Design Effect of Metallic (Durable) and Polymeric (Resorbable) Stents on Blood Flow and Platelet Activation.

Bioresorbable vascular scaffolds (BVS) provide transient vessel support for occluded coronary arteries while resorbing over time, potentially allowing vessel restoration approximating the native, healthy state. Clinical trials indicate that the Absorb BVS (Abbott Vascular, Santa Clara, CA) performance was similar to that of the Xience metallic drug-eluting stent (DES), with low long-term complications rates. However, when under-deployed in very small vessels (diameter < 2.25 mm), the thrombosis rate of BVS was higher, possibly due to the effect of strut thickness on the hemodynamics (157 µm BVS vs. 81 µm DES). This study aims to determine the influence of BVS design in vessels of varying diameter on the potential platelet activation. Sixteen computational fluid dynamics models of vessels of varying diameter (1.8-3.0 mm), strut thickness (81-157 µm), and BVS/DES designs were compared. Platelet stress accumulation (SA), a metric for the activation potential, was calculated along platelet flow trajectories and their probability distribution was compared. The models were consistent with clinical observations, indicating that devices deployed in very small vessels exhibited increased probability for platelet activity as compared to the same devices deployed in nominal sized vessels. Deployment, although with residual stenosis, increased probability for higher SA than in similar diameter straight vessels. Reducing BVS struts thickness while maintaining their pattern improved performance closer to that of DES. Our findings highlight the importance of appropriate vessel sizing and deployment technique for BVS, and may help designing future BVS with thinner struts, ultimately improving performance in very small vessels.

Comparative Fluid-Structure Interaction Analysis of Polymeric Transcatheter and Surgical Aortic Valves' Hemodynamics and Structural Mechanics.

Transcatheter aortic valve replacement (TAVR) has emerged as an effective alternative to conventional surgical aortic valve replacement (SAVR) in high-risk elderly patients with calcified aortic valve disease. All currently FDA-approved TAVR devices use tissue valves that were adapted to but not specifically designed for TAVR use. Emerging clinical evidence indicates that these valves may get damaged during crimping and deployment- leading to valvular calcification, thrombotic complications, and limited durability. This impedes the expected expansion of TAVR to lower-risk and younger patients. Viable polymeric valves have the potential to overcome such limitations. We have developed a polymeric SAVR valve, which was optimized to reduce leaflet stresses and offer a thromboresistance profile similar to that of a tissue valve. This study compares the polymeric SAVR valve's hemodynamic performance and mechanical stresses to a new version of the valve- specifically designed for TAVR. Fluid-structure interaction (FSI) models were utilized and the valves' hemodynamics, flexural stresses, strains, orifice area, and wall shear stresses were compared. The TAVR valve had 42% larger opening area and 27% higher flow rate versus the SAVR valve, while wall shear stress distribution and mechanical stress magnitudes were of the same order, demonstrating the enhanced performance of the TAVR valve prototype. The TAVR valve FSI simulation and Vivitro pulse duplicator experiments were compared in terms of the leaflets' kinematics and the effective orifice area. The numerical methodology presented can be further used as a predictive tool for valve design optimization for enhanced hemodynamics and durability.

A New Growth Model for Aortic Valve Calcification.

Calcific aortic valve disease (CAVD) is a progressive disease in which minerals accumulate in the tissue of the aortic valve cusps, stiffening them and preventing valve opening and closing. The process of valve calcification was found to be similar to that of bone formation including cell differentiation to osteoblast-like cells. Studies have shown the contribution of high strains to calcification initiation and growth process acceleration. In this paper, a new strain-based calcification growth model is proposed. The model aims to explain the unique shape of the calcification and other disease characteristics. The calcification process was divided into two stages: Calcification initiation and calcification growth. The initiation locations were based on previously published findings and a reverse calcification technique (RCT), which uses computed tomography (CT) scans of patients to reveal the calcification initiation point. The calcification growth process was simulated by a finite element model of one aortic valve cusp loaded with cyclic loading. Similar to Wolff's law, describing bone response to stress, our model uses strains to drive calcification formation. The simulation grows calcification from its initiation point to its full typical stenotic shape. Study results showed that the model was able to reproduce the typical calcification growth pattern and shape, suggesting that strain is the main driving force behind calcification progression. The simulation also sheds light on other disease characteristics, such as calcification growth acceleration as the disease progresses, as well as sensitivity to hypertension.

