Fake It Right: Injecting Anatomical Logic into Synthetic Supervised Pre-training for Medical Segmentation

Vision Transformers (ViTs) excel in 3D medical segmentation but require massive annotated datasets. While Self-Supervised Learning (SSL) mitigates this using unlabeled data, it still faces strict privacy and logistical barriers. Formula-Driven Supervised Learning (FDSL) offers a privacy-preserving alternative by pre-training on synthetic mathematical primitives. However, a critical semantic gap limits its efficacy: generic shapes lack the morphological fidelity, fixed spatial layouts, and inter-organ relationships of real anatomy, preventing models from learning essential global structural priors. To bridge this gap, we propose an Anatomy-Informed Synthetic Supervised Pre-training framework unifying FDSL's infinite scalability with anatomical realism. We replace basic primitives with a lightweight shape bank with de-identified, label-only segmentation masks from 5 subjects. Furthermore, we introduce a structure-aware sequential placement strategy to govern the patch synthesis process. Instead of random placement, we enforce physiological plausibility using spatial anchors for correct localization and a topological graph to manage inter-organ interactions (e.g., preventing impossible overlaps). Extensive experiments on BTCV and MSD datasets demonstrate that our method significantly outperforms state-of-the-art FDSL baselines and SSL methods by 1.74\% and up to 1.66\%, while exhibiting a robust scaling effect where performance improves with increased synthetic data volume. This provides a data-efficient, privacy-compliant solution for medical segmentation. The code will be made publicly available upon acceptance.