3D MRI-based anisotropic FSI models with cyclic bending for human coronary atherosclerotic plaque mechanical analysis

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

PURPOSE

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Haemodynamic Effects on the Development and Stability of Atherosclerotic Plaques in Arterial Blood Vessel

Studying the formation and stability of atherosclerotic plaques in the hemodynamic field is essential for understanding the growth mechanism and preventive treatment of atherosclerotic plaques. In this paper, based on a multiplayer porous wall model, we established a two-way fluid-solid interaction with time-varying inlet flow. The lipid-rich necrotic core (LRNC) and stress in atherosclerotic plaque were described for analyzing the stability of atherosclerotic plaques during the plaque growth by solving advection-diffusion-reaction equations with finite-element method. It was found that LRNC appeared when the lipid levels of apoptotic materials (such as macrophages, foam cells) in the plaque reached a specified lower concentration, and increased with the plaque growth. LRNC was positively correlated with the blood pressure and was negatively correlated with the blood flow velocity. The maximum stress was mainly located at the necrotic core and gradually moved toward the left shoulder of the plaque with the plaque growth, which increases the plaque instability and the risk of the plaque shedding. The computational model may contribute to understanding the mechanisms of early atherosclerotic plaque growth and the risk of instability in the plaque growth.

Considering the Influence of Coronary Motion on Artery-Specific Biomechanics Using Fluid-Structure Interaction Simulation

The endothelium in the coronary arteries is subject to wall shear stress and vessel wall strain, which influences the biology of the arterial wall. This study presents vessel-specific fluid-structure interaction (FSI) models of three coronary arteries, using directly measured experimental geometries and boundary conditions. FSI models are used to provide a more physiologically complete representation of vessel biomechanics, and have been extended to include coronary bending to investigate its effect on shear and strain. FSI both without- and with-bending resulted in significant changes in all computed shear stress metrics compared to CFD (p = 0.0001). Inclusion of bending within the FSI model produced highly significant changes in Time Averaged Wall Shear Stress (TAWSS) + 9.8% LAD, + 8.8% LCx, - 2.0% RCA; Oscillatory Shear Index (OSI) + 208% LAD, 0% LCx, + 2600% RCA; and transverse wall Shear Stress (tSS) + 180% LAD, + 150% LCx and + 200% RCA (all p < 0.0001). Vessel wall strain was homogenous in all directions without-bending but became highly anisotropic under bending. Changes in median cyclic strain magnitude were seen for all three vessels in every direction. Changes shown in the magnitude and distribution of shear stress and wall strain suggest that bending should be considered on a vessel-specific basis in analyses of coronary artery biomechanics.

On the nonlinear relationship between wall shear stress topology and multi-directionality in coronary atherosclerosis

BACKGROUND AND OBJECTIVE

In this paper we investigate twelve multi-directional/topological wall shear stress (WSS) derived metrics and their relationships with the formation of coronary plaques in both computational fluid dynamics (CFD) and dynamic fluid-structure interaction (FSI) frameworks. While low WSS is one of the most established biomechanical markers associated with coronary atherosclerosis progression, alone it is limited. Multi-directional and topological WSS derived metrics have been shown to be important in atherosclerosis related mechanotransduction and near-wall transport processes. However, the relationships between these twelve WSS metrics and the influence of both FSI simulations and coronary dynamics is understudied.

METHODS

We first investigate the relationships between these twelve WSS derived metrics, stenosis percentage and lesion length through a parametric, transient CFD study. Secondly, we extend the parametric study to FSI, both with and without the addition of coronary dynamics, and assess their correlations. Finally, we present the case of a patient who underwent invasive coronary angiography and optical coherence tomography imaging at two time points 18 months apart. Associations between each of the twelve WSS derived metrics in CFD, static FSI and dynamic FSI simulations were assessed against areas of positive/negative vessel remodelling, and changes in plaque morphology.

RESULTS

22-32% stenosis was the threshold beyond which adverse multi-directional/topological WSS results. Each metric produced a different relationship with changing stenoses and lesion length. Transient haemodynamics was impacted by coronary dynamics, with the topological shear variation index suppressed by up to 94%. These changes appear more critical at smaller stenosis levels, suggesting coronary dynamics could play a role in the earlier stages of atherosclerosis development. In the patient case, both dynamics and FSI vs CFD changes altered associations with measured changes in plaque morphology. An appendix of the linear fits between the various FSI- and CFD-based simulations is provided to assist in scaling CFD-based results to resemble the compliant walled characteristics of FSI more accurately.

CONCLUSIONS

These results highlight the potential for coronary dynamics to alter multi-directional/topological WSS metrics which could impact associations with changes in coronary atherosclerosis over time. These results warrant further investigation in a wider range of morphological settings and longitudinal cohort studies in the future.

Impact of cyclic bending on coronary hemodynamics

It remains unknown that the degree of bias in computational fluid dynamics results without considering coronary cyclic bending. This study aims to investigate the influence of different rates of coronary cyclic bending on coronary hemodynamics. To model coronary bending, a multi-ring-controlled fluid-structural interaction model was designed. A coronary artery was simulated with various cyclic bending rates (0.5, 0.75 and 1 s, corresponding to heart rates of 120, 80 and 60 bpm) and compared against a stable model. The simulated results show that the hemodynamic parameters of vortex Q-criterion, temporal wall shear stress (WSS), time-averaged WSS (TaWSS) and oscillatory shear index (OSI) were sensitive to the changes in cyclic rate. A higher heart rate resulted in higher magnitude and larger variance in the hemodynamic parameters. Whereas, the values and distributions of flow velocity and relative residence time (RRT) did not show significant differences between different bending periods. This study suggests that a stable coronary model is not sufficient to represent the hemodynamics in a bending coronary artery. Different heart rate conditions were found to have significant impact on the hemodynamic parameters. Thus, cyclic bending should be considered to mimic the realistic hemodynamics in future patient-specific coronary hemodynamics studies.

A comparative study of different tissue materials for bioprosthetic aortic valves using experimental assays and finite element analysis

BACKGROUND AND OBJECTIVE

Extracting the mechanical behaviors of bioprosthetic aortic valve leaflets is necessary for the appropriate design and manufacture of the prosthetic valves. The goal of this study was to opt a proper tissue for the valve leaflets by comparing the mechanical properties of the equine, porcine, and donkey pericardia with those of the bovine pericardium and human aortic valve leaflets.

METHODS

After tissue fixation in glutaraldehyde, the mechanical behaviors of the pericardial tissues were experimentally evaluated through computational methods. The relaxation tests were performed along the tissue fiber direction. The Mooney-Rivlin model was utilized to describe the hyperelastic behavior of the tissues at the ramp portion. The viscous behaviors at the hold portion were extracted using the Fung quasi-linear viscoelastic (QLV) model. Furthermore, the extracted parameters were used in the modeling of the bovine, equine, porcine, and donkey pericardia through finite element analysis (FEA).

