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Theme 1 Statistical techniques to investigate dynamic functional activity
9:00 AM Introduction
9:05 AM Robustness of connectome harmonics to local gray matter and long-range white matter connectivity changes
Sebastian Naze (QIMR Berghofer, Brisbane, Australia)
Recently, it has been proposed that the harmonic patterns emerging from the brain's structural connectivity underlie the resting state networks of the human brain. These harmonic patterns, termed connectome harmonics, are estimated as the Laplace eigenfunctions of the combined gray and white matters connectivity matrices and yield a connectome-specific extension of the well-known Fourier basis. However, it remains unclear how topological properties of the combined connectomes constrain the precise shape of the connectome harmonics and their relationships to the resting state networks. Here, we systematically study how alterations of the local and long-range connectivity matrices affect the spatial patterns of connectome harmonics. Specifically, the proportion of local gray matter homogeneous connectivity versus long-range white-matter heterogeneous connectivity is varied by means of weight-based matrix thresholding, distance-based matrix trimming, and several types of matrix randomizations. We demonstrate that the proportion of local gray matter connections plays a crucial role for the emergence of wide-spread, functionally meaningful, and originally published connectome harmonic patterns. This finding is robust for several different cortical surface templates, mesh resolutions, or widths of the local diffusion kernel. Finally, using the connectome harmonic framework, we also provide a proof-of-concept for how targeted structural changes such as the atrophy of inter-hemispheric callosal fibers and gray matter alterations may predict functional deficits associated with neurodegenerative conditions.
9:30 AM Harmonic modes and the structure-function relationship in fast network dynamics
Katharina Glomb (Lausanne University Hospital and University of Lausanne (CHUV-UNIL), Lausanne, Switzerland)
Tracking fast changes in macroscopic network activity is still a challenge in EEG because of low SNR and the effects of volume conduction. We took a multimodal approach to this problem and combined source-reconstructed EEG with the structural connectome. We obtained "building blocks" from the connectome using basic tools from graph signal processing, and then analyzed EEG activity in terms of these building blocks. We found that this approach provides a sparse basis for the EEG signal which is statistically powerful and highly interpretable. I will also take the opportunity to discuss new directions towards which our results may point.
9:55 AM Probing structure-function coupling of brain organization with graph signal processing
Dimitri Van De Ville (Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland)
State-of-the-art magnetic resonance imaging (MRI) provides unprecedented opportunities to study brain structure (anatomy) and function (physiology). Based on such data, graph representations can be built where nodes are associated to brain regions and edge weights to strengths of structural or functional connections. In particular, structural graphs capture major neural pathways in white matter, while functional graphs map out statistical interdependencies between pairs of regional activity traces. Network analysis of these graphs has revealed emergent system-level properties of brain structure or function, such as efficiency of communication and modular organization.
In this talk, graph signal processing (GSP) will be presented as a novel framework to integrate brain structure, contained in the structural graph, with brain function, characterized by activity traces that can be considered as time-dependent graph signals. Such a perspective allows to define novel meaningful graph-filtering operations of brain activity that take into account smoothness of signals on the anatomical backbone. This allows to define a new measure of “coupling” between structure and function based on how activity is expressed on structural graph harmonics. To provide statistical inference, we also extend the well-known Fourier phase randomization method to generate surrogate data to the graph setting. This new measure reveals a behaviorally relevant spatial gradient, where sensory regions tend to be more coupled with structure, and high-level cognitive ones less so. Finally, recent work will highlight how the spatial resolution of this type of analyses can be increased to the voxel level, representing a few hundredth thousands of nodes.
