5.72, 38 males), and 50 late MCI (LMCI) subjects (mean age = 73.86 – 6.20, 27 males). ADNI subjects were selected based on their clinical diagnosis as NC, EMCI, or LMCI. Only subjects with available resting-state fMRI data were included. Subjects were excluded if they had excessive motion artifacts in fMRI scans or incomplete diagnostic information. The second dataset is from the Open Access Series of Imaging Studies-3 (OASIS-3²⁸) project, a longitudinal, multimodal resource encompassing neuroimaging, clinical, cognitive, and biomarker data focused on normal aging and AD. Our OASIS data includes 1051 NC subjects (mean age = 69.17 – 8.90, 425 males), 209 MCI subjects (mean age = 75.44 – 6.90, 122 males), and 66 AD subjects (mean age = 74.29 – 8.94, 41 males). OASIS-3 subjects were included based on their clinical diagnosis (NC, MCI, AD) and the availability of resting-state fMRI data. Subjects with missing diagnostic information were excluded. The third dataset is from the Human Connectome Project (HCP), a large-scale neuroscience initiative that maps the brain’s structural and functional connectivity in unprecedented detail.²⁹ It serves as a comprehensive resource for understanding how different regions of the human brain are interconnected and how these connections support cognition, behavior, and neural function. Our HCP data includes 1206 young healthy subjects (mean age 28.19 – 7.15, 603 women). HCP subjects were included if they had available fMRI data and self-reported sex and sleep quality assessments.

The preprocessing of functional BOLD signals was conducted using the CONN toolbox,³⁰ including steps such as motion correction, spatial normalization to Montreal Neurological Institute space, and temporal band-pass filtering (0.01–0.1 Hz).

For the HCP and ADNI datasets, the effective networks were constructed with a dimensionality of 82 × 82, corresponding to 82 Region of Interests (ROIs) defined by FreeSurfer (version 6.0).³¹ For the OASIS dataset, we used a combined atlas approach incorporating both the Harvard–Oxford Atlas and the AAL Atlas to define 132 ROIs, resulting in 132 × 132 effective networks.

Experiments and Results

Significant analysis of functional biomarker

Experiment description.

In this section, we conduct a comprehensive analysis across multiple datasets to investigate if our proposed biomarker can serve as an effective indicator to distinguish various clinical and demographic groups. By investigating the biomarker across these various datasets and group comparisons, we aim to validate its robustness and relevance as a tool for understanding cognitive and clinical variability within and across different populations. For the ADNI dataset, we analyze differences in the biomarker across three distinct subject groups: the NC group, representing cognitively healthy individuals; the EMCI group, which includes participants with early-stage cognitive decline; and the LMCI group, representing individuals with more advanced cognitive impairment. By comparing these groups, we aim to evaluate the biomarker’s sensitivity to different stages of cognitive decline, capturing its potential responsiveness to progressive changes across the continuum of cognitive impairment. In our analysis of the OASIS dataset, we similarly examine differences in biomarker expression across three subject groups: the NC group, the MCI group, and the AD group. This study enables us to assess the biomarker’s relevance across a broader spectrum of cognitive health, from normal aging through mild impairment to confirmed AD, allowing for a finer understanding of its potential as a diagnostic indicator. Furthermore, using the HCP dataset, we conduct two additional analyses focused on demographic and behavioral factors. The first is a sex difference analysis, where we compare biomarker expression between male and female participants. The second analysis examines differences in sleep quality, utilizing the Pittsburgh Sleep Quality Index (PSQI), which evaluates various dimensions of sleep, including duration, latency, efficiency, and disturbances. The PSQI scores can be ranked into three levels: scores between 0 ≤ PSQI ≤ 5 indicate good sleep quality; scores between 6 ≤ PSQI ≤ 10 reflect moderate sleep quality; and scores of PSQI ≥ 11 represent bad sleep quality. This study allows us to evaluate the biomarker’s sensitivity to sleep-related factors, which are increasingly acknowledged for their significant impact on cognitive health and brain function.

