1
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Spaeth A, Haussler D, Teodorescu M. Model-agnostic neural mean field with a data-driven transfer function. NEUROMORPHIC COMPUTING AND ENGINEERING 2024; 4:034013. [PMID: 39310743 PMCID: PMC11413991 DOI: 10.1088/2634-4386/ad787f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/04/2024] [Revised: 09/02/2024] [Accepted: 09/09/2024] [Indexed: 09/25/2024]
Abstract
As one of the most complex systems known to science, modeling brain behavior and function is both fascinating and extremely difficult. Empirical data is increasingly available from ex vivo human brain organoids and surgical samples, as well as in vivo animal models, so the problem of modeling the behavior of large-scale neuronal systems is more relevant than ever. The statistical physics concept of a mean-field model offers a tractable way to bridge the gap between single-neuron and population-level descriptions of neuronal activity, by modeling the behavior of a single representative neuron and extending this to the population. However, existing neural mean-field methods typically either take the limit of small interaction sizes, or are applicable only to the specific neuron models for which they were derived. This paper derives a mean-field model by fitting a transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. The transfer function is fitted numerically to simulated spike time data, and is entirely agnostic to the underlying neuronal dynamics. The resulting mean-field model predicts the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. Furthermore, it enables an accurate approximate bifurcation analysis as a function of the level of recurrent input. This model does not assume large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.
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Affiliation(s)
- Alex Spaeth
- Electrical and Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States of America
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States of America
| | - David Haussler
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States of America
- Biomolecular Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States of America
| | - Mircea Teodorescu
- Electrical and Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States of America
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States of America
- Biomolecular Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States of America
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2
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Nandi MK, Valla M, di Volo M. Bursting gamma oscillations in neural mass models. Front Comput Neurosci 2024; 18:1422159. [PMID: 39281982 PMCID: PMC11392745 DOI: 10.3389/fncom.2024.1422159] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2024] [Accepted: 08/08/2024] [Indexed: 09/18/2024] Open
Abstract
Gamma oscillations (30-120 Hz) in the brain are not periodic cycles, but they typically appear in short-time windows, often called oscillatory bursts. While the origin of this bursting phenomenon is still unclear, some recent studies hypothesize its origin in the external or endogenous noise of neural networks. We demonstrate that an exact neural mass model of excitatory and inhibitory quadratic-integrate and fire-spiking neurons theoretically predicts the emergence of a different regime of intrinsic bursting gamma (IBG) oscillations without any noise source, a phenomenon due to collective chaos. This regime is indeed observed in the direct simulation of spiking neurons, characterized by highly irregular spiking activity. IBG oscillations are distinguished by higher phase-amplitude coupling to slower theta oscillations concerning noise-induced bursting oscillations, thus indicating an increased capacity for information transfer between brain regions. We demonstrate that this phenomenon is present in both globally coupled and sparse networks of spiking neurons. These results propose a new mechanism for gamma oscillatory activity, suggesting deterministic collective chaos as a good candidate for the origin of gamma bursts.
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Affiliation(s)
- Manoj Kumar Nandi
- Université Claude Bernard Lyon 1, Lyon, Rhône-Alpes, France
- INSERM U1208 Institut Cellule Souche et Cerveau, Bron, France
| | - Michele Valla
- Université Claude Bernard Lyon 1, Lyon, Rhône-Alpes, France
- INSERM U1208 Institut Cellule Souche et Cerveau, Bron, France
| | - Matteo di Volo
- Université Claude Bernard Lyon 1, Lyon, Rhône-Alpes, France
- INSERM U1208 Institut Cellule Souche et Cerveau, Bron, France
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3
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Alexandersen CG, Duprat C, Ezzati A, Houzelstein P, Ledoux A, Liu Y, Saghir S, Destexhe A, Tesler F, Depannemaecker D. A Mean Field to Capture Asynchronous Irregular Dynamics of Conductance-Based Networks of Adaptive Quadratic Integrate-and-Fire Neuron Models. Neural Comput 2024; 36:1433-1448. [PMID: 38776953 DOI: 10.1162/neco_a_01670] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 02/01/2024] [Indexed: 05/25/2024]
Abstract
Mean-field models are a class of models used in computational neuroscience to study the behavior of large populations of neurons. These models are based on the idea of representing the activity of a large number of neurons as the average behavior of mean-field variables. This abstraction allows the study of large-scale neural dynamics in a computationally efficient and mathematically tractable manner. One of these methods, based on a semianalytical approach, has previously been applied to different types of single-neuron models, but never to models based on a quadratic form. In this work, we adapted this method to quadratic integrate-and-fire neuron models with adaptation and conductance-based synaptic interactions. We validated the mean-field model by comparing it to the spiking network model. This mean-field model should be useful to model large-scale activity based on quadratic neurons interacting with conductance-based synapses.
