In the last five years, advances in processing power and computational efficiency in graphical processing units have catalyzed dozens of deep neural network segmentation algorithms for a variety of target tissues and malignancies. However, few of these algorithms preconfigure any biological context of their chosen segmentation tissues, instead relying on the neural network's optimizer to develop such associations de novo. We present a novel method for applying deep neural networks to the problem of glioma tissue segmentation that takes into account the structured nature of gliomas-edematous tissue surrounding mutually-exclusive regions of enhancing and non-enhancing tumor. We trained separate deep neural networks with a 3D U-Net architecture in a tree structure to create segmentations for edema, non-enhancing tumor, and enhancing tumor regions. Specifically, training was configured such that the whole tumor region including edema was predicted first, and its output segmentation was fed as input into separate models to predict enhancing and non-enhancing tumor. We trained our model on publicly available pre- and post-contrast T1 images, T2 images, and FLAIR images, and validated our trained model on patient data from an ongoing clinical trial.