M 3 amba: Multi-focus multi-domain Mamba network for liver tumor segmentation on multicenter MRI

Liver cancer is a prevalent malignancy with high global incidence and mortality rates, and accurate tumor segmentation is essential for clinical diagnosis and treatment. To address challenges posed by blurred tumor boundaries, class imbalance, and volume variations, we propose a multi-focus multi-domain Mamba network for liver tumor segmentation on multicenter MRI dataset, termed M 3 amba. For this study, we collected and annotated a multicenter MRI dataset of liver cancer, focusing on hepatocellular carcinoma (HCC). In the encoder, we propose a large-small mixing (LSMixing) module to enhance adaptability to tumors of different sizes, and a binary-sequence hybrid Mamba (BSHMamba) module to effectively integrate complementary information from multi-sequence MRI while maintaining the robustness of single-sequence branches. In the decoder, the multi-scale channel attention (MSCA) module is employed to improve the modeling of fine-grained features and boundary details. Furthermore, the triple-domains Mamba (TriMamba) module fuses channel, spatial and frequency domain features, partially alleviating the negative impact of class imbalance and blurred boundaries. The model is optimized with the multi-constraint tumor loss (MCT Loss), enforcing multi-level collaborative constraints. Extensive experiments on our multicenter dataset demonstrate that M 3 amba achieves superior performance over state-of-the-art methods, showing strong robustness in segmenting both large and small tumors. • We collected a large-scale, multicenter MRI dataset for HCC, with precise lesion annotations, providing a high-quality resource for liver tumor segmentation research. • On the encoder, we propose the LSMixing module to address tumor volume variability and the BSHMamba module to balance robustness and complementary information in multi-sequence MRI, thereby enhancing multi-scale feature representation. • On the decoder, we propose the TriMamba module to integrate channel, spatial, and frequency domains for class imbalance mitigation and long-range dependency modeling, while MSCA refines boundary details. • We propose the M3amba network and optimize it using the Multi-Constraint Tumor Loss (MCT Loss). Extensive experiments demonstrate superior performance and robustness in liver tumor segmentation compared with state-of-the-art methods.