Accumulation of network redundancy marks the early stage of Alzheimer's disease

Abstract

Brain wiring redundancy counteracts aging‐related cognitive decline by reserving additional communication channels as a neuroprotective mechanism. Such a mechanism plays a potentially important role in maintaining cognitive function during the early stages of neurodegenerative disorders such as Alzheimer's disease (AD). AD is characterized by severe cognitive decline and involves a long prodromal stage of mild cognitive impairment (MCI). Since MCI subjects are at high risk of converting to AD, identifying MCI individuals is essential for early intervention. To delineate the redundancy profile during AD progression and enable better MCI diagnosis, we define a metric that reflects redundant disjoint connections between brain regions and extract redundancy features in three high‐order brain networks—medial frontal, frontoparietal, and default mode networks—based on dynamic functional connectivity (dFC) captured by resting‐state functional magnetic resonance imaging (rs‐fMRI). We show that redundancy increases significantly from normal control (NC) to MCI individuals and decreases slightly from MCI to AD individuals. We further demonstrate that statistical features of redundancy are highly discriminative and yield state‐of‐the‐art accuracy of up to 96.8 ± 1.0% in support vector machine (SVM) classification between NC and MCI individuals. This study provides evidence supporting the notion that redundancy serves as a crucial neuroprotective mechanism in MCI.

We demonstrated the utility of our redundancy metric in differentiating the stages of AD progression. We reported a pattern of accrual of redundant connections in MCI to counter AD pathology. Our results provide evidence supporting redundancy as a neuroprotective mechanism in cognitive aging. By taking advantage of the high sensitivity of our metric, we showed that MCI individuals can be detected with high accuracy.

1. INTRODUCTION

Network redundancy preserves functions when connections are compromised (Glassman, 1987; Tononi et al., 1999). In physical sciences, redundancy refers to the repetition or duplication of elements within mechanical or electronic components to supply alternative functional channels in case of failure. In information theory, redundancy represents the repetition of parts or all of a message to circumvent transmission error (Tononi et al., 1999). Network redundancy analysis has also been applied to areas such as transportation, biology, and communication systems (Billinton & Allan, 1992; Corson, 2010; Härkegård & Glad, 2005; Steiglitz et al., 1969). In brain networks, redundant connections act as a neuroprotective mechanism in the early stages of neurodegenerative diseases, particularly Parkinson's disease and Alzheimer's disease (AD) (Arkadir et al., 2014; Ghanbari et al., 2021). AD is the leading cause of dementia resulting in progressive cognitive decline and irreversible memory loss (Liang et al., 2011). As a prodrome of AD, MCI is characterized by noticeable impairment of cognitive functions beyond decline due to aging, but not to the extent of significantly affecting activities of daily life (Binnewijzend et al., 2012; Gauthier et al., 2006; Misra et al., 2009; Petersen et al., 2001). With timely diagnosis and early treatment at the MCI stage, it is possible to alleviate specific symptoms (Binnewijzend et al., 2012; Misra et al., 2009) and the rate of reversion from MCI to healthy cognitive condition could exceed 50% (Shimada et al., 2019). Driven by the critical role of redundancy in safeguarding network integrity, here we investigate the redundancy profile of AD progression and demonstrate how this information can be harnessed for early diagnosis.

Despite its apparent role in maintaining cognitive function, it is unclear how brain network redundancy is altered with AD progression. As a compensatory mechanism, network redundancy might increase over time until the onset of MCI. The accumulated redundancy acts as the brain's reserve capacity to overcome possible damages from AD pathology to alleviate the decline in cognitive performance (Cabeza et al., 2018; Gregory et al., 2017; Montine et al., 2019). This reserve mechanism responds to aging and neurodegeneration to maintain normal brain functions (Arkadir et al., 2014; Cabeza et al., 2018; Cole & Kharasch, 2018; Montine et al., 2019). In other words, accrued redundant connections might reflect neuroprotective mechanisms that enable MCI individuals to compensate for the loss of connections due to synaptic disruption (Sadiq et al., 2021). However, it remains unknown whether AD pathology may accelerate the brain's reserve mechanism such that network redundancy significantly increases in MCI individuals compared with age‐matched healthy individuals to compensate for connection loss. Moreover, it is not completely clear how network redundancy changes with progression from MCI to AD, a more severe disease stage characterized by widespread synaptic loss (Hamos et al., 1989; Kashyap et al., 2019). Shedding light on AD‐related redundancy changes will provide deeper mechanistic insights into AD pathology and help develop better machine learning algorithms for early AD diagnosis.

