Mechanical analysis of heterogeneous, atherosclerotic human aorta

Endothelial Response to the Combined Biomechanics of Vessel Stiffness and Shear Stress Is Regulated via Piezo1

How endothelial cells sense and respond to dynamic changes in their biophysical surroundings as we age is not fully understood. Vascular stiffness is clearly a contributing factor not only in several cardiovascular diseases but also in physiological processes such as aging and vascular dementia. To address this gap, we utilized a microfluidic model to explore how substrate stiffness in the presence of shear stress affects endothelial morphology, senescence, proliferation, and inflammation. We also studied the role of mechanosensitive ion channel Piezo1 in endothelial responses under the combined effect of shear stress and substrate stiffness. To do so, we cultured endothelial cells inside microfluidic channels covered with fibronectin-coated elastomer with elastic moduli of 40 and 200 kPa, respectively, mimicking the stiffness of the vessel walls in young and aged arteries. The endothelial cells were exposed to atheroprotective and atherogenic shear stress levels of 10 and 2 dyn/cm2, respectively. Our findings show that substrate stiffness affects senescence under atheroprotective flow conditions and cytoskeleton remodeling, senescence, and inflammation under atherogenic flow conditions. Additionally, we found that the expression of Piezo1 plays a crucial role in endothelial adaptation to flow and regulation of inflammation under both atheroprotective and atherogenic shear stress levels. However, Piezo1 contribution to endothelial senescence was limited to the soft substrate and atheroprotective shear stress level. Overall, our study characterizes the response of endothelial cells to the combined effect of shear stress and substrate stiffness and reveals a previously unidentified role of Piezo1 in endothelial response to vessel stiffening, which potentially can be therapeutically targeted to alleviate endothelial dysfunction in aging adults.

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.

Bidirectional Ultrasound Elastographic Imaging Framework for Non-invasive Assessment of the Non-linear Behavior of a Physiologically Pressurized Artery

Studies of non-destructive bidirectional ultrasound assessment of non-linear mechanical behavior of the artery are scarce in the literature. We hereby propose derivation of a strain-shear modulus relationship as a new graphical diagnostic index using an ultrasound elastographic imaging framework, which encompasses our in-house bidirectional vascular guided wave imaging (VGWI) and ultrasound strain imaging (USI). This framework is used to assess arterial non-linearity in two orthogonal (i.e., longitudinal and circumferential) directions in the absence of non-invasive pressure measurement. Bidirectional VGWI estimates longitudinal (μ_L) and transverse (μ_T) shear moduli, whereas USI estimates radial strain (ɛ_r). Vessel-mimicking phantoms (with and without longitudinal pre-stretch) and in vitro porcine aortas under static and/or dynamic physiologic intraluminal pressure loads were examined. ɛ_r was found to be a suitable alternative to intraluminal pressure for representation of cyclic loading on the artery wall. Results revealed that μ_T values of all samples examined increased non-linearly with ε_r magnitude and more drastically than μ_L, whereas μ_L values of only the pre-stretched phantoms and aortas increased with ɛ_r magnitude. As a new graphical representation of arterial non-linearity and function, strain-shear modulus loops derived by the proposed framework over two consecutive dynamic loading cycles differentiated sample pre-conditions and corroborated direction-dependent non-linear mechanical behaviors of the aorta with high estimation repeatability.

A combination of experimental and numerical methods to investigate the role of strain rate on the mechanical properties and collagen fiber orientations of the healthy and atherosclerotic human coronary arteries

Atherosclerosis enables to alter not only the microstructural but also the physical properties of the arterial walls by plaque forming. Few studies so far have been conducted to calculate the isotropic or anisotropic mechanical properties of the healthy and atherosclerotic human coronary arteries. To date there is a paucity of knowledge on the mechanical response of the arteries under different strain rates. Therefore, the objective of the concurrent research was to comprehend whether the alteration in the strain rates of the human atherosclerotic arteries in comparison with the healthy ones contribute to the biomechanical behaviors. To do this, healthy and atherosclerotic human coronary arteries were removed from 18 individuals during autopsy. Histological analyses by both an expert histopathologist and an imaged-based recognizer software were performed to figure out the average angle of collagen fibers in the healthy and atherosclerotic arterial walls. Thereafter, the samples were subjected to 3 diverse strain rates, i.e., 5, 20, and 50 mm/min, until the material failure occurs. The stress-strain diagrams of the arterial tissues were calculated in order to capture their linear elastic and nonlinear hyperelastic mechanical properties. In addition, Artificial Neural Networks (ANNs) was employed to predict the alteration of mean angle of collagen fibers during load bearing up to failure. The findings suggest that strain rate has a significant (p < 0.05) role in the linear elastic and nonlinear hyperelastic mechanical properties as well as the mean angle of collagen fibers of the atherosclerotic arteries, whereas no specific impact on the healthy ones. Furthermore, the mean angle of collagen fibers during the load bearing up to the failure at each strain rate was well predicted by the proposed ANNs code.

