  Uncertainty estimation, which provides a means of building explainable neural
networks for medical imaging applications, have mostly been studied for single
deep learning models that focus on a specific task. In this paper, we propose a
method to propagate uncertainty through cascades of deep learning models in
medical imaging pipelines. This allows us to aggregate the uncertainty in later
stages of the pipeline and to obtain a joint uncertainty measure for the
predictions of later models. Additionally, we can separately report
contributions of the aleatoric, data-based, uncertainty of every component in
the pipeline. We demonstrate the utility of our method on a realistic imaging
pipeline that reconstructs undersampled brain and knee magnetic resonance (MR)
images and subsequently predicts quantitative information from the images, such
as the brain volume, or knee side or patient's sex. We quantitatively show that
the propagated uncertainty is correlated with input uncertainty and compare the
proportions of contributions of pipeline stages to the joint uncertainty
measure.
