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Instance segmentation plays a vital role in the morphological quantification of biomedical entities such as tissues and cells, enabling precise identification and delineation of different structures. Current methods often address the challenges of touching, overlapping or crossing instances through individual modeling, while neglecting the intrinsic interrelation between these conditions. In this work, we propose a Gradient Anomaly-aware Biomedical Instance Segmentation approach (GAInS), which leverages instance gradient information to perceive local gradient anomaly regions, thus modeling the spatial relationship between instances and refining local region segmentation. Specifically, GAInS is firstly built on a Gradient Anomaly Mapping Module (GAMM), which encodes the radial fields of instances through window sliding to obtain instance gradient anomaly maps. To efficiently refine boundaries and regions with gradient anomaly attention, we propose an Adaptive Local Refinement Module (ALRM) with a gradient anomaly-aware loss function. Extensive comparisons and ablation experiments in three biomedical scenarios demonstrate that our proposed GAInS outperforms other state-of-the-art (SOTA) instance segmentation methods. The code is available at https://github.com/DeepGAInS/GAInS.