Existing graph‐theoretic analyses primarily focus on utilizing various network metrics of resting‐state fMRI (rs‐fMRI) to investigate how network connections are disrupted in AD progression (Khazaee et al., 2016; Si et al., 2019). These metrics typically focus on network cost efficiency and include metrics such as the characteristic path length and its derivatives (e.g., modularity, hierarchy, assortativity, resilience, and small‐worldness) (Newman, 2002; Požar et al., 2020; Ravasz & Barabási, 2003; Seo et al., 2013). Although network redundancy analysis has been applied to study the importance of alternative connections in safeguarding the integrity of different kinds of networks (Corson, 2010; Di Lanzo et al., 2012; Härkegård & Glad, 2005; Steiglitz et al., 1969), redundancy studies on neuroprotection in neurodegenerative diseases are still limited (Langella et al., 2021b; Sadiq et al., 2021). Previous studies suggested that redundancy may act as a reserve mechanism to safeguard brain integrity and support functional connectivity (FC) to alleviate cognitive impairments (Langella et al., 2021a; Sadiq et al., 2021). However, these studies involve methodological limitations (e.g., limited connection path length) that hinder a more comprehensive redundant analysis of MCI. In addition, existing studies mainly focus on static FC for graph theoretical analysis, although dynamic FC is potentially more sensitive to changes in macroscopic activity (Hutchison et al., 2013) and is hence able to better characterize AD progression for more accurate MCI detection.

To overcome the limitations of previous studies and offer a more comprehensive account of redundancy, we examined network redundancy changes during AD progression using a novel metric (Ghanbari et al., 2021, 2022, 2020). Unlike previous approaches that indiscriminately consider all possible connections between nodes (Corson, 2010; Langella et al., 2021a; Langella et al., 2021b; Sadiq et al., 2021; Steiglitz et al., 1969), our metric considers only redundant connections without common nodes (Ghanbari et al., 2022, 2021, 2020). As removing a node shared by multiple connections causes the loss of all connections, our metric therefore accounts for truly redundant connections, partial removal of which will still ensure network integrity. Using this redundancy metric, we previously defined a 2‐connected network as having at least two redundant connections between every pair of regions. We examined changes in global redundancy associated with AD progression and observed that the whole‐brain networks of MCI individuals are more likely to be 2‐connected than NC and AD individuals (Ghanbari et al., 2021). We also utilized the redundancy features from the 2‐connected networks to classify MCI from AD individuals (Ghanbari et al., 2020). However, we have to date only considered global whole‐brain redundancy, neglecting more fine‐grained characterization in terms of inter‐regional variations in redundancy.

In this study, we investigated the redundant connections in the medial frontal (MF), frontoparietal (FP), and default mode (DM) networks in association with AD progression due to their essential roles in AD pathophysiology (Bahlmann et al., 2015; Betzel et al., 2014; Cole et al., 2013; Marek & Dosenbach, 2018; Smith et al., 2018; Turner & Spreng, 2012). For a particular network density, we computed the number of redundant connections for each pair of nodes. We employed a sliding window approach to characterize the average and variability of redundancy in dynamic functional connectivity. We observed that MCI individuals exhibit more redundant connections between brain regions compared with AD and NC individuals, suggesting that accrued redundant connections preserve the functionality of MCI individuals despite pathological disruptions. Further analysis shows significant accumulation of redundant connections in early‐MCI (EMCI) individuals compared with NC individuals. We further demonstrated that computer‐aided MCI or AD diagnosis with redundancy features yields a state‐of‐the‐art accuracy of 96.8 ± 1.0%. Overall, our results demonstrate that the accumulation of network redundancy marks the early stage of AD and that redundancy features can be a valuable biomarker for MCI diagnosis.

2. MATERIALS AND METHODS

2.1. Participants

We utilized rs‐fMRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) (http://adni.loni.usc.edu). NC subjects, with or without any subjective memory concerns, had Mini‐Mental State Examination (MMSE) scores between 24 and 30 inclusive, Clinical Dementia Ratings (CDRs) of 0, and Memory Box scores of 0. MCI subjects expressed subjective memory concerns and had MMSE scores between 24 and 30 inclusive, CDRs of 0.5, and Memory Box scores of at least 0.5. AD subjects expressed subjective memory concerns and had MMSE scores between 20 and 24 inclusive, and CDRs of 0.5 or 1.0. We selected 49 NC subjects (26/23 males/females, age 73.1 ± 6.5 years, MMSE score 29.1 ± 0.9), 49 MCI subjects (26/23 males/females, age 74.3 ± 9.8 years, MMSE 27.9 ± 1.6), and 49 AD subjects (26/23 males/females, age 73.3 ± 8.5 years, MMSE 23.1 ± 2.5) from the ADNI‐Go and ADNI‐2 studies, including only the baseline scans. We first selected 49 AD subjects with baseline fMRI data. We then selected 49 subjects each from the NC and MCI groups with age and gender matched with the AD group. For further validation, we selected in addition 49 early‐MCI (EMCI) subjects (26/23 males/females, age 74.1 ± 7.6 years, MMSE 28.2 ± 1.8) and 49 late‐MCI (LMCI) subjects (26/23 males/females, age 72.8 ± 7.7 years, MMSE 26.1 ± 1.9). All subjects were matched in terms of age (p = .752, one‐way analysis of variance [ANOVA]) and gender.

