  How will my face look when I get older? Or, for a more challenging question:
How will my brain look when I get older? To answer this question one must
devise (and learn from data) a multivariate auto-regressive function which
given an image and a desired target age generates an output image. While
collecting data for faces may be easier, collecting longitudinal brain data is
not trivial. We propose a deep learning-based method that learns to simulate
subject-specific brain ageing trajectories without relying on longitudinal
data. Our method synthesises images conditioned on two factors: age (a
continuous variable), and status of Alzheimer's Disease (AD, an ordinal
variable). With an adversarial formulation we learn the joint distribution of
brain appearance, age and AD status, and define reconstruction losses to
address the challenging problem of preserving subject identity. We compare with
several benchmarks using two widely used datasets. We evaluate the quality and
realism of synthesised images using ground-truth longitudinal data and a
pre-trained age predictor. We show that, despite the use of cross-sectional
data, our model learns patterns of gray matter atrophy in the middle temporal
gyrus in patients with AD. To demonstrate generalisation ability, we train on
one dataset and evaluate predictions on the other. In conclusion, our model
shows an ability to separate age, disease influence and anatomy using only 2D
cross-sectional data that should be useful in large studies into
neurodegenerative disease, that aim to combine several data sources. To
facilitate such future studies by the community at large our code is made
available at https://github.com/xiat0616/BrainAgeing.
