State-switching and high-order spatiotemporal organization of dynamic functional connectivity are disrupted by Alzheimer's disease

Abstract

Spontaneous activity during the resting state, tracked by BOLD fMRI imaging, or shortly rsfMRI, gives rise to brain-wide dynamic patterns of interregional correlations, whose structured flexibility relates to cognitive performance. Here, we analyze resting-state dynamic functional connectivity (dFC) in a cohort of older adults, including amnesic mild cognitive impairment (aMCI, N = 34) and Alzheimer's disease (AD, N = 13) patients, as well as normal control (NC, N = 16) and cognitively "supernormal" controls (SNC, N = 10) subjects. Using complementary state-based and state-free approaches, we find that resting-state fluctuations of different functional links are not independent but are constrained by high-order correlations between triplets or quadruplets of functionally connected regions. When contrasting patients with healthy subjects, we find that dFC between cingulate and other limbic regions is increasingly bursty and intermittent when ranking the four groups from SNC to NC, aMCI and AD. Furthermore, regions affected at early stages of AD pathology are less involved in higher order interactions in patient than in control groups, while pairwise interactions are not significantly reduced. Our analyses thus suggest that the spatiotemporal complexity of dFC organization is precociously degraded in AD and provides a richer window into the underlying neurobiology than time-averaged FC connections.

Keywords: Alzheimer’s disease; Dynamic functional connectivity; High-order Interactions; Mild cognitive impairment; Resting state; fMRI.

Figure 1.

Overview of approaches. (A) Subjects were stratified in four different clinical groups: supernormal controls (SNC), normal controls (NC), amnesic MCI (aMCI), and Alzheimer’s disease (AD). (B) We used two dynamic functional connectivity (dFC) methods to study the spatiotemporal properties of resting-state fMRI signals: a state-based dFC called point-based method (PBM) and a state-free dFC method called meta-connectivity (MC) approach. Both approaches address the dynamics of pairwise links of interactions, which we call here “dimers.” (C) The study of coordinated fluctuations of dimers is at the core of the MC approach. Coordination can occur between dimers converging on a common root (“trimers”) or between nonincident dimers (“tetramers”). (D) We focused on a limbic subnetwork based on the AAL parcellation that was divided into two zones: a ventrally located Zone I that included the temporal pole (superior and medial), parahippocampal gyrus, hippocampus proper, and amygdala; and a dorsally located Zone II included the anterior, medial, and posterior cingulate cortices.

Figure 2.

State-based dynamic functional connectivity (dFC) analyses: four dFC states. (A) BOLD time series of all subjects were concatenated temporally and then z-scored and clustered based on BOLD activation to extract four states. The associated FC-state matrices (FC^(λ), λ = 1 … 4) were constructed by evaluation BOLD fluctuation correlations limited to time points within a given state (cf. also Figure S1A). The centroids of activation of four states (middle) distinguished two subsets of regions (Zone I and Zone II), where their activity was transiently higher or lower than average. States 1 and 2 (or 3 and 4) showed above (or below) average level activation for Zones II and I, respectively, therefore were labeled as high (or low) activation states. We referred to States 2 and 4 as high synchronization states because the FC connection weights within Zone I tended to be stronger than States 1 and 3 (low synchronization; average within zone I FC weights = 0.23 ± 0.16 for States 1 and 3 vs. = 0.29 ± 0.18 for States 2 and 4). (B) Global and local efficiency as a measure of robustness in the communication pathways can be established between regions and was applied on the FC states. States 1 and 3 with low synchronization showed higher global and lower local efficiency compared to high synchronization States 2 and 4. (C) States with low synchronization showed decrease in mean dwell time across clinical groups (∼3.6 TR = 7.4 s, for SNC; ∼2.8 TR = 5.7 s, for AD), where the decrease of State 1 was significant (blue; p value ∼ 0.032; Mann-Whitney U test). States 2 and 4 showed a slight increase from the control groups to the patient groups. A decrease in average dwell time of states with relatively higher global efficiency indicates that they are less stable. (D) Analogously, the relative fraction of time spent in states with low synchronization was decreased in aMCI and AD compared to NC. Note the increase from SNC to AD groups for states with high synchronization.

Figure 3.

