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

Simulation of deposit formation in particle laden flows: thermal properties

Fatty deposits formed on arterial walls lead to atherosclerosis but it is the interplay between these deposits and the vessel walls which governs the growth of plaque formation. Cells in the vessel walls trigger the body's defenses and through a series of mechanisms lead to the promotion of plaque growth. Crucially however the vast majority of acute coronary syndromes such as, myocardial infarction, and sudden ischaemic cardiac death is caused by atherosclerotic plaque rupture and not from a stenosis growing and blocking the blood flow. Although the stress caused by the blood flow does play a role in plaque rupture, it has been found that the degree of stenosis is a relatively minor factor in predicting which plaques are most prone to rupture. In fact, atherosclerotic plaques expand into the vessel wall during much of their existence and this can make their detection problematic

Low thrust propulsion in a coplanar circular restricted four body problem

This paper formulates a circular restricted four body problem (CRFBP), where the three primaries are set in the stable Lagrangian equilateral triangle configuration and the fourth body is massless. The analysis of this autonomous coplanar CRFBP is undertaken, which identies eight natural equilibria; four of which are close to the smaller body, two stable and two unstable, when considering the primaries to be the Sun and two smaller bodies of the solar system. Following this, the model incorporates `near term' low-thrust propulsion capabilities to generate surfaces of articial equilibrium points close to the smaller primary, both in and out of the plane containing the celestial bodies. A stability analysis of these points is carried out and a stable subset of them is identied. Throughout the analysis the Sun-Jupiter-Asteroid-Spacecraft system is used, for conceivable masses of a hypothetical asteroid set at the libration point L4. It is shown that eight bounded orbits exist, which can be maintained with a constant thrust less than 1:5 10􀀀4N for a 1000kg spacecraft. This illustrates that, by exploiting low-thrust technologies, it would be possible to maintain an observation point more than 66% closer to the asteroid than that of a stable natural equilibrium point. The analysis then focusses on a major Jupiter Trojan: the 624-Hektor asteroid. The thrust required to enable close asteroid observation is determined in the simplied CRFBP model. Finally, a numerical simulation of the real Sun-Jupiter-624 Hektor-Spacecraft is undertaken, which tests the validity of the stability analysis of the simplied model

The Lattice Boltzmann equation for modelling arterial flow

The lattice Boltzmann model (LBM) is a relatively new development in computational fluid dynamics. Here we review the technique with particular emphasis on its application to biological systems. Further, we consider its application to arterial flows and discuss its potential for simulating flow on length-scales where traditional numerical approaches can be troublesome. Finally we present results from a preliminary investigation which demonstrate the suitability of the LBM