$Δ$t-Mamba3D: A Time-Aware Spatio-Temporal State-Space Model for Breast Cancer Risk Prediction

Longitudinal analysis of sequential radiological images is hampered by a fundamental data challenge: how to effectively model a sequence of high-resolution images captured at irregular time intervals. This data structure contains indispensable spatial and temporal cues that current methods fail to fully exploit. Models often compromise by either collapsing spatial information into vectors or applying spatio-temporal models that are computationally inefficient and incompatible with non-uniform time steps. We address this challenge with Time-Aware $\Delta$t-Mamba3D, a novel state-space architecture adapted for longitudinal medical imaging. Our model simultaneously encodes irregular inter-visit intervals and rich spatio-temporal context while remaining computationally efficient. Its core innovation is a continuous-time selective scanning mechanism that explicitly integrates the true time difference between exams into its state transitions. This is complemented by a multi-scale 3D neighborhood fusion module that robustly captures spatio-temporal relationships. In a comprehensive breast cancer risk prediction benchmark using sequential screening mammogram exams, our model shows superior performance, improving the validation c-index by 2-5 percentage points and achieving higher 1-5 year AUC scores compared to established variants of recurrent, transformer, and state-space models. Thanks to its linear complexity, the model can efficiently process long and complex patient screening histories of mammograms, forming a new framework for longitudinal image analysis.