Collaborative Research: NSF-UEFISCDI: RUI: Effects of the Interplay Between Connectivity Architecture and Distributed Delays in Brain Network Dynamics

Over the past two decades researchers have made significant progress in developing mathematical models and tools that are compatible with understanding the complexity of the human brain and similarly complex systems. These tools have been used to investigate how complex neural interactions underlie dynamic patterns found in processes like learning, memory formation and cognition. However, many questions on both healthy and pathological brain function remain intractable by existing mathematical approaches. That is because the system's components interact both spatially and temporally. Hence, in order to model and understand differences between healthy and pathological function in a neural circuit, one needs to simultaneously keep track of connectivity architecture in a massive network, and of its past activity. This poses a significant challenge for both analytical and computational approaches. This project aims to establish and use a tractable quantitative framework that considers both of these aspects, by employing networks of coupled equations that include time delays to capture how recent interactions between the elements of the system influence future interactions. A traditional model of neural population dynamics will be used as the building block for larger functional brain circuits, while additionally incorporating different types of time-delays. This will enable a well-studied framework to be embedded into a new mathematical environment that jointly considers the system's architecture and history. Preliminary joint work (on toy network models with selected types of time delays) has established in principle that this approach is computationally tractable, and that it can be used to contextualize transitions between healthy brain function and pathological patterns (such as those found in Parkinson's disease and emotional disorders). The project will support a vertically integrated team including a postdoctoral fellow, a co-advised Ph.D. student and five undergraduate students at a predominantly undergraduate institution, recruited from underrepresented groups. The collaboration capitalizes on the team's combined expertise in network science, delay differential equations and brain imaging techniques. The team will combine new network techniques with novel approaches to distributed time delays. The theoretical methods will be integrated with human brain data for potential clinical applications, via the collaboration with the Neurology Department at University at Buffalo. The approach will encompass three aspects that will develop simultaneously and support each other. (1) General networks under minimal assumptions on network architecture and shape of the delay kernels will be developed. (2) Numerical simulations will be used to demonstrate dynamic behaviors in specific classes of complex networks and for structured or stochastic distributions of delay kernels across the network nodes. (3) The new mathematical framework and numerical algorithms will be used to investigate how timing impacts information propagation in neural circuits that govern specific behaviors, in both computational models and in empirical data. The methods developed in this project will thus help us understand physiological mechanisms behind imaging and behavioral observations and help identify the underpinnings of pathological behaviors in neurological and psychiatric illnesses. 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.