{"title": "Infra-slow brain dynamics as a marker for cognitive function and decline", "book": "Advances in Neural Information Processing Systems", "page_first": 6949, "page_last": 6960, "abstract": "Functional magnetic resonance imaging (fMRI) enables measuring human brain activity, in vivo. Yet, the fMRI hemodynamic response unfolds over very slow timescales (<0.1-1 Hz), orders of magnitude slower than millisecond timescales of neural spiking. It is unclear, therefore, if slow dynamics as measured with fMRI are relevant for cognitive function. We investigated this question with a novel application of Gaussian Process Factor Analysis (GPFA) and machine learning to fMRI data. We analyzed slowly sampled (1.4 Hz) fMRI data from 1000 healthy human participants (Human Connectome Project database), and applied GPFA to reduce dimensionality and extract smooth latent dynamics. GPFA dimensions with slow (<1 Hz) characteristic timescales identified, with high accuracy (>95%), the specific task that each subject was performing inside the fMRI scanner. Moreover, functional connectivity between slow GPFA latents accurately predicted inter-individual differences in behavioral scores across a range of cognitive tasks. Finally, infra-slow (<0.1 Hz) latent dynamics predicted CDR (Clinical Dementia Rating) scores of individual patients, and identified patients with mild cognitive impairment (MCI) who would progress to develop Alzheimer\u2019s dementia (AD). Slow and infra-slow brain dynamics may be relevant for understanding the neural basis of cognitive function, in health and disease.", "full_text": "Infra-slow brain dynamics as a marker for cognitive\n\nfunction and decline\n\nShagun Ajmera\n\nCentre for Neuroscience\nIndian Institute of Science\n\nBangalore\n\najmerashagun@gmail.com\n\nShreya Rajagopal\n\nCentre for Neuroscience\nIndian Institute of Science\n\nBangalore\n\nshreyakr96@gmail.com\n\nRazi Ur Rehman\n\nComputer Science and Automation\n\nIndian Institute of Science\n\nBangalore\n\nrazirmp@gmail.com\n\nDevarajan Sridharan\u2217\nCentre for Neuroscience &\n\nComputer Science and Automation\n\nIndian Institute of Science\n\nBangalore\n\nsridhar@iisc.ac.in\n\nAbstract\n\nFunctional magnetic resonance imaging (fMRI) enables measuring human brain\nactivity, in vivo. Yet, the fMRI hemodynamic response unfolds over very slow\ntimescales (<0.1-1 Hz), orders of magnitude slower than millisecond timescales of\nneural spiking. It is unclear, therefore, if slow dynamics as measured with fMRI\nare relevant for cognitive function. We investigated this question with a novel\napplication of Gaussian Process Factor Analysis (GPFA) and machine learning to\nfMRI data. We analyzed slowly sampled (1.4 Hz) fMRI data from 1000 healthy\nhuman participants (Human Connectome Project database), and applied GPFA to\nreduce dimensionality and extract smooth latent dynamics. GPFA dimensions with\nslow (<1 Hz) characteristic timescales identi\ufb01ed, with high accuracy (>95%), the\nspeci\ufb01c task that each subject was performing inside the fMRI scanner. Moreover,\nfunctional connectivity between slow GPFA latents accurately predicted inter-\nindividual differences in behavioral scores across a range of cognitive tasks. Finally,\ninfra-slow (<0.1 Hz) latent dynamics predicted CDR (Clinical Dementia Rating)\nscores of individual patients, and identi\ufb01ed patients with mild cognitive impairment\n(MCI) who would progress to develop Alzheimer\u2019s dementia (AD). Slow and\ninfra-slow brain dynamics may be relevant for understanding the neural basis of\ncognitive function, in health and disease.\n\nIntroduction\n\n1\nFunctional magnetic resonance imaging (fMRI) is among the few techniques that enable non-invasive\nmeasurement of activity in the living human brain (in vivo) [1]. Although state-of-the-art fMRI scans\ncan measure activity at high (sub-millimeter) spatial resolution, the fMRI blood-oxygenation level\ndependent (BOLD) hemodynamic response occurs over very slow timescales of several seconds (~0.1\nHz), and is typically sampled at a rate of around 1 Hz or less [2] \u2013 orders of magnitude slower than\nthe millisecond timescales of underlying neural activity (>100 Hz). Moreover, fMRI measurements\nare noisy: sources of noise include scanner noise, head movement artifacts and physiological artifacts\nthat systematically confound the fMRI signal [3]. Thus, fMRI BOLD activity re\ufb02ects an indirect,\nnoisy measure of neural activity, mismatched to neural timescales by several orders of magnitude.\nPrevious studies have linked the BOLD response to underlying neurophysiological signals at various\n\n\u2217Corresponding author\n\n33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada.\n\n\ftimescales [4\u20136], and have shown that fMRI data can be used to directly measure slow (<1 Hz) and\ninfra-slow (<0.1 Hz) \ufb02uctuations in brain activity [7\u201310].