Defining information-based functional objectives for neurostimulation and control

Neurostimulation - the practice of applying exogenous excitation, e.g., via electrical current, to the brain - has been used for decades in clinical applications such as the treatment of motor disorders and neuropsychiatric illnesses. Over the past several years, more emphasis has been placed on understanding and designing neurostimulation from a systems-theoretic perspective, so as to better optimize its use. Particular questions of interest have included designing stimulation waveforms that best induce certain patterns of brain activity while minimizing expenditure of stimulus power. The pursuit of these designs faces a fundamental conundrum, insofar as they presume that the desired pattern (e.g., desyn-chronization of a neural population) is known a priori. In this paper, we present an alternative paradigm wherein the goal of the stimulation is not to induce a prescribed pattern, but rather to simply improve the functionality of the stimulated circuit/system. Here, the notion of functionality is defined in terms of an information-theoretic objective. Specifically, we seek closed loop control designs that maximize the ability of a controlled circuit to encode an afferent `hidden input,' without prescription of dynamics or output. In this way, the control attempts only to make the system `effective' without knowing beforehand the dynamics that are needed to be induced. We devote most of our effort to defining this framework mathematically, providing algorithmic procedures that demonstrate its solution and interpreting the results of this procedure for simple, prototypical dynamical systems. Simulation results are provided for more complex models, including an example involving control of a canonical neural mass model.

I. Introduction

Neurostimulation - the practice of exciting neural tissue using exogenous inputs (e.g., electrical fields) - is pervasive in both basic and clinical neuroscience [1], [2]. Usually, the objective of neurostimulation is to activate particular population of neurons within the brain and/or to induce a certain pattern of brain activity, such as oscillations. The complex dynamics present in neuronal circuits means that the design of such stimulation is quite nontrivial, especially as it relates to shaping open-loop stimulus waveforms [3], [4] and the design of closed-loop paradigms [5].