Transient Neural Dynamics Reconstruction

Anima Kujur, Zahra Monfared, Shervin Safavi

Keywords: Transient Neural Dynamics, Sharp Wave-Ripples, Hippocampal LFP, Koopman Operator, Dynamic Mode Decomposition, Time Series Reconstruction

TL;DR: Our PCA-DMD framework reconstructs hippocampal signals, capturing long-term dynamics and fast transients like sharp wave-ripples, advancing neuroscience research and clinical applications.

Abstract: Sharp wave-ripples (SWRs) are high-frequency ($\sim 100$--$250$ Hz) oscillatory bursts often observed in hippocampal local field potentials (LFPs), and are involved in a wide range of cognitive functions (memory consolidation to off-line and online planning). Reconstructing LFPs in the SWR regime is challenging due to the complexity of signals and the transient nature of these bursts. While many algorithms provide reasonable short-term predictions, most fail to reproduce long-term dynamics while preserving fast transients. In this study, we combine principal component analysis (PCA) with dynamic mode decomposition (DMD) to approximate the Koopman operator in a reduced latent space, allowing for the efficient reconstruction of multi-channel hippocampal LFPs. The Koopman framework shifts the focus from state-space trajectories to observable evolution in an infinite-dimensional function space, enhancing interpretability and understanding of nonlinear systems. Using 200{,}000 samples, our PCA-DMD framework achieves superior reconstruction accuracy compared to state-of-the-art DMD variants. Our results highlight PCA-DMD’s robustness in capturing complex neural dynamics and offer a powerful tool for analysis of transient dynamics (e.g., SWR) with significant implications for neuroscience research and clinical applications.

Submission Number: 55