\nHere, we examined whether slow and infra-slow dynamics, as measured with slowly sampled fMRI\ndata, are relevant for cognitive function, employing a novel combination of denoising, dimensionality\nreduction and machine learning. We applied Gaussian Process Factor Analysis (GPFA) \u2013 a recent\ntechnique for concurrent smoothing and dimensionality reduction of noisy data [11] \u2013 to fMRI signals\nsampled at ~0.3-1.4 Hz (scanner repetition time, TR of 0.72-3.3 s). GPFA enables the discovery\nof hidden (latent) dimensions in the data [11], with each latent dimension comprising a collection\nof channels that exhibit shared variance in their activity at a speci\ufb01c timescale. In our case, this\napproach enabled us to identify functionally connected networks of brain regions, whose dynamics\nevolve at diverse, characteristic timescales.\nWe also asked if slow \ufb02uctuations in fMRI latent dimensions discovered by GPFA would be suf-\n\ufb01ciently informative about task-speci\ufb01c cognitive states. While previous studies have examined\nslow, spontaneous dynamics in the resting state (e.g. [12]), we examined these dynamics with GPFA\napplied to both task-based and resting state fMRI scans, from 1000 healthy human participants\ndrawn from the human connectome project (HCP) database [13]. These fMRI scans were acquired\nas subjects performed each of seven cognitive tasks \u2013 including tasks of working memory, story\ncomprehension, gambling, and the like (Supporting Information Table S2) \u2013 or in the resting state. We\ndiscovered that GPFA activity in latent dimensions with characteristic slow and infra-slow timescales\nwas remarkably synchronized across individuals\u2019 brains. Moreover, these slow GPFA dynamics could\nbe used to predict with high accuracies (typically over 95%), task-speci\ufb01c cognitive states. Finally,\napplying GPFA to resting state fMRI data from patients with mild cognitive impairment (MCI), we\nshow that infra-slow oscillations in these latent dimensions suf\ufb01ced to distinguish, signi\ufb01cantly above\nchance, MCI patients who later developed AD from those who did not. We propose that slow and\ninfra-slow fMRI dynamics may be relevant for a complete understanding of cognitive function, in\nhealth and in disease.\n\nIdentifying latent fMRI dimensions with slow, characteristic timescales\n\n2\nGPFA extracts smooth, low-dimensional latent trajectories from noisy, high-dimensional time series\n[11]. Brie\ufb02y, GPFA \ufb01rst performs dimensionality reduction with conventional factor analysis (FA) to\nidentify an initial set of latent dimensions. This is followed by learning key parameters that specify\nthe temporal autocorrelation of the latent dimensions (Fig. 1A). The parameters of the GPFA model\nare learned with an expectation-maximization algorithm. GPFA, therefore, provides a method for\nsimultaneously performing smoothing and dimensionality reduction on the fMRI data. As with\nFA, GPFA incorporates an explicit noise model, which in the case of fMRI data enables estimating\nindependent noise variances across different brain regions. Details regarding the model are described\nin [11] and in the Supporting Information (section 1).\nWe analyzed fMRI data from 1000 human participants (529 females, typical age range: 22-35 years,\n10 subjects of age >36 years) drawn from the Human Connectome Project (HCP) database (total\nof 8000 scans). These scans were acquired when subjects were performing one of seven tasks\n(Supporting Information Table S2) or were resting inside the scanner (resting state); scanning and\nacquisition protocols are described elsewhere [13]. We used minimally preprocessed scans available\nfrom the HCP database; such preprocessing minimizes noise due to extraneous sources, such as\nscanner-related distortions or head movements inside the scanner [14]. Typically, each fMRI scan\ncomprises a 4-dimensional dataset (91\u00d7109\u00d791 voxels in space, and 176 \u2212 405 time points). As a\n\ufb01rst step, we parcellated the brain into 264 functionally-de\ufb01ned regions of interest (ROIs) using the\nPower et al [15] parcellation, which groups functionally related voxels into non-overlapping ROIs.\nGPFA was run on the parcellated fMRI time-series to extract task-speci\ufb01c latent dimensions, and\ntheir associated trajectories. For this, we employed scans from 100 subjects (IDs in red in Supporting\nInformation, Table S1), and the \ufb01rst 100 timepoints from each ROI (Fig. 1D, break in time axis).\nBefore applying GPFA, we con\ufb01rmed that a majority of these time series (~80%) satis\ufb01ed Gaussianity\nassumptions as assessed by the Lilliefors test for normality. These timeseries were z-scored for each\nROI separately and provided as input to the GPFA algorithm. Each subject was treated as a distinct\nexperimental trial, and the GPFA model was trained with 4-fold cross validation (parameters trained\non 75 subjects, and tested on 25 subjects, in each fold). Prediction errors were computed, with the test\nsubjects\u2019 data, across a range of latent dimensions (5-100). The optimal number of latent dimensions\n\n2\n\n\fFigure 1: Extracting latent dimensions at slow timescales with Gaussian Process Factor Analy-\nsis (GPFA). A Schematic depicting the application of GPFA to fMRI time series data for concurrent\nsmoothing and dimensionality reduction (see text for details). B Variation