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The dynamic brain: from spiking neurons to neural masses and cortical fields.

Deco G, Jirsa VK, Robinson PA, Breakspear M, Friston K - PLoS Comput. Biol. (2008)

Bottom Line: Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data.This makes dynamic models critical in integrating theory and experiments.We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

View Article: PubMed Central - PubMed

Affiliation: Institució Catalana de Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Department of Technology, Computational Neuroscience, Barcelona, Spain. Gustavo.Deco@upf.edu

ABSTRACT
The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

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Related in: MedlinePlus

Contraction of spike-timing differences due to synaptic inputs.A seed neuron is chosen at random and the interneuron spikedifference for all other neurons is plotted each time it spikes. (A)Solid and dashed lines show ±1 and ±1.5standard deviations of the ensemble spike timing. (B) The normalizedfourth moment (excess kurtosis) derived from a moving frame.
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pcbi-1000092-g007: Contraction of spike-timing differences due to synaptic inputs.A seed neuron is chosen at random and the interneuron spikedifference for all other neurons is plotted each time it spikes. (A)Solid and dashed lines show ±1 and ±1.5standard deviations of the ensemble spike timing. (B) The normalizedfourth moment (excess kurtosis) derived from a moving frame.

Mentions: The impact of the stimulus input on the density of the ensemble is shown inFigure 7, whichshows the spike-timing difference of all neurons in the ensemble withrespect to a randomly chosen seed-neuron. The mean spike-timing differenceis 0 ms throughout the simulation. This is because the system has completesymmetry, so that all neurons fire, on average, symmetrically before orafter any other neuron. However, as evident in Figure 7A, the variance in relativespike-timing decreases dramatically during the stimulus interval. Of note isthat the ensemble variance does not simply step down with the onset of thestimulus, but rather dynamically diminishes throughout the presence of thestimulus. When this occurs, the mean-field term continues to increase inamplitude. Figure 7Bshows the evolution of the kurtosis (normalized so that a Gaussiandistribution has a kurtosis of zero). Prior to the stimulus, and reflectingthe weak network coupling, the ensemble has a mesokurtotic (broad)distribution. It increases markedly following the stimulus onset, implying adynamical evolution towards a leptokurtotic (peaked) distribution. That is,although the parameter values are static, the ensemble mean, variance, andkurtosis evolve dynamically in an inter-related fashion. Hence this systemexhibits time-dependent interdependence between its first, second, andfourth moments. This is the sort of coupling (between moments of theensemble density) that neural mass models do not capture.


The dynamic brain: from spiking neurons to neural masses and cortical fields.

Deco G, Jirsa VK, Robinson PA, Breakspear M, Friston K - PLoS Comput. Biol. (2008)

Contraction of spike-timing differences due to synaptic inputs.A seed neuron is chosen at random and the interneuron spikedifference for all other neurons is plotted each time it spikes. (A)Solid and dashed lines show ±1 and ±1.5standard deviations of the ensemble spike timing. (B) The normalizedfourth moment (excess kurtosis) derived from a moving frame.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2519166&req=5

pcbi-1000092-g007: Contraction of spike-timing differences due to synaptic inputs.A seed neuron is chosen at random and the interneuron spikedifference for all other neurons is plotted each time it spikes. (A)Solid and dashed lines show ±1 and ±1.5standard deviations of the ensemble spike timing. (B) The normalizedfourth moment (excess kurtosis) derived from a moving frame.
Mentions: The impact of the stimulus input on the density of the ensemble is shown inFigure 7, whichshows the spike-timing difference of all neurons in the ensemble withrespect to a randomly chosen seed-neuron. The mean spike-timing differenceis 0 ms throughout the simulation. This is because the system has completesymmetry, so that all neurons fire, on average, symmetrically before orafter any other neuron. However, as evident in Figure 7A, the variance in relativespike-timing decreases dramatically during the stimulus interval. Of note isthat the ensemble variance does not simply step down with the onset of thestimulus, but rather dynamically diminishes throughout the presence of thestimulus. When this occurs, the mean-field term continues to increase inamplitude. Figure 7Bshows the evolution of the kurtosis (normalized so that a Gaussiandistribution has a kurtosis of zero). Prior to the stimulus, and reflectingthe weak network coupling, the ensemble has a mesokurtotic (broad)distribution. It increases markedly following the stimulus onset, implying adynamical evolution towards a leptokurtotic (peaked) distribution. That is,although the parameter values are static, the ensemble mean, variance, andkurtosis evolve dynamically in an inter-related fashion. Hence this systemexhibits time-dependent interdependence between its first, second, andfourth moments. This is the sort of coupling (between moments of theensemble density) that neural mass models do not capture.

Bottom Line: Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data.This makes dynamic models critical in integrating theory and experiments.We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

View Article: PubMed Central - PubMed

Affiliation: Institució Catalana de Recerca i Estudis Avançats (ICREA), Universitat Pompeu Fabra, Department of Technology, Computational Neuroscience, Barcelona, Spain. Gustavo.Deco@upf.edu

ABSTRACT
The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

Show MeSH
Related in: MedlinePlus