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Lombardi F, Pepić S, Shriki O, Tkačik G, De Martino D. Statistical modeling of adaptive neural networks explains co-existence of avalanches and oscillations in resting human brain. NATURE COMPUTATIONAL SCIENCE 2023; 3:254-263. [PMID: 38177880 PMCID: PMC10766559 DOI: 10.1038/s43588-023-00410-9] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Accepted: 02/02/2023] [Indexed: 01/06/2024]
Abstract
Neurons in the brain are wired into adaptive networks that exhibit collective dynamics as diverse as scale-specific oscillations and scale-free neuronal avalanches. Although existing models account for oscillations and avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically or intractable to infer from data rigorously. Here we propose a feedback-driven Ising-like class of neural networks that captures avalanches and oscillations simultaneously and quantitatively. In the simplest yet fully microscopic model version, we can analytically compute the phase diagram and make direct contact with human brain resting-state activity recordings via tractable inference of the model's two essential parameters. The inferred model quantitatively captures the dynamics over a broad range of scales, from single sensor oscillations to collective behaviors of extreme events and neuronal avalanches. Importantly, the inferred parameters indicate that the co-existence of scale-specific (oscillations) and scale-free (avalanches) dynamics occurs close to a non-equilibrium critical point at the onset of self-sustained oscillations.
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Affiliation(s)
- Fabrizio Lombardi
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
| | - Selver Pepić
- Institute of Science and Technology Austria, Klosterneuburg, Austria
| | - Oren Shriki
- Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel
| | - Gašper Tkačik
- Institute of Science and Technology Austria, Klosterneuburg, Austria.
| | - Daniele De Martino
- Biofisika Institute (CSIC, UPV-EHU) and Ikerbasque Foundation, Bilbao, Spain.
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Tian Y, Tan Z, Hou H, Li G, Cheng A, Qiu Y, Weng K, Chen C, Sun P. Theoretical foundations of studying criticality in the brain. Netw Neurosci 2022; 6:1148-1185. [PMID: 38800464 PMCID: PMC11117095 DOI: 10.1162/netn_a_00269] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2022] [Accepted: 07/12/2022] [Indexed: 05/29/2024] Open
Abstract
Criticality is hypothesized as a physical mechanism underlying efficient transitions between cortical states and remarkable information-processing capacities in the brain. While considerable evidence generally supports this hypothesis, nonnegligible controversies persist regarding the ubiquity of criticality in neural dynamics and its role in information processing. Validity issues frequently arise during identifying potential brain criticality from empirical data. Moreover, the functional benefits implied by brain criticality are frequently misconceived or unduly generalized. These problems stem from the nontriviality and immaturity of the physical theories that analytically derive brain criticality and the statistic techniques that estimate brain criticality from empirical data. To help solve these problems, we present a systematic review and reformulate the foundations of studying brain criticality, that is, ordinary criticality (OC), quasi-criticality (qC), self-organized criticality (SOC), and self-organized quasi-criticality (SOqC), using the terminology of neuroscience. We offer accessible explanations of the physical theories and statistical techniques of brain criticality, providing step-by-step derivations to characterize neural dynamics as a physical system with avalanches. We summarize error-prone details and existing limitations in brain criticality analysis and suggest possible solutions. Moreover, we present a forward-looking perspective on how optimizing the foundations of studying brain criticality can deepen our understanding of various neuroscience questions.
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Affiliation(s)
- Yang Tian
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
- Laboratory of Advanced Computing and Storage, Central Research Institute, 2012 Laboratories, Huawei Technologies Co. Ltd., Beijing, China
| | - Zeren Tan
- Institute for Interdisciplinary Information Science, Tsinghua University, Beijing, China
| | - Hedong Hou
- UFR de Mathématiques, Université de Paris, Paris, France
| | - Guoqi Li
- Institute of Automation, Chinese Academy of Science, Beijing, China
- University of Chinese Academy of Science, Beijing, China
| | - Aohua Cheng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Yike Qiu
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Kangyu Weng
- Tsien Excellence in Engineering Program, School of Aerospace Engineering, Tsinghua University, Beijing, China
| | - Chun Chen
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
| | - Pei Sun
- Department of Psychology & Tsinghua Laboratory of Brain and Intelligence, Tsinghua University, Beijing, China
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Liang J, Zhou T, Zhou C. Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale Variability. Front Syst Neurosci 2020; 14:580011. [PMID: 33324179 PMCID: PMC7725680 DOI: 10.3389/fnsys.2020.580011] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2020] [Accepted: 11/02/2020] [Indexed: 12/14/2022] Open
Abstract
Cortical neural circuits display highly irregular spiking in individual neurons but variably sized collective firing, oscillations and critical avalanches at the population level, all of which have functional importance for information processing. Theoretically, the balance of excitation and inhibition inputs is thought to account for spiking irregularity and critical avalanches may originate from an underlying phase transition. However, the theoretical reconciliation of these multilevel dynamic aspects in neural circuits remains an open question. Herein, we study excitation-inhibition (E-I) balanced neuronal network with biologically realistic synaptic kinetics. It can maintain irregular spiking dynamics with different levels of synchrony and critical avalanches emerge near the synchronous transition point. We propose a novel semi-analytical mean-field theory to derive the field equations governing the network macroscopic dynamics. It reveals that the E-I balanced state of the network manifesting irregular individual spiking is characterized by a macroscopic stable state, which can be either a fixed point or a periodic motion and the transition is predicted by a Hopf bifurcation in the macroscopic field. Furthermore, by analyzing public data, we find the coexistence of irregular spiking and critical avalanches in the spontaneous spiking activities of mouse cortical slice in vitro, indicating the universality of the observed phenomena. Our theory unveils the mechanism that permits complex neural activities in different spatiotemporal scales to coexist and elucidates a possible origin of the criticality of neural systems. It also provides a novel tool for analyzing the macroscopic dynamics of E-I balanced networks and its relationship to the microscopic counterparts, which can be useful for large-scale modeling and computation of cortical dynamics.
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Affiliation(s)
- Junhao Liang
- Department of Physics, Centre for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Key Laboratory of Computational Mathematics, Guangdong Province, and School of Mathematics, Sun Yat-sen University, Guangzhou, China
| | - Tianshou Zhou
- Key Laboratory of Computational Mathematics, Guangdong Province, and School of Mathematics, Sun Yat-sen University, Guangzhou, China
| | - Changsong Zhou
- Department of Physics, Centre for Nonlinear Studies, Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems, Institute of Computational and Theoretical Studies, Hong Kong Baptist University, Kowloon Tong, Hong Kong
- Department of Physics, Zhejiang University, Hangzhou, China
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