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Foundation models (FMs) show great promise for robust downstream performance across medical imaging tasks and modalities, including cardiac magnetic resonance (CMR), following task-specific adaptation. However, adaptation using single-site data may lead to suboptimal performance and increased model bias, while centralized fine-tuning on clinical data is often infeasible due to privacy constraints. Federated fine-tuning offers a privacy-preserving alternative; yet conventional approaches struggle under heterogeneous, non-IID multi-center data and incur substantial communication overhead when adapting large models. In this work, we study federated FM fine-tuning for 3D CMR disease detection and propose Med-DualLoRA, a client-aware parameter-efficient fine-tuning (PEFT) federated framework that disentangles globally shared and local low-rank adaptations (LoRA) through additive decomposition. Global and local LoRA modules are trained locally, but only the global component is shared and aggregated across sites, keeping local adapters private. This design improves personalization while significantly reducing communication cost, and experiments show that adapting only two transformer blocks preserves performance while further improving efficiency. We evaluate our method on a multi-center state-of-the-art cine 3D CMR FM fine-tuned for disease detection using ACDC and combined M\&Ms datasets, treating each vendor as a federated client. Med-DualLoRA achieves statistically significant improved performance (balanced accuracy 0.768, specificity 0.612) compared to other federated PEFT baselines, while maintaining communication efficiency. Our approach provides a scalable solution for local federated adaptation of medical FMs under realistic clinical constraints.