Aortic stenosis (AS) is a common heart valve condition, particularly among the aging population, with Transcatheter Aortic Valve Implantation (TAVI) being the standard intervention. However, TAVI is associated with complications such as leaflet thrombosis, detectable on computed tomography (CT) as hypo-attenuated leaflet thickening (HALT). Despite growing adoption, the haemodynamic factors driving thrombus development remain poorly understood. Computational fluid-structure interaction (FSI) models offer a promising approach to analysing these dynamics, but most current research lacks patient-specific models that incorporate the actual implanted prosthetic valve. To address this gap, we developed a framework for simulating patient-specific haemodynamics in TAVI using pre-procedural CT scans and reverse-engineered valve geometry. In our study, we focus on a cohort of 30 patients who underwent TAVI with the Sapien 3 valve (Edwards Lifesciences) and returned for follow-up between 3 and 6 months post-procedure. Reverse engineering of the Sapien 3 valve involved detailed 2D imaging of the leaflets and contact mechanics simulations to model valve closure under physiological pressure. To optimize valve placement, we developed an interactive platform for precise commissure alignment. These models were then used in FSI simulations, leveraging isogeometric analysis and variational multiscale methods. Preliminary results point to individual anatomical features leading to localized flow stagnation near the valve leaflets, thereby contributing to thrombosis formation, though the effect is modulated by preserved heart function, positioning and leaflet dynamics. These findings could lead to improved TAVI device design and patient-specific treatment strategies.