Inflation and Bi-Axial Tensile Testing of Healthy Porcine Carotid Arteries

Knowledge of the intrinsic material properties of healthy and diseased arterial tissue components is of great importance in diagnostics. This study describes an in vitro comparison of 13 porcine carotid arteries using inflation testing combined with functional ultrasound and bi-axial tensile testing. The measured tissue behavior was described using both a linear, but geometrically non-linear, one-parameter (neo-Hookean) model and a two-parameter non-linear (Demiray) model. The shear modulus estimated using the linear model resulted in good agreement between the ultrasound and tensile testing methods, GUS = 25 ± 5.7 kPa and GTT = 23 ± 5.4 kPa. No significant correspondence was observed for the non-linear model aUS = 1.0 ± 2.7 kPa vs. aTT = 17 ± 8.8 kPa, p ∼ 0); however, the exponential parameters were in correspondence (bUS = 12 ± 4.2 vs. bTT = 10 ± 1.7, p > 0.05). Estimation of more complex models in vivo is cumbersome considering the sensitivity of the model parameters to small changes in measurement data and the absence of intraluminal pressure data, endorsing the use of a simple, linear model in vivo.

Noninvasive Vascular Elastography With Plane Strain Incompressibility Assumption Using Ultrafast Coherent Compound Plane Wave Imaging

Plane strain tensor estimation using non-invasive vascular ultrasound elastography (NIVE) can be difficult to achieve using conventional focus beamforming due to limited lateral resolution and frame rate. Recent developments in compound plane wave (CPW) imaging have led to high speed and high resolution imaging. In this study, we present the performance of NIVE using coherent CPW. We show the impact of CPW beamforming on strain estimates compared to conventional focus sequences. To overcome the inherent variability of lateral strains, associated with the low lateral resolution of linear array transducers, we use the plane strain incompressibility to constrain the estimator. Taking advantage of the approximate tenfold increase in frame rate of CPW compared with conventional focus imaging, we introduce a time-ensemble estimation approach to further improve the elastogram quality. By combining CPW imaging with the constrained Lagrangian speckle model estimator, we observe an increase in elastography quality (∼ 10 dB both in signal-to-noise and contrast-to-noise ratios) over a wide range of applied strains (0.02 to 3.2%).

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.

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.

Biomechanics and inflammation in atherosclerotic plaque erosion and plaque rupture: implications for cardiovascular events in women

Objective

Although plaque erosion causes approximately 40% of all coronary thrombi and disproportionally affects women more than men, its mechanism is not well understood. The role of tissue mechanics in plaque rupture and regulation of mechanosensitive inflammatory proteins is well established, but their role in plaque erosion is unknown. Given obvious differences in morphology between plaque erosion and rupture, we hypothesized that inflammation in general as well as the association between local mechanical strain and inflammation known to exist in plaque rupture may not occur in plaque erosion. Therefore, our objective was to determine if similar mechanisms underlie plaque rupture and plaque erosion.

Methods and Results

We studied a total of 74 human coronary plaque specimens obtained at autopsy. Using lesion-specific computer modeling of solid mechanics, we calculated the stress and strain distribution for each plaque and determined if there were any relationships with markers of inflammation. Consistent with previous studies, inflammatory markers were positively associated with increasing strain in specimens with rupture and thin-cap fibroatheromas. Conversely, overall staining for inflammatory markers and apoptosis were significantly lower in erosion, and there was no relationship with mechanical strain. Samples with plaque erosion most closely resembled those with the stable phenotype of thick-cap fibroatheromas.

Conclusions

In contrast to classic plaque rupture, plaque erosion was not associated with markers of inflammation and mechanical strain. These data suggest that plaque erosion is a distinct pathophysiological process with a different etiology and therefore raises the possibility that a different therapeutic approach may be required to prevent plaque erosion.

EFFECT OF STRESS INTENSITY FACTOR IN EVALUATION OF INSTABILITY OF ATHEROSCLEROTIC PLAQUE

Understanding the relationship between coronary arterial blood pressure, plaque morphology and composition, and sites of fibrous cap (FC) bursting, has been the focus of many recent studies. Instability of atherosclerotic plaques, defined as the propensity for FCs to burst, has been thought to occur at places where FCs are thin and necrotic core (NC) areas are large and highly compliant. However, here we show quantitatively, using a fiber-reinforced, anisotropic and hyperelastic FE model, that FC thickness and NC size and compliance alone are limited in predicting vulnerable and high-risk plaques. We suggest that plaque instabilities primarily occur at sites of high and concentrated mechanical stresses irrespective of fibrous cap thickness or NC area and compliance. Also, limitations of imaging techniques, such as intravascular ultrasound and optical coherence tomography, for providing input into (FE) models of atherosclerosis are discussed. The proposed model can be used to predict vulnerable plaque sites and rupture risks in patients. The current study also provides a framework for future research in which three-dimensional platform and viscoelastic properties of plaque composition can be considered in time-dependent and fatigue studies.

Changes in biomechanical properties of the coronary artery wall contribute to maintained contractile responses to endothelin-1 in atherosclerosis

AIMS

Our aim was to determine whether alterations in biomechanical properties of human diseased compared to normal coronary artery contribute to changes in artery responsiveness to endothelin-1 in atherosclerosis.

MAIN METHODS

Concentration-response curves were constructed to endothelin-1 in normal and diseased coronary artery. The passive mechanical properties of arteries were determined using tensile ring tests from which finite element models of passive mechanical properties of both groups were created. Finite element modelling of artery endothelin-1 responses was then performed.

KEY FINDINGS

Maximum responses to endothelin-1 were significantly attenuated in diseased (27±3 mN, n=55) compared to normal (38±2 mN, n=68) artery, although this remained over 70% of control. There was no difference in potency (pD2 control=8.03±0.06; pD2 diseased=7.98±0.06). Finite element modelling of tensile ring tests resulted in hyperelastic shear modulus μ=2004±410 Pa and hardening exponent α=22.8±2.2 for normal wall and μ=2464±1075 Pa and α=38.3±6.7 for plaque tissue and distensibility of diseased vessels was decreased. Finite element modelling of active properties of both groups resulted in higher muscle contractile strain (represented by thermal reactivity) of the atherosclerotic artery model than the normal artery model. The models suggest that a change in muscle response to endothelin-1 occurs in atherosclerotic artery to increase its distensibility towards that seen in normal artery.

