Structural brain networks can be constructed from the white matter fiber tractography of diffusion tensor imaging (DTI), and the structural characteristics of the brain can be analyzed from its networks. When brain networks are constructed by the parcellation method, their network structures change according to the parcellation scale selection and arbitrary thresholding. To overcome these issues, we modified the Ɛ -neighbor construction method proposed by Chung et al. (2011). The purpose of this study was to construct brain networks for 14 control subjects and 16 subjects with autism using both the parcellation and the Ɛ-neighbor construction method and to compare their topological properties between two methods. As the number of nodes increased, connectedness decreased in the parcellation method. However in the Ɛ-neighbor construction method, connectedness remained at a high level even with the rising number of nodes. In addition, statistical analysis for the parcellation method showed significant difference only in the path length. However, statistical analysis for the Ɛ-neighbor construction method showed significant difference with the path length, the degree and the density.
The sparse regression framework has been widely used in medical image processing and analysis. However, it has been rarely used in anatomical studies. We present a sparse shape modeling framework using the Laplace- Beltrami (LB) eigenfunctions of the underlying shape and show its improvement of statistical power. Tradition- ally, the LB-eigenfunctions are used as a basis for intrinsically representing surface shapes as a form of Fourier descriptors. To reduce high frequency noise, only the first few terms are used in the expansion and higher frequency terms are simply thrown away. However, some lower frequency terms may not necessarily contribute significantly in reconstructing the surfaces. Motivated by this idea, we present a LB-based method to filter out only the significant eigenfunctions by imposing a sparse penalty. For dense anatomical data such as deformation fields on a surface mesh, the sparse regression behaves like a smoothing process, which will reduce the error of incorrectly detecting false negatives. Hence the statistical power improves. The sparse shape model is then applied in investigating the influence of age on amygdala and hippocampus shapes in the normal population. The advantage of the LB sparse framework is demonstrated by showing the increased statistical power.
DTI offers a unique opportunity to characterize the structural connectivity of the human brain non-invasively by
tracing white matter fiber tracts. Whole brain tractography studies routinely generate up to half million tracts
per brain, which serves as edges in an extremely large 3D graph with up to half million edges. Currently there
is no agreed-upon method for constructing the brain structural network graphs out of large number of white
matter tracts. In this paper, we present a scalable iterative framework called the ε-neighbor method for building
a network graph and apply it to testing abnormal connectivity in autism.
The second Laplace-Beltrami eigenfunction provides an intrinsic geometric way of establishing natural coordinates
for elongated 3D anatomical structures obtained from medical images. The approach is used to establish
the centerline of the human mandible from CT and provides automated anatomical landmarks across subjects.
These landmarks are then used to quantify the growth pattern of the mandible between ages 0 and 20.
Sparse partial correlation is a useful connectivity measure for brain networks when it is difficult to compute the
exact partial correlation in the small-n large-p setting. In this paper, we formulate the problem of estimating
partial correlation as a sparse linear regression with a l1-norm penalty. The method is applied to brain network
consisting of parcellated regions of interest (ROIs), which are obtained from FDG-PET images of the autism
spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. To validate the results, we check
their reproducibilities of the obtained brain networks by the leave-one-out cross validation and compare the
clustered structures derived from the brain networks of ASD and PedCon.