Collaborative Research: Phase-Amplitude-Based Reduced Order Modeling and Analysis of Strongly Coupled Neural Oscillators

This award supports fundamental research into mathematics that will enable a better understanding of the connection between neural rhythms and cognitive function. The research represents a necessary first step in the development of new treatment options for brain disorders caused by abnormal brain rhythms including schizophrenia, autism spectrum disorder, attention deficit hyperactivity disorder, and Parkinson's disease, promoting science and advancing national prosperity. Results of the project will contribute to the understanding of the biophysical mechanisms that support short-term memory, enabling a better understanding of how patients with disorders such as Alzheimer’s disease lose their ability to remember where they are. The award will support graduate students and researchers at the interface of neuroscience, mathematics, and engineering. The research plan includes two outreach efforts to encourage high school students to pursue careers in engineering and mathematics: 1) Week-long, hands-on research experiences with activities coordinated by the University of Tennessee, and 2) National mathematical modeling contests for regional high school and undergraduate students at the University of Florida. This project will advance the mathematical understanding of emergent behaviors in populations of coupled neural oscillators. Due to the size and dynamical complexity of most neural systems, model order reduction is often an imperative first step for mathematical analysis. However, the underlying assumptions required for the implementation of current approaches (e.g., weak coupling, symmetry, repetitive firing with a steady frequency) result in idealized phenomenological models that often give an incomplete and/or incorrect picture of the mechanisms governing the aggregate behavior. This fundamental limitation leads to gaps in our general understanding of how individual neurons organize to produce brain rhythms that ultimately support essential cognitive functions. The project aims to fill this gap in knowledge, significantly advancing coupled oscillator theory in neuroscientific contexts to accommodate strongly coupled neural networks, neural bursters, systems with nonnegligible heterogeneity, and higher order N-body interactions. Successful completion of this project will yield comprehensive, interpretable, mechanistic, and tractable techniques for the analysis of coupled oscillators, facilitating a deeper understanding of the mechanisms governing synchronization, rhythmic activity, and information processing in the brain. These techniques will be integrated with archival microelectrode data from rat entorhinal cortex to investigate the dynamical mechanisms that govern theta phase precession, a phenomenon that allows an animal to keep track of its precise location in space. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.