Local axial compressive mechanical properties of human carotid atherosclerotic plaques—characterisation by indentation test and inverse finite element analysis

Characterization of mouse artery tissue properties using experimental testing combined with finite element modelling

Indentation tests have been widely used to determine the material properties of arterial tissue. However, it remains a challenge to extract the relevant material parameters from the force-indentation curves that result from indentation tests. This paper presents a detailed procedure for determining the first-order Ogden parameters, μ and α, for mouse arterial tissue using a method that combines indentation tests with numerical simulations. The method builds on a previous study (Li and Masen, 2024) and has been expanded to account for the surface roughness of the indented specimen. It is assumed that hyperelastic material behaviour can be linearized for small strain increments, ɛji≤ 1%, allowing the model developed by Hayes (Hayes et al., 1972) to be applied to accommodate the contact behaviour in each increment. However, mouse arterial specimens have an irregular or rough surface which complicates the use of Hayes' model, as the thickness of the specimen is an input parameter into the model. To solve this, we introduce an 'equivalent thickness' that can be applied in Hayes' model by identifying the thickness that yields the smallest variance S2 of the shear moduli among a range of possible specimen thickness values. The shear moduli obtained for the equivalent thickness, denoted as the equivalent shear moduli Gi∗, along with the corresponding principal strains ɛj obtained from simulations, were used to calculate the principal stresses σj using Hooke's law. By combining the principal stresses σj across all increments, a nonlinear stress σj versus strain ɛj curve was generated, from which the first-order Ogden parameters μ and α were obtained. The proposed method is demonstrated by applying it to simulated force-indentation curves, successfully recovering the input parameters for both thickness and Ogden parameters. The method was subsequently applied to 26 experimentally obtained curves, yielding an average shear modulus G of 1.22 kPa for the indented mouse arterial tissue specimens, with values ranging from 0.27 to 5.02 kPa. Numerical simulations of the indentation process with the obtained values were used to verify the obtained material parameters.

Deciphering the complex mechanics of atherosclerotic plaques: A hybrid hierarchical theory-microrheology approach

Understanding the viscoelastic properties of atherosclerotic plaques at rupture-prone scales is crucial for assessing their vulnerability. Here, we develop a Hybrid Hierarchical theory-Microrheology (HHM) approach, enabling the analysis of multiscale mechanical variations and distribution changes in regional tissue viscoelasticity within plaques across different spatial scales. We disclose a universal two-stage power-law rheology in plaques, characterized by distinct power-law exponents (αshort and αlong), which serve as mechanical indexes for plaque components and assessing mechanical gradients. We further propose a self-similar hierarchical theory that effectively delineates plaque heterogeneity from the cytoplasm, cell, to tissue levels. Moreover, our proposed multi-layer perceptron model addresses the viscoelastic heterogeneity and gradients within plaques, offering a promising diagnostic strategy for identifying unstable plaques. These findings not only advance our understanding of plaque mechanics but also pave the way for innovative diagnostic approaches in cardiovascular disease management. STATEMENT OF SIGNIFICANCE: Our study pioneers a Hybrid Hierarchical theory-Microrheology (HHM) approach to dissect the intricate viscoelasticity of atherosclerotic plaques, focusing on distinct components including cap fibrosis, lipid pools, and intimal fibrosis. We unveil a universal two-stage power-law rheology capturing mechanical variations across plaque structures. The proposed hierarchical model adeptly captures viscoelasticity changes from cytoplasm, cell to tissue levels. Based on the newly proposed markers, we further develop a machine learning (ML) diagnostic model that sets precise criteria for evaluating plaque components and heterogeneity. This work not only reveals the comprehensive mechanical heterogeneity within plaques but also introduces a mechanical marker-based ML strategy for assessing plaque conditions, offering a significant leap towards understanding and diagnosing atherosclerotic risks.

Characterisation of human penile tissue properties using experimental testing combined with multi-target inverse finite element modelling

This paper presents an inverse finite element (FE) approach aimed at estimating multi-layered human penile tissues. The inverse FE approach integrates experimental force-displacement and boundary deformation data of penile tissues with a developed FE model and uses new experimental data on human penile tissue. The experimental study encompasses whole organ plate-compression tests and individual layer tensile and compression tests, providing comprehensive insights into the tissue's mechanical behaviour. The biomechanical characterisation of penile tissue is of crucial significance for understanding its mechanical behaviour under various physiological and pathological conditions. The FE model is constructed using the realistic geometry of the penile segment and appropriate constitutive models for each tissue layer to leverage the accuracy and consistency of the model. Through systematic variation of tissue parameters in the inverse FE algorithm, simulations achieve the best match with both force-displacement and deformed boundary results obtained from the whole organ plate-compression tests. Test results from individual tissue layers are also utilised to assess the estimated parameters. The proposed inverse FE approach allows for the estimation of penile tissue parameters with high precision and reliability, shedding light on the mechanical properties of this complex biological organ. This work has applications not only in urology but also for researchers in various disciplines of biomechanics. As a result, our study contributes to advancing the understanding of human penile tissue mechanics whilst the methodology could also be applied to a range of other soft biological tissues. STATEMENT OF SIGNIFICANCE: This research uses a multi-target inverse finite element (FE) approach for estimating the material parameters of human penile tissues. By integrating experimental data and a realistic FE model, this study achieves high-precision constitutive model parameter estimation, offering key insights into penile tissue mechanics under various loading conditions. The significance of this work lies in the use of this inverse FE approach for fresh-frozen human penile tissues, to identify the mechanical properties and constitutive models for both segregated tunica albuginea and corpus cavernosum as well as intact penile tissue segments. The study's scientific impact lies in its advancement of the understanding of human urological tissue mechanics, impacting researchers and clinicians alike.

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.

A Novel Artificial Coronary Plaque to Model Coronary Heart Disease

BACKGROUND

Experimental coronary artery interventions are currently being performed on non-diseased blood vessels in healthy animals. To provide a more realistic pathoanatomical scenario for investigations on novel interventional and surgical therapies, we aimed to fabricate a stenotic lesion, mimicking the morphology and structure of a human atherosclerotic plaque.

METHODS

In an interdisciplinary setting, we engineered a casting mold to create an atherosclerotic plaque with the dimensions to fit in a porcine coronary artery. Oscillatory rheology experiments took place along with long-term stability tests assessed by microscopic examination and weight monitoring. For the implantability in future in vivo setups, we performed a cytotoxicity assessment, inserted the plaque in resected pig hearts, and performed diagnostic imaging to visualize the plaque in its final position.

RESULTS

The most promising composition consists of gelatin, cholesterol, phospholipids, hydroxyapatite, and fine-grained calcium carbonate. It can be inserted in the coronary artery of human-sized pig hearts, producing a local partial stenosis and interacting like the atherosclerotic plaque by stretching and shrinking with the vessel wall and surrounding tissue.

CONCLUSION

This artificial atherosclerotic plaque model works as a simulating tool for future medical testing and could be crucial for further specified research on coronary artery disease and is going to help to provide information about the optimal interventional and surgical care of the disease.

