Background: Ischemic stroke is a major cause of death worldwide. Atherosclerosis in the carotid arteries is an established predictor of these events. Ideally, patient-specific prevention plans can be developed that target advanced plaque development prior to events. Morphometry of advanced calcified plaque phenotypes can be assessed through Computed Tomography Angiography (CTA) but predicting progression on morphometry alone is insufficient as atherosclerosis is nonlinear and heterogeneous. Therefore, it was hypothesized that biomechanical triggers stimulate advanced plaque growth. The biomechanical response can be observed through structural stress and strain in the vessel wall as a response to plaque composition, blood pressure and tethering. So, the research aim of this study is to develop a framework that allows for local and global assessment of structural biomechanical stimuli and morphometrical changes in atherosclerotic carotid arteries

Methods Nine CTA scans paired at baseline and follow-up were selected from the Plaque At RISK study. The carotid bifurcation at the cervical spine was segmented by two independent observers using QAngioCT (Medis Medical Imaging, Leiden, The Netherlands). Contour data was reconstructed into a 3D geometry using a two-phase developed method in which 3D surface was computed first, and the second phase converted this to volumetric parts. Finite Element (FE) models were developed for baseline geometries where Neo-Hookean for calcified and Holzapfel-Gasser-Ogden for non-calcified materials were assigned.
For both timepoints, local morphometry was defined in wall thickness (WT), principal curvatures and calcium localization. Contour maps allowed the local association analysis between biomechanics and morphometry. Global plaque progression was computed using the morphometrical parameters and overall plaque burden (PB).


Results: This pipeline was successfully run for nine different carotid arteries, which proved overall robustness. The Dice similarity index computed an average segmentation observer similarity of 0.80 (St. Dev. 0.06) and 0.87 (St. Dev. 0.07) for surface reconstruction. Throughout reconstruction, the FE-modeling set the requirements for reconstruction outcome thus the focus was laid on connecting these phases. No patient data was made available during this study, so standardized systolic blood pressure resulted in an average maximum stress of 269.07 kPa and 0.14 strain.
Morphometrical analysis detected diseased WT in seven out of nine cases at baseline and all at follow-up. Local principal curvatures uncovered a relation with diseased thickening, indicating its success in detection of irregularities on a surface. Calcified tissue was found in all cases but one at baseline. The average morphometrical change increased 2.71 mm (St. Dev. 7.86 mm) in maximum WT, 0.69 % (St. Dev. 5.75 %) for maximum PB and 12.91 mm³ (St. Dev. 12.50 mm³) for calcium. These preliminary results highlighted the importance of multicomponent morphometry analysis. Moreover, correlations between calcium growth and stress (R² = 0.33) and WT increase (R² = 0.67) indicate that future studies should focus on comprehending atherosclerotic pathways involved in calcified plaque formation.

Conclusion: This developed method has laid the groundwork for future research and exposed important relations between analysis methods. The close dependency between reconstruction and FE-modeling, and anatomy and biomechanics emphasize that there is still a lot to discover.