of prediction error with\nthe number of latent GPFA dimensions. Lines: curve \ufb01ts; triangles: minima for each curve. Dashed\nvertical line: Number of latent dimensions corresponding to minimum prediction error across tasks\n(42). Colors: Prediction errors for different tasks. rs: resting; W: working memory; L: language;\nM: motor; S: social cognition; G: gambling; R: relational processing; E: emotion processing. C\nCharacteristic timescale (\u03c4) distribution; data pooled across tasks. Dashed vertical line: Threshold\ncorresponding to slow (<1 Hz) timescale. D Representative spatial maps (column of C matrix in\npanel A) for a slow timescale dimension (\u03c4 = 3060 ms; top) and fast timescale dimension (\u03c4 = 447\nms; bottom). The slow timescale dimension shows a distributed spatial map characteristic of default\nmode network (DMN), a canonical resting state network comprising the medial prefrontal cortex\n(solid circle) and posterior cingulate cortex (dashed circle). For clarity, the spatial maps depict only\npositive values of C. In each row, the left and right images show, respectively, the lateral and medial\nviews of the brain\u2019s left hemisphere. Time series for the latent dimensions are shown below the\ncorresponding maps. Gray: time series for individual subjects; yellow: average time series.\n\nwas then determined as the one that minimized prediction error, using a leave-region-out approach\n(further elaborated in the Supporting Information, section 1).\nThis approach revealed a clear minimum of the prediction error, corresponding to optimal reduced\ndimensionality for the fMRI data (Fig. 1B) for each of the 7 tasks and resting state: the minimum\nnumber of latent dimensions ranged from 39-44, indicating a nearly 6-fold reduction in data dimen-\nsionality. For further analysis, we determined a common number of optimal latent dimensions (u=42)\nacross tasks, by minimizing the overall prediction error (Supporting Information, section 1). GPFA\nwas then run, again, for each task with this common number of latent dimensions.\nEach latent dimension i (= 1, ..., p) estimated by GPFA can be described by the following quantities\n(Fig. 1A): i) a time series given by xi,: = [xi,1, xi,2, . . . , xi,T ]; ii) the ith column of the mapping\nmatrix C, which speci\ufb01es the contribution of each of the 264 brain regions, to latent dimension\ni, which we term the \u201cspatial map\u201d associated with the ith latent dimension. This map may be\ninterpreted as a group (or network) of brain regions exhibiting shared latent dynamics governed by\nxi; and iii) a characteristic timescale for that latent dimension, \u03c4i.\nAcross all tasks GPFA latent dimensions exhibited a bimodal distribution of timescales (Supporting\nInformation, Fig. S2), with nearly 75% of dimensions exhibiting timescales slower than 1000 ms\n(1 Hz) (Fig. 1C, timescales pooled across tasks). Figure 1D shows a representative set of latent\ndimensions at slow and fast timescales obtained from the resting state scans. The slow timescale\ndimension (Figure 1D, top) exhibited a characteristic timescale of \u03c4=3060 ms. The spatial map\nfor this dimension revealed a pattern characteristic of the default mode network (DMN), a widely-\ndocumented resting-state brain network comprising the medial prefrontal cortex, posterior cingulate\ncortex, precuneus and angular gyrus [16]. On the other hand, the fast timescale dimension (Figure 1D,\nbottom) exhibited a characteristic timescale of \u03c4=447 ms, which was faster than the sampling\n\n3\n\n\fFigure 2: Classifying task-speci\ufb01c cognitive states with GPFA latent dimensions. A Schematic\nof classi\ufb01cation with template pattern matching, based on latent trajectories (top) or oscillatory\npower (bottom) in GPFA latent dimensions (see text for details). B Confusion matrix for an 8-way\nclassi\ufb01cation showing the proportion of task (or resting) scans that were correctly classi\ufb01ed or\nmisclassi\ufb01ed, using a template matching approach based on latent time series (see text for details).\nChance: 12.5%. C Synchronization index (y-axis), measuring the average correlation among latent\ntime series across subjects for each latent dimension, as a function of the characteristic timescale\nfor that dimension (x-axis), for the working memory task (all tasks shown in SI Fig. S2). D (left\npanel) Comparison of accuracies for classi\ufb01cation based on GPFA latent time series (left bar and\npoints) and that based on 42-ROI time series (right bar and points) for each of the 7 tasks. Bars: Mean\naccuracies; (right panel) Same as in left panel but using ROI oscillation spectra. Color conventions:\nsame as in Fig. 1B. E Same as in panel D but comparison with classi\ufb01cation accuracies based on\nPCA dimensions: time series (left panel) and oscillation spectra (right panel).\n\nfrequency of the fMRI timeseries (1.4 Hz). GPFA latents with such fast timescales likely re\ufb02ect\nartifacts, estimated from \ufb01ts to residual noise after accounting for slow latents (see also Supporting\nInformation, section 2).