Lagrangian stretching reveals stress topology in viscoelastic flows.

Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.

Rose Bengal Labeled Bovine Serum Albumin for Protein Transport Imaging in Subcutaneous Tissues Using Computed Tomography and Fluorescence Microscopy.

Subcutaneous (SC) injection of protein-based therapeutics is a convenient and clinically established drug delivery method. However, progress is needed to increase the bioavailability. Transport of low molecular weight (Mw) biotherapeutics such as insulin and small molecule contrast agents such as lipiodol has been studied using X-ray computed tomography (CT). This analysis, however, does not translate to the investigation of higher Mw therapeutics, such as monoclonal antibodies (mAbs), due to differences in molecular and formulation properties. In this study, an iodinated fluorescein analog rose bengal (RB) was used as a radiopaque and fluorescent label to track the distribution of bovine serum albumin (BSA) compared against unconjugated RB and sodium iodide (NaI) via CT and confocal microscopy following injection into ex vivo porcine SC tissue. Importantly, the high concentration BSA-RB exhibited viscosities more like that of viscous biologics than the small molecule contrast agents, suggesting that the labeled protein may serve as a more suitable formulation for the investigation of injection plumes. Three-dimensional (3D) renderings of the injection plumes showed that the BSA-RB distribution was markedly different from unconjugated RB and NaI, indicating the need for direct visualization of large protein therapeutics using conjugated tags rather than using small molecule tracers. Whereas this proof-of-concept study shows the novel use of RB as a label for tracking BSA distribution, our experimental approach may be applied to high Mw biologics, including mAbs. These studies could provide crucial information about diffusion in SC tissue and the influence of injection parameters on distribution, transport, and downstream bioavailability.

Concentration-Dependent Diffusion of Monoclonal Antibodies: Underlying Mechanisms of Anomalous Diffusion.

The development, storage, transport, and subcutaneous delivery of highly concentrated monoclonal antibody formulations pose significant challenges due to the high solution viscosity and low diffusion of the antibody molecules in crowded environments. These issues often stem from the self-associating behavior of the antibody molecules, potentially leading to aggregation. In this work, we used a dissipative particle dynamics-based coarse-grained model to investigate the diffusion behavior of IgG1 antibody molecules in aqueous solutions with 15 and 32 mM NaCl and antibody concentrations ranging from 10 to 400 mg/mL. We determined the coarse-grained interaction parameters by matching the calculated structure factor with the computational and experimental data from the literature. Our results indicate Fickian diffusion for antibody concentrations of 10 and 25 mg/mL and anomalous diffusion for concentrations exceeding 50 mg/mL. The anomalous diffusion was observed for ∼0.33 to 0.4 µs, followed by Fickian diffusion for all antibody concentrations. We observed a strong linear correlation between the diffusion behavior of the antibody molecules (diffusion coefficient D and anomalous diffusion exponent α) and the amount of aggregates present in the solution and between the amount of aggregates and the Coulomb interaction energy. The investigation of underlying mechanisms for anomalous diffusion revealed that in crowded environments at high antibody concentrations, the attractive interaction between electrostatically complementary regions of the antibody molecules could further bring the neighboring molecules closer to one another, ultimately resulting in aggregate formation. Further, the Coulomb attraction can continue to draw more molecules together, forming larger aggregates.

Rheology of bi-disperse dense fiber suspensions.

While significant progress has been made in the modeling and simulation of uniform fiber suspensions, no existing model has been validated for industrially-relevant concentrated suspensions containing fibers of multiple aspect ratios. In the present work, we investigate bi-disperse suspensions with two fiber populations in varying aspect ratios in a steady shear flow using direct numerical simulations. Moreover, we measure the suspension viscosity by creating a controlled length bidispersity for nylon fibers suspended in a Newtonian fluid. The results showed good agreement between the experimentally measured and numerically predicted viscosity for bi-disperse suspensions. The ratio between the aspect ratio of large to small fibers (size ratio) and the volume fraction of large fibers (composition) in bi-disperse systems strongly affected the rheological behavior of the suspension. The increment of relative viscosity associated with size ratio and composition can be explained by the decrease in the maximum flowable limit or jamming volume fraction. Moreover, the relative viscosity of bi-disperse suspensions collapses, when plotted against the reduced volume fraction, demonstrating the controlling influence of the jamming fraction in bi-disperse fiber suspensions.