Background: Atherosclerosis is a progressive arterial disease that gives rise to plaque. Rupture thereof is a main cause of myocardial infarction and ischaemic stroke. A plaque can have a fibrotic layer between its lipid pool and the arterial lumen, which is termed a fibrous cap (FC). Rupture of this FC can expose thrombogenic plaque content to the bloodstream. From a mechanical viewpoint, the FC is hypothesized to rupture when its strength is exceeded by the structural stresses imposed thereupon. Stresses in the FC can not be measured and are generally approximated by using digital analogs such as finite element models. Such models require among other things a definition of the FC its in-vivo composition. However, this is still poorly understood as it can presently not be measured in-vivo. To investigate the relations between a FC its composition and its mechanical properties, bio-engineered FCs (BE-FC) have been developed by researchers. These BE-FCs are reported to bear resemblance to human FCs in terms of bulk mechanical properties. This study aims to aid in the comprehension of the biomechanical behaviour of these BE-FCs.
Methods: A finite element modeling pipeline has been developed for BE-FCs. Following the pipeline provides a 2D BE-FC model and a total of 16 BE-FCs were modeled. Material behaviour is defined using the Holzapfel-Gasser-Ogden model. The BE-FC models their geometry and material parameters are acquired using geometry and collagen images in combination with self-developed and data-scaleable scripts. Model simulation results provide an approximation of the BE-FC its biomechanical behaviour. This study includes an investigation of the BE-FC models their global biomechanical behaviour as well as their stress and strain peak values, peak value locations, and distributions. In addition a parametric study has been performed; 1260 idealised BE-FC models were created. These models differ in geometry and composition, allowing a more in-depth investigation of the BE-FC models their stress and strain peak values and distributions.Results: The global biomechanical behaviour of the BE-FC models satisfyingly approximates that of their respective BE-FC. Peak stresses and strains in the BE-FC models are considerably higher than those found in the literature for ex-vivo uni-axially tensile tested FCs as well as compared to FC sections of finite element models. To the same extent the locations of the peak stresses and strains in the BE-FC models could not be co-localized to the rupture initiation locations of the BE-FCs. The stress and strain distributions are thoroughly examined using the simulation results of the idealised models. Depending on the specific stress and strain metric, each is contingent on different model characteristics and/or behaviours. In general however the most crucial of these are the collagen fibre dispersion \(\kappa\), the collagen fibre mean angle \(\Theta\), the degree of model compaction, and the model its soft inclusion shape and size.Conclusion: With this study, a novel modeling pipeline has been developed for 2D BE-FC finite element models. Results from simulations therewith give insight into the biomechanical behaviour of BE-FCs. In addition a parametric study has been performed, resulting in numerous idealised BE-FC models. The simulation results of these models aid considerably in the understanding of the BE-FCs their biomechanical behaviour. Taking everything in consideration, a contribution has been made to the comprehension of BE-FCs and along with that it therefore assists current research invested in answering how, why and when a FC ruptures. 

Background:
Ischemic stroke is a major cause of death worldwide. Atherosclerosis in the carotid arteries is an established predictor of these events. FSI shows its advantage in simulating the hemodynamic environments due to involving the multiphysics coupling of fluid dynamics and structural mechanics regulations. Therefore, the aim of this thesis was to establish and demonstrate a framework, starting with the segment data extracted from CTA images and leading to patient-specific FSI modeling. Thus the results can be used to gain insights into the relationship between plaque changes over time and biomechanical stresses induced by blood flow using FSI.

Method:
3D coordinates are firstly extracted from CTA scans of patients with calcified atherosclerotic plaques in their carotid arteries, sourced from the PARISK study. This data was then used to reconstruct 3D surfaces and volumes of the carotid bifurcation structure. Subsequently, the Backward Incremental method is employed to compute the initial stresses and establish the zero-pressure geometry of the vessel. Following this, FSI simulations were conducted on six carotid bifurcations to obtain preliminary results, providing an initial test of the pipeline's robustness. Morphological changes, including plaque burden, wall thickness, and calcium distance, are quantified to study plaque progression over time. The numerical simulation results provide insights into biomechanical stresses, including fluid and solid wall shear stress and von Mises stress. The simulation results are subjected to post-processing for further analysis. The results are mapped to a 2D configuration, with 1.5mm along the centerline and 45 degree per sector to study the local behavior.

Result:
The efficacy of the reconstruction and initial stress detection methods shows the robustness of the pipeline. The entire process is executed on six vessels, with a comprehensive examination of one case presented initially. This detailed analysis reveals metrics related to morphological changes, biomechanical stresses, and flow patterns. Subsequently, correlation and stress distribution analyses are conducted for all six vessels. Notably, negative correlations are discerned between stress and morphological changes, adding depth to the understanding of the relationship between biomechanics and morphological changes in these cases.