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Affiliation(s)
| | - Chloé Duprat
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, 13005 Marseille, France
| | - Aitakin Ezzati
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, 13005 Marseille, France
| | - Pierre Houzelstein
- Group for Neural Theory, LNC2, INSERM U960, DEC, École Normale Supérieure-PSL University, 75005 Paris, France
| | - Ambre Ledoux
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
| | - Yuhong Liu
- Institute of Physiological Chemistry, Johannes Gutenberg University of Mainz, 55128 Mainz, Germany
- Institute of Experimental Epileptology and Cognition Research, University of Bonn Medical Center, 53127 Bonn, Germany
| | - Sandra Saghir
- Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, 10623 Berlin, Germany
| | - Alain Destexhe
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
| | - Federico Tesler
- Paris-Saclay University, Institute of Neuroscience, CNRS, 91400 Saclay, France
| | - Damien Depannemaecker
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, 13005 Marseille, France
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4
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Linne ML. Computational modeling of neuron-glia signaling interactions to unravel cellular and neural circuit functioning. Curr Opin Neurobiol 2024; 85:102838. [PMID: 38310660 DOI: 10.1016/j.conb.2023.102838] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Revised: 12/22/2023] [Accepted: 12/29/2023] [Indexed: 02/06/2024]
Abstract
Glial cells have been shown to be vital for various brain functions, including homeostasis, information processing, and cognition. Over the past 30 years, various signaling interactions between neuronal and glial cells have been shown to underlie these functions. This review summarizes the interactions, particularly between neurons and astrocytes, which are types of glial cells. Some of the interactions remain controversial in part due to the nature of experimental methods and preparations used. Based on the accumulated data, computational models of the neuron-astrocyte interactions have been developed to explain the complex functions of astrocytes in neural circuits and to test conflicting hypotheses. This review presents the most significant recent models, modeling methods and simulation tools for neuron-astrocyte interactions. In the future, we will especially need more experimental research on awake animals in vivo and new computational models of neuron-glia interactions to advance our understanding of cellular dynamics and the functioning of neural circuits in different brain regions.
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Affiliation(s)
- Marja-Leena Linne
- Tampere University, Faculty of Medicine and Health Technology, Tampere, Finland.
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5
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Spaeth A, Haussler D, Teodorescu M. Model-Agnostic Neural Mean Field With The Refractory SoftPlus Transfer Function. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.02.05.579047. [PMID: 38370695 PMCID: PMC10871173 DOI: 10.1101/2024.02.05.579047] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/20/2024]
Abstract
Due to the complexity of neuronal networks and the nonlinear dynamics of individual neurons, it is challenging to develop a systems-level model which is accurate enough to be useful yet tractable enough to apply. Mean-field models which extrapolate from single-neuron descriptions to large-scale models can be derived from the neuron's transfer function, which gives its firing rate as a function of its synaptic input. However, analytically derived transfer functions are applicable only to the neurons and noise models from which they were originally derived. In recent work, approximate transfer functions have been empirically derived by fitting a sigmoidal curve, which imposes a maximum firing rate and applies only in the diffusion limit, restricting applications. In this paper, we propose an approximate transfer function called Refractory SoftPlus, which is simple yet applicable to a broad variety of neuron types. Refractory SoftPlus activation functions allow the derivation of simple empirically approximated mean-field models using simulation results, which enables prediction of the response of a network of randomly connected neurons to a time-varying external stimulus with a high degree of accuracy. These models also support an accurate approximate bifurcation analysis as a function of the level of recurrent input. Finally, the model works without assuming large presynaptic rates or small postsynaptic potential size, allowing mean-field models to be developed even for populations with large interaction terms.
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Affiliation(s)
- Alex Spaeth
- Electrical and Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States
| | - David Haussler
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States
- Biomolecular Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
| | - Mircea Teodorescu
- Electrical and Computer Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
- Genomics Institute, University of California, Santa Cruz, Santa Cruz, CA, United States
- Biomolecular Engineering Department, University of California, Santa Cruz, Santa Cruz, CA, United States
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6
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Shirani F, Choi H. On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks. J Comput Neurosci 2024; 52:73-107. [PMID: 37837534 DOI: 10.1007/s10827-023-00863-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Revised: 06/25/2023] [Accepted: 09/08/2023] [Indexed: 10/16/2023]
Abstract
Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory. Our study based on extensive bifurcation analyses thus reveal the functional optimality and criticality of structural and physiological parameters in establishing the baseline operating state of local cortical networks.
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Affiliation(s)
- Farshad Shirani
- School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, Georgia, USA.
| | - Hannah Choi
- School of Mathematics, Georgia Institute of Technology, Atlanta, 30332, Georgia, USA
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7
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Marrero D, Kern J, Urrea C. A Novel Robotic Controller Using Neural Engineering Framework-Based Spiking Neural Networks. SENSORS (BASEL, SWITZERLAND) 2024; 24:491. [PMID: 38257584 PMCID: PMC10819625 DOI: 10.3390/s24020491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2023] [Revised: 01/11/2024] [Accepted: 01/11/2024] [Indexed: 01/24/2024]
Abstract
This paper investigates spiking neural networks (SNN) for novel robotic controllers with the aim of improving accuracy in trajectory tracking. By emulating the operation of the human brain through the incorporation of temporal coding mechanisms, SNN offer greater adaptability and efficiency in information processing, providing significant advantages in the representation of temporal information in robotic arm control compared to conventional neural networks. Exploring specific implementations of SNN in robot control, this study analyzes neuron models and learning mechanisms inherent to SNN. Based on the principles of the Neural Engineering Framework (NEF), a novel spiking PID controller is designed and simulated for a 3-DoF robotic arm using Nengo and MATLAB R2022b. The controller demonstrated good accuracy and efficiency in following designated trajectories, showing minimal deviations, overshoots, or oscillations. A thorough quantitative assessment, utilizing performance metrics like root mean square error (RMSE) and the integral of the absolute value of the time-weighted error (ITAE), provides additional validation for the efficacy of the SNN-based controller. Competitive performance was observed, surpassing a fuzzy controller by 5% in terms of the ITAE index and a conventional PID controller by 6% in the ITAE index and 30% in RMSE performance. This work highlights the utility of NEF and SNN in developing effective robotic controllers, laying the groundwork for future research focused on SNN adaptability in dynamic environments and advanced robotic applications.