2.2. Data preprocessing

In ADNI, data quality control was enforced to ensure consistency across imaging centers in terms of the scanner, imaging protocol, and signal‐to‐noise ratio (Jack et al., 2008). Using a standard pipeline (Yan & Zang, 2010), 7‐min rs‐fMRI data (140 volumes) were preprocessed with AFNI (Cox, 1996). After discarding the first 10 volumes, the remaining volumes were corrected for head motion via rigid‐body registration and then nonlinearly registered to the Montreal Neurological Institutes (MNI) space. Individuals with more than 2.5‐min data (50 volumes) with excessive head motion (frame‐wise displacement >0.5) were excluded (Power et al., 2014). Mean rs‐fMRI time series of each brain region were band‐pass filtered (0.015–0.15 Hz) and then processed to reduce artifacts by regression analysis. Nuisance regressors include head motion parameters (the “Friston‐24” model), the mean BOLD signal of the white matter, and cerebrospinal fluid. FC matrices were computed via the Pearson's correlation of the BOLD rs‐fMRI signals between every pair of nodes using a sliding window of 60 s (20 TRs) and a step size of 3 s (1 TR).

2.3. Resting‐state networks

The brain was parcellated into 268 functionally coherent regions of interest (ROIs) using a parcellation atlas (Shen et al., 2013) made available through the BioImage Suite NITRC site (https://www.nitrc.org/frs/?group\_id=51). Using connectivity matrices from 45 subjects, a group‐wise spectral clustering algorithm was utilized to divide the 268 ROIs into eight networks: (1) medial frontal network, (2) frontoparietal network, (3) default mode network, (4) subcortical‐cerebellum network, (5) motor network, (6) visual I network, (7) visual II network, and (8) visual association network (Finn et al., 2015). These eight networks were identified and compared visually with existing definitions of resting‐state networks (Choi et al., 2012; Smith et al., 2009). Medial frontal (Cui et al., 2018), frontoparietal (Badhwar et al., 2017) and default mode (Banks et al., 2018; Cai et al., 2017; Xue et al., 2019) networks, commonly involved in AD studies, were selected for redundancy analysis (Figure 1).

FIGURE 1.

Visualization of the medial frontal (MF), frontoparietal (FP), and default mode (DM) networks.

2.4. Network and nodal redundancy

A network with at least one connection between every two nodes is a connected network (Figure 2a,b). Two connections joining two nodes, say $a$ and $b$, are redundant when the only shared nodes are $a$ and $b$. For instance, the multiple connections between $a$ and $b$ in Figure 2a are not redundant because they share node $c$. In contrast, the green and red connections between $a$ and $b$ in Figure 2b are redundant. A redundant network is a network with redundant connections between every pair of nodes. In Figure 2a, the resulting network after removing node $c$ is not connected so the network is not redundant. On the other hand, the redundant network in Figure 2b remains connected if any single node is removed.

FIGURE 2.

Illustration of redundant network. (a) A connected but not redundant network. (b) A connected and redundant network.

To calculate the number of redundant connections between two nodes $a$ and $b$ in a network $G$ with $N$ nodes,1 we employ the Menger's theorem (McCuaig, 1984):

If no set of fewer than $k$ nodes separates nonadjacent vertices $a$ and $b$ in an undirected or directed graph $G$, then there are $k$ internally disjoint ($a$, $b$)‐paths.

If there is no connection between $a$ and $b$, the number of redundant connections is zero. If $a$ and $b$ are directly connected, we remove the connection before taking the following steps. We remove in turn every possible subset of $k$ nodes, excluding $a$ and $b$, from $G$ and check whether $a$ and $b$ remain connected. This is repeated for $k=1,2,\dots ,N-2$ or until $a$ and $b$ are disconnected. At $k=N-2$, the remaining network consists of two isolated nodes $a$ and $b$. If $a$ and $b$ are not originally connected, the number of redundant connections between $a$ and $b$ is the minimum $k$ that disconnects $a$ and $b$, and $k+1$ otherwise.

The nodal redundancy for each network node is defined as the total number of redundant connections between the node and every other node in the network. In Figure 2a, the nodal redundancy of nodes $a$ and $c$ are 9 and 12, respectively.

2.5. Binarization of functional connectivity

Binarization of the functional connectivity matrices can be performed using absolute or proportional thresholding (van den Heuvel et al., 2017). Absolute thresholding retains edges with absolute values exceeding a threshold, resulting in networks with different numbers of connections. Proportional thresholding retains a fixed fraction or density of the strongest connections, leading to networks with an equal number of connections (Achard & Bullmore, 2007; Bassett et al., 2009; Jalili, 2016; van den Heuvel et al., 2008, 2017). For a more comprehensive analysis, we applied proportional thresholding using multiple densities.

2.6. Redundancy features

For each subject, we first extracted the MF, FP, and DM networks (Figure 3a). Then, for each brain network, we generated $T$ sliding windows of length 20 volumes (60 s) with a step size of one volume (3 s) (Leonardi & Van De Ville, 2015). Pairwise Pearson's correlation of the BOLD rs‐fMRI signals was utilized to calculate the dynamic FC (Figure 3b). We applied $D$ thresholds to every FC matrix to obtain $D$ binarized networks for every time window (Figure 3c), collectively denoted as $G\left(d,t\right)$, $1\le d\le D$ and $1\le t\le T$ (Figure 3c). We defined the following metrics:

• Tendency of redundancy (TOR): The fraction of 1's in $S$ (Figure 3d₁ ), a vector of length $T$, such that $S_t=1$ if $G\left(d,t\right)$ is a redundant network and $S_t=0$ otherwise, for a specific $d\in \left\{1,\dots ,D\right\}$.