Experimental results.

The p-values from the two-tailed Mann–Whitney U tests for NC versus EMCI and EMCI versus LMCI on the ADNI dataset are presented in Table 1. The results show that the p-values for NC versus EMCI and EMCI versus LMCI are both less than 0.05, indicating significant differences between these subject groups. These findings suggest that our proposed functional biomarker, IF, effectively distinguishes among NC, EMCI, and LMCI groups. Similarly, Table 2 presents the two-tailed p values for NC versus MCI and MCI versus AD on the OASIS dataset. Additionally, Table 3 displays the two-tailed p-values for male versus female, good versus moderate sleep quality, and moderate versus poor sleep quality on the HCP dataset. In all cases, the p values are less than 0.05, clearly demonstrating that our proposed functional biomarkers reveal significant differences between these subgroups.

Table 1.

The Two-Tailed p-Values of Early Mild Cognitive Impairment vs. Normal Control and Late Mild Cognitive Impairment vs. Early Mild Cognitive Impairment on Alzheimer’s Disease Neuroimaging Initiative Dataset

	NC	EMCI	LMCI
EMCI–NC	1.0898e-47	1.0926e-24	—
LMCI–EMCI	—	4.6464e-7	6.2183e-4

EMCI, early mild cognitive impairment; LMCI, late mild cognitive impairment; MCI, mild cognitive impairment; NC, normal control.

Table 2.

The Two-Tailed p-Values of Mild Cognitive Impairment vs. Normal Control and Alzheimer’s Disease vs. Mild Cognitive Impairment on Open Access Series of Imaging Studies Dataset

	NC	MCI	AD
MCI-NC	1.2743e-96	1.6747e-241	—
AD-MCI	—	7.7449e-12	6.7276e-5

AD, Alzheimer’s Disease.

Table 3.

The Two-Tailed p-Values of Gender Group Analysis and Sleep Quality Analysis on Human Connectome Project Dataset

Sex analysis	Female	Male	Sleep analysis	Good	Moderate	Bad
Male–female	7.071e-6	9.3067e-7	Moderate–good	4.5589e-4	6.7471e-6	—
—	—	—	Good-bad	—	9.8032e-4	8.1590e-32

Identification of distinct connectomes across groups

We perform a connectome-level analysis to identify the significant brain connectomes differentiated by our proposed functional biomarkers when comparing different subject groups. Specifically, we use two-tailed Mann–Whitney U tests to evaluate differences in IF sequences for each brain connectome across subject groups. A connectome is considered distinct between two groups if its IF shows a significant difference. To control for multiple comparisons, the two-sided p-values are compared against the threshold $\frac{0.05}{N\left(N-1\right)}$, where $N\left(N-1\right)$ represents the total number of brain connectomes. The group-specific distinct brain connectomes identified by the connectome IF are visualized in Figure 2A for the ADNI dataset, Figure 2B for the OASIS dataset, and Figure 2C for the HCP dataset. In the ADNI analysis, 680 brain connectomes show significant differences between the EMCI and LMCI groups, while 756 connectomes differ significantly between the NC and EMCI groups. The specific connectomes are annotated in Figure 2A with the corresponding brain ROI names provided in the full list of ROIs in Appendix B.

Fig. 2.

(A) Significantly different brain connectomes between EMCI and LMCI, as well as between NC and EMCI, on the ADNI dataset. (B) Significantly different brain connectomes between MCI and AD, as well as between NC and MCI on OASIS dataset. (C) Significantly different brain connectomes between females and males, as well as between different sleep quality states, in the HCP dataset. AD, Alzheimer’s Disease; ADNI, Alzheimer’s Disease Neuroimaging Initiative; EMCI, early mild cognitive impairment; HCP, Human Connectome Project; LMCI, late mild cognitive impairment; MCI, mild cognitive impairment; NC, normal control; OASIS, Open Access Series of Imaging Studies.

