  Abdominal aortic aneurysms (AAAs) are progressive dilatations of the
abdominal aorta that, if left untreated, can rupture with lethal consequences.
Imaging-based patient monitoring is required to select patients eligible for
surgical repair. In this work, we present a model based on implicit neural
representations (INRs) to model AAA progression. We represent the AAA wall over
time as the zero-level set of a signed distance function (SDF), estimated by a
multilayer perception that operates on space and time. We optimize this INR
using automatically extracted segmentation masks in longitudinal CT data. This
network is conditioned on spatiotemporal coordinates and represents the AAA
surface at any desired resolution at any moment in time. Using regularization
on spatial and temporal gradients of the SDF, we ensure proper interpolation of
the AAA shape. We demonstrate the network's ability to produce AAA
interpolations with average surface distances ranging between 0.72 and 2.52 mm
from images acquired at highly irregular intervals. The results indicate that
our model can accurately interpolate AAA shapes over time, with potential
clinical value for a more personalised assessment of AAA progression.