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Affiliation(s)
| | - John Kern
- Electrical Engineering Department, Faculty of Engineering, University of Santiago of Chile (USACH), Av. Víctor Jara 3519, Estación Central, Santiago 9170124, Chile; (D.M.); (C.U.)
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8
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Aquilué-Llorens D, Goldman JS, Destexhe A. High-Density Exploration of Activity States in a Multi-Area Brain Model. Neuroinformatics 2024; 22:75-87. [PMID: 37981636 PMCID: PMC10917847 DOI: 10.1007/s12021-023-09647-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 10/17/2023] [Indexed: 11/21/2023]
Abstract
To simulate whole brain dynamics with only a few equations, biophysical, mesoscopic models of local neuron populations can be connected using empirical tractography data. The development of mesoscopic mean-field models of neural populations, in particular, the Adaptive Exponential (AdEx mean-field model), has successfully summarized neuron-scale phenomena leading to the emergence of global brain dynamics associated with conscious (asynchronous and rapid dynamics) and unconscious (synchronized slow-waves, with Up-and-Down state dynamics) brain states, based on biophysical mechanisms operating at cellular scales (e.g. neuromodulatory regulation of spike-frequency adaptation during sleep-wake cycles or anesthetics). Using the Virtual Brain (TVB) environment to connect mean-field AdEx models, we have previously simulated the general properties of brain states, playing on spike-frequency adaptation, but have not yet performed detailed analyses of other parameters possibly also regulating transitions in brain-scale dynamics between different brain states. We performed a dense grid parameter exploration of the TVB-AdEx model, making use of High Performance Computing. We report a remarkable robustness of the effect of adaptation to induce synchronized slow-wave activity. Moreover, the occurrence of slow waves is often paralleled with a closer relation between functional and structural connectivity. We find that hyperpolarization can also generate unconscious-like synchronized Up and Down states, which may be a mechanism underlying the action of anesthetics. We conclude that the TVB-AdEx model reveals large-scale properties identified experimentally in sleep and anesthesia.
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Affiliation(s)
- David Aquilué-Llorens
- Paris-Saclay University, CNRS, Paris-Saclay Institute of Neuroscience (NeuroPSI), 91400, Saclay, France.
- Starlab Barcelona SL, Neuroscience BU, Av Tibidabo 47 bis, Barcelona, Spain.
| | - Jennifer S Goldman
- Paris-Saclay University, CNRS, Paris-Saclay Institute of Neuroscience (NeuroPSI), 91400, Saclay, France
| | - Alain Destexhe
- Paris-Saclay University, CNRS, Paris-Saclay Institute of Neuroscience (NeuroPSI), 91400, Saclay, France.
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9
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Lorenzi RM, Geminiani A, Zerlaut Y, De Grazia M, Destexhe A, Gandini Wheeler-Kingshott CAM, Palesi F, Casellato C, D'Angelo E. A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics. PLoS Comput Biol 2023; 19:e1011434. [PMID: 37656758 PMCID: PMC10501640 DOI: 10.1371/journal.pcbi.1011434] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2022] [Revised: 09/14/2023] [Accepted: 08/15/2023] [Indexed: 09/03/2023] Open
Abstract
Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.
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Affiliation(s)
| | - Alice Geminiani
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
| | - Yann Zerlaut
- Institut du Cerveau-Paris Brain Institute-ICM, Inserm, CNRS, APHP, Hôpital de la Pitié Salpêtrière, Paris, France
| | | | | | - Claudia A M Gandini Wheeler-Kingshott
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
- NMR Research Unit, Queen Square Multiple Sclerosis Centre, Department of Neuroinflammation, UCL Queen Square Institute of Neurology, UCL, London, United Kingdom
- Brain Connectivity Center, IRCCS Mondino Foundation, Pavia, Italy
| | - Fulvia Palesi
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
| | - Claudia Casellato
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
| | - Egidio D'Angelo
- Department of Brain and Behavioural Sciences, University of Pavia, Pavia, Italy
- Brain Connectivity Center, IRCCS Mondino Foundation, Pavia, Italy
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10
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Huang CH, Lin CCK. New biophysical rate-based modeling of long-term plasticity in mean-field neuronal population models. Comput Biol Med 2023; 163:107213. [PMID: 37413849 DOI: 10.1016/j.compbiomed.2023.107213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2022] [Revised: 05/20/2023] [Accepted: 06/25/2023] [Indexed: 07/08/2023]
Abstract
The formation of customized neural networks as the basis of brain functions such as receptive field selectivity, learning or memory depends heavily on the long-term plasticity of synaptic connections. However, the current mean-field population models commonly used to simulate large-scale neural network dynamics lack explicit links to the underlying cellular mechanisms of long-term plasticity. In this study, we developed a new mean-field population model, the plastic density-based neural mass model (pdNMM), by incorporating a newly developed rate-based plasticity model based on the calcium control hypothesis into an existing density-based neural mass model. Derivation of the plasticity model was carried out using population density methods. Our results showed that the synaptic plasticity represented by the resulting rate-based plasticity model exhibited Bienenstock-Cooper-Munro-like learning rules. Furthermore, we demonstrated that the pdNMM accurately reproduced previous experimental observations of long-term plasticity, including characteristics of Hebbian plasticity such as longevity, associativity and input specificity, on hippocampal slices, and the formation of receptive field selectivity in the visual cortex. In conclusion, the pdNMM is a novel approach that can confer long-term plasticity to conventional mean-field neuronal population models.
