Session LK: Biofluids: Cellular I

A Comparison of Multi-scale and Low-Dimensional Models of Red Blood Cells

A new low-dimensional dissipative particle dynamics (DPD) model of the red blood cell (LD-RBC) is tested against a multi-scale RBC (MS-RBC) model known to accurately capture the mechanical response of single human RBCs in a number of static and dynamic experiments. The MS-RBC model represents the RBC membrane with hundreds or even thousands of DPD-particles and includes membrane viscosity. In contrast, the LD-RBC is constructed as a closed torus-like ring of only 10 large, hard DPD-particles previously employed to represent a colloidal suspension. Except for channel sizes comparable to RBC diameters, suspensions of LD-RBCs also capture the essential hydrodynamics of blood flow in vessels as faithfully as do suspensions of MS-RBCs. In particular, the LD-RBC is in agreement with the experimental data for the apparent viscosity of blood and its cell-free layer over a wide range of hematocrits.   

Effects of Fibrinogen on RBC Aggregation and Rouleux Formation

We employ dissipative particle dynamics (DPD) to study human blood rheology. Specifically, using a multi-scale (MS-RBC) and low-dimensional model (LD-RBC) for modeling red blood cells (RBCs), we study the role of fibrinogen inter-cellular forces in the formation of rouleaux structures at low shear rates. In particular, both models verify that RBC aggregation into rouleaux determines non-Newtonian response and they also predict a non-zero yield stress whose value depends on the fibrinogen concentration.   

Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell

A 2D computer simulation model was proposed for tank-treading and tumbling motions of an elastic biconcave red blood cell (RBC) under shear flow. The RBC model consisted of an outer membrane and an inner fluid; the membrane's elastic properties were modeled by springs for stretch/compression and bending to consider the membrane's natural state in a practical manner. Membrane deformation was coupled with incompressible viscous flow of the inner and outer fluids of the RBC using a particle method. As a result of simulations using the same initial RBC shape with different natural states of the RBC membrane, only tank-treading motion was exhibited in the case of a uniform natural state of the membrane, and a nonuniform natural state was necessary to generate the rotational oscillation and tumbling motion. In the range of simulation parameters considered, the relative membrane elastic force versus fluid viscous force was $\sim $1 at the transition when the natural state nonuniformity was taken into account in estimating the membrane elastic force.   

The Contribution of Red Blood Cell Dynamics to Intrinsic Viscosity and Functional ATP Release

In shear flow, red blood cells (RBCs) exhibit a variety of behaviors such as rouleaux formation, tumbling, swinging, and tank-treading. The physiological consequences of these dynamic behaviors are not understood. \textit{In vivo,} ATP is known to signal vasodilation; however, to our knowledge, no one has deciphered the relevance of RBC microrheology to the functional release of ATP. Previously, we correlated RBC deformation and ATP release in microfluidic constrictions (Wan \textit{et al}., 2008). In this work, a cone-plate rheometer is used to shear a low hematocrit solution of RBCs at varying viscosity ratios ($\lambda )$ between the inner cytoplasmic hemoglobin and the outer medium, to determine the intrinsic viscosity of the suspension. Further, using a luciferin-luciferase enzymatic reaction, we report the relative ATP release at varying shear rates. Results indicate that for $\lambda $ = 1.6, 3.8 and 11.1, ATP release is constant up to 500 s$^{-1}$, which suggests that the tumbling-tanktreading transition does not alter ATP release in pure shear. For lower viscosity ratios, $\lambda $ = 1.6 and 3.8, at 500 s$^{-1}$ a change in slope occurs in the intrinsic viscosity data and is marked by an increase in ATP release. Based on microfluidic observations, this simultaneous change in viscosity and ATP release occurs within the tank-treading regime.   

Occlusion of Small Vessels by Malaria-Infected Red Blood Cells

We use dissipative particle dynamics (DPD) method to study malaria-infected red blood cells (i-RBC). We have developed a multi-scale model to describe both static and dynamic properties of RBCs. With this model, we study the adhesive interaction between RBCs as well as the interaction between the Plasmodium falciparum (Pf)-parasitized cells and a vessel wall coated with purified ICAM-1. In this talk, we will discuss the effect of the Pf-parasitized malaria cell on the flow resistance of the blood flow at different parasetimia levels. The blood flow in malaria disease shows high flow resistance as compared with the healthy case due to both the stiffening of the i-RBCs (up to ten times) as well as the adhesion dynamics. For certain sizes of of small vessels, the malaria-infected cells can even lead to occlusion of the blood flow, in agreement with recent experiments.   

