Role of Dimensionality in Predicting the Spontaneous Behavior of the Brain Using the Classical Ising Model and the Ising Model Implemented on a Structural Connectome

© Pubuditha M. Abeyasinghe et al. 2018. There is accumulating evidence that spontaneous fluctuations of the brain are sustained by a structural architecture of axonal fiber bundles. Various models have been used to investigate this structure-function relationship. In this work, we implemented the Ising model using the number of fibers between each pair of brain regions as input. The output of the Ising model simulations on a structural connectome was then compared with empirical functional connectivity data. A simpler two-dimensional classical Ising model was used as the baseline model for comparison purpose. Thermodynamic properties, such as the magnetic susceptibility and the specific heat, illustrated a phase transition from an ordered phase to a disordered phase at the critical temperature. Despite the differences between the two models, the lattice Ising model and the Ising model implemented on a structural connectome (the generalized Ising model) exhibited similar patterns of global properties. To study the behavior of the generalized Ising model around criticality, calculation of the dimensionality and critical exponents was performed for the first time, by introducing a new concept of distance based on structural connectivity. Same value inside the fitting error was found for the dimensionality in both models suggesting similar behavior of the models around criticality

Calculating the Dimensionality of the Brain, and Other Applications of an Optimized Generalized Ising Model in Predicting Brain\u27s Spontaneous Functions

Understanding a system as complex as the human brain is a very demanding task. Directly working with structural and functional neuroimaging data has led to most of the understanding we have gained about the human brain. However, performing only the direct statistical comparisons on the empirical function and the structure does not fully explain the observed long-range functional correlations. Therefore, implementations of mathematical models to gain further understanding of the relationship between the structure and function of the brain is critical. Additionally, spontaneous functions of the brain can only be predicted using computer simulated models; which will be pivotal for studying the patients with accidental brain injuries. Therefore, this research aims to present an optimized computer simulated model not only to further understand the structure-function relationship of the brain but also to predict the functional changes when anatomy is altered. Based on prior work, 2-dimensional classical Ising model stands out among the other models in modeling the functions of the brain due to its simplicity. Hence, a 2-dimensional Ising model was simulated on a structural connectome (generalized Ising model) that acts as a proxy for the anatomical connectivity in the brain. Simulations allowed the prediction of functional connectivity using the structure, at criticality. It also enabled the introduction of a novel methodology to calculate the ”dimensionality” of the brain. Our results showed the dimensionality of a healthy brain is two when it is defined using the information flow in the brain. Further research illustrated the dependency of dimensionality on the diffusion tractography method used to obtain the structural connectome. It was also concluded that an optimized generalized Ising model has to be simulated using a structural connectome generated by deterministic tractography to acquire the best predictions of empirical function. Additional investigations into a more generalized version of the Ising model—Potts model with different number of spin states—illustrated that increasing the number of spin states does not increase the predictability. It also supported the hypothesis that the model could be simulating the digital nature of direct neural activity rather than the indirect activity measured by brain imaging

Modeling an auditory stimulated brain under altered states of consciousness using the generalized ising model

Propofol is a short-acting medication that results in decreased levels of consciousness and is used for general anesthesia. Although it is the most commonly used anesthetic in the world, much remains unknown about the mechanisms by which it induces a loss of consciousness. Characterizing anesthesia-induced alterations to brain network activity might provide a powerful framework for understanding the neural mechanisms of unconsciousness. The aim of this work was to model brain activity in healthy brains during various stages of consciousness, as induced by propofol, in the auditory paradigm. We used the generalized Ising model (GIM) to fit the empirical fMRI data of healthy subjects while they listened to an audio clip from a movie. The external stimulus (audio clip) is believed to be at least partially driving a synchronization process of the brain activity and provides a similar conscious experience in different subjects. In order to observe the common synchronization among the subjects, a novel technique called the inter subject correlation (ISC) was implemented. We showed that the GIM—modified to incorporate the naturalistic external field—was able to fit the empirical task fMRI data in the awake state, in mild sedation, in deep sedation, and in recovery, at a temperature T* which is well above the critical temperature. To our knowledge this is the first study that captures human brain activity in response to real-life external stimuli at different levels of conscious awareness using mathematical modeling. This study might be helpful in future to assess the level of consciousness of patients with disorders of consciousness and help in regaining their consciousness

Studying Resting State and Stimulus Induced BOLD Activity using the Generalized Ising Model and Independent Component Graph Analysis

