Endoscopic operative scenes—subject to barrel distortion, specular glare, smoke/blood occlusion, and multi-instrument crossings—often display pronounced topological discontinuities and jagged boundaries, with segmentation masks prone to tearing and aliasing. To address these conditions, we propose a Graph-Dynamics Augmented Foundation Model for instrument segmentation that co-models structure and boundary behavior. The architecture comprises: a Topology-coupled Reasoning Field that regards grid pixels as graph nodes and adaptively propagates topological semantics to supply a global shape prior; a Boundary Dispersive Dynamics Field that interprets the structure-enhanced feature map as a continuous field and, via fourth-order Runge-Kutta integration of a nonlinear dispersive equation, suppresses high-frequency artefacts while repairing broken contours; and a Multi-scale Dynamic Synergy Field that, through gated weighting, balances the structural and dynamical streams to attain a morphology-boundary synergy. Experiments on Kvasir-Instrument, Synthetic MICCAI 2020, and UW-Sinus-Surgery-C/L indicate mean gains of 2.17 pp in Dice and 2.81 pp in IoU against strong contemporaries, suggesting that the integration of topological priors, physical dynamics, and visual foundation modelling improves spatial coherence and edge fidelity for instrument segmentation.