CANDO modelling report

Introduction

This is a report for the CANDO project on the ongoing computational modelling work that parallels the in vitro closed-loop optogenetic stimulation experiments (by Dr. Jackson and Dr. Hazra). The overall goal of both the modelling and experiments is to demonstrate that closed-loop optogenetic stimulation can alter ongoing (epileptic) activity in vitro. Of particular importance for the modelling part is to additionally explain the experimental observations on how the activity is altered through stimulation.

Briefly, the in vitro experiments used the 4AP model of epileptiform activity, and the optogenetic stimulation was delivered to principal neurons (EMX promotor) using Channelrhodopsin activation. The stimulation was delivered in a closed-loop manner, where the stimulus depends on the amplitude and phase of the ongoing activity (details are described in Methods).

We will use the approach of a simple neural population model to describe the experimentally observed ongoing activity, including epileptiform spikes and discharges (see Methods for details). Neural population models describe the activity of neural tissue in terms of the average activity (either firing activity, or field potential) of populations of neurons (Wilson 1972, Amari 1977, Jansen 1995). Usually, principal neurons are lumped into one population, and inhibitory neurons are lumped into a second population. In the most simple case, this will result in a system of two ordinary differential equations describing the activity of neural tissue (Wilson 1972, Amari 1977).

Such an abstract approach means that we are disregarding spatial variations in activity. This has been deemed justified, as we observed little spatial variation in the dynamics across different recording channels, and the experiments themselves did not aim to investigate spatial effects. However, dynamically, such an approach has been shown to be sufficient to capture most epileptiform dynamics observed in vitro and in vivo (Wang 2012). Therefore, a simple neural population model was the most immediate choice for a computational model, which did not require many explicit assumptions and is mathematically and computationally easy to handle.

Methods

In vitro stimulation protocol

The description of the exact in vitro experimental setup will be described in a separate report from the experimental side. I will only describe the closed-loop stimulation protocol here to enable understanding of the modelling results.

At each update step, the past time series determines what the LED output for the next time instance will be. The specific protocol that was used involved three operation. The past time series was essentially bandpass filtered at a specified centre frequency \(f\), then phase shifted by a specified phase angle \(\theta\), and finally rectified (setting all negative values to zero). This process is illustrated in Fig. \ref{Fig_CLalgo} (a). This new signal is used to determine the output signal from the LED at the next time instance for stimulation. The actual output of the LED is shown for an example in Fig. \ref{Fig_CLalgo} (b). The parameters \(f\) and \(\theta\) are adjustable and were tested in the in vitro experiments.

\label{Fig_CLalgo}Illustrative example of how the closed-loop feedback signal is obtained. (a) Raw signal and the three different steps of processing (filtering, rectifying, phase shifting) are shown. The phase shifted signal would be the output of the LED, where the exact phase shift is determined by the experimental setup. (b) Similar as in (a), but showing the actual LED output signal.