# Phase-Dependent Response to Electrical Stimulation of Cortical Networks during Recurrent Epileptiform Short Discharge Generation In Vitro

## TL;DR

This study explores how electrical stimulation at different phases affects epileptiform brain activity in a lab model, showing that timing influences control effectiveness.

## Contribution

A novel sensitivity function and phase-dependent stimulation analysis in epilepsy models, validated with in vitro experiments and multiple mathematical models.

## Key findings

- Sensitivity to stimulation increases with phase for most models, except the Epileptor-2B with after-spike depolarization.
- Epileptor-2B outperforms other models in capturing subthreshold oscillations under noise, aligning with experimental data.
- Closed-loop stimulation is more effective in later phases of interspike intervals, highlighting the stochastic nature of epileptiform discharges.

## Abstract

The closed-loop control of pathological brain activity is a challenging task. In this study, we investigated the sensitivity of continuous epileptiform short discharge generation to electrical stimulation applied at different phases between the discharges using an in vitro 4-AP-based model of epilepsy in rat hippocampal slices. As a measure of stimulation effectiveness, we introduced a sensitivity function, which we then measured in experiments and analyzed with different biophysical and abstract mathematical models, namely, (i) the two-order subsystem of our previous Epileptor-2 model, describing short discharge generation governed by synaptic resource dynamics; (ii) a similar model governed by shunting conductance dynamics (Epileptor-2B); (iii) the stochastic leaky integrate-and-fire (LIF)-like model applied for the network; (iv) the LIF model with potassium M-channels (LIF+KM), belonging to Class II of excitability; and (v) the Epileptor-2B model with after-spike depolarization. A semi-analytic method was proposed for calculating the interspike interval (ISI) distribution and the sensitivity function in LIF and LIF+KM models, which provided parametric analysis. Sensitivity was found to increase with phase for all models except the last one. The Epileptor-2B model is favored over other models for subthreshold oscillations in the presence of large noise, based on the comparison of ISI statistics and sensitivity functions with experimental data. This study also emphasizes the stochastic nature of epileptiform discharge generation and the greater effectiveness of closed-loop stimulation in later phases of ISIs.