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Affiliation(s)
- Chih-Hsu Huang
- Department of Neurology, College of Medicine, National Cheng Kung University, Tainan, Taiwan
| | - Chou-Ching K Lin
- Department of Neurology, College of Medicine, National Cheng Kung University, Tainan, Taiwan; Department of Neurology, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan; Innovation Center of Medical Devices and Technology, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan; Medical Device Innovation Center, National Cheng Kung University, Tainan, Taiwan.
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11
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Depannemaecker D, Ezzati A, Wang H, Jirsa V, Bernard C. From phenomenological to biophysical models of seizures. Neurobiol Dis 2023; 182:106131. [PMID: 37086755 DOI: 10.1016/j.nbd.2023.106131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2023] [Revised: 04/12/2023] [Accepted: 04/14/2023] [Indexed: 04/24/2023] Open
Abstract
Epilepsy is a complex disease that requires various approaches for its study. In this short review, we discuss the contribution of theoretical and computational models. The review presents theoretical frameworks that underlie the understanding of certain seizure properties and their classification based on their dynamical properties at the onset and offset of seizures. Dynamical system tools are valuable resources in the study of seizures. By analyzing the complex, dynamic behavior of seizures, these tools can provide insights into seizure mechanisms and offer a framework for their classification. Additionally, computational models have high potential for clinical applications, as they can be used to develop more accurate diagnostic and personalized medicine tools. We discuss various modeling approaches that span different scales and levels, while also questioning the neurocentric view, and emphasize the importance of considering glial cells. Finally, we explore the epistemic value provided by this type of approach.
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Affiliation(s)
- Damien Depannemaecker
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France.
| | - Aitakin Ezzati
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Huifang Wang
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Viktor Jirsa
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France
| | - Christophe Bernard
- Institut de Neurosciences des Syst' emes, Aix-Marseille University, INSERM, Marseille, France.
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12
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Clusella P, Köksal-Ersöz E, Garcia-Ojalvo J, Ruffini G. Comparison between an exact and a heuristic neural mass model with second-order synapses. BIOLOGICAL CYBERNETICS 2023; 117:5-19. [PMID: 36454267 PMCID: PMC10160168 DOI: 10.1007/s00422-022-00952-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2022] [Accepted: 10/23/2022] [Indexed: 05/05/2023]
Abstract
Neural mass models (NMMs) are designed to reproduce the collective dynamics of neuronal populations. A common framework for NMMs assumes heuristically that the output firing rate of a neural population can be described by a static nonlinear transfer function (NMM1). However, a recent exact mean-field theory for quadratic integrate-and-fire (QIF) neurons challenges this view by showing that the mean firing rate is not a static function of the neuronal state but follows two coupled nonlinear differential equations (NMM2). Here we analyze and compare these two descriptions in the presence of second-order synaptic dynamics. First, we derive the mathematical equivalence between the two models in the infinitely slow synapse limit, i.e., we show that NMM1 is an approximation of NMM2 in this regime. Next, we evaluate the applicability of this limit in the context of realistic physiological parameter values by analyzing the dynamics of models with inhibitory or excitatory synapses. We show that NMM1 fails to reproduce important dynamical features of the exact model, such as the self-sustained oscillations of an inhibitory interneuron QIF network. Furthermore, in the exact model but not in the limit one, stimulation of a pyramidal cell population induces resonant oscillatory activity whose peak frequency and amplitude increase with the self-coupling gain and the external excitatory input. This may play a role in the enhanced response of densely connected networks to weak uniform inputs, such as the electric fields produced by noninvasive brain stimulation.
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Affiliation(s)
- Pau Clusella
- Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003, Barcelona, Spain.
| | - Elif Köksal-Ersöz
- LTSI - UMR 1099, INSERM, Univ Rennes, Campus Beaulieu, 35000, Rennes, France
| | - Jordi Garcia-Ojalvo
- Department of Medicine and Life Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003, Barcelona, Spain
| | - Giulio Ruffini
- Brain Modeling Department, Neuroelectrics, Av. Tibidabo, 47b, 08035, Barcelona, Spain.
