Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling

TL;DR

This paper introduces a differentiable implicit neural representation (INR) for modeling complex 3D vascular structures, enabling accurate, continuous, and lightweight surface reconstructions from limited data, with applications in medical imaging.

Contribution

The authors propose using signed distance functions within INRs to model vascular surfaces, offering a novel implicit, continuous, and integrable approach for 3D vascular modeling.

Findings

Accurate watertight surface reconstruction from limited surface points

Simultaneous fitting of nested vessel walls without intersections

Smooth blending of individual artery models into a single surface

Abstract

Personalised 3D vascular models are valuable for diagnosis, prognosis and treatment planning in patients with cardiovascular disease. Traditionally, such models have been constructed with explicit representations such as meshes and voxel masks, or implicit representations such as radial basis functions or atomic (tubular) shapes. Here, we propose to represent surfaces by the zero level set of their signed distance function (SDF) in a differentiable implicit neural representation (INR). This allows us to model complex vascular structures with a representation that is implicit, continuous, light-weight, and easy to integrate with deep learning algorithms. We here demonstrate the potential of this approach with three practical examples. First, we obtain an accurate and watertight surface for an abdominal aortic aneurysm (AAA) from CT images and show robust fitting from as little as 200 points on the surface. Second, we simultaneously fit nested vessel walls in a single INR without intersections. Third, we show how 3D models of individual arteries can be smoothly blended into a single watertight surface. Our results show that INRs are a flexible representation with potential for minimally interactive annotation and manipulation of complex vascular structures.