  A surface-based diffeomorphic algorithm to generate 3D coordinate grids in
the cortical ribbon is described. In the grid, normal coordinate lines are
generated by the diffeomorphic evolution from the grey/white (inner) surface to
the grey/csf (outer) surface. Specifically, the cortical ribbon is described by
two triangulated surfaces with open boundaries. Conceptually, the inner surface
sits on top of the white matter structure and the outer on top of the gray
matter. It is assumed that the cortical ribbon consists of cortical columns
which are orthogonal to the white matter surface. This might be viewed as a
consequence of the development of the columns in the embryo. It is also assumed
that the columns are orthogonal to the outer surface so that the resultant
vector field is orthogonal to the evolving surface. Then the distance of the
normal lines from the vector field such that the inner surface evolves
diffeomorphically towards the outer one can be construed as a measure of
thickness. Applications are described for the auditory cortices in human adults
and cats with normal hearing or hearing loss. The approach offers great
potential for cortical morphometry.
