Dynamic mode decomposition of resting-state and task fMRI

Fast, accurate, and interpretable decoding of electrocorticographic signals using dynamic mode decomposition

Dynamic mode (DM) decomposition decomposes spatiotemporal signals into basic oscillatory components (DMs). DMs can improve the accuracy of neural decoding when used with the nonlinear Grassmann kernel, compared to conventional power features. However, such kernel-based machine learning algorithms have three limitations: large computational time preventing real-time application, incompatibility with non-kernel algorithms, and low interpretability. Here, we propose a mapping function corresponding to the Grassmann kernel that explicitly transforms DMs into spatial DM (sDM) features, which can be used in any machine learning algorithm. Using electrocorticographic signals recorded during various movement and visual perception tasks, the sDM features were shown to improve the decoding accuracy and computational time compared to conventional methods. Furthermore, the components of the sDM features informative for decoding showed similar characteristics to the high-γ power of the signals, but with higher trial-to-trial reproducibility. The proposed sDM features enable fast, accurate, and interpretable neural decoding.

Characterizing the temporal dynamics of intrinsic brain activities in depressed adolescents with prior suicide attempts

Converging evidence has revealed disturbances in the corticostriatolimic system are associated with suicidal behaviors in adults with major depressive disorder. However, the neurobiological mechanism that confers suicidal vulnerability in depressed adolescents is largely unknown. A total of 86 depressed adolescents with and without prior suicide attempts (SA) and 47 healthy controls underwent resting-state functional imaging (R-fMRI) scans. The dynamic amplitude of low-frequency fluctuations (dALFF) was measured using sliding window approach. We identified SA-related alterations in dALFF variability primarily in the left middle temporal gyrus, inferior frontal gyrus, middle frontal gyrus (MFG), superior frontal gyrus (SFG), right SFG, supplementary motor area (SMA) and insula in depressed adolescents. Notably, dALFF variability in the left MFG and SMA was higher in depressed adolescents with recurrent suicide attempts than in those with a single suicide attempt. Moreover, dALFF variability was capable of generating better diagnostic and prediction models for suicidality than static ALFF. Our findings suggest that alterations in brain dynamics in regions involved in emotional processing, decision-making and response inhibition are associated with an increased risk of suicidal behaviors in depressed adolescents. Furthermore, dALFF variability could serve as a sensitive biomarker for revealing the neurobiological mechanisms underlying suicidal vulnerability.

Dynamic Mode Decomposition of Multiphoton and Stimulated Emission Depletion Microscopy Data for Analysis of Fluorescent Probes in Cellular Membranes

An analysis of the membrane organization and intracellular trafficking of lipids often relies on multiphoton (MP) and super-resolution microscopy of fluorescent lipid probes. A disadvantage of particularly intrinsically fluorescent lipid probes, such as the cholesterol and ergosterol analogue, dehydroergosterol (DHE), is their low MP absorption cross-section, resulting in a low signal-to-noise ratio (SNR) in live-cell imaging. Stimulated emission depletion (STED) microscopy of membrane probes like Nile Red enables one to resolve membrane features beyond the diffraction limit but exposes the sample to a lot of excitation light and suffers from a low SNR and photobleaching. Here, dynamic mode decomposition (DMD) and its variant, higher-order DMD (HoDMD), are applied to efficiently reconstruct and denoise the MP and STED microscopy data of lipid probes, allowing for an improved visualization of the membranes in cells. HoDMD also allows us to decompose and reconstruct two-photon polarimetry images of TopFluor-cholesterol in model and cellular membranes. Finally, DMD is shown to not only reconstruct and denoise 3D-STED image stacks of Nile Red-labeled cells but also to predict unseen image frames, thereby allowing for interpolation images along the optical axis. This important feature of DMD can be used to reduce the number of image acquisitions, thereby minimizing the light exposure of biological samples without compromising image quality. Thus, DMD as a computational tool enables gentler live-cell imaging of fluorescent probes in cellular membranes by MP and STED microscopy.

Childhood adversities characterize the heterogeneity in the brain pattern of individuals during neurodevelopment

BACKGROUND

Several factors shape the neurodevelopmental trajectory. A key area of focus in neurodevelopmental research is to estimate the factors that have maximal influence on the brain and can tip the balance from typical to atypical development.

METHODS

Utilizing a dissimilarity maximization algorithm on the dynamic mode decomposition (DMD) of the resting state functional MRI data, we classified subjects from the cVEDA neurodevelopmental cohort (n = 987, aged 6-23 years) into homogeneously patterned DMD (representing typical development in 809 subjects) and heterogeneously patterned DMD (indicative of atypical development in 178 subjects).

RESULTS

Significant DMD differences were primarily identified in the default mode network (DMN) regions across these groups (p < 0.05, Bonferroni corrected). While the groups were comparable in cognitive performance, the atypical group had more frequent exposure to adversities and faced higher abuses (p < 0.05, Bonferroni corrected). Upon evaluating brain-behavior correlations, we found that correlation patterns between adversity and DMN dynamic modes exhibited age-dependent variations for atypical subjects, hinting at differential utilization of the DMN due to chronic adversities.

