A Mesoscopic Model for Blood Flow Prediction Based on Experimental Observation of Red Blood Cell Interaction

Abstract

In some species, including humans, red blood cells (RBCs) under low shear stress tend to clump together and form into regular stacks called rouleaux. These stacks are not static, and constantly move and break apart. This phenomenon is referred to as red blood cell aggregation and disaggregation. When modelled as a single liquid, blood behaves as a non-Newtonian fluid. Its viscosity varies, mainly due to the aggregation of RBCs. The aim of this research is to develop a mesoscale computational model for the simulation of RBCs in plasma. This model considers RBC interaction and aggregation to predict blood-flow characteristics such as viscosity, rouleaux size and velocity distribution. In this work, the population-balance modelling (PBM) approach is utilized to model the RBC aggregation process. The PBM approach is a known method that is used for modelling agglomeration and breakage in two-phase flow fluid mechanics to find aggregate size. The PBM model is coupled to the incompressible Navier-Stokes equations for the plasma. Both models are numerically solved simultaneously. The population-balance equation has been used previously in a more restricted form, the Smoluchowski equation, to model blood viscosity, but it has never been fully coupled with the Navier-Stokes equation directly for the numerical modelling of blood flow. This approach results in a comprehensive model which aims to predict RBC aggregate size and their velocities for different flow configurations, as well as their effects on the apparent macro-scale viscosity. The PBM approach does not treat the microscopic physics of aggregation directly but rather uses experimental correlations for aggregation and disaggregation rates to account for the effects of aggregation on the bulk. To find the aggregation rate, a series of experiments on RBC sedimentation due to gravity is designed. In these tests, aggregated RBCs (rouleaux) tend to settle faster than single RBCs and, due to low shear stresses, disaggregation is very low and can be neglected. A high-speed camera is used to acquire video-microscopic pictures of the process. The size of the aggregates and their velocities are extracted using image processing techniques. For image processing, a general Matlab program is developed which can analyze all the images and report the velocity and size distribution of rouleaux. An experimental correlation for disaggregation rate is found using results from a previous steady-state Couette flow experiment. Aggregation and disaggregation rates from these experiments are used to complete the PBM model. Pressure-driven channel flow experiments are then used for the final validation of the model. Comparisons of the apparent viscosity of whole blood in previous experiments show reasonable agreement with the developed model. This model fills a gap between micro-scale and macro-scale treatments and should be more accurate than traditional macro-scale models while being cheaper than direct treatment of RBCs at the micro-scale.