Control of Dynamic Patterns in Neuronal Networks

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The past decade has seen significant growth in the development and use of neurostimulation technology to manipulate neural activity in the brain. The applications of such technology range from scientific objectives, e.g., studying how different parts of the brain interact with each other, to clinical objectives, e.g., using stimulation to alleviate the symptoms of neurological disorders such as Parkinson's disease. Despite many technological advances associated with such stimulation, its use is still largely limited to perturbative paradigms, in which stereotyped inputs (waveforms) are used to activate or deactivate a neuronal network in its entirety. In other words, the stimulation is used to create a uniform circuit response, turning an entire population of brain cells (neurons) on or off, without regard for specificity (i.e., which cells in the population respond) or timing (i.e., when they turn on or off). In engineering, control is understood as not simply uniform stimulation, but as the precise creation or prevention of certain system maneuvers at each moment in time. This project will investigate fundamental questions regarding the use of neurostimulation to control neuronal networks in this temporally precise sense. That is, rather than simply stimulating the brain, the goal of this research is to develop new engineering theory and methods to allow practitioners to steer the activity in neural circuits so as to create complex patterns of activity, or neural spiking. Thus, this highly transdisciplinary project will elucidate enabling theory for the use of neurostimulation and will lead to new and fundamental contributions to systems theory and control engineering. The project will also support new initiatives to promote interdisciplinary education for students from traditionally underserved populations through the creation of summer workshops for students from local high schools in the city of St. Louis, MO.By bridging ensemble systems theory with computational neuroscience, general and versatile frameworks for neuronal control will be formulated. Specifically, oscillator and conductance-based neural models will be used to mathematically model both oscillatory and non-oscillatory regimes in brain networks. Using these models, the proposed work will determine fundamental limits on the controllability of neuronal spiking or synchronization by the application of external inputs. The notion of ensemble reachability is also proposed and will be examined via entropic gain analysis and dynamic optimization. These characterizations of fundamental control properties in both oscillatory and non-oscillatory neural dynamic regimes will then facilitate the development of control design paradigms to synthesize optimal controls for the creation of complex patterns in neuronal populations, such as firing or entrainment patterns. Methods of ensemble control and formal averaging will be employed to derive optimal sequence and pattern controls, and stochastic versions of these problems will also be treated using stochastic control techniques to ensure tolerance to noise and uncertainty, which are pervasive in neural circuits. Thus, the results of the proposed research will include a unified systems-theoretic framework for analyzing the control of physiologically relevant brain networks; and further, will include a set of formal neural control design methods that may be readily translated to a range of neurostimulation implementations.