\n\n3 Classifying task-speci\ufb01c cognitive states with slow latent dynamics\nNext, we tested whether these latent dimensions carried information about task-speci\ufb01c cognitive\nstates: Could examining these latent dimensions for each individual subject permit classifying the\ncognitive task that that subject was performing inside the scanner? For this, we designated the spatial\nmaps computed by running GPFA on 100 subjects\u2019 data as \u201ctemplate\u201d maps (42 per task scan) and\nthen averaged the latent trajectories across these subjects as \u201ctemplate\u201d trajectories (also 42 per task\nscan, each corresponding to one template map).\nWe employed these \u201ctemplate\u201d latent dimensions to classify task-speci\ufb01c cognitive states for the\nremaining 900 subjects (\u201ctest\u201d data; Supporting Information, Algorithm S1). Brie\ufb02y, the time series\nx(t) for some task scan s, for each subject in the test dataset, was projected onto the template maps\nof each of the eight tasks. This procedure generated a latent time series for each test subject\u2019s scan s,\nand was repeated with template maps from all eight scans. Following this the correlation between\neach test subject\u2019s projected (latent GPFA) trajectories and the template trajectories for each scan\nwas computed, and summed across components, to get an overall similarity score. The template scan\nwith the maximum overall similarity score with the test subject\u2019s scan, was assigned as the predicted\ntask label for the test subject\u2019s scan. This was repeated for each scan, s=1-8, for each of the 900 test\nsubjects, and all scans were assigned a speci\ufb01c label.\nThis approach (Fig. 2A) provided superlative accuracies for classifying among the seven different\ntask states (confusion matrix; Fig. 2B). Median accuracy was 97.8%, and accuracies ranged from\n96.7%-99.8%; all accuracies were signi\ufb01cantly above chance (permutation test, p < 0.001). A clear\nexception was the resting state scan, which was often misclassi\ufb01ed as a task scan. Nevertheless, this\nwas an expected outcome because resting state data are not expected to be time-locked across subjects\n\n4\n\n\fFigure 3: Predicting behavioral scores with connectivity among GPFA latents. A (Top) Spatial\nmap of the most representative latent dimension for the language (left) and motor (right) tasks. The\nlateral views of the left and right hemispheres are shown for positive values of C only. Maps for all\ntasks are shown in SI Fig. S1. (Bottom) Trajectories showing the joint activity for the most represen-\ntative (x-axis) and second most representative (y-axis) latent dimensions for the corresponding task.\nYellow and gray traces show average trajectories of template and test data, respectively. Red shading:\nnormalized distribution of occupancy of the joint activity in the GPFA space spanned by these latent\ndimensions (n=900 subjects). Timescales corresponding to each dimension are marked along the\nrespective axes. B Behavior scores across a range of cognitive tests (columns; refer SI Table S3) pre-\ndicted based on GPFA connectivity in each task (row). Black outlined squares: signi\ufb01cant predictions\nat the p<0.01 level with Benjamini-Hochberg correction for multiple comparisons. C Representative\ncorrelations of observed and predicted behavioral scores; all values were z-scored before plotting.\n(From left to right) picture-vocabulary test score based on the language task connectivity, strength\nscore based on motor task connectivity, \ufb02uid intelligence sub-score based on working memory task\nconnectivity and spatial orientation score based on relational task connectivity.\n\nand scans. Therefore, estimating temporal correlations across latent GPFA dimensions should not be\nable to meaningfully identify the resting state. On the other hand, because the tasks performed by\nsubjects all followed the same time-course, latent dimensions exhibited suf\ufb01cient temporal structure \u2013\nwhich was common and coordinated across subjects \u2013 to enable accurate classi\ufb01cation. We repeated\nthe classi\ufb01cation limiting the time series to only those GP dimensions with slow timescales (<1Hz)\nand found comparably superlative accuracies across the seven tasks (median: 98% , range: 96.5% -\n99.5% ). In addition, classi\ufb01cation analysis following GPFA with a different (90-node) functional\nparcellation [17] also produced similar classi\ufb01cation accuracies (Supporting Information, section 2,\nSI Fig. S3B), indicating that these results were not unique to a speci\ufb01c parcellation. Moreover, GPFA\ntime series could distinguish, with superlative accuracies (range: 81%-99%) distinct sub-tasks within\neach task performed by the subjects inside the scanner (SI, section 2, Fig. S3D).\nNext, we asked which spatial maps in the template data, were most representative of each task scan.