Droplet Microfluidics-Assisted Fabrication of Shape Controllable Iron-Alginate Microgels with Fluorescent Property.

Droplet-based microfluidics-assisted fabrication of alginate microgels has extensive applications in biomaterials, biomedicines, and related fields. This approach is typically achieved by crosslinking droplets of an aqueous solution of sodium alginate with various divalent and trivalent ions, such as Ca2+, Ba2+, Sr2+, etc. Despite the exceptional features exhibited by bulk alginate hydrogels when using iron ions as the crosslinking reagent, including stimulus responsiveness and complex chemistry, no attention has been given to studying the fabrication of Fe-alginate microgels through droplet microfluidics. In this work, a facile method is presented for fabricating Fe-alginate microgels using single emulsion droplets as templates and an off-chip crosslinking technique to solidify the droplets. The morphologies of the resulting microgels can be systematically adjusted by manipulating different parameters such as viscosities and ionic strength of the collecting solutions. It should be noted that these resulting microgels undergo a color change from light brown to dark brown due to presumed self-oxidation of iron ions within their skeleton structure. Furthermore, these Fe-alginate microgels are functionalized by decorating them with a positively charged linear polymer via electrostatic interactions to impart them with stable fluorescent property. These functionalized Fe-alginate microgels may find potential applications in drug delivery carriers and biomimetic structures.

Concentration-dependent diffusion of unlabeled protein within an in vitro hyaluronic acid matrix.

Diffusion and movement of subcutaneously injected biologics and high-concentration immunoglobulin G (IgG) therapeutics away from the injection site and through the subcutaneous (SC) tissue may be concentration dependent. This possibility was confirmed by in situ measurement of diffusion coefficients of unlabeled bovine IgG in phosphate-buffered saline within an in vitro hyaluronic acid matrix that represents the SC electrostatic environment. Diffusion decreased from 2.67 to 0.05 × 10-7 cm2 /s when IgG concentration increased from 25 to 73 mg/mL. The results demonstrated that in situ detection of unlabeled proteins within an in vitro SC environment provides another useful tool for the preclinical characterization of injectable biologics.

Stress and stretching regulate dispersion in viscoelastic porous media flows.

In this work, we study the role of viscoelastic instability in the mechanical dispersion of fluid flow through porous media at high Péclet numbers. Using microfluidic experiments and numerical simulations, we show that viscoelastic instability in flow through a hexagonally ordered (staggered) medium strongly enhances dispersion transverse to the mean flow direction with increasing Weissenberg number (Wi). In contrast, preferential flow paths can quench the elastic instability in disordered media, which has two important consequences for transport: first, the lack of chaotic velocity fluctuations reduces transverse dispersion relative to unstable flows. Second, the amplification of flow along preferential paths with increasing Wi causes strongly-correlated stream-wise flow that enhances longitudinal dispersion. Finally, we illustrate how the observed dispersion phenomena can be understood through the lens of Lagrangian stretching manifolds, which act as advective transport barriers and coincide with high stress regions in these viscoelastic porous media flows.

Rheology of 3D printable ceramic suspensions: effects of non-adsorbing polymer on discontinuous shear thickening.

