Non-uniform shrinkage for obtaining computational start shape for in-vivo MRI-based plaque vulnerability assessment

BackgroundCritical mechanical conditions, such as stress within the structure and shear stress due to blood flow, predicted from in-vivo magnetic resonance image (MRI)-based computational simulations have shown to be potential in assessing carotid plaque vulnerability. Plaque contours obtained from in-vivo MRI are a result of a pressurized configuration due to physiological loading. However, in order to make accurate predictions, the computational model must be based on the loading-free geometry. A shrinkage procedure can be used to obtain the computational start shape.MethodIn this study, electrocardiograph (ECG)-gated MR-images of carotid plaques were obtained from 28 patients. The contours of each plaque were segmented manually. Additional to a uniform shrinkage procedure, a non-uniform shrinkage refinement procedure was used. This procedure was repeated until the pressurized lumen contour and fibrous cap thickness had the best match with the in-vivo image.ResultsCompared to the uniform shrinkage procedure, the non-uniform shrinkage significantly reduced the difference in lumen shape and in cap thickness at the thinnest site. Results indicate that uniform shrinkage would underestimate the critical stress in the structure by 20.5±10.7%.ConclusionFor slices with an irregular lumen shape (the ratio of the maximum width to the minimum width is more than 1.05), the non-uniform shrinkage procedure is needed to get an accurate stress profile for mechanics and MRI-based carotid plaque vulnerability assessment.     

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.     

Human annulus fibrosus material properties from biaxial testing and constitutive modeling are altered with degeneration

The annulus fibrosus (AF) of the intervertebral disk undergoes large and multidirectional stresses and strains. Uniaxial tensile tests are limited for measuring AF material properties, because freely contracting edges can prevent fiber stretch and are not representative of in situ boundary conditions. The objectives of this study were to measure human AF biaxial tensile mechanics and to apply and validate a constitutive model to determine material properties. Biaxial tensile tests were performed on samples oriented along the circumferential–axial and the radial–axial directions. Data were fit to a structurally motivated anisotropic hyperelastic model composed of isotropic extra-fibrillar matrix, nonlinear fibers, and fiber–matrix interactions (FMI) normal to the fibers. The validated model was used to simulate shear and uniaxial tensile behavior, to investigate AF structure–function, and to quantify the effect of degeneration. The biaxial stress–strain response was described well by the model (R ²?>?0.9). The model showed that the parameters for fiber nonlinearity and the normal FMI correlated with degeneration, resulting in an elongated toe-region and lower stiffness with degeneration. The model simulations in shear and uniaxial tension successfully matched previously published circumferential direction Young’s modulus, provided an explanation for the low values in previously published axial direction Young’s modulus, and was able to simulate shear mechanics. The normal FMI were important contributors to stress and changed with degeneration, therefore, their microstructural and compositional source should be investigated. Finally, the biaxial mechanical data and constitutive model can be incorporated into a disk finite element model to provide improved quantification of disk mechanics.     

Nonlinear multiscale analysis of coronary atherosclerotic vulnerable plaque artery: fluid-structural modeling with micromechanics

Biomechanics and Modeling in Mechanobiology - A unique three-dimensional (3D) computational multiscale modeling approach is proposed to investigate the influence of presence of microcalcification...     

Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease

Kawasaki disease (KD) is the leading cause of acquired heart disease in children and can result in life-threatening coronary artery aneurysms in up to 25 % of patients. These aneurysms put patients at risk of thrombus formation, myocardial infarction, and sudden death. Clinicians must therefore decide which patients should be treated with anticoagulant medication, and/or surgical or percutaneous intervention. Current recommendations regarding initiation of anticoagulant therapy are based on anatomy alone with historical data suggesting that patients with aneurysms \(\ge \) 8 mm are at greatest risk of thrombosis. Given the multitude of variables that influence thrombus formation, we postulated that hemodynamic data derived from patient-specific simulations would more accurately predict risk of thrombosis than maximum diameter alone. Patient-specific blood flow simulations were performed on five KD patients with aneurysms and one KD patient with normal coronary arteries. Key hemodynamic and geometric parameters, including wall shear stress, particle residence time, and shape indices, were extracted from the models and simulations and compared with clinical outcomes. Preliminary fluid structure interaction simulations with radial expansion were performed, revealing modest differences in wall shear stress compared to the rigid wall case. Simulations provide compelling evidence that hemodynamic parameters may be a more accurate predictor of thrombotic risk than aneurysm diameter alone and motivate the need for follow-up studies with a larger cohort. These results suggest that a clinical index incorporating hemodynamic information be used in the future to select patients for anticoagulant therapy.     