Atherosclerosis is an arterial condition characterized by the accumulation mainly of lipid tissue, resulting in the narrowing and stiffening of arteries. It is the leading cause of death among cardiovascular diseases and its development has been associated with wall shear (WSS) and wall mechanical stress (WMS). This study aimed to analyse WSS and WMS with two morphometric measurements, serving as indicators of the initiation and progression of atherosclerosis. 30 coronary arteries from 10 adult familial hypercholesterolaemic pigs fed a high-fat diet were imaged at 3 time points, using intravascular ultrasound and optical coherence tomography. Two-dimensional geometries of the arteries and their lipid components, in combination with their arterial pressure, were used to calculate WMS both at T1 and T2. WSS data was obtained at T1 and T2 by combining the 3D geometry of the arterial lumen and local flow velocity measurements. Arteries were segmented into 3 mm length and 45° sectors for analysis. It was observed that atherosclerosis developed in response to a high-fat diet, evidenced by a gradual increase in wall thickness over time even in the absence of lipidic components. Areas with thicker walls were predominantly found in regions exposed to low WSS and low WMS. Additionally, low WSS was found to promote atherosclerosis initiation and progression whereas high WMS appeared to support atherosclerosis progression. Throughout all time points, it was observed that WSS had a higher contribution to the development of atherosclerosis compared to WMS.

Intro - The rapidly developing technology of cardiac finite element modelling aims to improve heart failure treatment by quantifying stresses acting in the cardiac tissue. Cardiac finite element modelling may improve heart failure treatment by providing more insight in the pathophysiology, enabling a patient-specific assessment and improving the efficiency of clinical trials and medical devices. An essential part of the cardiac finite element model is capturing the mechanical behaviour of the heart, including its active behaviour (contraction). This mechanical behaviour is captured by means of a material model. However, the active behaviour of the heart is not readily available in material models provided by commercial finite element software like Abaqus/CAE. Consequently, such active material model needs to be added in a user subroutine manually. This is a time-consuming task, prone to errors. Additionally, the availability of the documentation is limited, and in literature the methodology of the implementation is oftentimes not disclosed.

Thesis goal - The goal of this master-thesis is to implement a combination of the passive and active mathematical material models in a commercial finite element platform. This was done by implementing the combined material models in user subroutine UMAT that can be used in FEA-software Abaqus. Reproducibility of the UMAT is ensured by a detailed documentation. Also, the UMAT is provided in the supplementary material.

Methods - The UMAT consists of the Holzapfel Ogden constitutive law as passive component, and the Time Varying-Elastance contstitutive law as active component, which are combined by means of the active stress approach. Additionally, the UMAT requires computation of the elasticity tensor, which is computed by means of a numerical formulation. The incorporation of the passive and active constitutive laws in the UMAT was verified by means of multiple test-cases. The outcomes of the UMAT were compared to an analytical solution and a benchmark user subroutine in the form of UANISOHYPER_INV. Lastly, reality-check test-cases were carried out by comparing the UMAT outcomes to the results from similar test-cases found in literature.

Verification results - Verification of the implemented material models showed good agreement with the analytical computed solution of equibiaxial extension, equibiaxial compression and isometric contraction test-cases, as all cases showed an MAPEmax or APEmax error lower than 1%. Shear test-case results of the UMAT showed some bigger APEmax values (maximal 17%) with relation to the analytical solution, possibly caused by numerical errors during the elasticity tensor computation. Results of the reality-check cases showed similar trends to the mechanical experiments done on cardiac tissue on which these cases are based.

Conclusion - The public availability of the implemented passive and active material models in the user subroutine UMAT, which is working reasonably well according to conducted verification, forms a significant step forwards in the field of cardiac finite element modelling. The current work can be further extended by the incorporations of compressibility during contraction and viscoelasticity in the material models. This thesis provides the basis for future projects in the field of cardiac finite element modelling including an active material model. Also, the provided implementation of material models may aid in the implementation of other mathematical material models in a user subroutine like UMAT.