CONCLUSION

Adversities (particularly abuse) maximally influence the DMN during neurodevelopment and lead to the failure in the development of a coherent DMN system. While DMN's integrity is preserved in typical development, the age-dependent variability in atypically developing individuals is contrasting. The flexibility of DMN might be a compensatory mechanism to protect an individual in an abusive environment. However, such adaptability might deprive the neural system of the faculties of normal functioning and may incur long-term effects on the psyche.

Dynamic nonreversibility view of intrinsic brain organization and brain dynamic analysis of repetitive transcranial magnitude stimulation

Intrinsic neural activities are characterized as endless spontaneous fluctuation over multiple time scales. However, how the intrinsic brain organization changes over time under local perturbation remains an open question. By means of statistical physics, we proposed an approach to capture whole-brain dynamics based on estimating time-varying nonreversibility and k-means clustering of dynamic varying nonreversibility patterns. We first used synthetic fMRI to investigate the effects of window parameters on the temporal variability of varying nonreversibility. Second, using real test-retest fMRI data, we examined the reproducibility, reliability, biological, and physiological correlation of the varying nonreversibility substates. Finally, using repetitive transcranial magnetic stimulation-fMRI data, we investigated the modulation effects of repetitive transcranial magnetic stimulation on varying nonreversibility substate dynamics. The results show that: (i) as window length increased, the varying nonreversibility variance decreased, while the sliding step almost did not alter it; (ii) the global high varying nonreversibility states and low varying nonreversibility states were reproducible across multiple datasets and different window lengths; and (iii) there were increased low varying nonreversibility states and decreased high varying nonreversibility states when the left frontal lobe was stimulated, but not the occipital lobe. Taken together, these results provide a thermodynamic equilibrium perspective of intrinsic brain organization and reorganization under local perturbation.

Manifold alteration between major depressive disorder and healthy control subjects using dynamic mode decomposition in resting-state fMRI data

Background

The World Health Organization has reported that approximately 300 million individuals suffer from the mood disorder known as MDD. Non-invasive measurement techniques have been utilized to reveal the mechanism of MDD, with rsfMRI being the predominant method. The previous functional connectivity and energy landscape studies have shown the difference in the coactivation patterns between MDD and HCs. However, these studies did not consider oscillatory temporal dynamics.

Methods

In this study, the dynamic mode decomposition, a method to compute a set of coherent spatial patterns associated with the oscillation frequency and temporal decay rate, was employed to investigate the alteration of the occurrence of dynamic modes between MDD and HCs. Specifically, The BOLD signals of each subject were transformed into dynamic modes representing coherent spatial patterns and discrete-time eigenvalues to capture temporal variations using dynamic mode decomposition. All the dynamic modes were disentangled into a two-dimensional manifold using t-SNE. Density estimation and density ratio estimation were applied to the two-dimensional manifolds after the two-dimensional manifold was split based on HCs and MDD.

Results

The dynamic modes that uniquely emerged in the MDD were not observed. Instead, we have found some dynamic modes that have shown increased or reduced occurrence in MDD compared with HCs. The reduced dynamic modes were associated with the visual and saliency networks while the increased dynamic modes were associated with the default mode and sensory-motor networks.

Conclusion

To the best of our knowledge, this study showed initial evidence of the alteration of occurrence of the dynamic modes between MDD and HCs. To deepen understanding of how the alteration of the dynamic modes emerges from the structure, it is vital to investigate the relationship between the dynamic modes, cortical thickness, and surface areas.

Static and dynamic fMRI-derived functional connectomes represent largely similar information

Functional connectivity (FC) of blood oxygen level-dependent (BOLD) fMRI time series can be estimated using methods that differ in sensitivity to the temporal order of time points (static vs. dynamic) and the number of regions considered in estimating a single edge (bivariate vs. multivariate). Previous research suggests that dynamic FC explains variability in FC fluctuations and behavior beyond static FC. Our aim was to systematically compare methods on both dimensions. We compared five FC methods: Pearson's/full correlation (static, bivariate), lagged correlation (dynamic, bivariate), partial correlation (static, multivariate), and multivariate AR model with and without self-connections (dynamic, multivariate). We compared these methods by (i) assessing similarities between FC matrices, (ii) by comparing node centrality measures, and (iii) by comparing the patterns of brain-behavior associations. Although FC estimates did not differ as a function of sensitivity to temporal order, we observed differences between the multivariate and bivariate FC methods. The dynamic FC estimates were highly correlated with the static FC estimates, especially when comparing group-level FC matrices. Similarly, there were high correlations between the patterns of brain-behavior associations obtained using the dynamic and static FC methods. We conclude that the dynamic FC estimates represent information largely similar to that of the static FC.

