Using in vivo Cine and 3D multi-contrast MRI to determine human atherosclerotic carotid artery material properties and circumferential shrinkage rate and their impact on stress/strain predictions

In vivo magnetic resonance image (MRI)-based computational models have been introduced to calculate atherosclerotic plaque stress and strain conditions for possible rupture predictions. However, patient-specific vessel material properties are lacking in those models, which affects the accuracy of their stress/strain predictions. A noninvasive approach of combining in vivo Cine MRI, multicontrast 3D MRI, and computational modeling was introduced to quantify patient-specific carotid artery material properties and the circumferential shrinkage rate between vessel in vivo and zero-pressure geometries. In vivo Cine and 3D multicontrast MRI carotid plaque data were acquired from 12 patients after informed consent. For each patient, one nearly-circular slice and an iterative procedure were used to quantify parameter values in the modified Mooney-Rivlin model for the vessel and the vessel circumferential shrinkage rate. A sample artery slice with and without a lipid core and three material parameter sets representing stiff, median, and soft materials from our patient data were used to demonstrate the effect of material stiffness and circumferential shrinkage process on stress/strain predictions. Parameter values of the Mooney-Rivlin models for the 12 patients were quantified. The effective Young's modulus (YM, unit: kPa) values varied from 137 (soft), 431 (median), to 1435 (stiff), and corresponding circumferential shrinkages were 32%, 12.6%, and 6%, respectively. Using the sample slice without the lipid core, the maximum plaque stress values (unit: kPa) from the soft and median materials were 153.3 and 96.2, which are 67.7% and 5% higher than that (91.4) from the stiff material, while the maximum plaque strain values from the soft and median materials were 0.71 and 0.293, which are about 700% and 230% higher than that (0.089) from the stiff material, respectively. Without circumferential shrinkages, the maximum plaque stress values (unit: kPa) from the soft, median, and stiff models were inflated to 330.7, 159.2, and 103.6, which were 116%, 65%, and 13% higher than those from models with proper shrinkage. The effective Young's modulus from the 12 human carotid arteries studied varied from 137 kPa to 1435 kPa. The vessel circumferential shrinkage to the zero-pressure condition varied from 6% to 32%. The inclusion of proper shrinkage in models based on in vivo geometry is necessary to avoid over-estimating the stresses and strains by up 100%. Material stiffness had a greater impact on strain (up to 700%) than on stress (up to 70%) predictions. Accurate patient-specific material properties and circumferential shrinkage could considerably improve the accuracy of in vivo MRI-based computational stress/strain predictions.     

Cyclic Bending Contributes to High Stress in a Human Coronary Atherosclerotic Plaque and Rupture Risk: In Vitro Experimental Modeling and Ex Vivo MRI-Based Computational Modeling Approach

Many acute cardiovascular syndromes such as heart attack and stroke are caused by atherosclerotic plaque ruptures which often happen without warning. MRI-based models with fluid-structure interactions (FSI) have been introduced to perform flow and stress/strain analysis for atherosclerotic plaques and identify possible mechanical and morphological indices for accurate plaque vulnerability assessment. In this paper, cyclic bending was added to 3D FSI coronary plaque models for more accurate mechanical predictions. Curvature variation was prescribed using the data of a human left anterior descending (LAD) coronary artery. Five computational models were constructed based on ex vivo MRI human coronary plaque data to assess the effects of cyclic bending, pulsating pressure, plaque structure, and axial stretch on plaque stress/strain distributions. In vitro experiments using a hydrogel stenosis model with cyclical bending were performed to observe effect of cyclical bending on flow conditions. Our results indicate that cyclical bending may cause more than 100% or even up to more than 1000% increase in maximum principal stress values at locations where the plaque is bent most. Stress increase is higher when bending is coupled with axial stretch, non-smooth plaque structure, or resonant pressure conditions (zero phase angle shift). Effects of cyclic bending on flow behaviors are more modest (21.6% decrease in maximum velocity, 10.8% decrease in flow rate, maximum flow shear stress changes were < 5%). Computational FSI models including cyclic bending, plaque components and structure, axial stretch, accurate in vivo measurements of pressure, curvature, and material properties should lead to significant improvement on stress-based plaque mechanical analysis and more accurate coronary plaque vulnerability assessment.     