10:20 AM Time-varying Dynamic Network Model For Dynamic Resting State Functional Connectivity in fMRI and MEG imaging
Fei Jiang (University of California San Francisco, USA)
Dynamic resting state functional connectivity (RSFC) characterizes fluctuations that occur over time in functional brain networks. Existing methods to extract dynamic RSFCs include sliding-window and clustering methods with various limitations due to its inherent non-adaptive nature and high-dimensionality including an inability to reconstruct brain signals, insufficiency of data for reliable estimation, insensitivity to rapid changes in dynamics, and a lack of generalizability across multi-modal functional imaging datasets. To overcome these deficiencies, we develop a novel and unifying time-varying dynamic network (TVDN) framework for examining dynamic resting state functional connectivity. TVDN includes a generative model that de- scribes the relation between low-dimensional dynamic RSFC and the brain signals, and an inference algorithm that automatically and adaptively learns to detect dynamic state transitions in data and a low-dimensional manifold of dynamic RSFC. TVDN is generalizable to handle multimodal functional neuroimaging data (fMRI and MEG/EEG). The resulting estimated low-dimensional dynamic RSFCs manifold directly link to the brain signal frequencies, and we can evaluate TVDN performance by examining whether learnt features can reconstruct observed brain signals. We conduct comprehensive simulations to evaluate TVDN under hypothetical settings. We then demonstrate the application of TVDN with real fMRI and MEG data and compare the results with the existing benchmarks. Results demonstrate that TVDN is able to detect brain state switching more robustly both in resting state fMRI and MEG data.
10:45 AM Time-varying Paths in Functional Network Connectivity with Application to Schizophrenia
Haleh Falakshahi (Georgia Institute of Technology, USA)
Introduction A brain network is a model composed of a set of brain regions as nodes connected through a set of edges measuring brain interactions. The advances in computational tools of modern network science and graph theory have played an important role in understanding human brain networks in cognition and psychiatric disorders. However, our understanding of the mechanisms underlying sophisticated and complex human brain function still remains incomplete. In this study, by applying graph theoretical analysis methods, we propose a method to study altered pathways in time-varying brain graphs of patient group to identify possible path-based biomarkers from resting-state fMRI data.
Method We first propose a method to estimate dynamic brain graphs from resting-state fMRI data. We apply a combination of spatial independent component analysis (ICA), sliding time window, k-means clustering of windowed correlation matrices, and a Gaussian graphical model estimation within each cluster. Next, we analyze paths on the dynamic graphs of control and patient groups. Using the concept of the connected component in graph theory we provide an algorithm to estimate edges associated with missing and additional paths in dynamic patient group graphs with reference to the graphs of the control group. In addition, we examine paths that are in common across groups. To this end, we propose the use of a covariance decomposition method in a Gaussian graphical model to obtain the correlation weights for each path between pairs of brain components.
Results We analyzed eye-closed resting-state fMRI from 311 subjects, 151 with schizophrenia (SZ). We selected 53 out of 100 as ICNs for further analysis and categorized them into seven functional domains. The optimal number of clusters was determined to be five for k-means clustering. In group difference evaluations, the number of significant FDR corrected values (p<0.05) were 16 for State 1, 44 for State 2, 19 for State 3, 37 for State 4, and 30 for State 5. Results showed 14 missing edges and 16 additional edges associated with missing and additional paths respectively in SZ group across all states that were within and between functional domains, particularly within the default mode network and cognitive control domains. Examination of common paths across group showed that in some cases these paths take unique trajectories, and covariance decomposition approach assigns significant weight to those distinct paths.
Conclusion In this study, we analyzed paths in an estimated time-varying Gaussian graphical model from resting-state fMRI data and proposed an algorithm to estimate edges associated with altered pathways in individuals with mental disorders. Our proposed algorithm identified several missing edges associated with missing paths in SZ, particularly within the default mode network and cognitive control domains. Moreover, our algorithm detected additional edges associated with additional paths in the SZ group which may be related to a compensatory response that needs future study. Also, a path weight analysis revealed in some cases that paths exist between pairs of brain component in both group, these paths take unique trajectories and covariance decomposition showed those paths have significant weight. Thus, the proposed method showed promise for identifying possible path-based biomarkers of psychiatric disorders.
