Modeling the growth of multicellular cancer spheroids in a\ud bioengineered 3D microenvironment and their treatment with an\ud anti-cancer drug

A critical step in the dissemination of ovarian cancer cells is the formation of multicellular spheroids from cells shed from the primary tumor. The objectives of this study were to establish and validate bioengineered three-dimensional (3D) microenvironments for culturing ovarian cancer cells in vitro and simultaneously to develop computational models describing the growth of multicellular spheroids in these bioengineered matrices. Cancer cells derived from human epithelial ovarian carcinoma were embedded within biomimetic hydrogels of varying stiffness and cultured for up to 4 weeks. Immunohistochemistry was used to quantify the dependence of cell proliferation and apoptosis on matrix stiffness, long-term culture and treatment with the anti-cancer drug paclitaxel.\ud \ud Two computational models were developed. In the first model, each spheroid was treated as an incompressible porous medium, whereas in the second model the concept of morphoelasticity was used to incorporate details about internal stresses and strains. Each model was formulated as a free boundary problem. Functional forms for cell proliferation and apoptosis motivated by the experimental work were applied and the predictions of both models compared with the output from the experiments. Both models simulated how the growth of cancer spheroids was influenced by mechanical and biochemical stimuli including matrix stiffness, culture time and treatment with paclitaxel. Our mathematical models provide new perspectives on previous experimental results and have informed the design of new 3D studies of multicellular cancer spheroids

Lattice Boltzmann method for colloidal dispersions with phase change.

Colloidal dispersions are known to undergo phase transition in a number of processes. This often gives rise to formation of structures in a flowing medium. In this paper, we present a model for flow of a colloidal dispersion with phase change. Two distribution functions are used. The colloid is described as a non-ideal fluid capable of phase change, but rather than taking the dispersion medium as the second fluid, a better choice is the dispersion (water plus colloid) which can be considered as an incompressible fluid. This choice allows a standard Lattice Boltzmann (LB) model for incompressible fluids to be used in combination with for the 'free-energy' LB model for the colloid. The coupling between the two fluids is the drag force on the colloid and the dependence of the viscosity of the overall fluid on the particle volume fraction. The problems raised by characteristic times and lengths have been treated. The main application considered is the growth dynamics or domain structuration of protein dispersions during dead-end filtration on a membrane surface

Near wall hemodynamics: Modelling the glycocalyx and the endothelial surface

This paper was presented at the 3rd Micro and Nano Flows Conference (MNF2011), which was held at the Makedonia Palace Hotel, Thessaloniki in Greece. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, Aristotle University of Thessaloniki, University of Thessaly, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute.In this paper a coarse-grained model for blood flow in small arteries is presented. Blood is modelled as a two-component incompressible fluid: the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets having greater density and viscosity. Interfacial surface tension and membrane effects are present to mimic key properties and to avoid droplets’ coalescence. The mesoscopic model also includes the presence of the wavy wall, due to the endothelial cells and incorporates a representation of the glycocalyx, covering the vessel wall. The glycocalyx is modelled as a porous medium, the droplets being subjected to a repulsive elastic force when approaching it, during their transit. Preliminary simulations are intended to show the influence of the undulation on the wall together with that of the glycocalyx

Onsager’s variational principle in soft matter : introduction and application to the dynamics of adsorption of proteins onto fluid membranes

This book is the first collection of lipid-membrane research conducted by leading mechanicians and experts in continuum mechanics. It brings the overall intellectual framework afforded by modern continuum mechanics to bear on a host of challenging problems in lipid membrane physics. These include unique and authoritative treatments of differential geometry, shape elasticity, surface flow and diffusion, interleaf membrane friction, phase transitions, electroelasticity and flexoelectricity, and computational modelling. [Chapter] Lipid bilayers are unique soft materials operating in general in the low Reynolds limit. While their shape is predominantly dominated by curvature elasticity as in a solid shell, their in-plane behavior is that of a largely inextensible viscous fluid. Furthermore, lipid membranes are extremely responsive to chemical stimuli. Because in their biological context they are continuously brought out-of-equilibrium mechanically or chemically, it is important to understand their dynamics. Here, we introduce Onsager’s variational principle as a general and transparent modeling tool for lipid bilayer dynamics. We introduce this principle with elementary examples, and then use it to study the sorption of curved proteins on lipid membranes.Peer ReviewedPostprint (author's final draft