RESULTS

Based on the results, relaxation percentages of the equine, donkey, and bovine pericardia were greater than that of the porcine pericardium and similar to the native human aortic valve leaflets. Indeed, the equine and donkey pericardia were found more viscous and less elastic than the porcine pericardium. Compared with the porcine pericardium, the mechanical properties of the equine and donkey pericardia were rather closer to those of the native human leaflets and bovine pericardium. The computational analysis demonstrated that the donkey pericardium is preferable over other types of pericardium due to the low stress on the leaflets during the systolic and diastolic phases and the large geometric orifice area (GOA).

CONCLUSION

The donkey pericardium might be a good candidate valve leaflet material for bioprosthetic aortic valves.

Automated Coronary Optical Coherence Tomography Feature Extraction with Application to Three-Dimensional Reconstruction

Coronary optical coherence tomography (OCT) is an intravascular, near-infrared light-based imaging modality capable of reaching axial resolutions of 10–20 µm. This resolution allows for accurate determination of high-risk plaque features, such as thin cap fibroatheroma; however, visualization of morphological features alone still provides unreliable positive predictive capability for plaque progression or future major adverse cardiovascular events (MACE). Biomechanical simulation could assist in this prediction, but this requires extracting morphological features from intravascular imaging to construct accurate three-dimensional (3D) simulations of patients’ arteries. Extracting these features is a laborious process, often carried out manually by trained experts. To address this challenge, numerous techniques have emerged to automate these processes while simultaneously overcoming difficulties associated with OCT imaging, such as its limited penetration depth. This systematic review summarizes advances in automated segmentation techniques from the past five years (2016–2021) with a focus on their application to the 3D reconstruction of vessels and their subsequent simulation. We discuss four categories based on the feature being processed, namely: coronary lumen; artery layers; plaque characteristics and subtypes; and stents. Areas for future innovation are also discussed as well as their potential for future translation.

Accurate Calculation of FFR Based on a Physics-Driven Fluid‐Structure Interaction Model

Background: The conventional FFRct numerical calculation method uses a model with a multi-scale geometry based upon CFD, and rigid walls. Therefore, important interactions between the elastic vessel wall and blood flow are not routinely considered. Changes in the resistance of coronary microcirculation during hyperaemia are likewise not typically incorporated using a fluid–structure interaction (FSI) algorithm. It is likely that both have resulted in FFRct calculation errors.

Objective: In this study we incorporated both the influence of vascular elasticity and coronary microcirculatory structure on FFR, to improve the accuracy of FFRct calculation. Thus, in this study, a physics-driven 3D–0D coupled model including fluid–structure interaction was established to calculate accurate FFRct values.

Methods: Based upon a novel geometric multi-scale modeling technology, a FSI simulation approach was used. A lumped parameter model (0D) was used as the outlet boundary condition for the 3D FSI coronary artery model to incorporate physiological microcirculation, with bidirectional coupling between the two models.

Results: The accuracy, sensitivity, specificity, and both positive and negative predictive values of FFR_DC calculated based upon the coupled 3D–0D model were 86.7, 66.7, 84.6, 66.7, and 91.7%, respectively. Compared to the calculated value using the basic CFD model (MSE = 5.9%, accuracy rate = 80%), the FFR_CFD calculated based on the coupled 3D–0D model has a smaller MSE of 1.9%.

Conclusion: The physics-driven coupled 3D–0D model that incorporates fluid–structure interactions not only consider the influence of the elastic vessel wall on blood flow, but also provides reliable microvascular resistance boundary conditions for the 3D FSI model. This allows for a calculation that is based upon conditions that are closer to the physiological environment, and thus improves the accuracy of FFRct calculation. It is likely that more accurate information will provide an enhanced recommendation regarding percutaneous coronary intervention (PCI) in the clinic.

Effect of plaque compositions on fractional flow reserve in a fluid-structure interaction analysis

Coronary artery disease involves the reduction of blood flow to the myocardium due to atherosclerotic plaques. The findings of myocardial ischemia may indicate severe coronary stenosis, but many studies have demonstrated a mismatch between lumen stenosis and fractional flow reserve (FFR). Recently, some clinical studies have found that the composition of atherosclerotic plaques may be a potential missing link between stenosis and ischemia. To investigate the relationship between myocardial ischemia and plaque composition, we have developed and adopted a new fluid-structure interaction (FSI) patient-specific coronary plaque model, based on computed tomography angiography data, to assess the impact on FFR as a biomechanical indicator of ischemia. A total of 180 analyses have been performed in 3D-FSI coronary artery disease models based on plaque compositions, plaque location, and stenosis degree. Hemodynamic analysis of simulation results and comparisons with other methods has been conducted to validate our models. Our results have successfully verified that the different compositions of plaques have resulted in differences in the calculated FFR. The mean FFR values with lipid plaques are [Formula: see text] as compared to the mean FFR values in lesions with fibrous plaques [Formula: see text] and calcified plaques [Formula: see text]. Besides, FFR differences between the three different plaque compositions have been shown to increase as the diameter stenosis increased. Plaque composition affects vascular stiffness and vascular dilation ability, and thereby affects the stenosis degree, resulting in abnormal FFR leading to myocardial ischemia. This interrelationship can help to diagnose the cause of high-risk coronary artery disease, leading to myocardial ischemia.

Multicomponent Mechanical Characterization of Atherosclerotic Human Coronary Arteries: An Experimental and Computational Hybrid Approach

Atherosclerotic plaque rupture in coronary arteries, an important trigger of myocardial infarction, is shown to correlate with high levels of pressure-induced mechanical stresses in plaques. Finite element (FE) analyses are commonly used for plaque stress assessment. However, the required information of heterogenous material properties of atherosclerotic coronaries remains to be scarce. In this work, we characterized the component-wise mechanical properties of atherosclerotic human coronary arteries. To achieve this, we performed ex vivo inflation tests on post-mortem human coronary arteries and developed an inverse FE modeling (iFEM) pipeline, which combined high-frequency ultrasound deformation measurements, a high-field magnetic resonance-based artery composition characterization, and a machine learning-based Bayesian optimization (BO) with uniqueness assessment. By using the developed pipeline, 10 cross-sections from five atherosclerotic human coronary arteries were analyzed, and the Yeoh material model constants of the fibrous intima and arterial wall components were determined. This work outlines the developed pipeline and provides the knowledge of non-linear, multicomponent mechanical properties of atherosclerotic human coronary arteries.

