Cross frequency coupling in next generation inhibitory neural mass models

Ceni, Andrea; Olmi, Simona; Torcini, Alessandro; Angulo-Garcia, David

doi:10.1063/1.5125216

Cited by 30 publications

(27 citation statements)

References 57 publications

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“…This finding was unique for the oscillatory regime of the GPe. Similarly complex patterns of cross-frequency coupling have been reported previously in a instantaneously coupled two-population QIF model with sinusoidal forcing in the alpha frequency range (10 Hz) (Ceni et al, 2020). Thus, our results show under which conditions the GPe system can express the characteristic dynamics that have been identified in more abstract models of two populations with mutual inhibition.…”

Section: Discussionsupporting

confidence: 88%

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

Gast

Gong

Schmidt

et al. 2021

Preprint

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The external pallidum (GPe) plays a central role for basal ganglia functions and dynamics and, consequently, has been included in most computational studies of the basal ganglia. These studies considered the GPe as a homogeneous neural population. However, experimental studies have shown that the GPe contains at least two distinct cell types (prototypical and arkypallidal cells). In this work, we provide in silico insight into how pallidal heterogeneity modulates dynamic regimes inside the GPe and how they affect the GPe response to oscillatory input.We derive a mean-field model of the GPe system from a microscopic spiking neural network of recurrently coupled prototypical and arkypallidal neurons. Using bifurcation analysis, we examine the influence of the intra-pallidal connectivity on the GPe dynamics. We find that under healthy conditions, the inhibitory coupling determines whether the GPe is close to either a bi-stable or an oscillatory regime. Furthermore, we show that oscillatory input to the GPe, arriving from subthalamic nucleus or striatum, leads to characteristic patterns of cross-frequency coupling observed at the GPe. Based on these findings, we propose two different hypotheses of how dopamine depletion at the GPe may lead to phase-amplitude coupling between the parkinsonian beta rhythm and a GPe-intrinsic gamma rhythm. Finally, we show that these findings generalize to realistic spiking neural networks of sparsely coupled type-I excitable GPe neurons.Significant StatementOur work provides (a) insight into the theoretical implications of a dichotomous GPe organization for its macroscopic dynamic regimes, and (b) an exact mean-field model that allows for future investigations of the relationship between GPe spiking activity and local field potential fluctuations. We identify the major phase transitions that the GPe can undergo when subject to static or periodic input and link these phase transitions to the emergence of synchronized oscillations and cross-frequency coupling in the basal ganglia. Due to the close links between our model and experimental findings on the structure and dynamics of prototypical and arkypallidal cells, our results can be used to guide both experimental and computational studies on the role of the GPe for basal ganglia dynamics in health and disease.

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Section: Discussionsupporting

confidence: 88%

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

Gast

Gong

Schmidt

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore, it has been successfully employed to reveal the mechanisms at the basis of theta-nested gamma oscillations Segneri et al (2020); Ceni et al (2020) and the coexistence of slow and fast gamma oscillations Bi et al (2020). Finally it has been recently applied to modelling electrical synapses Montbrió and Pazó (2020) and working memory Taher et al (2020).…”

Section: Discussionmentioning

confidence: 99%

“…This new generation of neural mass models has been recently used to describe the emergence of collective oscillations in fully coupled networks Devalle et al (2017); Laing (2017); Coombes and Byrne (2019); Dumont and Gutkin (2019) as well as in balanced sparse networks di Volo and Torcini (2018). Furthermore, it has been successfully employed to reveal the mechanisms at the basis of theta-nested gamma oscillations Segneri et al (2020); Ceni et al (2020) and the coexistence of slow and fast gamma oscillations Bi et al (2020). Finally it has been recently applied to modelling electrical synapses Montbrió and Pazó (2020), working memory Taher et al (2020) and brain resting state activity Rabuffo et al (2020).…”

Section: Discussionmentioning

confidence: 99%

Patient-specific network connectivity combined with a next generation neural mass model to test clinical hypothesis of seizure propagation

Gerster¹,

Taher

Hlinka

et al. 2021

Preprint

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Modulations of the neuronal subthreshold activity, giving rise to rhythms at high firing rate, represent the high signal complexity of the brain dynamic repertoire. Together with neural network oscillations, they are a fundamental mechanism for cognition, perception and consciousness. Consequently, perturbations of network activity play an important role in the pathophysiology of brain disorders. Here we combine structural information from non-invasive brain imaging with mathematical modeling, thus leveraging an in-silico platform for the exploration of causal mechanisms of brain function and clinical hypothesis testing. In particular we use a recently derived set of exact mean-field equations for networks of quadratic integrate-and-fire neurons to provide a comprehensive study of the effect of external drives or perturbations on neuronal networks exhibiting multistability in order to investigate the role played by the neuroanatomical connectivity matrix in shaping the emergent dynamics.We demonstrate, along the example of 20 diffusion-weighted magnetic resonance imaging (MRI) connectomes of healthy subjects, 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. Moreover we studied patient-specific brain network models of 15 drug-resistant epilepsy patients with implanted stereotactic electroencephalography (SEEG) electrodes. Each personalized brain model was derived from structural data of MRI and diffusion tensor weighted imaging (DTI), while each patient’s virtual brain was further personalized through the integration of the clinically hypothesized epileptogenic zone (EZ), i.e. the local network where highly synchronous seizures originate. Across patients, it turns out that patient-specific network connectivity is predictive for the subsequent seizure propagation pattern thus opening the possibility of improving diagnosis and surgery outcome.

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“…In particu-lar, this formulation has allowed to derive a closed lowdimensional set of macroscopic equations describing exactly the evolution of the population firing rate and of the mean membrane potential [21]. In the very last years the Montbrió-Pazó-Roxin (MPR) model [21] is emerging as a representative of a new generation of neural mass models able to successfuly capture relevant aspects of neural dynamics [22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: L(y)mentioning

confidence: 99%

A reduction methodology for fluctuation driven population dynamics

Goldobin

Volo

Torcini

2021

Preprint

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Lorentzian distributions have been largely employed in statistical mechanics to obtain exact results for heterogeneous systems. Analytic continuation of these results is impossible even for slightly deformed Lorentzian distributions, due to the divergence of all the moments (cumulants). We have solved this problem by introducing a pseudo-cumulants’ expansion. This allows us to develop a reduction methodology for heterogeneous spiking neural networks subject to extrinsinc and endogenous noise sources, thus generalizing the mean-field formulation introduced in [E. Montbrió et al., Phys. Rev. X 5, 021028 (2015)].

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Cross frequency coupling in next generation inhibitory neural mass models

Cited by 30 publications

References 57 publications

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

On the role of arkypallidal and prototypical neurons for phase transitions in the external pallidum

Patient-specific network connectivity combined with a next generation neural mass model to test clinical hypothesis of seizure propagation

A reduction methodology for fluctuation driven population dynamics

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