Transient resting-state network dynamics in cognitive ageing

It is important to maintain cognitive function in old age, yet the neural substrates that support successful cognitive ageing remain unclear. One factor that might be crucial, but has been overlooked due to limitations of previous data and methods, is the ability of brain networks to flexibly reorganise and coordinate over a millisecond time-scale. Magnetoencephalography (MEG) provides such temporal resolution, and can be combined with Hidden Markov Models (HMMs) to characterise transient neural states. We applied HMMs to resting-state MEG data from a large cohort (N=594) of population-based adults (aged 18-88), who also completed a range of cognitive tasks. Using multivariate analysis of neural and cognitive profiles, we found that decreased occurrence of “lower-order” brain networks, coupled with increased occurrence of “higher-order” networks, was associated with both increasing age and impaired fluid intelligence. These results favour theories of age-related reductions in neural efficiency over current theories of age-related functional compensation.


Main
With the increasing proportion of older adults in the worldwide population 1 , there is a pressing need to understand the neurobiology of cognitive ageing. Normal ageing generally results in cognitive decline 2 , though not all cognitive functions follow the same trajectory. In particular, whereas age produces a marked impairment in fluid intelligence (the ability to solve new problems), crystallised intelligence (the ability to rely on acquired knowledge) shows more modest age-related changes [3][4][5][6][7] .
Moreover, functional neuroimaging has revealed that ageing is associated with changes in connectivity between brain regions, both within and between large-scale networks 8 . One factor that might play a crucial role in the ability to maintain cognition in old age, but which has been largely overlooked, is the ability of brain networks to flexibly reorganize and coordinate on a sub-second timescale. Indeed, the relationship between cognition and such transient brain connectivity, and how this relationship differs with age, remains unknown.
In recent decades, functional connectivity within the human brain has been measured mainly with functional magnetic resonance imaging (fMRI). In particular, differences in the brain's connectivity during the resting-state (rsfMRI) have proved effective in distinguishing various patient groups from controls (e.g., Alzheimer disease, major depression, schizophrenia; see for example 9 ). Substantial work has also used rsfMRI to examine age-related changes in functional connectivity [10][11][12][13][14][15] .
However interpreting such connectivity changes measured with fMRI is difficult owing to methodological challenges, such as confounding factors like vascular reactivity and head motion, which also change with age [16][17][18][19] . While some of these confounds, like neurovascular coupling, can be addressed by more sophisticated modelling 20 , the fact remains that fMRI has a fundamentally limited temporal resolution (owing to the sluggish vascular response and relatively slow image acquisition times), which precludes it from disclosing the potentially richer dynamics in brain connectivity above approximately 0.1 Hz.
An alternative, non-invasive way of measuring functional connectivity is offered by magnetoencephalography (MEG), which can sample neural activity at 1kHz and higher (at the cost of worse spatial resolution). Indeed, recent advances in analytical approaches offer the ability to measure dynamic functional connectivity, i.e., "microstates" of stable connectivity patterns that last a few hundred milliseconds 21 , well beyond the temporal resolution of fMRI. Importantly, MEG is less sensitive than fMRI to age-related changes in vascular factors and head motion. In the current study, we utilized these advantages of MEG to relate transient resting-state dynamics to cognitive ageing.
More specifically, we exploited a large resting-state MEG (rsMEG) dataset obtained from 594, population-based individuals sampled uniformly across the adult-lifespan (18 to 88 years of age) as part of the Cam-CAN project (www.cam-can.org). In addition to the rsMEG scan, these individuals also completed a wide range of cognitive tasks. We characterised transient network dynamics using the recent application of Hidden Markov Models (HMMs) in order to explore the temporal dynamics of rsMEG networks [21][22][23][24][25][26] . An HMM is a data-driven method that identifies a sequence of "states", where each state corresponds to a unique pattern of brain covariance that reoccurs at different points in time. By quantifying the time-series of MEG data as a sequence of transient states, the HMM provides information about the periods of time at which each state is active, enabling the characterisation of its temporal dynamics. While this technique has identified network dynamics in small resting-state or task MEG datasets 21,23,24 , these dynamics have not yet been linked to age and cognition. In particular, the size of the Cam-CAN cohort allowed us to take a multivariate approach, namely to use canonical correlation analysis (CCA) to relate the temporal properties of the data-driven HMM states to profiles of cognitive performance, and to test whether these relations differ with age.

