Huan Lei

Multiscale Modeling of Red Blood Cell Mechanics and Blood Flow in Malaria

Red blood cells (RBCs) infected by a Plasmodium parasite in malaria may lose their membrane deformability with a relative membrane stiffening more than ten-fold in comparison with healthy RBCs leading to potential capillary occlusions. Moreover, infected RBCs are able to adhere to other healthy and parasitized cells and to the vascular endothelium resulting in a substantial disruption of normal blood circulation. In the present work, we simulate infected RBCs in malaria using a multiscale RBC model based on the dissipative particle dynamics method, coupling scales at the sub-cellular level with scales at the vessel size. Our objective is to conduct a full validation of the RBC model with a diverse set of experimental data, including temperature dependence, and to identify the limitations of this purely mechanistic model. The simulated elastic deformations of parasitized RBCs match those obtained in optical-tweezers experiments for different stages of intra-erythrocytic parasite development. The rheological properties of RBCs in malaria are compared with those obtained by optical magnetic twisting cytometry and by monitoring membrane fluctuations at room, physiological, and febrile temperatures. We also study the dynamics of infected RBCs in Poiseuille flow in comparison with healthy cells and present validated bulk viscosity predictions of malaria-infected blood for a wide range of parasitemia levels (percentage of infected RBCs with respect to the total number of cells in a unit volume).

Quantifying the Rheological and Hemodynamic Characteristics of Sickle Cell Anemia

Sickle erythrocytes exhibit abnormal morphology and membrane mechanics under deoxygenated conditions due to the polymerization of hemoglobin S. We employed dissipative particle dynamics to extend a validated multiscale model of red blood cells (RBCs) to represent different sickle cell morphologies based on a simulated annealing procedure and experimental observations. We quantified cell distortion using asphericity and elliptical shape factors, and the results were consistent with a medical image analysis. We then studied the rheology and dynamics of sickle RBC suspensions under constant shear and in a tube. In shear flow, the transition from shear-thinning to shear-independent flow revealed a profound effect of cell membrane stiffening during deoxygenation, with granular RBC shapes leading to the greatest viscosity. In tube flow, the increase of flow resistance by granular RBCs was also greater than the resistance of blood flow with sickle-shape RBCs. However, no occlusion was observed in a straight tube under any conditions unless an adhesive dynamics model was explicitly incorporated into simulations that partially trapped sickle RBCs, which led to full occlusion in some cases.

Blood flow in small tubes: quantifying the transition to the non-continuum regime

In small vessels blood is usually treated as a Newtonian fluid down to diameters of ~200 μm. We investigate the flow of red blood cell (RBC) suspensions driven through small tubes (diameters 10-150 μm) in the range marking the transition from arterioles and venules to the largest capillary vessels. The results of the simulations combined with previous simulations of uniform shear flow and experimental data show that for diameters less than ~100 μm the suspensions stress cannot be described as a continuum, even a heterogeneous one. We employ the dissipative particle dynamics (DPD) model, which has been successfully used to predict human blood bulk viscosity in homogeneous shear flow. In tube flow the cross-stream stress gradient induces an inhomogeneous distribution of RBCs featuring a centreline cell density peak, and a cell-free layer (CFL) next to the wall. For a neutrally buoyant suspension the imposed linear shear-stress distribution together with the differentiable velocity distribution allow the calculation of the local viscosity across the tube section. The viscosity across the section as a function of the strain rate is found to be essentially independent of tube size for the larger diameters and is determined by the local haematocrit (H) and shear rate. Other RBC properties such as asphericity, deformation, and cell-flow orientation exhibit similar dependence for the larger tube diameters. As the tube size decreases below ~100 μm in diameter, the viscosity in the central region departs from the large-tube similarity function of the shear rate, since H increases significantly towards the centreline. The dependence of shear stress on tube size, in addition to the expected local shear rate and local haematocrit, implies that blood flow in small tubes cannot be described as a heterogeneous continuum. Based on the analysis of the DPD simulations and on available experimental results, we propose a simple velocity-slip model that can be used in conjunction with continuum-based simulations.

Probing red blood cell mechanics, rheology and dynamics with a two-component multi-scale model.

This study is partially motivated by the validation of a new two-component multi-scale cell model we developed recently that treats the lipid bilayer and the cytoskeleton as two distinct components. Here, the whole cell model is validated and compared against several available experiments that examine red blood cell (RBC) mechanics, rheology and dynamics. First, we investigated RBC deformability in a microfluidic channel with a very small cross-sectional area and quantified the mechanical properties of the RBC membrane. Second, we simulated twisting torque cytometry and compared predicted rheological properties of the RBC membrane with experimental measurements. Finally, we modelled the tank-treading (TT) motion of a RBC in a shear flow and explored the effect of channel width variation on the TT frequency. We also investigated the effects of bilayer–cytoskeletal interactions on these experiments and our simulations clearly indicated that they play key roles in the determination of cell membrane mechanical, rheological and dynamical properties. These simulations serve as validation tests and moreover reveal the capabilities and limitations of the new whole cell model.