Macro-indentation testing of soft biological materials and assessment of hyper-elastic material models from inverse finite element analysis

Mechanical characterization of hydrogels and ultra-soft tissues is a challenging task both from an experimental and material parameter estimation perspective because they are much softer than many biological materials, ceramics, or polymers. The elastic modulus of such materials is within the 1 - 100 kPa range, behaving as a hyperelastic solid with strain hardening capability at large strains. In the current study, indentation experiments have been performed on agarose hydrogels, bovine liver, and bovine lymph node specimens. This work reports on the reliable determination of the elastic modulus by indentation experiments carried out at the macro-scale (mm) using a spherical indenter. However, parameter identification of the hyperelastic material properties usually requires an inverse finite element analysis due to the lack of an analytical contact model of the indentation test. Hence a comprehensive study on the spherical indentation of hyperelastic soft materials is carried out through robust computational analysis. Neo-Hookean and first-order Ogden hyperelastic material models were found to be most suitable. A case study on known anisotropic hyperelastic material showed the inability of the inverse finite element method to uniquely identify the whole material parameter set.

Extending arterial stiffness assessment along the circumference using beam-steered ARFI and wave-tracking: A proof-of-principle study in phantoms and ex vivo

Background

To fully quantify arterial wall and plaque stiffness, acoustic radiation force impulse (ARFI)-induced wave-tracking along the entire vessel circumference is desired. However, attenuation and guided wave behavior in thin vessel walls limits wave-tracking to short trajectories. This study investigated the potential of beam-steered ARFI and wave-tracking to extend group velocity estimation over a larger proportion of the circumference compared to conventional 0° ARFI-induced wave-tracking.

Methods

Seven vessel-mimicking polyvinyl alcohol cryogel phantoms with various dimensions and compositions and an ex vivo human carotid artery were imaged in a dedicated setup. For every 20⁰ phantom rotation, transverse group wave velocity measurements were performed with an Aixplorer Ultimate system and SL18-5 transducer using 0⁰/20⁰/-20⁰-angled ultrasound pushes. Transmural angular wave velocities were derived along 60⁰-trajectories. A 360⁰-angular velocity map was composed from the top-wall 60⁰-trajectories 0°-data, averaged over all physical phantom rotations (reference). For each phantom rotation, 360⁰-angular velocity maps were composed using 0°-data (0⁰-approach) or data from all angles (beam-steered approach). Percentages of rotations with visible waves and relative angular velocity errors compared to the reference map as function of the circumferential angle were determined for both approaches.

Results

Reference 360°-angular velocity maps could be derived for all samples, representing their stiffness. Beam-steering decreased the proportion of the circumference where waves were untraceable by 20% in phantoms and 10% ex vivo, mainly at 0° push locations. Relative errors were similar for both approaches (phantoms: 10-15%, ex vivo: 15-35%).

Conclusion

Beam-steering enables wave-tracking along a higher proportion of the wall circumference than 0⁰ ARFI-induced wave-tracking.

Novel Imaging-Based Biomarkers for Identifying Carotid Plaque Vulnerability

Carotid artery disease has traditionally been assessed based on the degree of luminal narrowing. However, this approach, which solely relies on carotid stenosis, is currently being questioned with regard to modern risk stratification approaches. Recent guidelines have introduced the concept of the "vulnerable plaque," emphasizing specific features such as thin fibrous caps, large lipid cores, intraplaque hemorrhage, plaque rupture, macrophage infiltration, and neovascularization. In this context, imaging-based biomarkers have emerged as valuable tools for identifying higher-risk patients. Non-invasive imaging modalities and intravascular techniques, including ultrasound, computed tomography, magnetic resonance imaging, intravascular ultrasound, optical coherence tomography, and near-infrared spectroscopy, have played pivotal roles in characterizing and detecting unstable carotid plaques. The aim of this review is to provide an overview of the evolving understanding of carotid artery disease and highlight the significance of imaging techniques in assessing plaque vulnerability and informing clinical decision-making.

Understanding Atherosclerosis Pathophysiology: Can Additive Manufacturing Be Helpful?

Atherosclerosis is one of the leading causes of death worldwide. Although this subject arouses much interest, there are limitations associated with the biomechanical investigation done in atherosclerotic tissues, namely the unstandardized tests for the mechanical characterization of these tissues and the inherent non-consensual results obtained. The variability of tests and typologies of samples hampers direct comparisons between results and hinders the complete understanding of the pathologic process involved in atherosclerosis development and progression. Therefore, a consensual and definitive evaluation of the mechanical properties of healthy and atherosclerotic blood vessels would allow the production of physical biomodels that could be used for surgeons' training and personalized surgical planning. Additive manufacturing (AM), commonly known as 3D printing, has attracted significant attention due to the potential to fabricate biomodels rapidly. However, the existing literature regarding 3D-printed atherosclerotic vascular models is still very limited. Consequently, this review intends to present the atherosclerosis disease and the consequences of this pathology, discuss the mechanical characterization of atherosclerotic vessels/plaques, and introduce AM as a potential strategy to increase the understanding of atherosclerosis treatment and pathophysiology.

Advances in Noninvasive Carotid Wall Imaging with Ultrasound: A Narrative Review

Carotid atherosclerosis is a major cause for stroke, with significant associated disease burden morbidity and mortality in Western societies. Diagnosis, grading and follow-up of carotid atherosclerotic disease relies on imaging, specifically ultrasound (US) as the initial modality of choice. Traditionally, the degree of carotid lumen stenosis was considered the sole risk factor to predict brain ischemia. However, modern research has shown that a variety of other imaging biomarkers, such as plaque echogenicity, surface morphology, intraplaque neovascularization and vasa vasorum contribute to the risk for rupture of carotid atheromas with subsequent cerebrovascular events. Furthermore, the majority of embolic strokes of undetermined origin are probably arteriogenic and are associated with nonstenosing atheromas. Therefore, a state-of-the-art US scan of the carotid arteries should take advantage of recent technical developments and should provide detailed information about potential thrombogenic (/) and emboligenic arterial wall features. This manuscript reviews recent advances in ultrasonographic assessment of vulnerable carotid atherosclerotic plaques and highlights the fields of future development in multiparametric arterial wall imaging, in an attempt to convey the most important take-home messages for clinicians performing carotid ultrasound.

Towards a Digital Twin of Coronary Stenting: A Suitable and Validated Image-Based Approach for Mimicking Patient-Specific Coronary Arteries

Considering the field of application involving stent deployment simulations, the exploitation of a digital twin of coronary stenting that can reliably mimic the patient-specific clinical reality could lead to improvements in individual treatments. A starting step to pursue this goal is the development of simple, but at the same time, robust and effective computational methods to obtain a good compromise between the accuracy of the description of physical phenomena and computational costs. Specifically, this work proposes an approach for the development of a patient-specific artery model to be used in stenting simulations. The finite element model was generated through a 3D reconstruction based on the clinical imaging (coronary Optical Coherence Tomography (OCT) and angiography) acquired on the pre-treatment patient. From a mechanical point of view, the coronary wall was described with a suitable phenomenological model, which is consistent with more complex constitutive approaches and accounts for the in vivo pressurization and axial pre-stretch. The effectiveness of this artery modeling method was tested by reproducing in silico the stenting procedures of two clinical cases and comparing the computational results with the in vivo lumen area of the stented vessel.