Two-Component Fluid Membranes Near Repulsive Walls: Linearized Hydrodynamics of Equilibrium and Non-equilibrium States

We study the linearized hydrodynamics of a two-component fluid membrane near a repulsive wall, via a model which incorporates curvature- concentration coupling as well as hydrodynamic interactions. This model is a simplified version of a recently proposed one [J.-B. Manneville et al. Phys. Rev. E, 64, 021908 (2001)] for non-equilibrium force-centres embedded in fluid membranes, such as light-activated bacteriorhodopsin pumps incorporated in phospholipid (EPC) bilayers. The pump/membrane system is modeled as an impermeable, two-component bilayer fluid membrane in the presence of an ambient solvent, in which one component, representing active pumps, is described in terms of force dipoles displaced with respect to the bilayer midpoint. We first discuss the case in which such pumps are rendered inactive, computing the mode structure in the bulk as well as the modification of hydrodynamic properties by the presence of a nearby wall. We then discuss the fluctuations and mode structure in steady state of active two-component membranes near a repulsive wall. We find that proximity to the wall smoothens membrane height fluctuations in the stable regime, resulting in a logarithmic scaling of the roughness even for initially tensionless membranes. This explicitly non-equilibrium result, a consequence of the incorporation of curvature-concentration coupling in our treatment, also indicates that earlier scaling arguments which obtained an increase in the roughness of active membranes near repulsive walls may need to be reevaluated.Comment: 39 page Latex file, 3 encapsulated Postscript figure

Moving Domain Computational Fluid Dynamics to Interface with an Embryonic Model of Cardiac Morphogenesis

Peristaltic contraction of the embryonic heart tube produces time- and spatial-varying wall shear stress (WSS) and pressure gradients (∇P) across the atrioventricular (AV) canal. Zebrafish (Danio rerio) are a genetically tractable system to investigate cardiac morphogenesis. The use of Tg(fli1a:EGFP)y1 transgenic embryos allowed for delineation and two-dimensional reconstruction of the endocardium. This time-varying wall motion was then prescribed in a two-dimensional moving domain computational fluid dynamics (CFD) model, providing new insights into spatial and temporal variations in WSS and ∇P during cardiac development. The CFD simulations were validated with particle image velocimetry (PIV) across the atrioventricular (AV) canal, revealing an increase in both velocities and heart rates, but a decrease in the duration of atrial systole from early to later stages. At 20-30 hours post fertilization (hpf), simulation results revealed bidirectional WSS across the AV canal in the heart tube in response to peristaltic motion of the wall. At 40-50 hpf, the tube structure undergoes cardiac looping, accompanied by a nearly 3-fold increase in WSS magnitude. At 110-120 hpf, distinct AV valve, atrium, ventricle, and bulbus arteriosus form, accompanied by incremental increases in both WSS magnitude and ∇P, but a decrease in bi-directional flow. Laminar flow develops across the AV canal at 20-30 hpf, and persists at 110-120 hpf. Reynolds numbers at the AV canal increase from 0.07±0.03 at 20-30 hpf to 0.23±0.07 at 110-120 hpf (p< 0.05, n=6), whereas Womersley numbers remain relatively unchanged from 0.11 to 0.13. Our moving domain simulations highlights hemodynamic changes in relation to cardiac morphogenesis; thereby, providing a 2-D quantitative approach to complement imaging analysis. © 2013 Lee et al

Diffusion and permeation in binary solutions: Application to\ud protein ultrafiltration

During the ultrafiltration of colloidal solutions the particles can form a porous medium (filter cake) or a diffuse boundary layer (concentration polarization) above the semipermeable membrane depending on the magnitude of the filtration pressure. In order to provide a unified description of these phenomena the present work develops some connections between irreversible thermodynamics and poroelasticity. In particular, Fick’s and Darcy’s laws are shown to provide an equivalent description except in two limiting cases – infinite dilution and infinite rigidity of the solute. A new expression for the generalized Stokes-Einstein equation is also obtained, which incorporates the poroelastic Biot-Willis coefficient accounting for the compressibility of the solvent. The theory is utilized to predict the pressure and concentration profiles during the ultrafiltration of a protein solution. The model captures the formation of a diffuse polarization layer at low pressures and a nearly rigid filter cake at higher pressures, as well as intermediate stages. The predicted Darcy pressure profile across the polarization layer is in good quantitative agreement with experimental measurements