Results
Results were obtained following the data pre-processing and analyses procedures summarised in Figure 1 below. The raw data can be obtained by applying for access through the Cam-CAN data portal (https://camcan.mrc-cbu.cam.ac.uk/). All code used in the paper will be available via an online repository. Figure 2 shows the spatial maps of the 8 networks (states) derived from combing the MEG data across all participants. The states include three distributed frontotemporoparietal networks (FTP1, FTP2, FTP3), a higher-order visual network (HOV), two early visual networks (EV1, EV2) and two sensorimotor networks (SM1, SM2). They are similar to those obtained from young adults in previous studies [21][22][23] .  Group averages for each measure in each state are shown in Figure 3. Overall, primary (visuo-motor) states had higher number of occurrences than higher-order states. The most commonly-occurring networks were sensorimotor network SM2 and early visual network EV1, which had the highest mean FO and NO. The network with the most prolonged visits (highest MLT) was the high-order visual network HOV. Conversely, the least common network, with lowest FO and NO and with greatest MIL, was frontotemporoparietal network FTP3. These findings largely agree with Hawkins et al. 23 and (to a lesser extent) with other previous studies 21,22 , though now based on a much larger sample with a much larger age range.
Temporal Characteristics of HMM States Our next step was to apply CCA to relate the 32 temporal characteristics of the HMM states (4 metrics for each of the 8 states) to age (such a multivariate analysis is important in the presence of multicollinearity, given the co-dependence between the 4 metrics of HMM state dynamics). One participant who had no visits to one of the states (HOV) was excluded from these analyses. Only a single CCA mode was possible (given the unidimensional age variable), which explained 28.6% of the combined variance (Rc = .53, p < .001). Once we established age effects on the pattern of occurrence of brain states, we asked how the pattern of the states' occurrence relates to cognition. To this end, we related the temporal characteristics of the states to the 13 cognitive measures (see Methods). 12 CCA modes showed a significant correlation coefficient (Bonferroni corrected p-value across 13 modes < .05). Nevertheless, given the relatively low squared canonical correlation (R²c) of most modes (see Supplementary Figure   1), only the first mode which accounted for a substantial portion of the combined variance (24%) was explored further (see Sherry & Henson 28 for a similar approach). Figure 4 presents the structure coefficients (rs) of the first CCA mode. For the cognitive data, the coefficients resembled the pattern associated with poor (low) fluid intelligence reported before 3 . Specifically, rs was negative for all the fluid intelligence tests except the multitasking (MltTs) and motor speed (MRSp) tests, where higher values of these response-time measures represent worse performance, and the proverbs (ProV) and Spot-the-Word (STW) tests, which measure crystallised intelligence instead. Importantly, the four "higher-order" states (FTPs and HOV) were positively related to this cognitive profile, i.e., greater occurrence of these states (as indicated by increased FO, MLT, NO and decreased MIL) was associated with lower fluid intelligence. Furthermore, this cognitive profile was associated with decreased activation of the two early visual states (EVs). The two sensorimotor states did not show strong relations to this cognitive profile.
Finally, we asked whether the relationship between the brain profile of HMM measures and the cognitive profile differed with age. For this moderation analysis, we constructed a multiple linear regression model that included participants' scores for the HMM profile, their age and their interaction (HMM profile × age) as predictors, and participants' scores for the cognitive profile as the dependent variable. The HMM scores were significantly associated with cognitive scores after accounting for the main effect of age (β = .13, t(590) = 4.51, p < .001), demonstrating that the above brain-cognitive relationship was not driven solely by age effects. Moreover, the interaction between age and HMM profile was also significant (β = .11, t(590) = 4.33, p < .001), demonstrating that the brain-cognition relationship was moderated by age in a positive sense, i.e., becoming more positive with age. To visualise this moderation effect, the brain-cognition relation was repeated for six equallysized age groups (n=99 for each group; 18-34 years old; 34-45 years old; 45-55 years old; 55-66 years old; 66-76 years old; 76-88 years old). As shown in Figure 4, the brain-cognition relationship was stronger in the older groups.