For the OASIS dataset (Figure 2B), 974 brain connectomes show significant differences between the MCI and AD groups, and 4865 connectomes are significantly different between the NC and MCI groups. Similarly, the corresponding connectome details are in Figure 2B and the related brain ROI names are included in the full list of ROIs in Appendix A.

In the HCP dataset analysis (see Figure 2C), 2495 connectomes are significantly different between male and female groups, 1296 connectomes differ significantly between good and moderate sleep quality groups, and only 32 connectomes differ significantly between moderate and poor sleep quality groups. Detailed connectome locations and corresponding ROI names are provided in the full list of ROIs in Appendix B.

We compute the average IF (i.e., $-F_{i,j}$) of the identified connectomes over the group subjects as follow:

$$\overline{F_{i,j}}=\frac{1}{T}\frac{1}{\left|\mathcal{G}\right|}\sum _{t=1}^T\sum _{\mathcal{G}}{F}_{i,j},$$

where $T$ is the number of IF point and $\mathcal{G}$ is the number of subjects in each group. Then we visualize the average IF of the identified connectomes for the EMCI versus LMCI and for the NC versus EMCI on ADNI dataset in Figure 3. Similarly, the IF differences for the MCI versus AD, and NC versus MCI on OASIS dataset are shown in Figure 4. The IF differences for the male versus female, and different sleep qualities are shown in Figure 5. Meanwhile, we present the mean and standard deviations of these $-F_{i,j}$ over the highlighted connectomes in Figure 6 to illustrate how the average IF varies across different neurodegenerative disease stages and clinical phenotypes.

Fig. 3.

Average IF $\left(-F_{i,j}\right)$ of the identified connectomes for EMCI vs. LMCI and NC vs. EMCI on ADNI dataset.

Fig. 4.

Mean IF $\left(-F_{i,j}\right)$ of the identified connectomes for MCI vs. AD and NC vs. MCI on OASIS dataset.

Fig. 5.

Mean IF $\left(-F_{i,j}\right)$ of the identified connectomes for good vs. moderate, moderate vs. bad sleep quality, and female vs. male on HCP dataset.

Fig. 6.

Mean and s.t.d. values of $\left(-F_{i,j}\right)$ for the cognitive disease analysis on (A) ADNI dataset and (B) OASIS dataset, as well as for (C) sex and (D) sleep quality analyses on HCP dataset.

Discussions

IF as a marker of disease progression, sleep quality, and sex differences

Figure 7 presents histograms comparing IF distributions across various datasets, including clinical conditions (e.g., NC vs. EMCI vs. LMCI in ADNI and NC vs. MCI vs. AD in OASIS) and demographic factors (e.g., male vs. female and sleep quality levels in HCP). These distributions provide insights into how brain dynamics differ across disease stages, sex, and sleep quality categories. Meanwhile, Figure 6A and B presents that both the mean and variance of IF increase from the NC to EMCI stage, followed by a decrease from EMCI to LMCI. This pattern suggests an initial compensatory mechanism in the early stages of the disease, where increased neural activity may help maintain cognitive function, followed by a decline as the disease progresses. Previous studies have reported a rise in neural activity, particularly in the frontal regions, during the early stages of AD, which is believed to be a compensatory response to initial neuronal damage.^32,33 However, as cognitive impairment advances, this compensatory hyperactivity becomes insufficient to counteract the progressive neurodegeneration, leading to a decline in neural activity relative to healthy aging.³⁴

Fig. 7.

Histograms illustrating the distribution of IF values across different subject groups, including (A) NC vs. EMCI vs. LMCI on the ADNI dataset, (B) NC vs. MCI vs. AD on the OASIS dataset, (C) Male vs. Female on the HCP dataset, and (D) good vs. moderate vs. Bad sleep quality on the HCP dataset. The x-axis represents the IF values, while the y-axis shows the proportion of subjects within each group. Differences in IF distributions highlight variations in brain dynamics across clinical and demographic groups.