SIGNIFICANCE

Our data suggest that an adaptation occurs in medial smooth muscle of atherosclerotic coronary artery to maintain distensibility of the vessel wall in the presence of endothelin-1. This may contribute to the vasospastic effect of locally increased endothelin-1 production that is reported in this condition.

A direct vulnerable atherosclerotic plaque elasticity reconstruction method based on an original material-finite element formulation: theoretical framework

The peak cap stress (PCS) amplitude is recognized as a biomechanical predictor of vulnerable plaque (VP) rupture. However, quantifying PCS in vivo remains a challenge since the stress depends on the plaque mechanical properties. In response, an iterative material finite element (FE) elasticity reconstruction method using strain measurements has been implemented for the solution of these inverse problems. Although this approach could resolve the mechanical characterization of VPs, it suffers from major limitations since (i) it is not adapted to characterize VPs exhibiting high material discontinuities between inclusions, and (ii) does not permit real time elasticity reconstruction for clinical use. The present theoretical study was therefore designed to develop a direct material-FE algorithm for elasticity reconstruction problems which accounts for material heterogeneities. We originally modified and adapted the extended FE method (Xfem), used mainly in crack analysis, to model material heterogeneities. This new algorithm was successfully applied to six coronary lesions of patients imaged in vivo with intravascular ultrasound. The results demonstrated that the mean relative absolute errors of the reconstructed Young's moduli obtained for the arterial wall, fibrosis, necrotic core, and calcified regions of the VPs decreased from 95.3 ± 15.56%, 98.85 ± 72.42%, 103.29 ± 111.86% and 95.3 ± 10.49%, respectively, to values smaller than 2.6 × 10(-8) ± 5.7 × 10(-8)% (i.e. close to the exact solutions) when including modified-Xfem method into our direct elasticity reconstruction method.

A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

Does microcalcification increase the risk of rupture?

Rupture of atherosclerotic plaque, which is related to maximal stress conditions in the plaque among others, is a major cause of mortality. More careful examination of stress distributions in atherosclerotic plaques reports that it could be due to local stress behaviors at critical sites caused by cap thinning, inflammation, macroscopic heterogeneity, and recently, the presence of microcalcifications. However, the role of microcalcifications is not yet fully understood, and most finite element models of blood vessels with atheroma plaque ignore the heterogeneity of the plaque constituents at the microscale. The goal of this work is to investigate the effect of microcalcifications on the stress field of an atheroma plaque vessel section. This is achieved by performing a parametric finite element study, assuming a plane strain hypothesis, of a coronary artery section with eccentric atheroma plaque and one microcalcification incorporated. The geometrical parameters used to define and design the idealized coronary plaque anatomy and the microcalcification were the fibrous cap thickness and the microcalcification ratio, angle and eccentricity. We could conclude that microcalcifications should be considered in the modeling of this kind of problems since they cause a significant alteration of the vulnerable risk by increasing the maximum maximal principal stress up to 32%, although this increase of stress is not uniform (12% on average). The obtained results show that the fibrous cap thickness, the microcalcification ratio and the microcalcification eccentricity, in combination with the microcalcification angle, appear to be the key morphological parameters that play a determinant role in the maximal principal stress and accordingly in the rupture risk of the plaque.

A four-criterion selection procedure for atherosclerotic plaque elasticity reconstruction based on in vivo coronary intravascular ultrasound radial strain sequences

Plaque elasticity (i.e., modulogram) and morphology are good predictors of plaque vulnerability. Recently, our group developed an intravascular ultrasound (IVUS) elasticity reconstruction method which was successfully implemented in vitro using vessel phantoms. In vivo IVUS modulography, however, remains a major challenge as the motion of the heart prevents accurate strain field estimation. We therefore designed a technique to extract accurate strain fields and modulograms from recorded IVUS sequences. We identified a set of four criteria based on tissue overlapping, RF-correlation coefficient between two successive frames, performance of the elasticity reconstruction method to recover the measured radial strain, and reproducibility of the computed modulograms over the cardiac cycle. This four-criterion selection procedure (4-CSP) was successfully tested on IVUS sequences obtained in twelve patients referred for a directional coronary atherectomy intervention. This study demonstrates the potential of the IVUS modulography technique based on the proposed 4-CSP to detect vulnerable plaques in vivo.

Biomechanical modeling and morphology analysis indicates plaque rupture due to mechanical failure unlikely in atherosclerosis-prone mice

Spontaneous plaque rupture in mouse models of atherosclerosis is controversial, although numerous studies have discussed so-called "vulnerable plaque" phenotypes in mice. We compared the morphology and biomechanics of two acute and one chronic murine model of atherosclerosis to human coronaries of the thin-cap fibroatheroma (TCFA) phenotype. Our acute models were apolipoprotein E-deficient (ApoE(-/-)) and LDL receptor-deficient (LDLr(-/-)) mice, both fed a high-fat diet for 8 wk with simultaneous infusion of angiotensin II (ANG II), and our chronic mouse model was the apolipoprotein E-deficient strain fed a regular chow diet for 1 yr. We found that the mouse plaques from all three models exhibited significant morphological differences from human TCFA plaques, including the plaque burden, plaque thickness, eccentricity, and amount of the vessel wall covered by lesion as well as significant differences in the relative composition of plaques. These morphological differences suggested that the distribution of solid mechanical stresses in the walls may differ as well. Using a finite-element analysis computational solid mechanics model, we computed the relative distribution of stresses in the walls of murine and human plaques and found that although human TCFA plaques have the highest stresses in the thin fibrous cap, murine lesions do not have such stress distributions. Instead, local maxima of stresses were on the media and adventitia, away from the plaque. Our results suggest that if plaque rupture is possible in mice, it may be driven by a different mechanism than mechanics.

