# Implicit Neural Representations for Modeling of Abdominal Aortic Aneurysm Progression

arXiv: https://arxiv.org/abs/2303.01069 · HTML: https://mlsanity.com/paper/2303.01069/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 21 references that are in the map.
- First posted on arXiv 2 Mar 2023.

## Builds on (most cited first, 8 of 8)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [NeRP: Implicit Neural Representation Learning with Prior Embedding for Sparsely Sampled Image Reconstruction](https://mlsanity.com/paper/2108.10991/) (2021)
- [Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling](https://mlsanity.com/paper/2207.14663/) (2022)
- [Implicit Neural Representations for Generative Modeling of Living Cell Shapes](https://mlsanity.com/paper/2207.06283/) (2022)
- [Landmark-free Statistical Shape Modeling via Neural Flow Deformations](https://mlsanity.com/paper/2209.06861/) (2022)

## Built on by (most cited first, 6 of 6)

- [Implicit Neural Representation in Medical Imaging: A Comparative Survey](https://mlsanity.com/paper/2307.16142/) (2023)
- [Generative modeling of living cells with SO(3)-equivariant implicit neural representations](https://mlsanity.com/paper/2304.08960/) (2023)
- [Neural Implicit Heart Coordinates: 3D cardiac shape reconstruction from sparse segmentations](https://mlsanity.com/paper/2512.19316/) (2025)
- [Uncertainty modeling for fine-tuned implicit functions](https://mlsanity.com/paper/2406.12082/) (2024)
- [ST-NeRP: Spatial-Temporal Neural Representation Learning with Prior Embedding for Patient-specific Imaging Study](https://mlsanity.com/paper/2410.19283/) (2024)
- [Parametric shape models for vessels learned from segmentations via differentiable voxelization](https://mlsanity.com/paper/2507.02576/) (2025)

## Abstract (arXiv)

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.