DVasMesh: Deep Structured Mesh Reconstruction from Vascular Images for Dynamics Modeling of Vessels

TL;DR

A deep learning-based method to directly generate structured hexahedral vascular meshes from vascular images, taking advantage of end-to-end learning and discarding direct dependency on annotated labels, demonstrates outstanding performance in generating structured vascular meshes on cardiac and cerebral vascular images.

Abstract

Vessel dynamics simulation is vital in studying the relationship between geometry and vascular disease progression. Reliable dynamics simulation relies on high-quality vascular meshes. Most of the existing mesh generation methods highly depend on manual annotation, which is time-consuming and laborious, usually facing challenges such as branch merging and vessel disconnection. This will hinder vessel dynamics simulation, especially for the population study. To address this issue, we propose a deep learning-based method, dubbed as DVasMesh to directly generate structured hexahedral vascular meshes from vascular images. Our contributions are threefold. First, we propose to formally formulate each vertex of the vascular graph by a four-element vector, including coordinates of the centerline point and the radius. Second, a vectorized graph template is employed to guide DVasMesh to estimate the vascular graph. Specifically, we introduce a sampling operator, which samples the extracted features of the vascular image (by a segmentation network) according to the vertices in the template graph. Third, we employ a graph convolution network (GCN) and take the sampled features as nodes to estimate the deformation between vertices of the template graph and target graph, and the deformed graph template is used to build the mesh. Taking advantage of end-to-end learning and discarding direct dependency on annotated labels, our DVasMesh demonstrates outstanding performance in generating structured vascular meshes on cardiac and cerebral vascular images. It shows great potential for clinical applications by reducing mesh generation time from 2 hours (manual) to 30 seconds (automatic).

Figures (4)

• Figure 1: Schematic illustration of our DVasMesh. (a) Network structure of our DVasMesh. Given a vascular image and a graph template, we sample the extracted features of the encoder of a segmentation network and embed the sampled features into a graph. Taking the graph as input, we use graph convolutional networks (GCN) to infer the graph deformation $\mathcal{G}_\delta$, such as deformations on vertices. More details are given in "Method" section. The subfigure in the green circle shows feature sampling centered at centerline point $\boldsymbol{c}$ with radius $r$ in the cross-section of a vertex. (b) A vascular surface mesh (left) and a graph (right). Here, a vertex $\mathcal{V}_0$ of the graph contains a four-element vector containing the 3D coordinates and radius of the cross-section, i.e., $\mathcal{V}_0=(x_0, y_0, z_0, r_0)$. The estimated graph is used to create the hexahedral vascular mesh by a sweeping technique. The bottom subfigure illustrates three graph templates from sparse to dense.
• Figure 2: Qualitative comparisons of vascular volume meshes among different methods. The green circles mark the disconnected regions.
• Figure 3: Four examples of segmentation results (top) and vascular volume meshes (bottom) of left (red) and right (green) cerebral arteries reconstructed by DVasMesh.
• Figure 4: Two examples of coronary volume meshes reconstructed from time-series cardiac CTA. The green and blue meshes are diastolic and systolic phases, respectively.