Going Off-Grid: Continuous Implicit Neural Representations for 3D Vascular Modeling
This work addresses the need for efficient and flexible 3D modeling in cardiovascular disease diagnosis and treatment planning, offering a novel representation that is incremental over existing implicit methods.
The authors tackled the problem of creating personalized 3D vascular models by proposing a differentiable implicit neural representation (INR) for signed distance functions, achieving accurate surface fitting from as few as 200 points and enabling watertight, non-intersecting models of complex structures like abdominal aortic aneurysms.
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.