Enhanced Dynamic Laterality Based on Functional Subnetworks in Patients with Bipolar Disorder

An ocean of studies have pointed to abnormal brain laterality changes in patients with bipolar disorder (BD). Determining the altered brain lateralization will help us to explore the pathogenesis of BD. Our study will fill the gap in the study of the dynamic changes of brain laterality in BD patients and thus provide new insights into BD research. In this work, we used fMRI data from 48 BD patients and 48 normal controls (NC). We constructed the dynamic laterality time series by extracting the dynamic laterality index (DLI) at each sliding window. We then used k-means clustering to partition the laterality states and the Arenas-Fernandez-Gomez (AFG) community detection algorithm to determine the number of states. We characterized subjects' laterality characteristics using the mean laterality index (MLI) and laterality fluctuation (LF). Compared with NC, in all windows and state 1, BD patients showed higher MLI in the attention network (AN) of the right hemisphere, and AN in the left hemisphere showed more frequent laterality fluctuations. AN in the left hemisphere of BD patients showed higher MLI in all windows and state 3 compared to NC. In addition, in the AN of the right hemisphere in state 1, higher MLI in BD patients was significantly associated with patient symptoms. Our study provides new insights into the understanding of BD neuropathology in terms of brain dynamic laterality.

Leading basic modes of spontaneous activity drive individual functional connectivity organization in the resting human brain

Spontaneous activity of the human brain provides a window to explore intrinsic principles of functional organization. However, most studies have focused on interregional functional connectivity. The principles underlying rich repertoires of instantaneous activity remain largely unknown. We apply a recently proposed eigen-microstate analysis to three resting-state functional MRI datasets to identify basic modes that represent fundamental activity patterns that coexist over time. We identify five leading basic modes that dominate activity fluctuations. Each mode exhibits a distinct functional system-dependent coactivation pattern and corresponds to specific cognitive profiles. In particular, the spatial pattern of the first leading basis mode shows the separation of activity between the default-mode and primary and attention regions. Based on theoretical modelling, we further reconstruct individual functional connectivity as the weighted superposition of coactivation patterns corresponding to these leading basic modes. Moreover, these leading basic modes capture sleep deprivation-induced changes in brain activity and interregional connectivity, primarily involving the default-mode and task-positive regions. Our findings reveal a dominant set of basic modes of spontaneous activity that reflect multiplexed interregional coordination and drive conventional functional connectivity, furthering the understanding of the functional significance of spontaneous brain activity.

The arrow-of-time in neuroimaging time series identifies causal triggers of brain function

Moving from association to causal analysis of neuroimaging data is crucial to advance our understanding of brain function. The arrow-of-time (AoT), that is, the known asymmetric nature of the passage of time, is the bedrock of causal structures shaping physical phenomena. However, almost all current time series metrics do not exploit this asymmetry, probably due to the difficulty to account for it in modeling frameworks. Here, we introduce an AoT-sensitive metric that captures the intensity of causal effects in multivariate time series, and apply it to high-resolution functional neuroimaging data. We find that causal effects underlying brain function are more distinctively localized in space and time than functional activity or connectivity, thereby allowing us to trace neural pathways recruited in different conditions. Overall, we provide a mapping of the causal brain that challenges the association paradigm of brain function.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Static and dynamic functional connectomes represent largely similar information

Functional connectivity (FC) of blood-oxygen-level-dependent (BOLD) fMRI time series can be estimated using methods that differ in sensitivity to the temporal order of time points (static vs. dynamic) and the number of regions considered in estimating a single edge (bivariate vs. multivariate). Previous research suggests that dynamic FC explains variability in FC fluctuations and behavior beyond static FC. Our aim was to systematically compare methods on both dimensions. We compared five FC methods: Pearson's/full correlation (static, bivariate), lagged correlation (dynamic, bivariate), partial correlation (static, multivariate) and multivariate AR model with and without self-connections (dynamic, multivariate). We compared these methods by (i) assessing similarities between FC matrices, (ii) by comparing node centrality measures, and (iii) by comparing the patterns of brain-behavior associations. Although FC estimates did not differ as a function of sensitivity to temporal order, we observed differences between the multivariate and bivariate FC methods. The dynamic FC estimates were highly correlated with the static FC estimates, especially when comparing group-level FC matrices. Similarly, there were high correlations between the patterns of brain-behavior associations obtained using the dynamic and static FC methods. We conclude that the dynamic FC estimates represent information largely similar to that of the static FC.

