Alterations in Causal Functional Brain Networks in Alzheimer’s Disease: A Resting-State fMRI Study

Abstract

(1) Background: Alterations in brain functional connectivity (FC) precede clinical symptoms of Alzheimer’s disease (AD) by decades, presenting opportunities for early diagnosis. However, conventional FC analyses measure correlations between brain regions and do not provide insights into directional, causal interactions. Causal functional connectivity (CFC), which infers directed interactions between regions, addresses this limitation. This study aims to identify disrupted CFC networks in AD compared to cognitively normal (CN) individuals. (2) Methods: The recently developed Time-aware PC (TPC) algorithm was employed to infer directed CFC from functional magnetic resonance imaging (fMRI) data. These results were compared with traditional correlation-based FC obtained via sparse partial correlation. Network-based Statistics (NBS) for directed networks was used to identify altered CFC sub-networks, with corrections for multiple comparisons applied at the 5% significance level. (3) Results: Key causal networks, including the inferior frontal gyrus, superior temporal gyrus, middle temporal gyrus, and cerebellum, showed significantly reduced strength in AD compared to CN (p = 0.0299; NBS corrected). Instead of detecting disruptions at the level of individual edges, this study identifies network-level alterations, revealing systemic disruptions in brain connectivity. (4) Conclusions: This study demonstrates the utility of CFC analysis in uncovering network-level disruptions in AD. The identified disrupted networks align with published medical literature and provide a framework for future studies with larger datasets.

1. Introduction

Alzheimer’s disease (AD), a major cause of dementia globally, is marked by a gradual deterioration in cognitive abilities, including impairments with working memory, episodic memory, and attention/executive function [1,2]. Such cognitive function deficits in AD are believed to be due to abnormality in functional connectivity between different regions of the brain and neurodegeneration [3,4,5]. Evidence from many anatomical and functional studies suggest that AD is a “disconnection syndrome” [6,7,8]. For example, anatomically, AD is known to be characterized by progressive diffuse cortical atrophy, primarily located in the mesial-temporal regions [9,10]. At the same time, studies of functional connectivity (FC), which measures the degree of temporal synchrony between the activity of different brain regions, have found evidence of disrupted functional connectivity between brain regions [11,12,13].

Functional connectivity (FC) studies have extensively shown disruptions in key networks, such as the default mode network (DMN), salience network, and executive control network in AD [14,15,16]. These disruptions are associated with cognitive decline, including memory deficits and executive dysfunction, which are hallmarks of AD. However, conventional FC analyses focus on statistical correlations between regions, which provide valuable insights into synchrony but fail to capture the directionality of interactions or the flow of information between brain regions [17,18]. This limitation hinders understanding the mechanisms driving network-level disruptions in AD.

Several FC analyses measure the degree of statistical association between signals from different brain regions, in other words, associative FC (AFC) [19,20,21]. However, AFC is inherently limited because it does not account for the directionality and causality of information flow between regions [18,22]. In contrast, causal functional connectivity (CFC) extends beyond associations and addresses these gaps by capturing the direction and strength of causal interactions between brain regions. CFC can answer questions such as: Which brain regions act as drivers or receivers of disrupted network activity in AD? How do disruptions in one region influence downstream effects on others? These insights are critical to advancing our understanding of AD as a “disconnection syndrome”.

CFC represents the functional connectivity between brain regions using a directed graph [18,23]. The nodes of this graph represent brain regions, directed edges between the nodes represent causal relationships between the brain regions, and the weights of these edges measure the strength of these causal connections. Yet, there are very few studies that explore causality in functional connectivity [17]. In this paper, we aim to obtain CFC sub-networks that exhibit significant alteration in AD.

Functional magnetic resonance imaging (fMRI) is a widespread technique to record activity of different brain regions [24,25,26]. It measures the Blood Oxygen Level Dependent (BOLD) signal from different brain regions. Studies in functional connectivity have popularly used fMRI data to obtain functional connectivity [27,28,29]. While previous studies, such as Biswas and Sripada [13], performed edge-wise comparisons of CFC in AD, these methods lack the ability to evaluate network-level changes comprehensively. In contrast, this study uses network-based statistics (NBS) to identify altered CFC sub-networks, allowing for the detection of systemic changes in AD.