Probing vasoocclusion phenomena in sickle cell anemia via mesoscopic simulations

Vasoocclusion crisis is a key hallmark of sickle cell anemia. Although early studies suggest that this crisis is caused by blockage of a single elongated cell, recent experiments have revealed that vasoocclusion is a complex process triggered by adhesive interactions among different cell groups in multiple stages. However, the quantification of the biophysical characteristics of sickle cell anemia remains an open issue. Based on dissipative particle dynamics, we develop a multiscale model for the sickle red blood cells (SS-RBCs), accounting for diversity in both shapes and cell rigidities, to investigate the precise mechanism of vasoocclusion. First, we investigate the adhesive dynamics of a single SS-RBC in shear flow and static conditions, and find that the different cell groups (SS2: young-deformable SS-RBCs, ISCs: rigid-irreversible SS-RBCs) exhibit heterogeneous adhesive behavior due to the diverse cell morphologies and membrane rigidities. We quantify the observed adhesion behavior (in static conditions) in terms of a balance of free energies due to cell adhesion and deformation, and propose a power law that relates the free-energy increase as a function of the contact area. We further simulate postcapillary flow of SS-RBC suspensions with different cell fractions. The more adhesive SS2 cells interact with the vascular endothelium and trap ISC cells, resulting in vasoocclusion in vessels less than depending on the hematocrit. Under inflammation, adherent leukocytes may also trap ISC cells, resulting in vasoocclusion in even larger vessels.

Time-dependent and outflow boundary conditions for Dissipative Particle Dynamics

We propose a simple method to impose both no-slip boundary conditions at fluid-wall interfaces and at outflow boundaries in fully developed regions for Dissipative Particle Dynamics (DPD) fluid systems. The procedure to enforce the no-slip condition is based on a velocity-dependent shear force, which is a generalized force to represent the presence of the solid-wall particles and to maintain locally thermodynamic consistency. We show that this method can be implemented in both steady and time-dependent fluid systems and compare the DPD results with the continuum limit (Navier-Stokes) results. We also develop a force-adaptive method to impose the outflow boundary conditions for fully developed flow with unspecified outflow velocity profile or pressure value. We study flows over the backward-facing step and in idealized arterial bifurcations using a combination of the two new boundary methods with different flow rates. Finally, we explore the applicability of the outflow method in time-dependent flow systems. The outflow boundary method works well for systems with Womersley number of O(1), i.e., when the pressure and flowrate at the outflow are approximately in-phase.

Energy-conserving dissipative particle dynamics with temperature-dependent properties

The dynamic properties of fluid, including diffusivity and viscosity, are temperature-dependent and can significantly influence the flow dynamics of mesoscopic non-isothermal systems. To capture the correct temperature-dependence of a fluid, an energy-conserving dissipative particle dynamics (eDPD) model is developed by expressing the weighting terms of the dissipative force and the random force as functions of temperature. The diffusivity and viscosity of liquid water at various temperatures ranging from 273 K to 373 K are used as examples for verifying the proposed model. Simulations of a Poiseuille flow and a steady case of heat conduction for reproducing the Fourier law are carried out to validate the present eDPD formulation and the thermal boundary conditions. Results show that the present eDPD model recovers the standard DPD model when isothermal fluid systems are considered. For non-isothermal fluid systems, the present model can predict the diffusivity and viscosity consistent with available experimental data of liquid water at various temperatures. Moreover, an analytical formula for determining the mesoscopic heat friction is proposed. The validity of the formula is confirmed by reproducing the experimental data for Prandtl number of liquid water at various temperatures. The proposed method is demonstrated in water but it can be readily extended to other liquids.

Patient-specific blood rheology in sickle-cell anaemia

Sickle-cell anaemia (SCA) is an inherited blood disorder exhibiting heterogeneous cell morphology and abnormal rheology, especially under hypoxic conditions. By using a multiscale red blood cell (RBC) model with parameters derived from patient-specific data, we present a mesoscopic computational study of the haemodynamic and rheological characteristics of blood from SCA patients with hydroxyurea (HU) treatment (on-HU) and those without HU treatment (off-HU). We determine the shear viscosity of blood in health as well as in different states of disease. Our results suggest that treatment with HU improves or worsens the rheological characteristics of blood in SCA depending on the degree of hypoxia. However, on-HU groups always have higher levels of haematocrit-to-viscosity ratio (HVR) than off-HU groups, indicating that HU can indeed improve the oxygen transport potential of blood. Our patient-specific computational simulations suggest that the HVR level, rather than the shear viscosity of sickle RBC suspensions, may be a more reliable indicator in assessing the response to HU treatment.

Enhancing sparsity of Hermite polynomial expansions by iterative rotations

Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more sparse with new basis functions associated with the new random variables. This sparsity increases both the efficiency and accuracy of the compressive sensing-based uncertainty quantification method. Specifically, we consider rotation-based linear mappings which are determined iteratively for Hermite polynomial expansions. We demonstrate the effectiveness of the new method with applications in solving stochastic partial differential equations and high-dimensional ( O ( 100 ) ) problems.

Inflow/Outflow Boundary Conditions for Particle-Based Blood Flow Simulations: Application to Arterial Bifurcations and Trees

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the “all-or-nothing” phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.