In Vivo Based Fluid-Structure Interaction Biomechanics of the Left Anterior Descending Coronary Artery

A fluid-structure interaction-based biomechanical model of the entire left anterior descending coronary artery is developed from in vivo imaging via the finite element method in this paper. Included in this investigation is ventricle contraction, three-dimensional motion, all angiographically visible side branches, hyper/viscoelastic artery layers, non-Newtonian and pulsatile blood flow, and the out-of-phase nature of blood velocity and pressure. The fluid-structure interaction model is based on in vivo angiography of an elite athlete's entire left anterior descending coronary artery where the influence of including all alternating side branches and the dynamical contraction of the ventricle is investigated for the first time. Results show the omission of side branches result in a 350% increase in peak wall shear stress and a 54% decrease in von Mises stress. Peak von Mises stress is underestimated by up to 80% when excluding ventricle contraction and further alterations in oscillatory shear indices are seen, which provide an indication of flow reversal and has been linked to atherosclerosis localization. Animations of key results are also provided within a video abstract. We anticipate that this model and results can be used as a basis for our understanding of the interaction between coronary and myocardium biomechanics. It is hoped that further investigations could include the passive and active components of the myocardium to further replicate in vivo mechanics and lead to an understanding of the influence of cardiac abnormalities, such as arrythmia, on coronary biomechanical responses.

Analysis of sequential ultrasound frames for the measurement of hemodynamic stresses, critical bent buckling pressure, and critical buckling torque of human common carotid atherosclerosis

BACKGROUND

Structural properties of the arterial wall are important diagnostic parameters. The current study aimed at investigating the hemodynamic properties and intima-media thickness changes of the common carotid artery in human subjects with atherosclerosis in order to determine the relationships between these indices.

METHODS

This study presented methods to detect instantaneous changes in the lumen diameter, intima media thickness, longitudinal movement and acceleration, and velocity of the left side of common carotid artery. These parameters were measured in 155 male patients, categorized into control (n = 42), mild (n = 39), moderate (n = 37), and severe (n = 37) carotid stenosis groups by B-mode and Doppler ultrasonography. Extracted parameters were used to estimate the biomechanical properties of arteries, including radial strain, arterial stiffness index, Young's elastic modulus, circumferential stress, shear stress, axial stress, critical bent buckling pressure, and critical buckling torque.

FINDINGS

All biomechanical parameters of common carotid artery were significantly different in patients with mild, moderate, and severe stenosis, compared to the control group (P < 0.05). Moreover, the current results showed a significant correlation between intima media thickness and non-intima media thickness-based biomechanical indices including circumferential strain, stiffness index, and shear stress in different stenosis groups (P < 0.05).

INTERPRETATION

We concluded that the conventional and new indicators such as axial stress, critical bent buckling pressure, critical buckling torque could be useful for evaluating atherosclerosis development and also, may provide more information for physicians and interventional radiologists in designing strategies for decreasing risk in interventional treatment such as stent replacement and differentiation of vulnerable plaques.

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

A unique three-dimensional (3D) computational multiscale modeling approach is proposed to investigate the influence of presence of microcalcification particles on the stress field distribution in the thin cap layer of a coronary atherosclerotic vulnerable plaque system. A nested 3D modeling analysis framework spanning the multiscale nature of a coronary atherosclerotic vulnerable plaque is presented. At the microscale level, a micromechanical modeling approach, which is based on computational finite-element (FE) representative unit cell, is applied to obtain the homogenized nonlinear response of the calcified tissue. This equivalent response effectively allows the integration of extremely small microcalcification inclusions in a global biomechanical FE model. Next, at the macroscale level, a 3D patient-based fluid-structure interaction FE model, reconstructing a refined coronary artery geometry with calcified plaque lesion, is generated to study the mechanical behavior of such multi-component biomechanical system. It is shown that the proposed multiscale modeling approach can generate a higher resolution of stress and strain field distributions within the coronary atherosclerotic vulnerable plaque system and allow the assessment of the local concentration stress around the microcalcifications in plaque cap layers. A comparison of stress field distributions within cap layers with and without inclusion of microcalcifications is also presented.

Study on the association of wall shear stress and vessel structural stress with atherosclerosis: An experimental animal study

BACKGROUND AND AIMS

Artery is subject to wall shear stress (WSS) and vessel structural stress (VSS) simultaneously. This study is designed to explore the role of VSS in development of atherosclerosis.

METHODS

Silastic collars were deployed on the carotid to create two constrictions on 13 rabbits for a distinct mechanical environment at the constriction. MRI was performed to visualize arteries' configuration. Animals with high fat (n = 9; Model-group) and normal diet (n = 4; Control-group) were sacrificed after 16 weeks. 3D fluid-structure interaction analysis was performed to quantify WSS and VSS simultaneously.

RESULTS

Twenty plaques were found in Model-group and 3 in Control-group. In Model-group, 8 plaques located proximally to the first constriction (Region-1, close to the heart) and 7 distally to the second (Region-2, close to the head) and 5 plaques were found on the contralateral side of 3 rabbits. Plaques at Region-1 tended to be bigger than those at Region-2 and the macrophage density at these locations was comparable. Minimum time-averaged WSS (TAWSS) in Region-1 was significantly higher than that in Region-2, and both maximum oscillatory shear index (OSI) and particle relative residence time (RRT) were significantly lower. Peak and mean VSS in Region-1 were significantly higher than those in Region-2. Correlation analyses indicated that low TAWSS, high OSI and RRT were only associated with plaque in Region-2, while lesions in Region-1 were only associated with high VSS. Moreover, only VSS was associated with wall thickness of plaque-free regions in both regions.

CONCLUSIONS

VSS might contribute to the initialization and development of atherosclerosis solely or in combination with WSS.

Influence of bifurcation angle in left coronary artery with stenosis: A CFD analysis

BACKGROUND: The left coronary artery commonly known as LCA gets divided into two branches, such as the left circumflex (LCX) and left anterior descending (LAD) at a particular angle. This angle is varies from person to person. The present computational study contributes remarkable expertise about the influence of this angle variation on the hemodynamic parameters in the presence of 80% area stenosis at the LAD branch. OBJECTIVE: This study aimed to compare the effect of the bifurcation angle on hemodynamic parameters in the left coronary artery with 80% stenosis. METHOD: Computational models of left coronary bifurcation angles of 30°, 60°, 90°, 120° were developed to understand the flow behavior of left coronary artery branches. The 80% area stenosis (AS) is considered at the LAD branch immediate to bifurcation. RESULTS: Measurements of pressure, velocity and wall shear stress were carried out corresponding to various bifurcation angles. It was found that the drop-in pressure increases as the angle increases from narrow to wider. A slight elevation in the velocity at the stenosis was observed. In addition, the obtained results further reveal a recirculation region immediately after the plaque, which leads to more deposition of plaque in the flow obstructed area. It is known that the shear stress at the arterial wall across the stenosis increases as the angle of bifurcation increases from narrow to wider. CONCLUSIONS: The bifurcation of the left coronary artery and size of the stenosis have a notable impact on the pressure and wall shear stress. These two factors should be given due consideration by cardiologists to assess the complexity of stenosis in the LCA branches.