Figure 6C presents that poor sleep quality is associated with an increase in both the mean and variance of IF, indicating greater instability in neural oscillations. This finding is consistent with previous studies suggesting that disrupted sleep leads to irregular neural activity patterns, contributing to cognitive impairment and emotional dysregulation.^35,36 Poor sleepers often exhibit fragmented sleep architecture, characterized by frequent awakenings and reduced sleep efficiency, which may reflect underlying neural instability in maintaining sustained brain network coordination.

Additionally, Figure 6D reveals notable sex differences in brain activity. Specifically, males exhibit higher IF values, suggesting greater neural activity, while females demonstrate lower variance in IF, indicating more stable and consistent neural oscillations. These findings align with prior research reporting that males tend to show higher metabolic and electrophysiological activity in certain brain regions, whereas females often display more stable and efficient neural connectivity.^37–41 Studies have shown that sex differences in brain organization are influenced by factors such as hormonal regulation, genetic expression, and neurodevelopmental trajectories. For instance, females have been reported to exhibit stronger interhemispheric connectivity, particularly in the default mode network and limbic system, which may contribute to enhanced cognitive resilience and emotional processing.^38,39 Meanwhile, males tend to show increased intrahemispheric connectivity and localized activity in sensorimotor and visuospatial networks, which may account for higher IF values observed in this study.^40,41 These findings suggest that sex-specific neural dynamics should be considered when interpreting biomarkers derived from brain connectivity measures.

Future studies

While this study demonstrates the potential of IF as a functional biomarker for distinguishing clinical phenotypes and characterizing neural dynamics, several avenues remain for future exploration. First, the integration of multimodal data (e.g., EEG with fMRI) could enhance our understanding of how electrophysiological properties influence dynamic brain connectivity. EEG provides direct, high-temporal-resolution measurements of neural oscillations, making it particularly well-suited for capturing fast brain dynamics that may not be fully resolved by fMRI alone. Moreover, EEG-based frequency analysis could provide complementary insights into the underlying neurophysiological mechanisms driving IF changes, allowing for a more comprehensive characterization of brain state alterations. This multimodal approach could be particularly useful for studying neurodegenerative diseases, where disruptions in both slow hemodynamic responses (captured by fMRI) and rapid neural oscillatory changes (detected by EEG) contribute to disease progression. Additionally, expanding IF analysis to other neurological and psychiatric conditions, such as Parkinson’s disease and post-traumatic stress disorder, may reveal its broader applicability in clinical diagnostics and disease monitoring.

Conclusion

This study introduces IF as a novel functional biomarker derived from dynamic brain effective connectivity to quantify and model temporal fluctuations in brain network dynamics. The proposed IF metric exhibits significant differences across various brain disorder stages and clinical phenotypes, providing a sensitive indicator for distinguishing these conditions. By analyzing ADNI, OASIS, and HCP datasets, we demonstrate IF’s ability to identify distinct brain connectomes associated with cognitive decline, sex differences, and sleep quality variations, offering insights into the neural mechanisms underlying these variations. These findings highlight IF’s potential for characterizing disease-specific neural circuitry and individual variability in brain dynamics. Future research should explore its integration into clinical diagnostic pipelines and its applicability to broader neurological and psychiatric conditions.

Appendix

Appendix A:

