Cluster Analysis in Latent Space: Identifying Personalized Aortic Valve Prosthesis Shapes using Deep Representations

Due to the high inter-patient variability of anatomies, the field of personalized prosthetics gained attention during the last years. One potential application is the aortic valve. Even though its shape is highly patient-specific, state-of-the-art aortic valve prosthesis are not capable of reproducing this individual geometry. An appraoch to reach an economically reasonable personalization would be the identification of typical valve shapes using clustering, such that each patient could be treated with the prosthesis of the type that matches his individual geometry best. However, a cluster analysis directly in image space is not sufficient due to the curse of dimensionality and the high sensitivity to small translations or rotations. In this work, we propose representation learning to perform the cluster analysis in the latent space, while the evaluation of the identified prosthesis shapes is performed in image space using generative modeling. To this end, we set up a data set of 58 porcine aortic valves and provide a proof-of-concept of our method using convolutional autoencoders. Furthermore, we evaluated the learned representation regarding its reconstruction accuracy, compactness and smoothness. To the best of our knowledge, this work presents the first approach to derive prosthesis shapes data-drivenly using clustering in latent space.