Computational approaches for analyzing the mechanics of atherosclerotic plaques: a review

Impact of geometric and hemodynamic changes on a mechanobiological model of atherosclerosis

BACKGROUND AND OBJECTIVE

In this work, the analysis of the importance of hemodynamic updates on a mechanobiological model of atheroma plaque formation is proposed.

METHODS

For that, we use an idealized and axisymmetric model of carotid artery. In addition, the behavior of endothelial cells depending on hemodynamical changes is analyzed too. A total of three computational simulations are carried out and their results are compared: an uncoupled model and two models that consider the opposite behavior of endothelial cells caused by hemodynamic changes. The model considers transient blood flow using the Navier-Stokes equation. Plasma flow across the endothelium is determined with Darcy's law and the Kedem-Katchalsky equations, considering the three-pore model, which is also employed for the flow of substances across the endothelium. The behavior of the considered substances in the arterial wall is modeled with convection-diffusion-reaction equations, and the arterial wall is modeled as a hyperelastic Yeoh's material.

RESULTS

Significant variations are noted in both the morphology and stenosis ratio of the plaques when comparing the uncoupled model to the two models incorporating updates for geometry and hemodynamic stimuli. Besides, the phenomenon of double-stenosis is naturally reproduced in the models that consider both geometric and hemodynamical changes due to plaque growth, whereas it cannot be predicted in the uncoupled model.

CONCLUSIONS

The findings indicate that integrating the plaque growth model with geometric and hemodynamic settings is essential in determining the ultimate shape and dimensions of the carotid plaque.

Patient-Specific Numerical Simulations of Coronary Artery Hemodynamics and Biomechanics: A Pathway to Clinical Use

PURPOSE

Numerical models that simulate the behaviors of the coronary arteries have been greatly improved by the addition of fluid-structure interaction (FSI) methods. Although computationally demanding, FSI models account for the movement of the arterial wall and more adequately describe the biomechanical conditions at and within the arterial wall. This offers greater physiological relevance over Computational Fluid Dynamics (CFD) models, which assume the walls do not move or deform. Numerical simulations of patient-specific cases have been greatly bolstered by the use of imaging modalities such as Computed Tomography Angiography (CTA), Magnetic Resonance Imaging (MRI), Optical Coherence Tomography (OCT), and Intravascular Ultrasound (IVUS) to reconstruct accurate 2D and 3D representations of artery geometries. The goal of this study was to conduct a comprehensive review on CFD and FSI models on coronary arteries, and evaluate their translational potential.

METHODS

This paper reviewed recent work on patient-specific numerical simulations of coronary arteries that describe the biomechanical conditions associated with atherosclerosis using CFD and FSI models. Imaging modality for geometry collection and clinical applications were also discussed.

RESULTS

Numerical models using CFD and FSI approaches are commonly used to study biomechanics within the vasculature. At high temporal and spatial resolution (compared to most cardiac imaging modalities), these numerical models can generate large amount of biomechanics data.

CONCLUSIONS

Physiologically relevant FSI models can more accurately describe atherosclerosis pathogenesis, and help to translate biomechanical assessment to clinical evaluation.

Structural and Mechanical Properties of Human Superficial Femoral and Popliteal Arteries

The femoropopliteal artery (FPA) is the main artery in the lower limb. It supplies blood to the leg muscles and undergoes complex deformations during limb flexion. Atherosclerotic disease of the FPA (peripheral arterial disease, PAD) is a major public health burden, and despite advances in surgical and interventional therapies, the clinical outcomes of PAD repairs continue to be suboptimal, particularly in challenging calcified lesions and biomechanically active locations. A better understanding of human FPA mechanical and structural characteristics in relation to age, risk factors, and the severity of vascular disease can help develop more effective and longer-lasting treatments through computational modeling and device optimization. This review aims to summarize recent research on the main biomechanical and structural properties of human superficial femoral and popliteal arteries that comprise the FPA and describe their anatomy, composition, and mechanical behavior under different conditions.

The interplay of collagen, macrophages, and microcalcification in atherosclerotic plaque cap rupture mechanics

The rupture of an atherosclerotic plaque cap overlying a lipid pool and/or necrotic core can lead to thrombotic cardiovascular events. In essence, the rupture of the plaque cap is a mechanical event, which occurs when the local stress exceeds the local tissue strength. However, due to inter- and intra-cap heterogeneity, the resulting ultimate cap strength varies, causing proper assessment of the plaque at risk of rupture to be lacking. Important players involved in tissue strength include the load-bearing collagenous matrix, macrophages, as major promoters of extracellular matrix degradation, and microcalcifications, deposits that can exacerbate local stress, increasing tissue propensity for rupture. This review summarizes the role of these components individually in tissue mechanics, along with the interplay between them. We argue that to be able to improve risk assessment, a better understanding of the effect of these individual components, as well as their reciprocal relationships on cap mechanics, is required. Finally, we discuss potential future steps, including a holistic multidisciplinary approach, multifactorial 3D in vitro model systems, and advancements in imaging techniques. The obtained knowledge will ultimately serve as input to help diagnose, prevent, and treat atherosclerotic cap rupture.

Development of physiologically-informed computational coronary artery plaques for use in virtual imaging trials

BACKGROUND

As a leading cause of death, worldwide, cardiovascular disease is of great clinical importance. Among cardiovascular diseases, coronary artery disease (CAD) is a key contributor, and it is the attributed cause of death for 10% of all deaths annually. The prevalence of CAD is commensurate with the rise in new medical imaging technologies intended to aid in its diagnosis and treatment. The necessary clinical trials required to validate and optimize these technologies require a large cohort of carefully controlled patients, considerable time to complete, and can be prohibitively expensive. A safer, faster, less expensive alternative is using virtual imaging trials (VITs), utilizing virtual patients or phantoms combined with accurate computer models of imaging devices.

PURPOSE

In this work, we develop realistic, physiologically-informed models for coronary plaques for application in cardiac imaging VITs.

METHODS

Histology images of plaques at micron-level resolution were used to train a deep convolutional generative adversarial network (DC-GAN) to create a library of anatomically variable plaque models with clinical anatomical realism. The stability of each plaque was evaluated by finite element analysis (FEA) in which plaque components and vessels were meshed as volumes, modeled as specialized tissues, and subjected to the range of normal coronary blood pressures. To demonstrate the utility of the plaque models, we combined them with the whole-body XCAT computational phantom to perform initial simulations comparing standard energy-integrating detector (EID) CT with photon-counting detector (PCD) CT.

RESULTS

Our results show the network is capable of generating realistic, anatomically variable plaques. Our simulation results provide an initial demonstration of the utility of the generated plaque models as targets to compare different imaging devices.

CONCLUSIONS

Vast, realistic, and variable CAD pathologies can be generated to incorporate into computational phantoms for VITs. There they can serve as a known truth from which to optimize and evaluate cardiac imaging technologies quantitatively.

3D patient-specific modeling and structural finite element analysis of atherosclerotic carotid artery based on computed tomography angiography

The assessment of carotid plaque vulnerability is a relevant clinical information that can help prevent adverse cerebrovascular events. To this aim, in this study, we propose a patient-specific computational workflow to quantify the stress distribution in an atherosclerotic carotid artery, by means of geometric modeling and structural simulation of the plaque and vessel wall. Ten patients were involved in our study. Starting with segmentation of the lumen, calcific and lipid plaque components from computed tomography angiography images, the fibrous component and the vessel wall were semi-automatically reconstructed with an ad-hoc procedure. Finite element analyses were performed using local pressure values derived from ultrasound imaging. Simulation outputs were analyzed to assess how mechanical factors influence the stresses within the atherosclerotic wall. The developed reconstruction method was first evaluated by comparing the results obtained using the automatically generated fibrous component model and the one derived from image segmentation. The high-stress regions in the carotid artery wall around plaques suggest areas of possible rupture. In mostly lipidic and heterogeneous plaques, the highest stresses are localized at the interface between the lipidic components and the lumen, in the fibrous cap.

Fully automated construction of three-dimensional finite element simulations from Optical Coherence Tomography

Despite recent advances in diagnosis and treatment, atherosclerotic coronary artery diseases remain a leading cause of death worldwide. Various imaging modalities and metrics can detect lesions and predict patients at risk; however, identifying unstable lesions is still difficult. Current techniques cannot fully capture the complex morphology-modulated mechanical responses that affect plaque stability, leading to catastrophic failure and mute the benefit of device and drug interventions. Finite Element (FE) simulations utilizing intravascular imaging OCT (Optical Coherence Tomography) are effective in defining physiological stress distributions. However, creating 3D FE simulations of coronary arteries from OCT images is challenging to fully automate given OCT frame sparsity, limited material contrast, and restricted penetration depth. To address such limitations, we developed an algorithmic approach to automatically produce 3D FE-ready digital twins from labeled OCT images. The 3D models are anatomically faithful and recapitulate mechanically relevant tissue lesion components, automatically producing morphologies structurally similar to manually constructed models whilst including more minute details. A mesh convergence study highlighted the ability to reach stress and strain convergence with average errors of just 5.9% and 1.6% respectively in comparison to FE models with approximately twice the number of elements in areas of refinement. Such an automated procedure will enable analysis of large clinical cohorts at a previously unattainable scale and opens the possibility for in-silico methods for patient specific diagnoses and treatment planning for coronary artery disease.

