Computational Biorheology of Human Blood Flow in Health and Disease

Hematologic disorders arising from infectious diseases, hereditary factors and environmental influences can lead to, and can be influenced by, significant changes in the shape, mechanical and physical properties of red blood cells (RBCs), and the biorheology of blood flow. Hence, modeling of hematologic disorders should take into account the multiphase nature of blood flow, especially in arterioles and capillaries. We present here an overview of a general computational framework based on dissipative particle dynamics (DPD) which has broad applicability in cell biophysics with implications for diagnostics, therapeutics and drug efficacy assessments for a wide variety of human diseases. This computational approach, validated by independent experimental results, is capable of modeling the biorheology of whole blood and its individual components during blood flow so as to investigate cell mechanistic processes in health and disease. DPD is a Lagrangian method that can be derived from systematic coarse-graining of molecular dynamics but can scale efficiently up to arterioles and can also be used to model RBCs down to the spectrin level. We start from experimental measurements of a single RBC to extract the relevant biophysical parameters, using single-cell measurements involving such methods as optical tweezers, atomic force microscopy and micropipette aspiration, and cell-population experiments involving microfluidic devices. We then use these validated RBC models to predict the biorheological behavior of whole blood in healthy or pathological states, and compare the simulations with experimental results involving apparent viscosity and other relevant parameters. While the approach discussed here is sufficiently general to address a broad spectrum of hematologic disorders including certain types of cancer, this paper specifically deals with results obtained using this computational framework for blood flow in malaria and sickle cell anemia.National Institutes of Health (U.S.)Singapore-MIT Alliance for Research and Technology (SMART)United States. Dept. of Energy. Collaboratory on Mathematics for Mesoscopic Modeling of MaterialsUnited States. Dept. of Energy (INCITE Award

Numerical study of microfluidic effects and red blood cell dynamics in 'deterministic lateral displacement' geometries