ROI Names for Open Access Series of Imaging Studies Dataset

Number	ROI names
1	Frontal Pole Right
2	Frontal Pole Left
3	Insular Cortex Right
4	Insular Cortex Left
5	Superior Frontal Gyrus Right
6	Superior Frontal Gyrus Left
7	Middle Frontal Gyrus Right
8	Middle Frontal Gyrus Left
9	Inferior Frontal Gyrus, pars triangularis Right
10	Inferior Frontal Gyrus, pars triangularis Left
11	Inferior Frontal Gyrus, pars opercularis Right
12	Inferior Frontal Gyrus, pars opercularis Left
13	Precentral Gyrus Right
14	Precentral Gyrus Left
15	Temporal Pole Right
16	Temporal Pole Left
17	Superior Temporal Gyrus, anterior division Right
18	Superior Temporal Gyrus, anterior division Left
19	Superior Temporal Gyrus, posterior division Right
20	Superior Temporal Gyrus, posterior division Left
21	Middle Temporal Gyrus, anterior division Right
22	Middle Temporal Gyrus, anterior division Left
23	Middle Temporal Gyrus, posterior division Right
24	Middle Temporal Gyrus, posterior division Left
25	Middle Temporal Gyrus, temporooccipital part Right
26	Middle Temporal Gyrus, temporooccipital part Left
27	Inferior Temporal Gyrus, anterior division Right
28	Inferior Temporal Gyrus, anterior division Left
29	Inferior Temporal Gyrus, posterior division Right
30	Inferior Temporal Gyrus, posterior division Left
31	Inferior Temporal Gyrus, temporooccipital part Right
32	Inferior Temporal Gyrus, temporooccipital part Left
33	Postcentral Gyrus Right
34	Postcentral Gyrus Left
35	Superior Parietal Lobule Right
36	Superior Parietal Lobule Left
37	Supramarginal Gyrus, anterior division Right
38	Supramarginal Gyrus, anterior division Left
39	Supramarginal Gyrus, posterior division Right
40	Supramarginal Gyrus, posterior division Left
41	Angular Gyrus Right
42	Angular Gyrus Left
43	Lateral Occipital Cortex, superior division Right
44	Lateral Occipital Cortex, superior division Left
45	Lateral Occipital Cortex, inferior division Right
46	Lateral Occipital Cortex, inferior division Left
47	Intracalcarine Cortex Right
48	Intracalcarine Cortex Left
49	Frontal Medial Cortex
50	Juxtapositional Lobule Cortex -formerly Supplementary Motor Cortex-Right
51	Juxtapositional Lobule Cortex -formerly Supplementary Motor Cortex-Left
52	Subcallosal Cortex
53	Paracingulate Gyrus Right
54	Paracingulate Gyrus Left
55	Cingulate Gyrus, anterior division
56	Cingulate Gyrus, posterior division
57	Precuneous Cortex
58	Cuneal Cortex Right
59	Cuneal Cortex Left
60	Frontal Orbital Cortex Right
61	Frontal Orbital Cortex Left
62	Parahippocampal Gyrus, anterior division Right
63	Parahippocampal Gyrus, anterior division Left
64	Parahippocampal Gyrus, posterior division Right
65	Parahippocampal Gyrus, posterior division Left
66	Lingual Gyrus Right
67	Lingual Gyrus Left
68	Temporal Fusiform Cortex, anterior division Right
69	Temporal Fusiform Cortex, anterior division Left
70	Temporal Fusiform Cortex, posterior division Right
71	Temporal Fusiform Cortex, posterior division Left
72	Temporal Occipital Fusiform Cortex Right
73	Temporal Occipital Fusiform Cortex Left
74	Occipital Fusiform Gyrus Right
75	Occipital Fusiform Gyrus Left
76	Frontal Operculum Cortex Right
77	Frontal Operculum Cortex Left
78	Central Opercular Cortex Right
79	Central Opercular Cortex Left
80	Parietal Operculum Cortex Right
81	Parietal Operculum Cortex Left
82	Planum Polare Right
83	Planum Polare Left
84	Heschl’s Gyrus Right
85	Heschl’s Gyrus Left
86	Planum Temporale Right
87	Planum Temporale Left
88	Supracalcarine Cortex Right
89	Supracalcarine Cortex Left
90	Occipital Pole Right
91	Occipital Pole Left
92	Right-Thalamus
93	Left-Thalamus
94	Right-Caudate
95	Left-Caudate
96	Right-Putamen
97	Left-Putamen
98	Right-Pallidum
99	Left-Pallidum
100	Right-Hippocampus
101	Left-Hippocampus
102	Right-Amygdala
103	Left-Amygdala
104	Right-Accumbens
105	Left-Accumbens
106	Brain-Stem
107	Cerebelum Crus1 Left
108	Cerebelum Crus1 Right
109	Cerebelum Crus2 Left
110	Cerebelum Crus2 Right
111	Cerebelum 3 Left
112	Cerebelum 3 Right
113	Cerebelum 4 5 Left
114	Cerebelum 4 5 Right
115	Cerebelum 6 Left
116	Cerebelum 6 Right
117	Cerebelum 7 b Left
118	Cerebelum 7 b Right
119	Cerebelum 8 Left
120	Cerebelum 8 Right
121	Cerebelum 9 Left
122	Cerebelum 9 Right
123	Cerebelum 10 Left
124	Cerebelum 10 Right
125	Vermis 1 2
126	Vermis3
127	Vermis 4 5
128	Vermis6
129	Vermis7
130	Vermis8
131	Vermis9
132	Vermis10