Atherosclerosis is a lipid-driven inflammatory disease of the arteries. It causes
increased thickness of the intima layer of an artery, due to build-up of, among
others, lipid deposits. Eventually, this could cause rupture of the blood vessel’s
wall, leading to thrombus forming and possibly to clinical events. Clinically, the
degree of stenosis (degree of narrowing of the lumen) is used as a metric for risk
assessment. However, narrow arteries do not necessarily rupture, while wide arteries can still rupture. Since rupture is a mechanical event, (mechanical) stress
in the arteries could be a better metric to assess rupture. Stress could be calculated
through a chosen constitutive model. However, these constitutive models require
patient-specific constitutive parameters, which presently are challenging to obtain.
To retrieve the patient-specific constitutive parameter(s), the Virtual Fields
Method (VFM) could be used. This is a method based on the principle of virtual
work. By minimizing the difference between the internal and external virtual work,
the constitutive parameter(s) can be calculated. In this study, five atherosclerotic
plaques were modeled with a neo-Hookean material model, subjected to intraluminal pressure in a Finite Element (FE) environment. The nodal deformations were
used to apply the VFM in MATLAB. This was done at three levels: level 1 assumed
that, for each model, a single constitutive parameter dictated the stress behavior
of the entire atherosclerotic model. At level 2, the models were divided into four
mechanically relevant components: intima, wall, calcified tissue, and lipid component. The ground truth for the constitutive parameter of each component was
unique (120 kPa, 250 kPa, 5 kPa, and 423 kPa for intima, wall, lipid, and calcified tissue component respectively). For each of the components, a constitutive
parameter was calculated. At the last level, the nodes provided by the FE model
were used to create four-noded quadrilateral elements. For each element separately,
a constitutive parameter was calculated. This level presents two sublevels: at the
first sublevel (level 3a), the ground truth for the constitutive parameter of all elements was set at 100 kPa. At the second sublevel (level 3b), the ground truth for
the constitutive parameter of an element depended on the component the element
belonged to; the elements that belonged to the intima, wall, lipid, or calcified tissue
component had a ground truth value for their constitutive parameter of 120 kPa,
250 kPa, 5 kPa, or 423 kPa, respectively.
The results showed how for the first level, the VFM was able to calculate the
constitutive parameter within 0:2% of the ground truth. For level 2, some of the
atherosclerotic arteries’ components were calculated very accurately (within 2% of
their ground truth), while others differed greatly (by more than 20% of their ground
truth). For level 3a, it was shown how a good initial guess for the minimization
algorithm could produce very accurate results. For level 3b, a good initial guess
was lacking and the minimization algorithm was not capable of finding results that
were in close proximity to the ground truth.
Clinically, the application of the VFM can be an interesting approach for assisting clinicians to decide on intervening. However, this still requires some improvements from the current work. The current study serves as a foundation upon
which to build.

The rupture of atherosclerotic plaques present in vital arteries is the main trigger of fatal cardiovascular events, such as heart attacks and strokes. Plaque rupture is a mechanical failure of the fibrous plaque tissue that ensues upon large deformations of the tissue, induced by the blood pressure. Current knowledge on the rupture characteristics of plaque tissue is, however, scarce and limited to global, aggregate tissue properties, although plaque rupture is a local phenomenon. Hence, local mechanical and structural evaluations of the heterogeneous, highly collagenous plaque tissue are required for better understanding the plaque rupture.

To achieve this, a combination of mechanical and structural analyses was performed in this study. The collagen structure of human carotid plaques was imaged by means of Multiphoton microscopy using Second-Harmonic Generation signals (MPM-SHG), and it was characterized in terms of fiber orientation and dispersion. Subsequently, the imaged plaques were subjected to uniaxial tensile tests until rupture to characterize their mechanical response. Apart from the traditional global analysis, the local mechanical response was analyzed through Digital Image Correlation (DIC). This way, the structural heterogeneity of the plaque tissue was assessed and the role of collagen fiber organization in plaque mechanics was investigated locally.

