Simulation of deposit formation in particle laden flows

Fatty deposits formed on arterial walls lead to atherosclerosis but it is the interplay between these deposits and the vessel walls which govern the growth of plaque formation. Crucially however the vast majority of acute coronary syndromes such as, myocardial infarction, and sudden ischaemic cardiac death are caused by atherosclerotic plaque rupture and not from a stenosis growing and blocking the blood flow. In fact, atherosclerotic plaques expand into the vessel wall during much of their existence and this can make their detection problematic. However inflammation within the necrotic core of the plaque, can be used to detect which plaques may be vulnerable. Thermal mapping of arterial walls can help identify the most likely sites for plaque rupture. This paper aims to provide a direct link between the geometry of these deposits and their thermal properties in order that non-invasive imaging techniques could be used to spot vulnerable plaques. We will discuss a methodology for estimating the thermal conductivity which utilises self-similarity properties using fractal analysis and renormalisation. The selfsimilar microstructure is captured by a family of random fractals called shuffled Sierpinski carpets (SSC). The thermal conductivity of the SSC can then be predicted both from its box counting fractal dimension and via a generalised real space renormalisation method. This latter approach also affords an analysis of the percolation threshold of two phase fractal media