Sample size considerations in soft tissue biomechanics

Biomechanical experiments help link tissue morphology with load-deformation characteristics. A tissue-dependent minimum sample number is indispensable to obtain accurate material properties. Stress-strain properties were retrieved from human dura mater and scalp skin, exemplifying two distinct soft tissues. Minimum sample sizes necessary for a stable estimation of material properties were obtained in a simulation study. One-thousand random samples were sequentially drawn for calculating the point at which a majority of the estimators settled within a corridor of stability at given tolerance levels around a 'complete' reference for the mean, median and coefficient of variation. Stable estimations of means and medians can be achieved below sample sizes of 30 at a ± 20%-tolerance within 80%-conformity for scalp skin and dura. Lower tolerance levels or higher conformity dramatically increase the required sample size. Conformity was barely ever reached for the coefficient of variation. The parameter type appears decisive for achieving conformity. STATEMENT OF SIGNIFICANCE: Biomechanical trials utilizing human tissues are needed to obtain material properties for surgical repair, tissue engineering and modeling purposes. Linking tissue mechanics with morphology helps elucidate form-function relationships, the 'morpho-mechanical link'. For material properties to be accurate, it is vital to examine a minimum number of samples. This number may vary between tissues, and the effects of intrinsic tissue characteristics on data accuracy are unclear to date. This study used data obtained from human dura and skin to compute minimum sample sizes required for estimating material properties at a stable level. It was shown that stable estimations are possible at a ± 20%-tolerance within 80%-conformity below sample sizes of 30. Higher accuracy warrants much higher sample sizes for most material properties.

Comparison of multilayer and single-layer coronary plaque models on stress/strain calculations based on optical coherence tomography images

Mechanical stress and strain conditions are closely related to atherosclerotic plaque progression and rupture and have been under intensive investigations in recent years. It is well known that arteries have a three-layer structure: intima, media and adventitia. However, in vivo image-based multilayer plaque models are not available in the current literature due to lack of multilayer image segmentation data. A multilayer segmentation and repairing technique was introduced to segment coronary plaque optical coherence tomography (OCT) image to obtain its three-layer vessel structure. A total of 200 OCT slices from 20 patients (13 male; 7 female) were used to construct multilayer and single-layer 3D thin-slice models to calculate plaque stress and strain and compare model differences. Our results indicated that the average maximum plaque stress values of 20 patients from multilayer and single-layer models were 385.13 ± 110.09 kPa and 270.91 ± 95.86 kPa, respectively. The relative difference was 42.2%, with single-layer stress serving as the base value. The average mean plaque stress values from multilayer and single-layer models were 129.59 ± 32.77 kPa and 93.27 ± 18.20 kPa, respectively, with a relative difference of 38.9%. The maximum and mean plaque strain values obtained from the multilayer models were 11.6% and 19.0% higher than those from the single-layer models. Similarly, the maximum and mean cap strains showed increases of 9.6% and 12.9% over those from the single-layer models. These findings suggest that use of multilayer models could improve plaque stress and strain calculation accuracy and may have large impact on plaque progression and vulnerability investigation and potential clinical applications. Further large-scale studies are needed to validate our findings.

Local Characterization of Collagen Architecture and Mechanical Failure Properties of Fibrous Plaque Tissue of Atherosclerotic Human Carotid Arteries

Atherosclerotic plaque rupture in carotid arteries is a major cause of cerebrovascular events. Plaque rupture is the mechanical failure of the heterogeneous fibrous plaque tissue. Local characterization of the tissue's failure properties and the collagen architecture are of great importance to have insights in plaque rupture for clinical event prevention. Previous studies were limited to average rupture properties and global structural characterization, and did not provide the necessary local information. In this study, we assessed the local collagen architecture and failure properties of fibrous plaque tissue, by analyzing 30 tissue strips from 18 carotid plaques. Our study framework entailed second harmonic generation imaging for local collagen orientation and dispersion, and uniaxial tensile testing and digital image correlation for local tissue mechanics. The results showed that 87% of the imaged locations had collagen orientation close to the circumferential direction (0°) of the artery, and substantial dispersion locally. All regions combined, median [Q1:Q3] of the predominant angle measurements was -2° [-16°:16°]. The stretch ratio measurements clearly demonstrated a nonuniform stretch ratio distribution in the tissue under uniaxial loading. The rupture initiation regions had significantly higher stretch ratios (1.26 [1.15-1.40]) than the tissue average stretch ratio (1.11 [1.10-1.16]). No significant difference in collagen direction and dispersion was identified between the rupture regions and the rest of the tissue. The presented study forms an initial step towards gaining better insights into the characterization of local structural and mechanical fingerprints of fibrous plaque tissue in order to aid improved assessment of plaque rupture risk. STATEMENT OF SIGNIFICANCE: Plaque rupture risk assessment, critical to prevent cardiovascular events, requires knowledge on local failure properties and structure of collagenous plaque tissue. Our current knowledge is unfortunately limited to tissue's overall ultimate failure properties with scarce information on collagen architecture. In this study, local failure properties and collagen architecture of fibrous plaque tissue were obtained. We found predominant circumferential alignment of collagen fibers with substantial local dispersion. The tissue showed nonuniform stretch distribution under uniaxial tensile loading, with high stretches at rupture spots. This study highlights the significance of local mechanical and structural assessment for better insights into plaque rupture and the potential use of local stretches as risk marker for plaque rupture for patient-specific clinical applications.

Coronary artery plaque rupture and erosion: Role of wall shear stress profiling and biological patterns in acute coronary syndromes

AIMS

Wall shear stress (WSS) is involved in coronary artery plaque pathological mechanisms and modulation of gene expression. This study aims to provide a comprehensive haemodynamic and biological description of unstable (intact-fibrous-cap, IFC, and ruptured-fibrous-cap, RFC) and stable (chronic coronary syndrome, CCS) plaques and investigate any correlation between WSS and molecular pathways.

METHODS AND RESULTS

We enrolled 24 CCS and 25 Non-ST Elevation Myocardial Infarction-ACS patients with IFC (n = 11) and RFC (n = 14) culprit lesions according to optical coherence tomography analysis. A real-time PCR primer array was performed on peripheral blood mononuclear cells for 17 different molecules whose expression is linked to WSS. Computational fluid dynamics simulations were performed in high-fidelity 3D-coronary artery anatomical models for three patients per group. A total of nine genes were significantly overexpressed in the unstable patients as compared to CCS patients, with no differences between IFC and RFC groups (GPX1, MMP1, MMP9, NOS3, PLA2G7, PI16, SOD1, TIMP1, and TFRC) while four displayed different levels between IFC and RFC groups (TNFα, ADAMTS13, EDN1, and LGALS8). A significantly higher WSS was observed in the RFC group (p < 0.001) compared to the two other groups. A significant correlation was observed between TNFα (p < 0.001), EDN1 (p = 0.036), and MMP9 (p = 0.005) and WSS values in the RFC group.

CONCLUSIONS

Our data demonstrate that IFC and RFC plaques are subject to different WSS conditions and gene expressions, suggesting that WSS profiling may play an essential role in the plaque instability characterization with relevant diagnostic and therapeutic implications in the era of precision medicine.

Human Coronary Plaque Optical Coherence Tomography Image Repairing, Multilayer Segmentation and Impact on Plaque Stress/Strain Calculations

Coronary vessel layer structure may have a considerable impact on plaque stress/strain calculations. Most current plaque models use single-layer vessel structures due to the lack of available multilayer segmentation techniques. In this paper, an automatic multilayer segmentation and repair method was developed to segment coronary optical coherence tomography (OCT) images to obtain multilayer vessel geometries for biomechanical model construction. Intravascular OCT data were acquired from six patients (one male; mean age: 70.0) using a protocol approved by the local institutional review board with informed consent obtained. A total of 436 OCT slices were selected in this study. Manually segmented data were used as the gold standard for method development and validation. The edge detection method and cubic spline surface fitting were applied to detect and repair the internal elastic membrane (IEM), external elastic membrane (EEM) and adventitia-periadventitia interface (ADV). The mean errors of automatic contours compared to manually segmented contours were 1.40%, 4.34% and 6.97%, respectively. The single-layer mean plaque stress value from lumen was 117.91 kPa, 10.79% lower than that from three-layer models (132.33 kPa). On the adventitia, the single-layer mean plaque stress value was 50.46 kPa, 156.28% higher than that from three-layer models (19.74 kPa). The proposed segmentation technique may have wide applications in vulnerable plaque research.