Appendix B:

ROI Names for Human Connectome Project and Alzheimer’s Disease Neuroimaging Initiative Dataset

Number	ROI names
1	Left-Thalamus
2	Left-Caudate
3	Left-Putamen
4	Left-Pallidum
5	Left-Hippocampus
6	Left-Amygdala
7	Left-Accumbens-area
8	Right-Thalamus
9	Right-Caudate
10	Right-Putamen
11	Right-Pallidum
12	Right-Hippocampus
13	Right-Amygdala
14	Right-Accumbens-area
15	ctx-lh-bankssts
16	ctx-lh-caudalanteriorcingulate
17	ctx-lh-caudalmiddlefrontal
18	ctx-lh-cuneus
19	ctx-lh-entorhinal
20	ctx-lh-fusiform
21	ctx-lh-inferiorparietal
22	ctx-lh-inferiortemporal
23	ctx-lh-isthmuscingulate
24	ctx-lh-lateraloccipital
25	ctx-lh-lateralorbitofrontal
26	ctx-lh-lingual
27	ctx-lh-medialorbitofrontal
28	ctx-lh-middletemporal
29	ctx-lh-parahippocampal
30	ctx-lh-paracentral
31	ctx-lh-parsopercularis
32	ctx-lh-parsorbitalis
33	ctx-lh-parstriangularis
34	ctx-lh-pericalcarine
35	ctx-lh-postcentral
36	ctx-lh-posteriorcingulate
37	ctx-lh-precentral
38	ctx-lh-precuneus
39	ctx-lh-rostralanteriorcingulate
40	ctx-lh-rostralmiddlefrontal
41	ctx-lh-superiorfrontal
42	ctx-lh-superiorparietal
43	ctx-lh-superiortemporal
44	ctx-lh-supramarginal
45	ctx-lh-frontalpole
46	ctx-lh-temporalpole
47	ctx-lh-transversetemporal
48	ctx-lh-insula
49	ctx-rh-bankssts
50	ctx-rh-caudalanteriorcingulate
51	ctx-rh-caudalmiddlefrontal
52	ctx-rh-cuneus
53	ctx-rh-entorhinal
54	ctx-rh-fusiform
55	ctx-rh-inferiorparietal
56	ctx-rh-inferiortemporal
57	ctx-rh-isthmuscingulate
58	ctx-rh-lateraloccipital
59	ctx-rh-lateralorbitofrontal
60	ctx-rh-lingual
61	ctx-rh-medialorbitofrontal
62	ctx-rh-middletemporal
63	ctx-rh-parahippocampal
64	ctx-rh-paracentral
65	ctx-rh-parsopercularis
66	ctx-rh-parsorbitalis
67	ctx-rh-parstriangularis
68	ctx-rh-pericalcarine
69	ctx-rh-postcentral
70	ctx-rh-posteriorcingulate
71	ctx-rh-precentral
72	ctx-rh-precuneus
73	ctx-rh-rostralanteriorcingulate
74	ctx-rh-rostralmiddlefrontal
75	ctx-rh-superiorfrontal
76	ctx-rh-superiorparietal
77	ctx-rh-superiortemporal
78	ctx-rh-supramarginal
79	ctx-rh-frontalpole
80	ctx-rh-temporalpole
81	ctx-rh-transversetemporal
82	ctx-rh-insula