Model-based spatiotemporal analysis and control of a network of spiking Basal Ganglia neurons

Precise spatiotemporal control of the output of a network of intricately connected neurons through microstimulation is highly desirable in many neural prosthetic applications. This control, however, is challenging, in part due to the large number of unobserved variables in the system under consideration, the complexity underlying the local mechanisms of microstimulation, and the interplay between the intrinsic network structure and its dynamic response to external stimulation. In this work we use a simplified firing rate model, identified from a network of Hodgkin-Huxley (HH) type spiking Basal Ganglia (BG) neurons, to study the response of the network to patterned microstimulation, and to design effective feedback control laws to approximate a desired spatiotemporal pattern. Mathematical analysis of the simplified model using Singular Value Decomposition (SVD) suggests that the BG neural circuit under study exhibits strong spatiotemporal selectivity and only responds strongly to a range of specific spatiotemporal stimulation patterns. We use the concept of functional controllability based on SVD to evaluate the effectiveness of various combinations of stimulation sites for a given set of neurons to be controlled. The results suggest that the functional controllability is largely decided by the network connectivity and the connection strength. Finally, we demonstrate that the controller design based on the simplified model is indeed effective in driving the output neurons to follow a prescribed spatiotemporal firing pattern in the network output.