The last two decades have seen microfluidics gaining increasing interest from the fields of medical diagnostics and bio-chemical processes, due to its immense potential for point-of-care diagnostic applications. Since blood plays a crucial role in many physiological and diagnostic processes, red blood cells (RBCs) have been the focus of a large volume of microfluidics research. The isolation of red blood cells and other blood components, based on the manifest morphological characteristics, is required in many applications, e. g. flow cytometry. The deterministic lateral displacement (DLD) is one such popular microfluidic technique that has shown great promise toward cellular separations. The DLD technique separates particles based on their hydrodynamic size. It has been demonstrated for size-based separations down to unprecedented size resolutions of ~ 10 nm. The DLD consists of a large number of obstacle pillars placed in a microfluidic channel. The layout of these obstacles is such that the obstacle array presents a fixed angle to the average fluid flow through the microfluidic channel. Size-based separation comes about due to steric interaction of particles with the pillars. Particles larger than a ‘critical’ size are forced to move along the obstacle array incline. The larger particles, following the array incline, are displaced perpendicular to the average flow direction, and are said to be on the displacement mode. Particles smaller than this critical size flow along the average fluid flow direction, zigzagging around the obstacles. The trajectories followed by these smaller particles are classified as zigzag mode. Micro-particles therefore follow different trajectory modes based on their size, eventually leading to their spatial separation. The particles are separated passively, i. e. other than the pressure drop needed to drive the fluid flow through the DLD micro-channel, there is no need for any external forces for particle sorting. Numerous studies since the advent of the DLD have focussed on widening the scope of applications covered by the technique. In this thesis, I take a more physical approach, focussing on understanding the microhydrodynamics and RBC dynamics within the DLD geometries. For these investigations, I have used an in-house numerical solver that incorporates ingredients for fluid flow solution, RBC membrane deformation, and an explicit coupling algorithm between the two. The lattice Boltzmann method is used for obtaining a fluid flow solution at low Reynolds numbers, and the finite element method is used for computing the membrane energetics. The immersed boundary method explicitly couples these two solutions with non-matching boundaries, at each time step. Firstly, I investigate subtle flow hydrodynamic effects through DLD obstacle arrays. Here, fluid-only simulations uncover and map anisotropic flow permeability of the obstacle arrays. The research reveals that if the unit cell of the obstacle array geometrically forms a parallelogram, the array induces an anisotropic pressure gradient normal to the average flow direction. Contrarily, if the obstacle arrangement reflects a rotated square in its unit cell, anisotropy is entirely absent. Such anisotropic pressure conditions in the DLD cause local flow deviations and can lead to unintended particle motion arising from locally varying critical separation size. I find that elevated levels of such anisotropy are also brought about by pillar shape design and asymmetric array gaps. Furthermore, strategies to minimise anisotropic flow effects are proposed. The research on deformable RBC flow through the DLD tackles both single and collective cell dynamics in these arrays. Single cell dynamics is studied for special, non-cylindrical obstacle pillar shapes. In addition to the particle-obstacle steric contact, dynamic RBC motion leads to effects that influence cell trajectories in the DLD. Such effects are strongly tied to the interplay between RBC deformability, dynamic motion (such as tumbling and tank-treading) and the flow-field generated by the pillar shape. In certain cases, wall-induced hydrodynamic cell migration becomes significant enough such that the deformed tank-treading RBC undergoes displacement mode without steric contact with the pillars. Here, migration velocity experienced by the cells interacting with special pillar shapes causes a reversal of the phase-bifurcation trend. The uncovering of this mechanism, opens the door for research on novel DLD pillar designs that exploit wall-induced soft particle migration. Lastly, the research turns to collective RBC dynamics at high volume fractions, in standard DLD arrays with cylindrical pillars. Here, I research the effect of increasing cell volume fraction on the displacement and zigzag modes, with the help of appropriate statistical measures. I find that the displacement mode suffers a breakdown at higher volume fractions, while the zigzag mode remains robust. This has important implications for cell separation applications in the DLD, where smaller particles (e. g. platelets) need to be separated from a dense background of RBCs and vice versa. The investigations undertaken in this thesis identify subtle hydrodynamic and particle effects in DLD arrays that explain previously unresolved particle behaviour. This research should help improve the design and fabrication of DLD devices, especially those targeted at improved separation and manipulation of deformable RBCs

Numerical simulations of complex fluid-fluid interface dynamics

Interfaces between two fluids are ubiquitous and of special importance for industrial applications, e.g., stabilisation of emulsions. The dynamics of fluid-fluid interfaces is difficult to study because these interfaces are usually deformable and their shapes are not known a priori. Since experiments do not provide access to all observables of interest, computer simulations pose attractive alternatives to gain insight into the physics of interfaces. In the present article, we restrict ourselves to systems with dimensions comparable to the lateral interface extensions. We provide a critical discussion of three numerical schemes coupled to the lattice Boltzmann method as a solver for the hydrodynamics of the problem: (a) the immersed boundary method for the simulation of vesicles and capsules, the Shan-Chen pseudopotential approach for multi-component fluids in combination with (b) an additional advection-diffusion component for surfactant modelling and (c) a molecular dynamics algorithm for the simulation of nanoparticles acting as emulsifiers.Comment: 24 pages, 12 figure

Red Blood Cell Dynamics on Non-Uniform Grids using a Lattice Boltzmann Flux Solver and a Spring-Particle Red Blood Cell Model