Stress-Based Plaque Vulnerability Index and Assessment for Carotid Atherosclerotic Plaques Using Patient-Specific Vessel Material Properties

Cardiovascular diseases are closely linked to atherosclerotic plaque development and rupture. Assessment of plaque vulnerability is of fundamental significance to cardiovascular research and disease diagnosis, prevention, treatment and management. Magnetic resonance image (MRI) data of carotid atherosclerotic plaques from 8 patients (5 male, 3 female; age: 62-83, mean=71) were acquired at the University of Washington (UW), Seattle by the Vascular Imaging Laboratory (VIL) with written informed consent obtained. Patient-specific vessel material properties were quantified using Cine MRI data for modeling use. 3D thin-layer models were used to obtain plaque stress and strain for plaque assessment. A stress-based plaque vulnerability index (SPVI) was proposed to combine mechanical analysis, plaque morphology and composition for more complete carotid plaque vulnerability assessment. The five intervals (unit: kPa) [0, 46.8), [46.8, 80), [80, 92), [92, 103), and [103, +∞) from in vivo material models were used for SPVI values of 0, 1, 2, 3 and 4, respectively. The optimized agreement rate was 85.19%. The use of patient-specific material properties in plaque models could potentially improve the accuracy of model stress/strain calculations. SPVI has the potential to improve the current image-based screening and plaque vulnerability assessment schemes.     

Local critical stress correlates better than global maximum stress with plaque morphological features linked to atherosclerotic plaque vulnerability: an in vivo multi-patient study

Background  

It is believed that mechanical stresses play an important role in atherosclerotic plaque rupture process and may be used for better plaque vulnerability assessment and rupture risk predictions. Image-based plaque models have been introduced in recent years to perform mechanical stress analysis and identify critical stress indicators which may be linked to rupture risk. However, large-scale studies based on in vivo patient data combining mechanical stress analysis, plaque morphology and composition for carotid plaque vulnerability assessment are lacking in the current literature.     

Patient-Specific Artery Shrinkage and 3D Zero-Stress State in Multi-Component 3D FSI Models for Carotid Atherosclerotic Plaques Based on <i>In Vivo</i> MRI Data

Image-based computational models for atherosclerotic plaques have been developed to perform mechanical analysis to quantify critical flow and stress/strain conditions related to plaque rupture which often leads directly to heart attack or stroke. An important modeling issue is how to determine zero stress state from in vivo plaque geometries. This paper presents a method to quantify human carotid artery axial and inner circumferential shrinkages by using patient-specific ex vivo and in vivo MRI images. A shrink-stretch process based on patient-specific in vivo plaque morphology and shrinkage data was introduced to shrink the in vivo geometry first to find the zero-stress state (opening angle was ignored to reduce the complexity), and then stretch and pressurize to recover the in vivo plaque geometry with computed initial stress, strain, flow pressure and velocity conditions. Effects of the shrink-stretch process on plaque stress/strain distributions were demonstrated based on patient-specific data using 3D models with fluid-structure interactions (FSI). The average artery axial and inner circumferential shrinkages were 25% and 7.9%, respectively, based on a data set obtained from 10 patients. Maximum values of maximum principal stress and strain increased 349.8% and 249% respectively with 33% axial stretch. Influence of inner circumferential shrinkage (7.9%) was not very noticeable under 33% axial stretch, but became more noticeable under smaller axial stretch. Our results indicated that accurate knowledge of artery shrinkages and the shrink-stretch process will considerably improve the accuracy of computational predictions made based on results from those in vivo MRI-based FSI models.     