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.

Correlation Between Calcification Characteristics of Carotid Atherosclerotic Plaque and Plaque Vulnerability

Purpose

To investigate the relationship between calcification characteristics of carotid atherosclerotic plaque and lipid rich necrotic core (LRNC) and intraplaque hemorrhage (IPH).

Methods

Patients with severe carotid stenosis undergoing carotid endarterectomy (CEA) were selected. Ultrasound and CT angiography (CTA) were performed to evaluate the calcification characteristics of the plaque before the surgery.

Results

A total of 142 patients were included and 142 pathological specimens of postoperative plaque were obtained accordingly. There were 78 plaques (54.9%) with LRNC and 41 (28.9%) with IPH. The plaque with LRNC had higher calcification rate (93.6%) compared with the plaque with IPH (87.8%). LRNC was often found in multiple calcification (P = 0.003) and mixed type calcification (P = 0.001). Multiple calcification was more likely to combine with IPH (P = 0.008), while simple basal calcification was not likely to combine IPH (P = 0.002). Smaller granular calcification was more likely to be associated with IPH (P < 0.05). In multivariate regression analysis of IPH and calcification characteristics, simple basal calcification was still a protective factor for IPH (OR, 0.25; 95% CI, 0.09–0.66; P = 0.005), while multiple calcification was closely related to the occurrence of IPH (OR, 3.58; 95% CI, 1.49–8.61; P = 0.004).

Conclusion

Calcification characteristics of carotid atherosclerotic plaques are closely related to the vulnerability of plaques, especially multiple calcification and mixed type calcification.

Shear-Wave Elastography Enables Identification of Unstable Carotid Plaque

Shear-wave elastography (SWE) is a novel ultrasound technique for quantifying tissue elasticity. The aim of this study was to identify differences in atherosclerotic plaque elasticity measured using SWE among individuals with symptomatic, asymptomatic progressive and asymptomatic stable carotid plaques. Consecutive patients from the Atherosclerotic Plaque Characteristics Associated with a Progression Rate of the Plaque and a Risk of Stroke in Patients with the Carotid Bifurcation Plaque Study were screened for this research. Neurosonography examination of carotid arteries was performed to identify plaque stenosis of ≥50% using B-mode ultrasound and SWE imaging to measure the mean, maximal and minimal elasticity. The set consisted of 97 participants-74 with asymptomatic stable stenosis, 12 with asymptomatic progressive stenosis and 11 with symptomatic stenosis. The mean elasticity in the asymptomatic stable plaque group was significantly higher than in the asymptomatic progressive (52.2 vs. 30.4 kPa; p < 0.001) and symptomatic (52.2 vs. 36.4 kPa; p = 0.033) plaque groups. No significant differences were found between asymptomatic progressive and symptomatic (p > 0.1) plaque groups. Asymptomatic stable, asymptomatic progressive and symptomatic plaques did not differ in echogenicity, calcifications, homogeneity, occurrence of ulcerated surface, or intra-plaque hemorrhage (p > 0.05 in all cases). SWE was a helpful modality for differentiating between stable and unstable atherosclerotic plaques in carotid arteries.

Plaque Longitudinal Heterogeneity in Morphology, Property, and Mechanobiology

BACKGROUND AND PURPOSE

The hemodynamic environment of an atherosclerotic plaque varies along the longitudinal direction. Investigating the changes in plaque morphology and its biomechanical environment along the longitudinal direction and their correlations will enhance our understanding of plaque progression and arterial remodeling.

METHODS

Six male patients with carotid stenosis >70% were recruited. Multisequence high-resolution MRI was performed at the carotid bifurcation. Carotid endarterectomy was performed following MRI, and the plaque tissue was collected for histological and mechanical testing. Patient-specific biomechanical modeling and simulations were conducted to calculate the mechanical stresses (wall shear stress [WSS] and von Mises stress [VMS]). Changes in plaque cross-sectional morphology, WSS, and VMS as well as their correlations were evaluated.

RESULTS

Positive correlations were found between % stenosis and % inflammation (MA) (p = 0.019), % lipid area and % MA (p = 0.026), and % calcification area and VMS (p = 0.007). Negative correlations were found between VMS and % stenosis (p = 0.028) and VMS and average WSS (p = 0.034). Moreover, the peak stresses and neovessels were found to be in the shoulder regions. High-stress concentrations were found in the interface regions of the calcification and surrounding tissue, thereby increasing plaque vulnerability.

CONCLUSIONS

Correlations between the morphology and stresses suggest that arterial remodeling is a dynamic interaction between mechanical environment and plaque progression resulting in plaque heterogeneity. Our finding indicates that plaque heterogeneity is associated with plaque progression and can be combined with mechanical stresses for identifying high-risk plaques.

A comparative study unraveling the effects of TNF-α stimulation on endothelial cells between 2D and 3D culture

Endothelial cell (EC) dysfunction is an important predictor of and contributor to the pathobiology of cardiovascular diseases. However, most in vitro studies are performed using monolayer cultures of ECs on 2D tissue polystyrene plates (TCPs), which cannot reflect the physiological characteristics of cells in vivo. Here, we used 2D TCPs and a 3D culture model to investigate the effects of dimensionality and cardiovascular risk factors in regulating endothelial dysfunction. Cell morphology, oxidative stress, inflammatory cytokines and endothelial function were investigated in human umbilical vein endothelial cells (HUVECs) cultured in 2D/3D. The differentially expressed genes in 2D/3D-cultured HUVECs were analysed using Enrichr, Cytoscape and STRING services. Finally, we validated the proteins of interest and confirmed their relevance to TNF-α and the culture microenvironment. Compared with 2D TCPs, 3D culture increased TNF-α-stimulated oxidative stress and the inflammatory response and changed the mediators secreted by ECs. In addition, the functional characteristics, important pathways and key proteins were determined by bioinformatics analysis. Furthermore, we found that some key proteins, notably ACE, CD40, Sirt1 and Sirt6, represent a critical link between endothelial dysfunction and dimensionality, and these proteins were screened by bioinformatics analysis and verified by western blotting. Our observations provide insight into the interdependence between endothelial dysfunction and the complex microenvironment, which enhances our understanding of endothelial biology or provides a therapeutic strategy for cardiovascular-related diseases.

Calibration of hyperelastic constitutive models: the role of boundary conditions, search algorithms, and experimental variability

The calibration of hyperelastic constitutive models of soft tissue and tissue surrogates is often treated as an exercise in curve-fitting to the average experimental response, and many of the complicating factors such as experimental boundary conditions and data variability are ignored. In this work, we focus on three questions that arise in this area: the ramifications of ignoring the experimental boundary conditions, the use of local optimizers, and the role of data variability. Using data from a uniaxial extension experiment on a tissue surrogate, we study how these three factors affect the calibration of isotropic hyperelastic constitutive models. Our results show that even with the simplest of constitutive models, it is necessary to look beyond a "good fit" to the average.

