Continuum Scale Non Newtonian Particle Transport Model for Hæmorheology

Viscosity Modeling for Blood and Blood Analog Fluids in Narrow Gap and High Reynolds Numbers Flows

For the optimization of ventricular assist devices (VADs), flow simulations are crucial. Typically, these simulations assume single-phase flow to represent blood flow. However, blood consists of plasma and blood cells, making it a multiphase flow. Cell migration in such flows leads to a heterogeneous cell distribution, significantly impacting flow dynamics, especially in narrow gaps of less than 300 μm found in VADs. In these areas, cells migrate away from the walls, forming a cell-free layer, a phenomenon not usually considered in current VAD simulations. This paper addresses this gap by introducing a viscosity model that accounts for cell migration in microchannels under VAD-relevant conditions. The model is based on local particle distributions measured in a microchannels with a blood analog fluid. We developed a local viscosity distribution for flows with particles/cells and a cell-free layer, applicable to both blood and analog fluids, with particle volume fractions of up to 5%, gap heights of 150 μm, and Reynolds numbers around 100. The model was validated by comparing simulation results with experimental data of blood and blood analog fluid flow on wall shear stresses and pressure losses, showing strong agreement. This model improves the accuracy of simulations by considering local viscosity changes rather than assuming a single-phase fluid. Future developments will extend the model to physiological volume fractions up to 40%.

Continuum microhaemodynamics modelling using inverse rheology

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.