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13
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Shirani F, Choi H. On the physiological and structural contributors to the overall balance of excitation and inhibition in local cortical networks. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.01.10.523489. [PMID: 36711468 PMCID: PMC9882012 DOI: 10.1101/2023.01.10.523489] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/18/2023]
Abstract
Overall balance of excitation and inhibition in cortical networks is central to their functionality and normal operation. Such orchestrated co-evolution of excitation and inhibition is established through convoluted local interactions between neurons, which are organized by specific network connectivity structures and are dynamically controlled by modulating synaptic activities. Therefore, identifying how such structural and physiological factors contribute to establishment of overall balance of excitation and inhibition is crucial in understanding the homeostatic plasticity mechanisms that regulate the balance. We use biologically plausible mathematical models to extensively study the effects of multiple key factors on overall balance of a network. We characterize a network's baseline balanced state by certain functional properties, and demonstrate how variations in physiological and structural parameters of the network deviate this balance and, in particular, result in transitions in spontaneous activity of the network to high-amplitude slow oscillatory regimes. We show that deviations from the reference balanced state can be continuously quantified by measuring the ratio of mean excitatory to mean inhibitory synaptic conductances in the network. Our results suggest that the commonly observed ratio of the number of inhibitory to the number of excitatory neurons in local cortical networks is almost optimal for their stability and excitability. Moreover, the values of inhibitory synaptic decay time constants and density of inhibitory-to-inhibitory network connectivity are critical to overall balance and stability of cortical networks. However, network stability in our results is sufficiently robust against modulations of synaptic quantal conductances, as required by their role in learning and memory.
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14
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Goldman JS, Kusch L, Aquilue D, Yalçınkaya BH, Depannemaecker D, Ancourt K, Nghiem TAE, Jirsa V, Destexhe A. A comprehensive neural simulation of slow-wave sleep and highly responsive wakefulness dynamics. Front Comput Neurosci 2023; 16:1058957. [PMID: 36714530 PMCID: PMC9880280 DOI: 10.3389/fncom.2022.1058957] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/21/2022] [Indexed: 01/15/2023] Open
Abstract
Hallmarks of neural dynamics during healthy human brain states span spatial scales from neuromodulators acting on microscopic ion channels to macroscopic changes in communication between brain regions. Developing a scale-integrated understanding of neural dynamics has therefore remained challenging. Here, we perform the integration across scales using mean-field modeling of Adaptive Exponential (AdEx) neurons, explicitly incorporating intrinsic properties of excitatory and inhibitory neurons. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. We report that when AdEx mean-field neural populations are connected via structural tracts defined by the human connectome, macroscopic dynamics resembling human brain activity emerge. Importantly, the model can qualitatively and quantitatively account for properties of empirically observed spontaneous and stimulus-evoked dynamics in space, time, phase, and frequency domains. Large-scale properties of cortical dynamics are shown to emerge from both microscopic-scale adaptation that control transitions between wake-like to sleep-like activity, and the organization of the human structural connectome; together, they shape the spatial extent of synchrony and phase coherence across brain regions consistent with the propagation of sleep-like spontaneous traveling waves at intermediate scales. Remarkably, the model also reproduces brain-wide, enhanced responsiveness and capacity to encode information particularly during wake-like states, as quantified using the perturbational complexity index. The model was run using The Virtual Brain (TVB) simulator, and is open-access in EBRAINS. This approach not only provides a scale-integrated understanding of brain states and their underlying mechanisms, but also open access tools to investigate brain responsiveness, toward producing a more unified, formal understanding of experimental data from conscious and unconscious states, as well as their associated pathologies.
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Affiliation(s)
- Jennifer S. Goldman
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,*Correspondence: Jennifer S. Goldman ✉
| | - Lionel Kusch
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, Marseille, France
| | - David Aquilue
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France
| | - Bahar Hazal Yalçınkaya
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, Marseille, France
| | | | - Kevin Ancourt
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France
| | - Trang-Anh E. Nghiem
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,Laboratoire de Physique, Ecole Normale Supérieure, Université PSL, CNRS, Sorbonne Université, Université de Paris, Paris, France
| | - Viktor Jirsa
- Institut de Neurosciences des Systèmes, Aix-Marseille University, INSERM, Marseille, France
| | - Alain Destexhe
- CNRS, Institute of Neuroscience (NeuroPSI), Paris-Saclay University, Saclay, France,Alain Destexhe ✉
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15
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A Model for the Propagation of Seizure Activity in Normal Brain Tissue. eNeuro 2022; 9:ENEURO.0234-21.2022. [PMID: 36323513 PMCID: PMC9721309 DOI: 10.1523/eneuro.0234-21.2022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Revised: 09/23/2022] [Accepted: 09/29/2022] [Indexed: 11/29/2022] Open
Abstract
Epilepsies are characterized by paroxysmal electrophysiological events and seizures, which can propagate across the brain. One of the main unsolved questions in epilepsy is how epileptic activity can invade normal tissue and thus propagate across the brain. To investigate this question, we consider three computational models at the neural network scale to study the underlying dynamics of seizure propagation, understand which specific features play a role, and relate them to clinical or experimental observations. We consider both the internal connectivity structure between neurons and the input properties in our characterization. We show that a paroxysmal input is sometimes controlled by the network while in other instances, it can lead the network activity to itself produce paroxysmal activity, and thus will further propagate to efferent networks. We further show how the details of the network architecture are essential to determine this switch to a seizure-like regime. We investigated the nature of the instability involved and in particular found a central role for the inhibitory connectivity. We propose a probabilistic approach to the propagative/non-propagative scenarios, which may serve as a guide to control the seizure by using appropriate stimuli.
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16
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D'Angelo E, Jirsa V. The quest for multiscale brain modeling. Trends Neurosci 2022; 45:777-790. [PMID: 35906100 DOI: 10.1016/j.tins.2022.06.007] [Citation(s) in RCA: 40] [Impact Index Per Article: 20.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2022] [Revised: 05/20/2022] [Accepted: 06/21/2022] [Indexed: 01/07/2023]
Abstract
Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.