Concentrated suspensions of particles at volume fractions (ϕ) ≥ 0.5 often exhibit complex rheological behavior, transitioning from shear thinning to shear thickening as the shear stress or shear rate is increased. These suspensions can be extruded to form 3D structures, with non-adsorbing polymers often added as rheology modifiers to improve printability. Understanding how non-adsorbing polymers affect the suspension rheology, particularly the onset of shear thickening, is critical to the design of particle inks that will extrude uniformly. In this work, we examine the rheology of concentrated aqueous suspensions of colloidal alumina particles and the effects of adding non-adsorbing polyvinylpyrrolidone (PVP). First, we show that suspensions with ϕalumina = 0.560-0.575 exhibited discontinuous shear thickening (DST), where the viscosity increased by up to two orders of magnitude above an onset stress (τmin). Increasing ϕalumina from 0.550 to 0.575 increased the viscosity and yield stress in the shear thinning regime and decreased τmin. Next, PVP was added at concentrations within the dilute and semi-dilute non-entangled regimes of polymer conformation (ϕPVP = 0.005-0.050) to suspensions with constant ϕalumina = 0.550. DST was observed in all cases and increasing ϕPVP increased the viscosity and yield stress. Interestingly, increasing ϕPVP also increased τmin. We posit that the free PVP chains act as lubricants between alumina particles, increasing the stress needed to induce thickening. Finally, we demonstrate through direct comparisons of suspensions with and without PVP how non-adsorbing polymer addition can extend the extrusion processing window due to the increase in τmin.

Transport and lymphatic uptake of monoclonal antibodies after subcutaneous injection.

The subcutaneous injection has emerged to become a feasible self-administration practice for biotherapeutics due to the patient comfort and cost-effectiveness. However, the available knowledge about transport and absorption of these agents after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A three-dimensional poroelastic model is exploited to find the biomechanical response of the tissue by taking into account tissue deformation during the injection. The results show that including tissue deformability noticeably changes tissue poromechanical response due to the significant dependence of interstitial pressure on the tissue deformation. Moreover, the importance of the amount of lymph fluid at the injection site and the injection rate on the drug uptake to lymphatic capillaries is highlighted. Finally, variability of lymphatic uptake due to uncertainty in parameters including tissue poromechanical and lymphatic absorption parameters is evaluated. It is found that interstitial pressure due to injection is the major contributing factor in short-term lymphatic absorption, while the amount of lymph fluid at the site of injection determines the long-term absorption of the drug. Finally, it is shown that the lymphatic uptake results are consistent with experimental data available in the literature.

In vitro measurement of concentration of unlabeled protein within a hyaluronic acid matrix.

There are currently more than 560 therapeutic monoclonal antibodies (mAbs) at various stages of research and clinical testing, including candidates for administration by subcutaneous (SC) injection. Preclinical studies based on in vitro measurements of high molecular weight proteins within simulated SC matrices are assisting laboratory studies of interactions of injectable biotherapeutic proteins within the SC environment in relation to bioavailability. We report a new method for directly measuring diffusion of unlabeled, high molecular weight proteins injected into an in vitro matrix that simulates the negatively charged environment of the SC. The matrix consists of 10 mg/ml HA in a repurposed cell culture chamber. The measurement consists of pipetting triplicate 20 µl protein samples into the matrix, placing the chamber in a laboratory scanner, activating tryptophan residues in the protein at 280 nm, and imaging the resulting protein fluorescence at 384 nm over a 0.5-4 h time period thus tracking protein movement. This facile approach enables mapping of protein concentration as a function of time and distance within the matrix, and determination of diffusion coefficients, D, within ±10%. Bovine IgG and BSA gave D = 2.3 ± 0.2*10-7 and 4.6 ± 0.2*10-7 cm2 /s at 24°C, respectively, for initial protein concentrations of 21 mg/mL.

A forward reconstruction, holographic method to overcome the lens effect during 3D detection of semi-transparent, non-spherical particles.

