There are many natural and technological systems that undergo oscillations in mechanical, electrical, and/or chemical properties, ranging from simple pendula to pacemaker cells in the heart and blinking fireflies. When such oscillators interact, their dynamics can adjust to give synchronized behavior. Such synchronization can be beneficial: for example, generators of electrical power acting on a common load synchronize under appropriate conditions, a crucial effect for the normal functioning of power-generation networks. Synchronization can also be detrimental: for example, tremors arising from Parkinson's disease are due to pathological, synchronized brain activity. This project aspires to understand, use, and control the synchronization of individual and coupled oscillators to external signals and to each other. This work will enhance the understanding of entrainment and interactions of cellular circadian oscillators, and will provide a theoretical basis for the treatment of neurological disorders such as Parkinson's disease using the therapeutic technique known as deep brain stimulation. This work will also enhance the theoretical basis for new mechanical filtering and sensing capabilities, which exploit coupling between microelectromechanical oscillators. In addition to research activities, this project includes the development of a freely available, interactive website on oscillators and synchronization.
This grant funded research at the University of California, Santa Barbara which led to the development of a new control algorithm to desynchronize a population of neurons, which could lead to a more efficient method for treating neuromotor disorders such as Parkinson's disease. This algorithm, which has been verified through computer simulations of neurons, relies on a feedback mechanism in which the present state of the neurons is used to determine when an electrical current stimulus is necessary. The research was inspired by Deep Brain Stimulation (DBS), an FDA-approved therapeutic procedure used to treat brain disorders including Parkinson's disease. Here, a neurosurgeon guides a small electrode into the motor control region of the patient's brain, and then connects the electrode to a pacemaker implanted in their chest. The pacemaker sends electrical current signals directly into the brain tissue. Given evidence that Parkinson’s disease is associated with the pathological synchronization of neural activity in the motor control region of a patient's brain, the goal of DBS is to desynchronize the neural population. As presently implemented, the DBS signal is a simple waveform that is always on. The new algorithm involves applying a stimulus only when a voltage measurement shows that the population is pathologically synchronized. Furthermore, the stimulus is chosen to be optimal, in the sense that it most rapidly drives the neurons to their phaseless set, at which they are extremely sensitive to noisy, naturally occurring brain signals. The noise effectively randomizes the phases of the neurons, giving desynchronization, and, hopefully, relief from Parkinsonian tremors. This grant also funded other research involving the control of neurons, and other research on the dynamics and control of nonlinear oscillators of technological interest.
