Numerical method to characterise capsule membrane permeability for controlled drug delivery.

Design and characterisation of capsules is not an easy task owing to the multiple involved preparation factors and parameters. Here, a novel method to characterise capsule membrane permeability to solute molecules by an inverse approach is proposed. Transport of chemical species between the capsule core and the surrounding medium through the membrane is described by the Fick's second law with a position-dependent diffusion coefficient. Solutions are computed in spherical coordinates using a finite difference scheme developed for diffusion in multilayer configuration. They are validated using semi-analytical solutions and fully three-dimensional lattice Boltzmann simulations. As a proof of concept, the method is applied to experimental data available in the literature on the kinetics of glucose release and absorption to determine the membrane permeability of capsules. The proposed method is easy to use and determines correctly the permeability of capsule membranes for controlled drug release and absorption applications.

An Early Stage Researcher's Primer on Systems Medicine Terminology.

Background: Systems Medicine is a novel approach to medicine, that is, an interdisciplinary field that considers the human body as a system, composed of multiple parts and of complex relationships at multiple levels, and further integrated into an environment. Exploring Systems Medicine implies understanding and combining concepts coming from diametral different fields, including medicine, biology, statistics, modeling and simulation, and data science. Such heterogeneity leads to semantic issues, which may slow down implementation and fruitful interaction between these highly diverse fields. Methods: In this review, we collect and explain more than100 terms related to Systems Medicine. These include both modeling and data science terms and basic systems medicine terms, along with some synthetic definitions, examples of applications, and lists of relevant references. Results: This glossary aims at being a first aid kit for the Systems Medicine researcher facing an unfamiliar term, where he/she can get a first understanding of them, and, more importantly, examples and references for digging into the topic.

Squeezing multiple soft particles into a constriction: Transition to clogging.

We study numerically how multiple deformable capsules squeeze into a constriction. This situation is largely encountered in microfluidic chips designed to manipulate living cells, which are soft entities. We use fully three-dimensional simulations based on the lattice Boltzmann method to compute the flow of the suspending fluid and on the immersed boundary method to achieve the two-way fluid-structure interaction. The mechanics of the capsule membrane elasticity is computed with the finite-element method. We obtain two main states: continuous passage of the particles and their blockage that leads to clogging the constriction. The transition from one state to another is dictated by the ratio between the size of the capsules and the constriction width and by the capsule membrane deformability. The latter is found to enhance particle passage through narrower constrictions, where rigid particles with similar diameter are blocked and lead to clogging.

Algorithm to implement unsteady jump boundary conditions within the lattice Boltzmann method.

An algorithm is proposed to implement unsteady jump boundary conditions in the lattice Boltzmann method (LBM). This is useful for dealing with problems of mass transfer across membranes that exhibit resistance and discontinuity in concentration. The algorithm is simple to implement into an existing LBM-based code that computes diffusion and advection of a solute. Analytical solutions are recovered in the limiting case of a planar membrane. When combined with the immersed boundary method, the algorithm can handle moving deformable boundaries that adopt arbitrary geometries. Simulations of controlled solute release from stationary rigid and moving deformable particles are given as a proof of concept.

Computer simulations of drug release from a liposome into the bloodstream.

I propose two-dimensional simulations of drug release from a liposome into the bloodstream. I perform the fluid-structure coupling, between the particles deformation (the liposome and the red blood cells) and the plasma flow, using the immersed boundary method. I compute both the flow and the drug mass transport using the lattice Boltzmann method. The simulations allow computing the instantaneous amount of the released drug, its distribution and its accumulation in the blood vessel wall. These quantities are sensitive to multiple factors and parameters. Here, I briefly explore the impact of having surrounding red blood cells, which are found to enhance slightly the drug release at large Schmidt numbers. In the limit of extremely large permeability of the particles, the drug transport is mainly affected by the complex flow induced by the interplay between the applied flow and the collective motion of the particles.

Mechanistic modelling of drug release from multi-layer capsules.