Vascular Shear Wave Elastography in Atherosclerotic Arteries: A Systematic Review

Ischemic stroke is a leading cause of death and disability worldwide, so adequate prevention strategies are crucial. However, current stroke risk stratification is based on epidemiologic studies and is still suboptimal for individual patients. The aim of this systematic review was to provide a literature overview on the feasibility and diagnostic value of vascular shear wave elastography (SWE) using ultrasound (US) in (mimicked) human and non-human arteries affected by different stages of atherosclerotic diseases or diseases related to atherosclerosis. An online search was conducted on Pubmed, Embase, Web of Science and IEEE databases to identify studies using US SWE for the assessment of vascular elasticity. A quality assessment was performed using Quality Assessment of Diagnostic Accuracy Studies 2 (QUADAS-2) checklist, and relevant data were extracted. A total of 19 studies were included: 10 with human patients and 9 with non-human subjects (i.e., [excised] animal arteries and polyvinyl alcohol phantoms). All studies revealed the feasibility of using US SWE to assess individually stiffness of the arterial wall and plaques. Quantitative elasticity values were highly variable between studies. However, within studies, SWE could detect statistically significant elasticity differences in patient/subject characteristics and could distinguish different plaque types with good reproducibility. US SWE, with its unique ability to assess the elasticity of the vessel wall and plaque throughout the cardiac cycle, might be a good candidate to improve stroke risk stratification. However, more clinical studies have to be performed to assess this technique's exact clinical value.

The Importance of Mechanical Forces for in vitro Endothelial Cell Biology

Blood and lymphatic vessels are lined by endothelial cells which constantly interact with their luminal and abluminal extracellular environments. These interactions confer physical forces on the endothelium, such as shear stress, stretch and stiffness, to mediate biological responses. These physical forces are often altered during disease, driving abnormal endothelial cell behavior and pathology. Therefore, it is critical that we understand the mechanisms by which endothelial cells respond to physical forces. Traditionally, endothelial cells in culture are grown in the absence of flow on stiff substrates such as plastic or glass. These cells are not subjected to the physical forces that endothelial cells endure in vivo, thus the results of these experiments often do not mimic those observed in the body. The field of vascular biology now realize that an intricate analysis of endothelial signaling mechanisms requires complex in vitro systems to mimic in vivo conditions. Here, we will review what is known about the mechanical forces that guide endothelial cell behavior and then discuss the advancements in endothelial cell culture models designed to better mimic the in vivo vascular microenvironment. A wider application of these technologies will provide more biologically relevant information from cultured cells which will be reproducible to conditions found in the body.

IDENTIFICATION OF UNIAXIAL DEFORMATION BEHAVIOR AND ITS INITIAL TANGENT MODULUS FOR ATHEROMATOUS INTIMA IN THE HUMAN CAROTID ARTERY AND THORACIC AORTA USING THREE-PARAMETER ISOTROPIC HYPERELASTIC MODELS

Uniaxial stretching tests are used for mechanical identification of small fibrous regions of atheromatous arteries. Material constants in isotropic hyperelastic models are determined to minimize the fitting error for the stress–strain curve. We developed a novel method to better characterize the material constants in typical forms of Yeoh, Ogden, Chuong–Fung (CF) and Gasser–Ogden–Holzapfel (GOH) isotropic hyperelastic models for fibrous caps and normal intimal layers from human carotid artery and thoracic aorta by incorporating Young’s modulus, i.e., the initial tangent modulus of uniaxial stress–strain relationships, as one of three material constants. We derived a unified, isotropic form for the anisotropic exponential-type strain energy density functions of CF and GOH models. The uniaxial stress–strain relationship equations were expanded to Maclaurin series to identify Young’s modulus as a coefficient of the linear term of the strain and to examine the roles of the material constants in the nonlinear function. The remaining two material constants were determined by curvefitting. The incorporation of Young’s modulus into the CF and GOH models gave reasonable curvefitting, with errors [Formula: see text], whereas large errors ([Formula: see text]) were observed in one case for the Yeoh model and in two cases for the Ogden model.

Mechanical and structural properties of different types of human aortic atherosclerotic plaques

Atherosclerotic plaques are characterized by structural heterogeneity affecting aortic behaviour under mechanical loading. There is evidence of direct connections between the structural plaque arrangement and the risk of plaque rupture. As a consequence of aortic plaque rupture, plaque components are transferred by the bloodstream to smaller vessels, resulting in acute cardiovascular events with a poor prognosis, such as heart attacks or strokes. Hence, evaluation of the composition, structure, and biochemical profile of atherosclerotic plaques seems to be of great importance to assess the properties of a mechanically induced failure, indicating the strength and rupture vulnerability of plaque. The main goal of the research was to determine experimentally under uniaxial loading the mechanical properties of different types of the human abdominal aorta and human aortic atherosclerotic plaques identified based on vibrational spectra (ATR-FTIR and FT-Raman spectroscopy) analysis and validated by histological staining. The potential of spectroscopic techniques as a useful histopathological tool was demonstrated. Three types of atherosclerotic plaques - predominantly calcified (APC), lipid (APL), and fibrotic (APF) - were distinguished and confirmed by histopathological examinations. Compared to the normal aorta, fibrotic plaques were stiffer (median of E_H for circumferential and axial directions, respectively: 8.15 MPa and 6.56 MPa) and stronger (median of σ_M for APLc = 1.57 MPa and APLa = 1.64 MPa), lipidic plaques were the weakest (median of σ_M for APLc = 0.76 MPa and APLa = 0.51 MPa), and calcified plaques were the stiffest (median of E_H for circumferential and axial directions, respectively: 13.23 MPa and 6.67 MPa). Therefore, plaques detected as predominantly lipid and calcified are most prone to rupture; however, the failure process reflected by the simplification of the stress-stretch characteristics seems to vary depending on the plaque composition.

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.

A novel technique for the assessment of mechanical properties of vascular tissue

Accurate estimation of mechanical properties of the different atherosclerotic plaque constituents is important in assessing plaque rupture risk. The aim of this study was to develop an experimental set-up to assess material properties of vascular tissue, while applying physiological loading and being able to capture heterogeneity. To do so, a ring-inflation experimental set-up was developed in which a transverse slice of an artery was loaded in the radial direction, while the displacement was estimated from images recorded by a high-speed video camera. The performance of the set-up was evaluated using seven rubber samples and validated with uniaxial tensile tests. For four healthy porcine carotid arteries, material properties were estimated using ultrasound strain imaging in whole-vessel-inflation experiments and compared to the properties estimated with the ring-inflation experiment. A 1D axisymmetric finite element model was used to estimate the material parameters from the measured pressures and diameters, using a neo-Hookean and Holzapfel–Gasser–Ogden material model for the rubber and porcine samples, respectively. Reproducible results were obtained with the ring-inflation experiment for both rubber and porcine samples. Similar mean stiffness values were found in the ring-inflation and tensile tests for the rubber samples as 202 kPa and 206 kPa, respectively. Comparable results were obtained in vessel-inflation experiments using ultrasound and the proposed ring-inflation experiment. This inflation set-up is suitable for the assessment of material properties of healthy vascular tissue in vitro. It could also be used as part of a method for the assessment of heterogeneous material properties, such as in atherosclerotic plaques.