Effect of calcification on the mechanical stability of plaque based on a three-dimensional carotid bifurcation model

Background

This study characterizes the distribution and components of plaque structure by presenting a three-dimensional blood-vessel modelling with the aim of determining mechanical properties due to the effect of lipid core and calcification within a plaque. Numerical simulation has been used to answer how cap thickness and calcium distribution in lipids influence the biomechanical stress on the plaque.

Method

Modelling atherosclerotic plaque based on structural analysis confirms the rationale for plaque mechanical examination and the feasibility of our simulation model. Meaningful validation of predictions from modelled atherosclerotic plaque model typically requires examination of bona fide atherosclerotic lesions. To analyze a more accurate plaque rupture, fluid-structure interaction is applied to three-dimensional blood-vessel carotid bifurcation modelling. A patient-specific pressure variation is applied onto the plaque to influence its vulnerability.

Results

Modelling of the human atherosclerotic artery with varying degrees of lipid core elasticity, fibrous cap thickness and calcification gap, which is defined as the distance between the fibrous cap and calcification agglomerate, form the basis of our rupture analysis. Finite element analysis shows that the calcification gap should be conservatively smaller than its threshold to maintain plaque stability. The results add new mechanistic insights and methodologically sound data to investigate plaque rupture mechanics.

Conclusion

Structural analysis using a three-dimensional calcified model represents a more realistic simulation of late-stage atherosclerotic plaque. We also demonstrate that increases of calcium content that is coupled with a decrease in lipid core volume can stabilize plaque structurally.

CORRELATION OF MECHANICAL BEHAVIOR AND MMP-1 PRESENCE IN HUMAN ATHEROSCLEROTIC PLAQUE

Regions of matrix metalloproteinase (MMP) activity potentially increase the susceptibility of the atherosclerotic lesion to complications associated with plaque rupture. Assessing the risk posed by this mechanism requires investigating the stress-strain environment associated with matrix metalloproteinase production in heterogeneous plaque. To this end, an experimental-computational technique was developed to perform mechanical analysis of physiologically loaded, diseased human aorta in vitro and to investigate relationships between vascular mechanics, histology, and histochemistry. Mechanical data and specimen histology were coupled through a heterogeneous finite element model, and tissue constituent material properties were determined by an optimization method. The cross-sectional distribution of MMP-1 was quantified using immunohistochemical techniques. Results show stresses and strains are strongly influenced by lesion structure and composition, and MMP-1 presence is correlated with histology and lesion mechanics. Interactions between lipid presence, mechanical stimuli, and extracellular matrix metabolism-catabolism likely affect arterial plaque remodeling, progression, and the risk of disruption and clinical symptoms.

Arterial stiffness: a brief review

Physical stiffening of the large arteries is the central paradigm of vascular aging. Indeed, stiffening in the larger central arterial system, such as the aortic tree, significantly contributes to cardiovascular diseases in older individuals and is positively associated with systolic hypertension, coronary artery disease, stroke, heart failure and atrial fibrillation, which are the leading causes of mortality in the developed countries and also in the developing world as estimated in 2010 by World Health Organizations. Thus, better, less invasive and more accurate measures of arterial stiffness have been developed, which prove useful as diagnostic indices, pathophysiological markers and predictive indicators of disease. This article presents a review of the structural determinants of vascular stiffening, its pathophysiologic determinants and its implications for vascular research and medicine. A critical discussion of new techniques for assessing vascular stiffness is also presented.

On the potential of a new IVUS elasticity modulus imaging approach for detecting vulnerable atherosclerotic coronary plaques: in vitro vessel phantom study

Peak cap stress amplitude is recognized as a good indicator of vulnerable plaque (VP) rupture. However, such stress evaluation strongly relies on a precise, but still lacking, knowledge of the mechanical properties exhibited by the plaque components. As a first response to this limitation, our group recently developed, in a previous theoretical study, an original approach, called iMOD (imaging modulography), which reconstructs elasticity maps (or modulograms) of atheroma plaques from the estimation of strain fields. In the present in vitro experimental study, conducted on polyvinyl alcohol cryogel arterial phantoms, we investigate the benefit of coupling the iMOD procedure with the acquisition of intravascular ultrasound (IVUS) measurements for detection of VP. Our results show that the combined iMOD-IVUS strategy: (1) successfully detected and quantified soft inclusion contours with high positive predictive and sensitivity values of 89.7 ± 3.9% and 81.5 ± 8.8%, respectively, (2) estimated reasonably cap thicknesses larger than ∼300 µm, but underestimated thinner caps, and (3) quantified satisfactorily Young's modulus of hard medium (mean value of 109.7 ± 23.7 kPa instead of 145.4 ± 31.8 kPa), but overestimated the stiffness of soft inclusions (mean Young`s moduli of 31.4 ± 9.7 kPa instead of 17.6 ± 3.4 kPa). All together, these results demonstrate a promising benefit of the new iMOD-IVUS clinical imaging method for in vivo VP detection.

