Cerebellar Isolation, Parcellation, and Conformal Mapping

Why map the cerebellar surface? Because: (i) organization of motor, sensory and cognitive functions in the human cerebellum is poorly understood [1], (ii) the highly-folded structure conceals most of the cortical surface, and (iii) functional data analysis may improve with incorporation of surface organization [2]. We constructed a pipeline for extracting, labelling, and conformally mapping cerebellar surfaces from individuals’ coregistered anatomical and functional volumes. Conformal mappings preserve angular information; other approaches attempt to minimize areal and metric distortions [3]. Methods Cerebellar Template. The pipeline requires a parcellated template volume; we use the 27-scan MRI volume produced at the Montreal Neurological Institute [4] and used in Schmahmann’s cerebellar atlas [5]. We extended the atlas labelling to each voxel in the template cerebellum. Isolation of cerebellar subvolumes is landmark-driven, using the posterior commissure, the obex, and the apex of the fourth ventricle to define a standard orientation [6]. A template-to-subject warp serves to identify the cerebrum and a computerized cutplane then removes the brainstem by stepping through the volume [sparing wrap-around cerebellar tissue] until reaching the lingula. The final cut perimeter serves as the boundary necessary for flat mapping to a plane. Parcellation is produced by warping the template cerebellum to the subject’s, applying the same transform to the template’s parcellation volume, and and manually editing the labels to correct errors due to poorly resolved fissures and/or variable fissuration. Surface Extraction. Flat mapping requires a surface be free of defects and topologically equivalent to a sphere. An isolated cerebellum is equivalent to a sphere in principle; a typical isosurface exhibits "handles" as well as topological defects such as holes and fins. We are developing an algotihm that produces a "correct" surface [7]; currently we repair a Marching Cubes isosurface.