Charles D. Eggleton

Insoluble surfactants on a drop in an extensional flow: a generalization of the stagnated surface limit to deforming interfaces

A drop in an axisymmetric extensional flow is studied using boundary integral methods to understand the effects of a monolayer-forming surfactant on a strongly deforming interface. Surfactants occupy area, so there is an upper bound to the surface concentration that can be adsorbed in a monolayer, Γ∞. The surface tension is a highly nonlinear function of the surface concentration Γ because of this upper bound. As a result, the mechanical response of the system varies strongly with Γ for realistic material parameters. In this work, an insoluble surfactant is considered in the limit where the drop and external fluid viscosities are equal. For Γ << Γ∞, surface convection sweeps surfactant toward the drop poles. When surface diffusion is negligible, once the stable drop shapes are attained, the interface can be divided into stagnant caps near the drop poles, where Γ is non-zero, and tangentially mobile regions near the drop equator, where the surface concentration is zero. This result is general for any axisymmetric fluid particle. For Γ near Γ∞, the stresses resisting accumulation are large in order to prevent the local concentration from reaching the upper bound

Evaluating the Mechanical Behavior of Arterial Tissue using Digital Image Correlation

In this study, digital image correlation (DIC) was adopted to examine the mechanical behavior of arterial tissue from bovine aorta. Rectangular sections comprised of the intimal and medial layers were excised from the descending aorta and loaded in displacement control uniaxial tension up to 40 percent elongation. Specimens of silicon rubber sheet were also prepared and served as a benchmark material in the application of DIC for the evaluation of large strains; the elastomer was loaded to 50 percent elongation. The arterial specimens exhibited a non-linear hyperelastic stress-strain response and the stiffness increased with percent elongation. Using a bilinear model to describe the uniaxial behavior, the average minor and major elastic modulii were 192±8 KPa and 912±40 KPa, respectively. Poissons ratio of the arterial sections increased with the magnitude of axial strain; the average Poissons ratio was 0.17±0.02. Although the correlation coefficient obtained from image correlation decreased with the percent elongation, a correlation coefficient greater than 0.8 was achieved for the tissue experiments and exceeded that obtained in the evaluation of the elastomer. Based on results from this study, DIC may serve as a valuable method for the determination of mechanical properties of arteries and other soft tissues.

Cell deformation cytometry using diode-bar optical stretchers

The measurement of cell elastic parameters using optical forces has great potential as a reagent-free method for cell classification, identification of phenotype, and detection of disease; however, the low throughput associated with the sequential isolation and probing of individual cells has significantly limited its utility and application. We demonstrate a single-beam, high-throughput method where optical forces are applied anisotropically to stretch swollen erythrocytes in microfluidic flow. We also present numerical simulations of model spherical elastic cells subjected to optical forces and show that dual, opposing optical traps are not required and that even a single linear trap can induce cell stretching, greatly simplifying experimental implementation. Last, we demonstrate how the elastic modulus of the cell can be determined from experimental measurements of the equilibrium deformation. This new optical approach has the potential to be readily integrated with other cytometric technologies and, with the capability of measuring cell populations, enabling true mechanical-property-based cell cytometry.

Using computational fluid dynamics software to estimate circulation time distributions in bioreactors

Nonideal mixing in many fermentation processes can lead to concentration gradients in nutrients, oxygen, and pH, among others. These gradients are likely to influence cellular behavior, growth, or yield of the fermentation process. Frequency of exposure to these gradients can be defined by the circulation time distribution (CTD). There are few examples of CTDs in the literature, and experimental determination of CTD is at best a challenging task. The goal in this study was to determine whether computational fluid dynamics (CFD) software (FLUENT 4 and MixSim) could be used to characterize the CTD in a single‐impeller mixing tank. To accomplish this, CFD software was used to simulate flow fields in three different mixing tanks by meshing the tanks with a grid of elements and solving the Navier‐Stokes equations using the κ‐ϵ turbulence model. Tracer particles were released from a reference zone within the simulated flow fields, particle trajectories were simulated for 30 s, and the time taken for these tracer particles to return to the reference zone was calculated. CTDs determined by experimental measurement, which showed distinct features (log‐normal, bimodal, and unimodal), were compared with CTDs determined using CFD simulation. Reproducing the signal processing procedures used in each of the experiments, CFD simulations captured the characteristic features of the experimentally measured CTDs. The CFD data suggests new signal processing procedures that predict unimodal CTDs for all three tanks.

Measuring Cell Mechanics By Optical Alignment Compression Cytometry

To address the need for a high throughput, non-destructive technique for measuring individual cell mechanical properties, we have developed optical alignment compression (OAC) cytometry. OAC combines hydrodynamic drag in an extensional flow microfluidic device with optical forces created with an inexpensive diode laser to induce measurable deformations between compressed cells. In this, a low-intensity linear optical trap aligns incoming cells with the flow stagnation point allowing hydrodynamic drag to induce deformation during cell-cell interaction. With this novel approach, we measure cell mechanical properties with a throughput that improves significantly on current non-destructive individual cell testing methods.

Mathematical modeling of cell adhesion in shear flow: application to targeted drug delivery in inflammation and cancer metastasis.