Fluid–Solid Interaction Analysis on Iliac Bifurcation Artery: A Numerical Study

Atherosclerosis, which is commonly seen at regions with low wall shear stress (WSS) level in bifurcations, is a kind of fibro-fatty plaque accumulated on arterial walls. Aortic and iliac bifurcations have the highest proportion of patients among all atherosclerosis cases, thus it is necessary to numerically analyze the flow distribution and predict plaque positions in these bifurcations. Furthermore, using fluid–solid interaction (FSI) method could obtain a more exact flow pattern in arteries. In this study, a patient-specific model of aortic and iliac bifurcations was simulated with both FSI and rigid-wall cases. We analyzed the vessel deformation, WSS and flow distribution of this model. Computed tomography (CT) angiography was used in our study to create patient-specific model of aorto-iliac arteries. Real material properties and pulsatile fluid boundary conditions were applied in solid and fluid zones, respectively. We performed FSI and ordinary computational fluid dynamics (CFD) simulations with AYSYS 15.0 software (ANSYS Inc., Canonsburg, PA), and compared the diameter change, WSS and flow field between these two results. The diameter change between systolic phase and diastolic phase is 8–9% on abdominal aorta, and 3% on external and internal iliac arteries. The compliance of vessels corresponds to in-vivo observations. At peak systolic phase, the average WSS obtained in FSI simulation is 10% lower than in rigid-wall result, area of low-WSS region ([Formula: see text]) also increases by 78%. Wall deformation has a greater impact on WSS of those vessels with larger diameter, but hardly changes the shear level in smaller branches. Our result also shows that iliac bifurcations reveal more complicated secondary flow in systolic phase, comparing to other vessels, and stenosed iliac artery has more severe secondary flow than healthy artery. We obtained a feasible method for hemodynamic FSI research. The material parameters, boundary conditions and mesh could be used for further simulations, while the WSS and flow distribution may support clinical diagnosis and treatment. We concluded that compliance is a must-consider factor for simulating an accurate wall shear stress, because the vessel deformation in FSI simulation will significantly change the distribution of low-WSS zones. Moreover, more complicated secondary flow is detected in iliac arteries because it may interact between bifurcations. Stenosis in artery may also have a blocking effect on downstream blood flow.

Comparison of tensile properties of xenopericardium from three animal species and finite element analysis for bioprosthetic heart valve tissue

Bioprosthetic heart valves still have poor long-term durability due to calcification and mechanical failure. The function and performance of bioprostheses is known to depend on the collagen architecture and mechanical behavior of the target tissue. So it is necessary to select an appropriate tissue for such prostheses. In this study, porcine, equine, and bovine pericardia were compared histologically and mechanically. The specimens were analyzed under light microscopy. The planar biaxial tests were performed on the tissue samples by applying synchronic loads along the axial (fiber direction) and perpendicular directions. The measured biaxial data were then fitted into both the modified Mooney-Rivlin model and the anisotropic four parameter Fung-type model. The modified Mooney-Rivlin model was applied to the modeling of the bovine, equine, and porcine pericardia using finite element analysis. The equine pericardium illustrated a wavy collagen bundle architecture similar to bovine pericardium, whereas the collagen bundles in the porcine pericardium were thinner and structured. Wavy pericardia may be preferable candidates for transcutaneous aortic valves because they are less likely to be delaminated during crimping. Based on the biaxial tensile test, the specimens indicated some degree of anisotropy; the anisotropy rates of the equine specimens were almost identical, and higher than the other two specimens. In general, porcine pericardium appeared stiffer, based on the greater strain energy magnitude and the average slope of the stress-stretch curves. Moreover, it was less distensible (due to lower areal strain) than the other two pericardial tissues. Furthermore, the porcine model induced localized high stress regions during the systolic and diastolic phases of the cardiac cycle. However, increased mechanical stress on the bioprosthetic leaflets may cause tissue degeneration and reduce the long-term durability of the valve. Based on our observations, the pericardial specimens behaved as anisotropic and nonlinear tissues-well-characterized by both the modified Mooney-Rivlin and the Fung-type models. The results indicate that, compared to bovine pericardium, equine tissue is mechanically and histologically more appropriate for manufacturing heart valve prostheses. The results of this study can be used in the design and manufacture of bioprosthetic heart valves.

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

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

The influence of model order reduction on the computed fractional flow reserve using parameterized coronary geometries

Computational fluid dynamics (CFD) models combined with patient-specific imaging data are used to non-invasively predict functional significance of coronary lesions. This approach to predict the fractional flow reserve (FFR) is shown to have a high diagnostic accuracy when comparing against invasively measured FFR. However, one of the main drawbacks is the high computational effort needed for preprocessing and computations. Hence, uncertainty quantification may become unfeasible. Reduction of complexity is desirable, computationally inexpensive models with high diagnostic accuracy are preferred. We present a parametric comparison study for three types of CFD models (2D axisymmetric, Semi-3D and 3D) in which we study the impact of model reduction on three models on the predicted FFR. In total 200 coronary geometries were generated for seven geometrical characteristics e.g. stenosis severity, stenosis length and vessel curvature. The effect of time-averaged flow was investigated using unsteady, mean steady and a root mean square (RMS) steady flow. The 3D unsteady model was regarded as reference model. Results show that when using an unsteady or RMS flow, predicted FFR hardly varies between models contrary to using average flows. The 2D model with RMS flow has a high diagnostic accuracy (0.99), reduces computational time by a factor 162,000 and the introduced model error is well below the clinical relevant differences. Stenosis severity, length, curvature and tapering cause most discrepancies when using a lower order model. An uncertainty analysis showed that this can be explained by the low variability that is caused by variations in stenosis asymmetry.

A comprehensive fluid-structure interaction model of the left coronary artery

A fluid structure interaction model of a left anterior descending (LAD) coronary artery was developed, incorporating transient blood flow, cyclic bending motion of the artery, and myocardial contraction. The 3D geometry was constructed based on a patient's computed tomography angiography data. To simulate disease conditions, a plaque was placed within the LAD to create a 70% stenosis. The bending motion of the blood vessel was prescribed based on the LAD spatial information. The pressure induced by myocardial contraction was applied to the outside of the blood vessel wall. The fluid domain was solved using the Navier-Stokes equations. The arterial wall was defined as a nonlinear elastic, anisotropic, and incompressible material, and the mechanical behavior was described using the modified hyper-elastic Mooney-Rivlin model. The fluid (blood) and solid (vascular wall) domains were fully coupled. The simulation results demonstrated that besides vessel bending/stretching motion, myocardial contraction had a significant effect on local hemodynamics and vascular all stress/strain distribution. It not only transiently increased blood flow velocity and fluid wall shear stress, but also changed shear stress patterns. The presence of the plaque significantly reduced vascular wall tensile strain. Compared to the coronary artery models developed previously, the current model had improved physiological relevance.