11:10 AM Bayesian reconstruction of canonical brain networks from MEG data
Srikantan Nagarajan (University of California San Francisco, USA)
Many studies have characterized canonical structural and functional brain networks using diffusion MRI and functional MRI respectively, and the integrity of these networks are associated with cognition in health and disease. Neural oscillatory spectra corresponding to these canonical networks remain unknown, as there have not been clear methods to reconstruct network brain activity from MEG or EEG data. We have developed an integrated machine learning Bayesian inference framework to reconstruct brain network activity from MEG/EEG data. We directly estimate activity in canonical networks, either functional ones based on fMRI or structural ones based on diffusion MRI or both. Importantly, we leverage our recent work on sparse Bayesian inference of signal and noise subspaces in MEG/EEG data, by specifically accounting for different types of structured interference arising at the sensors, or from network independent activity at voxel or regional levels. We evaluated algorithm performance in simulations and real data, and provide benchmark comparisons (sLORETA and LCMV beamformer) of indirect estimation of network activity from voxel or regional-level source reconstructions. Accounting for the different sources of interference enables a more robust estimation of brain network activity and cross-network functional connectivity both in simulations and in real data. Reconstruction of resting-state functional networks in patients with Alzheimer’s disease (AD) and controls show clear alterations in network activity spectra in AD. In summary, we demonstrate a robust Bayesian network reconstruction framework for EEG and MEG data that enables investigating canonical brain network spectra at electrophysiological timescales and demonstrates the clinical translational potential of this approach.
11:35 AM Deep Linear Models for Mapping the Hierarchical Organization of Functional Connectivity in the Human Brain
Pratik Mukherjee (University of California San Francisco, USA)
The human brain exhibits hierarchical modular organization, which has not yet been depicted by conventional functional magnetic resonance imaging (fMRI) connectivity reconstruction methods. To map spatially hierarchical brain connectivity networks (BCNs), we propose novel deep (multilayer stacked) linear models that are constructed to decompose the features of the preceding layer. We present a novel deep linear model, Deep Matrix Fitting (MF), which incorporates a rank reduction technique for data-driven hyperparameter determination. Moreover, we introduce a novel framework for theoretical and experimental comparison of Deep MF with multilayer variants of Sparse Dictionary Learning (SDL), Non-Negative Matrix Factorization (NMF) and Fast Independent Component Analysis (FICA), based on their combination of mathematical operators, the predictions of which are validated using resting-state fMRI data with known ground truth BCNs. Deep MF provided the best overall performance, including reconstruction error and extraction of high-level BCNs. Compared with the other three deep linear models, Deep MF efficiently maps hierarchical BCNs without requiring the manual hyperparameter tuning, extensive fMRI training data or high-performance computing infrastructure needed by deep nonlinear networks (DNNs), such as convolutional neural networks (CNNs) or deep belief networks (DBNs), and their results are also more explainable from their mathematical structure. This proposed new model may advance the development of fMRI diagnostic and prognostic biomarkers, given the recent recognition of disparities between low-level vs high-level network connectivity across a wide range of neurological and psychiatric disorders.
12:00 PM Panel discussion
Organizers
12:15 PM Break
Theme 2 Mathematical modeling of dynamic functional activity
2:00 PM Introduction
2:05 PM Multiscale modeling from molecule to BOLD
Bill Lytton (SUNY Downstate Medical Center, USA)
The complexity of the brain requires multiple approaches in order to capture scales that range from the molecular scale of pharmaceuticals and neurotransmitters up to the whole region scale of fMRI or PET and even whole brain scales for cognition and behavior. Additionally one would wish to consider temporal scales from the millisecond of the action potential up to the years of brain maturation and, at the other end of life, brain degeneration. In addition to requiring multiscale modeling, these connections also require us to do multiphysics modeling and multi-algorithmic modeling. I will present some of our preliminary efforts to connect scales, physics and algorithms, demonstrating where some of the gaps are and how they might be bridged.
