Data-driven modeling of spatiotemporal dynamics using multimodal imaging data.

Understanding how biological systems evolve across space and time remains a fundamental challenge, particularly when dynamic processes vary substantially across individuals. We present a personalized graph-based dynamical modeling framework for characterizing spatiotemporal biological dynamics from longitudinal multimodal imaging data. The framework constructs individualized brain graphs from MRI and PET measurements and learns patient-specific dynamical parameters governing regional structural and molecular changes. Applied to 1,891 participants from the Alzheimer's Disease Neuroimaging Initiative, the model captures the coordinated evolution of amyloid-β, tau, neurodegeneration, and cognition and accurately predicts their future trajectories, outperforming established clinical and neuroimaging benchmarks. Patient-specific dynamical parameters reveal distinct patterns of biological progression and provide improved prediction of future cognitive decline compared with standard biomarkers. Sensitivity analysis further identifies regional network features associated with the propagation of pathological and structural changes, recovering known temporolimbic and frontal vulnerability patterns. These results demonstrate how data-driven dynamical modeling can integrate multimodal longitudinal measurements to uncover individualized spatiotemporal patterns and latent mechanisms of biological change. The framework provides a quantitative approach for studying complex biological dynamics across heterogeneous individuals and establishes a foundation for personalized modeling of progressive biological processes.