Meningeal lymphatic vessels (MLVs) are responsible for the drainage of waste products from the human brain. An impairment in their functionality has been associated with aging as well as brain disorders like multiple sclerosis and Alzheimer's disease. However, MLVs have only recently been described for the first time in magnetic resonance imaging (MRI), and their ramified structure renders manual segmentation particularly difficult. Further, as there is no consistent notion of their appearance, human-annotated MLV structures contain a high inter-rater variability that most automatic segmentation methods cannot take into account. In this work, we propose a new rater-aware training scheme for the popular nnU-Net model, and we explore rater-based ensembling strategies for accurate and consistent segmentation of MLVs. This enables us to boost nnU-Net's performance while obtaining explicit predictions in different annotation styles and a rater-based uncertainty estimation. Our final model, MLV$^2$-Net, achieves a Dice similarity coefficient of 0.806 with respect to the human reference standard. The model further matches the human inter-rater reliability and replicates age-related associations with MLV volume.

Explaining predictions of black-box neural networks is crucial when applied to decision-critical tasks. Thus, attribution maps are commonly used to identify important image regions, despite prior work showing that humans prefer explanations based on similar examples. To this end, ProtoPNet learns a set of class-representative feature vectors (prototypes) for case-based reasoning. During inference, similarities of latent features to prototypes are linearly classified to form predictions and attribution maps are provided to explain the similarity. In this work, we evaluate whether architectures for case-based reasoning fulfill established axioms required for faithful explanations using the example of ProtoPNet. We show that such architectures allow the extraction of faithful explanations. However, we prove that the attribution maps used to explain the similarities violate the axioms. We propose a new procedure to extract explanations for trained ProtoPNets, named ProtoPFaith. Conceptually, these explanations are Shapley values, calculated on the similarity scores of each prototype. They allow to faithfully answer which prototypes are present in an unseen image and quantify each pixel's contribution to that presence, thereby complying with all axioms. The theoretical violations of ProtoPNet manifest in our experiments on three datasets (CUB-200-2011, Stanford Dogs, RSNA) and five architectures (ConvNet, ResNet, ResNet50, WideResNet50, ResNeXt50). Our experiments show a qualitative difference between the explanations given by ProtoPNet and ProtoPFaith. Additionally, we quantify the explanations with the Area Over the Perturbation Curve, on which ProtoPFaith outperforms ProtoPNet on all experiments by a factor $>10^3$.