• $\overline{\mathrm{TOR}}$: Average TOR over all applied density levels for each brain network.

• Redundancy vector (RV): A vector of length $T$ encoding the number of redundant connections between a pair of nodes for a specific density and for every time window. For a network with $N$ nodes, $D\times \frac{N\left(N-1\right)}{2}$ RVs can be computed (Figure 3d₂ ).

• Mean of redundancy (MOR) and fluctuation of redundancy (FOR) were computed respectively as the mean and standard deviation of each RV across $T$ time windows (Figure 3e).

FIGURE 3.

Framework overview. (a) Network extraction. (b) Sliding window dynamic FC. (c) Binary networks for different time windows and various densities. (d1) Network redundancy for each time window and each density. (d2) The number of redundant connections between every two nodes for each density. (e) Mean of redundancy (MOR) and fluctuation of redundancy (FOR) features for each connection link. (f) Statistical analysis and MCI/AD classification based on redundancy features.

We investigated changes in TOR, a global feature, across groups and utilized MOR and FOR, local features, for MCI/AD diagnosis using machine learning (Figure 3f). We set $T=111$ and $D=9$ (5%, 10%,⋯,45%) for calculating $S$ and RV. The MF, FP, and DM networks consist of 29, 34, and 20 regions, respectively, amounting to 406, 561, and 190 region pairs (1157 total), giving 1157 RVs per density. Implementation was carried out using MATLAB 2019b, SAGE 8.6, Python 2.7, and SPSS 23.

2.7. Statistical analysis and MCI/AD diagnosis

We conducted a Kruskal‐Wallis test with correction for family‐wise error (FWE) to discover group differences among NC, MCI, and AD groups based on TOR indices. We further used Mann–Whitney U‐tests for post hoc pairwise comparisons based on significant Kruskal‐Wallis test results. The effectiveness of the redundancy metrics (MOR and FOR) was evaluated in MCI/AD diagnosis via machine learning. We employed an SVM classifier (Chang & Lin, 2011) with Weka 3 (Frank et al., 2004) (https://www.cs.waikato.ac.nz/ml/weka) using a linear kernel and grid search for parameter optimization. The evaluation was performed via 10‐repeated 10‐fold SVM classification with randomly partitioned training and testing sets using sensitivity (SEN), specificity (SPE), accuracy (ACC), the area under the ROC curve (AUC), balanced accuracy (BAC), and Youden's index (YI). We employed the wrapper attribute subset evaluator (Kohavi et al., 1997) to identify discriminative features.

3. RESULTS

3.1. Network redundancy increases in MCI

We found significant differences in $\overline{\mathrm{TOR}}$, a global redundancy feature, among NC, MCI, and AD individuals ($p<.001$, Kruskal‐Wallis test). As shown in Figure 4, MCI individuals exhibit the highest $\overline{\mathrm{TOR}}$ compared with NC and AD individuals. Specifically, the $\overline{\mathrm{TOR}}$ of MCI individuals is significantly higher than that of NC individuals ($p<.001$, FWE‐corrected), indicating the tendency to maintain connectedness in the presence of AD‐related pathology. In contrast, the $\overline{\mathrm{TOR}}$ is significantly lower in AD individuals than MCI individuals ($p<.001$, FWE‐corrected), potentially due to the disruption of connections associated with irreversible synaptic loss during the more advanced stage of AD (Hamos et al., 1989; Kashyap et al., 2019). While reduced, the $\overline{\mathrm{TOR}}$ of AD individuals is still significantly higher than that of NC individuals ($p<0.001$, FWE‐corrected).

FIGURE 4.

$\overline{\mathrm{TOR}}$ in three subject groups. Statistically significant FWE‐corrected results with p < .05, p < .01, p < .001, and p < .0001 are marked with *, **, ***, and ****, respectively.

Including the early‐ and late‐MCI (EMCI and LMCI [Edmonds et al., 2019]) groups in our analysis, we found significant differences in $\overline{\mathrm{TOR}}$ among NC, EMCI, MCI, LMCI, and AD individuals ($p<.001$, Kruskal‐Wallis test). As shown in Figure 5, the $\overline{\mathrm{TOR}}$ of EMCI individuals is significantly higher than that of NC individuals ($p<.001$, FWE‐corrected), indicating that the accrual of redundancy is an early sign of MCI. The $\overline{\mathrm{TOR}}$ of MCI individuals is significantly higher than that of EMCI individuals ($p<.01$, FWE‐corrected), indicating a gradual increase in redundancy with disease progression. EMCI and LMCI individuals have a lower $\overline{\mathrm{TOR}}$ than MCI individuals.

FIGURE 5.

$\overline{\mathrm{TOR}}$ in five subject groups. Statistically significant FWE‐corrected results with p < .05, p < .01, p < .001, and p < .0001 are marked with *, **, ***, and ****, respectively.

All density levels, except 5%, present significant group differences in TOR (Supplementary Table S1). Consistent with Figure 5, MCI individuals exhibit the highest TOR for all density levels (Supplementary Figure S1). The TOR increases significantly from NC to EMCI and from EMCI to MCI individuals. As expected, the TOR increases with the density level due to the increase in the number of connections (Supplementary Figure S1).

