Multi-scale parameterisation of static and dynamic continuum porous perfusion models using discrete anatomical data - Hyde, ER (2014)
The aim of this thesis is to replace the intractable problem of using discrete flow models within large vascular networks with a suitably parameterised and tractable continuum perfusion model. Through this work, we directly address the hypothesis that discrete vascular data can be incorporated within continuum perfusion models via spatially-averaged parameterisation techniques. Chapter 1 reviews biological perfusion from both clinical and computational modelling perspectives, with a particular focus on myocardial perfusion. In Chapter 2, a synthetic 3D vascular network was constructed, which was controllable in terms of its size and properties. A multi-compartment static Darcy perfusion model of this discrete system was parameterised via a number of techniques. Permeabilities were derived using: (i) porosity-scaled isotropic (ϕI); (ii) Huyghe and Van Campen (HvC); and (iii) projected-PCA parameterisation methods. It was found that HvC permeabilities and pressure-coupling fields derived from the discrete data produced the best comparison to the spatially-averaged Poiseuille pressure. In Chapter 3, the construction and analysis of high-resolution anatomical arterial vascular models was undertaken. In Chapter 4, various anatomically-derived vascular networks were used to parameterise our perfusion model, including a microCT-derived rat capillary network, a single arterial subtree, and canine and porcine whole-organ arterial models. Allowing for general-connectivity (as opposed to strictly-hierarchical connectivity) yielded a significant improvement on the continuum model pressure. For the whole-organ model however, it was found that the best results were obtained by using porosity-scaled isotropic permeabilities and anatomically-derived pressure-coupling fields. It was also discovered that naturally occurring small length but relatively large radius vessels were not suitable for the HvC method. In Chapter 5, the suitability of derived parameters for use within a dynamic perfusion model was examined. It was found that the parameters derived from the original static network were adequate for application throughout the cardiac cycle. Chapter 6 presents a concluding discussion, highlighting limitations and future directions to be investigated.