In this paper, we use fMRI recordings to obtain CFC for each individual subject. We infer the CFC from fMRI data using the recently developed Time-aware Peter-Clark (PC) algorithm [22]. The Time-aware PC algorithm infers causality in neural interactions instead of correlation, in a model-free non-parametric manner, computes whole brain-wide interactions, incorporates multi-regional interactions, and its utility has been demonstrated in fMRI data [13]. We then use network-based statistics (NBS) to obtain CFC subnetworks that significantly alter between the subjects with AD and cognitively normal (CN) subjects, while correcting for multiple comparisons [30,31,32]. Unlike previous studies that performed edge-wise comparisons [13], NBS allows us to identify network-level alterations by detecting clusters of altered edges, enhancing the biological interpretability of the results.

In summary, our contributions in this paper are as follows: (a) applying the TPC algorithm to calculate whole-brain CFC for each subject, (b) comparing CFC with AFC computed using sparse partial correlation for an example subject, (c) identifying CFC sub-networks with altered connectivity in subjects with AD compared to CN using NBS at a 5% level of significance, and (d) interpreting altered CFC sub-networks in the context of AD using domain-specific (neuropathological) knowledge. Our findings align with existing medical literature and demonstrate the potential of the TPC algorithm for computing whole-brain CFC from fMRI data, and offering prognostic and diagnostic insights.

2. Materials and Methods

2.1. Participants

We obtained the resting-state fMRI data of participants and their demographic information from the Alzheimer’s Disease Neuroimaging Initiative database (http://adni.loni.usc.edu/ (accessed on 15 August 2023)). This study includes 75 participants, comprising 41 individuals who are cognitively normal (CN) and 34 individuals with Alzheimer’s disease (AD).

A summary of the demographic and medical information of the participants is provided in

Table 1. Overview of demographic details and Mini-Mental State Examination (MMSE) scores for cognitively normal (CN) and Alzheimer’s disease (AD) participants. The second and third columns present group characteristics, mean ± SD. The fourth column displays the p-values indicating the statistical significance of differences between groups. A Chi-squared test was used to evaluate differences in sex, while age, education, and MMSE were compared using a non-parametric Kruskal-Wallis analysis of variance.

Characteristic	CN	AD	p
Number of subjects	41	34	-
Sex (M/F)	$19/22$	$16/18$	$0.42$
Age (years)	$74.9\pm 6.4$	$74.4\pm 7.4$	$0.76$
Education (years)	$16.5\pm 2.3$	$15.4\pm 2.5$	$0.11$
MMSE	$29.1\pm 1.4$	$21.9\pm 4.2$	<10−11

. Participants with AD are found to have a significantly lower score on the Mini-Mental State Examination (MMSE) compared to cognitively normal participants. Participants among the CN and AD groups do not significantly differ in age ($p>0.7$ in Kruskal-Wallis test), gender ($p>0.4$ in Chi-Squared test), and years of education ($p>0.1$ in Kruskal-Wallis test). The MMSE scores differed significantly between the CN and AD groups as expected ($p<{10}^{-11}$ in Kruskal-Wallis test).

2.2. Image Acquisition

Scanner from Philips Medical Systems was used to acquire the fMRI images. The imaging procedure utilized an echo planar imaging (EPI) sequence with a magnetic field strength of $3.0\mathrm{T}$. The repetition time (TR) was set to $3\mathrm{s}$, the echo time (TE) was $30\mathrm{ms}$, and the flip angle was configured at ${80}^{°}$. The acquisition matrix dimensions were $64\times 64\mathrm{pixels}$, producing $140\mathrm{volumes}$ comprising $48\mathrm{slices}$ per volume. Each slice had a thickness of $3.3\mathrm{mm}$, corresponding to a voxel size of $3.3\times 3.3\times 3.3{\mathrm{mm}}^3$.