3.2. Redundancy changes in MF, FP and DM networks

We next examined redundancy changes in individual networks. The $\overline{\mathrm{TOR}}$ of MF, FP, and DM networks changes significantly with AD progression (Table 1). As shown in Figure 6, the $\overline{\mathrm{TOR}}$ significantly increases in MCI individuals and even in EMCI individuals, compared with NC individuals. However, no such significant difference was found between MCI and AD subjects, except for the $\overline{\mathrm{TOR}}$ of the FP network, which is significantly decreased in AD when compared with MCI ($p<.024$, not corrected), but not the MF and DM networks. This finding potentially indicates that the FP network is more affected by AD. There are significant group differences in the TOR of these networks for most density levels (see Supplementary Tables S2–S4 and Supplementary Figures S2–S4). Consistent with Figure 6, MCI individuals exhibit the highest TOR with a significant increase compared with EMCI and NC individuals at each density level ($p<.002$, Kruskal‐Wallis test).

TABLE 1.

Groupwise and pairwise $\overline{\mathrm{TOR}}$ comparisons of MF, FP and DM networks of five subject groups

	MF	FP	DM
ANOVA	2.7 e‐8	4.1 e‐6	8.7 e‐6
MCI vs. NC	2.3 e‐9	2.9 e‐7	2.3 e‐6
MCI vs. AD	0.198	0.024	0.704
MCI vs. EMCI	0.334	0.376	0.348
MCI vs. LMCI	0.094	0.072	0.456
NC vs. AD	4.4 e‐6	0.002	2.7 e‐5
NC vs. EMCI	7.9 e‐6	5.1 e‐5	2.7 e‐5
NC vs. LMCI	1 e‐5	0.001	3.9 e‐5
AD vs. EMCI	0.893	0.218	0.582
AD vs. LMCI	0.717	0.776	0.853
EMCI vs. LMCI	0.647	0.35	0.712

Note: Statistically significant FWE‐corrected results are marked in bold.

FIGURE 6.

$\overline{\mathrm{TOR}}$ of MF, FP and DM networks in five subject groups. Statistically significant FWE‐corrected results with p < .05, p < .01, p < .001, and p < .0001 are marked with *, **, ***, and ****, respectively.

3.3. Elevated nodal redundancy in MCI

To reveal which brain regions underlie network redundancy changes, we calculated nodal redundancy during different phases of AD progression. We found that 15 ROIs of the MF network, 18 ROIs of the FP network, and 10 ROIs of the DM network present significant group differences (Supplementary Tables S5–S7). All of these 43 ROIs (Figure 7) show significantly higher nodal redundancy in MCI individuals than NC individuals. Most of these ROIs, such as the superior temporal gyrus, superior temporal sulcus, anterior fusiform gyrus, anterior middle temporal gyrus, middle temporal gyrus, anterior inferior temporal gyrus, medial occipitotemporal gyrus, belong to the temporal lobe, indicating that it is a major and early target of AD pathology, consistent with previous findings (Aggleton et al., 2016).

FIGURE 7.

ROIs with significant differences in nodal redundancy among NC, MCI and AD groups.

3.4. Association between redundancy and MMSE

To investigate how redundancy affects cognitive function, we studied the association between network redundancy and MMSE. We found that the $\overline{\mathrm{TOR}}$ is significantly associated with MMSE for the whole‐brain network and the MF network with $r=-0.296$ ($p<.0003$, FWE‐corrected) and $r=-0.269$ ($p<.0001$, FWE‐corrected), respectively (Figure 8). The highest $\overline{\mathrm{TOR}}$ is associated with an average MMSE of 24, corresponding to the MCI group. The average MMSE is 29.1 for NC individuals, 27.9 for MCI individuals, and 23.1 for AD individuals. Thus, network redundancy reflects different cognitive states during AD progression.

FIGURE 8.

Association between $\overline{\mathrm{TOR}}$ and MMSE for (a) the whole‐brain network and (b) the MF network for all subjects shown using a quadratic curve.

3.5. Redundancy features are sensitive to pathological changes

The redundancy features are sensitive to AD‐related changes. We demonstrated this using MCI/AD classification with MOR, FOR, or MOR + FOR features concatenated from all densities (9 × 1157 MOR, 9 × 1157 FOR, and 2 × 9 × 1157 MOR+FOR features per subject). The best SVM classification accuracies (10 times 10‐fold cross‐validation) for NC‐MCI, NC‐AD, and MCI‐AD are 96.8 ± 1.0%, 93.7 ± 0.9%, and 91.7 ± 2.3%, respectively (Table 2). For comparison, we listed results from other published studies using state‐of‐the‐art machine learning techniques in Table 3. Notably, the results based on redundancy features are comparable to the best‐performing methods (Jie et al., 2013). Compared with other studies (Gupta et al., 2019; Li et al., 2017; Shi et al., 2019; Suk et al., 2014; Suk & Shen, 2013; Wang et al., 2016), our method is more accurate in NC‐MCI than NC‐AD classification. The selected features are detailed in Supplementary Tables S8–S10 and summarized in Figure 9 (ROI names listed in Supplementary Table S11). The results suggest that the FP and MF networks are most discriminative between MCI and AD. Most of the selected ROIs are in the temporal lobe, including the anterior middle temporal gyrus, anterior superior temporal gyrus, inferior temporal gyrus, posterior inferior temporal gyrus, anterior inferior temporal gyrus, temporal pole, posterior superior temporal sulcus, and superior temporal sulcus (Aggleton et al., 2016).