Fluid-Structure Interaction Models of Bicuspid Aortic Valves: The Effects of Nonfused Cusp Angles.

Bicuspid aortic valve (BAV) is the most common type of congenital heart disease, occurring in 0.5-2% of the population, where the valve has only two rather than the three normal cusps. Valvular pathologies, such as aortic regurgitation and aortic stenosis, are associated with BAVs, thereby increasing the need for a better understanding of BAV kinematics and geometrical characteristics. The aim of this study is to investigate the influence of the nonfused cusp (NFC) angle in BAV type-1 configuration on the valve's structural and hemodynamic performance. Toward that goal, a parametric fluid-structure interaction (FSI) modeling approach of BAVs is presented. Four FSI models were generated with varying NFC angles between 120 deg and 180 deg. The FSI simulations were based on fully coupled structural and fluid dynamic solvers and corresponded to physiologic values, including the anisotropic hyper-elastic behavior of the tissue. The simulated angles led to different mechanical behavior, such as eccentric jet flow direction with a wider opening shape that was found for the smaller NFC angles, while a narrower opening orifice followed by increased jet flow velocity was observed for the larger NFC angles. Smaller NFC angles led to higher concentrated flow shear stress (FSS) on the NFC during peak systole, while higher maximal principal stresses were found in the raphe region during diastole. The proposed biomechanical models could explain the early failure of BAVs with decreased NFC angles, and suggests that a larger NFC angle is preferable in suture annuloplasty BAV repair surgery.

Effect of Balloon-Expandable Transcatheter Aortic Valve Replacement Positioning: A Patient-Specific Numerical Model.

Transcatheter aortic valve replacement (TAVR) has emerged as a life-saving and effective alternative to surgical valve replacement in high-risk, elderly patients with severe calcific aortic stenosis. Despite its early promise, certain limitations and adverse events, such as suboptimal placement and valve migration, have been reported. In the present study, it was aimed to evaluate the effect of various TAVR deployment locations on the procedural outcome by assessing the risk for valve migration. The deployment of a balloon-expandable Edwards SAPIEN valve was simulated via finite element analysis in a patient-specific calcified aortic root, which was reconstructed from CT scans of a retrospective case of valve migration. The deployment location was parametrized in three configurations and the anchorage was quantitatively assessed based on the contact between the stent and the native valve during the deployment and recoil phases. The proximal deployment led to lower contact area between the native leaflets and the stent which poses higher risk for valve migration. The distal and midway positions resulted in comparable outcomes, with the former providing a slightly better anchorage. The approach presented might be used as a predictive tool for procedural planning in order to prevent prosthesis migration and achieve better clinical outcomes.

Systematic adjustment of root dimensions to cusp size in aortic valve repair: a computer simulation.

OBJECTIVES: Aortic valve repair requires the creation of a normal geometry of cusps and aortic root. Of the different dimensions, geometric cusp height is the most difficult to change while annular and sinotubular dimensions can be easily modified. The objective of this study was to investigate, by computer simulation, ideal combinations of annular and sinotubular junction size for a given geometric height. METHODS: Based on a literature review of anatomical data, a computational biomechanics model was generated for a tricuspid aortic valve. We aimed to determine the ideal relationships for the root dimensions, keeping geometric height constant and creating different combinations of the annular and sinotubular junction dimensions. Using this model, 125 virtual anatomies were created, with 25 different combinations of annulus and sinotubular junction. Effective height, coaptation height and mechanical cusp stress were calculated with the valves in closed configuration. RESULTS: Generally, within the analysed range of geometric heights, changes to the annular diameter yielded a stronger impact than sinotubular junction diameter changes for optimal valve configuration. The best results were obtained with the sinotubular junction being 2-4 mm larger than the annulus, leading to higher effective height, normal coaptation height and lower stress. Within the range tested, stenosis did not occur due to annular reduction. CONCLUSIONS: In tricuspid aortic valves, the geometric height can be used to predict ideal post-repair annular and sinotubular junction dimensions for optimal valve configuration. Such an ideal configuration is associated with reduced cusp stress.

Fluid-structure interaction model of aortic valve with porcine-specific collagen fiber alignment in the cusps.

