A state observer for the computational network model of neural populations.

A state observer plays a vital role in the design of state feedback neuromodulation schemes used to prevent and treat neurological or psychiatric disorders. This paper aims to design a state observer to reconstruct all unmeasured states of the computational network model of neural populations that replicates patterns seen on the electroencephalogram by using the model inputs and outputs, as the theoretical basis for designing state feedback neuromodulation clinical schemes. The feasibility problem of linear matrix inequality conditions, which is the most important one for observer design of the computational network model of neural populations, is solved by using the input-output stability theory and the Lurie system theory. The observer matrices of the designed observer are formed by the optimal solution of the linear matrix inequality conditions. An illustrative example shows that the observer can simultaneously reproduce internal state variables of normal and lesion populations of the computational network model of neural populations under the background of focal origin brain dysfunction, and the designed observer has certain robustness toward input uncertainty and measurement noise. To the best of our knowledge, no observers have previously been designed for the computational network model of neural populations. The design of state feedback neuromodulation schemes based on the computational network model of neural populations is a new direction in the field of computational neuroscience.

Controllability of Networks of Multiple Coupled Neural Populations: An Analytical Method for Neuromodulation's Feasibility.

Neuromodulation plays a vital role in the prevention and treatment of neurological and psychiatric disorders. Neuromodulation's feasibility is a long-standing issue because it provides the necessity for neuromodulation to realize the desired purpose. A controllability analysis of neural dynamics is necessary to ensure neuromodulation's feasibility. Here, we present such a theoretical method by using the concept of controllability from the control theory that neuromodulation's feasibility can be studied smoothly. Firstly, networks of multiple coupled neural populations with different topologies are established to mathematically model complicated neural dynamics. Secondly, an analytical method composed of a linearization method, the Kalman controllable rank condition and a controllability index is applied to analyze the controllability of the established network models. Finally, the relationship between network dynamics or topological characteristic parameters and controllability is studied by using the analytical method. The proposed method provides a new idea for the study of neuromodulation's feasibility, and the results are expected to guide us to better modulate neurodynamics by optimizing network dynamics and network topology.