Pairwise maximum entropy model explains the role of white matter structure in shaping emergent co-activation states

Spontaneous Brain Activity Emerges from Pairwise Interactions in the Larval Zebrafish Brain

Brain activity is characterized by brainwide spatiotemporal patterns that emerge from synapse-mediated interactions between individual neurons. Calcium imaging provides access to in vivo recordings of whole-brain activity at single-neuron resolution and, therefore, allows the study of how large-scale brain dynamics emerge from local activity. In this study, we use a statistical mechanics approach-the pairwise maximum entropy model-to infer microscopic network features from collective patterns of activity in the larval zebrafish brain and relate these features to the emergence of observed whole-brain dynamics. Our findings indicate that the pairwise interactions between neural populations and their intrinsic activity states are sufficient to explain observed whole-brain dynamics. In fact, the pairwise relationships between neuronal populations estimated with the maximum entropy model strongly correspond to observed structural connectivity patterns. Model simulations also demonstrated how tuning pairwise neuronal interactions drives transitions between observed physiological regimes and pathologically hyperexcitable whole-brain regimes. Finally, we use virtual resection to identify the brain structures that are important for maintaining the brain in a physiological dynamic regime. Together, our results indicate that whole-brain activity emerges from a complex dynamical system that transitions between basins of attraction whose strength and topology depend on the connectivity between brain areas.

A Dynamic Entropy Approach Reveals Reduced Functional Network Connectivity Trajectory Complexity in Schizophrenia

Over the past decade and a half, dynamic functional imaging has revealed low-dimensional brain connectivity measures, identified potential common human spatial connectivity states, tracked the transition patterns of these states, and demonstrated meaningful transition alterations in disorders and over the course of development. Recently, researchers have begun to analyze these data from the perspective of dynamic systems and information theory in the hopes of understanding how these dynamics support less easily quantified processes, such as information processing, cortical hierarchy, and consciousness. Little attention has been paid to the effects of psychiatric disease on these measures, however. We begin to rectify this by examining the complexity of subject trajectories in state space through the lens of information theory. Specifically, we identify a basis for the dynamic functional connectivity state space and track subject trajectories through this space over the course of the scan. The dynamic complexity of these trajectories is assessed along each dimension of the proposed basis space. Using these estimates, we demonstrate that schizophrenia patients display substantially simpler trajectories than demographically matched healthy controls and that this drop in complexity concentrates along specific dimensions. We also demonstrate that entropy generation in at least one of these dimensions is linked to cognitive performance. Overall, the results suggest great value in applying dynamic systems theory to problems of neuroimaging and reveal a substantial drop in the complexity of schizophrenia patients' brain function.

Diagnostically distinct resting state fMRI energy distributions: A subject-specific maximum entropy modeling study

Objective

Existing neuroimaging studies of psychotic and mood disorders have reported brain activation differences (first-order properties) and altered pairwise correlation-based functional connectivity (second-order properties). However, both approaches have certain limitations that can be overcome by integrating them in a pairwise maximum entropy model (MEM) that better represents a comprehensive picture of fMRI signal patterns and provides a system-wide summary measure called energy. This study examines the applicability of individual-level MEM for psychiatry and identifies image-derived model coefficients related to model parameters.

Method

MEMs are fit to resting state fMRI data from each individual with schizophrenia/schizoaffective disorder, bipolar disorder, and major depression (n=132) and demographically matched healthy controls (n=132) from the UK Biobank to different subsets of the default mode network (DMN) regions.

Results

The model satisfactorily explained observed brain energy state occurrence probabilities across all participants, and model parameters were significantly correlated with image-derived coefficients for all groups. Within clinical groups, averaged energy level distributions were higher in schizophrenia/schizoaffective disorder but lower in bipolar disorder compared to controls for both bilateral and unilateral DMN. Major depression energy distributions were higher compared to controls only in the right hemisphere DMN.

Conclusions

Diagnostically distinct energy states suggest that probability distributions of temporal changes in synchronously active nodes may underlie each diagnostic entity. Subject-specific MEMs allow for factoring in the individual variations compared to traditional group-level inferences, offering an improved measure of biologically meaningful correlates of brain activity that may have potential clinical utility.