Although many technical advancements have been made, neuroscientists still struggle to explain the underlying behaviour of how brain regions communicate with each other to form large-scale functional networks. functional Magnetic Resonance Imaging (fMRI) has been commonly used to investigate changes between brain regions over time using the Blood Oxygen Level Dependent (BOLD) signal. The goal of this thesis is to show the applicability of novel techniques and tools, such as the generalized Ising model (GIM) and the independent component graph analysis (GraphICA), to obtain information on the functional connectivity of populations with altered perception of consciousness. The GIM was used to model brain activity in healthy brains during various stages of consciousness, as induced by an anesthetic agent, propofol, in the auditory paradigm. GraphICA, a tool that combines ICA and graph theory was used to investigate the functional connectivity of resting state networks (RSNs) in patients with altered perception caused by tinnitus and in patients with altered states of consciousness caused by severe brain injury. For the tinnitus patients, we examined whether a correlation exists between tinnitus behavioural scores and functional brain connectivity of RSNs. Moreover, for the severely brain injured patients, a multimodal neuroimaging approach with hybrid FDG-PET/MRI was implemented to study the functional connectivity changes of the RSNs. The GIM simulated with an external field was able to model the brain activity at different levels of consciousness under naturalistic stimulation, at a temperature in the super critical regime. Further, a strong correlation was observed between tinnitus distress and the connectivity pattern within and between the right executive control network and the other RSNs. This suggests that tinnitus distress is the consequence of a hyperactive attention condition. A variability was observed in the appearance and temporal/spatial patterns of RSNs among the two resting state fMRI acquisitions acquired within the same scanning session of the severely brain injured patients. This suggests the need for new strategies to be developed in order to pick the best RSN from each acquisition. Overall, this work demonstrated that the GIM and GraphICA were promising tools to investigate brain activity of populations with altered perception of consciousness and in future can be extended to investigate different neurological populations

The emergence of integrated information, complexity, and \u27consciousness\u27 at criticality

© 2020 by the authors. Integrated Information Theory (IIT) posits that integrated information (F) represents the quantity of a conscious experience. Here, the generalized Ising model was used to calculate F as a function of temperature in toy models of fully connected neural networks. A Monte-Carlo simulation was run on 159 normalized, random, positively weighted networks analogous to small five-node excitatory neural network motifs. Integrated information generated by this sample of small Ising models was measured across model parameter spaces. It was observed that integrated information, as an order parameter, underwent a phase transition at the critical point in the model. This critical point was demarcated by the peak of the generalized susceptibility (or variance in configuration due to temperature) of integrated information. At this critical point, integrated information was maximally receptive and responsive to perturbations of its own states. The results of this study provide evidence that F can capture integrated information in an empirical dataset, and display critical behavior acting as an order parameter from the generalized Ising model

A mean field approach to model levels of consciousness from EEG recordings

We introduce a mean-field model for analysing the dynamics of human consciousness. In particular, inspired by the Giulio Tononi's Integrated Information Theory and by the Max Tegmark's representation of consciousness, we study order-disorder phase transitions on Curie-Weiss models generated by processing EEG signals. The latter have been recorded on healthy individuals undergoing deep sedation. Then, we implement a machine learning tool for classifying mental states using, as input, the critical temperatures computed in the Curie-Weiss models. Results show that, by the proposed method, it is possible to discriminate between states of awareness and states of deep sedation. Besides, we identify a state space for representing the path between mental states, whose dimensions correspond to critical temperatures computed over different frequency bands of the EEG signal. Beyond possible theoretical implications in the study of human consciousness, resulting from our model, we deem relevant to emphasise that the proposed method could be exploited for clinical applications.Comment: 23 pages, 6 figures. Accepted for publication in Journal of Statistical Mechanics: Theory and Experimen

A mean field approach to model levels of consciousness from EEG recordings

We introduce a mean-field model for analysing the dynamics of human consciousness. In particular, inspired by the Giulio Tononi's Integrated Information Theory and by the Max Tegmark's representation of consciousness, we study order-disorder phase transitions on Curie-Weiss models generated by processing EEG signals. The latter have been recorded on healthy individuals undergoing deep sedation. Then, we implement a machine learning tool for classifying mental states using, as input, the critical temperatures computed in the Curie-Weiss models. Results show that, by the proposed method, it is possible to discriminate between states of awareness and states of deep sedation. Besides, we identify a state space for representing the path between mental states, whose dimensions correspond to critical temperatures computed over different frequency bands of the EEG signal. Beyond possible theoretical implications in the study of human consciousness, resulting from our model, we deem relevant to emphasise that the proposed method could be exploited for clinical applications

