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Deep learning (DL) has attracted interest in healthcare for disease diagnosis systems in medical imaging analysis (MedIA) and is especially applicable in Big Data environments like federated learning (FL) and edge computing. However, there is little research into mitigating the vulnerabilities and robustness of such systems against adversarial attacks, which can force DL models to misclassify, leading to concerns about diagnosis accuracy. This paper aims to evaluate the robustness and scalability of DL models for MedIA applications against adversarial attacks while ensuring their applicability in FL settings with Big Data. We fine-tune three state-of-the-art transfer learning models, DenseNet121, MobileNet-V2, and ResNet50, on several MedIA datasets of varying sizes and show that they are effective at disease diagnosis. We then apply the Fast Gradient Sign Method (FGSM) to attack the models and utilize adversarial training (AT) and knowledge distillation to defend them. We provide a performance comparison of the original transfer learning models and the defended models on the clean and perturbed data. The experimental results show that the defensive techniques can improve the robustness of the models to the FGSM attack and be scaled for Big Data as well as utilized for edge computing environments.