SPARNet: Breaking the Detail–Direction Trade-off in 3D Medical State-Space Models with Scale-Preserving Radial Scanning

State-space models (SSMs) have emerged as an efficient alternative to Transformers for 3D medical image segmentation, yet how volumetric features are tokenized and serialized for these models remains largely overlooked. We identify two coupled limitations in existing 3D SSMs. First, fixed and coarse token scales cause detail loss at the boundaries of small or low-contrast structures. Second, Cartesian-axis serialization separates neighboring voxels and introduces directional bias into state propagation. Because tokenization determines what information is preserved and scan order determines how it propagates, we argue that the two must be addressed jointly. We present SPAR-Net, a Scale-Preserving Adaptive Radial Network built on this principle. A Scale-Adaptive Feature Extractor aligns fine-, intermediate, and coarse-scale features on a shared high-resolution token grid, which adapts the receptive field without discarding spatial detail. Stochastic Layer Scanning replaces axis-aligned scans with center-referenced radial layers traversed along complementary inward and outward paths. A Feature Refinement block restores volumetric correspondence after sequence modeling, and a Bidirectional Progressive Fusion Block exchanges semantic and boundary cues across encoder levels. Under a unified protocol, SPARNet consistently improves both Dice and HD95 over existing 3D segmentation models. It achieves 85.25% mean Dice and 12.20 HD95 on Synapse multi-organ CT, and 64.02% mean Dice and 17.15 HD95 on MSD Pancreas. The largest gains appear on boundary-sensitive organs such as the gallbladder and pancreas, and on pancreatic tumors. Analyses of token scale, scan order, feature fusion, and efficiency show that every component contributes. They also show that fine multi-scale tokenization and radial bidirectional propagation are complementary.