\nFor this we identi\ufb01ed, for each task scan, the template dimension whose time series exhibited the\nhighest correlation with the latent dimensions of the test dataset, for the corresponding scan (average\ncorrelation across n=900 test subjects). In other words, these dimensions represent brain networks\nwhich exhibited the most consistent dynamics (across subjects) for each task. Distinct and meaningful\nstructure emerged in the spatial maps for each task. For instance, the language task showed clearly\nlateralized activation in the left superior temporal cortex, which includes the auditory cortex and\nlanguage processing regions (Fig. 3A top left). The motor task, on the other hand, showed bilateral\nactivation in the precentral gyrus, the location of the motor cortex (Fig. 3A top right). Other tasks,\nand the associated spatial maps, are shown in the Supporting Information (Fig. S1). Notably, we\nobserved a strongly right hemisphere lateralized map for the gambling task (Fig. S1D), consistent\nwith the \ufb01ndings of a recent study which showed that right lateralized brain activity was predictive of\nrisk-taking behaviors [18].\nWe observed highly synchronized dynamics in the latent dimensions across subjects for each task\n(Fig. S1, second row). The average two dimensional latent trajectory for the template subjects\n(Fig. 3A, bottom, and Fig. S1, third row, yellow traces), were closely aligned with the average\n\n5\n\n\ftrajectory for the test subjects (Fig. 3A, bottom, and Fig. S1, third row, gray traces), providing clear\nevidence for task-speci\ufb01c inter-subject synchronization of brain dynamics (see Discussion). We\nexamined the degree of inter-subject synchronization, with a view to distinguishing task-relevant\nlatent dimensions from task-irrelevant ones. We hypothesized that the strength of inter-subject\nsynchronization within each latent dimension would index the task-relevance of that dimension. For\nexample, artifacts, such as scanner noise or physiological noise, are unlikely to be synchronized\nacross subjects, whereas dimensions strongly locked to salient aspects of the task would be highly\nsynchronized. To quantify the degree of inter-subject synchronization for each latent dimension,\nwe computed a \u201csynchronization index\u201d: the average correlation between the template latent time\nseries and the projected latent time series of each of the test subjects. A higher synchronization\nindex indicates a higher degree of phase locking (or synchronization) of the test subjects\u2019 latent time\nseries with the template time series. Slower timescale dimensions exhibited systematically stronger\nsynchronization indices, as compared to faster dimensions; Fig. 2C shows this trend for working\nmemory task (all tasks shown in SI Fig. S2). These results are consistent with the proposal that,\nacross tasks, faster (>1 Hz) timescale dimensions re\ufb02ected scanner artifact and noise, and slower\n(<1 Hz) timescale dimensions re\ufb02ected task-relevant brain processes. They also suggest the potential\nutility of GPFA for denoising fMRI time series data (see Discussion).\nWe also tested if the power spectrum of GPFA latent dimensions contained suf\ufb01cient information\nto distinguish among the tasks. For this, we \ufb01rst estimated the power spectrum of each dimension\nfor each task using multitaper spectral estimation [19]. Next, we estimated and subtracted out the\nbroadband (fractal or 1/f) component, using the IRASA (irregular-resampling auto-spectral analysis)\nmethod [20], to retain speci\ufb01cally the oscillatory component of the spectrum up to one quarter of the\nsampling rate (0.35 Hz). These oscillation power spectra were averaged across the template subjects\n(n=100) to form a \u201ctemplate\u201d spectrum for each task and latent dimension (SI Fig. S4). As before, to\nclassify each task scan of the \u201ctest\u201d subjects\u2019 (n=900) data, we projected their timeseries based on\nthe template spatial maps, computed the oscillatory spectra and correlated these with the oscillatory\nspectra of each template to identify the best matching template (Fig. 2A). Again, we discovered\nabove-chance accuracies for task classi\ufb01cation based on oscillation spectra: accuracies ranged from\n34.7%-83.7% across the 7 tasks, with a median accuracy of 57.8% (p<0.01, permutation test).\nWe also performed additional control analyses to test if these results were speci\ufb01c to GPFA, or could\nbe achieved with other dimensionality reduction approaches; these are described in the Supporting\nInformation (section 2). Brie\ufb02y, we reduced dimensionality either by selecting a subset of regions\n(ROIs) based on their activity correlation with the fMRI task timeseries, or with principal components\nanalysis (PCA). In each case we compared the accuracy of task classi\ufb01cation based on GPFA features\n\u2013 time series or oscillation spectra \u2013 with the accuracies obtained with these other approaches. Both\nGPFA latent spectra and time series provided signi\ufb01cantly higher accuracies in classifying task-\nspeci\ufb01c cognitive states, compared with at least one of the features in each of the other approaches\n(p<0.05, Wilcoxon signed rank text, Fig. 2D and Fig. 2E; details in SI section 2) .