2.3. fMRI Preprocessing

Functional MRI preprocessing was performed using the CONN toolbox (version 21a), which runs in conjunction with Statistical Parametric Mapping (SPM12), which are cross-platform softwares based on MATLAB version R2023a [33,34]. The default preprocessing pipeline in the CONN toolbox (version 21a) was utilized, which follows a series of sequential steps. These include functional realignment and unwarping to correct for subject motion, centering the functional data at coordinates $(0,0,0)$ for alignment, slice-timing correction with interleaved acquisition order, and outlier detection using the Artifact Detection and Removal Tool. The data was segmented into gray matter, white matter, and cerebrospinal fluid, normalized to the standard Montreal Neurological Institute (MNI) space, and smoothed using an 8mm Gaussian kernel (full-width at half maximum). The preprocessing also involved detrending and bandpass filtering (0.001–0.1 Hz) to mitigate low-frequency drift and physiological noise. Additionally, the first four time points were excluded to remove any artifacts.

For extracting regions of interest (ROIs), the preprocessed resting-state fMRI data was parcellated using the automated anatomical labeling (AAL) atlas [35]. A detailed list of the regions within the AAL atlas, including their abbreviations and full names, is provided in Appendix A. This parcellation scheme has been widely recognized for its suitability in functional connectivity studies [36]. The average voxel time series within each ROI was computed to generate the corresponding time series.

2.4. Functional Connectivity Analyses

2.4.1. Associative FC

We employed Sparse Partial Correlation to obtain AFC from fMRI time series data [37,38,39]. The sparse partial correlation regularizes partial correlation with a graphical LASSO penalty, whose regularization parameters were selected by cross-validation [40]. We implemented this approach using the scikit-learn library in Python version 3.11, a widely-used toolkit for machine learning and data analysis [41].

2.4.2. Causal FC

In this study, CFC is estimated using the Time-aware PC (TPC) algorithm, a recently developed approach for inferring CFC from neural time-series data [22,42]. The TPC algorithm applies the Directed Markov Property to a time series context, modeling causal interactions as an unrolled Directed Acyclic Graph (DAG) that captures both spatial and temporal relationships in the time series. In this unrolled DAG, nodes represent regions of interest at specific times, and edges indicate directional causal influences between these nodes. Directional causal influence between nodes is established based on conditional independence relationships derived from neural activity at different time points. Using iterative conditional independence tests, the algorithm ensures that each causal edge represents a statistically significant direct interaction, rather than an indirect association mediated by other regions [22,23].

To estimate the CFC, the TPC algorithm first transforms time-series data into sequential variables with a maximum time lag ($\tau =1$ in this case) and then utilizes the Peter-Clark (PC) algorithm to estimate the unrolled DAG between (neuron, time) tuples. The unrolled DAG is then rolled back to construct a CFC network between neurons (see Figure 1). A complete version of the algorithm that is not used here and applicable for large number of recordings over time includes a subsampling step that further ensures robust edges. The Python package timeawarepc is used for implementing this approach. This method allows for the analysis of complex, multivariate interactions, does not require specific parametric equations for neural dynamics, and supports whole-brain CFC estimation, accommodating the BOLD signal’s temporal delays and feedback loops [13]. In particular, our approach is well-suited for fMRI data as it accommodates the relatively low temporal resolution of the BOLD signal and allows for the identification of both across-time and contemporaneous interactions within the brain network [13].

For comparison, various CFC approaches address different aspects of modeling neural causality [22]. For example, Granger Causality (GC) typically assumes a linear relationship between variables in its standard form, although more recent adaptations allow for non-linear and non-parametric extensions. Dynamic Causal Modeling (DCM) relies on strictly well-defined mechanistic biological models and compares competing models based on their evidence from data. In contrast, both PC and TPC are non-parametric and do not assume specific parametric equations for the neural dynamics. However, PC is designed for static variables and operates under the constraint of a directed acyclic graph (DAG) structure over neurons, making it unsuitable for modeling across-time relationships. TPC, in contrast, extends PC to the time-series setting, allowing it to capture both across-time and contemporaneous relationships. It models parent-child interactions between neurons as functional dependencies over time and can incorporate contemporaneous interactions that arise when neural interactions are faster than the sampling rate—capabilities that GC and PC lack. Another advantage of the TPC algorithm is its ability to model self-loops, which represent feedback mechanisms in neural activity, while the PC algorithm typically enforces a DAG structure that excludes such loops [22]. Although GC provides valuable insights into dynamic interactions, its interpretation of causality is based on predictability rather than definitive causal inference. DCM infers causal flow by estimating coupling parameters between hidden neural states, but its relevance to true causality depends on the accuracy of the competing models being compared [43]. In summary, TPC extends directed probabilistic graphical modeling to time-series data, providing a probabilistic framework for causal inference, in a manner that is predictive of the effects of interventions, such as neuron ablation or neuromodulation.