Patient specific characterization of artery and plaque material properties in peripheral artery disease

Patient-specific finite element (FE) modeling of atherosclerotic plaque is challenging, as there is limited information available clinically to characterize plaque components. This study proposes that for the limited data available in vivo, material properties of plaque and artery can be identified using inverse FE analysis and either a simple neo-Hookean constitutive model or assuming linear elasticity provides sufficient accuracy to capture the changes in vessel deformation, which is the available clinical metric. To test this, 10 human cadaveric femoral arteries were each pressurized ex vivo at 6 pressure levels, while intravascular ultrasound (IVUS) and virtual histology (VH) imaging were performed during controlled pull-back to determine vessel geometry and plaque structure. The VH images were then utilized to construct FE models with heterogeneous material properties corresponding to the vessel plaque components. The constitutive models were then fit to each plaque component by minimizing the difference between the experimental and the simulated geometry using the inverse FE method. Additionally, we further simplified the analysis by assuming the vessel wall had a homogeneous structure, i.e. lumping artery and plaque as one tissue. We found that for the heterogeneous wall structure, the simulated and experimental vessel geometries compared well when the fitted neo-Hookean parameters or elastic modulus, in the case of linear elasticity, were utilized. Furthermore, taking the median of these fitted parameters then inputting these as plaque component mechanical properties in the finite element simulation yielded differences between simulated and experimental geometries that were on average around 2% greater (1.30-5.55% error range to 2.33-11.71% error range). For the homogeneous wall structure the simulated and experimental wall geometries had an average difference of around 4% although when the difference was calculated using the median fitted value this difference was larger than for the heterogeneous fits. Finally, comparison to uniaxial tension data and to literature constitutive models also gave confidence to the suitability of this simplified approach for patient-specific arterial simulation based on data that may be acquired in the clinic.

Progressive changes of elastic moduli of arterial wall and atherosclerotic plaque components during plaque development in human coronary arteries

Stiffness of the arterial wall and atherosclerotic plaque components is a determinant of the stress field within plaques, which has been suggested to be an indicator of plaque vulnerability. The diversity and inhomogeneous structure of atherosclerotic lesions complicate the characterization of plaque components. In the present study, stiffness of the arterial wall and atherosclerotic plaque components in human coronary arteries was examined in early and developed atherosclerotic lesions. The force-spectroscopy mode of the atomic force microscope and histological examination were used for determination of elastic moduli at specified locations within samples. Fibrous cap (E = 14.1 ± 3.8 kPa) showed lower stiffness than the fibrous tissue beneath the lipid pool (E = 17.6 ± 3.2 kPa). Calcification zones (E = 96.1 ± 18.8 kPa) and lipid pools (E = 2.7 ± 1.8 kPa) were the stiffest and softest components of atherosclerotic lesions, respectively. The increase of media stiffness (%44.8) and reduction of the elastic modulus of the internal elastic lamina (%28.9) was observed in coronary arteries. Moreover, significant differences were observed between the stiffness of medial layer in diseased parts and free-plaque segments in incomplete plaques of coronary arteries. Our results can be used for better understanding of remodeling mechanisms of the arterial wall with plaque development. Graphical abstract Stiffness alteration of the arterial wall and atherosclerotic plaque components with plaque development in coronary arteries.

Biomimetic soft fibrous hydrogels for contractile and pharmacologically responsive smooth muscle

The ability to assess changes in smooth muscle contractility and pharmacological responsiveness in normal or pathological-relevant vascular tissue environments is critical to enable vascular drug discovery. However, major challenges remain in both capturing the complexity of in vivo vascular remodeling and evaluating cell contractility in complex, tissue-like environments. Herein, we developed a biomimetic fibrous hydrogel with tunable structure, stiffness, and composition to resemble the native vascular tissue environment. This hydrogel platform was further combined with the combinatory protein array technology as well as advanced approaches to measure cell mechanics and contractility, thus permitting evaluation of smooth muscle functions in a variety of tissue-like microenvironments. Our results demonstrated that biomimetic fibrous structure played a dominant role in smooth muscle function, while the presentation of adhesion proteins co-regulated it to various degrees. Specifically, fibre networks enabled cell infiltration and upregulated expression of actomyosin proteins in contrast to flat hydrogels. Remarkably, fibrous structure and physiologically relevant stiffness of hydrogels cooperatively enhanced smooth muscle contractility and pharmacological responses to vasoactive drugs at both the single cell and intact tissue levels. Together, this study is the first to demonstrate alterations of human vascular smooth muscle contractility and pharmacological responsiveness in biomimetic soft, fibrous environments with a cellular array platform. The integrated platform produced here could enable investigations for pathobiology and pharmacological interventions by developing a broad range of patho-physiologically relevant in vitro tissue models.

STATEMENT OF SIGNIFICANCE

Engineering functional smooth muscle in vitro holds the great potential for diseased tissue replacement and drug testing. A central challenge is recapitulating the smooth muscle contractility and pharmacological responses given its significant phenotypic plasticity in response to changes in environment. We present a biomimetic fibrous hydrogel with tunable structure, stiffness, and composition that enables the creation of functional smooth muscle tissues in the native-like vascular tissue microenvironment. Such fibrous hydrogel is further combined with the combinatory protein array technology to construct a cellular array for evaluation of smooth muscle phenotype, contraction, and cell mechanics. The integrated platform produced here could be promising for developing a broad range of normal or diseased in vitro tissue models.

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.

STRESS ANALYSIS OF INTERNAL CAROTID ARTERY WITH LOW STENOSIS LEVEL: THE EFFECT OF MATERIAL MODEL AND PLAQUE GEOMETRY

Stress concentration in carotid stenosis has been proven to assist plaque morphology in disease diagnosis and vulnerability. This work focuses on numerical analysis of stress and strain distribution in the cross-section of internal carotid artery using a 2D structure-only method. The influence of four different idealized plaque geometries (circle, ellipse, oval and wedge) is investigated. Numerical simulations are implemented utilizing linear elastic model along with four hyperelastic constitutive laws named neo-Hookean, Ogden, Yeoh and Mooney–Rivlin. Each case is compared to the real geometry. Results show significant strength of oval and wedged geometries in predicting stress and strain values. Our results emphasize that Yeoh and Ogden hyperelastic materials are more reliable in stress prediction with errors less than 3%. The same concept is observed in locating critical stresses where oval and wedged plaque geometries are the most accurate models. Similar results are observed in predicting maximum principal elastic strain with errors less than 1%. However, the strain distribution in idealized plaque models showed a considerable difference in comparison with real geometry.