Molecular-detailed simulation of red blood cells in Stokes flows

The red blood cell (RBC) membrane consists of a lipid bilayer and a cytoskeleton. By coupling a multiscale approach of RBC membranes with a boundary element method (BEM) for the exterior and interior fluids, we developed a numerical capacity to relate the fluid-structure interaction of RBCs in Stokes flows with detailed mechanical loads inside its molecular architecture. Our multiscale approach includes three models: in the whole cell level, a finite element method (FEM) is employed to model the lipid bilayer and the cytoskeleton as two distinct layers of continuum shells; the mechanical properties of the cytoskeleton are obtained from a molecular-based model; the spectrin, a major protein of the cytoskeleton, is simulated using a constitutive model. BEM is applied to predict the exterior and interior Stokes flows, and is coupled with the FEM of the membrane through a staggered coupling algorithm. Using this method, we simulated the tumbling and tank-treading behaviors of RBCs in shear flows, and investigated the RBC dynamics in capillary flows. The structural deformation of the cytoskeleton and the interaction force between the lipid bilayer and the cytoskeleton are predicted.   

Rheological characterization of cellular blood via a hybrid lattice-Boltzmann / coarse-grained spectrin-link method

In small vessels, the cellular nature of blood is of utmost importance. The investigation of the non-Newtonian effects of blood for a complete range of hematocrit values and shear rates requires the direct numerical simulation (DNS) of individual red blood cells (RBCs) immersed in Newtonian blood plasma with hemoglobin within. Consequently, a coarse-grained spectrin-link (SL) RBC membrane model is coupled with a highly scalable lattice-Boltzmann (LB) flow solver to capture RBC dynamics in isolation and in dense suspensions of ${\cal O}(1,000)$ RBCs at realistic hematocrit values. Validation results include experimental comparisons with results for isolated RBCs tumbling, tank-treading, deforming in the wheel configuration, and parachuting in a microvessel-sized rigid tube. The rheology of blood is analyzed via LB-SL simulations of RBC suspensions at physiological concentrations. The results characterize the effect of the RBC deformation on the viscosity, normal stress differences, and particle pressure. Also, a demonstration of the F\r{a}hraeus effect is included which correlates the cell-depleted wall layer thickness with tube diameter for a variety of rigid microvessel-sized tube sizes. Lastly, the F\r{a}hraeus--Lindqvist effect is demonstrated using the apparent viscosity obtained from these simulations.   

A symplectic integration algorithm for red blood cells

Blood is a complex biofluid that shows interesting non-Newtonian and viscoelastic behavior. Red blood cells are of particular relevance for blood rheology and dynamics because they can undergo shape transformations when subjected to shear flow as it occurs in small blood vessels. The equilibrium shape of red blood cells is a biconcave discocyte which is a result of the competing elastic energies. While in some previous works, this shape was explicitly built into the model, we here aim at a model that reproduces the discocyte as the minimizing shape with respect to the elastic constitutive laws. The computational model we propose describes the red blood cells as an elastic membrane. We have implemented a symplectic integration algorithm that preserves the Hamiltonian structure. This algorithm leads to highly accurate energy conservation and consequently superior stability. Our model reproduces the experimentally observed cell shapes.   

Numerical simulation of cell/cell and cell/particle interaction in microchannels

A spring model is applied to simulate the skeleton structure of the red blood cell membrane and to study the red blood cell rheology in Poiseuille flow with an immersed boundary method. The lateral migration properties of many cells in Poiseuille flow have been investigated. We also have combined the above methodology with a distributed Lagrange multiplier/fictitious domain method to simulate the interaction of the red blood cells and neutrally buoyant particles in a microchannel for studying the margination of particles.   

Accelerated Boundary Integral Method in Non-periodic Geometries and Applications to Flowing Capsules and Cells

We present a fast O(NlogN) solution technique for the Stokes flow boundary integral equation in an arbitrary geometry. The acceleration is achieved via the use of the General Geometry Ewald Like Method (GGEM) for computing the Green's function and its associated stress tensor in the geometry of interest. In this talk, we first present an alternative formulation of the boundary integral equation that allows the use of GGEM. In this formulation, we get a second kind integral for the unknown surface tractions rather than the unknown surface velocity as is common for problems with non-matched viscosities in interfacial flows. An efficient methodology is then presented for calculating the single and the double layer integrals in the resulting formulation using the Green's function mentioned above. Our method will be compared with other accelerated boundary integral techniques for Stokes flow. The efficacy of the method will be demonstrated by the solution of several large scale test problems involving the flow of capsules and red blood cells in a slit geometry.