Objectives: Convolutional neural networks (CNNs) have established state-of-the-art performance in computer vision tasks such as object detection and segmentation. One of the major remaining challenges concerns their ability to capture consistent spatial and anatomically plausible attributes in medical image segmentation. To address this issue, many works advocate to integrate prior information at the level of the loss function. However, prior-based losses often suffer from local solutions and training instability. The CoordConv layers are extensions of convolutional neural network wherein convolution is conditioned on spatial coordinates. The objective of this paper is to investigate CoordConv as a proficient substitute to convolutional layers for medical image segmentation tasks when trained under prior-based losses.Methods: This work introduces CoordConv-Unet which is a novel structure that can be used to accommodate training under anatomical prior losses. The proposed architecture demonstrates a dual role relative to prior constrained CNN learning: it either demonstrates a regularizing role that stabilizes learning while maintaining system performance, or improves system performance by allowing the learning to be more stable and to evade local minima.Results: To validate the performance of the proposed model, experiments are conducted on two well-known public datasets from the Decathlon challenge: a mono-modal MRI dataset dedicated to segmentation of the left atrium, and a CT image dataset whose objective is to segment the spleen, an organ characterized with varying size and mild convexity issues.Conclusion: Results show that, despite the inadequacy of CoordConv when trained with the regular dice baseline loss, the proposed CoordConv-Unet structure can improve significantly model performance when trained under anatomically constrained prior losses.