Association Between Carotid Atherosclerotic Plaque Calcification and Intraplaque Hemorrhage

Objective—

Carotid intraplaque hemorrhage (IPH) is associated with cardiovascular events. Calcification, which frequently accompanies IPH, may play a role in IPH occurrence. In this study, we aimed to investigate the associations between calcification characteristics and IPH in carotid plaques.

Approach and results—

One hundred seventeen patients with cerebrovascular symptoms and carotid plaques detected by ultrasound were recruited and underwent multicontrast magnetic resonance imaging. Advanced carotid plaques with composition measured by magnetic resonance imaging were included in the analysis. Carotid calcifications were divided into the following categories: surface, mixed, and deep calcification. They were also classified into single and multiple calcifications according to quantity. Logistic regression models utilizing generalized estimating equations were performed to evaluate the relationship between calcification and IPH. Of 117 subjects, 85 with 142 plaques were included in the final analysis, whereas 32 were excluded because of lack of plaque compositions. Of the 142 plaques, 40 (28.2%) had IPH. Plaques with IPH showed greater prevalence of calcification than those without (87.5% versus 55.9%; P =0.005). After adjusting for age, low-density lipoprotein, maximum wall thickness, and maximum soft plaque thickness, multiple calcifications (odd ratio, 10.1; 95% confidence interval, 3.3–30.4), surface calcification (odd ratio, 29.4; 95% confidence interval, 4.1–210.8), and mixed calcifications (odd ratio, 27.9; 95% confidence interval, 7.3–107.1) were found to be strongly associated with the presence of IPH (all P <0.05).

Conclusions—

Surface calcification and multiple calcifications in carotid atherosclerotic plaques are independently associated with the presence of IPH, suggesting that both quantity and location of calcification may play important roles in the occurrence of IPH. These findings may provide novel insights for understanding mechanisms of IPH.

High-Throughput Screening of Vascular Endothelium-Destructive or Protective Microenvironments: Cooperative Actions of Extracellular Matrix Composition, Stiffness, and Structure

Pathological modification of the subendothelial extracellular matrix (ECM) has closely been associated with endothelial activation and subsequent cardiovascular disease progression. To understand regulatory mechanisms of these matrix modifications, the majority of previous efforts have focused on the modulation of either chemical composition or matrix stiffness on 2D smooth surfaces without simultaneously probing their cooperative effects on endothelium function on in vivo like 3D fibrous matrices. To this end, a high-throughput, combinatorial microarray platform on 2D and 3D hydrogel settings to resemble the compositions, stiffness, and structure of healthy and diseased subendothelial ECM has been established, and further their respective and combined effects on endothelial attachment, proliferation, inflammation, and junctional integrity have been investigated. For the first time, the results demonstrate that 3D fibrous structure resembling native ECM is a critical endothelium-protective microenvironmental factor by maintaining the stable, quiescent endothelium with strong resistance to proinflammatory stimuli. It is also revealed that matrix stiffening, in concert with chemical compositions resembling diseased ECM, particularly collagen III, could aggravate activation of nuclear factor kappa B, disruption of endothelium integrity, and susceptibility to proinflammatory stimuli. This study elucidates cooperative effects of various microenvironmental factors on endothelial activation and sheds light on new in vitro model for cardiovascular diseases.

Shear Wave Elastography Imaging for the Features of Symptomatic Carotid Plaques: A Feasibility Study

OBJECTIVES

Shear wave elastography (SWE) was performed to evaluate the Young's modulus of carotid plaques in patients presenting with cerebrovascular incidents, to estimate the clinical value and feasibility of this approach.

METHODS

Sixty-one patients (mean age, 65 years; 45 men) underwent common duplex ultrasonic examination and SWE evaluation. The patients were divided into the symptomatic and asymptomatic groups based on the presence of unilateral focal neurological symptoms. Elasticity and echogenicity of the carotid plaque was assessed by Young's modulus and Gray-Weale classification, respectively.

RESULTS

A total of 271 carotid plaques were assessed through duplex ultrasonic examination and SWE imaging. The Bland-Altman test revealed a perfect reproducibility of Young's modulus measurement using SWE. The interframe coefficient of variation was 16% within the 271 plaques. In the 61 representative plaques, significant correlations were found between Gray-Weale classification and mean Young's modulus (r = 0.728, P < .01) when the confounding factors were controlled. The mean Young's modulus of representative plaques in symptomatic group was lower than those in asymptomatic groups (mean Young's modulus: 81 kPa versus 115 kPa; P < .01). Logistic regression combined with receiver operating characteristic analysis suggested increased sensitivity and specificity for the identification of symptomatic carotid plaques when the mean Young's modulus was combined with stenosis rate.

CONCLUSIONS

Shear wave elastography can evaluate the Young's modulus of carotid plaque stably, and could serve as an additional method for the detection of symptomatic carotid plaques, which, in combination with common ultrasound, can promote the efficiency of differentiating symptomatic carotid plaques.

Non-Invasive Identification of Vulnerable Atherosclerotic Plaques Using Texture Analysis in Ultrasound Carotid Elastography: An In Vivo Feasibility Study Validated by Magnetic Resonance Imaging

The aims of this study were to quantify the textural information of strain rate images in ultrasound carotid elastography and evaluate the feasibility of using the textural features in discriminating stable and vulnerable plaques with magnetic resonance imaging as an in vivo reference. Ultrasound radiofrequency data were acquired in 80 carotid plaques from 52 patients, mainly in the longitudinal imaging view, and axial strain rate images were estimated with an ultrasound carotid elastography technique based on an optical flow algorithm. Four textural features of strain rate images-contrast, homogeneity, correlation and angular second moment-were derived based on the gray-level co-occurrence matrix in plaque regions to quantify the deformation distribution pattern. Conventional elastographic indices based on the magnitude of the absolute strain rate, such as the maximum, mean, median, standard deviation and 99th percentile of the axial strain rate, were also obtained for comparison. Composition measurement with magnetic resonance imaging identified 30 plaques as vulnerable and the other 50 as stable. The four textural features, as well as the magnitude of strain rate images, significantly differed between the two groups of plaques. The best performing features for plaque classification were found to be the contrast and 99th percentile of the absolute strain rate, with a comparative area under the receiver operating characteristic curve of 0.81; a slightly higher maximum accuracy of plaque classification can be achieved by the textural feature of contrast (83.8% vs. 81.3%). The results indicate that the use of texture analysis in plaque classification is feasible and that larger local deformations and higher level of complexity in deformation patterns (associated with the elastic or stiffness heterogeneity of plaque tissues) are more likely to occur in vulnerable plaques.

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the 'computational dissection' of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.

