Partha Roy

A hybrid method to study flow-induced deformation of three-dimensional capsules

A hybrid method is proposed to study the transient deformation of liquid filled capsules with elastic membranes under flow. In this method, the immersed boundary concept is introduced into the framework of lattice Boltzmann method, and the multi-block strategy is employed to refine the mesh near the capsule to increase the accuracy and efficiency of computation. A finite element model is incorporated to obtain the forces acting on the membrane nodes of the three-dimensional capsule which is discretized into flat triangular elements. The present method was validated by studying the transient deformation of initially spherical and oblate-spheroidal capsules with various membrane constitutive laws under shear flow; and there were good agreements with previous theory or numerical results. The versatility of the present method was demonstrated by studying the effects of inertia on the deformation of capsules in shear flow; and the inertia effects were found to be significant. The transient deformation of capsules with initially biconcave discoid shape in shear flow was also studied. The unsteady tank-treading motion was observed, in which the capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside. To our knowledge, this motion of three-dimensional biconcave discoid capsules has not been fully recovered by numerical simulation so far.

Dynamic motion of red blood cells in simple shear flow

A three-dimensional numerical model is proposed to simulate the dynamic motion of red blood cells (RBCs) in simple shear flow. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes which take into account the membrane shear elasticity and the membrane area incompressibility. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to have the same physical properties as the matrix fluid. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the cells are found to carry out a swinging motion, in which periodic inclination oscillation and shape deform...

Mass Transport and Shear Stress in a Microchannel Bioreactor: Numerical Simulation and Dynamic Similarity

Microchannel bioreactors have been used in many studies to manipulate and investigate the fluid microenvironment around cells. In this study, substrate concentrations and shear stresses at the base were computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters were developed from a simplified analysis. The numerical results of substrate concentration were well correlated by the combined parameters. The generalized results may find applications in design analysis of microchannel bioreactors. The mass transport and shear stress were related in a generalized result. Based on the generalized results and the condition of dynamic similarity, various means to isolate their respective effects on cells were considered.

Controlled microscale diffusion gradients in quiescent extracellular fluid

Microchannels offer a means of establishing concentration gradients of soluble factors over micron length scales representative of those in tissues. Here, we report the development of a microfluidic channel system wherein a hydrogel has been patterned to generate temporally and spatially stable concentration gradients of multiple solutes in quiescent extracellular fluid. The fluorophore Alexa Fluor 488 and a fluorescent glucose analog are used as probes to illustrate the generation of stable, reproducible, and linear probe concentration gradients. A method is described for estimating the diffusivity and hydrogel permeability of a solute from in situ imaging data. Concentration gradients are also generated in the presence of a mouse insulinoma cell line to demonstrate the compatibility of the system with living cells. The net transport and metabolism rate of the glucose analog is found to be heterogeneous and independent of the applied extracellular gradient. This system may be suitable for the study of cell response to various extracellular gradients of soluble factors.

Magnetic nanoparticle migration in microfluidic two-phase flow

Continuous separation of superparamagnetic nanoparticles in a microfluidic system has numerous applications, especially in novel sensors based technology platforms. We have studied a simple microfluidic system with two fluidic inlets, resulting in two-phase flow of identical aqueous fluids. Magnetic nanoparticles were entrained in de-ionized water entering one inlet channel, while the other inlet channel had only de-ionized water input. The application of a magnetic field using a simple permanent magnet causes increased migration of nanoparticles into the pure fluid channel. In the absence of the magnetic field, the particles are able to diffuse into the particle free phase. A steady state convection diffusion model describes the transport of nanoparticles in the microchannel. Particle velocities are estimated from magnetic and hydrodynamic interaction forces. It is shown how particle separation is affected by Peclet number, channel length to width ratio, and magnetic field strength and field gradient. Ex...

Wall effects in continuous microfluidic magneto-affinity cell separation.