The structural analysis of the plaque tissue samples demonstrated a predominant overall fiber orientation along the circumferential direction of the artery. Yet, high local variability in collagen orientation and dispersion was measured. The global, average mechanical response of the plaques showed a non-linear behavior, typical to many soft biological tissues and the local mechanical analysis demonstrated highly heterogeneous strain distributions in the plaques. Furthermore, regions that were about to rupture, showed higher tensile strains compared to the overall plaque strain, implying the possibility of establishing strain as a predictive metric for rupture. Whereas the global analysis did not yield any important correlation between the overall collagen structural parameters and the global mechanical tissue response, the local analyses indicated that the regional predominant fiber angle might influence the regional strain, and probably the plaque rupture risk.

Atherosclerosis is a cardiovascular disease in the arteries and a primary cause of death in the industrialized world. Most deaths due to atherosclerosis occur when the fibrous cap covering the necrotic core ruptures, leading to a blood clot. To determine whether an atherosclerotic plaque will rupture requires the development of accurate computational models. One of the key aspects for these models is the material model, in which collagen fibres play a major role. This study aims to contribute to the making of a numerical model which accurately represents atherosclerotic plaque by comparing the elastic and rupture behaviour of engineered collagenous micro tissues and their respective finite element models in ABAQUS. The Holzapfel-Gasser-Ogden material model of these computational models is based on a combination of global material parameters and local material parameters based on the local fibre organisation. A framework developed to measure the local fibre organisation using provided imagery of a nuclear stained tissue engineered sample shows the collagen fibres align along the loading direction and the edges of the geometry. The fibers are less dispersed along the edges of the geometry and on the left and right of a formed soft inclusion. A uniaxial tensile test was performed on four tissue engineered samples. The elastic and rupture behaviour of the samples during the uniaxial tensile tests is replicated in ABAQUS using both isotropic and homogeneous material parameters, and anisotropic heterogenous material parameters. The stresses measured in the simulations are highly dependent on both the material parameters and the geometry of the model. The strains are mostly dependent on the geometry, but are affected by the material model. Due to the higher stiffness at the edges of the geometry of the anisotropic samples, the stresses increased greatly, and the strains decreased slightly. The rupture behaviour of the cultured samples is replicated in the FEM simulations using extended finite element method (XFEM). The damage in the samples with isotropic material parameters initiates both from the soft inclusion as the left and right edges of the geometry. The damage in the samples with anisotropic material parameters initiates, similarly to the cultured samples, only from the sides of the soft inclusion. The damage in both the cultured and simulated samples propagate mostly horizontal and from the soft inclusion outward. In three out of four isotropic samples however, damage propagates to varying degrees from the edge of the geometry inward. Based on these findings it is concluded that implementing the local fibre organisation in the material model can improve the accuracy of finite element simulations of collagenous soft tissues, which includes atherosclerotic plaque, as the rupture behaviour of the simulations with anisotropic material parameters more accurately represents the rupture behaviour of the engineered fibrous tissues in comparison with simulations with isotropic material parameters.

