Abstract
Modelling blood flow in microvascular networks is challenging due to the complex nature of haemorheology. Zero- and one-dimensional approaches cannot reproduce local haemodynamics, and models that consider individual red blood cells (RBCs) are prohibitively computationally expensive. Continuum approaches could provide an efficient solution, but dependence on a large parameter space and scarcity of experimental data for validation has limited their application. We describe a method to assimilate experimental RBC velocity and concentration data into a continuum numerical modelling framework. Imaging data of RBCs were acquired in a sequentially bifurcating microchannel for various flow conditions. RBC concentration distributions were evaluated and mapped into computational fluid dynamics simulations with rheology prescribed by the Quemada model. Predicted velocities were compared to particle image velocimetry data. A subset of cases was used for parameter optimisation, and the resulting model was applied to a wider data set to evaluate model efficacy. The pre-optimised model reduced errors in predicted velocity by 60% compared to assuming a Newtonian fluid, and optimisation further reduced errors by 40%. Asymmetry of RBC velocity and concentration profiles was demonstrated to play a critical role. Excluding asymmetry in the RBC concentration doubled the error, but excluding spatial distributions of shear rate had little effect. This study demonstrates that a continuum model with optimised rheological parameters can reproduce measured velocity if RBC concentration distributions are known a priori. Developing this approach for RBC transport with more network configurations has the potential to provide an efficient approach for modelling network-scale haemodynamics.
Highlights
Cardiovascular diseases are the foremost cause of death globally, and central to many of these conditions are altered blood flow dynamics
Blood rheology is determined predominantly by the red blood cells (RBCs), which are suspended in the plasma at a volume concentration that varies throughout the vasculature, with an average of 45% in large vessels
In order to provide a foundation for the inverse rheology process, Fig. 4 shows sample velocity, haematocrit and viscosity profiles
Summary
Cardiovascular diseases are the foremost cause of death globally, and central to many of these conditions are altered blood flow dynamics. Blood rheology is determined predominantly by the red blood cells (RBCs), which are suspended in the plasma at a volume concentration (haematocrit) that varies throughout the vasculature, with an average of 45% in large vessels. RBCs have a propensity to reversibly aggregate due to interactions with plasma proteins. Together, these RBC characteristics lead to shear thinning behaviour (Chien 1970) that is highly dependent on the haematocrit (Merrill et al 1963; Pries et al 1992), amongst other parameters. Macrohaemodynamic analyses typically treat blood as Newtonian or use shear-dependent non-Newtonian viscosity models. As blood rheology is dependent on local RBC concentration, the rheological environment of microvessels is correspondingly complex
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