Effect of distal thickening and stiffening of plaque cap on arterial wall mechanics

To investigate the effect of longitudinal variations of cap thickness and tissue properties on wall stresses and strains along the atherosclerotic stenosis, stenotic plaque models (uniformly thick, distally thickened, homogenous, and distally stiffened) were constructed and subjected to computational stress analyses with due consideration of fluid-structure interactions (FSI). The analysis considered three different cap thicknesses-45, 65, and 200 μm-and tissue properties-soft, fibrous, and hard. The maximum peak cap stress (PCS) and strain were observed in the upstream throat section and demonstrated increases of the order of 345 and 190%, respectively, as the cap thickness was reduced from 200 to 45 μm in uniformly thick models. Distal stiffening increased PCS in the downstream region; however, the overall effect of this increase was rather small. Distal thickening did not affect maximum PCS and strain values for cap thicknesses exceeding 65 μm; however, a noticeable increase in maximum PCS and corresponding longitudinal variation (or spatial gradient) in stress was observed in the very thin (45-μm-thick) cap. It was, therefore, inferred that existence of a rather thin upstream cap demonstrating distal cap thickening indicates an increased risk of plaque progression and rupture. Graphical Abstract ᅟ.

Nonlinear Dynamics of Dacron Aortic Prostheses Conveying Pulsatile Flow

This study addresses the dynamic response to pulsatile physiological blood flow and pressure of a woven Dacron graft currently used in thoracic aortic surgery. The model of the prosthesis assumes a cylindrical orthotropic shell described by means of nonlinear Novozhilov shell theory. The blood flow is modeled as Newtonian pulsatile flow, and unsteady viscous effects are included. Coupled fluid–structure Lagrange equations for open systems with wave propagation subject to pulsatile flow are applied. Physiological waveforms of blood pressure and velocity are approximated with the first eight harmonics of the corresponding Fourier series. Time responses of the prosthetic wall radial displacement are considered for two physiological conditions: at rest (60 bpm) and at high heart rate (180 bpm). While the response at 60 bpm reproduces the behavior of the pulsatile pressure, higher harmonics frequency contributions are observed at 180 bpm altering the shape of the time response. Frequency-responses show resonance peaks for heart rates between 130 bpm and 200 bpm due to higher harmonics of the pulsatile flow excitation. These resonant peaks correspond to unwanted high-frequency radial oscillations of the vessel wall that can compromise the long-term functioning of the prosthesis in case of significant physical activity. Thanks to this study, the dynamic response of Dacron prostheses to pulsatile flow can be understood as well as some possible complications in case of significant physical activity.

Assessment of superficial coronary vessel wall deformation and stress: validation of in silico models and human coronary arteries in vivo

Cyclic biomechanical stress at the lumen-intima interface plays a crucial role in the rupture of coronary plaque. We performed a comprehensive assessment of a novel angiography-based method for four-dimensional (4D) dynamic assessment of superficial wall stress (SWS) and deformation with a total of 32 analyses in virtual stenosis models with equal lumen dimensions and 16 analyses in human coronary arteries in vivo. The in silico model analyses demonstrated that the SWS, derived by the proposed global displacement method without knowledge of plaque components or blood pressure, was comparable with the result calculated by traditional finite element method. Cardiac contraction-induced vessel deformation increased SWS. Softer plaque and positive arterial remodeling, associated with a greater plaque burden, showed more variation in mean lumen diameter within the cardiac cycle and resulted in higher SWS. In vivo patient analyses confirmed the accuracy of computed superficial wall deformation. The centerlines predicted by our method at random selected time instant matched well with the actual one in angiograms by Procrustes analysis (scaling: 0.995 ± 0.018; dissimilarity: 0.007 ± 0.014). Over 50% of the maximum SWS occurred at proximal plaque shoulders. This novel 4D approach could be successfully to predict superficial wall deformation of coronary artery in vivo. The dynamic SWS might be more realistic to evaluate the risk of plaque rupture.

A multiscale approach for determining the morphology of endothelial cells at a coronary artery

The morphology of endothelial cells (ECs) may be an indication for determining atheroprone sites. Until now, there has been no clinical imaging technique to visualize the morphology of ECs in the arteries. The present study introduces a computational technique for determining the morphology of ECs. This technique is a multiscale simulation consisting of the artery scale and the cell scale. The artery scale is a fluid-structure interaction simulation. The input for the artery scale is the geometry of the coronary artery, that is, the dynamic curvature of the artery due to the cardiac motion, blood flow, blood pressure, heart rate, and the mechanical properties of the blood and the arterial wall, the measurements of which can be obtained for a specific patient. The results of the artery scale are wall shear stress (WSS) and cyclic strains as the mechanical stimuli of ECs. The cell scale is an inventive mass-and-spring model that is able to determine the morphological response of ECs to any combination of mechanical stimuli. The results of the multiscale simulation show the morphology of ECs at different locations of the coronary artery. The results indicate that the atheroprone sites have at least 1 of 3 factors: low time-averaged WSS, high angle of WSS, and high longitudinal strain. The most probable sites for atherosclerosis are located at the bifurcation region and lie on the myocardial side of the artery. The results also indicated that a higher dynamic curvature is a negative factor and a higher pulse pressure is a positive factor for protection against atherosclerosis.

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

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

THE MECHANICAL FACTORS INFLUENCING THE ASSESSMENT OF INTERMEDIATE STENOSIS SEVERITY EXPLAINED THROUGH FRACTIONAL FLOW RESERVE

Assessment of intermediate coronary lesions with diameter stenosis of 40% to 70% severity is being a challenge for cardiologist to identify potentially ischemic stenosis for revascularization and nonculprit stenosis which can be deferred from stenting. An invasive coronary angiography and intravascular ultrasound provide anatomic information of stenosis severity whereas an invasive fractional flow reserve index (FFR) provides the functional significance of the stenosis severity. The measurement of functional significance of stenosis severity minimizes the procedural complications such as coronary dissection, in stent restenosis etc. rather than anatomical significance measure. The FFR cutoff value of [Formula: see text]0.8 is used to distinguish ischemic and nonischemic stenosis. The FFR is clinically well validated even though it is influenced by the mechanical factors such as hyperemic flow and guide wire insertion. In recent times, noninvasive coronary computed tomography (CCTA) modality has become popular in the diagnosis of coronary artery disease. The CCTA permits the assessment of cross-sectional parameters such as minimum lumen area and lumen diameter, lesion length and plaque morphology. However, the CCTA provides limited information on the functional significance of stenotic lesions as compared to FFR. The purpose of this review is to discuss the mechanical factors influencing the invasive FFR while assessing the functional significance of intermediate stenosis severity. In addition, the hidden mechanical factors influencing the noninvasive CCTA assessment of stenosis severity will be discussed from the critical information obtained from FFR which could be beneficial for the clinician particularly in the assessment of intermediate stenosis severity.