Suspensions of semi-transparent particles such as polystyrene microparticles are commonly used as model systems in the study of micro-rheology, biology, and microfluidics. Holography is a valuable tool that allows one to obtain 3-D information for particle position and orientation, but forward reconstruction techniques often struggle to infer this information accurately for semi-transparent spheroids with an O(1) aspect ratio, since the lens effect from the particle introduces complex patterns. We propose a reconstruction method that uses image moment information to generate a mask over the sharp patterns from the lens effect and gives reasonable estimation of the 3-D position and orientation of the particle. The method proposed in this work uses the average particle geometry information to determine the process parameters and identify the appropriate detection zone. The average detection error for zc is less than 25% of the average particle thickness, and the average errors in the in-plane and out-of-plane orientations ϕ and θ are 2° and 4°, respectively. Our method provides comparable accuracy in the detection of the particle center of mass (xc, yc, zc) and in-plane orientation ϕ as a recent forward reconstruction method for semi-transparent particles proposed by Byeon et al. (H. Byeon, T. Go and S. J. Lee, Appl. Opt., 2016, 54, 2106-2112; H. Byeon, T. Go and S. J. Lee, Opt. Express, 2016, 24, 598-610). This method provides a clearly defined framework for identifying the particle's out-of-plane tilt angle θ. We finally demonstrate the applicability of the method to opaque, slender (aspect ratio AR ≫ 1) particles by analyzing the 3-D motion of E. coli cells from holographic video footage.

Assessment of Cavitation Intensity in Accelerating Syringes of Spring-Driven Autoinjectors.

PURPOSE: Cavitation is an undesired phenomenon that may occur in certain types of autoinjectors (AIs). Cavitation happens because of rapid changes of pressure in a liquid, leading to the formation of small vapor-filled cavities, which upon collapsing, can generate an intense shock wave that may damage the device container and the protein drug molecules. Cavitation occurs in the AI because of the syringe-drug relative displacement as a result of the syringe's sudden acceleration during needle insertion and the ensuing pressure drop at the bottom of the container. Therefore, it's crucial to analyze the potential effect of cavitation on AI. The goal of the current study is to investigate the effects of syringe and AI design parameters such as air gap size, syringe filling volume, fluid viscosity, and drive spring force (syringe acceleration) on the risk and severity of cavitation. METHODS: A model autoinjector platform is built to record the syringe and cavitation dynamics which we use to estimate the cavitation intensity in terms of extension rate and to study the effects of design parameters on the severity of cavitation. RESULTS: Our results show the generation of an intense shock wave and a high extension rate upon cavitation collapse. The induced extension rate increases with syringe acceleration and filling volume and decreases with viscosity and air gap size. CONCLUSION: The most severe cavitation occurred in an AI device with the larger drive spring force and the syringe of a smaller air gap size filled with a less viscous fluid and a larger filling volume.

New Model to Predict the Concentration-Dependent Viscosity of Monoclonal Antibody Solutions.

Concentrated monoclonal antibody solutions exhibit high solution viscosity, which is experimentally measured to be ∼1-2 orders of magnitude higher than the viscosity of water. However, physical processes responsible for the high antibody viscosity are not fully understood. We show that fluid occlusion due to the trapped solvent molecules within the boundaries formed by the aggregated antibodies is responsible for the elevated solution viscosity. We develop a theory to predict the viscosity of monoclonal antibodies based on the geometry of the antibody molecule and the aggregate morphology. We validate our theory with experiments and highlight useful insights obtained from the viscosity equation which could help in controlling the drug viscosity at the molecular design stage itself.

Monoclonal Antibody Aggregation near Silicone Oil-Water Interfaces.