Intrinsic macroscale oscillatory modes driving long range functional connectivity in female rat brains detected by ultrafast fMRI

Spontaneous fluctuations in functional magnetic resonance imaging (fMRI) signals correlate across distant brain areas, shaping functionally relevant intrinsic networks. However, the generative mechanism of fMRI signal correlations, and in particular the link with locally-detected ultra-slow oscillations, are not fully understood. To investigate this link, we record ultrafast ultrahigh field fMRI signals (9.4 Tesla, temporal resolution = 38 milliseconds) from female rats across three anesthesia conditions. Power at frequencies extending up to 0.3 Hz is detected consistently across rat brains and is modulated by anesthesia level. Principal component analysis reveals a repertoire of modes, in which transient oscillations organize with fixed phase relationships across distinct cortical and subcortical structures. Oscillatory modes are found to vary between conditions, resonating at faster frequencies under medetomidine sedation and reducing both in number, frequency, and duration with the addition of isoflurane. Peaking in power within clear anatomical boundaries, these oscillatory modes point to an emergent systemic property. This work provides additional insight into the origin of oscillations detected in fMRI and the organizing principles underpinning spontaneous long-range functional connectivity.

Hybrid brain model accurately predict human procrastination behavior

Procrastination behavior is quite ubiquitous, and should warrant cautions to us owing to its significant influences in poor mental health, low subjective well-beings and bad academic performance. However, how to identify this behavioral problem have not yet to be fully elucidated. 1132 participants were recruited as distribution of benchmark. 81 high trait procrastinators (HP) and matched low trait procrastinators (LP) were screened. To address this issue, we have built upon the hybrid brain model by using hierarchical machine learning techniques to classify HP and LP with multi-modalities neuroimaging data (i.e., grey matter volume, fractional anisotropy, static/dynamic amplitude of low frequency fluctuation and static/dynamic degree centrality). Further, we capitalized on the multiple Canonical Correlation Analysis (mCCA) and joint Independent Component Analysis algorithm (mCCA + jICA) to clarify its fusion neural components as well. The hybrid brain model showed high accuracy to discriminate HP and LP (accuracy rate = 87.04%, sensitivity rate = 86.42%, specificity rate = 85.19%). Moreover, results of mCCA + jICA model revealed several joint-discriminative neural independent components (ICs) of this classification, showing wider co-variants of frontoparietal cortex and hippocampus networks. In addition, this study demonstrated three modal-specific discriminative ICs for classification, highlighting the temporal variants of brain local and global natures in ventromedial prefrontal cortex (vmPFC) and PHC in HP. To sum-up, this research developed a hybrid brain model to identify trait procrastination with high accuracy, and further revealed the neural hallmarks of this trait by integrating neuroimaging fusion data.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-021-09765-z.

External drivers of BOLD signal's non-stationarity

A fundamental challenge in neuroscience is to uncover the principles governing how the brain interacts with the external environment. However, assumptions about external stimuli fundamentally constrain current computational models. We show in silico that unknown external stimulation can produce error in the estimated linear time-invariant dynamical system. To address these limitations, we propose an approach to retrieve the external (unknown) input parameters and demonstrate that the estimated system parameters during external input quiescence uncover spatiotemporal profiles of external inputs over external stimulation periods more accurately. Finally, we unveil the expected (and unexpected) sensory and task-related extra-cortical input profiles using functional magnetic resonance imaging data acquired from 96 subjects (Human Connectome Project) during the resting-state and task scans. This dynamical systems model of the brain offers information on the structure and dimensionality of the BOLD signal's external drivers and shines a light on the likely external sources contributing to the BOLD signal's non-stationarity. Our findings show the role of exogenous inputs in the BOLD dynamics and highlight the importance of accounting for external inputs to unravel the brain's time-varying functional dynamics.

Precision dynamical mapping using topological data analysis reveals a hub-like transition state at rest

In the absence of external stimuli, neural activity continuously evolves from one configuration to another. Whether these transitions or explorations follow some underlying arrangement or lack a predictable ordered plan remains to be determined. Here, using fMRI data from highly sampled individuals (~5 hours of resting-state data per individual), we aimed to reveal the rules that govern transitions in brain activity at rest. Our Topological Data Analysis based Mapper approach characterized a highly visited transition state of the brain that acts as a switch between different neural configurations to organize the spontaneous brain activity. Further, while the transition state was characterized by a uniform representation of canonical resting-state networks (RSNs), the periphery of the landscape was dominated by a subject-specific combination of RSNs. Altogether, we revealed rules or principles that organize spontaneous brain activity using a precision dynamics approach.

Image segmentation and separation of spectrally similar dyes in fluorescence microscopy by dynamic mode decomposition of photobleaching kinetics

Background

Image segmentation in fluorescence microscopy is often based on spectral separation of fluorescent probes (color-based segmentation) or on significant intensity differences in individual image regions (intensity-based segmentation). These approaches fail, if dye fluorescence shows large spectral overlap with other employed probes or with strong cellular autofluorescence.

