Through nanomedicine, game-changing methods are emerging to deliver drug molecules directly to diseased areas. One of the most promising of these is the targeted delivery of drugs and imaging agents via drug carrier-based platforms. Such drug delivery systems can now be synthesized from a wide range of different materials, made in a number of different shapes, and coated with an array of different organic molecules, including ligands. If optimized, these systems can enhance the efficacy and specificity of delivery compared with those of non-targeted systems. Emerging integrated multiscale experiments, models and simulations have opened the door for endless medical applications. Current bottlenecks in design of the drug-carrying particles are the lack of knowledge about the dispersion of these particles in the microvasculature and of their subsequent internalization by diseased cells (Bao et al. 2014 J. R. Soc. Interface11, 20140301 (doi:10.1098/rsif.2014.0301)). We describe multiscale modelling techniques that study how drug carriers disperse within the microvasculature. The immersed molecular finite-element method is adopted to simulate whole blood including blood plasma, red blood cells and nanoparticles. With a novel dissipative particle dynamics method, the beginning stages of receptor-driven endocytosis of nanoparticles can be understood in detail. Using this multiscale modelling method, we elucidate how the size, shape and surface functionality of nanoparticles will affect their dispersion in the microvasculature and subsequent internalization by targeted cells.

Transformation methods are a very powerful tool in finite element modelling. In many cases, an adequate mapping transforms the problem into an easier one or allows advantage to be taken of the symmetries. This paper demonstrates that any mapping can be handled automatically provided the classical vector analysis approach is given up for the benefit of a differential geometry approach. As a first example, it is shown that axisymmetrical problems need no more a particular treatment provided the mapping of the cylindrical coordinates on the cartesian ones is considered as it is. Furthermore, a novel axisymmetrical formulation is proposed which relies on one further transformation and improves considerably the quality of the interpolated field. Transformation methods are also of great help to model the infinite space by means of finite elements. Many authors have presented such transformations which are often instances of the same general shell transformation that is presented here.