Center for Imaging Science : About | Research | Publications | Education | Activities | Downloads | Visiting

Dynamic Programming Generation of Boundaries of Local Coordinatized Submanifolds of the Neocortex

    Cortical cartography has emerged as an important component of Computational Anatomy in which local coordinate systems are used in analyzing anatomical similarities and differences that arise in neurodevelopmental and neurodegenerative processes in the brain, particularly in the analysis of the exquisite macroscopic features of the neocortical surface and the cortical mantle composed of gray matter. To generate coordinatized systems, we use dynamic programming to construct principal curves forming the boundaries of the gyral and sulcal regions characterized by the reconstructed triangulated graph of the submanifold representing the gray/white cortical surface.

    Reconstructed triangulated graph of the temporal lobe
    The figure above shows an example of a reconstructed triangulated graph. Bright and dark colors correspond, respectively, to the maximal and minimal mean curvature computed from the graph. Shown is the right temporal lobe containing: superior temporal gyrus (STG, blue)• planum temporale (PT) that is bounded by the Heschl’s Gyrus (green), posterior STG and the geodesic (magenta) between the STG and the HG • planum temporale with parietal extension (red).

    In general, cortical submanifolds embedded in 3D are highly convoluted and thus difficult to visualize. For example, the buried principal sulcal curves are hidden. To visualize the buried regions, we generate an equivalent submanifold in 2D via a bijective map between the vertices in 3D and those in 2D with minimal angular distortion. Such quasi-conformal maps can be computed via either circle packing or a Laplace-Beltrami equation.

    We use circle packing which iteratively adjusts the vertices of the graph so that circles centered at these vertices are tangent to each other. To the computed planar submanifold we assign a local coordinate system with the origin and y-axis defined by a neuroanatomist.

    The figure below shows how the planum temporale can be viewed in a 2D coordinate system with the buried Heschl’s sulcus delineated as a blue curve via dynamic programming. With such coordinate systems, structural features on the submanifold can be quantified and compared across the population.

    Coordinatized PT submanifold
  
 




301 Clark Hall
3400 N. Charles Street
Baltimore, MD 21218
Office: (410) 516-3826
Fax: (410)516-4594
webmaster@cis.jhu.edu