Studying the effects of matrix stiffness on cellular function using acrylamide-based hydrogels

Tissue stiffness is an important determinant of cellular function, and changes in tissue stiffness are commonly associated with fibrosis, cancer and cardiovascular disease. Traditional cell biological approaches to studying cellular function involve culturing cells on a rigid substratum (plastic dishes or glass coverslips) which cannot account for the effect of an elastic ECM or the variations in ECM stiffness between tissues. To model in vivo tissue compliance conditions in vitro, we and others use ECM-coated hydrogels. In our laboratory, the hydrogels are based on polyacrylamide which can mimic the range of tissue compliances seen biologically. "Reactive" cover slips are generated by incubation with NaOH followed by addition of 3-APTMS. Glutaraldehyde is used to cross-link the 3-APTMS and the polyacrylamide gel. A solution of acrylamide (AC), bis-acrylamide (Bis-AC) and ammonium persulfate is used for the polymerization of the hydrogel. N-hydroxysuccinimide (NHS) is incorporated into the AC solution to crosslink ECM protein to the hydrogel. Following polymerization of the hydrogel, the gel surface is coated with an ECM protein of choice such as fibronectin, vitronectin, collagen, etc. The stiffness of a hydrogel can be determined by rheology or atomic force microscopy (AFM) and adjusted by varying the percentage of AC and/or bis-AC in the solution. In this manner, substratum stiffness can be matched to the stiffness of biological tissues which can also be quantified using rheology or AFM. Cells can then be seeded on these hydrogels and cultured based upon the experimental conditions required. Imaging of the cells and their recovery for molecular analysis is straightforward. For this article, we define soft substrata as those having elastic moduli (E) < 3000 Pascal and stiff substrata/tissues as those with E > 20,000 Pascal.

Vulnerable atherosclerotic plaque elasticity reconstruction based on a segmentation-driven optimization procedure using strain measurements: theoretical framework

It is now recognized that prediction of the vulnerable coronary plaque rupture requires not only an accurate quantification of fibrous cap thickness and necrotic core morphology but also a precise knowledge of the mechanical properties of plaque components. Indeed, such knowledge would allow a precise evaluation of the peak cap-stress amplitude, which is known to be a good biomechanical predictor of plaque rupture. Several studies have been performed to reconstruct a Young's modulus map from strain elastograms. It seems that the main issue for improving such methods does not rely on the optimization algorithm itself, but rather on preconditioning requiring the best estimation of the plaque components' contours. The present theoretical study was therefore designed to develop: 1) a preconditioning model to extract the plaque morphology in order to initiate the optimization process, and 2) an approach combining a dynamic segmentation method with an optimization procedure to highlight the modulogram of the atherosclerotic plaque. This methodology, based on the continuum mechanics theory prescribing the strain field, was successfully applied to seven intravascular ultrasound coronary lesion morphologies. The reconstructed cap thickness, necrotic core area, calcium area, and the Young's moduli of the calcium, necrotic core, and fibrosis were obtained with mean relative errors of 12%, 4% and 1%, 43%, 32%, and 2%, respectively.

An inverse method for imaging the local elasticity of atherosclerotic coronary plaques

The rupture of thin-cap fibroatheroma (TCFA) plaques is a major cause of acute coronary events. A TCFA has a trombogenic soft lipid core, shielded from the blood stream by a thin, possibly inflamed, stiff cap. The majority of atherosclerotic plaques resemble a TCFA in terms of overall structural composition, but have a more complex, heterogeneous morphology. An assessment of the material distribution is vital for quantifying the plaque's mechanical stability and for determining the effect of plaque-stabilizing pharmaceutical agents. We describe a new automated inverse elasticity method, intravascular ultrasound (IVUS) modulography, which is capable of reconstructing a heterogeneous Young's modulus distribution. The elastogram (i.e., spatial strain distribution) of the plaque is the input for the method, and is measured using the clinically available technique, IVUS elastography. Our method incorporates a novel divide-and-conquer strategy, allowing the reconstruction of TCFAs as well as heterogeneous plaques with localized regions of soft, weakened tissue. The method was applied to ex vivo elastograms, which were simulated from the cross sections of postmortem human coronary plaques. To demonstrate the clinical feasibility of the method, measured elastograms from human atherosclerotic coronary arteries were analyzed. One elastogram was measured in vitro; the other, in vivo. The method approximated the true Young's modulus distribution of all simulated plaques, while the in vitro reconstruction was in agreement with histology. In conclusion, the IVUS modulography in combination with the IVUS elastography has strong potential to become an all-encompassing modality for detecting plaques, for assessing the information related to their rupture-proneness, and for imaging their heterogeneous elastic material composition.

