Temporal Dynamics in Spatial Random Field Theory: A Methodological Advance in fMRI Data Analysis

Functional magnetic resonance imaging (fMRI) is a noninvasive tool for studying neural correlates of cognition by measuring task-evoked brain activity. Accurate interpretation of fMRI data depends on modeling the hemodynamic response (HR), which varies across brain regions and conditions. Brain plasticity adds complexity as functional changes during development and aging affect cognition, emotion, and behavior. BOLD signals display complex temporal dynamics influenced by both neural and physiological factors, challenging conventional models. This highlights the need for adaptive frameworks that account for temporal dependencies and spatial heterogeneity in neural activity detection. This current study enhances fMRI data analysis by integrating temporal dynamics into spatial random field theory. We developed a new test statistic, within the time-adaptive Gaussian Random Field Model, focusing on signal detection in fMRI data. It captures the global maximum across spatial and temporal dimensions. Our methodology, employing the Functional Autoregressive model order one(FAR (1)), focuses on temporal dependencies and spatial arrangements in data. This research utilizes a time-adaptive Gaussian random field model with the test statistic Xmax to enhance neural signal detection in fMRI data. Simulations assessed its performance under varying conditions, including amplitude (ξ), signal scale (σ0), spatial location (s0), temporal decay (σρ), and i multiple time points, demonstrating the model’s effectiveness in capturing complex spatial-temporal patterns. The results demonstrate that Xmax consistently outperforms the time-invariant Ymax, with detection power improving under higher amplitude, signal scale, and temporal factors, while spatial location has minimal impact. This study advances spatial random field theory by integrating temporal dynamics, enhancing neural signal detection in fMRI data. Future work should explore scale-space and rotation-space analyses and scenarios with multiple signals to increase model applicability.