Mechanical and histological characteristics of aortic dissection tissues

AIMS

This study investigated the association between the macroscopic mechanical response of aortic dissection (AoD) flap, its fibre features, and patient physiological features and clinical presentations.

METHODS

Uniaxial test was performed with tissue strips in both circumferential and longitudinal directions from 35 patients with (AoD:CC) and without (AoD:w/oCC) cerebral/coronary complications, and 19 patients with rheumatic or valve-related heart diseases (RH). A Bayesian inference framework was used to estimate the expectation of material constants (C₁, D₁, and D₂) of the modified Mooney-Rivlin strain energy density function. Histological examination was used to visualise the elastin and collagen in the tissue strips and image processing was performed to quantify their area percentages, fibre misalignment and waviness.

RESULTS

The elastin area percentage was negatively associated with age (p = 0.008), while collagen increased about 6% from age 40 to 70 (p = 0.03). Elastin fibre was less dispersed and wavier in old patients and no significant association was found between patient age and collagen fibre dispersion or waviness. Features of fibrous microstructures, either elastin or collagen, were comparable between AoD:CC and AoD:w/oCC group. Elastin and collagen area percentages were positively correlated with C₁ and D₂, respectively, while the elastin and collagen waviness were negatively correlated with C₁ and D₂, respectively. Elastin dispersion was negatively correlated to D₂. Multivariate analysis showed that D₂ was an effective parameter which could differentiate patient groups with different age and clinical presentations, as well as the direction of tissue strip.

CONCLUSION

Fibre dispersion and waviness in the aortic dissection flap changed with patient age and clinical presentations, and these can be captured by the material constants in the strain energy density function.

STATEMENT OF SIGNIFICANCE

Aortic dissection (AoD) is a severe cardiovascular disease. Understanding the mechanical property of intimal flap is essential for its risk evaluation. In this study, mechanical testing and histology examination were combined to quantify the relationship between mechanical presentations and microstructure features. A Bayesian inference framework was employed to estimate the expectation of the material constants in the modified Mooney-Rivlin constitutive equation. It was found that fibre dispersion and waviness in the AoD flap changed with patient age and clinical presentations, and these could be captured by the material constants. This study firstly demonstrated that the expectation of material constants can be used to characterise tissue microstructures and differentiate patients with different clinical presentations.

Investigating the effects of external pressure on coronary arteries with plaques and its role in coronary artery disease

The risk of an acute coronary event stems from the amount and type of plaque present, as well as the fluid and structural dynamics in the coronary artery. If the plaque's structural stress exceeds the mechanical strength, the fibrous cap may rupture and lead to thrombosis. The patient is then likely to face a sudden myocardial infarction. An association between Coronary Heart Disease (CHD) and Sudden Cardiac Death (SCD) has been long recognised. For the first time, we are reporting a correlation between applied external pressure, such as Cardiopulmonary Resuscitation (CPR), coughing, sneezing, blowing one's nose, etc., and diseased coronary artery plaque via 3 D coronary artery models and two-way Fluid-Solid Interaction (FSI) models. Shear and von Mises stresses inside arteries and plaques have been shown to play a major role in plaque development, progression of disease, and the likelihood of plaque rupture. Our results show a drastic change in maximum shear (300%) and von Mises stresses (500%) with increasing external pressure. This change may indicate an onset of imminent plaque rupture. Furthermore, FSI modelling indicates a strong correlation between plaque thickness, location, and external pressure. With further clinical and simulation studies, this information could be helpful in understanding potential limit pressure in the CPR process for patients with CHD.

The relationship between Hemoglobin A1c and the maximal plaque stress of culprit ruptured plaques in patients with ST-segment elevated myocardial infarction

BACKGROUND

Plaque rupture occurs when the structural stress inside plaques exceeds the capacity of the overlying fibrous cap. Plaque structural stress has been acknowledged as an index to evaluate the risk of plaque rupture. However, impacting factors associated with the level of plaque structural stress in ST-segment elevated myocardial infarction patients with ruptured plaques remain unknown.

METHODS

Based on optical coherence tomography, we analyzed the plaque characteristics and calculated the maximal plaque stress of the culprit lesions in 162 patients with plaque rupture by performing finite element analysis. All enrolled patients were divided into two groups according to the level of maximal plaque stress. Cardiovascular risk factors, laboratory findings and clinical outcomes were compared between the two groups.

RESULTS

Hemoglobin A1c (HbA1c) was significantly higher in the high stress group than in the low stress group (7.0% ± 1.8 vs. 6.3% ± 1.2, p = 0.003). The maximal plaque stress of patients with diabetes was significantly higher than that of patients without diabetes (538.7 kPa [346.2-810.6] vs. 425.9 kPa [306.2-571.4], p = 0.006). Moreover, the level of maximal plaque stress was significantly associated with HbA1c (Pearson's correlation coefficient: r = 0.289, P < 0.001). OCT findings showed that the fibrous cap thickness and maximal lipid arc were significantly associated with maximal plaque stress (r = -0.163, p = 0.038; r = 0.194, p = 0.013, respectively).

CONCLUSION

OCT-based finite-element analysis showed that HbA1c was independently associated with the level of maximal plaque stress in STEMI patients with plaque rupture, thus indicating the importance of glucose control in patients with coronary atherosclerotic disease.

Proximal Region of Carotid Atherosclerotic Plaque Shows More Intraplaque Hemorrhage: The Plaque at Risk Study

BACKGROUND AND PURPOSE

Intraplaque hemorrhage contributes to lipid core enlargement and plaque progression, leading to plaque destabilization and stroke. The mechanisms that contribute to the development of intraplaque hemorrhage are not completely understood. A higher incidence of intraplaque hemorrhage and thin/ruptured fibrous cap (upstream of the maximum stenosis in patients with severe [≥70%] carotid stenosis) has been reported. We aimed to noninvasively study the distribution of intraplaque hemorrhage and a thin/ruptured fibrous cap in patients with mild-to-moderate carotid stenosis.

MATERIALS AND METHODS

Eighty-eight symptomatic patients with stroke (<70% carotid stenosis included in the Plaque at Risk study) demonstrated intraplaque hemorrhage on MR imaging in the carotid artery plaque ipsilateral to the side of TIA/stroke. The intraplaque hemorrhage area percentage was calculated. A thin/ruptured fibrous cap was scored by comparing pre- and postcontrast black-blood TSE images. Differences in mean intraplaque hemorrhage percentages between the proximal and distal regions were compared using a paired-samples t test. The McNemar test was used to reveal differences in proportions of a thin/ruptured fibrous cap.

RESULTS

We found significantly larger areas of intraplaque hemorrhage in the proximal part of the plaque at 2, 4, and 6 mm from the maximal luminal narrowing, respectively: 14.4% versus 9.6% (P = .04), 14.7% versus 5.4% (P < .001), and 11.1% versus 2.2% (P = .001). Additionally, we found an increased proximal prevalence of a thin/ruptured fibrous cap on MR imaging at 2, 4, 6, and 8 mm from the MR imaging section with the maximal luminal narrowing, respectively: 33.7% versus 18.1%, P = .007; 36.1% versus 7.2%, P < .001; 33.7% versus 2.4%, P = .001; and 30.1% versus 3.6%, P = .022.

CONCLUSIONS

We demonstrated that intraplaque hemorrhage and a thin/ruptured fibrous cap are more prevalent on the proximal side of the plaque compared with the distal side in patients with mild-to-moderate carotid stenosis.

Collagen Fibril Orientation in Tissue Specimens From Atherosclerotic Plaque Explored Using Small Angle X-Ray Scattering

Atherosclerotic plaques can gradually develop in certain arteries. Disruption of fibrous tissue in plaques can result in plaque rupture and thromboembolism, leading to heart attacks and strokes. Collagen fibrils are important tissue building blocks and tissue strength depends on how fibrils are oriented. Fibril orientation in plaque tissue may potentially influence vulnerability to disruption. While X-ray scattering has previously been used to characterize fibril orientations in soft tissues and bones, it has never been used for characterization of human atherosclerotic plaque tissue. This study served to explore fibril orientation in specimens from human plaques using small angle X-ray scattering (SAXS). Plaque tissue was extracted from human femoral and carotid arteries, and each tissue specimen contained a region of calcified material. Three-dimensional (3D) collagen fibril orientation was determined along scan lines that started away from and then extended toward a given calcification. Fibrils were found to be oriented mainly in the circumferential direction of the plaque tissue at the majority of locations away from calcifications. However, in a number of cases, the dominant fibril direction differed near a calcification, changing from circumferential to longitudinal or thickness (radial) directions. Further study is needed to elucidate how these fibril orientations may influence plaque tissue stress-strain behavior and vulnerability to rupture.