Cell adhesion plays a pivotal role in diverse biological processes that occur in the dynamic setting of the vasculature, including inflammation and cancer metastasis. Although complex, the naturally occurring processes that have evolved to allow for cell adhesion in the vasculature can be exploited to direct drug carriers to targeted cells and tissues. Fluid (blood) flow influences cell adhesion at the mesoscale by affecting the mechanical response of cell membrane, the intercellular contact area and collisional frequency, and at the nanoscale level by modulating the kinetics and mechanics of receptor-ligand interactions. Consequently, elucidating the molecular and biophysical nature of cell adhesion requires a multidisciplinary approach involving the synthesis of fundamentals from hydrodynamic flow, molecular kinetics and cell mechanics with biochemistry/molecular cell biology. To date, significant advances have been made in the identification and characterization of the critical cell adhesion molecules involved in inflammatory disorders, and, to a lesser degree, in cancer metastasis. Experimental work at the nanoscale level to determine the lifetime, interaction distance and strain responses of adhesion receptor-ligand bonds has been spurred by the advent of atomic force microscopy and biomolecular force probes, although our current knowledge in this area is far from complete. Micropipette aspiration assays along with theoretical frameworks have provided vital information on cell mechanics. Progress in each of the aforementioned research areas is key to the development of mathematical models of cell adhesion that incorporate the appropriate biological, kinetic and mechanical parameters that would lead to reliable qualitative and quantitative predictions. These multiscale mathematical models can be employed to predict optimal drug carrier-cell binding through isolated parameter studies and engineering optimization schemes, which will be essential for developing effective drug carriers for delivery of therapeutic agents to afflicted sites of the host.

Viscoelasticity as a Biomarker for High-Throughput Flow Cytometry

The mechanical properties of living cells are a label-free biophysical marker of cell viability and health; however, their use has been greatly limited by low measurement throughput. Although examining individual cells at high rates is now commonplace with fluorescence activated cell sorters, development of comparable techniques that nondestructively probe cell mechanics remains challenging. A fundamental hurdle is the signal response time. Where light scattering and fluorescence signatures are virtually instantaneous, the cell stress relaxation, typically occurring on the order of seconds, limits the potential speed of elastic property measurement. To overcome this intrinsic barrier to rapid analysis, we show here that cell viscoelastic properties measured at frequencies far higher than those associated with cell relaxation can be used as a means of identifying significant differences in cell phenotype. In these studies, we explore changes in erythrocyte mechanical properties caused by infection with Plasmodium falciparum and find that the elastic response alone fails to detect malaria at high frequencies. At timescales associated with rapid assays, however, we observe that the inelastic response shows significant changes and can be used as a reliable indicator of infection, establishing the dynamic viscoelasticity as a basis for nondestructive mechanical analogs of current high-throughput cell classification methods.

Predictions of capillary oxygen transport in the presence of fluorocarbon additives

A mathematical model of capillary oxygen transport was formulated to determine the effect of increasing plasma solubility, e.g., by the addition of an intravascular fluorocarbon emulsion. The effect of increased plasma solubility is studied for two distributions of fluorocarbon, when the fluorocarbon droplets are uniformly distributed throughout the plasma and when the fluorocarbon droplets are concentrated in a layer adjacent to the endothelium. The model was applied to working hamster retractor muscle at normal and lowered hematocrit. The intracapillary mass transfer coefficient was found to increase by 18% as the solubility was increased by a factor of 1.7 at a hematocrit of 43%. An additional increase of 6% was predicted when the solubility increase was concentrated in the layer adjacent to the endothelium. At a hematocrit of 25%, the intracapillary mass transfer coefficient increased 14% when the solubility was increased by a factor of 1.7.A mathematical model of capillary oxygen transport was formulated to determine the effect of increasing plasma solubility, e.g., by the addition of an intravascular fluorocarbon emulsion. The effect of increased plasma solubility is studied for two distributions of fluorocarbon, when the fluorocarbon droplets are uniformly distributed throughout the plasma and when the fluorocarbon droplets are concentrated in a layer adjacent to the endothelium. The model was applied to working hamster retractor muscle at normal and lowered hematocrit. The intracapillary mass transfer coefficient was found to increase by 18% as the solubility was increased by a factor of 1.7 at a hematocrit of 43%. An additional increase of 6% was predicted when the solubility increase was concentrated in the layer adjacent to the endothelium. At a hematocrit of 25%, the intracapillary mass transfer coefficient increased 14% when the solubility was increased by a factor of 1.7.

Single-cell isolation using a DVD optical pickup

A low-cost single-cell isolation system incorporating a digital versatile disc burner (DVD RW) optical pickup has been developed. We show that these readily available modules have the required laser power and focusing optics to provide a steady Gaussian beam capable of optically trapping micron-sized colloids and red blood cells. Utility of the pickup is demonstrated through the non-destructive isolation of such particles in a laminar-flow based microfluidic device that captures and translates single microscale objects across streamlines into designated channel exits. In this, the integrated objective lens focusing coils are used to steer the optical trap across the channel, resulting in the isolation of colloids and red blood cells using a very inexpensive off-the-shelf optical component.

Dynamic ray tracing for modeling optical cell manipulation

Current methods for predicting stress distribution on a cell surface due to optical trapping forces are based on a traditional ray optics scheme for fixed geometries. Cells are typically modeled as solid spheres as this facilitates optical force calculation. Under such applied forces however, real and non-rigid cells can deform, so assumptions inherent in traditional ray optics methods begin to break down. In this work, we implement a dynamic ray tracing technique to calculate the stress distribution on a deformable cell induced by optical trapping. Here, cells are modeled as three-dimensional elastic capsules with a discretized surface with associated hydrodynamic forces calculated using the Immersed Boundary Method. We use this approach to simulate the transient deformation of spherical, ellipsoidal and biconcave capsules due to external optical forces induced by a single diode bar optical trap for a range of optical powers.