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P165: Using dynamical mean field theory to study synchronization in the brain.
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**Isabelle Harris**, **Anthony Burkitt**, **Hamish Meffin**, **Andre Peterson**

This work focuses on the dynamics of large networks of neurons, and particularly aims to study the effects of brain structures and functions on state transitions, such as those found in epilepsy.

Currently, the modelling framework in theoretical neuroscience focuses on using dynamical systems analysis of neural field models, and numerical simulations to disentangle the influences of structure and function on brain dynamics. Howver, these models and methods use continuous spatial averages of net- work connectivity. In this work, we are particularly interested in the spatial structures and functions that induce a state transition from a state of asynchronous, intrinsically fluctuating: a highly complex state (non-seizure state), to a state of intrinsic synchrony and hyper excitability: a simplistic state (seizure state). Using a first order neural network model with a discrete spatial field given by a coupling matrix, a set of self-consistent equations that describe the nature of the activity of network structures with populations of neurons, can be derived using dynamical mean field theory [Mastrogiuseppe and Ostojic, 2017]. This set of self-consistent equa- tions can be solved semi-analytically, and we use these solutions to derive a measure of spiking variability and hence, excitability: the coefficient of variation (CV). The CV is a common measure of spiking variability used in theoretical neuroscience [Meffin et al., 2004], but it has also been recently used as a measure of syncrhonisation in the analysis of animal model data [Fontenele et al., 2019]. We use the derived expression of CV to show that under certain network structure and function conditions there exists a state of asyncrhonous and intrinsic fluctuations, which is believed to be analagous to a normal resting brain state. Furthermore, the seizure state can be defined clinically as a much less complex state: a state of hyper-excitability and synchronisation of neural units. This work identifies possible key properties of the neural network that cause synchronous and hyper-excitable behaviour in the network, using dynamical systems, Random Matrix Theory, and DMFT.

Understanding how these network structure affect the nature of the neural dynamics is essential to advancing our current mathematical understanding of epileptic transitions, and here we have found a relationship between structure and dynamics. In particular, this work identifies network properties that cause normal brain function and properties that may cause seizure transitions.

References

[Fontenele et al., 2019] Fontenele, A. J., de Vasconcelos, N. A., Feliciano, T., Aguiar, L. A., Soares- Cunha, C., Coimbra, B., Dalla Porta, L., Ribeiro, S., Rodrigues, A. J., Sousa, N., et al. (2019). Criticality between cortical states. Physical review letters, 122(20):208101.

[Mastrogiuseppe and Ostojic, 2017] Mastrogiuseppe, F. and Ostojic, S. (2017). Intrinsically-generated fluctuating activity in excitatory-inhibitory networks. PLoS computational biology, 13(4):e1005498.

[Meffin et al., 2004] Meffin, H., Burkitt, A. N., and Grayden, D. B. (2004). An analytical model for the ‘large, fluctuating synaptic conductance state’typical of neocortical neurons in vivo. Journal of computational neuroscience, 16(2):159–175.

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Topic: P165: Using dynamical mean field theory to study synchronization in the brain.

Time: Jul 20, 2020 07:00 PM Amsterdam, Berlin, Rome, Stockholm, Vienna

Link: https://unimelb.zoom.us/j/94169410381?pwd=Z0FNQ0FYRHE5OWxmbGFEQTI3ZU1JQT09

Password: 162839

Using Dynamical Mean Field Theory (DMFT) to study state transitions in the brain

Currently, the modelling framework in theoretical neuroscience focuses on using dynamical systems analysis of neural field models, and numerical simulations to disentangle the influences of structure and function on brain dynamics. Howver, these models and methods use continuous spatial averages of net- work connectivity. In this work, we are particularly interested in the spatial structures and functions that induce a state transition from a state of asynchronous, intrinsically fluctuating: a highly complex state (non-seizure state), to a state of intrinsic synchrony and hyper excitability: a simplistic state (seizure state). Using a first order neural network model with a discrete spatial field given by a coupling matrix, a set of self-consistent equations that describe the nature of the activity of network structures with populations of neurons, can be derived using dynamical mean field theory [Mastrogiuseppe and Ostojic, 2017]. This set of self-consistent equa- tions can be solved semi-analytically, and we use these solutions to derive a measure of spiking variability and hence, excitability: the coefficient of variation (CV). The CV is a common measure of spiking variability used in theoretical neuroscience [Meffin et al., 2004], but it has also been recently used as a measure of syncrhonisation in the analysis of animal model data [Fontenele et al., 2019]. We use the derived expression of CV to show that under certain network structure and function conditions there exists a state of asyncrhonous and intrinsic fluctuations, which is believed to be analagous to a normal resting brain state. Furthermore, the seizure state can be defined clinically as a much less complex state: a state of hyper-excitability and synchronisation of neural units. This work identifies possible key properties of the neural network that cause synchronous and hyper-excitable behaviour in the network, using dynamical systems, Random Matrix Theory, and DMFT.

Understanding how these network structure affect the nature of the neural dynamics is essential to advancing our current mathematical understanding of epileptic transitions, and here we have found a relationship between structure and dynamics. In particular, this work identifies network properties that cause normal brain function and properties that may cause seizure transitions.

References

[Fontenele et al., 2019] Fontenele, A. J., de Vasconcelos, N. A., Feliciano, T., Aguiar, L. A., Soares- Cunha, C., Coimbra, B., Dalla Porta, L., Ribeiro, S., Rodrigues, A. J., Sousa, N., et al. (2019). Criticality between cortical states. Physical review letters, 122(20):208101.

[Mastrogiuseppe and Ostojic, 2017] Mastrogiuseppe, F. and Ostojic, S. (2017). Intrinsically-generated fluctuating activity in excitatory-inhibitory networks. PLoS computational biology, 13(4):e1005498.

[Meffin et al., 2004] Meffin, H., Burkitt, A. N., and Grayden, D. B. (2004). An analytical model for the ‘large, fluctuating synaptic conductance state’typical of neocortical neurons in vivo. Journal of computational neuroscience, 16(2):159–175.

PosterCNS2020
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Monday July 20, 2020 7:00pm - 8:00pm CEST

Slot 07

Slot 07