Constitutive models and failure properties of fibrous tissues of carotid artery atheroma based on their uniaxial testing

To obtain an experimental background for the description of mechanical properties of fibrous tissues of carotid atheroma, a cohort of 141 specimens harvested from 44 patients during endarterectomies, were tested. Uniaxial stress-strain curves and ultimate stress and strain at rupture were recorded. With this cohort, the impact of the direction of load, presence of calcifications, specimen location, patient's age and sex were investigated. A significant impact of sex was revealed for the stress-strain curves and ultimate strains. The response was significantly stiffer for females than for males but, in contrast to ultimate strain, the strength was not significantly different. The differences in strength between calcified and non-calcified atheromas have reached statistical significance in the female group. At most of the analysed stress levels, the loading direction was found significant for the male cohort which was also confirmed by large differences in ultimate strains. The representative uniaxial stress-strain curves (given by median values of strains at chosen stress levels) were fitted with an isotropic hyperelastic model for different groups specified by the investigated factors while the observed differences between circumferential and longitudinal direction were captured by an anisotropic hyperelastic model. The obtained results should be valid also for the tissue of the fibrous cap, the rupture of which is to be predicted in clinics using computational modelling because it may induce arterial thrombosis and consequently a brain stroke.

A computational multilayer model to simulate hollow needle insertion into biological porcine liver tissue

Modelling of needle insertion in soft tissue has developed significant interest in recent years due to its application in robot-assisted minimally invasive surgeries such as biopsies and brachytherapy. However, this type of surgery requires real-time feedback and processing which complex computational models may not be able to provide. In contrast to the existing mechanics-based kinetic models, a simple multilayer tissue model using a Coupled Eulerian Lagrangian based Finite Element method has been developed using the dynamic principle. The model simulates the needle motion for flexible hollow bevel-angled needle (15° and 30°, 22 Gauge) insertion into porcine liver tissue, which includes material parameters obtained from unconfined compression testing of porcine liver tissue. To validate simulation results, needle insertion force and cutting force within porcine liver tissue were compared with corresponding experimental results obtained from a custom-built needle insertion system. For the 15° and 30° bevel-angle needles, the percentage error for cutting force (mean) of each needle compared to computational model, were 18.7% and 11.9% respectively. Varying the needle bevel angle from 30° to 15° results in an increase of the cutting force, but insertion force does not vary among the tested bevel angles. The validation of this computationally efficient multilayer Finite Element model can help engineers to better understand the biomechanical behaviour of medical needle inside soft biological tissue. Ultimately, this multilayer approach can help advance state-of-art clinical applications such as robot-assisted surgery that requires real-time feedback and processing. STATEMENT OF SIGNIFICANCE: The significance of the work is in confirming the effectiveness of multilayer material based finite element (FE) method to model biopsy needle insertion into soft biological porcine liver tissue. A multilayer Coupled Eulerian Lagrangian (CEL) based FE modelling technique allowed testing of heterogeneous, non-linear viscoelastic porcine liver tissue in a system, so direct comparison of needle tissue interaction forces on the intrinsic material (tissue) behaviour could be made. To the best of the authors' knowledge, the present research investigates for the first time modelling of a three dimensional (3D) hollow needle insertion using a multilayer stiffness model of biological tissue using FE based CEL method and presents a comparison of simulation results with experimental data.

Multicomponent material property characterization of atherosclerotic human carotid arteries through a Bayesian Optimization based inverse finite element approach

OBJECTIVE

Plaque rupture in atherosclerotic carotid arteries is a main cause of ischemic stroke and it is correlated with high plaque stresses. Hence, analyzing stress patterns is essential for plaque specific rupture risk assessment. However, the critical information of the multicomponent material properties of atherosclerotic carotid arteries is still lacking greatly. This work aims to characterize component-wise material properties of atherosclerotic human carotid arteries under (almost) physiological loading conditions.

METHODS

An inverse finite element modeling (iFEM) framework was developed to characterize fibrous intima and vessel wall material properties of 13 cross sections from five carotids. The novel pipeline comprised ex-vivo inflation testing, pre-clinical high frequency ultrasound for deriving plaque deformations, pre-clinical high-magnetic field magnetic resonance imaging, finite element modeling, and a sample efficient machine learning based Bayesian Optimization.

RESULTS

The nonlinear Yeoh constants for the fibrous intima and wall layers were successfully obtained. The optimization scheme of the iFEM reached the global minimum with a mean error of 3.8% in 133 iterations on average. The uniqueness of the results were confirmed with the inverted Gaussian Process (GP) model trained during the iFEM protocol.

CONCLUSION

The developed iFEM approach combined with the inverted GP model successfully predicted component-wise material properties of intact atherosclerotic human carotids ex-vivo under physiological-like loading conditions.

SIGNIFICANCE

We developed a novel iFEM framework for the nonlinear, component-wise material characterization of atherosclerotic arteries and utilized it to obtain human atherosclerotic carotid material properties. The developed iFEM framework has great potential to be advanced for patient-specific in-vivo application.

An inverse method for mechanical characterization of heterogeneous diseased arteries using intravascular imaging

The increasing prevalence of finite element (FE) simulations in the study of atherosclerosis has spawned numerous inverse FE methods for the mechanical characterization of diseased tissue in vivo. Current approaches are however limited to either homogenized or simplified material representations. This paper presents a novel method to account for tissue heterogeneity and material nonlinearity in the recovery of constitutive behavior using imaging data acquired at differing intravascular pressures by incorporating interfaces between various intra-plaque tissue types into the objective function definition. Method verification was performed in silico by recovering assigned material parameters from a pair of vessel geometries: one derived from coronary optical coherence tomography (OCT); one generated from in silico-based simulation. In repeated tests, the method consistently recovered 4 linear elastic (0.1 ± 0.1% error) and 8 nonlinear hyperelastic (3.3 ± 3.0% error) material parameters. Method robustness was also highlighted in noise sensitivity analysis, where linear elastic parameters were recovered with average errors of 1.3 ± 1.6% and 8.3 ± 10.5%, at 5% and 20% noise, respectively. Reproducibility was substantiated through the recovery of 9 material parameters in two more models, with mean errors of 3.0 ± 4.7%. The results highlight the potential of this new approach, enabling high-fidelity material parameter recovery for use in complex cardiovascular computational studies.

Influence of balloon design, plaque material composition, and balloon sizing on acute post angioplasty outcomes: An implicit finite element analysis

In this work we propose a generic modeling approach for simulating percutaneous transluminal angioplasty (PTA) endovascular treatment, and evaluating the influence of balloon design, plaque composition, and balloon sizing on acute post-procedural outcomes right after PTA, without stent implantation. Clinically-used PTA balloons were classified into two categories according to their compliance characteristics, and were modeled correspondingly. Self-defined elastoplastic constitutive laws were implemented within the plaque and artery models, after calibration based on experimental and clinical data. Finite element method (FEM) implicit solver was used to simulate balloon inflation and deflation. Besides balloon profile at max inflation, results are mainly assessed in terms of the elastic recoil ratio (ERR) and lumen gain ratio (LGR) obtained immediately after PTA. No variations in ERR nor LGR values were detected when the balloon design changed, despite the differences observed in their profile at max inflation. Moreover, LGR and ERR inversely varied with the augmentation of calcification level within the plaque (-11% vs. +4% respectively, from fully lipidic to fully calcified plaque). Furthermore, results showed a direct correlation between balloon sizing and LGR and ERR, with noticeably higher rates of change for LGR (+18% and +2% for LGR and ERR respectively for a calcified plaque and a balloon pressure increasing from 10 to 14 atm). However a larger LGR comes with a higher risk of arterial rupture. This proposed methodology opens the way for evaluation of angioplasty balloon selections towards clinical procedure optimization.