The role of elasticity on adhesion and clustering of neurons on soft surfaces

The question of whether material stiffness enhances cell adhesion and clustering is still open to debate. Results from the literature are seemingly contradictory, with some reports illustrating that adhesion increases with surface stiffness and others suggesting that the performance of a system of cells is curbed by high values of elasticity. To address the role of elasticity as a regulator in neuronal cell adhesion and clustering, we investigated the topological characteristics of networks of neurons on polydimethylsiloxane (PDMS) surfaces - with values of elasticity (E) varying in the 0.55-2.65 MPa range. Results illustrate that, as elasticity increases, the number of neurons adhering on the surface decreases. Notably, the small-world coefficient - a topological measure of networks - also decreases. Numerical simulations and functional multi-calcium imaging experiments further indicated that the activity of neuronal cells on soft surfaces improves for decreasing E. Experimental findings are supported by a mathematical model, that explains adhesion and clustering of cells on soft materials as a function of few parameters - including the Young's modulus and roughness of the material. Overall, results indicate that - in the considered elasticity interval - increasing the compliance of a material improves adhesion, improves clustering, and enhances communication of neurons.

The quality and complexity of pairwise maximum entropy models for large cortical populations

We investigate the ability of the pairwise maximum entropy (PME) model to describe the spiking activity of large populations of neurons recorded from the visual, auditory, motor, and somatosensory cortices. To quantify this performance, we use (1) Kullback-Leibler (KL) divergences, (2) the extent to which the pairwise model predicts third-order correlations, and (3) its ability to predict the probability that multiple neurons are simultaneously active. We compare these with the performance of a model with independent neurons and study the relationship between the different performance measures, while varying the population size, mean firing rate of the chosen population, and the bin size used for binarizing the data. We confirm the previously reported excellent performance of the PME model for small population sizes N < 20. But we also find that larger mean firing rates and bin sizes generally decreases performance. The performance for larger populations were generally not as good. For large populations, pairwise models may be good in terms of predicting third-order correlations and the probability of multiple neurons being active, but still significantly worse than small populations in terms of their improvement over the independent model in KL-divergence. We show that these results are independent of the cortical area and of whether approximate methods or Boltzmann learning are used for inferring the pairwise couplings. We compared the scaling of the inferred couplings with N and find it to be well explained by the Sherrington-Kirkpatrick (SK) model, whose strong coupling regime shows a complex phase with many metastable states. We find that, up to the maximum population size studied here, the fitted PME model remains outside its complex phase. However, the standard deviation of the couplings compared to their mean increases, and the model gets closer to the boundary of the complex phase as the population size grows.

Intracranial EEG Structure-Function Coupling and Seizure Outcomes After Epilepsy Surgery

BACKGROUND AND OBJECTIVES

Surgery is an effective treatment for drug-resistant epilepsy, which modifies the brain's structure and networks to regulate seizure activity. Our objective was to examine the relationship between brain structure and function to determine the extent to which this relationship affects the success of the surgery in controlling seizures. We hypothesized that a stronger association between brain structure and function would lead to improved seizure control after surgery.

METHODS

We constructed functional and structural brain networks in patients with drug-resistant focal epilepsy by using presurgery functional data from intracranial EEG (iEEG) recordings, presurgery and postsurgery structural data from T1-weighted MRI, and presurgery diffusion-weighted MRI. We quantified the relationship (coupling) between structural and functional connectivity by using the Spearman rank correlation and analyzed this structure-function coupling at 2 spatial scales: (1) global iEEG network level and (2) individual iEEG electrode contacts using virtual surgeries. We retrospectively predicted postoperative seizure freedom by incorporating the structure-function connectivity coupling metrics and routine clinical variables into a cross-validated predictive model.

RESULTS

We conducted a retrospective analysis on data from 39 patients who met our inclusion criteria. Brain areas implanted with iEEG electrodes had stronger structure-function coupling in seizure-free patients compared with those with seizure recurrence (p = 0.002, d = 0.76, area under the receiver operating characteristic curve [AUC] = 0.78 [95% CI 0.62-0.93]). Virtual surgeries on brain areas that resulted in stronger structure-function coupling of the remaining network were associated with seizure-free outcomes (p = 0.007, d = 0.96, AUC = 0.73 [95% CI 0.58-0.89]). The combination of global and local structure-function coupling measures accurately predicted seizure outcomes with a cross-validated AUC of 0.81 (95% CI 0.67-0.94). These measures were complementary to other clinical variables and, when included for prediction, resulted in a cross-validated AUC of 0.91 (95% CI 0.82-1.0), accuracy of 92%, sensitivity of 93%, and specificity of 91%.

