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Effective, robust, and automatic tools for brain tumor segmentation are needed for the extraction of information useful in treatment planning from magnetic resonance (MR) images. Context-aware artificial intelligence is an emerging concept for the development of deep learning applications for computer-aided medical image analysis. In this work, it is investigated whether the addition of contextual information from the brain anatomy in the form of white matter, gray matter, and cerebrospinal fluid masks and probability maps improves U-Net-based brain tumor segmentation. The BraTS2020 dataset was used to train and test two standard 3D U-Net models that, in addition to the conventional MR image modalities, used the anatomical contextual information as extra channels in the form of binary masks (CIM) or probability maps (CIP). A baseline model (BLM) that only used the conventional MR image modalities was also trained. The impact of adding contextual information was investigated in terms of overall segmentation accuracy, model training time, domain generalization, and compensation for fewer MR modalities available for each subject. Results show that there is no statistically significant difference when comparing Dice scores between the baseline model and the contextual information models, even when comparing performances for high- and low-grade tumors independently. Only in the case of compensation for fewer MR modalities available for each subject did the addition of anatomical contextual information significantly improve the segmentation of the whole tumor. Overall, there is no overall significant improvement in segmentation performance when using anatomical contextual information in the form of either binary masks or probability maps as extra channels.