A reduction methodology for fluctuation driven population dynamics

Goldobin, Denis S.; Volo, Matteo di; Torcini, Alessandro

doi:10.1101/2021.01.28.428565

Cited by 9 publications

(9 citation statements)

References 57 publications

(113 reference statements)

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“…The possibility to exactly move through the scales has not been fully exploited in this study, since we have focused the analysis on the extension of the single neural mass model to a multipopulation model, without adding other relevant features to the original model. However, it is possible to easily introduce, in the multipopulation model, biologically relevant characteristics, keeping intact the exact correspondence between microscopic and macroscopic scales, such as short-term synaptic plasticity (Taher et al, 2020 ), synaptic delays (Devalle et al, 2018 ), electrical coupling via gap junctions (Montbrió and Pazó, 2020 ), chemical synapses (Coombes and Byrne, 2019 ), and extrinsinc and endogenous noise (Goldobin et al, 2021 ). By adding short-term synaptic plasticity we expect to be able to reproduce the emergence of self-sustained activity in the high-activity state and, therefore, to describe a fully developed seizure.…”

Section: Discussionmentioning

confidence: 99%

“…The largest neuronal cascades produce short-lived but robust co-fluctuations at pairs of regions across the brain, thus contributing to the organization of the slowly evolving spontaneous fluctuations in brain dynamics at rest. The introduction of extrinsic or endogenous noise sources in the framework of exact neural mass models is possible in terms of (pseudo)-cumulants expansion in Tyulkina et al ( 2018 ) and Goldobin et al ( 2021 ).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Gerster

Taher

Škoch

et al. 2021

Front. Syst. Neurosci.

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Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Gerster

Taher

Škoch

et al. 2021

Front. Syst. Neurosci.

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show abstract

“…The current fluctuations can be correctly incorporated in a MF formulation by developing a Fokker-Planck formalism for the problem, however this will give rise to high (infinite) dimensional MF models (Brunel and Hakim, 1999;Brunel, 2000). We are currently working on developing reduction formalisms for the Fokker-Planck equation to obtain low dimensional neural mass models for the evolution of the mean membrane potential and of the population rate which will include the intrinsic current fluctuations as a Poissonian term (Goldobin et al, 2021;Segneri et al, 2021). A further improvement would consist in including in a self-consistent manner the current fluctuations in the MF formulation for balanced sparse networks.…”

Section: Discussionmentioning

confidence: 99%

“…The presence of COs is expected from the MF analysis only in the regions (IV) and (V), but neither in (II) where the MF forecasts the existence of a stable focus nor in (I) where no stable solutions are envisaged. The origin of the discrepancies among the MF and the network simulations in region (II) is due to the fact that the considered neural mass neglects the dynamical fluctuations in the input currents present in the original networks, that can give rise to noise induced COs (Goldobin et al, 2021). However, as shown in (di Volo and Torcini, 2018;Bi et al, 2020) for purely inhibitory populations, the analysis of the neural mass model can still give relevant information on the network dynamics.…”

Section: Bifurcation Diagramsmentioning

confidence: 99%

Asynchronous and coherent dynamics in balanced excitatory-inhibitory populations

Volo

Torcini

2021

Preprint

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Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow to classify the possible asynchronous and coherent behaviours emerging in balanced E-I networks with structural heterogeneity for any finite in-degree K. In the limit N >> K >> 1 both supra and sub-threshold balanced asynchronous regimes can be observed in our system. Due to the heterogeneity the asynchronous states are characterized by the splitting of the neurons in three groups: silent, fluctuation and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasi-periodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism similar to the pyramidal-interneuron gamma (PING) one, usually invoked for the emergence of gamma-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations we report a novel mechanism of frequency locking among collective rhythms promoted by these intrinsic fluctuations. Our analysis suggest that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions finally result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.

show abstract

Section: Bifurcation Diagramsmentioning

confidence: 99%

Asynchronous and coherent dynamics in balanced excitatory-inhibitory spiking networks

Bi¹,

Volo²,

Torcini³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining extensive simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow to classify the possible asynchronous and coherent behaviours emerging in balanced E-I networks with structural heterogeneity for any finite indegree K. In the limit N >> K >> 1 both supra and sub-threshold balanced asynchronous regimes can be observed in our system. Due to the heterogeneity the asynchronous states are characterized by the splitting of the neurons in three groups: silent, fluctuation and mean driven. These features are consistent with experimental observations reported for heterogeneous neural circuits. The coherent rhythms observed in our system can range from periodic and quasiperiodic collective oscillations (COs) to coherent chaos. These rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence somehow similar to coherent fluctuations observed in the cortex over multiple spatial scales. The COs can emerge due to two different mechanisms. A first mechanism similar to the pyramidal-interneuron gamma (PING) one, usually invoked for the emergence of γ-oscillations. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. Fluctuation driven COs are usually observable in our system as quasi-periodic collective motions characterized by two incommensurate frequencies. However, for sufficiently strong current fluctuations we report a novel mechanism of frequency locking among collective rhythms promoted by these intrinsic fluctuations. Our analysis suggest that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions finally result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.

show abstract

A reduction methodology for fluctuation driven population dynamics

Cited by 9 publications

References 57 publications

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Asynchronous and coherent dynamics in balanced excitatory-inhibitory populations

Asynchronous and coherent dynamics in balanced excitatory-inhibitory spiking networks

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