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Affiliation(s)
- Egidio D'Angelo
- Department of Brain and Behavioral Sciences, University of Pavia, and Brain Connectivity Center, Istituto di Ricovero e Cura a Carattere Scientifico (IRCCS) Mondino Foundation, Pavia, Italy.
| | - Viktor Jirsa
- Institut National de la Santé et de la Recherche Médicale (INSERM) Unité 1106, Centre National de la Recherche Scientifique (CNRS), and University of Aix-Marseille, Marseille, France
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17
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Exact mean-field models for spiking neural networks with adaptation. J Comput Neurosci 2022; 50:445-469. [PMID: 35834100 DOI: 10.1007/s10827-022-00825-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 06/15/2022] [Indexed: 10/17/2022]
Abstract
Networks of spiking neurons with adaption have been shown to be able to reproduce a wide range of neural activities, including the emergent population bursting and spike synchrony that underpin brain disorders and normal function. Exact mean-field models derived from spiking neural networks are extremely valuable, as such models can be used to determine how individual neurons and the network they reside within interact to produce macroscopic network behaviours. In the paper, we derive and analyze a set of exact mean-field equations for the neural network with spike frequency adaptation. Specifically, our model is a network of Izhikevich neurons, where each neuron is modeled by a two dimensional system consisting of a quadratic integrate and fire equation plus an equation which implements spike frequency adaptation. Previous work deriving a mean-field model for this type of network, relied on the assumption of sufficiently slow dynamics of the adaptation variable. However, this approximation did not succeed in establishing an exact correspondence between the macroscopic description and the realistic neural network, especially when the adaptation time constant was not large. The challenge lies in how to achieve a closed set of mean-field equations with the inclusion of the mean-field dynamics of the adaptation variable. We address this problem by using a Lorentzian ansatz combined with the moment closure approach to arrive at a mean-field system in the thermodynamic limit. The resulting macroscopic description is capable of qualitatively and quantitatively describing the collective dynamics of the neural network, including transition between states where the individual neurons exhibit asynchronous tonic firing and synchronous bursting. We extend the approach to a network of two populations of neurons and discuss the accuracy and efficacy of our mean-field approximations by examining all assumptions that are imposed during the derivation. Numerical bifurcation analysis of our mean-field models reveals bifurcations not previously observed in the models, including a novel mechanism for emergence of bursting in the network. We anticipate our results will provide a tractable and reliable tool to investigate the underlying mechanism of brain function and dysfunction from the perspective of computational neuroscience.
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18
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A Modular Workflow for Model Building, Analysis, and Parameter Estimation in Systems Biology and Neuroscience. Neuroinformatics 2022; 20:241-259. [PMID: 34709562 PMCID: PMC9537196 DOI: 10.1007/s12021-021-09546-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 09/03/2021] [Indexed: 01/07/2023]
Abstract
Neuroscience incorporates knowledge from a range of scales, from single molecules to brain wide neural networks. Modeling is a valuable tool in understanding processes at a single scale or the interactions between two adjacent scales and researchers use a variety of different software tools in the model building and analysis process. Here we focus on the scale of biochemical pathways, which is one of the main objects of study in systems biology. While systems biology is among the more standardized fields, conversion between different model formats and interoperability between various tools is still somewhat problematic. To offer our take on tackling these shortcomings and by keeping in mind the FAIR (findability, accessibility, interoperability, reusability) data principles, we have developed a workflow for building and analyzing biochemical pathway models, using pre-existing tools that could be utilized for the storage and refinement of models in all phases of development. We have chosen the SBtab format which allows the storage of biochemical models and associated data in a single file and provides a human readable set of syntax rules. Next, we implemented custom-made MATLAB® scripts to perform parameter estimation and global sensitivity analysis used in model refinement. Additionally, we have developed a web-based application for biochemical models that allows simulations with either a network free solver or stochastic solvers and incorporating geometry. Finally, we illustrate convertibility and use of a biochemical model in a biophysically detailed single neuron model by running multiscale simulations in NEURON. Using this workflow, we can simulate the same model in three different simulators, with a smooth conversion between the different model formats, enhancing the characterization of different aspects of the model.
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19
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Di Volo M, Férézou I. Nonlinear collision between propagating waves in mouse somatosensory cortex. Sci Rep 2021; 11:19630. [PMID: 34608205 PMCID: PMC8490437 DOI: 10.1038/s41598-021-99057-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 09/13/2021] [Indexed: 11/22/2022] Open
Abstract
How does cellular organization shape the spatio-temporal patterns of activity in the cortex while processing sensory information? After measuring the propagation of activity in the mouse primary somatosensory cortex (S1) in response to single whisker deflections with Voltage Sensitive Dye (VSD) imaging, we developed a two dimensional model of S1. We designed an inference method to reconstruct model parameters from VSD data, revealing that a spatially heterogeneous organization of synaptic strengths between pyramidal neurons in S1 is likely to be responsible for the heterogeneous spatio-temporal patterns of activity measured experimentally. The model shows that, for strong enough excitatory cortical interactions, whisker deflections generate a propagating wave in S1. Finally, we report that two consecutive stimuli activating different spatial locations in S1 generate two waves which collide sub-linearly, giving rise to a suppressive wave. In the inferred model, the suppressive wave is explained by a lower sensitivity to external perturbations of neural networks during activated states.
