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IntroductionQuantum computing is increasingly being investigated for integration into medical radiology and healthcare applications worldwide. Given its potential to enhance clinical care and medical research, there is growing interest in evaluating its practical applications in clinical workflows. MethodsWe developed an evaluation of quantum computing-based auto-contouring methods to introduce medical physicists to this emerging technology. We implemented existing quantum algorithms as prototypes tailored for specific quantum hardware, focusing on their application to auto-contouring in medical imaging. The evaluation was performed using a medical resonance imaging (MRI) abdominal dataset, comprising 102 patient scans. ResultsThe quantum algorithms were applied to the dataset and assessed for their potential in auto-contouring tasks. One of the quantum-based auto contouring methods demonstrated conceptual feasibility, practical performance is still limited by current available quantum hardware and scalability constraints. DiscussionOur findings suggest that while quantum computing for auto-contouring shows promise, it remains in its early stages. At present, artificial intelligence-based algorithms continue to be the preferred choice for auto-contouring in treatment planning due to their greater efficiency and accuracy. As quantum hardware and algorithms mature, their integration into clinical workflows may become more viable. 

Accurate medical imaging segmentation is critical for precise and effective medi- cal interventions. However, despite the success of convolutional neural networks (CNNs) in medical image segmentation, they still face challenges in handling fine-scale features and variations in image scales. These challenges are particularly evident in complex and challenging segmentation tasks, such as the BraTS multi- label brain tumor segmentation challenge. In this task, accurately segmenting the various tumor sub-components, which vary significantly in size and shape, remains a significant challenge, with even state-of-the-art methods producing substantial errors. Therefore, we propose two architectures, FMG-Net and W-Net, that incor- porate the principles of geometric multigrid methods for solving linear systems of equations into CNNs to address these challenges. Our experiments on the BraTS 2020 dataset demonstrate that both FMG-Net and W-Net outperform the widely used U-Net architecture regarding tumor subcomponent segmentation accuracy and training efficiency. These findings highlight the potential of incorporating the principles of multigrid methods into CNNs to improve the accuracy and efficiency of medical imaging segmentation. 

The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a priori error estimates in the L 2 norm and in weighted energy norms. In addition, we prove almost optimal local error estimates in the energy norm for any approximation order. Further, almost optimal local error estimates in the L 2 norm are obtained for the case of piecewise linear approximations whereas suboptimal error bounds in the L 2 norm are shown for any polynomial degree. For the time-dependent case, convergence of semi-discrete and of backward Euler fully discrete scheme is established by proving error estimates in L 2 in time and in space. Numerical results for the elliptic problem are added to support the theoretical results.