Controllability analysis of the small-world network of neural populations

¹ Key Laboratory of Intelligent Rehabilitation and Neuromodulation of Hebei Province, Institute of Electrical Engineering, Yanshan University - Qinhuangdao, Hebei Province, China
² School of Mathematics and Big Data, Guizhou Education University - Guiyang, Guizhou Province 550018, China

^(a) E-mail: liuxian@ysu.edu.cn (corresponding author)

Received: 16 August 2022
Accepted: 15 September 2022

Abstract

Controllability analysis of brain networks is the theoretical foundation for neuromodulation feasibility. This paper presents a new framework for studying controllability of certain brain networks on the basis of neural mass models, the minimum driver node, the linearization technique and a controllability index. Firstly, a WS small-world network of Jansen-Rit's neural populations is established to mathematically model complicated neural dynamics. Secondly, an analytical method of analyzing controllability is built based on the bipartite graph maximum matching algorithm, the linearization technique and the matrix condition number. The bipartite graph maximum matching algorithm is applied to determine the minimum driver node sets for the established network while the matrix condition number is applied to define the controllability index which qualitatively evaluates the degree of the controllability of the established network. Finally, the effectiveness of the proposed analytical method is demonstrated by the influence of important parameters on the controllability and the comparison with an existing method. The proposed framework provides theoretical foundation for the study of neuromodulation feasibility, and the results are expected to lead us to better modulate neurodynamics by optimizing network dynamics or designing optimal stimulation protocols.