In this work, we study the hydrodynamic behavior of monoclonal antibodies in the presence of silicone oil-water interfaces. We model the antibody molecules using a coarse-grained 24-bead model, where two beads are used to represent each antibody domain. We consider the spatial variation of the antibody polarity in our model as each bead represents a set of hydrophilic or hydrophobic amino acids. We use the dissipative particle dynamics scheme to represent the coarse-grained force field which governs the motion of the beads. In addition, interprotein interactions are modeled using an electrostatic force field. The model parameters are determined by comparing the structure factor against experimental structure factor data ranging from a low concentration regime (10 mg/mL) to a high concentration regime (150 mg/mL). Next, we conduct simulations for a suspension of antibody molecules in the presence of silicone oil-water interfaces. Protein loss from the bulk solution is noticed as the molecules adsorb at the interface. We observe dynamic cluster formation in the solution bulk and at the interface, as the antibody molecules self-associate along their trajectories. We quantify the aggregation using a density clustering algorithm and investigate the effect of the antibody concentration on the diffusivity of the antibody solution, aggregation propensity, and protein loss from the bulk. Our study shows that numerical simulations can be an important tool for understanding the molecular mechanisms driving protein aggregation near hydrophobic interfaces.

The Interface Motion and Hydrodynamic Shear of the Liquid Slosh in Syringes.

PURPOSE: Interface motion and hydrodynamic shear of the liquid slosh during the insertion of syringes upon autoinjector activation may damage the protein drug molecules. Experimentally validated computational fluid dynamics simulations are used in this study to investigate the interfacial motion and hydrodynamic shear due to acceleration and deceleration of syringes. The goal is to explore the role of fluid viscosity, air gap size, syringe acceleration, syringe tilt angle, liquid-wall contact angle, surface tension and fill volume on the interface dynamics caused by autoinjector activation. METHODS: A simplified autoinjector platform submerged in water is built to record the syringe and liquid motion without obstruction of view. The syringe kinematics is imported to the simulations based on OpenFOAM InterIsoFoam solver, which is used to study the effects of various physical parameters. RESULTS: The simulations agree with experiments on the air-liquid interface profile and interface area. The interfacial area and the volume of fluid subject to high strain rate decrease with the solution viscosity, increase with the air gap height, syringe velocity, tilt angle and syringe wall hydrophobicity, and hardly change with the surface tension and liquid column height. The hydrodynamic shear mainly occurs near the syringe wall and entrained bubbles. CONCLUSION: For a given dose of drug solution, the syringe with smaller radius and larger length will generate less liquid slosh. Reducing the air volume and syringe wall hydrophobicity are also helpful to reduce interface area and effective shear. The interface motion is reduced when the syringe axis is aligned with the gravitational direction.

Isolation and mutational assessment of pancreatic cancer extracellular vesicles using a microfluidic platform.

Cancer cells release extracellular vesicles known as extracellular vesicles (EVs), containing tumor-derived DNA, RNA and proteins within their cargo, into the circulation. Circulating tumor-derived extracellular vesicles (TEV) can be used in the context of serial "liquid biopsies" for early detection of cancer, for monitoring disease burden in patients, and for assessing recurrence in the post-resection setting. Nonetheless, isolating sufficient TEV by ultracentrifugation-based approaches, in order to enable molecular assessment of EVs cargo, can be an arduous, time-consuming process and is inconsistent in the context of yield and purity among institutions. Herein, we describe a microfluidic platform, which we have named MITEV (Microfluidic Isolation of Tumor-derived Extracellular Vesicles) for the rapid isolation of TEV from the plasma of pancreatic cancer patients. The device, which has ~100,000 pillars placed in a zigzag pattern and is coated with antibodies against generic EV surface proteins (anti-CD63, -CD9, and -CD81 antibodies) or the TEV specific anti-Epithelial Cell Adhesion Molecule (EpCAM) antibody, is capable of high-throughput EVs isolation and yields sufficient DNA (total of ~2-14 ng from 2-ml plasma) for downstream genomic analysis. Using two independent quantitative platforms, droplet digital polymerase chain reaction (ddPCR) and molecular barcoding using nanoString nCounter® technology, we can reliably identify KRAS mutations within isolated TEV of treatment-naïve metastatic pancreatic cancer patients. Our study suggests that the MITEV device can be used for point-of-care applications, such as in the context of monitoring residual or recurrent tumor presence in pancreatic cancer patients undergoing therapy.

