Prefrontal Cortical Folding of the Preterm Brain: A Longitudinal Analysis of Preterm-Born Neonates - Longitudinal Registration and Shape Modeling - page 5

by calculating the sum of the triangle areas of each region. The correspondence
between the areas can be estimated and thus this defines a local measurement of
surface area change. Additionally, the volume enclosed in the triangular surface
mesh is computed using the divergence theorem.
The values for the mean and Gaussian curvature were corrected for brain
volume by dividing each value by the cube root of the ratio of the subject's PFC
white matter volume and mean PFC white matter volume of the 30 and 40 week
EGA. The difference in total curvature (sum of squared principal curvatures)
was corrected by taking into account the local area change between the 30 and
40 week subjects to obtain the bending energy. The total curvature value of each
vertex in the 40 week mesh was divided by the local area change at that vertex
and then mapped into the space of the 30 week mesh, where it was multiplied
by the local area change in the 30 week mesh.
We also carried out a group analysis, using JSM, by mapping all changes into
the space of one subject at 30 week and computed the surface parameters at each
vertex of the mesh. Again, we took into account the different volumes of each 30
week subject and corrected the mean and Gaussian curvature by dividing them
by the cube root of the ratio of the subject's PFC white matter volume and
mean PFC white matter volume of all 30 week subjects.
3 Results
FOCUSR and CPD Correspondence. We found a very good point qual-
itative correspondence between all 5 pairs of 30 and 40 week meshes of both
hemispheres for all subjects. Finding an initial correspondence was challenging
due to differences in shape, size and morphology of the meshes, but using a rigid
CPD for initialisation (Figure 3 B) improved the initial result (Figure 3 A).
Fig. 3. Initialization using FOCUSR with a wrong eigenvector ordering gives poor
correspondence (A). We use a method not prone to such issues, such as rigid CPD (B).
Longitudinal Correspondence Between 30 and 40 Weeks. Figure 4 and
5 shows an example of maps of mean curvature changes and Gaussian curvature
changes, respectively, for the prefrontal cortex white matter of a subject scanned