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# The role of onset location and edge resection in epileptic seizure propagation in mice brain: a computational study

Juliette Courson, Mathias Quoy, Yulia Timofeeva, Thanos Manos

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Juliette Courson, Mathias Quoy, Yulia Timofeeva, Thanos Manos. The role of onset location and edge resection in epileptic seizure propagation in mice brain: a computational study. NeuroFrance 2023, May 2023, Lyon, France. **hal-04115326**

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Submitted on 2 Jun 2023

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# The role of onset location and edge resection in epileptic seizure propagation in mice brain: a computational study

Juliette Courson¹,²,⁴*, Mathias Quoy²,³ and Yulia Timofeeva⁴,⁵ and Thanos Manos²

¹Laboratoire de Physique Théorique et Modélisation (LPTM), CNRS, UMR 8089, CY Cergy Paris Université, Cergy-Pontoise Cedex, France

²Equipes Traitement de l'Information et Systèmes (ETIS), CNRS, UMR 8051, ENSEA, CY Cergy Paris Université, Cergy-Pontoise Cedex, France

³IPAL CNRS Singapore

⁴Department of Computer Science, University of Warwick, Coventry, UK

⁵University College London Institute of Neurology, University College London, London, UK

* juliette.courson@cyu.fr

## Introduction

Recent results on seizures' propagation employing dynamical models [1] have reproduced the recruitment order of brain areas in a mouse brain network [2,3]. However, the exact mechanisms of the onset and propagation of a seizure are still not fully understood. We investigate how the location and connectivity of the Epileptogenic Zone affects the spatio-temporal propagation of the seizure in mice brain. Our goal is to identify the underlying properties of critical edges that prevent seizure propagation when being resected.

## The Epileptor model [1]

* Phenomenological model reproducing the main features of **epileptic seizures**: slow spiking ($x_1, y_1$) [4] and fast discharges ($x_2, y_2$) [5]

* Slow permittivity $z$ acts as a control parameter. **Epileptogenicity $x_0$** determines the system's ability to produce spontaneous seizures and their intensity.

* Seizure onset via Saddle-Node bifurcation, offset via Homoclinic bifurcation.

* $x_2-x_1$ mimics the surface tension.

$$ \dot{x}_{1,i} = y_{1,i} - f_1(x_{1,i}, x_{2,i}) - z_i + I_1 $$

$$ \dot{y}_{1,i} = 1 - 5x_{1,i}^2 - y_1, i $$

$$ \dot{z}_i = \begin{cases} r(4(x_{1,i} - x_{0,i}) - z_i - 0.1z_i^7) + K \sum_j c_{ij}(x_{1,i} - x_{1,j}) & \text{if } z_i < 0 \\ r(4(x_{1,i} - x_{0,i}) - z_i) + K \sum_j c_{ij}(x_{1,i} - x_{1,j}) & \text{if } z_i \ge 0 \end{cases} $$

$$ \dot{x}_{2,i} = -y_{2,i} + x_{2,i} - x_{2,i}^3 + I_2 + 0.002g(x_{1,i}) - 0.3(z_i - 3.5) $$

$$ \dot{y}_{2,i} = \frac{1}{\tau}(-y_{2,i} + f_2(x_{2,i})) $$

$$ \dot{g}(x_{1,i}) = -0.01(g - 0.1x_{1,i}) $$

<figure><img src="image_3.png" /><figcaption>Bifurcation diagram and trajectories of the Epileptor.</figcaption></figure>

$$ f_1(x_{1,i}, x_{2,i}) = \begin{cases} 3x_{1,i}^3 - x_{1,i}^2 & \text{if } x_{1,i} < 0 \\ (x_{2,i} - 0.6(z_i - 4)^2)x_{1,i} & \text{if } x_{1,i} \ge 0 \end{cases} $$

$$ f_2(x_{2,i}) = \begin{cases} 0 & \text{if } x_{2,i} < -0.25 \\ 6(x_{2,i} + 0.25) & \text{if } x_{2,i} \ge -0.25 \end{cases} $$