Ultrasound-Based Carotid Elastography for Detection of Vulnerable Atherosclerotic Plaques Validated by Magnetic Resonance Imaging

Ultrasound-based carotid elastography has been developed to estimate the mechanical properties of atherosclerotic plaques. The objective of this study was to evaluate the in vivo capability of carotid elastography in vulnerable plaque detection using high-resolution magnetic resonance imaging as reference. Ultrasound radiofrequency data of 46 carotid plaques from 29 patients (74 ± 5 y old) were acquired and inter-frame axial strain was estimated with an optical flow method. The maximum value of absolute strain rate for each plaque was derived as an indicator for plaque classification. Magnetic resonance imaging of carotid arteries was performed on the same patients to classify the plaques into stable and vulnerable groups for carotid elastography validation. The maximum value of absolute strain rate was found to be significantly higher in vulnerable plaques (2.15 ± 0.79 s(-1), n = 27) than in stable plaques (1.21 ± 0.37 s(-1), n = 19) (p < 0.0001). Receiver operating characteristic curve analysis was performed, and the area under the curve was 0.848. Therefore, the in vivo capability of carotid elastography to detect vulnerable plaques, validated by magnetic resonance imaging, was proven, revealing the potential of carotid elastography as an important tool in atherosclerosis assessment and stroke prevention.

Automatic Segmentation of Mechanically Inhomogeneous Tissues Based on Deformation Gradient Jump

Variations in properties, active behavior, injury, scarring, and/or disease can all cause a tissue's mechanical behavior to be heterogeneous. Advances in imaging technology allow for accurate full-field displacement tracking of both in vitro and in vivo deformation from an applied load. While detailed strain fields provide some insight into tissue behavior, material properties are usually determined by fitting stress-strain behavior with a constitutive equation. However, the determination of the mechanical behavior of heterogeneous soft tissue requires a spatially varying constitutive equation (i.e., one in which the material parameters vary with position). We present an approach that computationally dissects the sample domain into many homogeneous subdomains, wherein subdomain boundaries are formed by applying a betweenness based graphical analysis to the deformation gradient field to identify locations with large discontinuities. This novel partitioning technique successfully determined the shape, size and location of regions with locally similar material properties for: (1) a series of simulated soft tissue samples prescribed with both abrupt and gradual changes in anisotropy strength, prescribed fiber alignment, stiffness, and nonlinearity, (2) tissue analogs (PDMS and collagen gels) which were tested biaxially and speckle tracked (3) and soft tissues which exhibited a natural variation in properties (cadaveric supraspinatus tendon), a pathologic variation in properties (thoracic aorta containing transmural plaque), and active behavior (contracting cardiac sheet). The routine enables the dissection of samples computationally rather than physically, allowing for the study of small tissues specimens with unknown and irregular inhomogeneity.

Bayesian calibration of hyperelastic constitutive models of soft tissue

There is inherent variability in the experimental response used to characterize the hyperelastic mechanical response of soft tissues. This has to be accounted for while estimating the parameters in the constitutive models to obtain reliable estimates of the quantities of interest. The traditional least squares method of parameter estimation does not give due importance to this variability. We use a Bayesian calibration framework based on nested Monte Carlo sampling to account for the variability in the experimental data and its effect on the estimated parameters through a systematic probability-based treatment. We consider three different constitutive models to represent the hyperelastic nature of soft tissue: Mooney-Rivlin model, exponential model, and Ogden model. Three stress-strain data sets corresponding to the deformation of agarose gel, bovine liver tissue, and porcine brain tissue are considered. Bayesian fits and parameter estimates are compared with the corresponding least squares values. Finally, we propagate the uncertainty in the parameters to a quantity of interest (QoI), namely the force-indentation response, to study the effect of model form on the values of the QoI. Our results show that the quality of the fit alone is insufficient to determine the adequacy of the model, and due importance has to be given to the maximum likelihood value, the landscape of the likelihood distribution, and model complexity.

A Framework for Local Mechanical Characterization of Atherosclerotic Plaques: Combination of Ultrasound Displacement Imaging and Inverse Finite Element Analysis

Biomechanical models have the potential to predict plaque rupture. For reliable models, correct material properties of plaque components are a prerequisite. This study presents a new technique, where high resolution ultrasound displacement imaging and inverse finite element (FE) modeling is combined, to estimate material properties of plaque components. Iliac arteries with plaques were excised from 6 atherosclerotic pigs and subjected to an inflation test with pressures ranging from 10 to 120 mmHg. The arteries were imaged with high frequency 40 MHz ultrasound. Deformation maps of the plaques were reconstructed by cross correlation of the ultrasound radiofrequency data. Subsequently, the arteries were perfusion fixed for histology and structural components were identified. The histological data were registered to the ultrasound data to construct FE model of the plaques. Material properties of the arterial wall and the intima of the atherosclerotic plaques were estimated using a grid search method. The computed displacement fields showed good agreement with the measured displacement fields, implying that the FE models were able to capture local inhomogeneities within the plaque. On average, nonlinear stiffening of both the wall and the intima was observed, and the wall of the atheroslcerotic porcine iliac arteries was markedly stiffer than the intima (877 ± 459 vs. 100 ± 68 kPa at 100 mmHg). The large spread in the data further illustrates the wide variation of the material properties. We demonstrated the feasibility of a mixed experimental–numerical framework to determine the material properties of arterial wall and intima of atherosclerotic plaques from intact arteries, and concluded that, due to the observed variation, plaque specific properties are required for accurate stress simulations.

The effects of plaque morphology and material properties on peak cap stress in human coronary arteries

Heart attacks are often caused by rupture of caps of atherosclerotic plaques in coronary arteries. Cap rupture occurs when cap stress exceeds cap strength. We investigated the effects of plaque morphology and material properties on cap stress. Histological data from 77 coronary lesions were obtained and segmented. In these patient-specific cross sections, peak cap stresses were computed by using finite element analyses. The finite element analyses were 2D, assumed isotropic material behavior, and ignored residual stresses. To represent the wide spread in material properties, we applied soft and stiff material models for the intima. Measures of geometric plaque features for all lesions were determined and their relations to peak cap stress were examined using regression analyses. Patient-specific geometrical plaque features greatly influence peak cap stresses. Especially, local irregularities in lumen and necrotic core shape as well as a thin intima layer near the shoulder of the plaque induce local stress maxima. For stiff models, cap stress increased with decreasing cap thickness and increasing lumen radius (R = 0.79). For soft models, this relationship changed: increasing lumen radius and increasing lumen curvature were associated with increased cap stress (R = 0.66). The results of this study imply that not only accurate assessment of plaque geometry, but also of intima properties is essential for cap stress analyses in atherosclerotic plaques in human coronary arteries.

Influence of material property variability on the mechanical behaviour of carotid atherosclerotic plaques: a 3D fluid-structure interaction analysis

Mechanical analysis has been shown to be complementary to luminal stenosis in assessing atherosclerotic plaque vulnerability. However, patient-specific material properties are not available and the effect of material properties variability has not been fully quantified. Media and fibrous cap (FC) strips from carotid endarterectomy samples were classified into hard, intermediate and soft according to their incremental Young's modulus. Lipid and intraplaque haemorrhage/thrombus strips were classified as hard and soft. Idealised geometry-based 3D fluid-structure interaction analyses were performed to assess the impact of material property variability in predicting maximum principal stress (Stress-P1 ) and stretch (Stretch-P1 ). When FC was thick (1000 or 600 µm), Stress-P1 at the shoulder was insensitive to changes in material stiffness, whereas Stress-P1 at mid FC changed significantly. When FC was thin (200 or 65 µm), high stress concentrations shifted from the shoulder region to mid FC, and Stress-P1 became increasingly sensitive to changes in material properties, in particular at mid FC. Regardless of FC thickness, Stretch-P1 at these locations was sensitive to changes in material properties. Variability in tissue material properties influences both the location and overall stress/stretch value. This variability needs to be accounted for when interpreting the results of mechanical modelling.