Introduction: Atherosclerosis, the major source of cardiovascular diseases, is one of the leading causes of death. During atherosclerosis the arterial wall is affected by a complex process of lipid driven inflammation that leads to thickening of the arterial wall resulting in a so called plaque. Because of plaque growth, the lumen of the artery gradually narrows. As the lumen area is decreasing, reduction and even restriction of blood flow can occur, which can lead to a heart attack or stroke depending on the affected artery. Biomechanical stresses are known to influence the development of the disease. Those stress are the plaque structural stress (PSS) and wall shear stress (WSS) induced by the blood flow at the vessel wall. The aim of this project was to study the contribution of these biomechanical stresses and their combination to plaque progression in human coronary arteries. In order to investigate this effect a new methodology for the calculation of the stresses was introduced that utilizes the image modalities optical coherence tomography (OCT) and intravascular ultrasound (IVUS). The combination of those two image modalities can provide more accurate information regarding the plaque composition than the approaches that have been applied so far. In particular the cap thickness, which is the region shielding the lipid rich necrotic core from the blood flow, is crucial for structural stress calculations. Methods: The new methodology consisted of three steps. During the first step image data from the image modalities optical coherence tomography (OCT) and intravascular ultrasound (IVUS) were fused. The resulted images were cross-sections of the human coronary arteries that consisted of the lumen and the outer wall obtained from IVUS and the fibrous cap obtained from OCT. However, they did not contain information about the size of the necrotic core; thus, the second step was to reconstruct the necrotic core. For that purpose an algorithm from the literature was implemented that can reconstruct the necrotic core. The produced geometry resulting from the second step consisted of the same features as those from step one but they also included the contours of the necrotic core. The third step was the calculation of the PSS using those 2D geometries. The WSS data were obtained from another study. For the statistical analysis the data of both stress calculations were ranked as low, medium and high. Two different approaches for the definition of the thresholds of those ranks were used, vessel specific and absolute thresholds. In the vessel specific approach the thresholds of the aforementioned ranks were specific for each vessel, while in the second approach the threshold values were based on the whole sample size. Those two approaches were studied in order to explore if the response of the vessels depends to the absolute values of biomechanical stresses or it is relative to their respective biomechanical stresses. Change in wall thickness was used as metric to quantify the plaque progression. In order to study the contribution of the biomechanical stresses to the plaque progression in the human coronary arteries, statistical analysis was carried out using ANOVA with plaque progression as dependent variable and PSS and WSS as independent variables. Results: Plaque development was significantly related to WSS using both approaches to rank the WSS values into low, mid and high. In general, regions exposed to low WSS showed the most plaque progression. The individual effect of PSS was not statistically significant using both approaches, however there was a trend demonstrating that high PSS could promote plaque development. When PSS and WSS were combined using the vessel specific approach to rank the data, there was plaque progression for the cases of low WSS combined with any level of plaque structural stress. However, only WSS had a statistically significant effect in this case revealing that the resulted effect was entirely estimated by WSS. If absolute thresholds were used for both WSS and PSS, there was no statistical effect. Despite that, there was a trend showing that high PSS combined with high WSS could promote plaque development. Conclusions: During this project a new methodology was utilized in order to study the contribution of WSS, PSS and their combination to the plaque development in human coronary arteries. It was also the first study that utilized the combination of the image modalities OCT and IVUS in that topic. It was demonstrated that WSS could promote plaque development. PSS also enhanced plaque progression but with no statistically significant effect. Regarding the combination, it was demonstrated that the effect was explained completely by wall shear stress for the vessel specific approach. For the absolute thresholds approach, there was no statistically significant effect. However, more data are required to validate these results.

Atherosclerosis is a prevalent cardiovascular disease and defined as plaque formation inside the arterial intima layer. The atherosclerotic plaque is characterized as anisotropic, soft tissue and a potential plaque rupture could result in life-threatening clinical events, such as ischemic attack or stroke. The plaque rupture mechanism is still poorly understood due to the lack of real-time, in-vivo observations. Aiming to predict and describe the plaque damage behavior, numerical damage models have been implemented. This study focused on developing a theoretical and computational framework of Strain Energy Density Function (SEDF) with energy limiter damage model with atherosclerotic plaque-mimicking tissue-engineered applications. The generated damage model was implemented in Neo-Hookean and Holzapfel-Gasser-Ogden (HGO) SEDF via material user subroutines (UMAT codes) in finite element software. The computational models simulated 8 different experimental ruptured cases based on idealized and realistic geometrical models. In the material characterization process an iterative optimization algorithm was developed. The findings demonstrated that the case-specific computational models with SEDF with energy limiter damage model reproduced the plaque-mimicking rupture as they fitted the experimental crack initiation and propagation patterns. The results revealed that the anisotropic HGO material model generated the highest amount of Cauchy stresses and strain energy density. In addition, the geometrical configuration sensitivity of the damage model was emphasized as all cracks initiated from the inclusion and the results between idealized and realistic geometrical models deviated. A parametric study was conducted to investigate the influence of various energy limiters in matrix and fibers components via the SEDF and resulted in a matrix-dominated damage model. The SEDF with energy limiter model could be further optimized by developing a fully automated damage model and validated with clinical applications.

