The proposed research will use engineering techniques, mathematical principles, and computer simulations to understand how pathological neural synchronization associated with Parkinson's disease can be disrupted through the injection of current stimuli. This includes determining control inputs which optimally reset a neuron's phase by driving the state of the neuron to a phaseless set at which it is very sensitive to noise. When neurons in a population receive such a common stimulus, the noise serves to randomize the neurons' phases, thereby desychronizing the population. In this control scheme, such inputs will be triggered by the detection of population-level synchrony, giving an event-based feedback control algorithm for which the biological tissue is only stimulated when necessary, thereby reducing the overall accumulation of negative side effects of electrical stimulation, and also the amount of power used. In an alternative approach, nonlinear hybrid control, involving the application of a series of different control laws, will be used to break neural synchrony by stabilizing the splay state for the coupled neuron system, which is the state for which the neurons' phases are evenly distributed. Such control will also be generalized to an event-based framework, and optimized so that it minimizes the total input energy or the total time needed to reach the splay state. The robustness of the control algorithms will be explored with respect to uncertainties in the neuron model, uncertainties in the measurements of the firing events, different types of coupling, changes to the input stimulus, heterogeneity of the stimulus due to proximity to the electrode, and properties of the noise.
There is evidence that the tremors associated with Parkinson's disease are associated with the pathological synchronization of neurons in the motor control region of the patient's brain. An FDA-approved treatment for such tremors, called deep brain stimulation, involves the implantation of an electrode into this region, which is used to inject electrical current into the brain tissue. As presently implemented, the electrical current is typically a periodic sequence of pulses with a frequency around 100 Hertz, which has been shown empirically to be an effective treatment for some patients. This research will use engineering techniques, mathematical principles, and state-of-the-art computer simulations to develop the theoretical foundation for alternative electrical current stimuli for deep brain stimulation, which could lead to better treatments for Parkinson's disease. In particular, control algorithms will be developed which minimize the amount of current injected, which will minimize tissue damage and energy consumption, the latter reducing the need for surgery to replace the battery which is used for deep brain stimulation. This will also include the use of feedback control, in which the state of the neural population is monitored by an electrode and the electrical current stimulus is only injected as needed.
The brain is an amazing organ which is responsible for a number of important functions including cognition, attention, emotion, perception, memory, and motor control. Certain neurological diseases are associated with pathological brain activity. For example, it has been hypothesized that some symptoms of Parkinson's disease are caused by pathologically synchronized neural activity in the motor control region of the brain. With this in mind, we have developed a computational procedure for determining an electrical stimulus which optimally desynchronizes the activity of a group of neurons using the phenomenon of "chaos", a well-established concept which is important for many systems including the weather and fluid turbulence in which small disturbances to the system behavior grow exponentially in time. Our work suggests a potentially effective "brain control" method for treating Parkinson's disease using such stimuli delivered by a deep brain stimulation electrode. Our approach requires at least an order of magnitude less energy than existing deep brain stimulation methods, which could allow the deep brain stimulation battery to last longer, reducing the need for battery replacement surgery which is expensive and has risks of complications. We also undertook preliminary explorations of the use of related control methods to treat other disorders such as epilepsy, cardiac arrhythmias, and advanced/delayed sleep phase syndrome. These require different control objectives, but can also be addressed in an optimal control framework.
