Reaction Front in an A+B -> C Reaction-Subdiffusion Process

We study the reaction front for the process A+B -> C in which the reagents move subdiffusively. Our theoretical description is based on a fractional reaction-subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process. We design numerical simulations to check our theoretical results, describing the simulations in some detail because the rules necessarily differ in important respects from those used in diffusive processes. Comparisons between theory and simulations are on the whole favorable, with the most difficult quantities to capture being those that involve very small numbers of particles. In particular, we analyze the total number of product particles, the width of the depletion zone, the production profile of product and its width, as well as the reactant concentrations at the center of the reaction zone, all as a function of time. We also analyze the shape of the product profile as a function of time, in particular its unusual behavior at the center of the reaction zone

COAST: Modelling Restenosis and Stent Based Therapies

COAST (Complex Automata Simulation Technique) is a European Union FP6 funded project which has developed a methodology for multi-science, multi-scale simulation of complex systems. The resulting framework (MUSCLE: Multiscale Simulation Coupling Library and Environment is now publically available. As an exemplar, MUSCLE has been applied to the model of a complex biomedical pathology, that of in-stent restenosis, resulting in a hierarchical aggregation of coupled cellular automata and agent based models coined "complex automaton". Currently, three simple, single scale models have been coupled to simulate the pathological response of the arterial wall to stent-deployment: an agent based model of smooth muscle cell dynamics (modeling cell cycle and cell-cell interaction), a lattice Boltzmann model of blood flow (defining wall shear stress and oscillatory shear index at the vessel surface) and a finite difference drug diffusion model (defining stent-eluted drug concentrations across the vessel wall). These sub-models operate on distinct temporal scales and can be plotted on a scale separation map. This conceptual tool defines the temporal separation of the processes and the coupling template required for interaction between them. Coupling is implemented using smart conduits and in some situations, mapper agents, which transfer information between models with lattice based domains (blood flow, drug diffusion) to those with continuous domains (smooth muscle behaviour). Here we present preliminary output of a simple 2D model of in-stent restenosis. The present model captures the relationship between degree of stent induced injury and the smooth muscle cell hyperplastic response. The generation of realistic output correlates well with experimental data and paves the way for computer-aided design of stent-based therapies