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).
This project is supported by NSF Grant DMS-2408407 and UEFISCDI Grant ROSUA-2024-0002.