Native aortic valve cusps are composed of collagen fibers embedded in their layers. Each valve cusp has its own distinctive fiber alignment with varying orientations and sizes of its fiber bundles. However, prior mechanical behavior models have not been able to account for the valve-specific collagen fiber networks (CFN) or for their differences between the cusps. This study investigates the influence of this asymmetry on the hemodynamics by employing two fully coupled fluid-structure interaction (FSI) models, one with asymmetric-mapped CFN from measurements of porcine valve and the other with simplified-symmetric CFN. The FSI models are based on coupled structural and fluid dynamic solvers. The partitioned solver has nonconformal meshes and the flow is modeled by employing the Eulerian approach. The collagen in the CFNs, the surrounding elastin matrix, and the aortic sinus tissues have hyperelastic mechanical behavior. The coaptation is modeled with a master-slave contact algorithm. A full cardiac cycle is simulated by imposing the same physiological blood pressure at the upstream and downstream boundaries for both models. The mapped case showed highly asymmetric valve kinematics and hemodynamics even though there were only small differences between the opening areas and cardiac outputs of the two cases. The regions with a less dense fiber network are more prone to damage since they are subjected to higher principal stress in the tissues and a higher level of flow shear stress. This asymmetric flow leeward of the valve might damage not only the valve itself but also the ascending aorta.

A numerical study of a left ventricular expander for heart failure with preserved ejection fraction.

Increased cardiac stiffness hinders proper left ventricular (LV) expansion, resulting in decreased volume and diastolic dysfunction. LV expanders are spring-like devices designed to improve diastolic function by facilitating mechanical outward expansion. Implantations in animals and humans have shown promising results, yet further evaluation is needed to assess a range of functions and the risk of use. In this computational study, the effectiveness and potential use of a generic LV expander were assessed by using previously generated finite-element models of induced heart failure with preserved ejection fraction (HFpEF). Following implantation, the treated models were compared to the corresponding untreated and healthy pre-induction models. The influence of device orientation and its material properties was also examined. Our results demonstrated a reduction in LV pressure and a volumetric improvement. Computed LV stresses have shown no gross irregularities. The device contributed to stress elevation during diastole while having a minor effect during systole, supporting a basic safety profile. This is the first study to use numerical analysis to assess LV expanders' performance on different HFpEF phenotypes. Improvement in heart function was demonstrated in both subjects, suggesting its potential use in various HFpEF manifestations, yet customization and optimal deployment are essential to improve heart performance.

The effect of stent graft curvature on the hemodynamic displacement force after abdominal aortic aneurysm endovascular repair.

Endovascular aortic aneurysm repair is a minimally invasive procedure with low mortality and morbidity. Clinical studies have revealed that a displacement force (DF) can cause stent graft (SG) migration in some circumstances requiring repeated intervention. This study aims to determine the relationship between the SG curvature and the calculated DF from four patient-specific computational fluid dynamics models. The SG's curvature was defined according to the centrelines of the implanted SG's branches. The centrelines were defined as either intersecting or separated lines. The centreline curvature (CLC) metrics were calculated based on the local curvature radii and the distances from the centrelines of idealized straight branches. The average CLC value and average variation were calculated to represent the entire graft's curvature. These CLC calculations were compared, and the method that gave the best correlation to the calculated DF was found. The optimal correlation is obtained from calculating the CLC average variation using separated centrelines and distance from straight lines, with an R2 = 0.89. Understanding the relationship between vascular morphology and DF can help identify at-risk patients before the procedure. In these cases, we can provide appropriate treatment and follow up with the patient to prevent future failure.

Numerical modeling for efficiency and endurance assessment of an indirect mitral annuloplasty device.

In recent years, several transcatheter systems have been introduced for treatment of common mitral regurgitation (MR). Such a system that is based on indirect mitral annuloplasty (IMA) is currently indicated for functional MR. Very few clinical studies have been performed to assess the efficiency and durability of such devices, despite their high risk of fracture resulting from ongoing exposure to large cyclic deformations. In this study, numerical models of moderate primary MR were created to test the implantation procedure of a customized IMA device and its sealing efficiency. The ability of the implanted device to reduce systolic leakage was evaluated and affirmed with a model of a more generic device. The long-term durability of the device was tested using a range of Nickel Titanium material properties. Our results demonstrated a considerable reduction in leakage for both the simplified generic device and the more detailed customized device models. The device met different fatigue criteria, confirming its resiliency and safety even after 10 years, even under the harsher conditions of primary MR. This is the first study to assess the performance and fatigue risk of IMA devices for the treatment of more complicated MR conditions. These findings may pave the way for further research to ultimately consider the device in selective cases of PMR.

