Recently, Test-Time Adaptation (TTA) has gained increasing attention in medical imaging due to its ability to improve model generalization under domain shifts without retraining. In particular, directly applying a well-trained model across various medical centers faces significant performance degradation caused by variations in equipment, operators, imaging conditions, and scanning skill levels of sonographers. Existing TTA methods either rely on parameter adaptation that increases computational cost or apply simple prediction fusion that ignores anatomical structure knowledge. To address these limitations, we propose a novel backward-free Topology-aware TTA framework named T^3 that integrates Structural Perception Modeling (SPM) and Box Regression Adaptation (BRA). SPM is implemented through an organ space heatmap generated via Gaussian kernel superposition. This heatmap encodes anatomical topology without requiring additional training or source data. BRA further improves localization and classification by fusing detection outputs based on the contribution of detected results to anatomically meaningful peak points from the heatmaps. Extensive experiments were conducted across six cross-domain scenarios, and the results demonstrate that our method achieves state-of-the-art cross-domain detection performance while maintaining high efficiency, offering a practical and robust solution for real-world medical diagnostic applications. All source codes will be publicly available.