We propose a novel in silico model for computing drug release from multi-layer capsules. The diffusion problem in such heterogeneous layer-by-layer composite medium is described by a system of coupled partial differential equations, which we solve analytically using separation of variables. In addition to the conventional partitioning and mass transfer interlayer conditions, we consider a surface finite mass transfer resistance, which corresponds to the case of a coated capsule. The drug concentration in the core and through all the layers, as well as in the external release medium, is given in terms of a Fourier series that we compute numerically to describe and characterize the drug release mechanism.

Squeezing bio-capsules into a constriction: deformation till break-up.

We study experimentally the deformation and break-up of liquid-filled capsules trapped at an axisymmetric step constriction, and subjected to increasing pressure drops. We considered biological (trout fish eggs) and bioartificial (made of ovalbumin and alginate) ones, with the objective to characterize the transition to break-up. We find that both capsule populations behave as a brittle material. They do not exhibit any plastic deformation prior to break-up. Moreover critical pressure drop exhibits a stochastic behavior as known for the fracture of disordered media. The break-up probability follows a three-parameter Weibull distribution, from which one can deduce the capsule rupture characteristics.

Flow and mass transfer around a core-shell reservoir.

I have developed an alternative numerical approach to study mass transfer from a stationary core-shell reservoir under channel flow conditions. I use the lattice Boltzmann method to compute both the solvent fluid flow and the diffusion and advection of the solute. I have investigated the impact of the flow by reporting mass transfer quantities such as the instantaneous solute concentration and the local Sherwood number at the surface of the reservoir. The flow is found to enhance the release of the encapsulated material, but it prevents the released material from reaching the channel walls.

Inversion of hematocrit partition at microfluidic bifurcations.

Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<20% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough ϕ0, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.

Hierarchical line-defect patterns in wrinkled surfaces.

We demonstrate a novel approach for controlling the formation of line-defects in wrinkling patterns by introducing step-like changes in the Young's modulus of elastomeric substrates supporting thin, stiff layers. Wrinkles are formed upon treating the poly(dimethylsiloxane) (PDMS) substrates by UV/Ozone (UVO) exposure in a uniaxially stretched state and subsequent relaxation. Line defects such as minutiae known from fingerprints are a typical feature in wrinkling patterns. The position where these defects occur is random for homogenous substrate elasticity and film thickness. However, we show that they can be predetermined by using PDMS substrates consisting of areas with different cross-linking densities. While changing the cross-linking density is well known to influence the wrinkling wavelength, we use this parameter in this study to force defect formation. The defect formation is monitored in situ using light microscopy and the mechanical parameters/film thicknesses are determined using imaging AFM indentation measurements. Thus the observed wrinkle-wavelengths can be compared to theoretical predictions. We study the density and morphology of defects for different changes in elasticity and compare our findings with theoretical considerations based on a generalized Swift-Hohenberg-equation to simply emulate the observed pattern-formation process, finding good agreement. The fact that for suitable changes in elasticity, well-ordered defect patterns are observed is discussed with respect to formation of hierarchical structures for applications in optics and nanotechnology.

Forced transport of deformable containers through narrow constrictions.

We study, numerically and analytically, the forced transport of deformable containers through a narrow constriction. Our central aim is to quantify the competition between the constriction geometry and the active forcing, regulating whether and at which speed a container may pass through the constriction and under what conditions it gets stuck. We focus, in particular, on the interrelation between the force that propels the container and the radius of the channel, as these are the external variables that may be directly controlled in both artificial and physiological settings. We present lattice Boltzmann simulations that elucidate in detail the various phases of translocation and present simplified analytical models that treat two limiting types of these membrane containers: deformational energy dominated by the bending or stretching contribution. In either case we find excellent agreement with the full simulations, and our results reveal that not only the radius but also the length of the constriction determines whether or not the container will pass.

Interplay between microdynamics and macrorheology in vesicle suspensions.

The microscopic dynamics of objects suspended in a fluid determines the macroscopic rheology of a suspension. For example, as shown by Danker and Misbah [Phys. Rev. Lett., 2007, 98, 088104], the viscosity of a dilute suspension of fluid-filled vesicles is a non-monotonic function of the viscosity contrast (the ratio between the viscosities of the internal encapsulated and the external suspending fluids) and exhibits a minimum at the critical point of the tank-treading-to-tumbling transition. By performing numerical simulations, we recover this effect and demonstrate that it persists for a wide range of vesicle parameters such as the concentration, membrane deformability, or swelling degree. We also explain why other numerical and experimental studies lead to contradicting results. Furthermore, our simulations show that this effect even persists in non-dilute and confined suspensions, but that it becomes less pronounced at higher concentrations and for more swollen vesicles. For dense suspensions and for spherical (circular in 2D) vesicles, the intrinsic viscosity tends to depend weakly on the viscosity contrast.