Angiography-Based 4-Dimensional Superficial Wall Strain and Stress: A New Diagnostic Tool in the Catheterization Laboratory

A novel method for four-dimensional superficial wall strain and stress (4D-SWS) is derived from the arterial motion as pictured by invasive coronary angiography. Compared with the conventional finite element analysis of cardiovascular biomechanics using the estimated pulsatile pressure, the 4D-SWS approach can calculate the dynamic mechanical state of the superficial wall in vivo, which could be directly linked with plaque rupture or stent fracture. The validation of this approach using in silico models showed that the distribution and maximum values of superficial wall stress were similar to those calculated by conventional finite element analysis. The in vivo deformation was validated on 16 coronary arteries, from the comparison of centerlines predicted by the 4D-SWS approach against the actual centerlines reconstructed from angiograms at a randomly selected time-point, which demonstrated a good agreement of the centerline morphology between both approaches (scaling: 0.995 ± 0.018 and dissimilarity: 0.007 ± 0.014). The in silico vessel models with softer plaque and larger plaque burden presented more variation in mean lumen diameter and resulted in higher superficial wall stress. In more than half of the patients (n = 16), the maximum superficial wall stress was found at the proximal lesion shoulder. Additionally, in three patients who later suffered from acute coronary syndrome, the culprit plaque rupture sites co-localized with the site of highest superficial wall stress on their baseline angiography. These representative cases suggest that angiography-based superficial wall dynamics have the potential to identify coronary segments at high-risk of plaque rupture and fracture sites of implanted stents. Ongoing studies are focusing on identifying weak spots in coronary bypass grafts, and on exploring the biomechanical mechanisms of coronary arterial remodeling and aneurysm formation. Future developments involve integration of fast computational techniques to allow online availability of superficial wall strain and stress in the catheterization laboratory.

Multi-patient study for coronary vulnerable plaque model comparisons: 2D/3D and fluid-structure interaction simulations

Several image-based computational models have been used to perform mechanical analysis for atherosclerotic plaque progression and vulnerability investigations. However, differences of computational predictions from those models have not been quantified at multi-patient level. In vivo intravascular ultrasound (IVUS) coronary plaque data were acquired from seven patients. Seven 2D/3D models with/without circumferential shrink, cyclic bending and fluid–structure interactions (FSI) were constructed for the seven patients to perform model comparisons and quantify impact of 2D simplification, circumferential shrink, FSI and cyclic bending plaque wall stress/strain (PWS/PWSn) and flow shear stress (FSS) calculations. PWS/PWSn and FSS averages from seven patients (388 slices for 2D and 3D thin-layer models) were used for comparison. Compared to 2D models with shrink process, 2D models without shrink process overestimated PWS by 17.26%. PWS change at location with greatest curvature change from 3D FSI models with/without cyclic bending varied from 15.07% to 49.52% for the seven patients (average = 30.13%). Mean Max-FSS, Min-FSS and Ave-FSS from the flow-only models under maximum pressure condition were 4.02%, 11.29% and 5.45% higher than those from full FSI models with cycle bending, respectively. Mean PWS and PWSn differences between FSI and structure-only models were only 4.38% and 1.78%. Model differences had noticeable patient variations. FSI and flow-only model differences were greater for minimum FSS predictions, notable since low FSS is known to be related to plaque progression. Structure-only models could provide PWS/PWSn calculations as good approximations to FSI models for simplicity and time savings in calculation.

Extraction of Coronary Atherosclerotic Plaques From Computed Tomography Imaging: A Review of Recent Methods

Background: Atherosclerotic plaques are the major cause of coronary artery disease (CAD). Currently, computed tomography (CT) is the most commonly applied imaging technique in the diagnosis of CAD. However, the accurate extraction of coronary plaque geometry from CT images is still challenging.

Summary of Review: In this review, we focused on the methods in recent studies on the CT-based coronary plaque extraction. According to the dimension of plaque extraction method, the studies were categorized into two-dimensional (2D) and three-dimensional (3D) ones. In each category, the studies were analyzed in terms of data, methods, and evaluation. We summarized the merits and limitations of current methods, as well as the future directions for efficient and accurate extraction of coronary plaques using CT imaging.

Conclusion: The methodological innovations are important for more accurate CT-based assessment of coronary plaques in clinical applications. The large-scale studies, de-blooming algorithms, more standardized datasets, and more detailed classification of non-calcified plaques could improve the accuracy of coronary plaque extraction from CT images. More multidimensional geometric parameters can be derived from the 3D geometry of coronary plaques. Additionally, machine learning and automatic 3D reconstruction could improve the efficiency of coronary plaque extraction in future studies.

Mechanical Properties of the Cranial Meninges: A Systematic Review

The meninges are membranous tissues that are pivotal in maintaining homeostasis of the central nervous system. Despite the importance of the cranial meninges in nervous system physiology and in head injury mechanics, our knowledge of the tissues' mechanical behavior and structural composition is limited. This systematic review analyzes the existing literature on the mechanical properties of the meningeal tissues. Publications were identified from a search of Scopus, Academic Search Complete, and Web of Science and screened for eligibility according to Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. The review details the wide range of testing techniques employed to date and the significant variability in the observed experimental findings. Our findings identify many gaps in the current literature that can serve as a guide for future work for meningeal mechanics investigators. The review identifies no peer-reviewed mechanical data on the falx and tentorium tissues, both of which have been identified as key structures in influencing brain injury mechanics. A dearth of mechanical data for the pia-arachnoid complex also was identified (no experimental mechanics studies on the human pia-arachnoid complex were identified), which is desirable for biofidelic modeling of human head injuries. Finally, this review provides recommendations on how experiments can be conducted to allow for standardization of test methodologies, enabling simplified comparisons and conclusions on meningeal mechanics.

[Calcification and atherosclerosis of the coronary arteries]

Calcification is a very common phenomenon in the coronary arteries, which is part of the atherosclerotic process, and the degree of calcification can predict clinical outcomes in patients at high risk of coronary events. Both the degree of calcification and the patterns of its distribution are of prognostic importance, but the relationship of coronary artery calcification with atherosclerotic plaque instability is extremely complex and not fully understood. This article is devoted to the study of calcification markers and their influence on the development of atherosclerotic foci.

Rupture Risk Assessment of Cervical Spinal Manipulations on Carotid Atherosclerotic Plaque by a 3D Fluid-Structure Interaction Model

Method

The FSI model, based on MRI data of an atherosclerosis patient, was used to simulate the deformations of the plaque and lumen during the process of two kinds of typical cSMT (the high-speed, low-amplitude spinal manipulation and the cervical rotatory manipulation). The biomechanical parameters were recorded, such as the highest wall shear stress (WSS), the maximum plaque wall stress (PWS), the wall tensile stress (Von mises stress, VWTS), and the strain.

Result

The max_WSS was 33.77 kPa in the most extensive deformation. The highest WSS region on the plaque surface was also the highest PWS region. The max_PWS in a 12% stretch was 55.11 kPa, which was lower than the rupture threshold. The max_VWTS of the cap in 12% stretch which approached the fracture stress level was 116.75 kPa. Moreover, the vessel's max_VWTS values in 10% and 12% stretch were 554.21 and 855.19 kPa. They were higher than the fracture threshold, which might cause media fracture. Meanwhile, the 7% stretched strain was 0.29, closed to the smallest experimental green strains at rupture.

Conclusion

The carotid arteries' higher stretch generated the higher stress level of the plaque. Cervical rotatory manipulation might cause plaque at a high risk of rupture in deformation after 12% stretch and more. Lower deformation of the plaque and artery caused by the high-speed, low-amplitude spinal manipulation might be safer.

The influence of angioplasty balloon sizing on acute post-procedural outcomes: a Finite Element Analysis

Atherosclerosis is one of the most common vascular pathologies in the world. Among the most commonly performed endovascular treatments, percutaneous transluminal angioplasty (PTA) has been showing significantly positive clinical outcomes. Due to the complex geometries, material properties and interactions that characterize PTA procedures, finite element analyses of acute angioplasty balloon deployment are limited. In this work, finite element method (FEM) was used to simulate the inflation and deflation of a semi-compliant balloon within the 3D model of a stenosed artery with two different plaque types (lipid and calcified). Self-defined constitutive models for the balloon and the plaque were developed based on experimental and literature data respectively. Balloon deployment was simulated at three different inflation pressures (10, 12 and 14 atm) within the two plaque types. Balloon sizing influence on the arterial elastic recoil obtained immediately after PTA was then investigated. The simulated results show that calcified plaques may lead to higher elastic recoil ratios compared to lipid stenosis, when the same balloon inflation pressures are applied. Also, elastic recoil increases for higher balloon inflation pressure independent of the plaque type. These findings open the way for a data-driven assessment of angioplasty balloon sizing selection and clinical procedures optimization.Clinical Relevance- The FE model developed in this work aims at providing quantitative evaluation of recoil after balloon angioplasty. It may be useful for both manufacturers and clinicians to improve efficiency of angioplasty balloon device design and sizing selection with respect to plaque geometry and constitution, consequently enhancing clinical outcomes.