High Structural Stress and Presence of Intraluminal Thrombus Predict Abdominal Aortic Aneurysm 18F-FDG Uptake: Insights From Biomechanics

Supplemental Digital Content is available in the text.

Background—

Abdominal aortic aneurysm (AAA) wall inflammation and mechanical structural stress may influence AAA expansion and lead to rupture. We hypothesized a positive correlation between structural stress and fluorine-18-labeled 2-deoxy-2-fluoro-d-glucose (¹⁸F-FDG) positron emission tomography–defined inflammation. We also explored the influence of computed tomography–derived aneurysm morphology and composition, including intraluminal thrombus, on both variables.

Methods and Results—

Twenty-one patients (19 males) with AAAs below surgical threshold (AAA size was 4.10±0.54 cm) underwent ¹⁸F-FDG positron emission tomography and contrast-enhanced computed tomography imaging. Structural stresses were calculated using finite element analysis. The relationship between maximum aneurysm ¹⁸F-FDG standardized uptake value within aortic wall and wall structural stress, patient clinical characteristics, aneurysm morphology, and compositions was explored using a hierarchical linear mixed-effects model. On univariate analysis, local aneurysm diameter, thrombus burden, extent of calcification, and structural stress were all associated with ¹⁸F-FDG uptake (P<0.05). AAA structural stress correlated with ¹⁸F-FDG maximum standardized uptake value (slope estimate, 0.552; P<0.0001). Multivariate linear mixed-effects analysis revealed an important interaction between structural stress and intraluminal thrombus in relation to maximum standardized uptake value (fixed effect coefficient, 1.68 [SE, 0.10]; P<0.0001). Compared with other factors, structural stress was the best predictor of inflammation (receiver-operating characteristic curve area under the curve =0.59), with higher accuracy seen in regions with high thrombus burden (area under the curve =0.80). Regions with both high thrombus burden and high structural stress had higher ¹⁸F-FDG maximum standardized uptake value compared with regions with high thrombus burdens but low stress (median [interquartile range], 1.93 [1.60–2.14] versus 1.14 [0.90–1.53]; P<0.0001).

Conclusions—

Increased aortic wall inflammation, demonstrated by ¹⁸F-FDG positron emission tomography, was observed in AAA regions with thick intraluminal thrombus subjected to high mechanical stress, suggesting a potential mechanistic link underlying aneurysm inflammation.

Impact of Fiber Structure on the Material Stability and Rupture Mechanisms of Coronary Atherosclerotic Plaques

The rupture of an atherosclerotic plaque in the coronary circulation remains the main cause of heart attack. As a fiber-oriented structure, the fiber structure, in particular in the fibrous cap (FC), may affect both loading and material strength in the plaque. However, the role of fiber orientation and dispersion in plaque rupture is unclear. Local orientation and dispersion of fibers were calculated for the shoulder regions, mid FC, and regions with intimal thickening (IT) from histological images of 16 human coronary atherosclerotic lesions. Finite element analysis was performed to assess the effect of these properties on mechanical conditions. Fibers in shoulder regions had markedly reduced alignment (Median [interquartile range] 12.9° [6.6, 18.0], p < 0.05) compared with those in mid FC (6.1° [5.5, 9.0]) and IT regions (6.7° [5.1, 8.6]). Fiber dispersion was highest in shoulders (0.150 [0.121, 0.192]), intermediate in IT (0.119 [0.103, 0.144]), and lowest in mid FC regions (0.093 [0.081, 0.105], p < 0.05). When anisotropic properties were considered, stresses were significantly higher for the mid FC (p = 0.030) and IT regions (p = 0.002) and no difference was found for the shoulder or global regions. Shear (sliding) stress between fibers in each region and their proportion of maximum principal stress were: shoulder (25.8 kPa [17.1, 41.2], 12.4%), mid FC (13.9 kPa [5.8, 29.6], 13.8%), and IT (36.5 kPa [25.9, 47.3], 15.5%). Fiber structure within the FC has a marked effect on principal stresses, resulting in considerable shear stress between fibers. Fiber structure including orientation and dispersion may determine mechanical strength and thus rupture of atherosclerotic plaques.

The influence of artery wall curvature on the anatomical assessment of stenosis severity derived from fractional flow reserve: a computational fluid dynamics study

This study aims to investigate the influence of artery wall curvature on the anatomical assessment of stenosis severity and to identify a region of misinterpretation in the assessment of per cent area stenosis (AS) for functionally significant stenosis using fractional flow reserve (FFR) as standard. Five artery models of different per cent AS severity (70, 75, 80, 85 and 90%) were considered. For each per cent AS severity, the angle of curvature of the arterial wall varied from straight to an increasingly curved model (0°, 30°, 60°, 90° and 120°). Computational fluid dynamics was performed under transient physiologic hyperemic flow conditions to investigate the influence of artery wall curvature on the pressure drop and the FFR. The findings in this study may be useful in in vitro anatomical assessment of functionally significant stenosis. The FFR decreased with increasing stenosis severity for a given curvature of the artery wall. Moreover, a significant decrease in FFR was found between straight and curved models discussed for a given severity condition. These findings indicate that the curvature effect was included in the FFR assessment in contrast to minimum lumen area (MLA) or per cent AS assessment. The MLA or per cent AS assessment may lead to underestimation of stenosis severity. From this numerical study, an uncertainty region could be evaluated using the clinical FFR cutoff value of 0.8. This value was observed at 81.98 and 79.10% AS for arteries with curvature angles of 0° and 120° respectively. In conclusion, the curvature of the artery should not be neglected in in vitro anatomical assessment.

The influence of constitutive law choice used to characterise atherosclerotic tissue material properties on computing stress values in human carotid plaques

Calculating high stress concentration within carotid atherosclerotic plaques has been shown to be complementary to anatomical features in assessing vulnerability. Reliability of stress calculation may depend on the constitutive laws/strain energy density functions (SEDFs) used to characterize tissue material properties. Different SEDFs, including neo-Hookean, one-/two-term Ogden, Yeoh, 5-parameter Mooney–Rivlin, Demiray and modified Mooney–Rivlin, have been used to describe atherosclerotic tissue behavior. However, the capacity of SEDFs to fit experimental data and the difference in the stress calculation remains unexplored. In this study, seven SEDFs were used to fit the stress–stretch data points of media, fibrous cap, lipid and intraplaque hemorrhage/thrombus obtained from 21 human carotid plaques. Semi-analytic solution, 2D structure-only and 3D fully coupled fluid-structure interaction (FSI) analyses were used to quantify stress using different SEDFs and the related material stability examined. Results show that, except for neo-Hookean, all other six SEDFs fitted the experimental points well, with vessel stress distribution in the circumferential and radial directions being similar. 2D structural-only analysis was successful for all seven SEDFs, but 3D FSI were only possible with neo-Hookean, Demiray and modified Mooney–Rivlin models. Stresses calculated using Demiray and modified Mooney–Rivlin models were nearly identical. Further analyses indicated that the energy contours of one-/two-term Ogden and 5-parameter Mooney–Rivlin models were not strictly convex and the material stability indictors under homogeneous deformations were not always positive. In conclusion, considering the capacity in characterizing material properties and stabilities, Demiray and modified Mooney–Rivlin SEDF appear practical choices for mechanical analyses to predict the critical mechanical conditions within carotid atherosclerotic plaques.