Theoretical and electrophysiological evidence for axial loading about aortic baroreceptor nerve terminals in rats

Arterial baroreceptors are essential for neurocirculatory control, providing rapid hemodynamic feedback to the central nervous system. The pressure-dependent discharge of carotid and aortic baroreceptor afferents has been extensively studied. A common assumption has been that circumferential deformation of the arterial wall is the predominant mechanical force affecting baroreceptor discharge. However, in vivo the arterial tree is under significant longitudinal tension, leading to the hypothesis that axially directed forces may contribute to baroreceptor function. To test this hypothesis, we utilized a combination of finite element modeling methods and an in vitro rat aortic arch preparation. Model formulation utilized traditional analytic constructs available in the literature followed by refinement of model material parameters through direct comparison of computationally and experimentally generated pressure-diameter curves. The numerical simulations strongly indicated a functional role for axial loading within the region of the baroreceptive nerve terminal. This prediction was confirmed through single-fiber recording of baroreceptor nerve discharge under conditions with and without longitudinal tension in the vessel preparation. The recordings (n = 5) demonstrated that longitudinal tension significantly (P < 0.02) lowered both the pressure threshold (P(th), mmHg) for baroreceptor discharge and sensitivity (S(th), Hz/mmHg). The effect was nearly instantaneous and sustained; i.e., under longitudinal tension average P(th) was 84 +/- 3 mmHg and S(th) was 0.71 +/- 0.15 Hz/mmHg, which immediately increased to a P(th) of 94 +/- 4 mmHg and a S(th) of 1.20 +/- 0.32 Hz/mmHg with loss of axial tension. Possible explanations of how an abrupt change in axial loading could result in a synchronized increase in afferent drive of the baroreceptor reflex, and the potentiating effect this could have on neurogenically mediated orthostatic intolerance are discussed.

Physical properties of tissues relevant to arterial ultrasound imaging and blood velocity measurement

A review was undertaken of physical phenomena and the values of associated physical quantities relevant to arterial ultrasound imaging and measurement. Arteries are multilayered anisotropic structures. However, the requirement to obtain elasticity measurements from the data available using ultrasound imaging necessitates the use of highly simplified constitutive models involving Young's modulus, E. Values of E are reported for healthy arteries and for the constituents of diseased arteries. It is widely assumed that arterial blood flow is Newtonian. However, recent studies suggest that non-Newtonian behavior has a strong influence on arterial flow, and the balance of published evidence suggests that non-Newtonian behavior is associated primarily with red cell deformation rather than with aggregation. Hence, modeling studies should account for red cell deformation and the shear thinning effect that this produces. Published literature in healthy adults gives an average hematocrit and high-shear viscosity of 0.44 +/- 0.03 and 3.9 +/- 0.6 mPa.s, respectively. Published data on the acoustic properties of arteries and blood is sufficiently consistent between papers to allow compilation and derivation of best-fit equations summarizing the behavior across a wide frequency range, which then may be used in future modeling studies. Best-fit equations were derived for the attenuation coefficient vs. frequency in whole arteries (R(2) = 0.995), plasma (R(2) = 0.963) and blood with hematocrit near 45% (R(2) = 0.999), and for the backscatter coefficient vs. frequency from blood with hematocrit near 45% (R(2) = 0.958).

Quantifying effects of plaque structure and material properties on stress distributions in human atherosclerotic plaques using 3D FSI models

BACKGROUND

Atherosclerotic plaques may rupture without warning and cause acute cardiovascular syndromes such as heart attack and stroke. Methods to assess plaque vulnerability noninvasively and predict possible plaque rupture are urgently needed.

METHOD

MRI-based three-dimensional unsteady models for human atherosclerotic plaques with multi-component plaque structure and fluid-structure interactions are introduced to perform mechanical analysis for human atherosclerotic plaques.

RESULTS

Stress variations on critical sites such as a thin cap in the plaque can be 300% higher than that at other normal sites. Large calcification block considerably changes stress/strain distributions. Stiffness variations of plaque components (50% reduction or 100% increase) may affect maximal stress values by 20-50%. Plaque cap erosion causes almost no change on maximal stress level at the cap, but leads to 50% increase in maximal strain value.

CONCLUSIONS

Effects caused by atherosclerotic plaque structure, cap thickness and erosion, material properties, and pulsating pressure conditions on stress/strain distributions in the plaque are quantified by extensive computational case studies and parameter evaluations. Computational mechanical analysis has good potential to improve accuracy of plaque vulnerability assessment.

Local maximal stress hypothesis and computational plaque vulnerability index for atherosclerotic plaque assessment

It is believed that atherosclerotic plaque rupture may be related to maximal stress conditions in the plaque. More careful examination of stress distributions in plaques reveals that it may be the local stress/strain behaviors at critical sites such as very thin plaque cap and locations with plaque cap weakness that are more closely related to plaque rupture risk. A "local maximal stress hypothesis" and a stress-based computational plaque vulnerability index (CPVI) are proposed to assess plaque vulnerability. A critical site selection (CSS) method is proposed to identify critical sites in the plaque and critical stress conditions which are be used to determine CPVI values. Our initial results based on 34 2D MRI slices from 14 human coronary plaque samples indicate that CPVI plaque assessment has an 85% agreement rate (91% if the square root of stress values is used) with assessment given by histopathological analysis. Large-scale and long-term patient studies are needed to further validate our findings for more accurate quantitative plaque vulnerability assessment.

Quantitative assessment of coronary artery plaque vulnerability by high-resolution magnetic resonance imaging and computational biomechanics: a pilot study ex vivo

The risk of atherosclerotic plaque disruption is thought to be closely related to plaque composition and rupture triggers such as external mechanical forces. The purpose of this study was to integrate MR imaging and computational techniques for the quantification of plaque vulnerability with morphologic data and biomechanical stress/strain distributions that were all based on high-resolution MR images of coronary artery plaque specimens ex vivo. Twenty-two coronary artery plaque specimens were selectively collected from 10 cadavers. Multislice T(2)-weighted spin echo images were acquired with a resolution of 100 x 100 microm(2). Histopathological images were used as the gold standard for the identification of plaque components and vulnerability. Plaque components were classified on MR images, and the stress/strain components were calculated with a two-dimensional computational model with fluid-structure interactions. As expected, vulnerable plaques appeared to result from a large lipid pool, a thin fibrous cap, and some critical stress/strain conditions. An empiric vulnerability marker was derived and was closely related to the vulnerability score that was determined through pathologic examination. Noninvasive quantification of the MR contrast and mechanical properties of plaque may provide a comprehensive biomarker for the assessment of vulnerability of atherosclerotic plaques.