Self-organized criticality as a framework for consciousness: A review study

Objective: No current model of consciousness is univocally accepted on either theoretical or empirical grounds, and the need for a solid unifying framework is evident. Special attention has been given to the premise that self-organized criticality (SOC) is a fundamental property of neural system. SOC provides a competitive model to describe the physical mechanisms underlying spontaneous brain activity, and thus, critical dynamics were proposed as general gauges of information processing representing a strong candidate for a surrogate measure of consciousness. As SOC could be a neurodynamical framework, which may be able to bring together existing theories and experimental evidence, the purpose of this work was to provide a comprehensive overview of progress of research on SOC in association with consciousness. Methods: A comprehensive search of publications on consciousness and SOC published between 1998 and 2021 was conducted. The Web of Science database was searched, and annual number of publications and citations, type of articles, and applied methods were determined. Results: A total of 71 publications were identified. The annual number of citations steadily increased over the years. Original articles comprised 50.7% and reviews/theoretical articles 43.6%. Sixteen studies reported on human data and in seven studies data were recorded in animals. Computational models were utilized in n = 12 studies. EcoG data were assessed in n = 4 articles, fMRI in n = 4 studies, and EEG/MEG in n = 10 studies. Notably, different analytical tools were applied in the EEG/MEG studies to assess a surrogate measure of criticality such as the detrended fluctuation analysis, the pair correlation function, parameters from the neuronal avalanche analysis and the spectral exponent. Conclusion: Recent studies pointed out agreements of critical dynamics with the current most influencing theories in the field of consciousness research, the global workspace theory and the integrated information theory. Thus, the framework of SOC as a neurodynamical parameter for consciousness seems promising. However, identified experimental work was small in numbers, and a heterogeneity of applied analytical tools as a surrogate measure of criticality was observable, which limits the generalizability of findings

DEVELOPMENT OF A CEREBELLAR MEAN FIELD MODEL: THE THEORETICAL FRAMEWORK, THE IMPLEMENTATION AND THE FIRST APPLICATION

Brain modeling constantly evolves to improve the accuracy of the simulated brain dynamics with the ambitious aim to build a digital twin of the brain. Specific models tuned on brain regions specific features empower the brain simulations introducing bottom-up physiology properties into data-driven simulators. Despite the cerebellum contains 80 % of the neurons and is deeply involved in a wide range of functions, from sensorimotor to cognitive ones, a specific cerebellar model is still missing. Furthermore, its quasi-crystalline multi-layer circuitry deeply differs from the cerebral cortical one, therefore is hard to imagine a unique general model suitable for the realistic simulation of both cerebellar and cerebral cortex. The present thesis tackles the challenge of developing a specific model for the cerebellum. Specifically, multi-neuron multi-layer mean field (MF) model of the cerebellar network, including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells, was implemented, and validated against experimental data and the corresponding spiking neural network microcircuit model. The cerebellar MF model was built using a system of interdependent equations, where the single neuronal populations and topological parameters were captured by neuron-specific inter- dependent Transfer Functions. The model time resolution was optimized using Local Field Potentials recorded experimentally with high-density multielectrode array from acute mouse cerebellar slices. The present MF model satisfactorily captured the average discharge of different microcircuit neuronal populations in response to various input patterns and was able to predict the changes in Purkinje Cells firing patterns occurring in specific behavioral conditions: cortical plasticity mapping, which drives learning in associative tasks, and Molecular Layer Interneurons feed-forward inhibition, which controls Purkinje Cells activity patterns. The cerebellar multi-layer MF model thus provides a computationally efficient tool that will allow to investigate the causal relationship between microscopic neuronal properties and ensemble brain activity in health and pathological conditions. Furthermore, preliminary attempts to simulate a pathological cerebellum were done in the perspective of introducing our multi-layer cerebellar MF model in whole-brain simulators to realize patient-specific treatments, moving ahead towards personalized medicine. Two preliminary works assessed the relevant impact of the cerebellum on whole-brain dynamics and its role in modulating complex responses in causal connected cerebral regions, confirming that a specific model is required to further investigate the cerebellum-on- cerebrum influence. The framework presented in this thesis allows to develop a multi-layer MF model depicting the features of a specific brain region (e.g., cerebellum, basal ganglia), in order to define a general strategy to build up a pool of biology grounded MF models for computationally feasible simulations. Interconnected bottom-up MF models integrated in large-scale simulators would capture specific features of different brain regions, while the applications of a virtual brain would have a substantial impact on the reality ranging from the characterization of neurobiological processes, subject-specific preoperative plans, and development of neuro-prosthetic devices