Results

Here, a novel model-free approach is presented which determines bleaching characteristics based on dynamic mode decomposition (DMD) and uses the inferred photobleaching kinetics to distinguish different probes or dye molecules from autofluorescence. DMD is a data-driven computational method for detecting and quantifying dynamic events in complex spatiotemporal data. Here, DMD is first used on synthetic image data and thereafter used to determine photobleaching characteristics of a fluorescent sterol probe, dehydroergosterol (DHE), compared to that of cellular autofluorescence in the nematode Caenorhabditis elegans. It is shown that decomposition of those dynamic modes allows for separating probe from autofluorescence without invoking a particular model for the bleaching process. In a second application, DMD of dye-specific photobleaching is used to separate two green-fluorescent dyes, an NBD-tagged sphingolipid and Alexa488-transferrin, thereby assigning them to different cellular compartments.

Conclusions

Data-based decomposition of dynamic modes can be employed to analyze spatially varying photobleaching of fluorescent probes in cells and tissues for spatial and temporal image segmentation, discrimination of probe from autofluorescence and image denoising. The new method should find wide application in analysis of dynamic fluorescence imaging data.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12859-022-04881-x.

Dynamic Mode Decomposition of Fluorescence Loss in Photobleaching Microscopy Data for Model-Free Analysis of Protein Transport and Aggregation in Living Cells

The phase separation and aggregation of proteins are hallmarks of many neurodegenerative diseases. These processes can be studied in living cells using fluorescent protein constructs and quantitative live-cell imaging techniques, such as fluorescence recovery after photobleaching (FRAP) or the related fluorescence loss in photobleaching (FLIP). While the acquisition of FLIP images is straightforward on most commercial confocal microscope systems, the analysis and computational modeling of such data is challenging. Here, a novel model-free method is presented, which resolves complex spatiotemporal fluorescence-loss kinetics based on dynamic-mode decomposition (DMD) of FLIP live-cell image sequences. It is shown that the DMD of synthetic and experimental FLIP image series (DMD-FLIP) allows for the unequivocal discrimination of subcellular compartments, such as nuclei, cytoplasm, and protein condensates based on their differing transport and therefore fluorescence loss kinetics. By decomposing fluorescence-loss kinetics into distinct dynamic modes, DMD-FLIP will enable researchers to study protein dynamics at each time scale individually. Furthermore, it is shown that DMD-FLIP is very efficient in denoising confocal time series data. Thus, DMD-FLIP is an easy-to-use method for the model-free detection of barriers to protein diffusion, of phase-separated protein assemblies, and of insoluble protein aggregates. It should, therefore, find wide application in the analysis of protein transport and aggregation, in particular in relation to neurodegenerative diseases and the formation of protein condensates in living cells.

Stability Analysis of fMRI BOLD Signals for Disease Diagnosis

Previous studies have demonstrated that the stability changes in physiological signals can reflect individuals' pathological conditions. Apart from this, according to system science theory, a large-scale system can generally be divided into many subsystems whose stability level govern its overall performance. Therefore, this study attempts to investigate the possibility of analyzing the stability of decomposed subsystems of resting-state fMRI (rs-fMRI) BOLD signals in order to assess the overall characteristic of the human brain and individuals' health conditions. We used attention deficit/hyperactive disorder (ADHD) as an example to illustrate our method. Rs-fMRI BOLD signals were first decomposed into dynamic modes (DMs) which can illuminate the patterns of brain subsystems. Each DM is associated with one eigenvalue that determines its stability as well as oscillation frequency. Accordingly, we divided the DMs within common BOLD frequency bands into stable and unstable DMs. Then, the features related to the stability of those DMs were extracted, and nine common classifiers were used to differentiate healthy controls from ADHD patients taken from ADHD-200, a well-known dataset. The results showed that almost all features were statistically significant. Additionally, our proposed approach outperforms all existing methods with the highest possible precision, recall, and area under the receiver operating characteristic curve of 100%. In sum, we are the first to evaluate the stability of BOLD signals and demonstrate its possibility for disease diagnosis. This method can unveil new mechanisms of brain function, and could be widely used in medicine and engineering.

Data and model considerations for estimating time-varying functional connectivity in fMRI

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Time-varying FC models sometimes fail to detect temporal changes in fMRI data.

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Between-subject and within-session FC variability affect model stasis.

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The choice of parcellation affects model stasis in real fMRI data.

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The number of observations and free parameters per state critically affect model stasis.

Functional connectivity (FC) in the brain has been shown to exhibit subtle but reliable modulations within a session. One way of estimating time-varying FC is by using state-based models that describe fMRI time series as temporal sequences of states, each with an associated, characteristic pattern of FC. However, the estimation of these models from data sometimes fails to capture changes in a meaningful way, such that the model estimation assigns entire sessions (or the largest part of them) to a single state, therefore failing to capture within-session state modulations effectively; we refer to this phenomenon as the model becoming static, or model stasis. Here, we aim to quantify how the nature of the data and the choice of model parameters affect the model's ability to detect temporal changes in FC using both simulated fMRI time courses and resting state fMRI data. We show that large between-subject FC differences can overwhelm subtler within-session modulations, causing the model to become static. Further, the choice of parcellation can also affect the model's ability to detect temporal changes. We finally show that the model often becomes static when the number of free parameters per state that need to be estimated is high and the number of observations available for this estimation is low in comparison. Based on these findings, we derive a set of practical recommendations for time-varying FC studies, in terms of preprocessing, parcellation and complexity of the model.

