Continuous Energy Landscape Models for Predicting Cognitive Decline in Brain Tumor Patients

Abstract

Large-scale brain activity exhibits metastable dynamics, recurrently visiting a limited set of configurations whose transitions can be summarized by an energy landscape. Most neuroimaging studies estimate this landscape using pairwise maximum-entropy models applied to binarized signals, which discards amplitude information and limits the representation of higher-order interactions. This dissertation introduces two complementary advances to address these limitations. First, it extends the discrete framework to a high-order formulation that aggregates regions into ensembles using k-means clustering and represents interactions among ensembles through exact state enumeration at the group level. Second, it proposes a continuous energy landscape model that operates directly on real-valued time series data, estimating a normalized density that eliminates the need for binarization prior to energy calculation. This approach results in a more expressive model with richer parameterization.The proposed methods were evaluated on synthetic data generated from Kuramoto oscillator networks and switching linear dynamical systems, assessing their ability to recover basin geometry, transition matrices, and latent state distributions. In addition, a real-world case study was considered using a resting-state functional magnetic resonance imaging (fMRI) dataset, where the proposed energy landscape model was applied to predict postoperative cognitive outcomes, such as working memory, executive function, and reaction time, in patients with brain tumors. Together, these findings underscore the effectiveness and translational potential of the proposed framework for modeling complex brain dynamics.