Electrical conduction in brain tissue is commonly modeled using classical bidomain models. These models fundamentally assume that the discrete nature of brain tissue can be represented by homogenized equations where the extracellular space, the cell membrane, and the intracellular spare are continuous and exist everywhere. Consequently, they do not allow simulations highlighting the effect of a nonuniform distribution of ion channels along the cell membrane or the complex morphology of the cells. In this talk, we present a more accurate framework for cerebral electrodiffusion with an explicit representation of the geometry of the cell, the cell membrane and the extracellular space. To take full advantage of this framework, a numerical solution scheme capable of efficiently handling three-dimensional, complicated geometries is required. We propose a novel numerical solution scheme using a mortar finite element method, allowing for the coupling of variational problems posed over the non-overlapping intra and extracellular domains by weakly enforcing interface conditions on the cell membrane. This solution algorithm flexibly allows for arbitrary geometries and efficient solution of the separate subproblems. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the presented framework can give new insights in this setting. Simulations of 9 idealized, tightly packed axons show that inducing action potentials in one or more axons yields ephaptic currents that have a pronounced excitatory effect on neighboring axons, but fail to induce action potentials there [1].
This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement 714892 (Waterscales), and from the Research Council of Norway (BIOTEK2021 Digital Life project ‘DigiBrain’, project 248828).
[1] Ellingsrud A J, Solbrå A, Einevoll G T, et al. Finite element simulation of ionic electrodiffusion in cellular geometries. arXiv.org. 2019.
Spontaneous, synchronized activity is a well-established feature of cortical networks in vitro and in vivo. The landmark of this activity is the repetitive emergence of bursts propagating across networks as spatio-temporal patterns. Cortical bursts are governed by excitatory and inhibitory synapses via AMPA, NMDA and GABAa receptors. Although spontaneous activity is a well known phenomenon in developing networks, its specific underlying mechanisms in health and disease are not fully understood. In order to study the synaptic mechanisms regulating the propagation of cortical activity it is important to combine the experimental wet-lab studies with in silico modeling and build detailed, realistic, computational models of cortical network activity. Moreover, experimental studies and analysis of microelectrode array (MEA) data are not typically designed to support computational modeling. We show here how the synaptic AMPA, NMDA and GABAa receptors shape the initiation, propagation and termination of the cortical burst activity in rodent networks in vitro and in silico and develop model-driven data analysis workflow to support the development of spiking and biophysical network models in silico[1].
We created a model-driven data analysis workflow with multiple steps to examine the contributions of synaptic receptors to burst dynamics both in vitro and in silico neuronal networks (Fig.1). First, the cortical networks were prepared from the forebrains of the postnatal rats and maintained on MEA plates. Second, network-wide activity was recorded by MEA technique under several pharmacological conditions of receptor antagonists. Third, multivariate data analysis was conducted in a way that supports both neurobiological questions as well as the fitting and validation of computational models to quantitatively produce the experimental results. Fourth, the computational models were simulated with different parameters to test putative mechanisms responsible for network activity.
The experimental results obtained in this study show that AMPA receptors initiate bursts by rapidly recruiting cells whereas NMDA receptors maintain them. GABAa receptors inhibit the spiking frequency of AMPA receptor-mediated spikes at the onset of bursts and attenuate the NMDA receptor-mediated late phase. These findings highlight the importance of both excitatory and inhibitory synapses in activity propagation and demonstrate a specific interaction between AMPA and GABAa receptors for fast excitation and inhibition. In the presence of this interaction, the spatio-temporal propagation patterns of activity are richer and more diverse than in its absence. Moreover, we emphasize the systematic data analysis approach with model-driven workflow throughout the study for comparison of results obtained from multiple in vitro networks and for validation of data-driven model development in silico. A well-defined workflow can reduce the amount of biological experiments, promote more reliable and efficient use of the MEA technique, and improve the reproducibility of research. It helps reveal in detail how excitatory and inhibitory synapses shape cortical activity propagation and dynamics in rodent networks in vitro and in silico.
Reference
[1] Teppola H, Aćimović J, Linne M-L. Unique features of network bursts emerge from the complex interplay of excitatory and inhibitory receptors in rat neocortical networks. Front Cell Neurosci. 2019,13(377):1-22.
Paula Sanz-Leon, Leonardo L Gollo, James A Roberts
**Background.** Neural activity organizes in constantly evolving spatiotemporal patterns of activity, also known as brain waves (Roberts et al., 2019). Indeed, wave-like patterns have been observed across multiple neuroimaging modalities and across multiple spatiotemporal scales (Muller et al., 2016; Contreras et al. 1997; Destexhe et al. 1999). However, due to experimental constraints most attention has thus far been given to localised wave dynamics in the range of micrometers to a few centimeters, rather than at the global or large-scale that would encompass the whole brain. Existing toolboxes (Muller et al., 2016; Townsend et al., 2018) are geared particularly for 2D spatial domains (e.g., LFPs or VSDs on structured rectangular grids). No tool exists to study spatiotemporal waves naturally unfolding in 3D+t as recorded with different non-invasive neuroimaging techniques (e.g, EEG, MEG, and fMRI). In this work, we present results of using our toolbox neural flows (shown in Fig. 1).
**Methods and Results.** Our toolbox handles irregularly sampled data such as those produced via brain network modelling (Sanz-Leon et al., 2015; Breakspear, 2017) or source-reconstructed M/EEG, and regularly sampled data such as voxel-based fMRI. The toolbox performs the following steps: 1) Estimation of neural flows (Destexhe et al. 1999; Townsend et al., 2018; Sanz- Leon et al. 2020). 2) Detection of 3D singularities (i.e., points of vanishing flow). 3) Classification of 3D singularities. In that regard, the key flow singularities detected so far had been sources and sinks (from where activity emerges and vanishes, respectively), but no methods or tools existed to detect 3D saddles (around which activity is redirected to other parts of the brain). 4) Quantification of singularity statistics. 5) Finally, modal decomposition of neural flow dynamics. This decomposition allows for the detection and prediction of the most common spatiotemporal patterns of activity found in empirical data.
**Conclusions.** Representation of neural activity based on singularities (commonly known as critical points) is essentially a dimensionality reduction framework to understand large-scale brain dynamics. The distribution of singularities in physical space allows us to simplify the complex structure of flows into areas with similar dynamical behavior (e.g., fast versus slow, stagnant, laminar, or rotating). For modelling work, this compact representation allows for an intuitive and systematic understanding of the effects of various parameters in brain network dynamics such as spatial heterogeneity, lesions and noise. For experimental work, neural flows enable a rational understanding of large-scale brain dynamics directly in anatomical space which facilitates the interpretation and comparison of results across multiple modalities. Toolbox capabilities are presented in the accompanying figure. Watch this space for the open-source code: [ https://github.com/brain- modelling-group](https://github.com/brain-modelling-group)
References
Contreras et al. 1997 _J. Neurosci. 17, 1179-1196. _ Destexhe et al. 1999 J. Neurosci. _19 (11) 4595-4608. _ Muller et al., 2016 _eLife 5:e17267. _ Roberts et al., 2019 _Nat. Commun. 5;10(1):1056. _ Townsend et al., 2018 _PLoS Comput Biol_. 2018;14(12):e1006643. Sanz-Leon et al. 2020 _Neuroimage toolbox_ \- in preparation