In vivo serial MRI-based models and statistical methods to quantify sensitivity and specificity of mechanical predictors for carotid plaque rupture: location and beyond

It has been hypothesized that mechanical risk factors may be used to predict future atherosclerotic plaque rupture. Truly predictive methods for plaque rupture and methods to identify the best predictor(s) from all the candidates are lacking in the literature. A novel combination of computational and statistical models based on serial magnetic resonance imaging (MRI) was introduced to quantify sensitivity and specificity of mechanical predictors to identify the best candidate for plaque rupture site prediction. Serial in vivo MRI data of carotid plaque from one patient was acquired with follow-up scan showing ulceration. 3D computational fluid-structure interaction (FSI) models using both baseline and follow-up data were constructed and plaque wall stress (PWS) and strain (PWSn) and flow maximum shear stress (FSS) were extracted from all 600 matched nodal points (100 points per matched slice, baseline matching follow-up) on the lumen surface for analysis. Each of the 600 points was marked "ulcer" or "nonulcer" using follow-up scan. Predictive statistical models for each of the seven combinations of PWS, PWSn, and FSS were trained using the follow-up data and applied to the baseline data to assess their sensitivity and specificity using the 600 data points for ulcer predictions. Sensitivity of prediction is defined as the proportion of the true positive outcomes that are predicted to be positive. Specificity of prediction is defined as the proportion of the true negative outcomes that are correctly predicted to be negative. Using probability 0.3 as a threshold to infer ulcer occurrence at the prediction stage, the combination of PWS and PWSn provided the best predictive accuracy with (sensitivity, specificity)?=?(0.97, 0.958). Sensitivity and specificity given by PWS, PWSn, and FSS individually were (0.788, 0.968), (0.515, 0.968), and (0.758, 0.928), respectively. The proposed computational-statistical process provides a novel method and a framework to assess the sensitivity and specificity of various risk indicators and offers the potential to identify the optimized predictor for plaque rupture using serial MRI with follow-up scan showing ulceration as the gold standard for method validation. While serial MRI data with actual rupture are hard to acquire, this single-case study suggests that combination of multiple predictors may provide potential improvement to existing plaque assessment schemes. With large-scale patient studies, this predictive modeling process may provide more solid ground for rupture predictor selection strategies and methods for image-based plaque vulnerability assessment.     

An efficient two-stage approach for image-based FSI analysis of atherosclerotic arteries

Patient-specific biomechanical modeling of atherosclerotic arteries has the potential to aid clinicians in characterizing lesions and determining optimal treatment plans. To attain high levels of accuracy, recent models use medical imaging data to determine plaque component boundaries in three dimensions, and fluid–structure interaction is used to capture mechanical loading of the diseased vessel. As the plaque components and vessel wall are often highly complex in shape, constructing a suitable structured computational mesh is very challenging and can require a great deal of time. Models based on unstructured computational meshes require relatively less time to construct and are capable of accurately representing plaque components in three dimensions. These models unfortunately require additional computational resources and computing time for accurate and meaningful results. A two-stage modeling strategy based on unstructured computational meshes is proposed to achieve a reasonable balance between meshing difficulty and computational resource and time demand. In this method, a coarsegrained simulation of the full arterial domain is used to guide and constrain a fine-scale simulation of a smaller region of interest within the full domain. Results for a patient-specific carotid bifurcation model demonstrate that the two-stage approach can afford a large savings in both time for mesh generation and time and resources needed for computation. The effects of solid and fluid domain truncation were explored, and were shown to minimally affect accuracy of the stress fields predicted with the two-stage approach.     

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.     

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

Vulnerable and stable atherosclerotic plaques are heterogeneous living materials with peculiar mechanical behaviors depending on geometry, composition, loading and boundary conditions. Computational approaches have the potential to characterize the three-dimensional stress/strain distributions in patient-specific diseased arteries of different types and sclerotic morphologies and to estimate the risk of plaque rupture which is the main trigger of acute cardiovascular events. This review article attempts to summarize a few finite element (FE) studies for different vessel types, and how these studies were performed focusing on the used stress measure, inclusion of residual stress, used imaging modality and material model. In addition to histology the most used imaging modalities are described, the most common nonlinear material models and the limited number of models for plaque rupture used for such studies are provided in more detail. A critical discussion on stress measures and threshold stress values for plaque rupture used within the FE studies emphasizes the need to develop a more location and tissue-specific threshold value, and a more appropriate failure criterion. With this addition future FE studies should also consider more advanced strain-energy functions which then fit better to location and tissue-specific experimental data.     