DISCUSSION

Our study showed that the strength of structure-function connectivity coupling may play a crucial role in determining the success of epilepsy surgery. By quantitatively incorporating structure-function coupling measures and standard-of-care clinical variables into presurgical evaluations, we may be able to better localize epileptogenic tissue and select patients for epilepsy surgery.

CLASSIFICATION OF EVIDENCE

This is a Class IV retrospective case series showing that structure-function mapping may help determine the outcome from surgical resection for treatment-resistant focal epilepsy.

A framework For brain atlases: Lessons from seizure dynamics

Brain maps, or atlases, are essential tools for studying brain function and organization. The abundance of available atlases used across the neuroscience literature, however, creates an implicit challenge that may alter the hypotheses and predictions we make about neurological function and pathophysiology. Here, we demonstrate how parcellation scale, shape, anatomical coverage, and other atlas features may impact our prediction of the brain's function from its underlying structure. We show how network topology, structure-function correlation (SFC), and the power to test specific hypotheses about epilepsy pathophysiology may change as a result of atlas choice and atlas features. Through the lens of our disease system, we propose a general framework and algorithm for atlas selection. This framework aims to maximize the descriptive, explanatory, and predictive validity of an atlas. Broadly, our framework strives to provide empirical guidance to neuroscience research utilizing the various atlases published over the last century.

Inferring excitation-inhibition dynamics using a maximum entropy model unifying brain structure and function

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 macroscale processes, we present a novel framework based on the maximum entropy model to infer a hybrid resting-state structural connectome, representing functional interactions constrained by structural connectivity. We demonstrate that the structurally informed network outperforms the unconstrained model in simulating brain dynamics, wherein by constraining the inference model with the network structure we may improve the estimation of pairwise BOLD signal interactions. Further, we simulate brain network dynamics using Monte Carlo simulations with the new hybrid connectome to probe connectome-level differences in excitation-inhibition balance between apolipoprotein E (APOE)-ε4 carriers and noncarriers. Our results reveal sex differences among APOE-ε4 carriers in functional dynamics at criticality; specifically, female carriers appear to exhibit a lower tolerance to network disruptions resulting from increased excitatory interactions. In sum, the new multimodal network explored here enables analysis of brain dynamics through the integration of structure and function, providing insight into the complex interactions underlying neural activity such as the balance of excitation and inhibition.

The small world coefficient 4.8 ± 1 optimizes information processing in 2D neuronal networks

Small world networks have recently attracted much attention because of their unique properties. Mounting evidence suggests that communication is optimized in networks with a small world topology. However, despite the relevance of the argument, little is known about the effective enhancement of information in similar graphs. Here, we provide a quantitative estimate of the efficiency of small world networks. We used a model of the brain in which neurons are described as agents that integrate the signals from other neurons and generate an output that spreads in the system. 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Building up a clinical microbiota profiling: a quality framework proposal

Extensive characterization of the human microbiota has revealed promising relationships between microbial composition and health or disease, generating interest in biomarkers derived from microbiota profiling. However, microbiota complexity and technical challenges strongly influencing the results limit the generalization of microbiota profiling and question its clinical utility. In addition, no quality management scheme has been adapted to the specificities of microbiota profiling, notably due to the heterogeneity in methods and results. In this review, we discuss possible adaptation of classical quality management tools routinely used in diagnostic laboratories to microbiota profiling and propose a specific framework. Multiple quality controls are needed to cover all steps, from sampling to data processing. Standard operating procedures, primarily developed for wet lab analyses, must be adapted to the use of bioinformatic tools. Finally, requirements for test validation and proficiency testing must take into account expected discrepancies in results due to the heterogeneity of the processes. The proposed quality management framework should support the implementation of routine microbiota profiling by clinical laboratories to support patient care. Furthermore, its use in research laboratories would improve publication reproducibility as well as transferability of methods and results to routine practice.