2:30 PM Neuronal cascades shape whole-brain functional dynamics at rest
Giovanni Rabuffo (Institut de Neurosciences des Systemes - Aix-Marseille University)
Functional connectivity and its dynamics are widely used as proxy of brain function and dysfunction. Their neuronal underpinnings remain unclear. Using full-brain network modeling, we show that neuronal cascades spontaneously emerge on a slow timescale when neuronal populations are coupled via a detailed structural connectome. Neuronal cascades occur under conditions of near-criticality and are characterized by epochs of increased deviations from baseline firing rate activity. The ignition and subsequent propagation of cascades depend upon the brain state and connectivity of each region. The largest cascades produce bursts of Blood-Oxygen-Level-Dependent (BOLD) co-fluctuations at pairs of regions across the brain, which shape resting state network dynamics. We experimentally confirm these theoretical predictions. We demonstrate the existence and stability of intermittent epochs of functional connectivity comprising BOLD co-activation bursts in mice. We then provide evidence for the leading role of the neuronal cascades in humans with simultaneous EEG/fMRI recordings. These results show that neuronal cascades are a major determinant of spontaneous fluctuations in brain dynamics at rest.
2:55 PM Predicting time-resolved brain networks from structural eigenmodes and applications to disorders of consciousness
Prejaas Tewarie (Vrije Universiteit Amsterdam, the Netherlands)
How temporal modulations in functional interactions are shaped by the underlying anatomical connections remains an open question. Here, we analyse the role of ‘hidden’ spatial connection patterns, so called structural eigenmodes, in the formation and dissolution of temporally evolving functional brain networks using resting-state magnetoencephalography and diffusion MRI data at the individual subject level. Our results show that even at short timescales, phase and amplitude connectivity can partly be expressed by structural eigenmodes, but hardly by direct structural connections. Eigenmode expression is related to overall cognitive performance and co-occurs with fluctuations in community structure of functional networks. These results implicate that ongoing time-resolved resting-state networks, even at short timescales, can to some extent be understood in terms of activation and deactivation of structural eigenmodes and play a role in the dynamic integration and segregation of information across the cortex, subserving cognitive functions. We further apply this approach to functional MRI data in disorders of consciousness. We demonstrate a loss of metastability and the functional network repertoire in disorders of consciousness, which co-occurred with a loss of dynamic interplay with structural eigenmodes.
3:20 PM A biophysical spectral graph theory-based model of brain oscillations
Parul Verma and Ashish Raj (University of California San Francisco, USA)
Understanding the relationship between the functional activity and the structural wiring of the brain is an important question in neuroscience. To address this, various mathematical modeling approaches have been undertaken in the past, which largely consisted of non-linear and biophysically detailed mathematical models with regionally varying model parameters. While such models provide us a rich repertoire of dynamics that can be displayed by the brain, they are computationally demanding. Moreover, although neuronal dynamics at the microscopic level are nonlinear and chaotic, it is unclear if such detailed nonlinear models are required to capture the emergent meso- (regional population ensemble) and macro-scale (whole brain) behavior, which is largely deterministic and reproducible across individuals. Indeed, recent modeling effort based on spectral graph theory has shown that a linear and analytical model without regionally varying parameters can capture the empirical magnetoencephalography frequency spectra and the spatial patterns of the alpha and beta frequency bands accurately.
In this work, we explore the properties of an improved hierarchical, linearized, and analytic spectral graph theory-based model that can capture the frequency spectra obtained from magnetoencephalography recordings. The model consists of coupled excitatory and inhibitory dynamics of the neural ensembles for every brain region, and white-matter structural wiring-based long-range excitatory macroscopic dynamics. We demonstrate that this model, with just a parsimonious set of global and biophysically interpretable model parameters, can display frequency-rich spectra. In particular, we show that even without any oscillations on the regional level, the macroscopic model alone can exhibit oscillations with a frequency in the alpha band. We also show that depending on the parameters, the model can exhibit damped oscillations, limit cycles, or unstable oscillations that blow up with time. We further determined bounds on these parameters to ensure stability of the modeled oscillations. These biophysically interpretable model parameters can be employed to investigate correlates of differences in frequency spectra observed in different brain states and neurological diseases.