Analytical modeling for heat transfer in sheared flows of nanofluids.

We developed a model for the enhancement of the heat flux by spherical and elongated nanoparticles in sheared laminar flows of nanofluids. Besides the heat flux carried by the nanoparticles, the model accounts for the contribution of their rotation to the heat flux inside and outside the particles. The rotation of the nanoparticles has a twofold effect: it induces a fluid advection around the particle and it strongly influences the statistical distribution of particle orientations. These dynamical effects, which were not included in existing thermal models, are responsible for changing the thermal properties of flowing fluids as compared to quiescent fluids. The proposed model is strongly supported by extensive numerical simulations, demonstrating a potential increase of the heat flux far beyond the Maxwell-Garnett limit for the spherical nanoparticles. The road ahead, which should lead toward robust predictive models of heat flux enhancement, is discussed.

Two-dimensional vesicle dynamics under shear flow: effect of confinement.

Dynamics of a single vesicle under shear flow between two parallel plates is studied in two-dimensions using lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a nonmonotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.

Why do red blood cells have asymmetric shapes even in a symmetric flow?

Understanding why red blood cells (RBCs) move with an asymmetric shape (slipperlike shape) in small blood vessels is a long-standing puzzle in blood circulatory research. By considering a vesicle (a model system for RBCs), we discovered that the slipper shape results from a loss in stability of the symmetric shape. It is shown that the adoption of a slipper shape causes a significant decrease in the velocity difference between the cell and the imposed flow, thus providing higher flow efficiency for RBCs. Higher membrane rigidity leads to a dramatic change in the slipper morphology, thus offering a potential diagnostic tool for cell pathologies.

Vesicles under simple shear flow: elucidating the role of relevant control parameters.

The dynamics of vesicles under shear flow are carefully analyzed in the regime of a small vesicle excess area relative to a sphere. This regime corresponds to the quasispherical limit, for which several groups have analytically extracted simple nonlinear differential equations. Under shear flow, vesicles are known to exhibit three types of motion: (i) tank-treading (TT): the vesicle assumes a steady inclination angle with respect to the flow direction, while its membrane undergoes a tank-treading motion, (ii) tumbling (TB), and (iii) vacillating-breathing (VB): the vesicle main axis oscillates about the flow direction, whereas the overall shape undergoes a breathinglike motion. The region of existence for each regime depends on material and control parameters. The whole set of parameters can be cast into three dimensionless control parameters: (i) the viscosity ratio between the internal and external fluid, lambda , (ii) the excess area relative to a sphere (this parameter measures the degree of the vesicle deflation), Delta , and (iii) the capillary number (the ratio between the vesicle relaxation time toward its equilibrium shape after cessation of the flow and the flow time scale, which is the inverse shear rate), Ca. Recent studies [Danker, Phys. Rev. E 76, 041905 (2007)] have focused on the shape of the phase diagram (representing the TT, TB, and VB regimes in the Ca-lambda plane). In this paper, the physical quantities are analyzed in detail and attention is brought to features that are essential for future experimental studies. It is shown that the boundaries delimiting different dynamical regimes (TT, TB, and VB) in parameter space depend on the three dimensionless control parameters, in contrast with a recent study [V. V. Lebedev, Phys. Rev. Lett. 99, 218101 (2007)] where it is claimed that only two parameters are relevant. Consideration of the amplitude of oscillation (of the vesicle orientation angle and its shape deformation) in the VB mode reveals an even more significant dependence on the three parameters. It is also shown that the inclination angle in the TT regime significantly depends on the shear rate (Ca), which runs contrary to common belief. Finally, we show that the TB and VB periods are quite insensitive to Ca, in marked contrast with a recent study [H. Noguchi and G. Gompper, Phys. Rev. Lett. 98, 128103 (2007)].