The Computational Haemodynamics Research Group (CHRG) in Technological University Dublin is developing a computational fluid dynamics (CFD) software package aimed specifically at physiologically-realistic modelling of blood flow. A physiologically-realistic model of blood flow involves calculating the deformation of individual red blood cells (RBCs) and the contribution of this deformation to the overall blood flow. The CHRG has developed an enhanced spring-particle RBC structural model that is capable of modelling the full stomatocyte-discocyteechinocyte (SDE) transformation. This RBC model, incorporated into a fluid dynamics solver, will provide a physiologically-realistic blood flow model. In this work the overall plasma flow is modelled using a novel technique: the lattice Boltzmann flux solver (LBFS). This is an innovative approach to solving the NavierStokes (N-S) equations for fluid flow. It involves solving the macroscopic equations using the finite volume method (FVM) and calculating the flux across the cell interfaces via a local reconstruction of the lattice Boltzmann equation (LBE). Fluidstruture interaction between the RBC and the plasma is captured by coupling the RBC solver to the LBFS via the immersed boundary method (IBM). Numerical experiments investigating RBC dynamics are performed using non-uniform grids and validated against existing experimental data in the literature. Finally all numerical solvers are developed using general purpose GPU programming (GPGPU) and this is shown to accelerate simulation runtimes significantly

Multiscale Modelling of Malaria-Infected Red Blood Cells

Red blood cells (RBCs) are the type of human cells that are most accessible to biophysical multiscale modelling because they feature a regular molecular cell envelope organization and lack internal organelles. Extensive previous research on how their physical properties are shaped by the actin-spectrin network and other molecular constituents provides a good basis to understand the physical consequences of becoming infected by malaria parasites, which use RBCs to hide from the immune system. After invasion, the malaria parasite rebuilds the RBC-envelope, relying on the self-assembly of parasite proteins released into the cytoplasm. Optical tweezer experiments have shown that infected RBCs (iRBCs) become stiffer. Here, the underlying mechanisms are investigated by quantitative analysis of the flickering spectrum of iRBCs. Extending the membrane Hamiltonian by anchoring points, we find that the parasite stiffens the membrane mostly by introducing more connections between the lipid bilayer and the underlying cytoskeleton. To identify the exact points of attack in the RBC-cytoskeleton, a reaction-diffusion model is developed to investigate the dynamical equilibrium of the RBC-cytoskeleton, allowing us to simulate different scenarios of parasite protein self-assembly and to compare these results with experimental data. The parasite induces protrusions to make the iRBC adhesive, thus increasing residence time in the vasculature and avoiding clearance by the spleen. The number of new transmembrane receptors incorporated into the cell membrane is estimated by quantitative analysis of fluorescence and electron microscopy data. We develop a finite element model aiming to predict the effect of these changes on the movement of iRBCs in hydrodynamic flow. Finally, as an instructive contrast to RBC-mechanics, we investigate the spreading of tissue cells onto micropatterned substrates leading to a complete change in their actin cytoskeleton. A Cellular Potts Model is used to describe this highly dynamic situation. We find that due to its focus on geometrical aspects, it predicts reliably how a family of actin stress fibres is formed, which serves as memory of the spreading process

Pathophysiology of human red blood cell probed by quantitative phase microscopy by YongKeun Park.

Thesis (Ph. D.)--Harvard-MIT Division of Health Sciences and Technology, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 53-58).There is a strong correlation between the membrane fluctuations and the material properties of living cells. The former, consisting of submicron displacements, can be altered by changing the cells' pathophysiological conditions. It is our hypothesis that the material properties of cells can be retrieved when we quantify cell membrane fluctuation and combine that result with an appropriate physical model. We have developed: (1) an optical imaging technique to noninvasively quantify membrane fluctuations in red blood cells at the nanometer and millisecond scales; and (2) a model to retrieve the material properties of red blood cell membrane. The technique employs laser interferometry and provides full-field quantitative topographical information of living cells with unprecedented stability. Integration with the mathematical model provides the specific material properties from individual cell membrane fluctuations: shear modulus of the membrane; bending modulus; and viscosity of the cytoplasm. Employing these methods, we have systemically studied the material properties of human red blood cells altered by various pathophysiological conditions: morphological transition of red blood cell; parasitization by the P. falciparum parasites; and metabolic remodeling of the membrane driven by Adenosine-5'- triphosphate (ATP). We envision that this investigation could offer a means to link cell membrane fluctuations with the pathological conditions that lead to human disease states by quantitatively providing the alternation in material properties. A clear understanding of the mechanical alteration of red blood cells is important to studying the human diseases which cause their infection.Ph.D