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Brain age estimation from Magnetic Resonance Images (MRI) derives the difference between a subject's biological brain age and their chronological age. This is a potential biomarker for neurodegeneration, e.g. as part of Alzheimer's disease. Early detection of neurodegeneration manifesting as a higher brain age can potentially facilitate better medical care and planning for affected individuals. Many studies have been proposed for the prediction of chronological age from brain MRI using machine learning and specifically deep learning techniques. Contrary to most studies, which use the whole brain volume, in this study, we develop a new deep learning approach that uses 3D patches of the brain as well as convolutional neural networks (CNNs) to develop a localised brain age estimator. In this way, we can obtain a visualization of the regions that play the most important role for estimating brain age, leading to more anatomically driven and interpretable results, and thus confirming relevant literature which suggests that the ventricles and the hippocampus are the areas that are most informative. In addition, we leverage this knowledge in order to improve the overall performance on the task of age estimation by combining the results of different patches using an ensemble method, such as averaging or linear regression. The network is trained on the UK Biobank dataset and the method achieves state-of-the-art results with a Mean Absolute Error of 2.46 years for purely regional estimates, and 2.13 years for an ensemble of patches before bias correction, while 1.96 years after bias correction.