Identifying Graph Characteristics in Growing Vascular Networks

Abstract: One of the ways that a vascular network grows is through the process of angiogenesis, wherebya new blood vessel forms as a branch from an existing vessel towards an area which isstimulating vascular growth. Due to the demands for nutrients and waste transport, growingtumour cells will access the surrounding vascular network by inducing angiogenesis. Once thetumour is connected with the vascular system it can grow further and colonize distant organs.Given the critical nature of this step in tumour development, there is a demand for mathematicaland computational models to provide an understanding of the process for treatment in predictivemedicine. These models allow us to generate vascular networks that demonstrate similarbehaviour to that of the observed networks; however, there is a lack of quantifiable measures ofsimilarity between generated networks, or, of a generated and real network. Furthermore, thereis not an established way to determine which measures hold the most relevance todistinguishing similarity. To construct such a measure we transform our generated vascularnetworks into an abstract graph representation which allows exploration of the plethora of graphcentralities. We propose to determine the relevance of a centrality by finding one that acts as asynthetic likelihood function for estimating the model's parameters with minimal error.Evaluating the relevance of many centralities, it is then possible to suggest which centralitiesshould be used to quantitatively determine similarity. This allows for a way to measure howrealistic a model's growth is, and if given sufficient data, to distinguish between regular andtumour-induced angiogenesis and use it within cancer screening.