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Affiliation(s)
- M Di Volo
- Laboratoire de Physique Théorique et Modélisation, CY Cergy Paris Université, 95302, Cergy-Pontoise Cedex, France.
| | - I Férézou
- Université Paris-Saclay, CNRS, Institut des Neurosciences Paris-Saclay, Gif-sur-Yvette, France
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20
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Osborne H, Lai YM, Lepperød ME, Sichau D, Deutz L, de Kamps M. MIIND : A Model-Agnostic Simulator of Neural Populations. Front Neuroinform 2021; 15:614881. [PMID: 34295233 PMCID: PMC8291130 DOI: 10.3389/fninf.2021.614881] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2020] [Accepted: 05/24/2021] [Indexed: 11/13/2022] Open
Abstract
MIIND is a software platform for easily and efficiently simulating the behaviour of interacting populations of point neurons governed by any 1D or 2D dynamical system. The simulator is entirely agnostic to the underlying neuron model of each population and provides an intuitive method for controlling the amount of noise which can significantly affect the overall behaviour. A network of populations can be set up quickly and easily using MIIND's XML-style simulation file format describing simulation parameters such as how populations interact, transmission delays, post-synaptic potentials, and what output to record. During simulation, a visual display of each population's state is provided for immediate feedback of the behaviour and population activity can be output to a file or passed to a Python script for further processing. The Python support also means that MIIND can be integrated into other software such as The Virtual Brain. MIIND's population density technique is a geometric and visual method for describing the activity of each neuron population which encourages a deep consideration of the dynamics of the neuron model and provides insight into how the behaviour of each population is affected by the behaviour of its neighbours in the network. For 1D neuron models, MIIND performs far better than direct simulation solutions for large populations. For 2D models, performance comparison is more nuanced but the population density approach still confers certain advantages over direct simulation. MIIND can be used to build neural systems that bridge the scales between an individual neuron model and a population network. This allows researchers to maintain a plausible path back from mesoscopic to microscopic scales while minimising the complexity of managing large numbers of interconnected neurons. In this paper, we introduce the MIIND system, its usage, and provide implementation details where appropriate.
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Affiliation(s)
- Hugh Osborne
- Institute for Artificial Intelligence and Biological Computation, School of Computing, University of Leeds, Leeds, United Kingdom
| | - Yi Ming Lai
- School of Medicine, University of Nottingham, Nottingham, United Kingdom
| | | | - David Sichau
- Department of Computer Science, Eidgenössische Technische Hochschule Zurich, Zurich, Switzerland
| | - Lukas Deutz
- Institute for Artificial Intelligence and Biological Computation, School of Computing, University of Leeds, Leeds, United Kingdom
| | - Marc de Kamps
- School of Computing and Leeds Institute for Data Analytics, University of Leeds, Leeds, United Kingdom
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21
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Depannemaecker D, Destexhe A, Jirsa V, Bernard C. Modeling seizures: From single neurons to networks. Seizure 2021; 90:4-8. [PMID: 34219016 DOI: 10.1016/j.seizure.2021.06.015] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 06/11/2021] [Accepted: 06/11/2021] [Indexed: 11/26/2022] Open
Abstract
Dynamical system tools offer a complementary approach to detailed biophysical seizure modeling, with a high potential for clinical applications. This review describes the theoretical framework that provides a basis for theorizing certain properties of seizures and for their classification according to their dynamical properties at onset and offset. We describe various modeling approaches spanning different scales, from single neurons to large-scale networks. This narrative review provides an accessible overview of this field, including non-exhaustive examples of key recent works.
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Affiliation(s)
- Damien Depannemaecker
- Paris-Saclay University, French National Centre for Scientific Research (CNRS), Institute of Neuroscience (NeuroPSI), 91198 Gif sur Yvette, France.
| | - Alain Destexhe
- Paris-Saclay University, French National Centre for Scientific Research (CNRS), Institute of Neuroscience (NeuroPSI), 91198 Gif sur Yvette, France.
| | - Viktor Jirsa
- Aix Marseille Univ, INSERM, INS, Institut des Neurosciences des Systèmes, Marseille, France.
| | - Christophe Bernard
- Aix Marseille Univ, INSERM, INS, Institut des Neurosciences des Systèmes, Marseille, France.
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22
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Shine JM, Müller EJ, Munn B, Cabral J, Moran RJ, Breakspear M. Computational models link cellular mechanisms of neuromodulation to large-scale neural dynamics. Nat Neurosci 2021; 24:765-776. [PMID: 33958801 DOI: 10.1038/s41593-021-00824-6] [Citation(s) in RCA: 80] [Impact Index Per Article: 26.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2020] [Accepted: 02/23/2021] [Indexed: 02/02/2023]
Abstract
Decades of neurobiological research have disclosed the diverse manners in which the response properties of neurons are dynamically modulated to support adaptive cognitive functions. This neuromodulation is achieved through alterations in the biophysical properties of the neuron. However, changes in cognitive function do not arise directly from the modulation of individual neurons, but are mediated by population dynamics in mesoscopic neural ensembles. Understanding this multiscale mapping is an important but nontrivial issue. Here, we bridge these different levels of description by showing how computational models parametrically map classic neuromodulatory processes onto systems-level models of neural activity. The ensuing critical balance of systems-level activity supports perception and action, although our knowledge of this mapping remains incomplete. In this way, quantitative models that link microscale neuronal neuromodulation to systems-level brain function highlight gaps in knowledge and suggest new directions for integrating theoretical and experimental work.