FSI SIMULATION OF A HEALTHY CORONARY BIFURCATION FOR STUDYING THE MECHANICAL STIMULI OF ENDOTHELIAL CELLS UNDER DIFFERENT PHYSIOLOGICAL CONDITIONS

Atherosclerosis is a world-spread and well-known disease. This disease strongly relates to the endothelial cells (ECs) function. Normally, the endothelial cells align in the flow direction in the atheroprotected sites; however, in the case of atheroprone sites these cells orient randomly. The mechanical stimuli such as wall shear stress and strains could determine the morphology and function of the endothelial cells. In the present study, we numerically simulated the left main coronary artery (LCA) and its branches to left anterior descending (LAD) and left circumflex coronary (LCX) artery using fluid–structure interaction (FSI) modeling. The results were presented as longitudinal and circumferential strains of ECs as well as wall shear stress. Wide ranges of heart rate, cardiac motion, systolic and diastolic pressures were considered and their effects on mechanical stimuli were described in detail. The results showed that these factors could greatly influence the risk of atherosclerosis and the location of atherosclerotic lesions.

Mathematical modeling and simulation of the evolution of plaques in blood vessels

In this paper, a model is developed for the evolution of plaques in arteries, which is one of the main causes for the blockage of blood flow. Plaque rupture and spread of torn-off material may cause closures in the down-stream vessel system and lead to ischemic brain or myocardial infarctions. The model covers the flow of blood and its interaction with the vessel wall. It is based on the assumption that the penetration of monocytes from the blood flow into the vessel wall, and the accumulation of foam cells increasing the volume, are main factors for the growth of plaques. The dynamics of the vessel wall is governed by a deformation gradient, which is given as composition of a purely elastic tensor, and a tensor modeling the biologically caused volume growth. An equation for the evolution of the metric is derived quantifying the changing geometry of the vessel wall. To calculate numerically the solutions of the arising free boundary problem, the model system of partial differential equations is transformed to an ALE (Arbitrary Lagrangian-Eulerian) formulation, where all equations are given in fixed domains. The numerical calculations are using newly developed algorithms for ALE systems. The results of the simulations, obtained for realistic system parameters, are in good qualitative agreement with observations. They demonstrate that the basic modeling assumption can be justified. The increase of stresses in the vessel wall can be computed. Medical treatment tries to prevent critical stress values, which may cause plaque rupture and its consequences.

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.

Artery buckling stimulates cell proliferation and NF-κB signaling

Tortuous carotid arteries are often seen in aged populations and are associated with atherosclerosis, but the underlying mechanisms to explain this preference are unclear. Artery buckling has been suggested as one potential mechanism for the development of tortuous arteries. The objective of this study, accordingly, was to determine the effect of buckling on cell proliferation and associated NF-κB activation in arteries. We developed a technique to generate buckling in porcine carotid arteries using long artery segments in organ culture without changing the pressure, flow rate, and axial stretch ratio. Using this technique, we examined the effect of buckling on arterial wall remodeling in 4-day organ culture under normal and hypertensive pressures. Cell proliferation, NF-κB p65, IκB-α, ERK1/2, and caspase-3 were detected using immunohistochemistry staining and immunoblot analysis. Our results showed that cell proliferation was elevated 5.8-fold in the buckling group under hypertensive pressure (n = 7, P < 0.01) with higher levels of NF-κB nuclear translocation and IκB-α degradation (P < 0.05 for both). Greater numbers of proliferating cells were observed on the inner curve side of the buckled arteries compared with the outer curve side (P < 0.01). NF-κB colocalized with proliferative nuclei. Computational simulations using a fluid-structure interaction model showed reduced wall stress on the inner side of buckled arteries and elevated wall stress on the outer side. We conclude that arterial buckling promotes site-specific wall remodeling with increased cell proliferation and NF-κB activation. These findings shed light on the biomechanical and molecular mechanisms of the pathogenesis of atherosclerosis in tortuous arteries.

Stability of carotid artery under steady-state and pulsatile blood flow: a fluid-structure interaction study

It has been shown that arteries may buckle into tortuous shapes under lumen pressure, which in turn could alter blood flow. However, the mechanisms of artery instability under pulsatile flow have not been fully understood. The objective of this study was to simulate the buckling and post-buckling behaviors of the carotid artery under pulsatile flow using a fully coupled fluid-structure interaction (FSI) method. The artery wall was modeled as a nonlinear material with a two-fiber strain-energy function. FSI simulations were performed under steady-state flow and pulsatile flow conditions with a prescribed flow velocity profile at the inlet and different pressures at the outlet to determine the critical buckling pressure. Simulations were performed for normal (160 ml/min) and high (350 ml/min) flow rates and normal (1.5) and reduced (1.3) axial stretch ratios to determine the effects of flow rate and axial tension on stability. The results showed that an artery buckled when the lumen pressure exceeded a critical value. The critical mean buckling pressure at pulsatile flow was 17-23% smaller than at steady-state flow. For both steady-state and pulsatile flow, the high flow rate had very little effect (&lt;5%) on the critical buckling pressure. The fluid and wall stresses were drastically altered at the location with maximum deflection. The maximum lumen shear stress occurred at the inner side of the bend and maximum tensile wall stresses occurred at the outer side. These findings improve our understanding of artery instability in vivo.

Artery buckling affects the mechanical stress in atherosclerotic plaques

Background

Tortuous arteries are often seen in patients with hypertension and atherosclerosis. While the mechanical stress in atherosclerotic plaque under lumen pressure has been studied extensively, the mechanical stability of atherosclerotic arteries and subsequent effect on the plaque stress remain unknown. To this end, we investigated the buckling and post-buckling behavior of model stenotic coronary arteries with symmetric and asymmetric plaque.

Methods

Buckling analysis for a model coronary artery with symmetric and asymmetric plaque was conducted using finite element analysis based on the dimensions and nonlinear anisotropic materials properties reported in the literature.

Results

Artery with asymmetric plaque had lower critical buckling pressure compared to the artery with symmetric plaque and control artery. Buckling increased the peak stress in the plaque and led to the development of a high stress concentration in artery with asymmetric plaque. Stiffer calcified tissue and severe stenosis increased the critical buckling pressure of the artery with asymmetric plaque.

