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Abstract: In this work, we explore deep learning model design and application in the context of multi-dimensional data in medical image analysis. A lot of medical image analysis problems come with 3D or even 4D spatio-temporal data that requires appropriate processing. While higher-dimensional processing allows for exploiting a lot of context, model design becomes very challenging due to exponentially increasing model parameters and risk of overfitting. Therefore, we design a variety of deep learning models for low- and high-dimensional data processing, including 1D up to 4D convolutional neural networks, convolutional-recurrent models, and Siamese architectures. Across a large number of applications, we find that using high-dimensional data is often effective when using well-designed deep learning models.