Consideration of stiffness of wall layers is decisive for patient-specific analysis of carotid artery with atheroma

The paper deals with the impact of chosen geometric and material factors on maximal stresses in carotid atherosclerotic plaque calculated using patient-specific finite element models. These stresses are believed to be decisive for the plaque vulnerability but all applied models suffer from inaccuracy of input data, especially when obtained in vivo only. One hundred computational models based on ex vivo MRI are used to investigate the impact of wall thickness, MRI slice thickness, lipid core and fibrous tissue stiffness, and media anisotropy on the calculated peak plaque and peak cap stresses. The investigated factors are taken as continuous in the range based on published experimental results, only the impact of anisotropy is evaluated by comparison with a corresponding isotropic model. Design of Experiment concept is applied to assess the statistical significance of these investigated factors representing uncertainties in the input data of the model. The results show that consideration of realistic properties of arterial wall in the model is decisive for the stress evaluation; assignment of properties of fibrous tissue even to media and adventitia layers as done in some studies may induce up to eightfold overestimation of peak stress. The impact of MRI slice thickness may play a key role when local thin fibrous cap is present. Anisotropy of media layer is insignificant, and the stiffness of fibrous tissue and lipid core may become significant in some combinations.

Numerical simulations of patient-specific models with multiple plaques in human peripheral artery: a fluid-structure interaction analysis

Atherosclerotic plaque in the femoral is the leading cause of peripheral artery disease (PAD), the worse consequence of which may lead to ulceration and gangrene of the feet. Numerical studies on fluid-structure interactions (FSI) of atherosclerotic femoral arteries enable quantitative analysis of biomechanical features in arteries. This study aims to investigate the hemodynamic performance and its interaction with femoral arterial wall based on the patient-specific model with multiple plaques (calcified and lipid plaques). Three types of models, calcification-only, lipid-only and calcification-lipid models, are established. Hyperelastic material coefficients of the human femoral arteries obtained from experimental studies are employed for all simulations. Oscillation of WSS is observed in the healthy downstream region in the lipid-only model. The pressure around the plaques in the two-plaque model is lower than that in the corresponding one-plaque models due to the reduction of blood flow domain, which consequently diminishes the loading forces on both plaques. Therefore, we found that stress acting on the plaques in the two-plaque model is lower than that in the corresponding one-plaque models. This finding implies that the lipid plaque, accompanied by the calcified plaque around, might reduce its risk of rupture due to the reduced the stress acting on it.

Stress-Relaxation and Cyclic Behavior of Human Carotid Plaque Tissue

Atherosclerotic plaque rupture is a catastrophic event that contributes to mortality and long-term disability. A better understanding of the plaque mechanical behavior is essential for the identification of vulnerable plaques pre-rupture. Plaque is subjected to a natural dynamic mechanical environment under hemodynamic loading. Therefore, it is important to understand the mechanical response of plaque tissue under cyclic loading conditions. Moreover, experimental data of such mechanical properties are fundamental for more clinically relevant biomechanical modeling and numerical simulations for risk stratification. This study aims to experimentally and numerically characterize the stress-relaxation and cyclic mechanical behavior of carotid plaque tissue. Instron microtester equipped with a custom-developed setup was used for the experiments. Carotid plaque samples excised at endarterectomy were subjected to uniaxial tensile, stress-relaxation, and cyclic loading protocols. Thirty percent of the underlying load level obtained from the uniaxial tensile test results was used to determine the change in mechanical properties of the tissue over time under a controlled testing environment (Control tests). The stress-relaxation test data was used to calibrate the hyperelastic (neo-Hookean, Ogden, Yeoh) and linear viscoelastic (Prony series) material parameters. The normalized relaxation force increased initially and slowly stabilized toward the end of relaxation phase, highlighting the viscoelastic behavior. During the cyclic tests, there was a decrease in the peak force as a function of the cycle number indicating mechanical distension due to repeated loading that varied with different frequencies. The material also accumulated residual deformation, which increased with the cycle number. This trend showed softening behavior of the samples. The results of this preliminary study provide an enhanced understanding of in vivo stress-relaxation and cyclic behavior of the human atherosclerotic plaque tissue.

Biomechanical Stress Profiling of Coronary Atherosclerosis: Identifying a Multifactorial Metric to Evaluate Plaque Rupture Risk

OBJECTIVES

The purpose of this study was to derive a biomechanical stress metric that was based on the multifactorial assessment of coronary plaque morphology, likely related to the propensity of plaque rupture in patients.

BACKGROUND

Plaque rupture, the most frequent cause of coronary thrombosis, occurs at locations of elevated tensile stress in necrotic core fibroatheromas (NCFAs). Finite element modeling (FEM), typically used to calculate tensile stress, is computationally intensive and impractical as a clinical tool for locating rupture-prone plaques. This study derived a multifactorial stress equation (MSE) that accurately computes peak stress in NCFAs by combining the influence of several morphological parameters.

METHODS

Intravascular ultrasound and optical frequency domain imaging were conducted in 30 patients, and plaque morphological parameters were defined in 61 NCFAs. Multivariate regression analysis was applied to derive the MSE and compute a peak stress metric (PSM) that was based on the analysis of plaque morphological parameters. The accuracy of the MSE was determined by comparing PSM with FEM-derived peak stress values. The ability of the PSM in locating plaque rupture sites was tested in 3 additional patients.

RESULTS

The following parameters were found to be independently associated with peak stress: fibrous cap thickness (p < 0.0001), necrotic core angle (p = 0.024), necrotic core thickness (p < 0.0001), lumen area (p < 0.0001), necrotic core including calcium areas (p = 0.017), and plaque area (p = 0.003). The PSM showed excellent correlation (R = 0.85; p < 0.0001) with FEM-derived peak stress, thus confirming the accuracy of the MSE. In only 56% (n = 34) of plaques, the thinnest fibrous cap thickness was a determining parameter in identifying the cross section with highest PSM. In coronary segments with plaque ruptures, the MSE precisely located the rupture site.

CONCLUSIONS

The MSE shows potential to calculate the PSM in coronary lesions rapidly. However, further studies are warranted to investigate the use of biomechanical stress profiling for the prognostic evaluation of patients with atherosclerosis.

Assessment of mechanical indicators of carotid plaque vulnerability: Geometrical curvature metric, plaque stresses and damage in tissue fibres

Stroke is a major cause of death worldwide. The rupture of atherosclerotic carotid plaques is the leading single cause of stroke. Currently there is no accepted clinical measure to quantitatively assess the risk of carotid plaque rupture. Structural analyses of vulnerable plaques, using finite element (FE) analysis, have retrospectively found that regions of high stress tend to be the site of plaque rupture. The current study proposes a new clinical measure, based on plaque geometry, to assess the risk of carotid plaque rupture. This measure, named the weighted curvature difference, is based on the curvature of both the lumen and intima-media boundary, and the local plaque thickness. A series of idealized and realistic, 2-D and 3-D geometries are used to systematically assess this novel geometrical metric. The areas predicted to be at high risk of rupture using this geometrical metric are compared with areas of high stress, obtained from both isotropic and anisotropic material models. These results are also compared with areas in diseased carotid arteries that are predicted to have high damage accumulation in collagen fibres using a continuum damage model. Results show the new geometrical metric consistently predicts the locations of high stress in all of the vessel geometries examined. The drawbacks of using lumen curvature only as a risk measure are highlighted; particularly in the case of outward remodelled vessels. Weighted curvature difference shows great potential to be used as a metric to efficiently distinguish the rupture prone areas in a diseased vessels in a way that is independent of material properties.

Different histological types of active intraplaque calcification underlie alternative miRNA-mRNA axes in carotid atherosclerotic disease

Arterial calcification is an actively regulated process, with different morphological manifestations. Micro-RNAs emerged as potential regulators of vascular calcification; they may become novel diagnostic tools and be used for a finest staging of the carotid plaque progression. The present study aimed at characterizing the different miRNA-mRNA axes in carotid plaques according to their histological patterns of calcification. Histopathological analysis was performed on 124 retrospective carotid plaques, with clinical data and preoperatory angio-CT. miRNA analysis was carried out with microfluidic cards. Real-time PCR was performed for selected miRNAs validation and for RUNX-2 and SOX-9 mRNA levels. CD31, CD68, SMA, and SOX-9 were analyzed by immunohistochemistry. miRNA levels on HUVEC cells were analyzed for confirming results under in vitro osteogenic conditions. Histopathological analysis revealed two main calcification subtypes of plaques: calcific cores (CC) and protruding nodules (PN). miRNA array and PCR validation of miR-1275, miR-30a-5p, and miR-30d indicated a significant upregulation of miR-30a-5p and miR-30d in the PN plaques. Likewise, the miRNA targets RUNX-2 and SOX-9 resulted poorly expressed in PN plaques. The inverse correlation between miRNA and RUNX-2 levels was confirmed on osteogenic-differentiated HUVEC. miR-30a-5p and miR-30d directly correlated with calcification extension and thickness at angio-CT imaging. Our study demonstrated the presence of two distinct morphological subtypes of calcification in carotid atheromatous plaques, supported by different miRNA signatures, and by different angio-CT features. These results shed the light on the use of miRNA as novel diagnostic markers, suggestive of plaque evolution.

