The recent success of deep learning together with the availability of large medical imaging datasets have enabled researchers to improve our understanding of complex chronic medical conditions such as neurodegenerative diseases. The possibility of predicting realistic and accurate images would be a breakthrough for many clinical healthcare applications. However, current image simulators designed to model neurodegenerative disease progression present limitations that preclude their utility in clinical practice. These limitations include personalization of disease progression and the ability to synthesize spatiotemporal images in high resolution. In particular, memory limitations prohibit full 3D image models, necessitating various techniques to discard spatiotemporal information, such as patch-based approaches. In this work, we introduce a novel technique to address this challenge, called Profile Weight Functions (PWF). We demonstrate its effectiveness integrated within our new deep learning framework, showing that it enables the extension to 3D of a recent state-of-the-art 2D approach. To our knowledge, we are the first to implement a personalized disease progression simulator able to predict accurate, personalised, high-resolution, 3D MRI. In particular, we trained a model of ageing and Alzheimer's disease progression using 9652 T1-weighted (longitudinal) MRI from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and validated on a separate test set of 1283 MRI (also from ADNI, random partition). We validated our model by analyzing its capability to synthesize MRI that produce accurate volumes of specific brain regions associated with neurodegeneration. Our experiments demonstrate the effectiveness of our solution to provide a 3D simulation that produces accurate and convincing synthetic MRI that emulate ageing and disease progression.