RBC Modeling Using NURBS Based Isogeometric Analysis

The Red Blood Cell(RBC) is the transporter of oxygen to the entire human body via the circulatory system. Its journey spans across pathways which step down orders of magnitude; from large arteries which are O(cm) to tiny capillaries which are O(μm). This four-fold reduction in the diameters of the circulatory pathways necessitates the RBC to be extremely deformable. One of the most intriguing facets of the RBC is that it achieves this extreme deformability with ease; and also with a very minimal area dilatation[1]. Modeling the RBC has been an active area of research since the 1950’s. However, conventional methods to model RBCs rely on simplistic Finite Element Methods(FEM) involving mostly triangular elements. The extreme deformability of the RBCs mandate the use of a large number of elements, usually O(thousands) to accurately resolve and visualize the motion of an RBC [2], which is biconcave when unstressed and assumes myriad shapes as it travels through the microcirculation. The extremely large number of elements per cell makes the calculations highly computationally intensive for a single cell alone. This becomes particularly important when attempting to simulate the motion of a large number of cells, leading to a very computationally intensive simulation. The current paper proposes a novel method to analyze and resolve the RBC as a smooth entity using greatly reduced number of elements for resolution. This approach is based on exploiting the properties of Non-Uniform Rational B-Spline (NURBS) surfaces [3]. The results obtained from utilizing the NURBS surfaces can be considered to be a more realistic representation of the behavior of the RBC. Though this article specifically deals with the RBC, it can be applied to a deformable cell of any shape.