Introduction: Carotid atherosclerosis is characterized by the build-up of the so-called plaque tissue in the wall of the carotid artery. The rupture of carotid plaques can lead to acute manifestations, including ischemic stroke and transient ischaemic attack (TIA). The mechanism responsible for rupture is not yet unravelled, complicating the medical management of the disease. There are indications that plaque morphology plays a role in plaque rupture risk. Previous histopathological studies found that ruptured plaques and non-ruptured plaques tend to differ in their structural composition. These studies did not perform a detailed analysis of the local plaque features at the rupture sites, even though this might increase the insight in the rupture event. The aim of this thesis was to investigate the relation between local plaque composition and rupture in carotid plaques. Methods: Digitized histological sections of 21 ruptured carotid endarterectomy samples (obtained from fourteen different patients) were segmented for the following nine tissue structures: cholesterol crystals,plaque, calcium, necrotic core, fresh haemorrhage, foam cells, neovessels, macrophages and old haemorrhage. The rupture site on the sections was identified as a luminal disruption in the presence of red blood cells. The digitized sections were then divided into 8 bins (pie slices), resulting in a total of 168 bins (21 sections x eight bins). Of these observations, 23 contained rupture, whereas the other 145 were rupture-free. The plaque area in each bin was measured and the other tissue structure sizes were calculated relative to the plaque area in the bin. Spatial heatmaps demonstrated the location of the tissue structures relative to the rupture site. They were created for the three variables cholesterol crystals, calcium and macrophages, as these tissue structures were often recognized close to the rupture sites. Kendall Tau-b correlation coefficients were calculated to determine the relation between tissue structures in close proximity. The two-sided clustered Wilcoxon rank sum test (with clusters at the patient level) was used to investigate differences between the composition of ruptured and non-ruptured bins. Additionally, the association of tissue structures with rupture was tested by a generalized estimating equations (GEE) logistic regression model (working correlation matrix:independence). Clusters were assigned at the patient level. A sensitivity analysis was carried out (using 2-,4- and 16-bins) to determine the effect of the bin size on the outcome of the statistical analyses. Results: Visual analysis demonstrated that ruptures tended to extend to (or start at) areas of calcification or cholesterol crystals and that the rupture sites could be markedly inflamed. The spatial heatmaps showed that areas of calcification were closer to the rupture sites than areas with cholesterol crystals. Moreover, the prevalence of macrophages near the rupture sites was lower when compared to the prevalence of calcium and cholesterol crystals. In ruptured bins, the strongest tissue structure correlation was found between calcium and cholesterol crystals (tau_b= -0.44, p ≤ 0.05). This correlation was less evident when ruptured and non-ruptured bins were analysed together (tau_b= -0.07, p > 0.05). The clustered Wilcoxon rank sum tests howed that calcium (p=0.05) and fresh haemorrhage (p=2.17x10-11) tended to take on higher values in the ruptured bins, when compared to the non-ruptured bins. Lastly, with the GEE logistic regression model an association was found between rupture and the predictor variables calcium (p= 0.00094) and plaque (p=0.049).The odds ratio of rupture was 1.05 [1.02-1.07] for a plaque size increase of 0.34 mm2, if the other plaque characteristics in the bin were held fixed. The odds ratios of rupture belonging to plaque-bins that contained10% calcium and 50% calcium were 1.96 [1.60-2.40] and 3.01 [2.16-4.20], respectively, relative to plaque-bins with 0% calcium content and equal other plaque characteristics in the bin. The sensitivity analysis showed that the choice for an 8-bin approach was reasonable. Conclusion. The rupture sites of the carotid sections showed an enhanced calcium content. Moreover, the calcium content and the plaque size showed to be significantly associated with plaque rupture. The developmental progress of non-invasive imaging techniques, using magnetic resonance imaging and ultrasound, is promising for the characterization of carotid plaques in vivo. Understanding the relation between plaque composition and plaque rupture at a local level can contribute to rupture risk assessment and eventually to the medical management of atherosclerosis.