\nWe asked if, in addition to being able to identify task-speci\ufb01c cognitive states, GPFA latent dynamics\nwould also be relevant as a marker of cognitive traits. We computed the functional connectivity\nbetween every pair of GPFA latent dimensions, based on partial correlations, for each subject. With\nthese functional connectivity matrices as features, we sought to predict inter-individual differences in\n27 cognitive scores acquired outside of the scanning session [21] (SI Table S3), using connectome-\nbased predictive modeling (CPM; [22]). Behavioral scores were selected from Alertness, Cognition\nand Motor categories (HCP Data Dictionary), with the goal of avoiding redundant scores (e.g.\nsensitivity and speci\ufb01city were included, but not also true and false positive rates). All scores were\nselected \u201cblind\u201d to (without a priori knowledge of) the results of these prediction analyses. Scores\nwere predicted with 10-fold cross validation: by estimating the CPM model on a training fold with\nnine-tenths of the data while predicting scores on each left-out \u201ctest\u201d fold (one-tenth of the data), in\nturn.\nMany scores could be predicted signi\ufb01cantly and almost universally across tasks (Fig. 3B, black\nsquares; p<0.01 with Benjamini-Hochberg correction for multiple comparisons). These included\nscores of motor performance, \ufb02uid intelligence, linguistic ability and spatial orientation (Fig. 3B-C).\nAlthough the proportion of explained variance was comparatively low (mean r=0.16, range: 0.08-\n0.34), this range of correlations were similar to that observed in previous studies employing functional\nconnectivity features for behavioral score predictions [23, 24]). On the other hand, scores associated\nwith sustained attention, mental state or memory were predicted well with only some tasks or not at all.\n\n6\n\n\fWe speculate that these differences may arise from the degree of mismatch between fMRI timescales\nand characteristic timescales for behavioral tasks used to measure these scores: Tasks engaging neural\nprocesses at timescales matching fMRI timescales (e.g. language or \ufb02uid intelligence) were possibly\nbetter predicted than those engaging processes at much faster (e.g. attention) or much slower (e.g.\nmental state) timescales. Overall, the results suggest that connectivity estimated with slow, latent\nfMRI processes may be relevant for predicting traits across several cognitive domains.\n\n4 Predicting cognitive decline with infra-slow latent dynamics\n\nAs a second, key application of our approach, we sought to test whether infra-slow brain dynamics\ncould serve as markers of cognitive decline. For this, we obtained resting state brain imaging (fMRI)\nscans from the Alzheimers Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu).\nAmong the large number of patient datasets in this database, we utilized data from a subset of\npatients with Mild Cognitive impairment (MCI). MCI patients typically exhibit symptoms associated\nwith decline of memory, language or thinking, that are usually more pronounced than normally\naging adults. Nevertheless, only some proportion of such MCI patients progress to develop severe\nforms of dementia, like Alzheimer\u2019s Dementia (AD), as assessed by standard clinical ratings (e.g.\nclinical dementia rating, CDR). We term those MCI patients who progressed to develop AD as \u201cMCI\nconverters\u201d (MCIc) and those who did not as \u201cMCI stable\u201d (MCIs) (Fig. 4B). Our goal was to test if\ninfra-slow brain dynamics, as estimated with GPFA on resting fMRI data, would enable classifying\nMCIc from MCIs patients.\nWe analyzed resting state fMRI data for n=23 MCIc (age:72.7 \u00b1 6.9 yrs, 11 females) and n=72\nMCIs patients (age:71.6 \u00b1 6.8 yrs, 32 females). For MCIs patients, scans were included only if\nthe patient remained stably diagnosed as MCI for at least two years. For MCIc patients, scans\nwere typically acquired 6 to 36 months (median: 12 months) prior to conversion to AD. One MCIc\nsubject was excluded due to corrupted brain imaging data, so that data from a total of n=94 patients\nwas analyzed. A standard pipeline was used to preprocess the scans and parcellate the brain into\n264 regions, based on the Power et al. parcellation [15]. We then extracted latent dimensions by\napplying GPFA to parcellated fMRI time series, concatenated across all subjects (MCIc and MCIs).\nAs before, we obtained an optimal number of latent dimensions (u=77) with a prediction error\nminimization approach. Because only resting state fMRI data was available from MCI patients no\nuseful information could be obtained by examining correlations between different patients\u2019 latent\ntrajectories. This is because brain \ufb02uctuations in the resting state are uncontrolled, in the absence\nof external task events. Thus, we sought features in the resting state GPFA dimensions that did not\nrequire consistent phase relationships between latent time series across subjects.