A1421
Title: Metric statistics for geometric graphs with application to cardiac fibrosis
Authors: Arstanbek Okenov - Gent University (Belgium)
Anna Calissano - Imperial College London (United Kingdom) [presenting]
Alexander Panfilov - Gent University (Belgium)
Timur Nezlobinsky - Gent University (Belgium)
Abstract: Geometric graphs (or spatial networks) are graphs in which the nodes are embedded as points in Euclidean space, and the edges encode certain geometrical properties of an underlying object. Such graphs can describe the skelethon of a shape, often depicted in an image. The purpose is to describe how the fused Gromov-Wasserstain metric can be used to compare different geometric graphs with different numbers of nodes and edges. The metric is adjusted to leverage rotations between the graphs, and we use the metric to perform clustering and testing procedures. As a motivational case study, the geometry and the topology of cardiac fibrosis are studied in the human heart. Cardiac fibrosis is the pathological increase of fibroblast in the heart. The data consists of histopathological images of human hearts showing cardiac fibrosis. Each image representing the fibroblast is turned into a bidimensional spatial network using skelethonization. Via clustering procedure and metric-based ANOVA, the question of how cardiac fibrosis is structured in terms of its geometrical and topological characteristics is addressed, along with the existing variability within a single patient and across patients.
