In the field of Medical Imaging, extensive research has been dedicated to leveraging its potential in uncovering critical diagnostic features in patients. Artificial Intelligence (AI)-driven medical diagnosis relies on sophisticated machine learning and deep learning models to analyze, detect, and identify diseases from medical images. Despite the remarkable performance of these models, characterized by high accuracy, they grapple with trustworthiness issues. The introduction of a subtle perturbation to the original image empowers adversaries to manipulate the prediction output, redirecting it to other targeted or untargeted classes. Furthermore, the scarcity of publicly available medical images, constituting a bottleneck for reliable training, has led contemporary algorithms to depend on pretrained models grounded on a large set of natural images -- a practice referred to as transfer learning. However, a significant {\em domain discrepancy} exists between natural and medical images, which causes AI models resulting from transfer learning to exhibit heightened {\em vulnerability} to adversarial attacks. This paper proposes a {\em domain assimilation} approach that introduces texture and color adaptation into transfer learning, followed by a texture preservation component to suppress undesired distortion. We systematically analyze the performance of transfer learning in the face of various adversarial attacks under different data modalities, with the overarching goal of fortifying the model's robustness and security in medical imaging tasks. The results demonstrate high effectiveness in reducing attack efficacy, contributing toward more trustworthy transfer learning in biomedical applications.