A Topological Data Analysis Framework for Quantifying Necrosis in Glioblastomas

In this paper, we introduce a shape descriptor that we call "interior function". This is a Topological Data Analysis (TDA) based descriptor that refines previous descriptors for image analysis. Using this concept, we define subcomplex lacunarity, a new index that quantifies geometric characteristics of necrosis in tumors such as conglomeration. Building on this framework, we propose a set of indices to analyze necrotic morphology and construct a diagram that captures the distinct structural and geometric properties of necrotic regions in tumors. We present an application of this framework in the study of MRIs of Glioblastomas (GB). Using cluster analysis, we identify four distinct subtypes of Glioblastomas that reflect geometric properties of necrotic regions.