Myocardial infarction (MI) is one of the most common causes of death in the world. Image-based biomarkers commonly used in the clinic, such as ejection fraction, fail to capture more complex patterns in the heart's 3D anatomy and thus limit diagnostic accuracy. In this work, we present the multi-objective point cloud autoencoder as a novel geometric deep learning approach for explainable infarction prediction, based on multi-class 3D point cloud representations of cardiac anatomy and function. Its architecture consists of multiple task-specific branches connected by a low-dimensional latent space to allow for effective multi-objective learning of both reconstruction and MI prediction, while capturing pathology-specific 3D shape information in an interpretable latent space. Furthermore, its hierarchical branch design with point cloud-based deep learning operations enables efficient multi-scale feature learning directly on high-resolution anatomy point clouds. In our experiments on a large UK Biobank dataset, the multi-objective point cloud autoencoder is able to accurately reconstruct multi-temporal 3D shapes with Chamfer distances between predicted and input anatomies below the underlying images' pixel resolution. Our method outperforms multiple machine learning and deep learning benchmarks for the task of incident MI prediction by 19% in terms of Area Under the Receiver Operating Characteristic curve. In addition, its task-specific compact latent space exhibits easily separable control and MI clusters with clinically plausible associations between subject encodings and corresponding 3D shapes, thus demonstrating the explainability of the prediction.

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