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.     

Finite elasticity modeling of the biaxial and uniaxial properties of compliant vascular grafts

Compliant vascular grafts were modeled by finite elasticity theory. A linear, biaxial model satisfactorily described the stress-strain behavior in inflation tests, where the sample length was fixed longitudinally and inflated. The model was then used to predict the behavior in a longitudinal test (where the longitudinal stretch was varied while keeping the pressure zero), and in a uniaxial test of a circumferential strip. The model satisfactorily predicted the longitudinal Young's modulus measured in the longitudinal test. The model was less successful in predicting the circumferential Young's modulus measured in the uniaxial test, possibly because the state of stress was not purely uniaxial.     

Strategies for the assessment of genetic coronary artery disease risk.

In atherosclerotic diseases, genetic factors have a substantial influence on the age of onset and the frequency and severity of clinical symptoms, as well as response to therapy. In myocardial infarctions occurring at young age, genetics may be the leading causative factor. Despite such a prominent role of genetics in the pathophysiology of atherosclerosis clinical risk assessment and therapeutic decision making are still based on classical risk factors. In this paper we analyse the reasons for the current lack of predictive power of genetics-based algorithms and we speculate why future developments might open the door to a role for genetics in the clinical management of atherosclerosis.     

Torsion of the human left ventricle: experimental analysis and computational modeling

We set a twofold investigation: we assess left ventricular (LV) rotation and twist in the human heart through 3D-echocardiographic speckle tracking, and use representative experimental data as benchmark with respect to numerical results obtained by solving our mechanical model of the LV. We aim at new insight into the relationships between myocardial contraction patterns and the overall behavior at the scale of the whole organ. It is concluded that torsional rotation is sensitive to transmural gradients of contractility which is assumed linearly related to action potential duration (APD). Pressure-volume loops and other basic strain measures are not affected by these gradients. Therefore, realistic torsional behavior of human LV may indeed correspond to the electrophysiological and functional differences between endocardial and epicardial cells recently observed in non-failing hearts. Future investigations need now to integrate the mechanical model proposed here with minimal models of human ventricular APD to drive excitation-contraction coupling transmurally.     

A new imaging technique to study 3-D plaque and shear stress distribution in human coronary artery bifurcations in vivo

OBJECTIVE: Bifurcations of coronary arteries are predilection sites for atherosclerosis and expansive remodeling, the latter being associated with plaque vulnerability. Both are related to blood flow-induced shear stress (SS). We present a new approach to generate 3-D reconstructions of coronary artery bifurcations in vivo and investigate the relationship between SS, wall thickness (WT) and remodeling. METHODS: The patient specific 3-D reconstruction of the main branch of the bifurcation was obtained by combining intravascular ultrasound and biplane angiography, and the 3-D lumen of the side branch was based on biplane angiography only. The two data sets were fused and computational methods were applied to determine the SS distribution, using patient derived flow and viscosity data. The intravascular ultrasound data allowed us to measure local WT and remodeling in the main branch. RESULTS: The lumen reconstruction procedure was successful and it was shown that the impact of the side branch on SS distribution in the main branch diminished within 3mm. Distal to the bifurcation, two continuous regions in the main branch were identified. In the proximal region, we observed lumen preservation, and expansive remodeling. Although a plaque was observed in the low SS region at the non-divider wall, no relationship between SS and WT was found. In the distal region, we observed lumen narrowing and a significant positive relationship between SS and WT. CONCLUSIONS: A new imaging technique was applied to generate a 3-D reconstruction of a human coronary artery bifurcation in vivo. The observed relationship between SS, WT and remodeling in this specific patient illustrates the spatial heterogeneity of the atherosclerosis in the vicinity of arterial bifurcations.     