2.5. Alterations of CFC Edges in Alzheimer’s Disease

NBS is a popular non-parametric statistical method for identifying inter-group differences in large brain networks while controlling for multiple comparisons [30,31,32,44,45,46]. It is a method for controlling the FWER when a large number of univariate tests are conducted over the connections in the network. NBS method outputs the connected components in the brain network that exhibit inter-group difference and a corresponding FWER-corrected p-value for each such component. The FWER-corrected p-values are calculated for each component using permutation testing. We used 10,000 random permutations for the permutation tests. For implementation, we used the dNBS Toolbox in MATLAB which extends NBS for directed networks (https://www.nitrc.org/projects/nbs/ (accessed on 18 February 2024)) [30]. In the implementation of NBS, we used a primary threshold of 1.8 and FWER corrected significance level of 0.05. At that significance level, the critical threshold of cluster size was 6. For finding altered sub-networks between CN and AD groups, NBS considers the direction of each connection in the whole CFC among subjects in CN and AD groups. We outlined detailed steps of implementing NBS in Appendix B.

We applied NBS to the subject-specific CFCs estimated by TPC, to identify connected components of the CFC that are altered in strength for subjects with AD compared to the CN.

3. Results

3.1. Subject-Specific CFC

Figure 2 shows the AFC obtained by sparse partial correlation and CFC obtained by TPC for an example subject who is CN. The AFC (top row) revealed an extensive associative network, as evidenced by dense symmetric adjacency matrix and dense undirected graphical representations. The CFC is expected to be a directed subgraph of the AFC, reflecting the overall structure observed in the AFC. The general connectivity patterns in the CFC derived using the TPC algorithm are consistent with those in the AFC, as visualized in their respective adjacency matrices (refer to Figure 2, left column). Yet, at a detailed level, TPC results in a directed graph with an asymmetric adjacency matrix where $22.42\%$ of its edges are unidirectional, thus capturing directional interaction between regions through its edges. In comparison, the AFC yields an undirected graph having a symmetric adjacency matrix, thus not identifying any directional interactions. Furthermore, we quantify the sparsity level of a graph by the proportion of edges in the graph out of all possible edges, i.e., $116\times 116=\mathrm{13,456}$ all possible edges between 116 brain regions. The sparsity level of the AFC graph is $18.15\%$ (2442 edges) whereas the sparsity level of the CFC graph is $1.23\%$ (165 edges). Thus, in contrast to the dense AFC graph, the CFC obtained by TPC results in a sparse graph. Such a sparsity in the CFC graph is desirable because the CFC identifies directeional edges whereas the AFC is unable to identify directional edges, CFC reduces spurious edges from the AFC, and the connections in the CFC are filtered by conditional dependence tests in the TPC algorithm thereby reducing noise [22].

3.2. Altered CFC Sub-Networks in AD

Figure 3 shows the significantly altered ($p<0.05$; NBS corrected) CFC sub-networks in AD compared to CN. In the implementation of NBS, t-statistic thresholds of 0.1 to 3.1 in steps of 0.1 were tried out. Among those, thresholds of 1.8, 2.2 and 2.3 yielded altered sub-networks at $5\%$ level of significance. At each of these thresholds, a sparse thresholded adjacency matrix is obtained (Figure 3-left row). A subset of the thresholded edges is outputted by NBS as an altered sub-network at $5\%$ level of significance. Figure 3 shows the altered sub-network’s adjacency matrix representation (2nd column from left) as well as graphical representation (3rd to 5th columns from left) on brain schematics.