Continuous microfluidic magneto‐affinity cell separator combines unique microscale flow phenomenon with advantageous nanobead properties, to isolate cells with high specificity. Owing to the comparable size of the cell–bead complexes and the microchannels, the walls of the microchannel exert a strong influence on the separation of cells by this method. We present a theoretical and experimental study that provides a quantitative description of hydrodynamic wall interactions and wall rolling velocity of cells. A transient convection model describes the transport of cells in two‐phase microfluidic flow under the influence of an external magnetic field. Transport of cells along the microchannel walls is also considered via an additional equation. Results show the variation of cell flux in the fluid phases and the wall as a function of a dimensionless parameter arising in the equations. Our results suggest that conditions may be optimized to maximize cell separation while minimizing contact with the wall surfaces. Experimentally measured cell rolling velocities on the wall indicate the presence of other near‐wall forces in addition to fluid shear forces. Separation of a human colon carcinoma cell line from a mixture of red blood cells, with folic acid conjugated 1 µm and 200 nm beads, is reported. Biotechnol. Bioeng. 2010; 106: 68–75.

THE TRANSIENT DEFORMATION OF RED BLOOD CELLS IN SHEAR FLOW

The transient deformation of red blood cells (RBCs) in a shear flow is studied by a three-dimensional numerical model proposed by the present authors. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to be the same to the fluid outside. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the present results show that the cells carry out a swinging motion, in which periodic inclination-oscillation and shape deformation superimpose on the membrane tank treading motion. With the shear rat...

Ligand Binding Kinetics of Cell Surface Receptors by Microfluidic Displacement

Cell Surface binding kinetics of bio-molecular interaction is of fundamental importance in advancing our understanding of numerous biological processes and developing bioengineered systems. We have adopted a displacement technique, wherein a ligand is displaced from the binding site, by an excess of a ligand analog perfused through the microchannel. The theoretical model describes transient convection and diffusion in the microchannel volume following dissociation of the ligand from the cell surface receptors. To incorporate living cell processes, the model includes cell surface receptor trafficking. The decay of eluting ligand concentration follows a mono-exponential curve for one receptor sub-type or kinetic dissociation rate constant. A numerical solution is obtained using the method of finite differences and verified with an analytical solution for the case of negligible dispersion. Results illustrate how the fluid velocity and receptor internalization rate influence the ligand concentration at the microchannel outlet. This modeling effort is expected to allow better experimental design and subsequently more accurate measurement of kinetic rate constants.

Directed Transport in Renal Proximal Tubule Cells

A method is proposed to quantify the directed transport flux resulting from a monolayer of polarized proximal tubule cells seeded onto a microporous membrane. The experimental system is comprised of two well mixed fluidic chambers sandwiching the membrane-cell construct. A mathematical model is developed to describe active and passive transport independently across the cell monolayer. The model is comprised of three coupled ordinary differential equations describing the transported solute concentrations in the two chambers and the cell layer. The main parameters in the model are the membrane permeability, cell layer permeability and transporter constants. An analytical solution is derived for the linear equations arising from the assumption of first order transporter activity. The method is more direct as it does not require application of inhibitors of transporter activity, and thereby reduces the number of experiments and simplifies data interpretation. Some limiting features are also discussed.

Determination of Affinity Constant from Microfluidic Binding Assay

We present a method of determining the affinity constant of a receptor-ligand pair using equilibrium binding in a microfluidic channel. This technique involves the immobilization of the receptor to the microchannel surface and perfusion of the ligand at a fixed flow rate. The ligand concentration in the eluent is monitored in real time. The break-through time of the ligand is then determined and compared with that of an appropriate, non-binding, reference molecule. The difference in break-through time can then be used in a mathematical model we have developed to determine the affinity constant of the receptor-ligand pair. Using this method, we have determined the equilibrium dissociation constant, K D , of a rat anti-insulin immunoglobulin and a fluorescein-conjugated human insulin. Fluorescein-conjugated aprotinin was used as the non-binding reference molecule. Our experiments yielded a K D value of 0.76 µM for this anti-insulin IgG and insulin-FITC pair.