Carotid plaque elasticity estimation using ultrasound elastography, MRI, and inverse FEA - A numerical feasibility study

The material properties of atherosclerotic plaques govern the biomechanical environment, which is associated with rupture-risk. We investigated the feasibility of noninvasively estimating carotid plaque component material properties through simulating ultrasound (US) elastography and in vivo magnetic resonance imaging (MRI), and solving the inverse problem with finite element analysis. 2D plaque models were derived from endarterectomy specimens of nine patients. Nonlinear neo-Hookean models (tissue elasticity C1) were assigned to fibrous intima, wall (i.e., media/adventitia), and lipid-rich necrotic core. Finite element analysis was used to simulate clinical cross-sectional US strain imaging. Computer-simulated, single-slice in vivo MR images were segmented by two MR readers. We investigated multiple scenarios for plaque model elasticity, and consistently found clear separations between estimated tissue elasticity values. The intima C1 (160 kPa scenario) was estimated as 125.8 ± 19.4 kPa (reader 1) and 128.9 ± 24.8 kPa (reader 2). The lipid-rich necrotic core C1 (5 kPa) was estimated as 5.6 ± 2.0 kPa (reader 1) and 8.5 ± 4.5 kPa (reader 2). A scenario with a stiffer wall yielded similar results, while realistic US strain noise and rotating the models had little influence, thus demonstrating robustness of the procedure. The promising findings of this computer-simulation study stimulate applying the proposed methodology in a clinical setting.

Cell-stiffness-induced mechanosignaling - a key driver of leukocyte transendothelial migration

The breaching of cellular and structural barriers by migrating cells is a driving factor in development, inflammation and tumor cell metastasis. One of the most extensively studied examples is the extravasation of activated leukocytes across the vascular endothelium, the inner lining of blood vessels. Each step of this leukocyte transendothelial migration (TEM) process is regulated by distinct endothelial adhesion receptors such as the intercellular adhesion molecule 1 (ICAM1). Adherent leukocytes exert force on these receptors, which sense mechanical cues and transform them into localized mechanosignaling in endothelial cells. In turn, the function of the mechanoreceptors is controlled by the stiffness of the endothelial cells and of the underlying substrate representing a positive-feedback loop. In this Commentary, we focus on the mechanotransduction in leukocytes and endothelial cells, which is induced in response to variations in substrate stiffness. Recent studies have described the first key proteins involved in these mechanosensitive events, allowing us to identify common regulatory mechanisms in both cell types. Finally, we discuss how endothelial cell stiffness controls the individual steps in the leukocyte TEM process. We identify endothelial cell stiffness as an important component, in addition to locally presented chemokines and adhesion receptors, which guides leukocytes to sites that permit TEM.

Local anisotropic mechanical properties of human carotid atherosclerotic plaques - characterisation by micro-indentation and inverse finite element analysis

Biomechanical models have the potential to predict failure of atherosclerotic plaques and to improve the risk assessment of plaque rupture. The applicability of these models depends strongly on the used material models. Current biomechanical models employ isotropic material models, although it is generally accepted that plaque tissue behaves highly anisotropic. The aim of the present study is to determine the local anisotropic mechanical properties of human atherosclerotic plaque tissue by means of micro-indentation tests. The indentation was performed on top of an inverted confocal microscope allowing the visualisation and quantification of the collagen fibre deformations perpendicular to the indentation direction of the plaque. Based on this, the anisotropic properties of plaque tissue perpendicular to the indentation direction (middle of the fibrous cap, shoulder of the cap, remaining intima tissue) were derived. There were no significant differences between the different indentation locations for the fibre stiffness (total median 80.6kPa, 25th-75th percentile 17.7-157.0kPa), and fibre dispersion.

Colorful protein-based fluorescent probes for collagen imaging

Real-time visualization of collagen is important in studies on tissue formation and remodeling in the research fields of developmental biology and tissue engineering. Our group has previously reported on a fluorescent probe for the specific imaging of collagen in live tissue in situ, consisting of the native collagen binding protein CNA35 labeled with fluorescent dye Oregon Green 488 (CNA35-OG488). The CNA35-OG488 probe has become widely used for collagen imaging. To allow for the use of CNA35-based probes in a broader range of applications, we here present a toolbox of six genetically-encoded collagen probes which are fusions of CNA35 to fluorescent proteins that span the visible spectrum: mTurquoise2, EGFP, mAmetrine, LSSmOrange, tdTomato and mCherry. While CNA35-OG488 requires a chemical conjugation step for labeling with the fluorescent dye, these protein-based probes can be easily produced in high yields by expression in E. coli and purified in one step using Ni2+-affinity chromatography. The probes all bind specifically to collagen, both in vitro and in porcine pericardial tissue. Some first applications of the probes are shown in multicolor imaging of engineered tissue and two-photon imaging of collagen in human skin. The fully-genetic encoding of the new probes makes them easily accessible to all scientists interested in collagen formation and remodeling.

Shear wave elastography imaging of carotid plaques: feasible, reproducible and of clinical potential

Background

Shear Wave Elastography (SWE) imaging is a novel ultrasound technique for quantifying tissue elasticity. Studies have demonstrated that SWE is able to differentiate between diseased and normal tissue in a wide range clinical applications. However its applicability to atherosclerotic carotid disease has not been established. The aim of this study was to assess the feasibility and potential clinical benefit of using SWE imaging for the assessment of carotid plaques.

Methods

Eighty-one patients (mean age 76 years, 51 male) underwent greyscale and SWE imaging. Elasticity was quantified by measuring mean Young’s Modulus (YM) within the plaque and within the vessel wall. Echogenicity was assessed using the Gray-Weale classification scale and the greyscale median (GSM).

Results

Fifty four plaques with stenosis greater than 30% were assessed. Reproducibility of YM measurements, quantified by the inter-frame coefficient of variation, was 22% within the vessel wall and 19% within the carotid plaque. Correlation with percentage stenosis was significant for plaque YM (p = 0.003), but insignificant for plaque GSM (p = 0.46). Plaques associated with focal neurological symptoms had significantly lower mean YM than plaques in asymptomatic patients (62 kPa vs 88 kPa; p = 0.01). Logistic regression and Receiver Operating Characteristic (ROC) analysis showed improvements in sensitivity and specificity when percentage stenosis was combined with the YM (area under ROC = 0.78).

Conclusions

Our study showed SWE is able to quantify carotid plaque elasticity and provide additional information that may be of clinical benefit to help identify the unstable carotid plaque.

Electronic supplementary material

The online version of this article (doi:10.1186/1476-7120-12-49) contains supplementary material, which is available to authorized users.