Neural deformation fields for template-based reconstruction of cortical surfaces from MRI

TL;DR

Vox2Cortex-Flow (V2C-Flow) presents a template-based, end-to-end mesh-deformation method for cortical surface reconstruction from MRI. It models the deformation from a template cortex to subject-specific surfaces as a neural ordinary differential equation implemented via graph NODEs, conditioning on hypercolumn features from a 3D U-Net and jointly deforming white matter and pial surfaces to avoid intersections. The method delivers state-of-the-art surface accuracy with rapid inference (<2s) and establishes per-vertex correspondences to a template, enabling direct cortical parcellation and group analyses without extensive spherical registrations. Across diverse public datasets, V2C-Flow demonstrates strong generalization, robustness to white-matter lesions, and consistent per-vertex correspondences, offering practical impact for scalable clinical and population studies. The approach integrates segmentation, topology preservation, surface extraction, and parcellation into a single forward pass, challenging the necessity of traditional multi-step pipelines."

Abstract

The reconstruction of cortical surfaces is a prerequisite for quantitative analyses of the cerebral cortex in magnetic resonance imaging (MRI). Existing segmentation-based methods separate the surface registration from the surface extraction, which is computationally inefficient and prone to distortions. We introduce Vox2Cortex-Flow (V2C-Flow), a deep mesh-deformation technique that learns a deformation field from a brain template to the cortical surfaces of an MRI scan. To this end, we present a geometric neural network that models the deformation-describing ordinary differential equation in a continuous manner. The network architecture comprises convolutional and graph-convolutional layers, which allows it to work with images and meshes at the same time. V2C-Flow is not only very fast, requiring less than two seconds to infer all four cortical surfaces, but also establishes vertex-wise correspondences to the template during reconstruction. In addition, V2C-Flow is the first approach for cortex reconstruction that models white matter and pial surfaces jointly, therefore avoiding intersections between them. Our comprehensive experiments on internal and external test data demonstrate that V2C-Flow results in cortical surfaces that are state-of-the-art in terms of accuracy. Moreover, we show that the established correspondences are more consistent than in FreeSurfer and that they can directly be utilized for cortex parcellation and group analyses of cortical thickness.

Figures (13)

• Figure 1: The smooth and tightly folded geometry of the cortex is better represented by mesh-based surface extraction methods than by voxel-based segmentation methods. Inner white matter (WM) and outer pial surfaces of each hemisphere were extracted from a T1-weighted MRI scan with the proposed V2C-Flow method (mesh-based) and the popular nnUNet isensee2020 with subsequent application of Marching Cubes (voxel-based). While voxel-based methods attempt to classify each voxel, mesh-based approaches focus on delineating the contours between distinct tissue types; this fundamental difference is depicted on the left for an axial slice of the MRI scan.
• Figure 1: The curvature-weighted Chamfer loss re-weights the ratio between point and regularization loss terms locally based on ground-truth curvature. Thereby, it enhances the accuracy in highly curved regions compared to the standard Chamfer loss (with the same regularization terms). The FreeSurfer surface is shown as a reference.
• Figure 2: V2C-Flow extracts inner white matter (WM) and outer (pial) cortical surface meshes from MRI. Computed surfaces have point-wise correspondences to the input template. The rainbow-colored surfaces are real distinct surfaces extracted by V2C-Flow, with corresponding vertices having identical colors. To this end, a deformation field relative to the template's vertices $V(t)$, modeled as a neural ordinary differential equation (NODE), is predicted. The deformation is conditioned on the input MRI scan. The boundary condition of the ODE is given at $t=0$ by the template. The network consists of a fully-convolutional neural network (F-CNN) and a graph neural network (GNN), operating in image and mesh space, respectively. Both networks are connected by a feature-sampling module that maps image features onto vertices. Skip connections within CNN blocks are omitted for the sake of clarity.
• Figure 2: Illustration of the deformation in V2C-Flow from the fsaverage template to the individual white matter (top) and pial (bottom) surfaces with two flow fields ($S=2$). Each flow is integrated numerically with the forward Euler method. We plot the per-vertex distance for white matter and pial surfaces of the left hemisphere to the FreeSurfer silver standard for a sample from the ADNI test set .The error decreases with the evolution of the mesh. For an animation of the deformation process see supplemental videos.
• Figure 3: V2C-Flow yields accurate and smooth surfaces while alternative methods introduce artifacts in this sample from the ADNI test set. The required inference time is measured in seconds (s) or hours (h) for the reconstruction of the four cortical surfaces of one subject on an Nvidia A6000 GPU for DL-based methods and on a single CPU for FreeSurfer (v7.2).