Construction of a 4D Brain Atlas and Growth Model Using Diffeomorphic Registration - Longitudinal Registration and Shape Modeling - page 33

4 Conclusions

We presented a method for the construction of a spatio-temporal atlas of high
anatomical detail based on the Log-Euclidean mean of transformations which
belong to the one-parameter subgroup of diffeomorphisms. We also utilized the
numerous pairwise inter-subject transformations used to construct the atlas time
series to derive a longitudinal deformation model of mean growth. This avoids
additional intensity-driven registration of the atlas time points. A longitudinal
registration of the template images has to account for the MR intensity changes
which are associated with the ongoing myelination and other processes during
early brain development such that these are not reflected in the deformation.
By opportunely combining the cross-sectional transformations which map the
individual to each atlas time point, we obtain a mean growth model directly
from the inter-subject registrations. While the atlas itself captures brain growth
only at discrete time points, our continuous growth model allows the analysis of
growth trajectories between any two time points of the captured age range.
Compared to the first months after birth, the MR intensity changes are rela-
tively moderate within the neonatal age range that we focused on in this work.
The NMI similarity measure used for the pairwise registrations is, however, a
well-established image similarity measure in inter-subject and multi-modality
image registration [ 16 ]. It has demonstrated to be robust to wide intensity varia-
tions and could thus be employed for the construction of a spatio-temporal atlas
from infant brain images. Pairwise registrations are also only required between
images of similar ages due to the limited support of the regression kernel.

References

1. Aljabar, P., Bhatia, K.K., Hajnal, J.V., Boardman, J.P., Srinivasan, L., Rutherford,
M.A., Dyet, L.E., Edwards, A.D., Rueckert, D.: Analysis of growth in the developing
brain using non-rigid registration. In: ISBI, pp. 201-204 (2006)
2. Arsigny, V., Commowick, O., Pennec, X., Ayache, N.: A log-euclidean framework
for statistics on diffeomorphisms. In: Larsen, R., Nielsen, M., Sporring, J. (eds.)
MICCAI 2006. LNCS, vol. 4190, pp. 924-931. Springer, Heidelberg (2006)
3. Avants, B.B., Epstein, C.L., Grossman, M., Gee, J.C.: Symmetric diffeomorphic
image registration with cross-correlation: Evaluating automated labeling of elderly
and neurodegenerative brain. Med. Image Anal. 12 (1), 26-41 (2008)
4. Bossa, M., Hernandez, M., Olmos, S.: Contributions to 3D diffeomorphic atlas esti-
mation: application to brain images. In: Ayache, N., Ourselin, S., Maeder, A. (eds.)
MICCAI 2007, Part I. LNCS, vol. 4791, pp. 667-674. Springer, Heidelberg (2007)
5. Cheng, S.H.U.N., Higham, N.J., Kenney, C.S., Laub, A.J.: Approximating the
logarithm of a matrix to specified accuracy. SIAM J. Matrix Anal. Appl. 22 (4),
1112-1125 (1999)
6. Davis, B.C., Fletcher, P.T., Bullitt, E., Joshi, S.: Population shape regression from
random design data. In: ICCV, pp. 1-7 (2007)
7. Habas, P.A., Kim, K., Corbett-Detig, J.M., Rousseau, F., Glenn, O.A., Barkovich,
A.J., Studholme, C.: A spatiotemporal atlas of MR intensity, tissue probability
and shape of the fetal brain with application to segmentation. NeuroImage 53 (2),
460-470 (2010)