Cardiovascular disease is the leading cause of mortality worldwide. Atherosclerosis, one of the most common forms of the disease, is characterized by a gradual formation of atherosclerotic plaque, hardening, and narrowing of the arteries. Nanomaterials can serve as powerful delivery platforms for atherosclerosis treatment. However, their therapeutic efficacy is substantially limited in vivo due to nonspecific clearance by the mononuclear phagocytic system.

In this paper, we consider a multi-layer diffusion model of drug release from a composite spherical microcapsule into an external surrounding medium. Based on this model, we present two approaches for estimating the release time, i.e. the time required for the drug-filled capsule to be depleted. Both approaches make use of temporal moments of the drug concentration at the centre of the capsule, which provide useful insight into the timescale of the process and can be computed exactly without explicit calculation of the full transient solution of the multi-layer diffusion model.

We explore the impact of geometrical corrugations on the near-wall flow properties of a soft material driven in a confined rough microchannel. By means of numerical simulations, we perform a quantitative analysis of the relation between the flow rate ? and the wall stress ?w for a number of setups, by changing both the roughness values as well as the roughness shape. Roughness suppresses the flow, with the existence of a characteristic value of ?w at which flow sets in. Just above the onset of flow, we quantitatively analyze the relation between ? and ?w.

Much work has been devoted to analysing thermodynamic models for solid dispersions with a view to identifying regions in the phase diagram where amorphous phase separation or drug recrystallization can occur. However, detailed partial differential equation non-equilibrium models that track the evolution of solid dispersions in time and space are lacking. Hence theoretical predictions for the timescale over which phase separation occurs in a solid dispersion are not available.

We consider the Erdös-Rényi random graph G(n,p) and we analyze the simple irreversible epidemic process on the graph, known in the literature as bootstrap percolation. We give a quantitative version of some results by Janson et al. (2012), providing a fine asymptotic analysis of the final size A_n of active nodes, under a suitable super-critical regime. More specifically, we establish large deviation principles for the sequence of random variables n-A_n/f (n) with explicit rate functions and allowing the scaling function f to vary in the widest possible range.

We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as those imposing a finite mass resistance at the external surface of the sphere. While the work is applicable to the generic problem of heat or mass transfer in a multi-layer sphere, the analysis and results are presented in the context of drug kinetics for desorbing and absorbing spherical microcapsules.

The migration of endothelial cells (ECs) is critical for various processes including vascular wound healing, tumor angiogenesis, and the development of viable endovascular implants. EC migration is regulated by intracellular ATP and recent observations in our laboratory on ECs cultured on line patterns - surfaces where cellular adhesion is limited to 15 m-wide lines that physically confine the cells - have demonstrated very different migration behavior from cells on control unpatterned surfaces.