Atherosclerotic plaque rupture is the main cause of acute myocardial infarction and stroke, the two leading causes of death worldwide. Rupture of plaque tissue is a mechanical event, where plaque stress or strain locally exceeds its strength. Biomechanical studies agree with histopathological findings that a large lipid pool and thin fibrous cap overlying the lipid pool increase the likelihood of rupture, by showing increased plaque stresses for these geometries. Another plaque morphological feature that is frequently encountered is calcification. However, its role in the vulnerability of plaques to rupture is not fully understood, and biomechanical modeling studies do not agree on the effect of calcifications on plaque stress. These studies used isotropic material properties for the anisotropic and collagen rich plaque tissue, and generally focused on the effect of calcification on lumen stress or cap stress. However, histopathological findings revealed tissue damage at the interface between calcification and surrounding tissue.

This study investigated stresses and strains at the interface between calcification and fibrous tissue, how these stresses and strains are influenced by local anisotropy of the fibrous tissue and how geometric features of the calcification are related to these metrics. A morphometric study was conducted first, to investigate and categorize different patterns of fiber alignment around the calcifications, and to measure the calcification geometric features including its location in the plaque, its shape and its size. Biomechanical models including the local anisotropic material properties were constructed next, based on the observations and measurements made in the morphometric analysis. Stress and strain metrics were investigated at the calcification boundary, and subsequently related to fiber patterns and calcification geometric features.

Hundred forty five calcifications were segmented and measured in the morphometric analysis, and surrounding fiber alignments were studied. The analysis revealed that four main fiber patterns in the fibrous tissue surrounding calcifications exist: the Attached pattern, Pushed Aside pattern, Encircling pattern and Random pattern. Collagen fibers are attached to the calcification in the Attached pattern, are pushed aside by the calcification in the second pattern, encircle the calcification in the third pattern, and show a disorganized alignment in the Random pattern. The Attached pattern was the most prevalent fiber pattern, and its corresponding calcifications had larger aspect ratios and were on average larger than the other three fiber patterns. Large peak stresses and strains at the calcification boundary were identified in the biomechanical models for the Attached pattern and Pushed Aside pattern, while these metrics showed generally lower peak values for the Encircling pattern and Random pattern. Peak values for all stress and strain metrics were attained at the tip of the calcifications. Multivariate analysis showed that stresses and strains are related to the calcification geometric features; calcification interface stress and strain increased if the calcification was closer to the lumen, had a larger length/width ratio and was larger in size.

Histopathological examination of plaques evidenced damage at the interface between calcification and fibrous tissue, potentially caused by an adverse mechanical state at this boundary. Most studies focused on stresses at the lumen or in the cap however, and this study for the first time specifically investigated stresses and strains at the calcification boundary while simultaneously introducing local fibrous tissue anisotropy in the computational models. Results show that peak stresses and strains can develop at this boundary, which will remain undiscovered if isotropic materials are used. This study was also the first to extensively analyze calcification geometric features and surrounding fiber alignment in relation to these interface stresses and strains. Peak values were found to be dependent on these features and fiber alignment patterns, indicating a relation between these characteristics and mechanical stability of the plaque. The findings of this study further increase the clinical relevance of finite element modeling in rupture risk prediction by showing previously undiscovered peak stress and strain values for interfaces and geometric configurations which already were deemed to be destabilizing in clinical and histopathological studies.