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In medical image analysis, transfer learning is a powerful method for deep neural networks (DNNs) to generalize well on limited medical data. Prior efforts have focused on developing pre-training algorithms on domains such as lung ultrasound, chest X-ray, and liver CT to bridge domain gaps. However, we find that model fine-tuning also plays a crucial role in adapting medical knowledge to target tasks. The common fine-tuning method is manually picking transferable layers (e.g., the last few layers) to update, which is labor-expensive. In this work, we propose a meta-learning-based LR tuner, named MetaLR, to make different layers automatically co-adapt to downstream tasks based on their transferabilities across domains. MetaLR learns appropriate LRs for different layers in an online manner, preventing highly transferable layers from forgetting their medical representation abilities and driving less transferable layers to adapt actively to new domains. Extensive experiments on various medical applications show that MetaLR outperforms previous state-of-the-art (SOTA) fine-tuning strategies. Codes are released.