Conclusions

Arteries with atherosclerotic plaques are prone to mechanical buckling which leads to a high stress concentration in the plaques that can possibly make the plaques prone to rupture.

Fluid-structure interaction analysis of the left coronary artery with variable angulation

The aim of this study is to elucidate the correlation between coronary artery branch angulation, local mechanical and haemodynamic forces at the vicinity of bifurcation. Using a coupled fluid-structure interaction (FSI) modelling approach, five idealized left coronary artery models with various angles ranging from 70° to 110° were developed to investigate the influence of branch angulations. In addition, one CT image-based model was reconstructed to further demonstrate the medical application potential of the proposed FSI coupling method. The results show that the angulation strongly alters its mechanical stress distribution, and the instantaneous wall shear stress distributions are substantially moderated by the arterial wall compliance. As high tensile stress is hypothesized to cause stenosis, the left circumflex side bifurcation shoulder is indicated to induce atherosclerotic changes with a high tendency for wide-angled models.

Numerical simulation of the fluid structure interactions in a compliant patient-specific arteriovenous fistula

The objective of the study is to investigate numerically the fluid-structure interactions (FSI) in a patient-specific arteriovenous fistula (AVF) and analyze the degree of complexity that such a numerical simulation requires to provide clinically relevant information. The reference FSI simulation takes into account the non-Newtonian behavior of blood, as well as the variation in mechanical properties of the vascular walls along the AVF. We have explored whether less comprehensive versions of the simulation could still provide relevant results. The non-Newtonian blood model is necessary to predict the hemodynamics in the AVF because of the predominance of low shear rates in the vein. An uncoupled fluid simulation provides informative qualitative maps of the hemodynamic conditions in the AVF; quantitatively, the hemodynamic parameters are accurate within 20% maximum. Conversely, an uncoupled structural simulation with non-uniform wall properties along the vasculature provides the accurate distribution of internal wall stresses, but only at one instant of time within the cardiac cycle. The FSI simulation advantageously provides the time-evolution of both the hemodynamic and structural stresses. However, the higher computational cost renders a clinical use still difficult in routine.

Image-based modeling for better understanding and assessment of atherosclerotic plaque progression and vulnerability: data, modeling, validation, uncertainty and predictions

Medical imaging and image-based modeling have made considerable progress in recent years in identifying atherosclerotic plaque morphological and mechanical risk factors which may be used in developing improved patient screening strategies. However, a clear understanding is needed about what we have achieved and what is really needed to translate research to actual clinical practices and bring benefits to public health. Lack of in vivo data and clinical events to serve as gold standard to validate model predictions is a severe limitation. While this perspective paper provides a review of the key steps and findings of our group in image-based models for human carotid and coronary plaques and a limited review of related work by other groups, we also focus on grand challenges and uncertainties facing the researchers in the field to develop more accurate and predictive patient screening tools.

A finite element investigation on plaque vulnerability in realistic healthy and atherosclerotic human coronary arteries

Atherosclerosis is the most common arterial disease. It has been shown that stresses that are induced during blood circulation can cause plaque rupture and, in turn, lead to thrombosis and stroke. In this study, finite element method is used to predict plaque vulnerability based on peak plaque stress using human samples. A total of 23 healthy and atherosclerotic human coronary arteries of 14 healthy and 9 atherosclerotic patients are excised within 5 h postmortem. The samples are mounted on an uniaxial tensile test machine, and the obtained mechanical properties are used in two-dimensional and three-dimensional finite element models. The results including the Neo-Hookean hyperelastic coefficients of the samples as well as peak plaque stresses are analyzed. The results indicate that the atherosclerotic human coronary arteries have significantly (p < 0.05) higher stiffness compared with the healthy ones. The hypocellular plaque also has the highest stress values and, as a result, is most likely (vulnerable) to rupture, while the calcified type has the lowest stress values and, consequently, is expected to remain stable. The results could be used in the plaque vulnerability anticipation and have clinical implications in interventions and surgeries, including balloon angioplasty, bypass, and stenting.

Artery buckling: new phenotypes, models, and applications

Arteries are under significant mechanical loads from blood pressure, flow, tissue tethering, and body movement. It is critical that arteries remain patent and stable under these loads. This review summarizes the common forms of buckling that occur in blood vessels including cross-sectional collapse, longitudinal twist buckling, and bent buckling. The phenomena, model analyses, experimental measurements, effects on blood flow, and clinical relevance are discussed. It is concluded that mechanical buckling is an important issue for vasculature, in addition to wall stiffness and strength, and requires further studies to address the challenges. Studies of vessel buckling not only enrich vascular biomechanics but also have important clinical applications.

COMPUTER-BASED MECHANICAL ANALYSIS OF STENOSED ARTERY WITH THROMBOTIC PLAQUE: THE INFLUENCES OF IMPORTANT PHYSIOLOGICAL PARAMETERS

The thrombus is the inappropriate activation of hemostasis in vascular system. In this paper, biomechanical factors affecting the behaviors of artery with intraluminal thrombus were studies. Results indicated that heart rate and blood viscosity had strong impact on the compliance of the stenosis artery and flow pattern. The alteration in blood viscosity had stronger influence than cardiac cycle on the volume change of the fluid region surrounded by thrombus. von Mises stress measured at the thinnest region of the plaque had the largest time-averaged value. The alteration of these parameters could potentially lead to stress redistribution at intraluminal thrombus.

Microcalcifications increase coronary vulnerable plaque rupture potential: a patient-based micro-CT fluid-structure interaction study

Asymptomatic vulnerable plaques (VP) in coronary arteries accounts for significant level of morbidity. Their main risk is associated with their rupture which may prompt fatal heart attacks and strokes. The role of microcalcifications (micro-Ca), embedded in the VP fibrous cap, in the plaque rupture mechanics has been recently established. However, their diminutive size offers a major challenge for studying the VP rupture biomechanics on a patient specific basis. In this study, a highly detailed model was reconstructed from a post-mortem coronary specimen of a patient with observed VP, using high resolution micro-CT which captured the microcalcifications embedded in the fibrous cap. Fluid-structure interaction (FSI) simulations were conducted in the reconstructed model to examine the combined effects of micro-Ca, flow phase lag and plaque material properties on plaque burden and vulnerability. This dynamic fibrous cap stress mapping elucidates the contribution of micro-Ca and flow phase lag VP vulnerability independently. Micro-Ca embedded in the fibrous cap produced increased stresses predicted by previously published analytical model, and corroborated our previous studies. The 'micro-CT to FSI' methodology may offer better diagnostic tools for clinicians, while reducing morbidity and mortality rates for patients with vulnerable plaques and ameliorating the ensuing healthcare costs.