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.     

Construction of healthy arteries using computed tomography and virtual histology intravascular ultrasound

Vessel geometry for numerical analysis is generally obtained by computed tomography (CT) or magnetic resonance imaging (MRI) and intravascular ultrasound (IVUS). Most medical imaging is obtained from patients for hemodynamic analysis due to the properties of vascular disease and the difficulties in angiography. To predict the site where plaque occurs and understand the progression of the lesion, however, it is necessary to take into consideration not only the diseased artery, but also the blood flow characteristics of healthy artery. In order to simulate healthy vessels prior to lesion formation, we performed CT and virtual histology intravascular ultrasound (VH-IVUS) on three actual patients and this data was used to develop criteria for healthy vessel construction, a method that virtually removes all intravascular plaque. The lumen of a vessel generated by CT and the lumen from VH-IVUS were compared, and the cross-sectional areas of plaque components (fibrous, fibrofatty, dense calcium, and necrotic) and the lumen from VH-IVUS were analyzed. Geometric differences in the healthy vessel and diseased vessel were analyzed, and flow characteristics of the healthy vessel and diseased vessel were compared through computational fluid dynamics simulation. Low average wall shear stress (AWSS) was distributed in the site where plaque was removed from the healthy vessel, and a high oscillatory shear index (OSI) was observed in the region proximal to the site where plaque previously existed. Low AWSS and high OSI are widely accepted indicators of plaque formation or the direction of plaque progression. A numerical model that effectively predicts lesion forming sites was also generated based on the healthy vessel construction method presented in this study.     

On the sensitivity of wall stresses in diseased arteries to variable material properties

Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.     

Specimen-specific predictions of contact stress under physiological loading in the human hip: validation and sensitivity studies

Hip osteoarthritis may be initiated and advanced by abnormal cartilage contact mechanics, and finite element (FE) modeling provides an approach with the potential to allow the study of this process. Previous FE models of the human hip have been limited by single specimen validation and the use of quasi-linear or linear elastic constitutive models of articular cartilage. The effects of the latter assumptions on model predictions are unknown, partially because data for the instantaneous behavior of healthy human hip cartilage are unavailable. The aims of this study were to develop and validate a series of specimen-specific FE models, to characterize the regional instantaneous response of healthy human hip cartilage in compression, and to assess the effects of material nonlinearity, inhomogeneity and specimen-specific material coefficients on FE predictions of cartilage contact stress and contact area. Five cadaveric specimens underwent experimental loading, cartilage material characterization and specimen-specific FE modeling. Cartilage in the FE models was represented by average neo-Hookean, average Veronda Westmann and specimen- and region-specific Veronda Westmann hyperelastic constitutive models. Experimental measurements and FE predictions compared well for all three cartilage representations, which was reflected in average RMS errors in contact stress of less than 25 %. The instantaneous material behavior of healthy human hip cartilage varied spatially, with stiffer acetabular cartilage than femoral cartilage and stiffer cartilage in lateral regions than in medial regions. The Veronda Westmann constitutive model with average material coefficients accurately predicted peak contact stress, average contact stress, contact area and contact patterns. The use of subject- and region-specific material coefficients did not increase the accuracy of FE model predictions. The neo-Hookean constitutive model underpredicted peak contact stress in areas of high stress. The results of this study support the use of average cartilage material coefficients in predictions of cartilage contact stress and contact area in the normal hip. The regional characterization of cartilage material behavior provides the necessary inputs for future computational studies, to investigate other mechanical parameters that may be correlated with OA and cartilage damage in the human hip. In the future, the results of this study can be applied to subject-specific models to better understand how abnormal hip contact stress and contact area contribute to OA.     