Biofilms at interfaces: microbial distribution in floating films.

Cellular motility is a key function guiding microbial adhesion to interfaces, which is the first step in the formation of biofilms. The close association of biofilms and bioremediation has prompted extensive research aimed at comprehending the physics of microbial locomotion near interfaces. We study the dynamics and statistics of microorganisms in a 'floating biofilm', i.e., a confinement with an air-liquid interface on one side and a liquid-liquid interface on the other. We use a very general mathematical model, based on a multipole representation and probabilistic simulations, to ascertain the spatial distribution of microorganisms in films of different viscosities. Our results reveal that microorganisms can be distributed symmetrically or asymmetrically across the height of the film, depending on their morphology and the ratio of the film's viscosity to that of the fluid substrate. Long-flagellated, elongated bacteria exhibit stable swimming parallel to the liquid-liquid interface when the bacterial film is less viscous than the underlying fluid. Bacteria with shorter flagella on the other hand, swim away from the liquid-liquid interface and accumulate at the free surface. We also analyze microorganism dynamics in a flowing film and show how a microorganism's ability to resist 'flow-induced-erosion' from interfaces is affected by its elongation and mode of propulsion. Our study generalizes past efforts on understanding microorganism dynamics under confinement by interfaces and provides key insights on biofilm initiation at liquid-liquid interfaces.

Towards an analytical description of active microswimmers in clean and in surfactant-covered drops.

Geometric confinements are frequently encountered in the biological world and strongly affect the stability, topology, and transport properties of active suspensions in viscous flow. Based on a far-field analytical model, the low-Reynolds-number locomotion of a self-propelled microswimmer moving inside a clean viscous drop or a drop covered with a homogeneously distributed surfactant, is theoretically examined. The interfacial viscous stresses induced by the surfactant are described by the well-established Boussinesq-Scriven constitutive rheological model. Moreover, the active agent is represented by a force dipole and the resulting fluid-mediated hydrodynamic couplings between the swimmer and the confining drop are investigated. We find that the presence of the surfactant significantly alters the dynamics of the encapsulated swimmer by enhancing its reorientation. Exact solutions for the velocity images for the Stokeslet and dipolar flow singularities inside the drop are introduced and expressed in terms of infinite series of harmonic components. Our results offer useful insights into guiding principles for the control of confined active matter systems and support the objective of utilizing synthetic microswimmers to drive drops for targeted drug delivery applications.

Effect of external shear flow on sperm motility.

The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.

Hydrodynamics-mediated trapping of micro-swimmers near drops.

In this paper, we investigate the swimming characteristics and dynamics of a model micro-swimmer in the vicinity of a clean drop, and of a surfactant covered drop. We model the swimmer as a force dipole and utilize the image-singularity system to study the dynamical behavior of the swimmer. Motivated by bacterial bio-remediation of insoluble hydrocarbons (HCs) released during oil spills, we report the 'trapping characteristics' - critical trapping radius, basin of attraction and trapping time distribution - of deterministic and stochastic swimmers, as a function of viscosity ratio, and dimensionless surface viscosity. We find that addition of surfactant reduces the critical trapping radius of a drop by ∼30%. The basin of attraction though, is not affected acutely for any combination in the parameter space of viscosity ratio and surface viscosity. We also carry out a dynamical system analysis of our problem, for deterministic swimmers, to clarify the aforementioned concepts. For hydrodynamics combined with diffusion based motion, we note increments ranging from ∼5-25% in the interface-retention times of surfactant-laden drops, as compared to clean drops. These differences occur for low values of surface viscosity, and saturate rapidly as the surface viscosity increases. With potential applications in bioremediation, our results highlight the importance of considering dispersant-addition in oil spills involving insoluble hydrocarbons.