Deep learning (DL) applied to breast tissue segmentation in magnetic resonance imaging (MRI) has received increased attention in the last decade, however, the domain shift which arises from different vendors, acquisition protocols, and biological heterogeneity, remains an important but challenging obstacle on the path towards clinical implementation. In this paper, we propose a novel Multi-level Semantic-guided Contrastive Domain Adaptation (MSCDA) framework to address this issue in an unsupervised manner. Our approach incorporates self-training with contrastive learning to align feature representations between domains. In particular, we extend the contrastive loss by incorporating pixel-to-pixel, pixel-to-centroid, and centroid-to-centroid contrasts to better exploit the underlying semantic information of the image at different levels. To resolve the data imbalance problem, we utilize a category-wise cross-domain sampling strategy to sample anchors from target images and build a hybrid memory bank to store samples from source images. We have validated MSCDA with a challenging task of cross-domain breast MRI segmentation between datasets of healthy volunteers and invasive breast cancer patients. Extensive experiments show that MSCDA effectively improves the model's feature alignment capabilities between domains, outperforming state-of-the-art methods. Furthermore, the framework is shown to be label-efficient, achieving good performance with a smaller source dataset. The code is publicly available at \url{https://github.com/ShengKuangCN/MSCDA}.
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