Predicting behavior through dynamic modes in resting-state fMRI data

Dynamic properties of resting-state functional connectivity (FC) provide rich information on brain-behavior relationships. Dynamic mode decomposition (DMD) has been used as a method to characterize FC dynamics. However, it remains unclear whether dynamic modes (DMs), spatial-temporal coherent patterns computed by DMD, provide information about individual behavioral differences. This study established a methodological approach to predict individual differences in behavior using DMs. Furthermore, we investigated the contribution of DMs within each of seven specific frequency bands (0-0.1,...,0.6-0.7 Hz) for prediction. To validate our approach, we tested whether each of 59 behavioral measures could be predicted by performing multivariate pattern analysis on a Gram matrix, which was created using subject-specific DMs computed from resting-state functional magnetic resonance imaging (rs-fMRI) data of individuals. DMD successfully predicted behavior and outperformed temporal and spatial independent component analysis, which is the conventional data decomposition method for extracting spatial activity patterns. Most of the behavioral measures that were predicted with significant accuracy in a permutation test were related to cognition. We found that DMs within frequency bands <0.2 Hz primarily contributed to prediction and had spatial structures similar to several common resting-state networks. Our results indicate that DMD is efficient in extracting spatiotemporal features from rs-fMRI data.

Analysis of ECG Signals by Dynamic Mode Decomposition

OBJECTIVE

Based on cybernetics, a large system can be divided into subsystems, and the stability of each can determine the overall properties of the system. However, this stability analysis perspective has not yet been employed in electrocardiogram (ECG) signals. This is the first study to attempt to evaluate whether the stability of decomposed ECG subsystems can be analyzed in order to effectively investigate the overall performance of ECG signals, and aid in disease diagnosis.

METHODS

We used seven different cardiac pathologies (myocardial infarction, cardiomyopathy, bundle branch block, dysrhythmia, hypertrophy, myocarditis, and valvular heart disease) to illustrate our method. Dynamic mode decomposition (DMD) was first used to decompose ECG signals into dynamic modes (DMs) which can be regarded as ECG subsystems. Then, the features related to the DMs stabilities were extracted, and nine common classifiers were implemented for classification of these pathologies.

RESULTS

Most features were significant for differentiating the above-mentioned groups (value<0.05 after Bonferroni correction). In addition, our method outperformed all existing methods for cardiac pathology classification.

CONCLUSION

We have provided a new spatial and temporal decomposition method, namely DMD, to study ECG signals.

SIGNIFICANCE

Our method can reveal new cardiac mechanisms, which can contribute to the comprehensive understanding of its underlying mechanisms and disease diagnosis, and thus, can be widely used for ECG signal analysis in the future.

Electrophysiological signatures of dedifferentiation differ between fit and less fit older adults

Cardiorespiratory fitness was found to influence age-related changes of resting state brain network organization. However, the influence on dedifferentiated involvement of wider and more unspecialized brain regions during task completion is barely understood. We analyzed EEG data recorded during rest and different tasks (sensory, motor, cognitive) with dynamic mode decomposition, which accounts for topological characteristics as well as temporal dynamics of brain networks. As a main feature the dominant spatio-temporal EEG pattern was extracted in multiple frequency bands per participant. To deduce a pattern’s stability, we calculated its proportion of total variance among all activation patterns over time for each task. By comparing fit (N = 15) and less fit older adults (N = 16) characterized by their performance on a 6-min walking test, we found signs of a lower task specificity of the obtained network features for the less fit compared to the fit group. This was indicated by fewer significant differences between tasks in the theta and high beta frequency band in the less fit group. Repeated measures ANOVA revealed that a significantly lower proportion of total variance can be explained by the main pattern in high beta frequency range for the less fit compared to the fit group [F(1,29) = 12.572, p = .001, partial η² = .300]. Our results indicate that the dedifferentiation in task-related brain activation is lower in fit compared to less fit older adults. Thus, our study supports the idea that cardiorespiratory fitness influences task-related brain network organization in different task domains.

Modeling brain connectivity dynamics in functional magnetic resonance imaging via particle filtering

Interest in the studying of functional connections in the brain has grown considerably in the last decades, as many studies have pointed out that alterations in the interaction among brain areas can play a role as markers of neurological diseases. Most studies in this field treat the brain network as a system of connections stationary in time, but dynamic features of brain connectivity can provide useful information, both on physiology and pathological conditions of the brain. In this paper, we propose the application of a computational methodology, named Particle Filter (PF), to study non-stationarities in brain connectivity in functional Magnetic Resonance Imaging (fMRI). The PF algorithm estimates time-varying hidden parameters of a first-order linear time-varying Vector Autoregressive model (VAR) through a Sequential Monte Carlo strategy. On simulated time series, the PF approach effectively detected and enabled to follow time-varying hidden parameters and it captured causal relationships among signals. The method was also applied to real fMRI data, acquired in presence of periodic tactile or visual stimulations, in different sessions. On these data, the PF estimates were consistent with current knowledge on brain functioning. Most importantly, the approach enabled to detect statistically significant modulations in the cause-effect relationship between brain areas, which correlated with the underlying visual stimulation pattern presented during the acquisition.