TABLE 2.

Classification using MOR, FOR, or MOR + FOR features

		SEN	SPE	ACC	AUC	F‐score	BAC	YI
MOR	NC vs. MCI	96.7 ± 1.7	92.0 ± 1.5	94.4 ± 1.0	94.8 ± 2.0	94.5 ± 1.0	94.4 ± 1.0	88.8 ± 2.0
	NC vs. AD	94.1 ± 1.5	88.6 ± 2.8	91.3 ± 1.9	91.3 ± 1.9	91.6 ± 1.8	91.3 ± 1.9	82.7 ± 3.8
	MCI vs. AD	97.1 ± 2.4	86.3 ± 2.9	91.7 ± 2.3	91.7 ± 2.3	92.2 ± 2.1	91.7 ± 2.3	83.5 ± 4.6
FOR	NC vs. MCI	94.9 ± 1.1	93.3 ± 1.9	94.1 ± 1.2	94.1 ± 1.2	94.1 ± 1.1	94.1 ± 1.2	88.2 ± 2.3
	NC vs. AD	89.8 ± 1.0	91.2 ± 1.0	90.5 ± 0.7	90.5 ± 0.7	90.4 ± 0.7	90.5 ± 0.7	81.0 ± 1.4
	MCI vs. AD	79.0 ± 3.7	83.1 ± 2.2	81.0 ± 2.3	81.0 ± 2.3	80.6 ± 2.6	81.0 ± 2.3	62.0 ± 4.6
MOR+FOR	NC vs. MCI	97.6 ± 0.9	96.1 ± 1.8	96.8 ± 1.0	96.8 ± 1.0	96.9 ± 1.0	96.8 ± 1.0	93.7 ± 2.0
	NC vs. AD	94.5 ± 1.0	92.9 ± 1.1	93.7 ± 0.9	93.7 ± 0.9	93.7 ± 0.9	93.7 ± 0.9	87.3 ± 1.9
	MCI vs. AD	81.8 ± 0.6	84.3 ± 2.7	83.1 ± 1.6	83.1 ± 1.6	82.9 ± 1.5	83.1 ± 1.6	66.1 ± 3.2

Note: The best results are marked in bold.

TABLE 3.

Comparison between this study and existing studies

	Paper	Subjects	Accuracy	Model	Features
NC vs. MCI	(Suk & Shen, 2013)	52/99	85 ± 1.2	10‐fold SVM	Stacked auto‐encoder
	(Jie et al., 2013)	25/12	91.9	LOO SVM	Local clustering coefficients
	(Suk et al., 2014)	101/204	85.7 ± 5.2	10‐fold SVM	Patch‐level feature learning
	(Chen et al., 2016)	30/29	88	LOO SVM	Low and high‐order FC networks
	(Wang et al., 2016)	101/202	78.1	10‐fold pGTL	Multi‐modal image features
	(Xu et al., 2016)	117/110	76.7	10‐fold grid search	Multi‐modal and single‐modality
	(Li et al., 2017)	117/110	82.8	10‐fold SVM	Modalities from sMRI FDG‐PET, florbetapir‐PET
	(Qiu et al., 2018)	303/83	83.3 ± 4.1	5‐fold majority vote	MMSE scores, logical memory
	(Shi et al., 2019)	52/99	80.7	10‐fold SVM	Leveraging coupled interactions
	(Gupta et al., 2019)	196/356	86.4 ± 3.4	5‐layer DNN	FC between ROIs
	(Ghanbari et al., 2020)	565/653	90 ± 2	10‐fold Decision Tree	2‐connected/minimal connected
	This study	49/49	96.8 ± 1.0	10‐fold SVM	MOR+FOR‐concatenate
NC vs. AD	(Suk & Shen, 2013)	52/51	95.9 ± 1.1	10‐fold SVM	Stacked auto‐encoder
	(Suk et al., 2014)	101/93	95.3 ± 5.2	10‐fold SVM	Patch‐level feature learning
	(Wang et al., 2016)	101/99	92.6	10‐fold pGTL	Multi‐modal image features
	(Li et al., 2017)	117/113	98.5	10‐fold SVM	Modalities from sMRI FDG‐PET, florbetapir‐PET
	(Shi et al., 2019)	52/51	94.9	10‐fold SVM	Leveraging coupled interactions
	(Gupta et al., 2019)	196/103	92.0 ± 4.3	5‐layer DNN	FC between ROIs
	This study	49/49	93.7 ± 0.9	10‐fold SVM	MOR+FOR‐concatenate
MCI vs. AD	(Li et al., 2017)	110/113	74.4	5‐fold MKSCDDL	Modalities from sMRI FDG‐PET, florbetapir‐PET
	(Lin et al., 2018)	401/188	81.4	LOO ELM	Deep learning from CNN
	(Gupta et al., 2019)	356/103	92.4 ± 3.2	5‐layer DNN	FC between ROIs
	This study	49/49	91.7 ± 2.3	10‐fold SVM	MOR‐concatenate

Abbreviations: CNN, Convolutional Neural networks; ELM, Extreme Learning Machine; LOO, Leave One Out; MKSCDDL, Multi‐feature Kernel Supervised within‐class‐similar Discriminative Dictionary Learning; DNN, Deep Neural Network; pGTL, progressive Graph‐based Transductive Learning; SVM, Support Vector Machine.

