Neural Deformable Models for 3D Bi-Ventricular Heart Shape Reconstruction and Modeling from 2D Sparse Cardiac Magnetic Resonance Imaging

TL;DR

A novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data that can learn to densify a sparse cardiac point cloud and generate high-quality triangular meshes automatically.

Abstract

We propose a novel neural deformable model (NDM) targeting at the reconstruction and modeling of 3D bi-ventricular shape of the heart from 2D sparse cardiac magnetic resonance (CMR) imaging data. We model the bi-ventricular shape using blended deformable superquadrics, which are parameterized by a set of geometric parameter functions and are capable of deforming globally and locally. While global geometric parameter functions and deformations capture gross shape features from visual data, local deformations, parameterized as neural diffeomorphic point flows, can be learned to recover the detailed heart shape.Different from iterative optimization methods used in conventional deformable model formulations, NDMs can be trained to learn such geometric parameter functions, global and local deformations from a shape distribution manifold. Our NDM can learn to densify a sparse cardiac point cloud with arbitrary scales and generate high-quality triangular meshes automatically. It also enables the implicit learning of dense correspondences among different heart shape instances for accurate cardiac shape registration. Furthermore, the parameters of NDM are intuitive, and can be used by a physician without sophisticated post-processing. Experimental results on a large CMR dataset demonstrate the improved performance of NDM over conventional methods.

Figures (9)

• Figure 1: Cardiac MR standard scan views and bi-ventricular shape reconstruction. (a-c) Short axis (SAX) views at the basal/middle/apex region of the left ventricle (LV). (d-f) Long axis (LAX) 2/3/4 chamber (CH) views. Green points show the endo-/epi-cardial border of LV and the border of right ventricle (RV). (g) Sparse cardiac point cloud with 10 SAX and 3 LAX slices' data. (h) Bi-ventricular mesh reconstructed from (g) by our neural deformable model, in which the LV endo-cardial, epi-cardial and RV surfaces are shown in red, blue and yellow, respectively.
• Figure 2: Geometry representation of a deformable surface model. (a) Material coordinate domain $\mathbf{\Omega}$. (b) The shape primitive and deformed surface mapped from the material coordinate domain (illustrated with $w=0$) by a neural deformable model (NDM).
• Figure 3: (a) A deformable shape primitive with aspect ratios $a_{1}$, $a_{2}$, $a_{3}$. (b) Blended deformable shape primitives for the modeling of bi-ventricular geometry. (c) Axis offset deformations $e_{xo}$, $e_{yo}$ that translate the center of the ellipse from $\boldsymbol{c}_{e}$ to $\boldsymbol{c}'_{e}$.
• Figure 4: Neural deformable models (NDMs) for bi-ventricular cardiac point cloud upsampling and automated triangular mesh generation. Each deformation parameter vector $\boldsymbol{q}_{N}=(\boldsymbol{q}_{g}^{\top}, \boldsymbol{q}_{d}^{\top})^{\top}$ of a NDM is learned in a coarse-to-fine fashion, from the learning of global deformation ($\boldsymbol{q}_{g}$) to local deformation ($\boldsymbol{q}_{d}$). $\boldsymbol{q}_{g}$ captures gross target shape features, leaving only small shape details to be refined by $\boldsymbol{q}_{d}$.
• Figure 5: Shape registration via the implicitly learned dense correspondence by NDM.