Biaxial elastic material properties of porcine coronary media and adventitia

The importance of mechanical stresses and strains has become well recognized in vascular physiology and pathology. To compute the stress and strain on the various components of the vessel wall, we must know the constitutive equations for the different layers of the vessel wall. The objective of the present study is to determine the constitutive equation of the coronary artery treated as a two-layer composite: intima-media and adventitial layers. Twelve hearts were obtained from a local slaughterhouse, and the right coronary artery and left anterior descending artery were dissected free from the myocardium. The vessel wall was initially mechanically tested biaxially (inflation and axial extension) as a whole (intact wall) and subsequently as intima-media or adventitial layer. A Fung-type exponential strain energy function was used to curve fit the experimental data for the intact wall and individual layers for the right coronary artery and left anterior descending artery. Two methods were used for the determination of material constants, including the Marquardt-Levenberg nonlinear least squares method and the genetic algorithm method. Our results show that there were no statistically significant differences in the material constants obtained from the two methods and that either set of elastic constants results in good fit of the data. Furthermore, at an in vivo value of axial stretch ratio, we find that the stiffness is as follows: intima-media > intact > adventitia. These results underscore the composite nature of coronary arteries with different material properties in each layer. The present results are necessary for analysis of coronary artery mechanics and to provide a fundamental understanding of vessel physiology.     

Haemodynamic assessment of human coronary arteries is affected by degree of freedom of artery movement

Abnormal haemodynamic parameters are associated with atheroma plaque progression and instability in coronary arteries. Flow recirculation, shear stress and pressure gradient are understood to be important pathogenic mediators in coronary disease. The effect of freedom of coronary artery movement on these parameters is still unknown. Fluid–structure interaction (FSI) simulations were carried out in 25 coronary artery models derived from authentic human coronaries in order to investigate the effect of degree of freedom of movement of the coronary arteries on flow recirculation, wall shear stress (WSS) and wall pressure gradient (WPG). Each FSI model had distinctive supports placed upon it. The quantitative and qualitative differences in flow recirculation, maximum wall shear stress (MWSS), areas of low wall shear stress (ALWSS) and maximum wall pressure gradient (MWPG) for each model were determined. The results showed that greater freedom of movement was associated with lower MWSS, smaller ALWSS, smaller flow recirculation zones and lower MWPG. With increasing percentage diameter stenosis (%DS), the effect of degree of freedom on flow recirculation and WSS diminished. Freedom of movement is an important variable to be considered for computational modelling of human coronary arteries, especially in the setting of mild to moderate stenosis.

Abbreviations: 3D: Three-dimensional; 3DR: Three-dimensional Reconstruction; 3D-QCA: Three-dimensional quantitative coronary angiography; ALWSS: Areas of low wall shear stress; CAD: Coronary artery disease; CFD: Computational fluid dynamics; %DS: Diameter stenosis percentage; EPCS: End point of counter-rotating streamlines; FSI: Fluid–structure interaction; IVUS: Intravascular ultrasound; LAD: Left anterior descending; MWSS: Maximum wall shear stress; SST: Shear stress transport; TAWSS: Time-averaged wall shear stress; WSS: wall shear stress; WPG: Wall pressure gradient; MWPG: Maximum wall pressure gradient; FFR: Fractional flow reserve; iFR: Instantaneous wave-free ratio     

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.     

A combined experimental and computational study on the material properties of shape memory polyurethane

A type of shape memory polyurethane with 60 wt% hard segments (SMPU60) was prepared. Its material properties were tested by dynamic mechanical analysis (DMA) and Instron, and simulated using fully atomistic molecular dynamics (MD). The glass transition temperature (T _g) of SMPU60 determined by DMA is 316 K, which is slightly lower than that estimated through MD simulations (T _g = 328 K) , showing the calculated T _g is in good agreement with experimental data. A complex hydrogen bonding network was revealed with the calculation of radial distribution functions (RDFs). The C═O⋯H bond is the predominant hydrogen-bonding interaction. With increasing temperature, both the hydrogen bonding and the moduli decreased, and the dissociation of intermolecular hydrogen bonding induced the decrease of the moduli.     

Hydrodynamic properties of rigid particles: comparison of different modeling and computational procedures.

The hydrodynamic properties of rigid particles are calculated from models composed of spherical elements (beads) using theories developed by Kirkwood, Bloomfield, and their coworkers. Bead models have usually been built in such a way that the beads fill the volume occupied by the particles. Sometimes the beads are few and of varying sizes (bead models in the strict sense), and other times there are many small beads (filling models). Because hydrodynamic friction takes place at the molecular surface, another possibility is to use shell models, as originally proposed by Bloomfield. In this work, we have developed procedures to build models of the various kinds, and we describe the theory and methods for calculating their hydrodynamic properties, including approximate methods that may be needed to treat models with a very large number of elements. By combining the various possibilities of model building and hydrodynamic calculation, several strategies can be designed. We have made a quantitative comparison of the performance of the various strategies by applying them to some test cases, for which the properties are known a priori. We provide guidelines and computational tools for bead modeling.     

