Atherosclerotic plaque rupture in carotid arteries can lead to stroke which is one of the leading causes of death or disability worldwide. The accumulation of atherosclerotic plaque in an artery changes the mechanical properties of the vessel. Whilst healthy arteries can continuously adapt to mechanical loads by remodelling their internal structure, particularly the load-bearing collagen fibres, diseased vessels may have limited remodelling capabilities. In this study, a local stress modulated remodelling algorithm is proposed to explore the mechanical response of arterial tissue to the remodelling of collagen fibres. This stress driven remodelling algorithm is used to predict the optimum distribution of fibres in healthy and diseased human carotid bifurcations obtained using Magnetic Resonance Imaging (MRI). In the models, healthy geometries were segmented into two layers: media and adventitia and diseased into four components: adventitia, media, plaque atheroma and lipid pool (when present in the MRI images). A novel meshing technique for hexahedral meshing of these geometries is also demonstrated. Using the remodelling algorithm, the optimum fibre patterns in various patient specific plaques are identified and the role that deviations from these fibre configurations in plaque vulnerability is shown. This study provides critical insights into the collagen fibre patterns required in carotid artery and plaque tissue to maintain plaque stability.