Impact of tissue porosity and asymmetry on the oxygen uptake of the human placenta: A numerical study.

INTRODUCTION: This study proposes a computational fluid dynamics model of a human placenta's independent exchange unit (placentome) to assess the effect that the inner villi distribution and decidual veins (DVs) location and number, have on the oxygen uptake. METHODS: The internal placentome porosity distribution was altered in symmetric morphology, while asymmetry was introduced by varying the location and number of DVs. The DV asymmetry was introduced by either displacing them circumferentially, thereby changing the angle between them, or by adding DVs in the inlet cross-section. The results were analyzed by the changes in the normalized oxygen mass fraction and the oxygen uptake. RESULTS: Oxygenated blood was shown to be delivered deeper into the placentome when the area of non-homogeneous porosity was larger. The largest oxygen uptake was achieved in the asymmetric model with the smallest angle distance between the DVs, where a 10% decrease relative to the farthest case was obtained. Placing DVs adjacent to the spiral artery opening enhanced the drainage of oxygenated blood. DISCUSSION: This study demonstrates the importance of the local porosity distribution for the proper perfusion of the intervillous space and proposes a novel approach to improve our understanding of the role of the DVs in placental oxygen uptake.

Numerical biomechanics modelling of indirect mitral annuloplasty treatments for functional mitral regurgitation.

Mitral valve regurgitation (MR) is a common valvular heart disease where an improper closure leads to leakage from the left ventricle into the left atrium. There is a need for less-invasive treatments such as percutaneous repairs for a large inoperable patient population. The aim of this study is to compare several indirect mitral annuloplasty (IMA) percutaneous repair techniques by finite-element analyses. Two types of generic IMA devices were considered, based on coronary sinus vein shortening (IMA-CS) to reduce the annulus perimeter and based on shortening of the anterior-posterior diameter (IMA-AP). The disease, its treatments, and the heart function post-repair were modelled by modifying the living heart human model (Dassault Systèmes). A functional MR pathology that represents ischaemic MR was generated and the IMA treatments were simulated in it, followed by heart function simulations with the devices and leakage quantification from blood flow simulations. All treatments were able to reduce leakage, the IMA-AP device achieved better sealing, and there was a correlation between the IMA-CS device length and the reduction in leakage. The results of this study can help in bringing IMA-AP to market, expanding the use of IMA devices, and optimizing future designs of such devices.

Cardiac mesh morphing method for finite element modeling of heart failure with preserved ejection fraction.

Numerical modeling of heart biomechanics can realistically capture morphological variations in diseases and has been helpful in advancing our understanding of the physiology. Subject-specific models require anatomic representation of medical images, and it is desirable to have a consistently repeatable models for any given morphology. In this study, we propose a novel and easily adaptable cardiac reconstruction algorithm by morphing an existing discretized mesh of an advanced finite element (FE) model, to match anatomies acquired from porcine cardiac magnetic resonance imaging (cMRI) scans. The morphing algorithm involves iterative FE simulations with visco-hyperelastic material properties. The living heart porcine model (LHPM) was chosen as the input baseline FE mesh, in order to preserve detailed anatomical features that cannot be captured in routine scans such as myofiber orientations and conduction pathways. The algorithm was demonstrated for the recreation of porcine hearts of a healthy subject and of a subject induced with heart failure with preserved ejection fraction (HFpEF) conditions, where there were substantial hypertrophy and anatomical alterations. We further used the morphed meshes for FE modeling of cardiac contraction and relaxation, thus demonstrating the applicability of the proposed algorithm in producing viable meshes. The results show that our algorithm can recreate the characteristic anatomical changes of cardiac remodeling, including heart muscle thickening, as well as replicate the reduction in ventricular volume. This algorithm allows for the creation of subject-specific models with the same mesh connectivity, thus enabling spatial comparison and analysis of pathologic progress.

Material property alterations for phenotypes of heart failure with preserved ejection fraction: A numerical study of subject-specific porcine models.