3.3. Brain Regions in the Altered CFC Sub-Networks

Table 2. CFC edges in significantly altered CFC sub-networks with greater weight in CN compared to AD group at NBS corrected $5\%$ level of significance. The sub-networks are obtained at different NBS’s t-statistic thresholds: (a) $1.80$, (b) $2.20$ and (c) $2.30$ yielding altered sub-networks with p-values of $0.0299$, $0.0465$ and $0.0233$ respectively. The identified source brain regions correspond to those reported in the literature (right column) as being affected in Alzheimer’s disease (AD).

(a) CFC sub-network for CN > AD at thresh = 1.80 having p-value = 0.0299
Edge	Region Name	Reported by
IFGorb_R → TPOsup_R	Inferior frontal gyrus	Eliasova et al. [47], Cajanus et al. [48]
TPOmid_R → TPOsup_R	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]
TPOmid_R → TPOmid_L	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]
CER8_R → TPOmid_R	Cerebellum	Joachim et al. [51], Jacobs et al. [52]
TPOmid_R → CER8_R	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]
CER9_R → CER8_R	Cerebellum	Joachim et al. [51], Jacobs et al. [52]
CER8_R → CER9_R	Cerebellum	Joachim et al. [51], Jacobs et al. [52]
(b) CFC sub-network for CN > AD at thresh = 2.20 having p-value = 0.0465
Edge	Region Name	Reported by
IFGorb_R → TPOsup_R	Inferior frontal gyrus	Eliasova et al. [47], Cajanus et al. [48]
TPOmid_R → TPOsup_R	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]
TPOmid_R → TPOmid_L	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]
(c) CFC sub-network for CN > AD at thresh = 2.30 having p-value = 0.0233
Edge	Region Name	Reported by
IFGorb_R → TPOsup_R	Inferior frontal gyrus	Eliasova et al. [47], Cajanus et al. [48]
TPOmid_R → TPOsup_R	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]
TPOmid_R → TPOmid_L	Temporal pole: middle temporal gyrus	Harasty et al. [49], Convit et al. [50]

presents the CFC edges within altered sub-networks that show higher average strength in cognitively normal (CN) individuals compared to Alzheimer’s disease (AD) subjects, with significance corrected at the 5% level using NBS. The identified brain regions align with findings from existing medical literature referenced in the table. No sub-networks with lower average strength in CN compared to AD reached significance at the 5% threshold after NBS correction.

4. Discussion

In this study, we identified whole-brain CFC sub-networks that differ between AD and CN individuals using resting-state fMRI data. The analysis employed the TPC algorithm, a recent approach that utilizes directed graphical modeling of time-series data for CFC estimation. First, subject-specific CFCs were generated using TPC and compared to AFCs obtained through sparse partial correlation. We then used the CFC results from TPC to further investigate changes in CFC sub-networks associated with AD. In this regard, we used NBS to obtain CFC sub-networks that alter in AD compared to CN subjects at $5\%$ level of significance, while correcting for multiple comparisons in those sub-networks. The brain regions within those altered sub-networks were consistent with medical literature regarding areas affected by AD.

Our findings align with the growing body of literature that highlights AD as a “disconnection syndrome”, characterized by both structural and functional network disrupti- ons [6,7,8]. These disruptions are closely associated with patterns of neurodegeneration, as well as the deposition of pathological tau and amyloid-beta proteins, which have been shown to preferentially affect specific brain networks. For instance, the inferior frontal gyrus and the temporal pole: middle temporal gyrus—prominent regions in our results—are part of the default mode network (DMN), which is one of the earliest and most severely affected networks in AD [14,16,53]. Our findings of altered CFC sub-networks involving these regions support the hypothesis that functional network disruptions in AD are closely tied to neurodegenerative changes and the progression of tau and amyloid pathology.

