Dynamic Programming Applications in Defining Cortical Manifold Boundaries

J. Tilak Ratnanather
Johns Hopkins University

Sophisticated methods for constructing gray/white cortical manifolds from MRI
data have emerged in recent years. The reconstructed manifolds are triangulated
graphs that permit the computation of principal maximal and minimal curvature at
each point on the manifold via the fitting of the shape operator at each vertex
of the graph. We describe how dynamic programming can be used to track gyral and
sulcal principal curves corresponding to the locus path between two points with
maximal and minimal curvature respectively; a third path which is the shortest
distance between any two points irrespective of the curvature is deemed as the
geodesic. These curves are used to identify and extract cortical sub-manifolds
permitting the construction of local coordinate systems on the sub-manifold. We
can then quantify regional cortical metrics via distribution maps as a function
of these localized cortical coordinates.

Application of dynamic programming to extract the planum
temporale (PT) from a reconstructed superior temporal gyrus (STG) surface
from one brain. Panel 1 tracks the Heschl's gyrus; panel 2 tracks the STG
as far as the posterior ramus; panel 3 tracks the geodesic from the end of
the STG to the retro-insular end of the Heschl's gyrus; panel 4 shows the
delineation of the STG surface into two with the PT as the red region that
is extracted. Thick blue lines have been added for emphasis.

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