FIGURE 9.

Selected redundancy features for NC‐MCI, NC‐AD, and MCI‐AD classification.

The classification results for each density level are reported in Supplementary Tables S12–S14. The best result is given by MOR+FOR features. The highest classification accuracies for NC‐MCI, NC‐AD, and MCI‐AD are 96.4 ± 0.7%, 93.4 ± 1.8%, and 89.7 ± 2.8%, respectively. The selected features are detailed in Supplementary Table S15. NC‐MCI classification using our redundancy features yields the highest accuracy compared with previous studies (Gupta et al., 2019; Jie et al., 2013; Li et al., 2017; Shi et al., 2019; Suk et al., 2014; Suk & Shen, 2013; Wang et al., 2016).

4. DISCUSSION

AD is associated with the accrual of amyloid $\beta$ ‐ plaques and neurofibrillary tau‐tangles (Aisen et al., 2010), which disrupts neural communication and cause adverse functional and structural changes leading to neurodegeneration and cognitive decline (Jack et al., 2013; Nelson et al., 2012). Although MCI is present in a noticeable percentage of individuals over 65 years of age, with probable conversion to AD (Petersen et al., 1999), a high percentage of older adults present normal cognitive function (Jack et al., 2013). Neuroprotective mechanisms might be instrumental in helping a brain in early neurodegeneration to maintain normal cognitive function. In our study, we hypothesized that neuroprotective mechanisms are reflected by network redundancy.

Redundancy, in the form of alternate connections, supports functional adaptation by mitigating the effects of aging on cognitive abilities (Arkadir et al., 2014; Rossini, 2000; Sadiq et al., 2021). Researchers have shown that redundancy is more correlated with age than metrics such as clustering coefficient, average weighted degree, and system segregation (Sadiq et al., 2021). Based on our redundancy definition, we found elevated functional redundancy in MCI, significant even at its onset. Consistent with previous findings on the benefits of redundancy in biological systems (Nguyen et al., 2019; Pitkow & Angelaki, 2017), we observed evidence that redundant connections serve as a neuroprotective mechanism in subjects with early signs of AD. Specifically, we found that redundant connections accrue with MCI to compensate for connection loss due to synaptic disruption (Sadiq et al., 2021) and to maintain cognitive ability in the presence of neurodegeneration (Barulli & Stern, 2013; Cabeza et al., 2018; Liang et al., 2011; Papoutsi et al., 2014; Scheller et al., 2014). A recent study revealed that functional redundancy accrues throughout the lifespan and mitigates the effects of age on cognition (Sadiq et al., 2021). In the same vein, we showed that functional redundancy increases to mitigate the effects of pathology on cognition. We also found that nodal redundancy increases in the MF, FP, and, DM networks. This finding is consistent with previous studies indicating regions with increased connectivity maintain normal behavior despite neuronal loss (Barulli & Stern, 2013; Cabeza et al., 2018; Papoutsi et al., 2014; Scheller et al., 2014). Aging individuals with more reserve in the form of redundant connections are likely to exhibit better cognitive outcomes.

In this study, we observed that redundant connections might come into play during pathological network disruption. Redundancy is associated with brain reserve that mitigates the effects of age‐associated neural decline (Barulli & Stern, 2013). In general, redundancy increases in MCI, particularly in its early stage, and may act as a compensatory response to the accumulation of pathology to benefit cognition. This is in line with the observation that cognitive demands are affected by reserve, maintenance, and compensation mechanisms (Cabeza et al., 2018). We showed that significant elevation in redundancy can be detected even at the early stage of MCI. The tendency of redundancy increases from NC individuals to MCI individuals and decreases slightly to AD individuals. An increase in redundancy might be a compensatory response to the accumulation of early pathology. Redundant connections may be further impaired with disease progression.

We found that three high‐order MF, FP, and DM functional networks reserve redundant connections in the early onset of MCI to support cognitive function in the event of network disruption. We observed that the nodal redundancy of more than 50% of nodes in the MF, FP, and DM networks significantly increases in MCI individuals compared with NC individuals. Interestingly, most ROIs with significant increases in nodal redundancy in MCI are related to memory performance. We further observed that the tendency of redundancy of both the whole‐brain network and the medial frontal network are significantly associated with MMSE in AD progression. Specifically, consistent with the main findings of this study, the highest tendency of redundancy was observed for individuals with an average MMSE of 24, corresponding to MCI individuals.

