Session AJ: Bio-Fluids: Cell/Vesicle Dynamics I

Red Blood Cell Deformation Under Shear Flow: The Effect of Changing Cell Properties

The deformability of red blood cells plays a major role in the pathology of several diseases, including malaria, sickle cell anemia and spherocytosis. Moreover, deformations are believed to trigger the release of adenosine triphosphate, which helps regulate vascular tone and is consequently an important factor in various vascular diseases. Here we investigate single-cell viscoelastic responses to increased shear stress in poly(dimethylsiloxane) channels with a single constriction 2-4 times larger than a typical erythrocyte. These channels mimic arteriole-sized vessels, and have the advantage that the cell membrane is not in contact with the channel walls which have vastly different mechanical and material properties than living tissue. High-speed video and image analysis were used to quantify the trajectories and deformations of cells exposed to varied doses of diamide, a chemical known to ``rigidify'' erythrocytes. Our results show that (i) deformation is proportional to shear rate and (ii) the deformability of diamide-treated cells is greater than that of untreated cells. The latter is an unforeseen result because micropipette aspiration experiments have shown the opposite. We expect that the experimental procedure described here will be useful for characterizing the effect of different therapeutic agents on cellular deformability.   

Measuring morphological response of endothelial cells in shear flow

The normal physiological endothelial cell response to hemodynamic loadings can be categorized into morphological and biological responses. Cell morphological response includes changes in shape, size, height, and orientation. Cells sense mechanical stimuli and transduce them into chemical signals involving gene and protein expression, mechanotransduction. Abnormal endothelial response has been implicated in the localization of arterial disease like atherosclerosis. Though mechanotransduction involves a coupled ($i.e.$ morphological and biological) process, to date many investigations into endothelial cells are still done in the decoupled way. The ultimate goal of our study is simultaneous flow and biological measurements to better understand arterial disease at the cellular and sub-cellular level. \textit{In vitro} $\mu$ PIV measurements have been made in steady flow over live human aortic endothelial cells flush-mounted in a small rectangular channel. Cells are subjected to a step change in shear stress from zero to 15 dynes/cm$^{2}$. Cell surface maps, surface pressure, and wall shear stress are extracted from measurements taken 0, 3, 6, 12, 18, and 24 hours after applying shear. This work has laid a framework for future simultaneous measurements.   

Deformation of Elastic Particles in Viscous Shear Flow

The dynamics of two dimensional elastic particles in a Newtonian viscous shear flow is studied numerically. A constitutive equation is constructed for an incompressible ``Neo-Hookean'' elastic solid where the extra stress tensor is assumed to be linearly proportional to the Almansi strain tensor. A monolithic finite element solver which uses Arbitrary Lagrangian-Eulerian moving mesh technique is then implemented to solve the velocity, pressure and stress in both fluid and solid phase simultaneously. It is found that the deformation of the particle in the shear flow is governed the Reynolds number (Re) and the Capillary number (Ca). In the Stokes flow regime, the particle deforms into an ellipse while the material points inside experience a tank- treading like motion, and the deformation of the elastic particle is observed to vary linearly with Ca. Interactions between two particles in a viscous shear flow show that after the initial complicated interactions, both particles reach an equilibrium elliptic shape which is consistent with that of a single particle. Both rigid body rotation and buckling motion are observed when an elastic long particle is suspended in a shear flow.   

Simulating Cell Deformation with Optical Forces using the Immersed Boundary Method

The mechanical deformation of biological cells is an efficient experimental method to study the cellular properties and identify diseased cells. Optical forces have been successfully used to induce small and even large scale deformations that do not alter the cellular properties, mainly due to minimal direct contact, compared to other experimental techniques (micro-pipette aspiration, atomic force microscopy). A review on the recent advances in the area of optical cell deformation shows that a variety of deforming conditions can be imposed using different methods (optical tweezers and optical stretcher) to simulate the different biological conditions. Computational simulations, on the other hand, can be used to guide and explain the experimental observations. In this work, we will present a new numerical simulation of cell optical deformability using the immersed boundary method. Cells are considered as 3D elastic capsules immersed in a fluid. Optical forces are calculated using the ray optics technique and applied on the capsule membrane that inducing transient Stokes flow. The current study is primarily focused on the deformation of spherical cells as well as biconcave discoid representing red blood cells. The deformation pattern and relaxation time will be reported over a range of forces.   

