Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

Water droplet accumulation and motion in PEM (Proton Exchange Membrane) fuel cell mini-channels

Effective water management is one of the key strategies for improving low temperature Proton Exchange Membrane (PEM) fuel cell performance and durability. Phenomena such as membrane dehydration, catalyst layer flooding, mass transport and fluid flow regimes can be affected by the interaction, distribution and movement of water in flow plate channels. In this paper a literature review is completed in relation to PEM fuel cell water flooding. It is clear that droplet formation, movement and interaction with the Gas Diffusion Layer (GDL) have been studied extensively. However slug formation and droplet accumulation in the flow channels has not been analysed in detail. In this study, a Computational Fluid Dynamic (CFD) model and Volume of Fluid (VOF) method is used to simulate water droplet movement and slug formation in PEM fuel cell mini-channels. In addition, water slug visualisation is recorded in ex situ PEM fuel cell mini-channels. Observation and simulation results are discussed with relation to slug formation and the implications to PEM fuel cell performance

A Moving Boundary Flux Stabilization Method for Cartesian Cut-Cell Grids using Directional Operator Splitting

An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional operator splitting, implementation of the scheme is rather straightforward. Extending the method for static walls from Klein et al., Phil. Trans. Roy. Soc., A367, no. 1907, 4559-4575 (2009), the scheme calculates fluxes needed for a conservative update of the near-wall cut-cells as linear combinations of standard fluxes from a one-dimensional extended stencil. Here the standard fluxes are those obtained without regard to the small sub-cell problem, and the linear combination weights involve detailed information regarding the cut-cell geometry. This linear combination of standard fluxes stabilizes the updates such that the time-step yielding marginal stability for arbitrarily small cut-cells is of the same order as that for regular cells. Moreover, it renders the approach compatible with a wide range of existing numerical flux-approximation methods. The scheme is extended here to time dependent rigid boundaries by reformulating the linear combination weights of the stabilizing flux stencil to account for the time dependence of cut-cell volume and interface area fractions. The two-dimensional tests discussed include advection in a channel oriented at an oblique angle to the Cartesian computational mesh, cylinders with circular and triangular cross-section passing through a stationary shock wave, a piston moving through an open-ended shock tube, and the flow around an oscillating NACA 0012 aerofoil profile.Comment: 30 pages, 27 figures, 3 table

Investigation of bone resorption within a cortical basic multicellular unit using a lattice-based computational model

In this paper we develop a lattice-based computational model focused on bone resorption by osteoclasts in a single cortical basic multicellular unit (BMU). Our model takes into account the interaction of osteoclasts with the bone matrix, the interaction of osteoclasts with each other, the generation of osteoclasts from a growing blood vessel, and the renewal of osteoclast nuclei by cell fusion. All these features are shown to strongly influence the geometrical properties of the developing resorption cavity including its size, shape and progression rate, and are also shown to influence the distribution, resorption pattern and trajectories of individual osteoclasts within the BMU. We demonstrate that for certain parameter combinations, resorption cavity shapes can be recovered from the computational model that closely resemble resorption cavity shapes observed from microCT imaging of human cortical bone.Comment: 17 pages, 11 figures, 1 table. Revised version: paper entirely rewritten for a more biology-oriented readership. Technical points of model description now in Appendix. Addition of two new figures (Fig. 5 and Fig. 9) and removal of former Fig.

Modelling shared space users via rule-based social force model

The promotion of space sharing in order to raise the quality of community living and safety of street surroundings is increasingly accepted feature of modern urban design. In this context, the development of a shared space simulation tool is essential in helping determine whether particular shared space schemes are suitable alternatives to traditional street layouts. A simulation tool that enables urban designers to visualise pedestrians and cars trajectories, extract flow and density relation in a new shared space design and achieve solutions for optimal design features before implementation. This paper presents a three-layered microscopic mathematical model which is capable of representing the behaviour of pedestrians and vehicles in shared space layouts and it is implemented in a traffic simulation tool. The top layer calculates route maps based on static obstacles in the environment. It plans the shortest path towards agents' respective destinations by generating one or more intermediate targets. In the second layer, the Social Force Model (SFM) is modified and extended for mixed traffic to produce feasible trajectories. Since vehicle movements are not as flexible as pedestrian movements, velocity angle constraints are included for vehicles. The conflicts described in the third layer are resolved by rule-based constraints for shared space users. An optimisation algorithm is applied to determine the interaction parameters of the force-based model for shared space users using empirical data. This new three-layer microscopic model can be used to simulate shared space environments and assess, for example, new street designs

Modelling Oscillator synchronisation during vertebrate axis segmentation

he somitogenesis clock regulates the periodicity with which somites form in the posterior pre-somitic mesoderm. Whilst cell heterogeneity results in noisy oscillation rates amongst constituent cells, synchrony within the population is maintained as oscillators are entrained via juxtracine signalling mechanisms. Here we consider a population of phase-coupled oscillators and investigate how biologically motivated perturbations to the entrained state can perturb synchrony within the population. We find that the ratio of mitosis length to clock period can influence levels of desynchronisation. Moreover, we observe that random cell movement, and hence change of local neighbourhoods, increases synchronisation