Determination of layer-specific mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling

At autopsy, 13 nonstenotic human left anterior descending coronary arteries [71.5 +/- 7.3 (mean +/- SD) yr old] were harvested, and related anamnesis was documented. Preconditioned prepared strips (n = 78) of segments from the midregion of the left anterior descending coronary artery from the individual layers in axial and circumferential directions were subjected to cyclic quasi-static uniaxial tension tests, and ultimate tensile stresses and stretches were documented. The ratio of outer diameter to total wall thickness was 0.189 +/- 0.014; ratios of adventitia, media, and intima thickness to total wall thickness were 0.4 +/- 0.03, 0.36 +/- 0.03, and 0.27 +/- 0.02, respectively; axial in situ stretch of 1.044 +/- 0.06 decreased with age. Stress-stretch responses for the individual tissues showed pronounced mechanical heterogeneity. The intima is the stiffest layer over the whole deformation domain, whereas the media in the longitudinal direction is the softest. All specimens exhibited small hysteresis and anisotropic and strong nonlinear behavior in both loading directions. The media and intima showed similar ultimate tensile stresses, which are on average three times smaller than ultimate tensile stresses in the adventitia (1,430 +/- 604 kPa circumferential and 1,300 +/- 692 kPa longitudinal). The ultimate tensile stretches are similar for all tissue layers. A recently proposed constitutive model was extended and used to represent the deformation behavior for each tissue type over the entire loading range. The study showed the need to model nonstenotic human coronary arteries with nonatherosclerotic intimal thickening as a composite structure composed of three solid mechanically relevant layers with different mechanical properties. The intima showed significant thickness, load-bearing capacity, and mechanical strength compared with the media and adventitia.     

Mitral leaflet modeling: Importance of in vivo shape and material properties

The anterior mitral leaflet (AML) is a thin membrane that withstands high left ventricular (LV) pressure pulses 100,000 times per day. The presence of contractile cells determines AML in vivo stiffness and complex geometry. Until recently, mitral valve finite element (FE) models have neglected both of these aspects. In this study we assess their effect on AML strains and stresses, hypothesizing that these will differ significantly from those reported in literature. Radiopaque markers were sewn on the LV, the mitral annulus, and AML in sheep hearts, and their four-dimensional coordinates obtained with biplane video fluoroscopy. Employing in vivo data from three representative hearts, AML FE models were created from the marker coordinates at the end of isovolumic relaxation assumed as the unloaded reference state. AML function was simulated backward through systole, applying the measured trans-mitral pressure on AML LV surface and marker displacements on AML boundaries. Simulated AML displacements and curvatures were consistent with in vivo measurements, confirming model accuracy. AML circumferential strains were mostly tensile (1-3%), despite being compressive (-1%) near the commissures. Radial strains were compressive in the belly (-1 to -0.2%), and tensile (2-8%) near the free edge. These results differ significantly from those of previous FE models. They reflect the synergy of high tissue stiffness, which limits tensile circumferential strains, and initial compound curvature, which forces LV pressure to compress AML radially. The obtained AML shape may play a role not only in preventing mitral regurgitation, but also in optimizing LV outflow fluid dynamics.     

The roles of myeloperoxidase in coronary artery disease and its potential implication in plaque rupture

Atherosclerosis is the main pathophysiological process underlying coronary artery disease (CAD). Acute complications of atherosclerosis, such as myocardial infarction, are caused by the rupture of vulnerable atherosclerotic plaques, which are characterized by thin, highly inflamed, and collagen-poor fibrous caps. Several lines of evidence mechanistically link the heme peroxidase myeloperoxidase (MPO), inflammation as well as acute and chronic manifestations of atherosclerosis. MPO and MPO-derived oxidants have been shown to contribute to the formation of foam cells, endothelial dysfunction and apoptosis, the activation of latent matrix metalloproteinases, and the expression of tissue factor that can promote the development of vulnerable plaque. As such, detection, quantification and imaging of MPO mass and activity have become useful in cardiac risk stratification, both for disease assessment and in the identification of patients at risk of plaque rupture. This review summarizes the current knowledge about the role of MPO in CAD with a focus on its possible roles in plaque rupture and recent advances to quantify and image MPO in plasma and atherosclerotic plaques.