A large number of models have been developed to replicate the complex behavior of neurons in the human brain, ranging from single neuron phase models to population-level models. When drug treatments are not sufficient, researchers and clinicians use external stimuli (similar to a pacemaker or defibrillator) to help treat neurological conditions such as epilepsy and Parkinson’s disease. Despite the popularity and prolific number of neuroscience models, the kinds of stimulus that should be delivered into the brain is, however, poorly understood. Nearly all of the techniques to-date involve ad-hoc methods to shape preset pulses or pulse trains.
In this work we aim to cast the problem of steering cortical areas of the brain away from pathological behavior found in neural disorders as optimal control problems. Applying this methodology from control theory permits a systematic way to design input to be used in implant devices. By applying methods from optimal ensemble control, we can design stimuli which are robust to variation and uncertainty in system parameters. We have done this for both single neuron models and population level models. Population level models offer several advantages – namely the measurements that are made by clinical equipment (e.g., EEG) and stimulus we deliver are typically at this aggregated level rather than at the individual neuron level.
An exciting direction that we are currently exploring, because the brain is a complex system relatively well characterized by its neural connectivity, is connecting some of this work to our research into control of networks.