# Anatomy-Informed Neural Networks: Encoding Anatomic Priors in Loss and Architecture, with an SE(3) Formulation of Guidewire-Induced Aortoiliac Deformation

arXiv: https://arxiv.org/abs/2608.21332 · HTML: https://mlsanity.com/paper/2608.21332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 45 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 20 of 20)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems](https://mlsanity.com/paper/1903.12394/) (2019)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Anatomically Constrained Neural Networks (ACNN): Application to Cardiac Image Enhancement and Segmentation](https://mlsanity.com/paper/1705.08302/) (2017)
- [Coordinate Independent Convolutional Networks -- Isometry and Gauge Equivariant Convolutions on Riemannian Manifolds](https://mlsanity.com/paper/2106.06020/) (2021)
- [Constrained-CNN losses for weakly supervised segmentation](https://mlsanity.com/paper/1805.04628/) (2018)
- [Mesh Neural Networks for SE(3)-Equivariant Hemodynamics Estimation on the Artery Wall](https://mlsanity.com/paper/2212.05023/) (2022)
- [Sliced-Wasserstein Distances and Flows on Cartan-Hadamard Manifolds](https://mlsanity.com/paper/2403.06560/) (2024)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [A survey on shape-constraint deep learning for medical image segmentation](https://mlsanity.com/paper/2101.07721/) (2021)
- [Incorporating prior knowledge in medical image segmentation: a survey](https://mlsanity.com/paper/1607.01092/) (2016)
- [SE(3) symmetry lets graph neural networks learn arterial velocity estimation from small datasets](https://mlsanity.com/paper/2302.08780/) (2023)
- [Anatomy-informed Data Augmentation for Enhanced Prostate Cancer Detection](https://mlsanity.com/paper/2309.03652/) (2023)
- [Optimal Transport on the Lie Group of Roto-translations](https://mlsanity.com/paper/2402.15322/) (2024)
- [A Real-time and Registration-free Framework for Dynamic Shape Instantiation](https://mlsanity.com/paper/1801.00182/) (2017)
- [Anatomy-Informed Deep Learning for Abdominal Aortic Aneurysm Segmentation](https://mlsanity.com/paper/2604.10312/) (2026)

## Abstract (arXiv)

Deep-learning models of anatomy can be numerically plausible yet anatomically impossible, and they generalize poorly when data are scarce. We introduce Anatomy-Informed Neural Networks (AINN), in which soft anatomic priors enter as penalty terms in the loss (e.g., a branching penalty that treats a renal transplant artery off the iliac instead of the aorta as unexpected rather than impossible), in direct analogy to a physics-informed neural network, and hard anatomic priors (e.g., continuity of the vessel) are built into the architecture and state representation, making such invalid predictions impossible by construction wherever the prior admits architectural enforcement. We develop it on a clinical test case with limited data: how the aortoiliac tree deforms when a stiff wire is introduced endoluminally. This is important to contemporary aortic surgery and will matter to autonomous endovascular navigation. We lift the vessel centerline and the wire path from R^3 to curves of frames in the Lie group SE(3), and couple a Cosserat-rod wire to a tortuosity-modulated, anatomically anchored vessel through a unilateral lumen-contact inequality. The prediction is a constrained minimizer of the coupled elastic energy, with contact forces as its Lagrange multipliers. Supervision is a Wasserstein-2 optimal-transport loss between the predicted projection through the C-arm geometry and the observed angiogram, so a 2D angiogram can train a 3D prediction. The kinematics, loss and projection are verified against known ground truth; the mechanics solver only against its own optimality conditions, and predicted displacement is not yet mesh-converged. Here, no network is trained. Future work will transfer this in silico model to real CT scans and test whether it improves predictive accuracy and reduces the training data required.