The study of haemodynamics, or the mechanics of blood flow, has been a topic of significant interest since ancient times, as it provides critical insights into both the normal functioning of the circulatory system and the mechanisms underlying various diseases. A robust scientific understanding of these dynamics facilitates the development of innovative prevention and intervention strategies, such as advanced, less invasive surgical techniques and cost-effective medical devices, which can dramatically improve global health outcomes. Over the centuries, experimental, analytical, and, more recently, computational methods have enhanced our knowledge of cardiovascular and cerebrovascular conditions, leading to improved diagnostic and therapeutic approaches that enhance life quality and expectancy.

Despite these advancements, substantial challenges remain, particularly in diagnosing and understanding haemodynamic complications such as stroke, stenosis, and regurgitation. Modern imaging techniques like MRI and sonography are limited by spatial and temporal resolution, requiring significant hardware improvements to overcome these constraints. Moreover, while analytical models have evolved to address the complex nature of blood flow and vessel behavior, they often struggle to accurately represent in vivo scenarios, especially in areas like the cerebral vasculature that are difficult to image. The presence of anomalies such as medial calcifications - which are responsible behind numerous life altering conditions and diseases such as, diabetes, kidney disease and hypertension - further complicates the accurate modeling of blood flow dynamics by introducing departure from axisymmetry, changes in material properties of the tissue and impacting the physics at localized scale.

To address the impact of medial calcifications, this thesis presents a detailed approach starting with the development of a three-dimensional (3D) model that represents the physiological fluid-structure interaction (FSI) phenomenon of pulsatile blood flow through an Internal Carotid Artery (ICA) with medial calcification. ICA is a critical vessel within the Circle of Willis which itself is one of the most crucial cerebro-vascular networks. Following this, a physics based one-dimensional (1D) Reduced Order Model (ROM) is developed, integrated with which is a data-driven constitutive modelling framework trained on the 3D simulation data, to account for changes in material proeprties introduced by medial calcifications. This ROM aims to provide a computationally efficient yet accurate representation of the physiological changes caused by medial calcifications. The thesis includes a comprehensive theoretical framework, detailed validation and verification processes, and comparisons between the 1D and 3D models to ensure accuracy and clinical relevance. The overarching goal is to create a well-validated ROM that maintains essential physical details while reducing computational costs, with an emphasis on evaluating its performance in clinical scenarios and exploring its potential applications and future research directions.

The internal carotid arteries (ICAs) are of vital importance in cerebral blood supply. Hence, accurate modeling of its biomechanical behavior is essential for understanding various pathologies and developing effective treatments. However, computational modeling of the ICA often omits the surrounding tissue environment, which likely limits the accuracy of biomechanical simulations. This study aimed to assess the impact of including surrounding tissues in ICA models on simulation outcomes. Using a single patient-specific ICA geometry, four finite element (FE) models were developed and analyzed: an isolated artery (Model 0), an artery with soft tissue interactions (Model 1), an artery with bone interactions (Model 2), and an artery with both soft tissue and bone interactions (Model 3). The surrounding tissues were modeled using elastic spring elements attached to the outer surface of the arterial wall. Different spring stiffness values were assigned to simulate the distinct properties of surrounding tissues in their corresponding artery segments. Simulations were performed using the FEBio software, the models were analyzed for displacement, stress, and strain distributions. Results showed that surrounding tissues significantly affect arterial biomechanics, with bone having a more dominant effect than soft tissue. The combined tissue model (Model 3) provided the most comprehensive and physiologically accurate representation of the ICA, with a 60.5\% reduction in peak displacement, a 6.8\% reduction in peak stress, and a 33.0\% reduction in peak strain compared to the isolated artery model. However, these preliminary findings using a single ICA geometry prevent us from drawing definitive conclusions. Therefore, our study serves as the groundwork for future investigations and highlights the significance of including surrounding tissues in ICA modeling.