\nFirst, we computed partial correlations (PC) and lagged covariance (LC) between every pair of latent\ndimensions for each subject (Supporting Information, Section 4). These features are indicative of\ninstantaneous or lagged connectivity across brain regions for each subject [25], and do not require\nactivity to be synchronized across subjects. We then trained a linear classi\ufb01er based on support\nvector machines (SVM) with PC and LC features as input, and distinct labels for the MCIc and MCIs\npatients, using Matlab\u2019s \ufb01tclinear function (Fig. 4A). As the numbers of selected MCIc scans (n=22)\nand MCIs scans (n=72) were substantially different, a balanced classes approach was used prior to\nclassi\ufb01cation to prevent classi\ufb01er bias (Supporting Information, section 4).\nClassi\ufb01cation accuracy based on PC connectivity features was 61.2% whereas that based on LC\nconnectivity features was 71.0%. Combining the two sets of features provided a marginally lower\nclassi\ufb01cation accuracy of 63.6%; each of these accuracies were signi\ufb01cantly above chance as assessed\nwith a permutation test based on shuf\ufb02ing labels (p<0.05; Supporting Information, section 4). To \ufb01nd\na minimal set of features that provided the highest cross-validation accuracy (area-under-the-curve\nor AUC) we applied recursive feature elimination (RFE) including both PC and LC features [26]\n(Supporting Information, section 4). RFE retained only 15% (1332) features of the 8855 PC+LC\nfeatures, and these few features suf\ufb01ced to achieve a comparatively high classi\ufb01cation accuracy of\n73.6%. The top ranked three features, with the highest SVM beta weights, were all PC connections:\nthe highest beta weights occurred for a PC connection between a predominantly left lateralized\noccipito-parietal map and a bilateral temporal map (Fig. 4C). The next two beta weights occurred for\nconnections involving the fronto-insular cortex, and the anterior cingulate cortex (SI Fig. S5). These\nmaps overlap strongly with the fronto-parietal \u201cattention\u201d network, and a cingulo-opercular \u201csalience\u201d\nnetwork, conventionally implicated in attention and executive control, respectively [27].\n\n7\n\n\fFigure 4: Predicting cognitive decline with GPFA latent dynamics. A Schematic of classi\ufb01cation\nbetween MCI-converter and MCI-stable patients based on resting state connectivity and oscillatory\ndynamics (see text for details). B Progression of clinical dementia rating (CDR, sum of boxes) score\nfor a representative MCI-converter (left) and an MCI-stable (right) patient across visits (months).\nBlack data point in left graph denotes diagnosis of Alzheimer\u2019s Dementia (AD) onset. C Spatial maps\nof the most discriminative GPFA-latent connection for the MCIc versus MCIs classi\ufb01cation (partial\ncorrelation between GP components 29 and 50). Dashed oval: occipito-parietal map. Solid circle:\ntemporal map. D Oscillation power spectra across all 77 latent dimensions for MCIc patients (left)\nand MCIs patients (right). Black lines: average spectra across dimensions, show marked differences\nbetween MCIc and MCIs patients. E Observed CDR (sum-of-boxes) scores versus scores predicted\nwith oscillation spectral features (left panel) and lagged covariance and partial correlations (right\npanel) of GPFA trajectories. Dashed line: linear \ufb01t.\n\nSecond, we tested if the power spectrum of the latent dimensions suf\ufb01ced to classify between MCIc\nand MCIs subjects. As before, we computed the power spectrum for each component and subject and\nremoved the broadband (1/f) component to retain only the oscillatory component (with IRASA). We\nthen used these oscillatory power spectra (Fig. 4D) as features in an SVM classi\ufb01er using a balanced\nclasses approach, as discussed above. In this case, due to the slower sampling rate (longer repeat\ntime) of the fMRI scan (0.3 Hz) compared to the HCP data (1.4 Hz), we included for the classi\ufb01cation\nonly frequencies up to ~0.08 Hz (infra-slow band), sampled uniformly at 32 values (total of 2464\nfeatures). Classi\ufb01cation accuracy based on the SVM was 65.1%, and signi\ufb01cantly above chance, as\nassessed by a permutation test (p<0.05). As before, following RFE, we discovered that, on average,\nonly 28% (681/2464) features were retained whereas accuracy following RFE improved marginally\nto 67.2%.\nFinally, we evaluated the ability of slow latent dynamics to predict a graded measure of cognitive\ndecline. We predicted individual patients\u2019 CDR-SOB (CDR-sum of boxes) scores that measure\nseverity of dementia [28], based on the resting fMRI scan obtained in the same visit. We \ufb01t a\nregression model with an L1 penalty (Matlab\u2019s lasso function) to predict CDR-SOB scores, separately,\nwith power spectral features and with LC and PC features, with a k-fold cross validation approach\n(k=2, 4, 23, 46, 92; Supporting Information, section 4). The accuracy of prediction increased steadily\nwith more folds, perhaps because of the small sample size and consequent bias with limited training\ndata for small k. Leave-one-out cross-validation provided the most accurate predictions with power\nspectral features yielding a strong correlation (r=0.56, p<0.001, Fig. 4E left) between predicted and\nobserved scores. LC and PC features yielded a marginally lower, but signi\ufb01cant, prediction (r=0.34,\np<0.001, Fig. 4E right).