Spatial Graphs for Intra-cranial Vascular Network Characterization, Generation, and Discrimination

Abstract

Abstract. Graph methods that summarize vasculature by its branching topology are not sufficient for the statistical characterization of a population of intra-cranial vascular networks. Intra-cranial vascular networks are typified by topological variations and long, wandering paths between branch points.We present a graph-based representation, called spatial graphs, that captures both the branching patterns and the spatial locations of vascular networks. Furthermore, we present companion methods that allow spatial graphs to (1) statistically characterize populations of vascular networks, (2) generate the central vascular network of a population of vascular networks, and (3) distinguish between populations of vascular networks. We evaluate spatial graphs by using them to distinguish the gender and handedness of individuals based on their intra-cranial vascular networks.

Studying Cerebral Vasculature Using Structure Proximity and Graph Kernels

“…Furthermore, vascular graph comparisons are typically performed using summary statistics in order to circumvent computational complexity issues inherent to many graph similarity metrics. Additionally, while progress has been made in representing cerebral vasculature as graphs [4] and even as graphs that span intracranial space [1], no prior work, to our knowledge, has augmented vascular graph encodings with brain structure information , e.g., hippocampus, thalamic nuclei and so forth.…”

“…Our contribution is two-fold: First, we augment the spatial graph representation of [1] with brain structure information at each vertex to enhance expressiveness. Second, we draw upon recent advances in machine learning with graph-structured data [8] to quantify gender-related differences in cerebrovascular architecture using a graph-kernel based discriminant classifier.…”

“…In this section, we introduce the concept of functional graphs , an extension of spatial graphs [1] with vertex labels that encode information about proximal brain structures. Our approach has the following requirements: For a population of N individuals, we require MRA and T1-weighted MRI images, as well as extracted cerebral vasculature in a centerline + radius representation.…”

“…We further require that the atlas has an associated voxel-wise labeling of brain structures (e.g., see [6]). For clarity of presentation, we briefly recapitulate spatial graph construction [1] and then discuss our contribution.…”

“…Second, [1] proposes a centroidal Voronoi tessellation (CVT) of the density atlas to identify regions of approximately equal probability. Specifically, CVT is applied to $\overline{\mathcal{D}}$ to generate C cells ${\mathrm{scriptC}}_1,\dots ,{\mathrm{scriptC}}_C$.…”