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.

Cardiovascular diseases continue to be the primary cause of death worldwide, where the buildup of plaque within arterial walls, known as atherosclerosis, is a major contributor to various acute cardiovascular events. Determining the material properties and the resulting stress distributions is crucial in the risk assessment of atherosclerotic plaques, as stress is considered an indicator of plaque vulnerability. Material models can be found with stress-strain pairs, but experimentally determining stress tensors is challenging. To address this limitation, we use a recently developed technique called EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) for material characterisation of a two-dimensional multicomponent atherosclerotic plaque, based solely on displacement and force data. A finite element model was developed to simulate the mechanical behaviour of the plaque using the neo-Hookean hyperelastic model, and noisy data was introduced into the model by applying Gaussian noise on the displacements. An L-BFGS gradient descent optimiser was used to minimise the objective function, which is the residual error between predicted internal forces and true external forces. Results showed that at the expected noise level in clinical imaging modalities, no physically relevant stress distributions were obtained, where the plaque’s heterogeneity was observed to affect the accuracy. Clinical imaging was further emulated by systematically removing data to determine the effect of missing data on the model. No significant deterioration of the accuracy of obtained parameters was seen until using 10% of the total data, indicating good robustness to missing data. While the study has limitations, the proposed approach could have implications for the future diagnosis and treatment of atherosclerosis. Future research could explore alternative optimisation algorithms or techniques to improve the model’s accuracy under these conditions.

Introduction: Atherosclerosis is characterised by the buildup of plaque within the arterial wall and it is often the underlying cause effect of deaths related to cardiovascular diseases. Thin cap fibroatheromas are plaques with a high risk of causing clinical events due to rupture and espousal of thrombogenic components to the bloodstream. The rupture of the plaque is not yet fully understood and for this reason, tissue engineered plaques were created in a previous study to assess the rupture of the plaques based on the displacement field registered with Digital Image Correlation during a uniaxial tensile experiment. The knowledge of the material properties of the tissue-engineered fibrous cap structures makes it possible to link deformations to external loads and contributes to the understanding of plaque rupture. The study aims to create a pipeline for local mechanical property characterisation of tissue engineered fibrous plaque structures.
Methods: In this novel method inverse Finite Element Method (iFEM) was combined with the Differential Evolution machine learning algorithm to assess global and local mechanical properties of tissue engineered fibrous plaque structures. The method required three main steps. Step one was the implementation of the uniaxial tensile test into a computational model using ABAQUS version 2016 Finite Element Method (FEM) software. To couple loads and deformations the hyperelastic reduced polynomial function of second order was implemented in the FEM. The characterisation of the c10 [kPa] and c_20 [kPa] parameters in the model is the main focus of this study. After the creation of the FEM, the computed displacement field and the previously registered DIC displacement field were implemented into the iFEM pipeline. Preliminary to the experimental data study, the pipeline was tested on a synthetically generated displacement field, in order to investigate the expected accuracy of the method. In step two the global mechanical properties of the fibrous plaque structures were investigated, using the assumption of homogeneous material property distribution in the samples. The resulting material properties after the global estimation served as an initial guess for the local estimation procedure. In step three the local material properties were investigated by creating sections with independently variable material properties, thus introducing heterogeneous distribution of material properties within the samples.
Results: The global mechanical property assessment was carried out successfully and the resulting material properties are within the range of previously reported stiffness values of plaques with a similar composition. Local mechanical properties were characterised using up to twelve independently variable material parameters to investigate the heterogeneous mechanical behaviour of the constructs.
Conclusion: During this project a new method was established to assess the local mechanical properties of tissue engineered fibrous cap structures. The pipeline shows high potential to be useful when investigating plaque rupture in a controlled environment using tissue engineered constructs. The knowledge of local material properties in combination with local deformations is a great addition to the understanding of plaque rupture.

Cardiovascular disease has caused 3.9 million deaths in Europe and over 1.8 million deaths in the European Union, which accounts for 45\% of all deaths in Europe and 37\% of all death in the European Union in 2017. Cardiovascular disease is mainly caused by atherosclerosis. Atherosclerosis is a kind of disease where the inside of the artery gets narrow due to the build-up of plaque. Plaque is an abnormal accumulation of material in the inner layer of the arterial wall. A swelling can be formed by the accumulated material. The swelling may intrude into the channel of the artery wall, which will make the channel get narrower and restrict blood flow. Based on current medical technology, images of the plaques can be taken. However, there are no efficient simulation tools for plaque rupture. In order to set up sufficient simulation tools, a good representation of the material behaviour and the progression of the failure is needed. There are material models for the arterial wall accounting for large deformations (hyperelasticity) and anisotropy in the material response. And, there are also failure models. However, the material models and the failure models have not been combined. In this thesis, three material models and one failure model are included. The three material models are Neo-Hookean material model and two anisotropic models developed for arterial wall tissue developed by Holzapfel and Gasser. They are combined with anisotropic damage model to obtain three new constitutive models for failure of hyperelastic material. After the three constitutive models are set up, a parameter study is performed to explore the material properties of the new constitutive models. Verification of the material models is also included. Finally, the performance of the model is demonstrated with failure analyses on different geometries: a simple plane, a bar, a plane with an imperfection and a plane with a rectangular hole in the middle.

The majority of cardiovascular clinical events, which are the main causes of mortality and morbidity worldwide, are caused by atherosclerotic plaque rupture. This biomechanical event occurs when the local plaque stresses exceed its strength. The plaque stresses can be assessed by computational models to predict these events. Current approaches to obtaining the plaque material stiffness properties that these models require as input have large computational costs and are therefore far from being implemented for clinical use. This study aims to develop, validate, and apply for the first time, an approach to obtaining the material stiffness properties of atherosclerotic plaque tissue much faster by employing the virtual fields method (VFM). With this method, the virtual work principle is employed with boundary problem specific, kinematically admissible virtual fields to solve energy balance equations for the material stiffness parameters that are of interest. In this study a method is presented for obtaining the virtual fields for the specific application of intraluminally pressurised atherosclerotic plaque tissue. For the purpose of validation, full field displacement maps were computed at 100 mmHg using Finite Element (FE) models based on histological slides of atherosclerotic plaque tissue. To mimic a realistic situation, the resolution and noise levels of a clinical and high frequency ultrasound scanner were used. Although higher resolution deformation maps with smaller noise levels were shown to provide more accurate results, the VFM-based technique demonstrated good performance for both the high frequency and clinical ultrasound scanner settings tested. VFM was also used in a single case study to estimate the c₁ material parameter for a Neo-Hookean incompressible material model in the case of an atherosclerotic human coronary artery. The estimated c₁-values for this case were: 21.5 kPa for diseased intima, 13.3 kPa for lipid, and 23.6 kPa for wall tissue. These values were in good agreement with the reported values from literature. In this study, VFM was applied successfully for the material characterization of atherosclerotic plaques for the first time. It is more attractive than current approaches as it is computationally less expensive and has a great potential to be extended for material characterization of even more plaque components than employed in the current study.