Finding parametric representations of the cortical sulci using an active contour model

The cortical sulci are brain structures resembling thin convoluted ribbons embedded in three dimensions. The importance of the sulci lies primarily in their relation to the cytoarchitectonic and functional organization of the underlying cortex and in their utilization as features in non-rigid registration methods. This paper presents a methodology for extracting parametric representations of the cerebral sulci from magnetic resonance images. The proposed methodology is based on deformable models utilizing characteristics of the cortical shape. Specifically, a parametric representation of a sulcus is determined by the motion of an active contour along the medial surface of the corresponding cortical fold. The active contour is initialized along the outer boundary of the brain and deforms toward the deep root of a sulcus under the influence of an external force field, restricting it to lie along the medial surface of the particular cortical fold. A parametric representation of the medial surface of the sulcus is obtained as the active contour traverses the sulcus. Based on the first fundamental form of this representation, the location and degree of an interruption of a sulcus can be readily quantified; based on its second fundamental form, shape properties of the sulcus can be determined. This methodology is tested on magnetic resonance images and it is applied to three medical imaging problems: quantitative morphological analysis of the central sulcus; mapping of functional activation along the primary motor cortex and non-rigid registration of brain images.