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Affiliation(s)
- James M Shine
- Brain and Mind Center, The University of Sydney, Camperdown, New South Wales, Australia.,Center for Complex Systems, The University of Sydney, Camperdown, New South Wales, Australia
| | - Eli J Müller
- Brain and Mind Center, The University of Sydney, Camperdown, New South Wales, Australia.,Center for Complex Systems, The University of Sydney, Camperdown, New South Wales, Australia
| | - Brandon Munn
- Brain and Mind Center, The University of Sydney, Camperdown, New South Wales, Australia.,Center for Complex Systems, The University of Sydney, Camperdown, New South Wales, Australia
| | - Joana Cabral
- Life and Health Sciences Research Institute (ICVS), School of Medicine, University of Minho, Braga, Portugal
| | | | - Michael Breakspear
- School of Psychology, College of Engineering, Science and the Environment, University of Newcastle, Callaghan, New South Wales, Australia. .,School of Medicine and Public Health, College of Health and Medicine, University of Newcastle, Callaghan, New South Wales, Australia.
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23
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Deschle N, Ignacio Gossn J, Tewarie P, Schelter B, Daffertshofer A. On the Validity of Neural Mass Models. Front Comput Neurosci 2021; 14:581040. [PMID: 33469424 PMCID: PMC7814001 DOI: 10.3389/fncom.2020.581040] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Accepted: 12/01/2020] [Indexed: 11/26/2022] Open
Abstract
Modeling the dynamics of neural masses is a common approach in the study of neural populations. Various models have been proven useful to describe a plenitude of empirical observations including self-sustained local oscillations and patterns of distant synchronization. We discuss the extent to which mass models really resemble the mean dynamics of a neural population. In particular, we question the validity of neural mass models if the population under study comprises a mixture of excitatory and inhibitory neurons that are densely (inter-)connected. Starting from a network of noisy leaky integrate-and-fire neurons, we formulated two different population dynamics that both fall into the category of seminal Freeman neural mass models. The derivations contained several mean-field assumptions and time scale separation(s) between membrane and synapse dynamics. Our comparison of these neural mass models with the averaged dynamics of the population reveals bounds in the fraction of excitatory/inhibitory neuron as well as overall network degree for a mass model to provide adequate estimates. For substantial parameter ranges, our models fail to mimic the neural network's dynamics proper, be that in de-synchronized or in (high-frequency) synchronized states. Only around the onset of low-frequency synchronization our models provide proper estimates of the mean potential dynamics. While this shows their potential for, e.g., studying resting state dynamics obtained by encephalography with focus on the transition region, we must accept that predicting the more general dynamic outcome of a neural network via its mass dynamics requires great care.
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Affiliation(s)
- Nicolás Deschle
- Faculty of Behavioural and Movement Sciences, Amsterdam Movement Sciences & Institute for Brain and Behavior Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, Netherlands.,Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Aberdeen, United Kingdom
| | - Juan Ignacio Gossn
- Consejo Nacional de Investigaciones Científicas y Técnicas, Instituto de Astronomía y Física del Espacio, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, Argentina
| | - Prejaas Tewarie
- Sir Peter Mansfield Imaging Centre, School of Physics and Astronomy, University of Nottingham, Nottingham, United Kingdom.,Department of Clinical Neurophysiology and MEG Center, Amsterdam UMC, Vrije Universiteit Amsterdam, Amsterdam Neuroscience, Amsterdam, Netherlands
| | - Björn Schelter
- Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, Aberdeen, United Kingdom
| | - Andreas Daffertshofer
- Faculty of Behavioural and Movement Sciences, Amsterdam Movement Sciences & Institute for Brain and Behavior Amsterdam, Vrije Universiteit Amsterdam, Amsterdam, Netherlands
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24
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James A, Krestinskaya O, Maan A. Recursive Threshold Logic-A Bioinspired Reconfigurable Dynamic Logic System With Crossbar Arrays. IEEE TRANSACTIONS ON BIOMEDICAL CIRCUITS AND SYSTEMS 2020; 14:1311-1322. [PMID: 32991290 DOI: 10.1109/tbcas.2020.3027554] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The neuron behavioral models are inspired by the principle of the firing of neurons, and weighted accumulation of charge for a given set of input stimuli. Biological neurons show dynamic behavior through its feedback and feedforward time-dependent responses. The principle of the firing of neurons inspires threshold logic design by applying threshold functions on the weight summation of inputs. In this article, we present a recursive threshold logic unit that uses the output feedback from standard threshold logic gates to emulate Boolean expressions in a time-sequenced manner. The Boolean expression is implemented with an analog resistive divider in memristive crossbars and a hard-threshold function designed with CMOS comparator for realizing the sums (OR) and products (AND) operators. The method benefits from reliable programming of the memristors in 1T1R crossbar configuration to suppress sneak path currents and thus enable larger crossbar sizes, which in turn allow a higher number of Boolean inputs. The reference threshold voltage for the decision comparators is tuned to implement AND and OR logic. The threshold value range is limited by the number of inputs to the crossbar. Simultaneously, the resistance of the memristors is kept constant at RON. The circuit's tolerance to the memristor variability and aging are analyzed, showing sufficient resilience. Also, the proposed recursive logic uses fewer cross-points, and has lower power dissipation than other memristive logic and CMOS implementation.
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