Micro-scale blood particulate dynamics using a non-uniform rational B-spline-based isogeometric analysis

Abstract

The current research presents a novel method in which blood particulates - biconcave red blood cells (RBCs) and spherical cells are modeled using isogeometric analysis, specifically Non-Uniform Rational B-Splines (NURBS) in 3-D. The use of NURBS ensures that even with a coarse representation, the geometry of the blood particulates maintains an accurate description when subjected to large deformations. The fundamental advantage of this method is the coupling of the geometrical description and the stress analysis of the cell membrane into a single, unified framework. Details on the modeling approach, implementation of boundary conditions and the membrane mechanics analysis using isogeometric modeling are presented, along with validation cases for spherical and biconcave cells. Using NURBS - based isogeometric analysis, the behavior of individual cells in fluid flow is presented and analyzed in different flow regimes using as few as 176 elements for a spherical cell and 220 elements for a biconcave RBC. This work provides a framework for modeling a large number of 3-D deformable biological cells, each with its own geometric description and membrane properties. To the best knowledge of the authors, this is the first application of the NURBS - based isogeometric analysis to model and simulate blood particulates in flow in 3D.