Delineating between-subject heterogeneity in alpha networks with Spatio-Spectral Eigenmodes

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A data-driven modal decomposition describes oscillations by their resonant frequency, damping time and network structure.

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We show that the full multivariate transfer function can be rewritten as a linear superposition of these modes.

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These modal coordinates factorise oscillatory systems without pre-specification of frequency bands or regions of interest.

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Using these modes, we find a spatial gradient in alpha peak frequency between Occipital and Parietal cortex .

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This gradient is highly variable between participants, showing shifts in spatial structure and peak frequency.

Between subject variability in the spatial and spectral structure of oscillatory networks can be highly informative but poses a considerable analytic challenge. Here, we describe a data-driven modal decomposition of a multivariate autoregressive model that simultaneously identifies oscillations by their peak frequency, damping time and network structure. We use this decomposition to define a set of Spatio-Spectral Eigenmodes (SSEs) providing a parsimonious description of oscillatory networks. We show that the multivariate system transfer function can be rewritten in these modal coordinates, and that the full transfer function is a linear superposition of all modes in the decomposition. The modal transfer function is a linear summation and therefore allows for single oscillatory signals to be isolated and analysed in terms of their spectral content, spatial distribution and network structure. We validate the method on simulated data and explore the structure of whole brain oscillatory networks in eyes-open resting state MEG data from the Human Connectome Project. We are able to show a wide between participant variability in peak frequency and network structure of alpha oscillations and show a distinction between occipital ’high-frequency alpha’ and parietal ’low-frequency alpha’. The frequency difference between occipital and parietal alpha components is present within individual participants but is partially masked by larger between subject variability; a 10Hz oscillation may represent the high-frequency occipital component in one participant and the low-frequency parietal component in another. This rich characterisation of individual neural phenotypes has the potential to enhance analyses into the relationship between neural dynamics and a person’s behavioural, cognitive or clinical state.

Dynamics of task-related electrophysiological networks: a benchmarking study

Motor, sensory and cognitive functions rely on dynamic reshaping of functional brain networks. Tracking these rapid changes is crucial to understand information processing in the brain, but challenging due to the great variety of dimensionality reduction methods used at the network-level and the limited evaluation studies. Using Magnetoencephalography (MEG) combined with Source Separation (SS) methods, we present an integrated framework to track fast dynamics of electrophysiological brain networks. We evaluate nine SS methods applied to three independent MEG databases (N=95) during motor and memory tasks. We report differences between these methods at the group and subject level. We seek to help researchers in choosing objectively the appropriate SS method when tracking fast reconfiguration of functional brain networks, due to its enormous benefits in cognitive and clinical neuroscience.

Differential contributions of static and time-varying functional connectivity to human behavior

Measures of human brain functional connectivity acquired during the resting-state track critical aspects of behavior. Recently, fluctuations in resting-state functional connectivity patterns-typically averaged across in traditional analyses-have been considered for their potential neuroscientific relevance. There exists a lack of research on the differences between traditional "static" measures of functional connectivity and newly considered "time-varying" measures as they relate to human behavior. Using functional magnetic resonance imagining (fMRI) data collected at rest, and a battery of behavioral measures collected outside the scanner, we determined the degree to which each modality captures aspects of personality and cognitive ability. Measures of time-varying functional connectivity were derived by fitting a hidden Markov model. To determine behavioral relationships, static and time-varying connectivity measures were submitted separately to canonical correlation analysis. A single relationship between static functional connectivity and behavior existed, defined by measures of personality and stable behavioral features. However, two relationships were found when using time-varying measures. The first relationship was similar to the static case. The second relationship was unique, defined by measures reflecting trialwise behavioral variability. Our findings suggest that time-varying measures of functional connectivity are capable of capturing unique aspects of behavior to which static measures are insensitive.