We further demonstrated that redundancy features are sensitive to AD pathology and are effective for computer‐aided diagnosis. MCI individuals have an AD conversion rate of 10–15% (Petersen et al., 1999) and reversion‐to‐normal rate of more than 50% (Shimada et al., 2019). Reliably differentiating MCI from NC individuals is critical for timely intervention. To the best of our knowledge, prior to our study, the highest MCI‐NC classification accuracy was 91.9% (Jie et al., 2013), characteristically lower than NC‐AD classification (Gupta et al., 2019; Li et al., 2017; Shi et al., 2019; Suk et al., 2014; Suk & Shen, 2013; Wang et al., 2016). Our redundancy features are sensitive to MCI‐related changes, leading to a substantially higher MCI‐NC classification accuracy of 96.8%. Moreover, several studies showed that metrics such as local and global efficiency exhibit significant changes in AD compared with NC individuals (Buldú et al., 2011; Ewers et al., 2021; Kim et al., 2015; Phillips et al., 2015; Tewarie et al., 2015; Yao et al., 2010), but less so in MCI compared with NC individuals. Our redundancy metric is sensitive to changes in MCI.

Brain network redundancy might cope with disturbances associated with aging or diseases. For example, it has been conjectured that redundant brain mass promotes the recovery of brain function in adults with hydrocephalus (Smith & Kemler, 1977). In AD progression, cognitive decline is the most common symptom from the onset of the disease (Musicco et al., 2009). Redundancy is related to the brain's reserve capacity to withstand perturbation and to reduce the effects of aging on cognition (Cabeza et al., 2018). Neural reserve widens the gap between the extent of brain damage and its outward clinical and cognitive presentations (Cabeza et al., 2018; Montine et al., 2019). In the current study, we demonstrated that redundancy acts as a potential marker of the reserve of neural resources that accrues in MCI to allow the brain to be more resilient to damage. Thus, network redundancy may be an integral component of cognitive reserve, an active neural progress that contributes to the adaptability and efficiency of cognitive function in face of brain aging or pathology (Stern et al., 2020). Indeed, cognitive reserve is believed to be supported by more adaptable functional brain processes, which can be substantiated by superfluous functional connections under disease disturbances. Importantly, cognitive reserve is not fixed but individually shaped by factors such as intelligence, education, occupation, and physical activities (Stern et al., 2020). Thus, individual differences in network redundancy may also be attributable to distinct life experiences, which determine how well a person copes with brain changes or damages. It should be noted that cognitive reserve, an active form of reserve, is conceptually different from brain reserve, a more passive form of reserve based on the neurobiological substrate or capital such as the number of neurons and synapses (Stern et al., 2020). As cognitive reserve depends on brain reserve, functional network redundancy likely relies on structural brain connectivity.

Our redundancy metric can be employed to characterize network attack tolerance in preserving topological integrity (Rubinov & Sporns, 2010). Attack tolerance is typically quantified by removing nodes based on their degrees (Albert & Barabási, 2002). A study reported that Parkinson's disease patients exhibit significantly reduced attack tolerance compared with healthy subjects (Cascone et al., 2021). Based on our metric, a network with at least $k$ redundant connections between every two nodes can tolerate $k-1$ attacks to preserve network connectivity. Unlike previous studies that measure the attack tolerance of a network by intentionally removing nodes with high degrees (Joyce et al., 2013), our redundancy metric allows network attack tolerance to be measured via the removal of random nodes.

Our study has several limitations. First, we only considered whether independent connections exist between nodes. A possible extension is to characterize the degree of redundancy based on the number of independent connections between nodes. For example, we can define a network as $k$ ‐ redundant if there are $k$ nonoverlapping connections between every pair of nodes ($k\ge 3$). Second, our analysis was performed based only on binary graphs. Generalization to weighted graphs can expand the utility of our redundancy metric. Lastly, subject grouping was based on clinical outcomes (i.e., MMSE scores) rather than biomarker measurements (e.g., amyloid beta levels). Inclusion of the latter can potentially improve diagnostic accuracy.

5. CONCLUSION

We demonstrated the utility of our redundancy metric in differentiating the stages of AD progression. We reported a pattern of accrual of redundant connections in MCI to counter AD pathology. Our results provide evidence supporting redundancy as a neuroprotective mechanism in cognitive aging. By taking advantage of the high sensitivity of our metric, we showed that MCI individuals can be detected with high accuracy.

AUTHOR CONTRIBUTIONS

Maryam Ghanbari performed the research, analyzed the data, interpreted the results, and drafted and revised the manuscript. Guoshi Li analyzed the data and revised the manuscript. Li‐Ming Hsu analyzed the data. Pew‐Thian Yap conceptualized and designed the study, interpreted the results, and revised the manuscript. All authors read and approved the final manuscript.

FUNDING INFORMATION

This work was supported in part by the United States National Institutes of Health (NIH) under grants EB008374, MH125479, and EB006733.

CONFLICT OF INTEREST STATEMENT

The authors declare that they have no competing financial interests.

Supporting information

Data S1: Supporting Information

Ghanbari, M. , Li, G. , Hsu, L.‐M. , & Yap, P.‐T. (2023). Accumulation of network redundancy marks the early stage of Alzheimer's disease. Human Brain Mapping, 44(8), 2993–3006. 10.1002/hbm.26257

DATA AVAILABILITY STATEMENT

Data used from ADNI is publicly available from http://adni.loni.usc.edu/.