Figure 3 and Table 2 show CFC sub-networks with edge weights higher in AD than in CN, which aligns with findings reported in the literature. The absence of CFC sub-networks with weight of edges in AD lower than that in CN supports the notion of AD as a syndrome of disrupted functional and causal connectivity [6,7,8]. This aligns with studies showing that tau pathology spreads in a network-dependent manner, disrupting connectivity along established anatomical pathways [54,55].

In Table 2, the brain regions of the Inferior frontal gyrus (Inferior frontal gyrus, pars orbitalis Right → Temporal pole: superior temporal gyrus Right) and Temporal pole: middle temporal gyrus (Temporal pole: middle temporal gyrus Right → Temporal pole: superior temporal gyrus Right, Temporal pole: middle temporal gyrus Right → Temporal pole: middle temporal gyrus Left) are prominent within sub-networks where CFC weights are lower in AD compared to CN individuals. The Inferior frontal gyrus is associated with attentional control [56] and language processing [57] and has been reported as a region affected in AD [47,48]. The temporal pole: middle temporal gyrus, another region in Table 2, is considered to be important in word memory and meaning [58,59,60,61,62,63,64,65]. It has been reported to be impacted by AD [49,50]. Also present in Table 2(a) is the Cerebellum (Lobule VIII of cerebellar hemisphere Right → Temporal pole: middle temporal gyrus Right, Lobule IX of cerebellar hemisphere Right → Lobule VIII of cerebellar hemisphere Right, Lobule VIII of cerebellar hemisphere Right → Lobule IX of cerebellar hemisphere Right), which plays an essential role in motor control and perception [66,67,68], and has been reported to be impacted by AD [51,52].

The involvement of the cerebellum in the altered sub-networks is noteworthy. While traditionally associated with motor control, recent studies have highlighted the cerebellum’s role in higher-order cognitive processes such as attention and language [69,70]. In fact, emerging evidence suggests that the cerebellum is impacted by amyloid deposition and tau pathology in AD, particularly in later stages of the disease [51,52,71].

Our findings highlight the potential utility of interpreting altered causal sub-networks in Alzheimer’s Disease. Specifically, this approach enables the identification of regions that serve as causal drivers of network disruptions, such as the inferior frontal gyrus and temporal pole, which are critical for memory and attention [72,73]. This knowledge provides a foundation for future early diagnostic biomarkers and can inform neuromodulation therapies targeting network hubs (Fox et al., 2014). Moreover, understanding the direction of interactions rather than mere correlations offers a mechanistic perspective on disease progression, supporting the development of personalized treatment strategies [74]. Ultimately, our approach can be scaled to larger datasets and longitudinal studies, enhancing its utility for tracking disease progression and evaluating the efficacy of targeted interventions [75].

Overall, by identifying altered causal functional connectivity (CFC) sub-networks, this study contributes to understanding the directional flow of information in affected networks and suggests the potential utility of CFC in studying AD-related connectivity changes. Future studies integrating multi-modal imaging, such as structural MRI and PET imaging of tau and amyloid, will be critical for further elucidating the relationship between functional disruptions and pathological changes in AD.

Conclusions

In this study, we applied the TPC algorithm to estimate whole-brain CFC from resting-state fMRI data, a novel approach compared to traditional correlation-based methods. Using NBS, we identified significant alterations in causal sub-networks between AD and CN subjects, moving beyond earlier edge-wise comparisons to detect network-level disruptions. Our analysis revealed that key regions, such as the inferior frontal gyrus and temporal pole, exhibit reduced CFC strength in AD, consistent with the literature on neurodegenerative network disruptions. By comparing CFC to AFC, we demonstrated that causal inference provides richer insights by capturing the directional flow of neural interactions.

The use of NBS strengthened the analysis by identifying clusters of altered connections at the sub-network level after correcting for multiple comparisons, underscoring the robustness of the findings. These results highlight the novelty of using whole-brain CFC analysis to understand AD-related disruptions and demonstrate the potential of the TPC algorithm for detecting complex, multivariate brain interactions. This research contributes to the growing body of work on causal connectivity and presents CFC as a promising biomarker for early diagnosis and monitoring of AD progression. Future studies with larger, longitudinal datasets could enhance the generalizability of these results and further investigate the temporal dynamics of causal connectivity changes.