\nTaken together, these analyses indicate that slow and infra-slow \ufb02uctuations in resting state fMRI data\nare reliable biomarkers that distinguish between MCI patients who converted to AD versus those who\ndid not. Moreover, the results suggested compromised function in putative attention-related brain\nnetworks that could be indicative of progression to AD. Finally, slow dynamics in these networks\npredicted inter-individual differences in cognitive decline, as assessed by CDR-SOB scores.\n\n8\n\n\f5 Discussion\nSlow (0.1-1 Hz) and infra-slow (<0.1 Hz) \ufb02uctuations in spontaneously generated electrical activity\nof the brain have been widely observed with various recording modalities, including local \ufb01eld\npotential microelectrode recordings [29], optical recordings [30], electrocorticography [31, 32] and\nelectro- and magnetoencephalography [33]. Here, we examined whether such slow \ufb02uctuations,\nas estimated with GPFA applied on fMRI data, would be informative for understanding cognitive\nprocesses in healthy brains, and cognitive decline in diseased brains.\nApplying GPFA to fMRI data revealed several key insights. First, GPFA reduced the dimensionality\nof the data by 3-6 fold, indicating signi\ufb01cant redundancy in the data. This signi\ufb01cant reduction\nin dimensionality is a consequence of the shared variance of the fMRI BOLD response across\nmultiple regions. This shared variance could be exploited to produce sparse representations of fMRI\nbrain activity. Moreover, it is possible that an even higher reduction in dimensionality could be\nobtained with GPFA applied to voxel-level fMRI data. At present, computational costs associated\nwith scaling up GPFA to the voxel level prohibit such an application, and highlight the need for\ndeveloping more ef\ufb01cient algorithms for voxel-level GPFA. Second, GPFA provides a key advantage\nover other dimensionality reduction techniques, like independent components analysis (ICA) [34], in\nthat GPFA directly estimates latent dimensions with distinct, characteristic timescales. This feature\nenabled us to show that GP dimensions with fast timescale dynamics (>1 Hz) were not synchronized\nacross subjects, and likely re\ufb02ected artifactual processes (e.g. high frequency scanner noise). Prior\nknowledge about the timescales of scanner or physiological artifacts could be directly incorporated\ninto the EM algorithm when estimating GPFA parameters, thereby permitting concurrent denoising\nof fMRI data.\nOn the other hand, GPFA latent dimensions with comparatively slower timescale dynamics (<1 Hz)\nwere strongly synchronized across subjects (Fig. 2C, SI Fig. S2). Previous studies have reported\ninter-subject synchronization of cortical responses, at multiple different timescales. Studies that\nused either fMRI [35] or MEG [36] to image brain activity showed that cortical activity is highly\nsynchronized across subjects experiencing naturalistic stimuli, either visual (e.g. movies) or auditory\n(e.g. music), particularly when salient events occur in the stimulus stream [37, 38]. A related study\nwith task-based fMRI identi\ufb01ed brain networks that showed consistent synchrony across the subject\npopulation[39]. Moreover, a key advantage of using GPFA over previous approaches is that GPFA\nprovides considerable \ufb02exibility with identifying a variety of brain network dynamics. Alternative\nGP covariance kernels, such as a periodic kernel or a linear kernel [40] can help identify periodic\n\ufb02uctuations or drifts, respectively, in the fMRI data, which could then be matched with relevant task\ncovariates of interest, or factored out as noisy confounds. For example, some types of motion artifacts,\narising due to overt behavioral responses in the scanner, could be synchronized across subjects, and\nthese could be identi\ufb01ed and denoised with GPFA.\nOur results suggest that BOLD dynamics that occur at infra-slow (~0.1Hz) timescales may serve\nas markers for cognitive function in health, and, cognitive decline, in disease. Understanding\nthe link between these BOLD dynamics and dynamics of underlying neural processes remains an\nimportant open question. Despite this caveat, our approach is relevant for developing non-invasive,\nimaging-based biomarkers for early detection of cognitive impairment. For example, changes in slow\nand infra-slow BOLD dynamics can be measured longitudinally, over several years, as a potential\nbiomarker for predicting the onset and trajectory of cognitive decline in AD, and could form the basis\nfor early intervention before severe behavioral symptoms of cognitive decline manifest.\n\n6 Acknowledgements\nWe wish to thank Byron Yu and Abhijit Chinchani for guidance with GPFA analysis. This re-\nsearch was funded by a Wellcome Trust-Department of Biotechnology India Alliance Intermediate\nfellowship [IA/I/15/2/502089], a Science and Engineering Research Board Early Career award\n[ECR/2016/000403], a Pratiksha Trust Young Investigator award, a Department of Biotechnology-\nIndian Institute of Science Partnership Program grant, a Sonata Software grant and a Tata Trusts\ngrant (to DS). 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