Cortical surface reconstruction using a topology preserving geometric deformable model

Accurate reconstruction of the cortical surface of the brain from magnetic resonance images is an important objective in biomedical image analysis. Parametric deformable surface models are usually used because they incorporate prior information, yield subvoxel accuracy, and automatically preserve topology. These algorithms are very computationally costly, however, particularly if self-intersection prevention is imposed. Geometric deformable surface models, implemented using level set methods, are computationally fast and are automatically free from self-intersections, but are unable to guarantee the correct topology. This paper describes both a new geometric deformable surface model which preserves topology and an overall strategy for reconstructing the inner, central, and outer surfaces of the brain cortex. The resulting algorithm is fast and numerically stable, and yields accurate brain surface reconstructions that are guaranteed to be topologically correct and free from self intersections. We ran the algorithm on 21 data sets and show detailed results for a typical data set. We also show a preliminary validation using landmarks manually placed as a truth model on six of the data sets.

1. Introduction

Reconstructing the surface of the cerebral cortex from magnetic resonance (MR) images is an important step in brain visualization, quantitative analysis of brain geometry, multimodal registration, surgical planning, and unfolding and mapping the cortex [1], [2]. Conventionally, the interface between the gray matter (GM) and white matter (WM) is first sought, largely because this interface is readily visualized by Tl-weighted MR images. In some cases, the central cortical surface is sought because this surface best represents the overall cortical geometry and algorithms designed to find it tend to be robust to noise and other imaging artifacts. Despite their highly convoluted geometries, when either surface is connected across the corpus callosum and diencephalon, it has a topology equivalent to that of a sphere. Unfolding the cortex and mapping it to a sphere (or other topologically equivalent surface) can then be accomplished for visualization, measurement, and the establishment of a global coordinate system on the cortex.