Cancer is one of the leading causes of death in the western world, with medical imaging playing a key role for early diagnosis. Focusing on breast cancer, one of the emerging imaging methodologies is Dynamic Contrast Enhanced-Magnetic Resonance Imaging (DCE-MRI). The flip side of using DCE-MRI is in its long acquisition times, often causing the patient to move, resulting in motion artefacts, namely distortions in the acquired image that can affect DCE-MRI analysis. A possible solution consists in the use of Motion Correction Techniques (MCTs), i.e. procedures intended to re-align the post-contrast image to the corresponding pre-contrast (reference) one. This task is particularly critic in DCE-MRI, due to brightness variations introduced in post-contrast images by the contrast-agent flowing. To face this problem, in this work we introduce a new MCT for breast DCE-MRI leveraging Physiologically Based PharmacoKinetic (PBPK) modelling and Artificial Neural Networks (ANN) to determine the most suitable physiologically-compliant transformation. To this aim, we propose a Neural Registration Network relying on a very task-specific loss function explicitly designed to take into account the contrast agent flowing while enforcing a correct re-alignment. We compared the obtained results against some conventional motion correction techniques, evaluating the performance on a patient-by-patient basis. Results clearly show the effectiveness of the proposed approach, resulting as the best performing even when compares against other techniques designed to take into account for brightness variations.