Morphological and Stress Vulnerability Indices for Human Coronary Plaques and Their Correlations with Cap Thickness and Lipid Percent: An IVUS-Based Fluid-Structure Interaction Multi-patient Study

Plaque vulnerability, defined as the likelihood that a plaque would rupture, is difficult to quantify due to lack of in vivo plaque rupture data. Morphological and stress-based plaque vulnerability indices were introduced as alternatives to obtain quantitative vulnerability assessment. Correlations between these indices and key plaque features were investigated. In vivo intravascular ultrasound (IVUS) data were acquired from 14 patients and IVUS-based 3D fluid-structure interaction (FSI) coronary plaque models with cyclic bending were constructed to obtain plaque wall stress/strain and flow shear stress for analysis. For the 617 slices from the 14 patients, lipid percentage, min cap thickness, critical plaque wall stress (CPWS), strain (CPWSn) and flow shear stress (CFSS) were recorded, and cap index, lipid index and morphological index were assigned to each slice using methods consistent with American Heart Association (AHA) plaque classification schemes. A stress index was introduced based on CPWS. Linear Mixed-Effects (LME) models were used to analyze the correlations between the mechanical and morphological indices and key morphological factors associated with plaque rupture. Our results indicated that for all 617 slices, CPWS correlated with min cap thickness, cap index, morphological index with r = -0.6414, 0.7852, and 0.7411 respectively (p<0.0001). The correlation between CPWS and lipid percentage, lipid index were weaker (r = 0.2445, r = 0.2338, p<0.0001). Stress index correlated with cap index, lipid index, morphological index positively with r = 0.8185, 0.3067, and 0.7715, respectively, all with p<0.0001. For all 617 slices, the stress index has 66.77% agreement with morphological index. Morphological and stress indices may serve as quantitative plaque vulnerability assessment supported by their strong correlations with morphological features associated with plaque rupture. Differences between the two indices may lead to better plaque assessment schemes when both indices were jointly used with further validations from clinical studies.     

Hemodynamics in the carotid artery bifurcation: a comparison between numerical simulations and in vitro MRI measurements

The presence of atherosclerotic plaques has been shown to be closely related to the vessel geometry. Studies on postmortem human arteries and on the experimental animal show positive correlation between the presence of plaque thickness and low shear stress, departure of unidirectional flow and regions of flow separation and recirculation. Numerical simulations of arterial blood flow and direct blood flow velocity measurements by magnetic resonance imaging (MRI) are two approaches for the assessment of arterial blood flow patterns. In order to verify that both approaches give equivalent results magnetic resonance velocity data measured in a compliant anatomical carotid bifurcation model were compared to the results of numerical simulations performed for a corresponding computational vessel model. Cross sectional axial velocity profiles were calculated and measured for the midsinus and endsinus internal carotid artery. At both locations a skewed velocity profile with slow velocities at the outer vessel wall, medium velocities at the side walls and high velocities at the flow divider (inner) wall were observed. Qualitative comparison of the axial velocity patterns revealed no significant differences between simulations and in vitro measurements. Even quantitative differences such as for axial peak flow velocities were less than 10%. Secondary flow patterns revealed some minor differences concerning the form of the vortices but maximum circumferential velocities were in the same range for both methods.     

Effects of intima stiffness and plaque morphology on peak cap stress

Background  

Rupture of the cap of a vulnerable plaque present in a coronary vessel may cause myocardial infarction and death. Cap rupture occurs when the peak cap stress exceeds the cap strength. The mechanical stress within a cap depends on the plaque morphology and the material characteristics of the plaque components. A parametric study was conducted to assess the effect of intima stiffness and plaque morphology on peak cap stress.     

How preconditioning affects the measurement of poro-viscoelastic mechanical properties in biological tissues