Finite element modelling and simulations in cardiovascular mechanics and cardiology: A bibliography 1993–2004

The paper gives a bibliographical review of the finite element modelling and simulations in cardiovascular mechanics and cardiology from the theoretical as well as practical points of views. The bibliography lists references to papers, conference proceedings and theses/dissertations that were published between 1993 and 2004. At the end of this paper, more than 890 references are given dealing with subjects as: Cardiovascular soft tissue modelling; material properties; mechanisms of cardiovascular components; blood flow; artificial components; cardiac diseases examination; surgery; and other topics.

Assessment of vulnerable plaque composition by matching the deformation of a parametric plaque model to measured plaque deformation

Intravascular ultrasound (IVUS) elastography visualizes local radial strain of arteries in so-called elastograms to detect rupture-prone plaques. However, due to the unknown arterial stress distribution these elastograms cannot be directly interpreted as a morphology and material composition image. To overcome this limitation we have developed a method that reconstructs a Young's modulus image from an elastogram. This method is especially suited for thin-cap fibroatheromas (TCFAs), i.e., plaques with a media region containing a lipid pool covered by a cap. Reconstruction is done by a minimization algorithm that matches the strain image output, calculated with a parametric finite element model (PFEM) representation of a TCFA, to an elastogram by iteratively updating the PFEM geometry and material parameters. These geometry parameters delineate the TCFA media, lipid pool and cap regions by circles. The material parameter for each region is a Young's modulus, EM, EL, and EC, respectively. The method was successfully tested on computer-simulated TCFAs (n = 2), one defined by circles, the other by tracing TCFA histology, and additionally on a physical phantom (n = 1) having a stiff wall (measured EM = 16.8 kPa) with an eccentric soft region (measured EL = 4.2 kPa). Finally, it was applied on human coronary plaques in vitro (n = 1) and in vivo (n = 1). The corresponding simulated and measured elastograms of these plaques showed radial strain values from 0% up to 2% at a pressure differential of 20, 20, 1, 20, and 1 mmHg respectively. The used/reconstructed Young's moduli [kPa] were for the circular plaque EL = 50/66, EM = 1500/1484, EC = 2000/2047, for the traced plaque EL = 25/1, EM = 1000/1148, EC = 1500/1491, for the phantom EL = 4.2/4 kPa, EM = 16.8/16, for the in vitro plaque EL = n.a./29, EM = n.a./647, EC = n.a./1784 kPa and for the in vivo plaque EL = n.a./2, EM = n.a./188, Ec = n.a./188 kPa.

Mechanisms, pathophysiology, and therapy of arterial stiffness

Arterial stiffness is a growing epidemic associated with increased risk of cardiovascular events, dementia, and death. Decreased compliance of the central vasculature alters arterial pressure and flow dynamics and impacts cardiac performance and coronary perfusion. This article reviews the structural, cellular, and genetic contributors to arterial stiffness, including the roles of the scaffolding proteins, extracellular matrix, inflammatory molecules, endothelial cell function, and reactive oxidant species. Additional influences of atherosclerosis, glucose regulation, chronic renal disease, salt, and changes in neurohormonal regulation are discussed. A review of the hemodynamic impact of arterial stiffness follows. A number of lifestyle changes and therapies that reduce arterial stiffness are presented, including weight loss, exercise, salt reduction, alcohol consumption, and neuroendocrine-directed therapies, such as those targeting the renin-angiotensin aldosterone system, natriuretic peptides, insulin modulators, as well as novel therapies that target advanced glycation end products.

Effect of a lipid pool on stress/strain distributions in stenotic arteries: 3-D fluid-structure interactions (FSI) models

Nonlinear 3-D models with fluid-structure interactions (FSI) based on in vitro experiments are introduced and solved by ADINA to perform flow and stress/strain analysis for stenotic arteries with lipid cores. Navier-Stokes equations are used as the governing equations for the fluid. Hyperelastic Mooney-Rivlin models are used for both the arteries and lipid cores. Our results indicate that critical plaque stress/strain conditions are affected considerably by stenosis severity, eccentricity, lipid pool size, shape and position, plaque cap thickness, axial stretch, pressure, and fluid-structure interactions, and may be used for possible plaque rupture predictions.