Discussion
Our results show that transient neural dynamics, particularly those of high-order and earlyvisual states, differ across the healthy adult lifespan, with an increasing importance for cognitive function in older than younger adults. Importantly, by using a novel data-driven method to infer brain states from MEG data, we were able to overcome some of the limitations of the more common use of fMRI to examine ageing and cognition, such as confounding effects of vascular health, head motion and the ability to examine only very slow dynamics owing to low-frequency fluctuations of the fMRI response. More specifically, our finding that age and impaired fluid intelligence are associated with increased occurrence of brain states involving "higher-order" networks (such as those straddling frontal, temporal and parietal cortex) are less consistent with theories of functional compensation in ageing, and more consistent with theories of reduced neural efficiency in ageing, as we expand below.
We used multivariate analysis (CCA) to relate the pattern of brain dynamics (HMM profile) to age and to cognition, and to examine whether the brain-cognition relationship was moderated by age.
This first analysis relating brain dynamics to age showed that the occurrence (e.g., frequency and duration) of states involving frontotemporoparietal and higher-order visual regions increase with age, whereas the occurrence of states involving early-visual regions decrease with age. The second analysis relating brain dynamics to cognitive performance revealed that a similar profile of increased occurrence of higher-order states and reduced occurrence of early-visual states is associated with a pattern of poorer performance on tests of fluid intelligence, but not tests of crystallised intelligence.
Importantly, our final moderation analysis showed that this relationship between brain and cognitive profiles is not simply a result of shared influences of age (since age was included as a covariate).
Moreover, this moderation analysis showed that the brain-cognitive relationship gets stronger with increased age, such that reduced cognitive performance in older participants is more strongly associated with the shift from early visual to higher-order networks than in younger participants.
To our knowledge, this is the first study to report a resting state shift from lower to higherorder networks that is linked to both age and cognition. This finding nevertheless shares some similarity with previous fMRI findings. For example, Davis et al. 29 summarised a pattern across a number of fMRI experiments (first observed by Grady et al. 30 ) in which older adults show increased activity in anterior (e.g., frontal) brain regions, and decreased activity in posterior (e.g., visual) brain regions, and called this the "Posterior-to-Anterior Shift with Ageing" (PASA). Furthermore, it has been hypothesised that one reason for this shift is "functional compensation", whereby older people activate frontal regions to compensate for age-related impairments in posterior brain regions, that is, in order to maintain levels of cognitive performance 29,31,32 . However, this pattern and interpretation are based on activations during task-based fMRI, i.e., while participants are performing a cognitive task, rather than the current resting state. Moreover, more recent fMRI studies have questioned whether PASA reflects functional compensation, and suggest instead that the increased frontal activation reflects reduced neural efficiency or specificity [33][34][35][36][37][38] . The difference between these two interpretations of the PASA finding is that, whereas the functional compensation hypothesis predicts that anterior increases correlate with better cognitive performance, the inefficiency hypothesis predicts the opposite pattern of anterior increases correlating with worse cognitive performance. Our findings support the latter account, i.e., that increased occurrence of higher-order states is associated with worse cognitive performance, specifically in measures of fluid intelligence and particularly in older adults. Importantly, unlike previous reports of the PASA pattern, the current shift was observed during rest, suggesting that it might reflect a stable property of the ageing brain.
The results of our moderation analysis resemble those obtained in a previous study 39 , which also showed that the relationship between brain connectivity and cognition increased with age, but using rsfMRI instead. In that case, the authors showed that the cognitive function of older adults becomes increasingly dependent on the balance of excitatory connectivity between networks, and the stability of intrinsic neural representations within networks. Importantly, they used biophysical modelling to account for the confounding effects of vascular health on the fMRI response. However, their results were still limited to static connectivity driven by the low-frequency fluctuations that are visible to fMRI, and to a small subset of three brain networks (owing to the complexity of the biophysical modelling). The current study overcomes these issues by utilising rsMEG to measure i) neural activity directly, rather than indirectly via a vascular response, ii) dynamic connectivity with much higher temporal resolution and iii) whole-brain networks (within the limits of MEG resolution).
One caveat of the current study is that we used cross-sectional data, which precludes direct inferences about ageing (as distinct from cohort effects, owing to year of birth). However, we are not aware of any longitudinal MEG data on such a large, representative population, and until such time, our results can be used to justify and inform hypotheses for future rsMEG studies of ageing. Furthermore, the HMM approach comes with some assumptions. For example, it relies on group concatenation that here assumes anatomical correspondence across the lifespan (though our use of relatively large ROIs minimizes this issue), it requires a priori specification of the number of states, and it uses a Gaussian observation model which may be an oversimplification of the underlying network dynamics 21 . Nevertheless, despite these limitations, our study offers novel insights on the relationship between the cognitive sequelae of ageing and the underlying patterns of functional brain dynamics, which may be used in the future for mechanistic justification and assessment of interventions to reduce the personal and societal burden of cognitive impairments in old age.  Table 1. Of these, only participants with full neuroimaging data (resting state MEG data and structural MRI data) were considered for the current study (n = 610). Fifteen additional participants were excluded from analyses due to poor MEG-MRI co-registration (details below). Thus, the final sample included 595 participants (299 women and 296 men, age range 18-88).

