Global energy minimisation of arterial trees with application to embolic stroke

Computer generation of optimal arterial trees has previously been limited to the production of locally optimal configurations. The application of a global optimisation algorithm allows for the generation of vasculatures with consistent structure. Comparison of this structure to that of in-vivo vasculatures allows the determination of to what extent the vascular structure is the result of energy minimisation. In this thesis an algorithm capable of generation globally optimal vascular trees in geometries derived from medical imaging is developed. We begin by outlining a small set of constraints which capture physiological principles guiding the organisation of arterial trees. The constraints are then used to produce an algorithm capable of finding the minimal energy configuration of a given arterial tree. The algorithm is used to produce both coronary and cerebral vasculature, and the latter is generated in geometries segmented from MRI data of a human brain. The trees are compared both morphologically and structurally to those found in-vivo. The morphological comparisons for the coronary vasculature show excellent agreement with experiment. The positions of the larger coronary arteries in the generated trees agree extremely well with experiment, suggesting that structure of the coronary vasculature is the result of energy minimisation. The generated cerebral vasculature approximates the vascular territories of the major cerebral arteries, however the morphological comparisons show that the structure of the cerebral arteries is likely not the result of energy minimisation. The cerebral vasculatures is used to extend a statistical model of embolic stroke to include the effects of branching asymmetry, and an analytic approximation to the statistical model of embolic stroke is developed and validated. It is found that branching asymmetry produces an overall reduction in the level of blockage occuring during an embolic event