<figure><img src="image_4.png" /><figcaption>Time series of an epileptogenic (bottom) and a non-epileptogenic (upper) Epileptor.</figcaption></figure>

## Seizure propagation in a large brain network

* Network of Epileptors coupled via mouse brain structural connectivity [6], using The Virtual Brain framework

* Definition of an **Epileptogenic Zone** [7] (EZ) and a **Propagation Zone** (PZ). EZ's activity triggers **seizure propagation** in PZ

<figure><img src="image_5.png" /></figure>

## References

* [1] Jirsa, V. K., Stacey, W. C., Quilichini, P. P., Ivanov, A. I., & Bernard, C. (2014). On the nature of seizure dynamics. Brain, 137(8), 2210-2230.

* [2] Melozzi, F., Woodman, M. M., Jirsa, V. K., & Bernard, C. (2017). The Virtual Mouse Brain: A Computational Neuroinformatics Platform to Study Whole Mouse Brain Dynamics. Eneuro, 4(3), ENEURO.0111-17.2017.

* [3] Proix, T., Bartolomei, F., Guye, M., & Jirsa, V. K. (2017). Individual brain structure and modelling predict seizure propagation. Brain, 140(3), 641-654.

* [4] Hindmarsh, J. & Rose, R. (1984). A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London. Series B. Biological Sciences, 221(1222), 87-102.

* [5] Roy, D., Ghosh, A., & Jirsa, V. K. (2011). Phase description of spiking neuron networks with global electric and synaptic coupling. Physical Review E, 83(5), 051909.

* [6] Oh, S. W. et al. (2014). A mesoscale connectome of the mouse brain. Nature, 508(7495), 207-214.

* [7] Jehi L. (2018). The Epileptogenic Zone: Concept and Definition. Epilepsy currents, 18(1), 12-16.

* [8] Courson, J., Quoy, M., Timofeeva, Y., & Manos, T. (2023). The role of onset location and edge resection in epileptic seizure propagation in mice brain: a computational study, in preparation.

## Results: 1. Effect of the EZ's connectivity on seizure propagation

* To characterize the network's nodes, we use their average shortest path length and their eigenvector centrality

$$ x_v = \frac{1}{\lambda} \sum_{t \in V} a_{v,t} x_t $$

* EZ with high centrality and low shortest path length generate global seizures

* EZ with high shortest path length only generate local seizures

* **Hippocampal nodes** have intermediate values. **CA1** and **Dentate Gyrus (DG)** generate global seizures. **CA3** generate local seizures.

<figure><img src="image_6.png" /><figcaption>Map of the nodes' connectivity properties. Red nodes generate global seizures when being set as the EZ. Seizure initiating at the blue nodes do not spread.</figcaption></figure>

## 2. Connectivity of the Hippocampal nodes

* I CA1, I DG: stronger connections to left **Enthorinal lateral cortex** (I ENTI) and **left Subiculum** (I SUB) areas and right Hippocampus.

* I CA3: mainly connected to the Hippocampus

<figure><img src="image_7.png" /><figcaption>Subnetworks of the outgoing connections from the three hippocampal nodes, with weights higher than 0.1.</figcaption></figure>

* A: standard seizure propagation in a mice brain network, when the EZ is left CA1.

* B, C: delayed seizure propagation. Removing the strongest outgoing connections of I CA1 within the left hemisphere (resp. with the right hemisphere) slows down seizure propagation, mostly in the left (resp. right) hemisphere.

* D: halted seizure propagation when removing these three connections.

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>Upper: graph of the brain network. The red node is the EZ, the red edges are removed. Bottom: projection of the time distance from seizure in the brain template.</figcaption></figure>

## Conclusions

* Global seizures are produced by the brain network's hubs, but also by some less central areas.

* Both strong connections within the hippocampal loop (Hippocampus, Enthorinal cortex, Subiculum) and between right and left Hippocampus have strong impact in the seizure propagation [8].

* Seizure confinement can be achieved by removing a minimal number of three connections [8] instead of all as presented in [2]