As Simple as Possible (But Not Simpler): Model Reduction in the Treatment of Neurological and Cardiological Disease

Mechanical and Aerospace Engineering
Department Seminar Series

Dan Wilson
Ph.D. Candidate
Department of Mechanical Engineering
University of California, Santa Barbara
Santa Barbara, CA

As technology continues to evolve at a rapid pace, scientists are able to observe and record more and more of the underlying dynamical behavior contributing to biological diseases. With these advances in technology comes a growing interest in applying dynamical systems and control theoretic tools to provide new insight into treatment options for medically intractable diseases. My particular focus has been on the creation and utilization of mathematical tools which can reduce the dimensionality and complexity of the differential equations describing nonlinear biological systems, making them amenable for further study. Attention is given to the problem of understanding the role deep brain stimulation (DBS) as a treatment for patients with Parkinson’s disease. Model reduction strategies provide starting point for merging two competing hypotheses for the therapeutic mechanism of DBS as a treatment for Parkinson’s disease and can also be used to suggest better stimulation strategies than those currently available. In addition to neuroscience applications, model reduction techniques facilitate the development of low energy electrical stimulation methods for the elimination of cardiac arrhythmias such as alternans, tachycardia, and fibrillation; all of which are associated with the emergence of cardiac arrest, a leading cause of death in the industrialized world. 

Biosketch

Dan Wilson is a doctoral candidate at the University of California, Santa Barbara. His work spans multiple subdisciplines in computational biology, including cardiology, neuroscience, and circadian rhythms. Dan has published multiple papers with emphasis on strategies for the reduction of complex and high dimensional systems with the goal of understanding their fundamental features that contribute to biological dysfunction.