# Sensitivity analysis enlightens effects of connectivity in a Neural Mass Model under Control-Target mode

## TL;DR

This paper explores how inhibitory connections between brain regions can enable inhibitory control in a biophysical model of the brain.

## Contribution

The study introduces inhibitory connectivity into a neural mass model and identifies conditions under which inhibitory control can emerge.

## Key findings

- Inhibitory control can only emerge in 'Target inhibition by Control' and 'mutual inhibition' connectivity types.
- The model's sensitivity depends on the strength of self-inhibition within the Target region.
- The analytical framework can be extended to study more complex brain network configurations.

## Abstract

Biophysical models of human brain represent the latter as a graph of inter-connected neural regions. Building from the model by Naskar et al. (Network Neuroscience, 2021), our motivation was to understand how these brain regions can be connected at neural level to implement some inhibitory control, which calls for inhibitory connectivity rarely considered in such models. In this model, regions are made of inter-connected excitatory and inhibitory pools of neurons, but are long-range connected only via excitatory pools (mutual excitation). We thus extend this model by generalizing connectivity, and we analyse how connectivity affects the behaviour of this model. Focusing on the simplest paradigm made of a Control area and a Target area, we explore four typical kinds of connectivity: mutual excitation, Target inhibition by Control, Control inhibition by Target, and mutual inhibition. For this, we build an analytical sensitivity framework, nesting up sensitivities of isolated pools, of isolated regions, and of the full system. We show that inhibitory control can emerge only in Target inhibition by Control and mutual inhibition connectivities. We next offer an analysis of how the model sensitivities depends on connectivity structure, depending on a parameter controling the strength of the self-inhibition within Target region. Finally, we illustrate the effect of connectivity structure upon control effectivity in response to an external forcing in the Control area. Beyond the case explored here, our methodology to build analytical sensitivities by nesting up levels (pool, region, system) lays the groundwork for expressing nested sensitivities for more complex network configurations, either for this model or any other one.

Biophysical models of the human brain involve representing how its neurons interact among each other. In the brain, connectivity can be excitatory or inhibitory but only excitation is usually considered in biophysical models. Here, we propose a biophysical model including inhibition to give account of inhibitory control. We consider the simplest model that consists of a Control and a Target area, and we explore four types of connectivities: mutual excitation, Target inhibition by Control, Control inhibition by Target and mutual inhibition. We develop an analytical expression of the system’s response and show that inhibitory control happens only in cases of Target inhibition by Control and mutual inhibition. We illustrate how the system responds when the control area is excited by an external stimulus, and highlight the role of a parameter that drives the strength of self-inhibition within the Target region. Our analytical framework paves the way to study more complex brain network configurations using such biophysical models.