Establishing Metrics to Quantify Underlying Structure in Vascular Red Blood Cell Distributions

Abstract

Simulations of the microvasculature can elucidate the effects of various blood flow parameters on micro-scale cellular and fluid phenomena. At this scale, the non-Newtonian behavior of blood requires the use of explicit cell models, which are necessary for capturing the full dynamics of cell motion and interactions. Over the last few decades, fluid-structure interaction models have emerged as a method to accurately capture the behavior of deformable cells in the blood. However, as computational power increases and systems with millions of red blood cells can be simulated, it is important to note that varying spatial distributions of cells may affect simulation outcomes. Since a single simulation may not represent the ensemble behavior, many different configurations may need to be sampled to adequately assess the entire collection of potential cell arrangements. In order to determine both the number of distributions needed and which ones to run, we must first establish methods to identify well-generated, randomly-placed cell distributions and to quantify distinct cell configurations. In this work, we utilize metrics to assess 1) the presence of any underlying structure to the initial cell distribution and 2) similarity between cell configurations. We propose the use of the radial distribution function to identify long-range structure in a cell configuration and apply it to a randomly-distributed and structured set of red blood cells. To quantify spatial similarity between two configurations, we make use of the Jaccard index, and characterize sets of red blood cell and sphere initializations.