A substantial proportion of heart failure patients have a preserved left ventricular (LV) ejection fraction (HFpEF). This condition carries a high burden of morbidity and mortality and has limited therapeutic options. left ventricular pressure overload leads to an increase in myocardial collagen content, causing left ventricular stiffening that contributes to the development of heart failure patients have a preserved left ventricular ejection fraction. Although several heart failure patients have a preserved left ventricular ejection fraction models have been developed in recent years to aid the investigation of mechanical alterations, none has investigated different phenotypes of the disease and evaluated the alterations in material properties. In this study, two similar healthy swine were subjected to progressive and prolonged pressure overload to induce diastolic heart failure characteristics, providing a preclinical model of heart failure patients have a preserved left ventricular ejection fraction. Cardiac magnetic resonance imaging (cMRI) scans and intracardiac pressures were recorded before and after induction. In both healthy and disease states, a corresponding finite element (FE) cardiac model was developed via mesh morphing of the Living Heart Porcine model. The material properties were derived by calibrating to its passive and active behavior. The change in the passive behavior was predominantly isotropic when comparing the geometries before and after induction. Myocardial thickening allowed for a steady transition in the passive properties while maintaining tissue incompressibility. This study highlights the importance of hypertrophy as an initial compensatory response and might also pave the way for assessing disease severity.

Numerical Models of Spinal Cord Trauma: The Effect of Cerebrospinal Fluid Pressure and Epidural Fat on the Results.

Spinal cord injury (SCI) is commonly caused by traumatic mechanical damage. Although numerical models can help predict the mechanics of SCI without putting the subjects in danger, previous studies did not focus on alternations in cerebrospinal fluid (CSF) pressure and did not account for the presence of epidural fat. This study aims to numerically compare the mechanical behavior of the human spine when subjected to contusion and burst fracture with varying CSF pressure, either normal or elevated pressure that represents intracranial hypertension. An additional aim is to find out how the presence of the fat in the model affects the SCI calculations. CSF and epidural fat were modeled as smoothed-particle hydrodynamics (SPH) and the soft tissues were modeled as hyperelastic. This approach made it possible to account for CSF pressure alteration and its effect on the cord. Validation models resulted in good correlation with previous numerical and experimental studies. The results were able to capture the fluid dynamics of the CSF while demonstrating a considerable change in the stresses of the spinal cord. The comparison of the CSF pressures demonstrated that SCI in patients with elevated pressure and in regions where insufficient epidural fat exists might lead to higher spinal cord stresses. Yet, in regions with enough fat, the fat can absorb energy and counteract the effect of the elevated pressure. These results indicate important aspects that need to be accounted for in future numerical models of SCI while also demonstrating how the injury might be aggravated by preexisting conditions.

Numerical Biomechanics Models of the Interaction Between a Novel Transcatheter Mitral Valve Device and the Subvalvular Apparatus.

OBJECTIVE: Mitral valve regurgitation (MR) is a common valvular heart disease where improper closing causes leakage. Currently, no transcatheter mitral valve device is commercially available. Raanani (co-author) and colleagues have previously proposed a unique rotational implantation, ensuring anchoring by metallic arms that pull the chordae tendineae. This technique is now being implemented in a novel device design. The aim of this study is to quantify the rotational implantation effect on the mitral annulus kinematics and on the stresses in the chordae and papillary muscles. METHODS: Finite element analysis of the rotational step of the implantation in a whole heart model is employed to compare 5 arm designs with varying diameters (25.9 mm to 32.4 mm) and rotation angles (up to 140°). The arm rotation that grabs the chordae was modeled when the valve was in systolic configuration. RESULTS: An increase in the rotation angle results in reduced mitral annulus perimeters. Larger rotation angles led to higher chordae stresses with the 29.8 mm experiencing the maximum stresses. The calculated chordae stresses suggest that arm diameter should be <27.8 mm and the rotation angle <120°. CONCLUSIONS: The upper limit of this diameter range is preferred in order to reduce the stresses in the papillary muscles while grabbing more chords. The findings of this study can help improving the design and performance of this unique device and procedural technique.

Impact of BASILICA on the thrombogenicity potential of valve-in-valve implantations.