It is known that initial loading curves of soft biological tissues are substantially different from subsequent loadings. The later loading curves are generally used for assessing the mechanical properties of a tissue, and the first loading cycles, referred to as preconditioning, are omitted. However, slow viscoelastic phenomena related to fluid flow or collagen viscoelasticity are initiated during these first preconditioning loading cycles and may persist during the actual data collection. When these data are subsequently used for fitting of material properties, the viscoelastic phenomena that occurred during the initial cycles are not accounted for. The aim of the present study is to explore whether the above phenomena are significant for articular cartilage, by evaluating the effect of such time-dependent phenomena by means of computational modeling. Results show that under indentation, collagen viscoelasticity dominates the time-dependent behavior. Under UC, fluid-dependent effects are more important. Interestingly, viscoelastic and poroelastic effects may act in opposite directions and may cancel each other out in a stress–strain curve. Therefore, equilibrium may be apparent in a stress–strain relationship, even though internally the tissue is not in equilibrium. Also, the time-dependent effects of viscoelasticity and poroelasticity may reinforce each other, resulting in a sustained effect that lasts longer than suggested by their individual effects. Finally, the results illustrate that data collected from a mechanical test may depend on the preconditioning protocol. In conclusion, preconditioning influences the mechanical response of articular cartilage significantly and therefore cannot be neglected when determining the mechanical properties. To determine the full viscoelastic and poroelastic properties of articular cartilage requires fitting to both preconditioning and post-preconditioned loading cycles.     

Cap inflammation leads to higher plaque cap strain and lower cap stress: An MRI-PET/CT-based FSI modeling approach

Plaque rupture may be triggered by extreme stress/strain conditions. Inflammation is also implicated and can be imaged using novel imaging techniques. The impact of cap inflammation on plaque stress/strain and flow shear stress were investigated. A patient-specific MRI-PET/CT-based modeling approach was used to develop 3D fluid-structure interaction models and investigate the impact of inflammation on plaque stress/strain conditions for better plaque assessment. 18FDG-PET/CT and MRI data were acquired from 4 male patients (average age: 66) to assess plaque characteristics and inflammation. Material stiffness for the fibrous cap was adjusted lower to reflect cap weakening causing by inflammation. Setting stiffness ratio (SR) to be 1.0 (fibrous tissue) for baseline, results for SR=0.5, 0.25, and 0.1 were obtained. Thin cap and hypertension were also considered. Combining results from the 4 patients, mean cap stress from 729 cap nodes was lowered by 25.2% as SR went from 1.0 to 0.1. Mean cap strain value for SR=0.1 was 0.313, 114% higher than that from SR=1.0 model. The thin cap SR=0.1 model had 40% mean cap stress decrease and 81% cap strain increase compared with SR=1.0 model. The hypertension SR=0.1 model had 19.5% cap stress decrease and 98.6% cap strain increase compared with SR=1.0 model. Differences of flow shear stress with 4 different SR values were limited (<10%). Cap inflammation may lead to large cap strain conditions when combined with thin cap and hypertension. Inflammation also led to lower cap stress. This shows the influence of inflammation on stress/strain calculations which are closely related to plaque assessment.     

Structural analysis of two different stent configurations

Two different stent configurations (i.e. the well known Palmaz–Schatz (PS) and a new stent configuration) are mechanically investigated. A finite element model was used to study the two geometries under combining loads and a computational fluid dynamic model based on fluid structure interaction was developed investigating the plaque and the artery wall reactions in a stented arterial segment. These models determine the stress and displacement fields of the two stents under internal pressure conditions. Results suggested that stent designs cause alterations in vascular anatomy that adversely affect arterial stress distributions within the wall, which have impact in the vessel responses such as the restenosis. The hemodynamic analysis shows the use of new stent geometry suggests better biofluid mechanical response such as the deformation and the progressive amount of plaque growth.     

The structure and mechanical properties of the mitral valve leaflet-strut chordae transition zone

Biaxial testing, histological measurements and theoretical continuum mechanics modeling were employed to investigate the structure and mechanical properties of the mitral valve leaflet-strut chordae transition zone (LCT). The results showed that geometry changes and collagen fiber angle distribution contribute to variations in mechanical properties in the LCT zone. A simple three-coefficient exponential constitutive law was able to simulate the variation in stress-stretch behavior in the LCT zone by spatially varying a single coefficient and incorporating collagen fiber angle and degree of alignment. This quantitative information can greatly improve the predictions from biomechanical valve models by incorporating regional variations of structure and properties in the mitral leaflet-chordae tendineae system. These data provide the foundation for a computational model for studying stress distributions before and following chordal rupture, which may indicate the underlying reasons for the development of valve insufficiency in patients.