State-based dFC analyses: increase of intermittency in interzone links. (A) To construct the state-based dFC temporal network, a specific FC^(λ) graph was assigned to each BOLD signal intensity time point (we show here 416 time points = 20 min of rsfMRI acquisition, for two concatenated subjects). Consequently, there is a time course for every FC link where they can assume up to four possible different strength values (link dynamics due to state switching). (B) The temporal organization of link fluctuations can be assessed by determining intervals of link activation and inactivation (via a thresholding of dynamic strengths with a global threshold θ on all the links). The threshold θ ranges from 1 to 10% of the maximum strength over the dataset. The figure shows binarization for a representative dFC dimer. (C) The degree of temporal regularity in link activation/deactivation was assessed by quantifying the burstiness coefficient β, the mean activation time μ and the total activation time τ for every link and subject. The burstiness coefficient is bounded in the range −1 ≤ β ≤ 1 where it approaches to −1 if the link is tonic/periodic (blue lines), or it can approach to 0 if it has Poissonian (random-like) patterns of activation (red lines); β = +1 corresponds to links with bursty-like events of activation. (D) Distributions of β, μ, and τ for the NC group, later used as reference. Upper and lower rows represent distributions over, respectively, intrazone and interzone links (for an intermediate threshold, 0.0087 < θ < 0.0870). Left: distribution of burstiness coefficients across different thresholds averaged over two subsets of intra- and interzone links. The β of intrazone dimers approach to −1 and have more tonic/periodic patterns of activation (β = −0.890 ± 0.027, median ± MAD), while the β interzone are closer to 0 and show more Poisson-like intermittency (β = −0.229 ± 0.020, median ± MAD). Middle: the mean duration μ which is bounded to the length of time series for one subject (208 time points), for the intrazone links was longer than interzone links. Right: Analogously, the normalized total activation time (τ) of intrazone links were longer than interzone links. (E) Mean values for the NC group were used as reference and percent relative variations were computed for the other SNC, aMCI, and AD groups, combining relative values for different thresholds (see Materials and Methods). Upper and lower rows refer to intra- and interzone links. Left: notice the large burstiness increase across groups for the interzone links (∼1.8% for aMCI and ∼9% for AD; green stars, p < 0.001; Mann-Whitney U test) compared to a slight increase in the burstiness values of intrazone links (∼0.5%). In contrast, SNCs showed a significant decrease of ∼−6.5% relative to NC group in the interzone links. Comparisons between SNC, aMCI, and AD for both intra- and interzone links were all significant (black stars). Middle: the mean activation durations of interzone links showed a relative negative decrease of roughly −1% for aMCI and AD subjects. Right: total activation time τ was reduced to roughly −2% in aMCI and AD compared to NCs. Thus, temporal dynamics of dFC dimers are more tonic/periodic in SNCs than NCs and more intermittent in aMCI and AD subjects, particularly for interzone dimers.

Figure 4.

State-free dFC: meta-connectivity. (A) We slid a window of length ω = 5 TRs (10 s) with no overlap on the BOLD signals from the n considered regions. We then computed n × n FC matrices for each window using Pearson’s correlation between pair of regions. In this way each of the l possible pairwise links of FC becomes associated to a continuous time series of varying FC strength. Correlations between these link time series can be compiled in a l × l meta-connectivity (MC) matrix. We represent here trimer and tetramers with a spring between the involved dimers, as, in presence of meta-connectivity, pairwise links are not free to fluctuate independently. (B) Group average MC matrices for the four clinical groups. Louvain algorithm was applied on the MC matrices resulting in five modules. (C) A graph representation of the MC for the NC group, together with a chord diagram of FC for the same group. Each node in the MC graph corresponds to a link in the FC graph. The different MC graph modules correspond thus to different types of links: MC modules 1, 2, and 3 include interzone links incident, respectively, to medial, anterior, and posterior cingulate cortices (edges within these modules are thus interzone trimers rooted in Zone II); MC module 4 and 5 include links, respectively, within zones II and I. (D) Modules are also connected between them. The relative amount of intermodule meta-links is captured by the global participation coefficient (averaged over the five modules) which showed a significant decrease across the clinical groups (Mann-Whitney U test, p < 0.001).

Figure 5.

State-free dFC: Interrelations between dFC trimers and FC dimers. We studied whether regions with a large FC strength (“FC hubs,” i.e., they are the center of a star of links strong on average) also have a large trimer strength (MC “meta-hubs,” i.e., they are the center of a star of links whose fluctuations are temporally correlated). (A) To do so we computed the correlation between dimer and FC strengths, for both within- and between-zone trimers and dimers. As shown by the scatter plots, these correlations were low, both at the global (light green cloud) and at the single clinical group (colored solid lines; green: SNC; yellow: NC; orange: aMCI; red: AD) levels. Within each group, they were furthermore moderately negative. Therefore, FC hubness and MC meta-hubness tend to be slightly anticorrelated. (B) Trimers were divided into three groups dependent on the location of their roots and leaves. We considered genuine a trimer such that the MC between the two dimers composing the trimer is stronger than the FC between the trimer leaves. The violin plots at the right show fractions of genuine trimers (for all trimers and subjects) as a function of the trimer type. For all types, there were substantial fractions of genuine trimers (i.e., higher order interactions not fully explained by the underlying dimer interactions arrangement). See Figure S3 for analogous analyses on tetramers.

Figure 6.

State-free dFC: strengths of interzone FC dimers, trimers, and tetramers across clinical groups. (A) Average strength of interzone FC dimers decreased from SNC to AD both globally (left) and locally at the level of individual regions (right). At the global level, significant differences were found between the SNC and AD groups (p = 0.005, Mann-Whitney U test, Bonferroni correction). Locally the decrease was significant in anterior and posterior cingulate gyrus, bilaterally (Mann-Whitney U test, Bonferroni correction). (B) Interzone trimer strengths, similarly to FC dimers, showed a reduction trend across the groups, both globally (left) and locally (right). At the regional level the reductions in dFC trimers were widespread among regions, including early-affected regions without noticeable FC strength variations across clinical groups, with an interesting tendency toward negative trimer strengths in the AD group, associated to developing “frustration” of higher order interactions in a statistical mechanics sense (and, correspondingly, increased dynamical disorder and conflict; see Discussion). Finally, (C and D) tetramers strength showed a significant drop from SNC to AD groups in both brain-wide averaged intrazone (C) and interzone (D) subsets. See Figure S4 for intrazone dimer and trimer strengths, not showing significant variations across groups.