Neural distance field representations with applications in 3D cardiac CT

Atrial Fibrillation is a heart arrhythmia, which is characterized by an irregular and often rapid heartbeat resulting from abnormal electrical signals in the upper chambers of the heart. Patients with atrial fibrillation are at risk for having a cardioembolic stroke, where a thrombus forms inside the heart and travels with the bloodstream to the brain, where it can occlude the small blood vessels and cause damage to the brain tissue. The left atrial appendage is an ear-shaped pouch on the left atrium with no clear function in healthy individuals. For patients with atrial fibrillation, the left atrial appendage is however a common place for thrombus formation. The morphology of the left atrial appendage varies greatly between individuals and can have complex traits such as sharp bends, multiple lobes, and a sponge-like trabeculated surface. Clinical research shows that higher stroke risk is associated with more complex morphologies, but the lack of quantifiable shape measurements makes it difficult to make robust conclusions.
This Ph.D. project addresses the need for deriving quantifiable and robust measurements of complex anatomical shapes to characterize the morphology. The developed methods are based on distance fields, where a 3D shape is represented by an implicit function mapping a continuous point in space to a scalar describing the signed or unsigned distance between the point and the nearest point on the surface. We show that this representation can preserve detailed shape information and utilize it to create accurate segmentations of the left atrial appendage from cardiac computed tomography images. We further demonstrate that the distance representation can be used for representation learning, to learn lowdimensional feature spaces to characterize 3D shapes and that these shape features can be concatenated with features learned from other types of data, which allows for integrating imaging and non-imaging data in the same model. The advances in computed tomography allow for temporal scans to assess cardiac function, and we underline the versatility of the distance field representation by showing that it seamlessly extends to the spatio-temporal domain to model cardiac anatomy and function jointly.
The contributions from this thesis are general methods that have advanced the use of distance fields in deep learning with a focus on the medical image- and shape analysis domain. The developed methods can be used to describe 3D shapes in general and have provided useful methods and insights into how the morphology of the left atrial appendage can be quantified. The immense variation in individual shapes however complicates the quantification of morphology and thrombus formation is dependent on many other factors besides left atrial appendage shape, which highlights the necessity for close cross-domain collaborations between clinical experts and computational specialists.