Subclinical leaflet thrombosis is becoming a major concern in valve-in-valve procedures, whereby a transcatheter aortic valve device is deployed inside a failed bioprosthetic surgical valve. Blood flow stagnation and prolonged residence times in the neo-sinuses have been suggested as possible explanations for leaflet thrombosis. The BASILICA technique, which was originally developed to treat coronary flow obstruction, has also been proposed as an alternative to reduce the risk of thrombus formation. The aim of this study is to understand the impact of BASILICA on the valve-in-valve thrombogenicity using computational fluid dynamics simulations. To this end, two Eulerian and two Lagrangian approaches were employed to estimate near-wall stagnation measures in eight valve-in-valve models. The models included an intact or lacerated Sorin Mitroflow surgical valve, and either a SAPIEN or Evolut transcatheter aortic valve device. The Lagrangian approaches predicted a high number of particles and vortices concentration in the proximal areas of the neo-sinuses, while the Eulerian approaches did so in the distal areas. As a consequence, this study demonstrated that Lagrangian approaches are better predictors of subclinical leaflet thrombosis, since they match experimental and clinical findings. Additionally, the SAPIEN valve possess a higher risk for developing leaflet thrombosis, and two lacerations are shown to provide the best results in terms of development of vortices and accumulation of particles within the neo-sinuses. This study highlights the potential of computational modeling in aiding clinicians in their decision-making in valve-in-valve and BASILICA procedures.

The effect of clinically recommended Evolut sizes on anchorage forces after BASILICA.

Coronary artery obstruction (CAO), a fatal complication of transcatheter aortic valve replacement (TAVR), is commonly found after Valve-in-Valve implantation inside a degenerated bioprosthetic valve. Leaflet laceration (BASILICA technique) has been proposed to prevent CAO and to potentially reduce the risk of leaflet thrombosis. We have previously demonstrated that this technique can reduce the anchorage forces of the TAVR device, which may lead to future complications. In this short communication, we hypothesize that the anchorage force reduction can be minimized by implanting a TAVR with a larger diameter, if two sizes are clinically recommended. We evaluated this hypothesis by employing finite element models of the deployments of the Evolut 26 and 29 mm inside a 27 mm Mitroflow valve, with and without leaflet lacerations. The results show that a laceration substantially decreases the contact area between the Evolut stent and the Mitroflow valve. The larger Evolut has a larger contact area and stronger anchorage forces. Additionally, the anchorage forces are less sensitive to additional lacerations in the larger Evolut (29 case). The results suggest that a larger self-expending device can ensure stronger anchorage and can lower the risk of possible migration, when TAVR is performed in a lacerated bioprosthesis.

New Insights into Valve Hemodynamics.

Heart valve diseases are common disorders with five million annual diagnoses being made in the United States alone. All heart valve disorders alter cardiac hemodynamic performance; therefore, treatments aim to restore normal flow. This paper reviews the state-of-the-art clinical and engineering advancements in heart valve treatments with a focus on hemodynamics. We review engineering studies and clinical literature on the experience with devices for aortic valve treatment, as well as the latest advancements in mitral valve treatments and the pulmonic and tricuspid valves on the right side of the heart. Upcoming innovations will potentially revolutionize treatment of heart valve disorders. These advancements, and more gradual enhancements in the procedural techniques and imaging modalities, could improve the quality of life of patients suffering from valvular disease who currently cannot be treated.

Numerical models for assessing the risk of leaflet thrombosis post-transcatheter aortic valve-in-valve implantation.

Leaflet thrombosis has been suggested as the reason for the reduced leaflet motion in cases of hypoattenuated leaflet thickening of bioprosthetic aortic valves. This work aimed to estimate the risk of leaflet thrombosis in two post-valve-in-valve (ViV) configurations, using five different numerical approaches. Realistic ViV configurations were calculated by modelling the deployments of the latest version of transcatheter aortic valve devices (Medtronic Evolut PRO, Edwards SAPIEN 3) in the surgical Sorin Mitroflow. Computational fluid dynamics simulations of blood flow followed the dry models. Lagrangian and Eulerian measures of near-wall stagnation were implemented by particle and concentration tracking, respectively, to estimate the thrombogenicity and to predict the risk locations. Most of the numerical approaches indicate a higher leaflet thrombosis risk in the Edwards SAPIEN 3 device because of its intra-annular implantation. The Eulerian approaches estimated high-risk locations in agreement with the wall sheer stress (WSS) separation points. On the other hand, the Lagrangian approaches predicted high-risk locations at the proximal regions of the leaflets matching the low WSS magnitude regions of both transcatheter aortic valve implantation models and reported clinical and experimental data. The proposed methods can help optimizing future designs of transcatheter aortic valves with minimal thrombotic risks.