Predictive haemodynamics of the human carotid artery
This thesis employs parametrically defined geometry of the human carotid artery bifurcation to better understand the relationship between a range of parameters and the associated haemodynamics and to devise strategies to provide guidance for clinical interventions and to assist in the design of stents and grafts. Initially, detailed statistical analysis is applied to a three dimensional parametric computer aided design (CAD) model of the human carotid bifurcation. A Bayesian surrogate modelling technique is proposed and discrete locations in the CAD model are taken as random parameters to form inputs for the surrogate model. A metric, maximal wall shear stress (MWSS) is used as an output for constructing the surrogate model and key geometric parameters which influence MWSS are identified by performing three dimensional steady state simulations on the candidate geometries. The ability of the surrogate model to predict arterial geometries which have minimum and maximum MWSS is also discussed. Using these geometries, techniques are proposed for evaluating the degree of severity with respect to the metric MWSS for any patient. Subsequently, a new metric, the integral of negative mean shear stress (INMSS) is used as an output for constructing a new surrogate model and three dimensional pulsatile simulations are performed on the candidate geometries. An optimisation problem is solved to find out the arterial geometries which have minimum and maximum values of INMSS. Due to the computational expense of performing three dimensional pulsatile studies, further parametric analyses are applied to the design of stents and bypass grafts using a one dimensional model capable of simulating fluid-wall interactions. Subsequently, a cost-effective diagnostic technique is proposed for identifying patients with carotid stenosis who could most benefit from angioplasty followed by stenting. For this purpose, pressure variation factor (PVF) and maximum pressure (pm) are used as metrics to rank the performance of each case. Finally, the Bayesian surrogate modelling technique is used to predict optimal bypass graft configurations which have minimal values of PVF.