The basal ganglia are a group of nuclei that play an important role in the generation of movement. Dysfunction of the basal ganglia is associated with movement disorders such as Parkinson's disease and Huntington's chorea. Structures within the basal ganglia have in fact been the target of recent therapeutic surgical procedures including pallidotomy and deep brain stimulation. Numerous experiments have demonstrated that neurons within the basal ganglia display a variety of dynamic behaviors; moreover, patterns of neuronal activity differ between normal and pathological states. Neither the origins of these neural firing patterns nor the mechanisms that underlie the patterns are understood. The primary goals of the project are to develop detailed computational models, based on experimental data, for basal ganglia activity and to develop mathematical tools for analyzing these models. The investigator systematically studies mechanisms underlying complex activity patterns found in a broad class of excitatory-inhibitory neuronal networks. These include a recently constructed model for neurons within the so-called indirect pathway of the basal ganglia. He also uses geometric, dynamical systems methods to explore how these networks transform incoming firing patterns.
The investigator develops a computational model for neuronal activity in the basal ganglia. The model is used to formulate and test hypotheses concerning the functional role of the basal ganglia in both healthy and diseased states. As it evolves, the model serves as a tool that can be used to test hypotheses about the function basal ganglia, the pathologies that develop in motor disorders, and the mechanisms through which therapeutic interventions such as deep brain stimulation (DBS) may prove effective. In particular, a central aspect of this research is to test hypotheses about how DBS reduces parkinsonian motor symptoms. This may lead to new strategies by which DBS can be applied. Topics in this project present tremendous opportunities for cross-disciplinary seminars, workshops and collaborations. The principal investigator has been very active in the training of undergraduate, graduate, and postdoctoral students. He has organized numerous workshops at international conferences and has lectured at several summer educational programs. A primary goal of these activities is to help nurture a community of scholars from different disciplines involved in the mathematical biosciences.