Cognitive Tasks
13 cognitive tasks, performed outside the scanner, were used to assess five broad cognitive domains, including executive functions, memory, language functions, processing speed, and emotional processing. The tasks are summarized in Table 2, and are fully detailed in Shafto et al 40 . Task data were obtained from Borgeest et al. 3 , in which missing data (<12% in all tasks) were interpolated using the Full Information Maximum Likelihood (FIML) method 44 in the Lavaan R package 45 to allow unbiased estimates, applied to the full Stage 2 sample (n = 708).

MEG data acquisition and pre-processing
Data were collected using a 306-channel

MEG source reconstruction, parcellation, and envelope calculation
The MEG data were co-registered to each participant's structural T1-weighted MRI, using three anatomical fiducial points (nasion, and left and right pre-auricular points) that were digitized for the MEG data and identified manually on the MRIs. The median distance between each scalp headshape point and its nearest vertex was calculated for each participant, and those with a median distance greater than 6 mm (n=15; see Participants section above) were excluded from subsequent analyses.
Source space activity was then estimated for each participant at every point of an 8 mm whole-brain grid using a single-shell lead-field model and a linearly constrained minimum variance (LCMV) scalar beamformer 47,48 , combining data from both magnetometers and gradiometers. Source-

Group level exploratory analysis of networks (Hidden Markov Model)
The HMM procedure assumes that the same set of microstates underpin the HMM-derived states across participants. Therefore, demeaned and normalized envelope data for each participant were concatenated temporally across all participants to produce a single dataset, using the grouplevel exploratory analysis of networks (GLEAN) toolbox (https://github.com/OHBA-analysis/GLEAN 25 ).
We set the analysis a-priori to derive 8 states from the data, based on previous work suggesting that this number represents a reasonable trade-off between a sufficiently rich but not overly complex representation 21 . HMMs describe the dynamics of brain activity as a sequence of transient events, each of which corresponds to a visit to a particular brain state. Each state describes the data as coming from a unique 38-dimensional multivariate normal distribution, defined by a covariance matrix and a mean vector. Therefore, each state corresponds to a unique pattern of amplitude envelope variance and covariance that reoccurs at different time points. The HMM state time-courses then define the points in time at which each state was "active" or "visited". We obtained these estimated state timecourses, represented by a binary sequence showing the points in time when that state was most probable, using the Viterbi algorithm 51 . We then partially correlated the time-courses onto wholebrain parcel-wise amplitude envelopes concatenated across subjects in order to produce spatial maps of the changes in amplitude envelope activity associated with each state. The resulting state maps show the brain areas whose amplitude envelopes increase or decrease together (covary) when that state is active, compared to what happens on average over time. Mean Interval Length (MIL): the average duration between recurring visits to that state.

