Fundamentals of Data Analysis Methods in Functional MRI - Advance Image Processing in Magnetic Resonance Imaging - page 486

15.7 SEGMENTATION, SURFACE

RECONSTRUCTION, AND MORPHING

Projection of the functional data onto a standardized or an individual anatomical
3-D volume not only has certain advantages (ease of use and widespread accep-
tance) but also several drawbacks. For example, on a 3-D volume, the distance
between two activated regions on the cortical surface is in most of the cases
substantially underestimated compared to the true distance along the cortical
sheet. This is due to the intrinsic topology of the cerebral cortex, a bidimensional
sheet with a highly folded and curved geometry. Furthermore, some of the features
and organizational principles that distinguish cortical areas (e.g., retinotopy, tono-
topy, somatotopy) are better analyzed with a 2-D surface-based representation.
Finally, individual cortical surfaces can be used as anatomical constraints for
hypothesis- [38, 43] and data-driven [44] statistical analysis of the functional
time series. Therefore, representation of functional maps on the folded and mor-
phed surface reconstruction of individual brains often reveals topographical infor-
mation that may remain hidden in the conventional slices or 3-D volumetric
visualization. In the following text, the steps required to obtain these types of
representation are briefly described.
The first step in obtaining a reconstruction of a cortical surface is to derive, for
each hemisphere, the border between white and gray matter from the set of slices

of a 3-D anatomical volume ( Figure 15.6 ). In general, this can be done by using

one of the many existing segmentation algorithms that allow separating gray matter,
white matter, and the other structures of the brain [45]. In our approach, the
segmentation algorithm also ensures that the following tessellation will lead to a
topologically correct representation of the cortex (i.e., without “bridges” or “holes”;

see Reference 46 for details). After segmentation, the high-resolution, voxel-based

partition of each hemisphere is transformed by triangularization of the outside voxel
faces to a vertex-based surface S 0 = ( V 0 , K ), where V 0 is the N Vo × 3 matrix of vertex

3 matrix of vertex indices, and N Vo and N K are the number
of vertices and faces. Because the surface S 0 reflects the coarse voxel-based dis-
cretized approximation to the (real) underlying surface, which is assumed to be
spatially smooth (i.e., local curvature values are bound by some maximum value),
the coordinates described by V 0 are spatially smoothed with respect to the local
vertex neighborhood (100-200 iterations). V 0 is thus transformed to a smooth
representation of the white matter surface S W

coordinates, K is an N K ×

( V W , K ). In the next step, a surface
lying within the gray matter sheet is identified by translating the vertices in V W
using an interactive morphing algorithm. This gives a representation of the under-
lying gray matter surface S G

=

(V G , K) that may be used as the reference mesh for
the visualization of functional data (Figure 15.6).
The iterative morphing algorithm may be further used to compute an
I I
representation of the cortical surface aims to provide a representation of the
cortical hemisphere that retains much of the shape and metric properties of the
original surface, but allows the visualization of functional activity occurring

=

“inflated” surface S = ( V , K ) of each hemisphere ( Figure 15.7 ). The inflated