Unraveling reproducible dynamic states of individual brain functional parcellation

Data-driven parcellations are widely used for exploring the functional organization of the brain, and also for reducing the high dimensionality of fMRI data. Despite the flurry of methods proposed in the literature, functional brain parcellations are not highly reproducible at the level of individual subjects, even with very long acquisitions. Some brain areas are also more difficult to parcellate than others, with association heteromodal cortices being the most challenging. An important limitation of classical parcellations is that they are static, that is, they neglect dynamic reconfigurations of brain networks. In this paper, we proposed a new method to identify dynamic states of parcellations, which we hypothesized would improve reproducibility over static parcellation approaches. For a series of seed voxels in the brain, we applied a cluster analysis to regroup short (3 min) time windows into "states" with highly similar seed parcels. We split individual time series of the Midnight scan club sample into two independent sets of 2.5 hr (test and retest). We found that average within-state parcellations, called stability maps, were highly reproducible (over 0.9 test-retest spatial correlation in many instances) and subject specific (fingerprinting accuracy over 70% on average) between test and retest. Consistent with our hypothesis, seeds in heteromodal cortices (posterior and anterior cingulate) showed a richer repertoire of states than unimodal (visual) cortex. Taken together, our results indicate that static functional parcellations are incorrectly averaging well-defined and distinct dynamic states of brain parcellations. This work calls to revisit previous methods based on static parcellations, which includes the majority of published network analyses of fMRI data. Our method may, thus, impact how researchers model the rich interactions between brain networks in health and disease.

Revisiting correlation-based functional connectivity and its relationship with structural connectivity

Patterns of brain structural connectivity (SC) and functional connectivity (FC) are known to be related. In SC-FC comparisons, FC has classically been evaluated from correlations between functional time series, and more recently from partial correlations or their unnormalized version encoded in the precision matrix. The latter FC metrics yield more meaningful comparisons to SC because they capture ‘direct’ statistical dependencies, that is, discarding the effects of mediators, but their use has been limited because of estimation issues. With the rise of high-quality and large neuroimaging datasets, we revisit the relevance of different FC metrics in the context of SC-FC comparisons. Using data from 100 unrelated Human Connectome Project subjects, we first explore the amount of functional data required to reliably estimate various FC metrics. We find that precision-based FC yields a better match to SC than correlation-based FC when using 5 minutes of functional data or more. Finally, using a linear model linking SC and FC, we show that the SC-FC match can be used to further interrogate various aspects of brain structure and function such as the timescales of functional dynamics in different resting-state networks or the intensity of anatomical self-connections.

A naturalistic neuroimaging database for understanding the brain using ecological stimuli

Neuroimaging has advanced our understanding of human psychology using reductionist stimuli that often do not resemble information the brain naturally encounters. It has improved our understanding of the network organization of the brain mostly through analyses of 'resting-state' data for which the functions of networks cannot be verifiably labelled. We make a 'Naturalistic Neuroimaging Database' (NNDb v1.0) publically available to allow for a more complete understanding of the brain under more ecological conditions during which networks can be labelled. Eighty-six participants underwent behavioural testing and watched one of 10 full-length movies while functional magnetic resonance imaging was acquired. Resulting timeseries data are shown to be of high quality, with good signal-to-noise ratio, few outliers and low movement. Data-driven functional analyses provide further evidence of data quality. They also demonstrate accurate timeseries/movie alignment and how movie annotations might be used to label networks. The NNDb can be used to answer questions previously unaddressed with standard neuroimaging approaches, progressing our knowledge of how the brain works in the real world.

Organization of Propagated Intrinsic Brain Activity in Individual Humans

Spontaneous infra-slow (<0.1 Hz) fluctuations in functional magnetic resonance imaging (fMRI) signals are temporally correlated within large-scale functional brain networks, motivating their use for mapping systems-level brain organization. However, recent electrophysiological and hemodynamic evidence suggest state-dependent propagation of infra-slow fluctuations, implying a functional role for ongoing infra-slow activity. Crucially, the study of infra-slow temporal lag structure has thus far been limited to large groups, as analyzing propagation delays requires extensive data averaging to overcome sampling variability. Here, we use resting-state fMRI data from 11 extensively-sampled individuals to characterize lag structure at the individual level. In addition to stable individual-specific features, we find spatiotemporal topographies in each subject similar to the group average. Notably, we find a set of early regions that are common to all individuals, are preferentially positioned proximal to multiple functional networks, and overlap with brain regions known to respond to diverse behavioral tasks-altogether consistent with a hypothesized ability to broadly influence cortical excitability. Our findings suggest that, like correlation structure, temporal lag structure is a fundamental organizational property of resting-state infra-slow activity.

Resting brain dynamics at different timescales capture distinct aspects of human behavior

Linking human behavior to resting-state brain function is a central question in systems neuroscience. In particular, the functional timescales at which different types of behavioral factors are encoded remain largely unexplored. The behavioral counterparts of static functional connectivity (FC), at the resolution of several minutes, have been studied but behavioral correlates of dynamic measures of FC at the resolution of a few seconds remain unclear. Here, using resting-state fMRI and 58 phenotypic measures from the Human Connectome Project, we find that dynamic FC captures task-based phenotypes (e.g., processing speed or fluid intelligence scores), whereas self-reported measures (e.g., loneliness or life satisfaction) are equally well explained by static and dynamic FC. Furthermore, behaviorally relevant dynamic FC emerges from the interconnections across all resting-state networks, rather than within or between pairs of networks. Our findings shed new light on the timescales of cognitive processes involved in distinct facets of behavior.