Impact of age and hyperglycemia on the mechanical behavior of intact human coronary arteries: an ex vivo intravascular ultrasound study

Despite their advantages, percutaneous coronary interventional procedures are less effective in diabetic patients. Changes in the mechanical properties of vascular walls secondary to long-term hyperglycemia as well as other factors such as age may influence coronary distensibility. This investigation is aimed at deciphering the extent of these effects on distensibility of postmortem human coronary arteries in a controlled manner. Excised human left anterior descending (LAD) coronary arteries were obtained within 24 h postmortem. With the use of intravascular ultrasound, vascular deformation was analyzed at midregions of 51 moderate lesions. Intraluminal pressure was systematically altered using a computerized pressure pump system and monitored by a pressure-sensing guidewire. Distensibility, a normalized compliance term, was defined as the change in lumen area normalized by the initial reference area over a given pressure interval. With the use of multivariate analysis and repeated-measures ANOVA, coronary distensibility was independently influenced by hyperglycemia and age (P < 0.05) through the entire pressure range. Within physiological pressure range, distensibility was significantly reduced with age in nonhyperglycemic coronary specimens (10.55 +/- 4.41 vs. 6.99 +/- 2.45, x10(3) kPa(-1), P = 0.01), whereas the hyperglycemic vessels were stiff even in the younger group (7.90 +/- 5.82 vs. 7.20 +/- 3.36, x10(3) kPa(-1), P = 0.79). Similar results were observed with stiffness index and elastic modulus of the arteries. Hyperglycemia and age independently influenced the distensibility of moderately atherosclerotic LAD coronary arteries. The stiffening with age was overshadowed in the hyperglycemic group by as-yet-undetermined factors.

Blood vessel constitutive models-1995-2002

Knowledge of blood vessel mechanical properties is fundamental to the understanding of vascular function in health and disease. Analytic results can help physicians in the clinic, both in designing and in choosing appropriate therapies. Understanding the mechanical response of blood vessels to physiologic loads is necessary before ideal therapeutic solutions can be realized. For this reason, blood vessel constitutive models are needed. This article provides a critical review of recent blood vessel constitutive models, starting with a brief overview of the structure and function of arteries and veins, followed by a discussion of experimental techniques used in the characterization of material properties. Current models are classified by type, including pseudoelastic, randomly elastic, poroelastic, and viscoelastic. Comparisons are presented between the various models and existing experimental data. Applications of blood vessel constitutive models are also briefly presented, followed by the identification of future directions in research.

Computational modeling of arterial biomechanics: insights into pathogenesis and treatment of vascular disease

We review how advances in computational techniques are improving our understanding of the biomechanical behavior of the healthy and diseased cardiovascular system. Numerical modeling of biomechanics is being used in a wide variety of ways, including assessment of effects of mural and hemodynamically induced stresses on atherogenesis, development of risk measures for aneurysm rupture, improvement in interpretation of medical images, and quantification of oxygen transport in diseased and healthy arteries. Although not amenable to routine clinical use, numerical modeling of cardiovascular biomechanics is a powerful research tool.

Biochemical characterization of atherosclerotic plaque constituents using FTIR spectroscopy and histology

The behavior of vulnerable atherosclerotic plaques is believed to be closely related to plaque composition. There is a need for an effective in vivo technique for examining plaque constituent properties. In this study, Fourier transform infrared spectroscopy using attenuated total reflectance (FTIR-ATR) was used to assess and analyze the biochemical properties of human atherosclerotic plaques. FTIR spectra clearly revealed prominent spectral features corresponding to plaque constituents of interest: the 2930 cm(-1) and 2850 cm(-1) peaks (indicating the presence of lipids), the 1730 cm(-1) peak (lipid esters), the 1550 cm(-1) and 1650 cm(-1) peaks (fibrous tissues), and the 1100-1000 cm(-1) broad phosphate peak (calcification). Spectral data examined on a qualitative basis correlated well with both gross tissue anatomy and histologic features. Gross spatial mappings of tissue sections of both lipidic and calcified plaques were performed. Spectra from various regions of the plaques demonstrated the evolution of lipid peaks, fibrous tissue peaks, and the phosphate calcification band within the plaques. Histologic analysis corroborated the spectral findings in this study.

A novel experimental method to estimate stress-strain behavior of intact coronary arteries using intravascular ultrasound (IVUS)

Most arterial mechanics studies have focused on excised non-coronary vessels, with few studies validating the application of ex-vivo results to in-vivo conditions. A method was developed for testing the mechanical properties of intact left anterior descending coronary arteries under a variety of conditions. Vascular deformation and pressure were simultaneously measured with intravascular ultrasound and a pressure transducer guidewire, respectively. Results suggest the importance of understanding in-vivo factors such as myocardial support, vascular tone and local pressure fluctuations when applying ex-vivo coronary characterization data. With further development, this method can more accurately characterize the true in-vivo constitutive behavior in normal and atherosclerotic coronaries.

In-vivo prediction of human coronary plaque rupture location using intravascular ultrasound and the finite element method

BACKGROUND

Spontaneous rupture of atherosclerotic plaques is known to be involved in the mechanism leading to acute coronary syndromes. Means to detect plaques prone to rupture and predict rupture location would then be very valuable for clinical diagnosis.

DESIGN

In this study, finite element (FE) analysis based on intravascular ultrasound (IVUS) images of atherosclerotic arteries was used to predict in-vivo plaque rupture locations. In four patients with coronary artery diseases, IVUS images were recorded before and after balloon angioplasty. Pre-angioplasty images were recorded after injection of ATP. This caused a brief drop of arterial blood pressure down to values of about 20 mmHg, and thus allowed the recording of the unloaded configurations of arteries used to initiate FE analysis. Plaque rupture was triggered by balloon inflation (coronary angioplasty). FE simulations were performed under physiological loading conditions. Stress distributions within the plaque and the arterial wall were determined. The corresponding stress maps are presented.

RESULTS

Circumferential tensile peak stress areas were compared with plaque rupture locations on postangioplasty IVUS images. They were found to coincide in all four studied cases.

CONCLUSION

Our results agreed with those reported in previous studies based on ex-vivo postnecropsic data and showed the feasibility of in-vivo prediction of atherosclerotic plaque rupture location.