The Geometric Effects on the Stress of Arterial Atherosclerotic Plaques: a Computational Study

BACKGROUND

The rupture of atherosclerotic plaques could cause serious clinical events. The wall shear stress (WSS) and axial plaque stress (APS) could reflect the risk of plaque rupture. This study aimed to quantitatively investigate the geometric effects on WSS and APS using computational fluid dynamics (CFD).

METHODS

63 plaque models were developed from three severities (75%, 82%, and 89% in area), three eccentricities (the deviation of plaque throat from the arterial centerline: 0, 0.375 and 0.75mm), and 7 different length combinations of the proximal and distal stenotic segments (2mm-5mm, 3mm-5mm, 4mm-5mm, 5mm-5mm, 5mm-4mm, 5mm-3mm, 5mm-2mm). For each model, CFD simulation was performed to calculate the maximum and area-averaged WSS and APS on the proximal and distal stenotic segments. The multivariate analysis of variance and linear regression analysis were performed to quantitatively investigate the geometry-stress relationship.The results showed that, the severity and eccentricity of a plaque were linearly related to its WSS and APS. APS value on a segment (proximal or distal) of the plaque depended on the segmental length It was also shown that the difference of APS between proximal and distal segments depended exclusively on the difference of length between segments (all p<; 0.05).

CONCLUSION

The geometry of a plaque influences its WSS and APS. APS and its proximal/distal difference depend on the segmental lengths.

Moderate thickness of lipid core in shoulder region of atherosclerotic plaque determines vulnerable plaque A parametric study

Peak stress in the fibrous cap of atherosclerotic plaque is largely determined by the cap thickness which cannot be accurately estimated in vivo. This parametric study investigates idealized atherosclerotic plaque geometries. Finite element modeling is applied to search for larger morphological features associated with high cap stresses. By varying seven geometrical and two loading parameters, 100 3D model geometries of atherosclerotic plaques in common iliac artery were generated. In each model peak cap stress was calculated, and statistical comparison of the geometries generating the highest and lowest peak cap stresses was performed. The analysis showed that, compared to geometries generating the lowest stresses, those with high peak cap stress had a significantly lower cap thickness, higher stenosis ratio, lower relative lipid core volume, and cap shoulder radius larger than lipid core radius. High cap stress was observed for cap thicknesses up to 0.13 mm. It can be concluded that vulnerable plaques contain thin fibrous cap, large stenosis ratio and only moderate small-radius lipid core which reaches the shoulder region of the fibrous cap.

Vulnerability analysis on the interaction between Asymmetric stent and arterial layer

The utilization of Asymmetric stent for recovering atherosclerotic diseases, particularly non-symmetric obstruction, is a quite challenging breakthrough treatment. In terms of eccentric plaque, the non-uniform stiffness of arterial layer causes the increasingly complex issues of vulnerability. This study investigated the vulnerability of the interaction between the Asymmetric stent and the surrounding arterial layer using structural transient dynamic analysis in ANSYS. Four combinations of stent deployment, i.e. the Sinusoidal stent expanded by the offset balloon, the Sinusoidal stent expanded by the ordinary cylindrical balloon, the Asymmetric stent expanded by the offset balloon, and the Asymmetric stent expanded by the ordinary cylindrical balloon, are generated for this comparative study. Multilayer material properties from recent in vitro experiments are adopted for the surrounding arterial layer, such as a fibrous cap, lipid core, diseased-healthy intima, and diseased-healthy media. In order to address plaque vulnerability, the Cauchy stresses and Hencky strains are used for stress measure because of convenience in comparison with the uniaxial/biaxial tension test data. The location-specific threshold value from the diseased human carotid artery is adopted for rupture criteria. The simulation indicated that as regards the eccentric plaque, the plaque vulnerability is caused by the plaque shape and components rather than caused by the geometrical structure of the stent or balloon expansion method. Nevertheless, the non-symmetric inflation of balloon, which leads against the plaque, contributed to an increase in the vulnerability of fibrous cap of fibroatheroma plaque.

Simultaneous evaluation of plaque stability and ischemic potential of coronary lesions in a fluid-structure interaction analysis

The measurement of fractional flow reserve (FFR) and superficial wall stress (SWS) identifies inducible myocardial ischemia and plaque vulnerability, respectively. A simultaneous evaluation of both FFR and SWS is still lacking, while it may have a major impact on therapy. A new computational model of one-way fluid-structure interaction (FSI) was implemented and used to perform a total of 54 analyses in virtual coronary lesion models, based on plaque compositions, arterial remodeling patterns, and stenosis morphologies under physiological conditions. Due to a greater lumen dilation and more induced strain, FFR in the lipid-rich lesions (0.81 ± 0.15) was higher than that in fibrous lesions (0.79 ± 0.16, P = 0.001) and calcified lesions (0.79 ± 0.16, P = 0.001). Four types of lesions were further defined, based on the combination of cutoff values for FFR (0.80) and maximum relative SWS (30 kPa): The level of risk increased from (1) plaques with mild-to-moderate stenosis but negative remodeling for lipid-rich (Type A: non-ischemic, stable) to (2) lipid-rich plaques with mild-to-moderate stenosis and without-to-positive remodeling (Type B: non-ischemic, unstable) or plaques with severe stenosis but negative remodeling for lipid-rich (Type C: ischemic, stable) to (3) lipid-rich plaques with severe stenosis and without-to-positive remodeling (Type D: ischemic, unstable). The analysis of FSI to simultaneously evaluate inducible myocardial ischemia and plaque stability may be useful to identify coronary lesions at a high risk and to ultimately optimize treatment. Further research is warranted to assess whether a more aggressive treatment may improve the prognosis of patients with non-ischemic, intermediate, and unstable lesions.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

A novel four-dimensional angiographic approach to assess dynamic superficial wall stress of coronary arteries in vivo: initial experience in evaluating vessel sites with subsequent plaque rupture

AIMS

Repetitive, fluctuating stress is an important biomechanical mechanism that underlies the rupture of atherosclerotic plaques. We developed a novel coronary angiography-based method for in vivo four-dimensional analysis of dynamic superficial wall stress (SWS) in coronary plaques and applied it for the first time in two clinical cases. Our aim was to investigate the potential relationship between dynamic stress concentration at baseline and plaque rupture during acute coronary syndrome (ACS) several months later.

METHODS AND RESULTS

Three-dimensional angiographic reconstructions of the interrogated arteries were performed at several phases of the cardiac cycle, followed by finite element analysis to obtain the dynamic SWS data. The peak stress at baseline was found at the distal and proximal lesion longitudinal shoulders, being 121.8 kPa and 98.0 kPa, respectively. Intriguingly, in both cases, the sites with the highest SWS concentration at baseline co-registered with the location of plaque rupture during ACS, respectively six and 18 months after the baseline angiographic assessment.

CONCLUSIONS

A novel angiography-based analysis method for four-dimensional evaluation of dynamic SWS was feasible for investigating plaque biomechanical behaviour in vivo. Initial experience suggests that this technique could be useful in exploring mechanisms of future plaque rupture.

Combining IVUS and Optical Coherence Tomography for More Accurate Coronary Cap Thickness Quantification and Stress/Strain Calculations: A Patient-Specific Three-Dimensional Fluid-Structure Interaction Modeling Approach

Accurate cap thickness and stress/strain quantifications are of fundamental importance for vulnerable plaque research. Virtual histology intravascular ultrasound (VH-IVUS) sets cap thickness to zero when cap is under resolution limit and IVUS does not see it. An innovative modeling approach combining IVUS and optical coherence tomography (OCT) is introduced for cap thickness quantification and more accurate cap stress/strain calculations. In vivo IVUS and OCT coronary plaque data were acquired with informed consent obtained. IVUS and OCT images were merged to form the IVUS + OCT data set, with biplane angiography providing three-dimensional (3D) vessel curvature. For components where VH-IVUS set zero cap thickness (i.e., no cap), a cap was added with minimum cap thickness set as 50 and 180 μm to generate IVUS50 and IVUS180 data sets for model construction, respectively. 3D fluid-structure interaction (FSI) models based on IVUS + OCT, IVUS50, and IVUS180 data sets were constructed to investigate cap thickness impact on stress/strain calculations. Compared to IVUS + OCT, IVUS50 underestimated mean cap thickness (27 slices) by 34.5%, overestimated mean cap stress by 45.8%, (96.4 versus 66.1 kPa). IVUS50 maximum cap stress was 59.2% higher than that from IVUS + OCT model (564.2 versus 354.5 kPa). Differences between IVUS and IVUS + OCT models for cap strain and flow shear stress (FSS) were modest (cap strain <12%; FSS <6%). IVUS + OCT data and models could provide more accurate cap thickness and stress/strain calculations which will serve as basis for further plaque investigations.