3:45 PM Dynamic Functional Connectivity, Neuromodulatory switches and the Network Organization of Human connectome
Patricio Orio (Universidad de Valparaíso, Valparaíso, Chile)
Brain activity, as observed by large-scale recording techniques, is characterized by a rich dynamical repertoire. Either in resting state or while performing a task, the patterns of activity and synchrony between different areas are constantly shifting. This allows the brain to dynamically adjust itself to different environmental demands, explore new configurations, and accordingly shift the balance between segregation and integration of information processing. The structural and dynamical factors that allow this dynamical richness are subject of active research with the use of computational models, which bring together the empirical connectivity obtained from DTI resonance in humans (or others), and the biophysically-inspired dynamics of brain areas. Using this approach, we have been dissecting the structural motifs of the human connectome that best permit the existence of multistable dynamics and the modulation of the integration/segregation balance by neuromodulatory systems.
We have shown that the large-scale structural connectivity found in the brain, has a unique core-shell organization that maximizes a graded activation of areas, which is not achieved by random surrogate connectomes. Consequently, the brain is allowed to show more intermediate (less integrated) activated configurations. When the transitions between integrated and segregated states is promoted by neuromodulators, our simulations suggest that the best targets to promote a global transition are the nodes belonging to the rich club, or the nodes with the highest connection weights. Interestingly, these two subsets overlap only partially. Our results deliver interesting facts about how the structural motifs and features, at the local and global scales, can enable and promote a richer dynamical repertoire for the brain function.
This work has been supported by Fondecyt Grants 1181076 and 11181072, the Advanced Center for Electrical and Electronic Engineering (ANID FB0008), and ANID—Millennium Science Initiative Program ICN09-022 (Centro Interdisciplinario de Neurociencia de Valparaíso CINV). CC-O is funded by Beca Doctorado Nacional ANID 2018-21180995.
4:10 PM Understanding Excitation-Inhibition Balance: A Maximum Entropy Model to Unify Brain Structure and Function
Alex Leow (University of Illinois at Chicago, USA)
Neural activity coordinated across different scales from neuronal circuits to large-scale brain networks gives rise to complex cognitive functions. Bridging the gap between micro- and macro-scale processes, we present a novel framework based on the Maximum Entropy model to infer a resting state structural connectome, which represents functional interactions constrained by structural connectivity. We demonstrate that the structurally informed network outperforms the unconstrained model in simulating brain dynamics and traditional measures of functional connectivity. Further, we evaluate magnetization, susceptibility and by extension criticality to probe connectome-level excitation-inhibition balance in cognitively intact middle-aged apolipoprotein E (APOE) ε4 carriers and noncarriers. Criticality differences in female carriers suggest a global shift to a more disordered state. In sum, this new multimodal network allows for analysis of brain dynamics beyond the confines of traditional or unimodal methods, providing insight into the complex interactions underpinning neural function such as the balance of excitation and inhibition.
4:35 PM Parcels and particles: Markov blankets in the brain
Adeel Razi (Monash University, Australia)
At the inception of human brain mapping, two principles of functional anatomy underwrote most conceptions—and analyses—of distributed brain responses: namely, functional segregation and integration. There are currently two main approaches to characterizing functional integration. The first is a mechanistic modeling of connectomics in terms of directed effective connectivity that mediates neuronal message passing and dynamics on neuronal circuits. The second phenomenological approach usually characterizes undirected functional connectivity (i.e., measurable correlations), in terms of intrinsic brain networks, self-organized criticality, dynamical instability, and so on. This paper describes a treatment of effective connectivity that speaks to the emergence of intrinsic brain networks and critical dynamics. It is predicated on the notion of Markov blankets that play a fundamental role in the self-organization of far from equilibrium systems. Using the apparatus of the renormalization group, we show that much of the phenomenology found in network neuroscience is an emergent property of a particular partition of neuronal states, over progressively coarser scales. As such, it offers a way of linking dynamics on directed graphs to the phenomenology of intrinsic brain networks.
5:00 PM Panel discussion
Organizers
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