Relating HMM states to age and cognition (Canonical Correlation Analyses)
To identify how the temporal characteristics of the HMM states relate to age and cognition, are maximized, resulting in CCA components, or "modes". This multivariate approach is useful when the observed variables within each set are correlated (as is the case for the above HMM temporal characteristics, and for the cognitive scores).
CCA was employed via canoncorr in Matlab. The number of modes produced by this analysis is always equal to the number of variables in the small dataset (though not all modes necessarily explain a substantial portion of the variance, see Results section above). In canoncorr's terminology (see also studies mentioned above [52][53][54], each CCA mode is associated with canonical "coefficients" across the variables in each set and "scores" across the observations (participants). This correlation between the participant scores of each set (for a given mode) is termed the "canonical correlation" (denoted by Rc), and its squared value (R²c) represents the proportion of variance shared between the variable sets. The correlation between the participant scores and each original variable (for a given set and given mode) is called the "structure coefficient" (denoted by rs), and the set of structure coefficients represents the "profile" of the CCA mode across those variables. Structure coefficients are often used to guide interpretation of multivariate analyses, and are particularly useful in the presence of multicollinearity 28 .
All variables were z-scored before subjected to CCA, in order to make the various parameters

Additional control analyses
We performed several additional analyses in order to ensure that the results are robust and interpretable. First, some of the temporal measures of the HMM states (and MIL in particular) included a relatively large number of outliers (see Figure 3). Therefore, in order to ascertain that the results are not biased by these outliers, we repeated the main CCA and moderation analyses after excluding 98 participants depicting outliers (SD>3, n=496) in one or more measures. Following this removal, the first CCA mode remained highly significant (Rc = .512, R²c = 26%, p < .001), and the pattern of structure correlations remained remarkably similar to that observed with the full sample (see Supplementary Figure 2). The results of the moderation analysis were also similar, with a significant association between HMM and cognitive profiles after accounting for the main effect of age (β = .16, t(492) = 5.18, p < .001), together with a significant interaction between age and HMM profile (β = .13, t(492) = 4.84, p < .001).
Moreover, in order to confirm the significance of Rc of the first CCA mode as determined by parametric assumptions, we also estimated Rc against a distribution of 10,000 correlation coefficients based on permuting across participants their canonical scores for the cognitive data. The canonical coefficient for the true data (Rc = .49) was greater than for any of the random permutations (equivalent to p < .0001, see Supplementary Figure 3). We also carried out a separate cross-validation analysis in which the CCA was only run on a subset of the data, and the outputs tested against the rest. In each of 10,000 iterations, we randomly chose 80% of the subjects for the "training" subset, leaving the other 20% for the "testing" subset. The canonical correlations across training sets for the first mode was similar to the original result (ranging between .45 and .56). For each iteration, we took the CCA HMM and cognition weight vectors for the first mode from the training subset, and multiplied them by the testing subset, in order to estimate participant scores for HMM and cognition. We then computed the correlation between these scores to estimate the canonical coefficient for the testing subset. Mean Rc was .32 (mean p = .007, see Supplementary Figure 3 for the full distribution).
Importantly, the canonical coefficient was significant at p < .05 for 96.7% of the testing subsets and at p < .001 for 63.7% of the testing subsets. Taken together, the results of these analyses confirm that the first CCA mode was highly significant.
Finally, we repeated the HMM-age CCA analysis with an additional quadratic term, in order to account for potential non-linear (quadratic) age-effects. We computed a quadratic age term, orthogonal to the linear age term, and ran a CCA analysis that relates the 4 HMM measures across all 8 states (Set 1, 32 variables) to both age terms (Set 2, 2 variables). Both possible CCA modes were significant (p < .001) and explained 28.6% and 12.3% of the shared variance, respectively. The structure coefficients (rs) are shown in Table 3 below. As apparent from the table, the first CCA mode captured the linear relations between the HMM measures and age, whereas the second CCA mode captured the quadratic relations. Importantly, we have observed an age-related shift from lower to higher-order states (captured by the first CCA mode), which was nearly identical to that observed in our initial analysis (which did not include the quadratic age term). This suggests that this neural profile remains stable even when accounting for non-linear age effects.

Code Availability Statement
All code used for the analyses reported in the manuscript is available for peer-review on OSF, and will be made publically available upon acceptance of the manuscript.

Author contribution
R.T: directed the project together with R.H; designed, planned, and carried out the analyses; wrote the paper with input from all authors. K.A.T: consulted on CCA analyses; provided input on the paper; D.P: consulted on pre-processing; provided input on the paper; D.N; provided input on results at early stages; provided input on the paper. R.H: directed the project together with R.T; commented on structure and analysis approach; provided input on the paper.