Extreme deformation of vesicle membrane under DC electric fields

Electrodeformation refers to the deformation of cell or vesicle lipid membranes under the application of an electric field. This phenomenon often accompanies electroporation, an important technique to introduce molecules into the cells \textit{via} electric-field-induced membrane permeabilization. On the other hand, it can be also harnessed to probe the mechanical and dynamic properties of the lipid membranes. Recent studies suggest that the electrical conductivity difference across the membrane is a dominant factor in determining the regimes of deformation. In this work, the deformation of vesicular cellular mimics is systematically investigated, in particular with respect to varying electric field strengths, and a wide range of conductivity ratios. The results reveal that, under moderate values of the conductivity ratio, the membranes exhibited moderate deformations, in agreement with previous reports in the literature. Furthermore, under high conductivity ratios ($\sim $100), the vesicle membranes exhibited atypical, extreme elongations previous not reported. This phenomenon suggests a new regime of membrane electrodeformation which awaits further study. The current work also attempts to establish the correlation between the extreme deformation and membrane permeabilization (electroporation).   

The deformed behavior of multiple red blood cells in a capillary flow

The detailed deformation of multiple red blood cells in capillary flows is investigated computationally and hydrodynamics in the capillary flow accompanied with the deformation of red blood cells are analyzed. The membrane of red blood cell is modeled as a hyperelastic thin-shell and the immersed boundary method is used for the fluid-structure coupling in the present simulations. Numerical results show that the apparent viscosity in the capillary flow increases with the increase of the shear coefficient in the membrane of red blood cell, while this change for the viscosity is not obvious when the stiffness of the membrane changes. The distribution of multiple red blood cells in a capillary with branches is also simulated which shows that the apparent viscosity in the flow and the distribution of the cells affect each other interactively.   

Lateral migration and deformation of a vesicle in Poiseuille flow

The lateral migration and deformation of a suspended vesicle in Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider two cases, the external suspended fluid is unbounded or bounded by a steady infinite solid wall. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and we track explicitly the vesicle dynamics in 2D. Here we limited our study to vesicles without viscosity contrast between their internal and external fluids. In the unbounded geometry case, we find that the nonlinear character of the Poiseuille flow causes the lateral migration of the vesicles towards the flow centerline, this is in a marked contrast to the migration of droplets, which are known to migrate outward the centerline in the absence of a viscosity contrast. Once the vesicles reach the centerline they keep moving just parallel to the flow direction with a steady parachute-like shape. We find that the lateral migration velocity normalized by the curvature of the Poiseuille flow velocity profile is a universal function of the local capillary number. In the wall-bounded geometry, an additional lift force caused by the presence of the wall appears. Here we considered one wall in order to be able to investigate the interplay between the wall- and the Poiseuille flow curvature- induced lift forces. We find that the closer the vesicle is to the centerline, the more the curvature induced lift force is dominant.   

Motion and deformation of a vesicle in a Wall-Bounded Shear Flow

The motion of a lipid vesicle near a plane wall is studied using a 3-d boundary integral method. Initially the vesicle is considered to be immersed in a quiescent semi infinite fluid and its motion is driven by the buoyant force due to which the vesicle moves downwards towards the wall. A contact area is formed between the vesicle and wall which will depend on the magnitude of the buoyant force and the elastic properties of the membrane (relationship characterized by the Bond number). Results are compared to experimental data obtained using giant lipid vesicles. When the external fluid is set to a shear flow, the motion of the vesicle is driven by the hydrodynamic forces acting on it. These forces deform the vesicle and sets it in motion. The shape and velocity of the vesicle depend on the intensity of the flow and the vesicle's membrane elastic properties (relationship characterized by the dimensionless capillary number). The velocity of motion of the particle is reported as function of both the Bond and the capillary numbers and different flow regimes are identified.   

The effect of electrical conductivity on pore resistance and electroporation

Electroporation is an elegant means to gain access to the cytoplasm, and to deliver molecules into the cell while simultaneously maintaining viability and functionality. In this technique, an applied electric pulse transiently permeabilizes the cell membrane, through which biologically active agents such as DNA, RNA, and amino acids can enter the cell, and perform tasks such as gene and cancer therapy. Despite wide applications, current electroporation technologies fall short of desired efficiency and reliability, in part due to the lack of fundamental understanding and quantitative modeling tools. This work focuses on the modeling of cell membrane conductance due to the formation of aqueous conducting pores. An analytical expression is developed to determine effective pore resistance as a function of the membrane thickness, pore size, and intracellular and extracellular conductivities. The availability of this expression avoids empirical or \textit{ad hoc} specification of the conductivity of the pore-filling solution which was adopted in previous works. Such pore resistance model is then incorporated into a whole-cell electroporation simulation to investigate the effect of conductivity ratio on membrane permeabilization. The results reveal that the degree of permeabilization strongly depends on the specific values of the extracellular and intracellular conductivities.