Previous studies have indicated that white matter hyperintensities (WMH), the main radiological feature of small vessel disease, may evolve (i.e., shrink, grow) or stay stable over a period of time. Predicting these changes are challenging because it involves some unknown clinical risk factors that leads to a non-deterministic prediction task. In this study, we propose a deep learning model to predict the evolution of WMH from baseline to follow-up (i.e., 1-year later), namely \``Disease Evolution Predictor" (DEP) model, which can be adjusted to become a non-deterministic model. The DEP model receives a baseline image as input and produces a map called \``Disease Evolution Map" (DEM), which represents the evolution of WMH from baseline to follow-up. Two DEP models are proposed, namely DEP-UResNet and DEP-GAN, which are representatives of the supervised (i.e., need expert-generated manual labels to generate the output) and unsupervised (i.e., do not require manual labels produced by experts) deep learning algorithms respectively. To simulate the non-deterministic and unknown parameters involved in WMH evolution, we modulate a Gaussian noise array to the DEP model as auxiliary input. This forces the DEP model to imitate a wider spectrum of alternatives in the prediction results. The alternatives of using other types of auxiliary input instead, such as baseline WMH and stroke lesion loads are also proposed and tested. Based on our experiments, the fully supervised machine learning scheme DEP-UResNet regularly performed better than the DEP-GAN which works in principle without using any expert-generated label (i.e., unsupervised). However, a semi-supervised DEP-GAN model, which uses probability maps produced by a supervised segmentation method in the learning process, yielded similar performances to the DEP-UResNet and performed best in the clinical evaluation. Furthermore, an ablation study showed that an auxiliary input, especially the Gaussian noise, improved the performance of DEP models compared to DEP models that lacked the auxiliary input regardless of the model's architecture. To the best of our knowledge, this is the first extensive study on modelling WMH evolution using deep learning algorithms, which deals with the non-deterministic nature of WMH evolution.### Competing Interest StatementThe authors have declared no competing interest.

Automatic Spatial Estimation of White Matter Hyperintensities Evolution in Brain MRI using Disease Evolution Predictor Deep Neural Networks