Numerical Investigation of the Effects of Red Blood Cell Cytoplasmic Viscosity Contrasts on Single Cell and Bulk Transport Behaviour

Abstract

In-silico cellular models of blood are invaluable to gain understanding about the many interesting properties that blood exhibits. However, numerical investigations that focus on the effects of cytoplasmic viscosity in these models are not very prevalent. We present a parallelised method to implement cytoplasmic viscosity for HemoCell, an open-source cellular model based on immersed boundary lattice Boltzmann methods, using an efficient ray-casting algorithm. The effects of the implementation are investigated with single-cell simulations focusing on the deformation in shear flow, the migration due to wall induced lift forces, the characteristic response time in periodic stretching and pair collisions between red blood cells and platelets. Collective transport phenomena are also investigated in many-cell simulations in a pressure driven channel flow. The simulations indicate that the addition of a viscosity contrast between internal and external fluids significantly affects the deformability of a red blood cell, which is most pronounced during very short time-scale events. Therefore, modelling the cytoplasmic viscosity contrast is important in scenarios with high velocity deformation, typically high shear rate flows.

Effect of Cytoplasmic Viscosity on Red Blood Cell Migration in Small Arteriole-level Confinements

“…One important feature to note is that for both systems we see fluctuations in the distribution that occur over very long times and these fluctuations persist even after 500 dimensionless times. Previous studies often implicitly assume that times shorter than the time of the presented distribution are sufficient to reach a steady state (de Haan et al, 2018;Shen et al, 2016;Qi, 2017), but it appears that no such steady state exists and that there is a constant state of fluctuation. Therefore, a time sequence of concentration profile is used here to interpret the results.…”

“…Due to the complexity of blood suspension dynamics, large scale simulation tools are required to understand much of the salient physics. Many approaches have been developed including the boundary integral method (Zhao et al, 2012;Sinha and Graham, 2015;Pozrikidis, 1992), the immersed boundary method coupled with the Lattice Boltzmann method (Shen et al, 2016;Krüger, 2012;Reasor et al, 2013;Závodszky et al, 2017;de Haan et al, 2018), and other immersed boundary approaches coupled to finite volume/difference/element solvers (Ye et al, 2016;Doddi, 2008;Balogh and Bagchi, 2018;Sigüenza et al, 2016;Saadat et al, 2018). The boundary integral method (BEM) has had great success in simulating smaller suspensions of cells, but poor scaling in particle number often reduces the ability to study larger suspensions via BEM.…”

“…Additionally, many authors report instabilities when studying large viscosity contrasts when studying suspensions. The Lattice Boltzmann method has shown extremely good scaling in particle number and also the ability to study important features like the viscosity contrast -the viscosity ratio of inner cell cytoplasm to the outer plasma -which makes it a promising simulation technique (Shen et al, 2016;de Haan et al, 2018). In a similar manner, immersed boundary methods coupled to finite volume solvers or finite element solvers have also shown great promise in simulating these large suspensions and we will be utilizing this method to further elucidate the physics of these suspensions (Saadat et al, 2018;Balogh and Bagchi, 2018).…”

“…Viscosity contrast affects shape, mode of motion, and collision dynamics (Sinha and Graham, 2015;Omori et al, 2014;Lanotte et al, 2016;de Haan et al, 2018;Ye et al, 2010;Freund and Orescanin, 2011;Zhao et al, 2010). A large body of simulations in the literature have been conducted with the viscosity ratio in the range of λ ≤ 3 (Zhao et al, 2012;Qi and Shaqfeh, 2017;Narsimhan et al, 2013;Fedosov et al, 2010;Foessel et al, 2011), however, the physiological value is nearly 5 (Secomb, 2017;Lanotte et al, 2016).…”

“…2D LB simulations of Shen et al (2016) in a bifurcated channel suggested that there is a significant impact on the local RBC distribution of the parent channel when λ = 10 compared to no viscosity contrast. Recent LB simulations of de Haan et al (2018) indicated increasing impact of the viscosity contrast for higher flow strength (Reynolds number). They performed the simulations for large channels (70 µm in diameter) and observed negligible importance of λ on cell-free-layer and also local hematocrit for Ht values down to 20%.…”