Multi-organ segmentation using deep learning requires large amounts of annotated patient data; however, institutions often lack sufficiently large and diverse annotated datasets. Privacy constraints further prevent institutions from sharing patient data to overcome this limitation. Moreover, due to the labor-intensive nature of annotation and the scarcity of diverse expertise, institutions typically have labels for only a small portion of their local data, leaving the larger unlabeled portion unused. In this work, we propose a flexible semi-supervised federated multi-task student-teacher framework that leverages federated learning (FL) to improve multi-organ segmentation using both labeled and unlabeled data across participating sites. At each communication round, the proposed framework initiates local training, where clients with labels for the same task form a federation to produce an aggregated teacher model. The resulting teachers generate task-specific features for all data at each client. Subsequently, all clients form a second federation to train a multi-task student model with a shared encoder and task-specific decoders that replicate the teacher-generated features across all segmentation tasks. The aggregated student model is then used to update the local teachers and initiate the next training round. Extensive experiments demonstrated the effectiveness of the proposed method compared with local and federated single-organ models, yielding an average performance gain of 13 percent across clients. The experiments also demonstrated the impact of multi-task learning and unlabeled data and the applicability of the framework in relaxing labeled-data requirements for client participation. The code is available at https://github.com/AshknMrd/FedMust.

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