Development of asymmetric stent for treatment of eccentric plaque

The selection of stent and balloon type is decisive in the stenting process. In the treatment of an eccentric plaque obstruction, a symmetric expansion from stent dilatation generates nonuniform stress distribution, which may aggravate fibrous cap prone to rupture. This paper developed a new stent design to treat eccentric plaque using structural transient dynamic analysis in ANSYS. A non-symmetric structural geometry of stent is generated to obtain reasonable stress distribution safe for the arterial layer surrounding the stent. To derive the novel structural geometry, a Sinusoidal stent type is modified by varying struts length and width, adding bridges, and varying curvature width of struts. An end ring of stent struts was also modified to eliminate dogboning phenomenon and to reduce the Ectropion angle. Two balloon types were used to deploy the stent, an ordinary cylindrical and offset balloon. Positive modification results were used to construct the final non-symmetric stent design, called an Asymmetric stent. Analyses of the deformation characteristics, changes in surface roughness and induced stresses within intact arterial layer were subsequently examined. Interaction between the stent and vessel wall was implemented by means of changes in surface roughness and stress distribution analyses. The Palmaz and the Sinusoidal stent were used for a comparative study. This study indicated that the Asymmetric stent types reduced the central radial recoiling and the dogboning phenomenon. In terms of changes in surface roughness and induced stresses, the Asymmetric stent has a comparable effect with that of the Sinusoidal stent. In addition, it could enhance the distribution of surface roughening as expanded by an offset balloon.

Bench testing and coronary artery bifurcations: a consensus document from the European Bifurcation Club

This is a consensus document from the European Bifurcation Club concerning bench testing in coronary artery bifurcations. It is intended to provide guidelines for bench assessment of stents and other strategies in coronary bifurcation treatment where the United States Food and Drug Administration (FDA) or International Organization for Standardization (ISO) guidelines are limited or absent. These recommendations provide guidelines rather than a step-by-step manual. We provide data on the anatomy of bifurcations and elastic response of coronary arteries to aid model construction. We discuss testing apparatus, bench testing endpoints and bifurcation nomenclature.

Intima heterogeneity in stress assessment of atherosclerotic plaques

Atherosclerotic plaque rupture is recognized as the primary cause of cardiac and cerebral ischaemic events. High structural plaque stresses have been shown to strongly correlate with plaque rupture. Plaque stresses can be computed with finite-element (FE) models. Current FE models employ homogeneous material properties for the heterogeneous atherosclerotic intima. This study aimed to evaluate the influence of intima heterogeneity on plaque stress computations. Two-dimensional FE models with homogeneous and heterogeneous intima were constructed from histological images of atherosclerotic human coronaries (n = 12). For homogeneous models, a single stiffness value was employed for the entire intima. For heterogeneous models, the intima was subdivided into four clusters based on the histological information and different stiffness values were assigned to the clusters. To cover the reported local intima stiffness range, 100 cluster stiffness combinations were simulated. Peak cap stresses (PCSs) from the homogeneous and heterogeneous models were analysed and compared. By using a global variance-based sensitivity analysis, the influence of the cluster stiffnesses on the PCS variation in the heterogeneous intima models was determined. Per plaque, the median PCS values of the heterogeneous models ranged from 27 to 160 kPa, and the PCS range varied between 43 and 218 kPa. On average, the homogeneous model PCS values differed from the median PCS values of heterogeneous models by 14%. A positive correlation (R² = 0.72) was found between the homogeneous model PCS and the PCS range of the heterogeneous models. Sensitivity analysis showed that the highest main sensitivity index per plaque ranged from 0.26 to 0.83, and the average was 0.47. Intima heterogeneity resulted in substantial changes in PCS, warranting stress analyses with heterogeneous intima properties for plaque-specific, high accuracy stress assessment. Yet, computations with homogeneous intima assumption are still valuable to perform sensitivity analyses or parametric studies for testing the effect of plaque geometry on PCS. Moreover, homogeneous intima models can help identify low PCS, stable type plaques with thick caps. Yet, for thin cap plaques, accurate stiffness measurements of the clusters in the cap and stress analysis with heterogeneous cap properties are required to characterize the plaque stability.

A multiphysics approach for modeling early atherosclerosis

This work is devoted to the development of a mathematical model of the early stages of atherosclerosis incorporating processes of all time scales of the disease and to show their interactions. The cardiovascular mechanics is modeled by a fluid-structure interaction approach coupling a non-Newtonian fluid to a hyperelastic solid undergoing anisotropic growth and a change of its constitutive equation. Additionally, the transport of low-density lipoproteins and its penetration through the endothelium is considered by a coupled set of advection-diffusion-reaction equations. Thereby, the permeability of the endothelium is wall-shear stress modulated resulting in a locally varying accumulation of foam cells triggering a novel growth and remodeling formulation. The model is calibrated and applied to an murine-specific case study, and a qualitative validation of the computational results is performed. The model is utilized to further investigate the influence of the pulsatile blood flow and the compliance of the artery wall to the atherosclerotic process. The computational results imply that the pulsatile blood flow is crucial, whereas the compliance of the aorta has only a minor influence on atherosclerosis. Further, it is shown that the novel model is capable to produce a narrowing of the vessel lumen inducing an adaption of the endothelial permeability pattern.

Intravascular ultrasound elastography analysis of the elastic mechanical properties of atherosclerotic plaque

To assess the elastic mechanical properties of atherosclerotic plaque with different morphological properties by intravascular ultrasound elastography (IVUSE). 30 purebred New Zealand rabbits were fed a high-cholesterol diet; the abdominal aorta endothelium was balloon-injured after 2 weeks; at week 12, 2 plaques with moderate echo from each rabbit were chosen for in situ imaging, and 2 consecutive frames near the end-diastole images in situ were used to construct an IVUS elastogram. Shear strain (SS) and area strain (AS) were greater for eccentric than centripetal plaque (SS: 2.65(2.45)% vs. 1.79 ± 0.97%, p < 0.05; AS: 4.81(4.99)% vs. 3.23 ± 1.75%, p < 0.05) but were lower with low than high plaque burden (SS: 2.14 ± 0.37% vs. 3.40 ± 0.34%, p < 0.05; AS: 3.88 ± 0.60% vs. 5.81 ± 0.54%, p < 0.05). SS and AS were significantly greater for plaque with negative than no remodeling (SS: 3.98 ± 1.53% vs. 1.82(1.40)%, p < 0.017; AS: 6.94 ± 2.24% vs. 2.59(2.87)%, p < 0.017) and were found correlated with eccentric index and plaque burden (R² = 0.365 and R² = 0.359, both p < 0.05). Plaques associated with eccentricity, high plaque burden and negative remodeling showed greater strain than those with centripetalism, low plaque burden and positive remodeling. Eccentric index and plaque burden may be useful to predict the elastic stability of plaque.

Quantification of Calcified Particles in Human Valve Tissue Reveals Asymmetry of Calcific Aortic Valve Disease Development

Recent studies indicated that small calcified particles observable by scanning electron microscopy (SEM) may initiate calcification in cardiovascular tissues. We hypothesized that if the calcified particles precede gross calcification observed in calcific aortic valve disease (CAVD), they would exhibit a regional asymmetric distribution associated with CAVD development, which always initiates at the base of aortic valve leaflets adjacent to the aortic outflow in a region known as the fibrosa. Testing this hypothesis required counting the calcified particles in histological sections of aortic valve leaflets. SEM images, however, do not provide high contrast between components within images, making the identification and quantification of particles buried within tissue extracellular matrix difficult. We designed a new unique pattern-matching based technique to allow for flexibility in recognizing particles by creating a gap zone in the detection criteria that decreased the influence of non-particle image clutter in determining whether a particle was identified. We developed this flexible pattern particle-labeling (FpPL) technique using synthetic test images and human carotid artery tissue sections. A conventional image particle counting method (preinstalled in ImageJ) did not properly recognize small calcified particles located in noisy images that include complex extracellular matrix structures and other commonly used pattern-matching methods failed to detect the wide variation in size, shape, and brightness exhibited by the particles. Comparative experiments with the ImageJ particle counting method demonstrated that our method detected significantly more (p < 2 × 10^-7) particles than the conventional method with significantly fewer (p < 0.0003) false positives and false negatives (p < 0.0003). We then applied the FpPL technique to CAVD leaflets and showed a significant increase in detected particles in the fibrosa at the base of the leaflets (p < 0.0001), supporting our hypothesis. The outcomes of this study are twofold: (1) development of a new image analysis technique that can be adapted to a wide range of applications and (2) acquisition of new insight on potential early mediators of calcification in CAVD.