Terms Of Leakage Research Articles

Higher order compact finite difference schemes for steady and transient solutions of space–time neutron diffusion model

One of the most difficult tasks in the numerical simulation of nuclear reactors is to find solution of a system arising from spatial discretization of multidimensional multigroup neutron diffusion equations by finite difference method. The big disadvantage is that it requires smaller mesh spacing. Using smaller mesh spacing produces reasonable results but it consumes huge computational effort. In this work, we overcome this flaw by constructing higher order compact finite difference schemes to approximate the neutron leakage terms. The technique is based on using concentrated points around a central point instead of minimizing the mesh spacing taking into account the location of the diffusion coefficients. Beside the accuracy of the proposed schemes, the dimension of the coefficient matrix and therefore the complexity of the system still the same. Five point stencils with equally distance h in each direction are used to produce more than one of standard central difference formulas to be combined producing the fourth order finite difference scheme with order of accuracy O(h4). Also, seven point stencils are used to get the sixth order scheme with accuracy O(h6). The proposed fourth and sixth order schemes are highlighted through two theories. The maximum error norms and the convergence rates of the proposed schemes are discussed. For the time discretization, multi-step differential transform method MDTM is employed to solve the neutron diffusion model. To illustrate the applicability and accuracy of the proposed schemes, results are tested on some multidimensional homogenous and heterogeneous benchmark problems. Our static normalized assembly power densities that are obtained by dividing the whole core into just few dozens or hundreds of fuel assemblies are compared with the Improved SIDK, FLUENT and BRBFCM methods that divide the core into many thousands of fuel assemblies. It is proved that the obtained results are very close to those methods.

Global exponential stability of discrete-time Hopfield neural network models with unbounded delays

In this paper, a general setting is presented to study the exponential stability of discrete-time systems with bounded or unbounded delays. Based on the M-matrix theory, we establish sufficient conditions to ensure the global exponential stability of the zero equilibrium of low-order, and high-order, discrete-time Hopfield neural network models with unbounded delays and delay in the leakage terms. A comparison of the literature shows that our results generalize and improve some in recent publications.

The Atacama Cosmology Telescope: measurement and analysis of 1D beams for DR4

We describe the measurement and treatment of the telescope beams for the Atacama Cosmology Telescope's fourth data release, DR4. Observations of Uranus are used to measure the central portion (<12') of the beams to roughly -40 dB of the peak. Such planet maps in intensity are used to construct azimuthally averaged beam profiles, which are fit with a physically motivated model before being transformed into Fourier space. We investigate and quantify a number of percent-level corrections to the beams, all of which are important for precision cosmology. Uranus maps in polarization are used to measure the temperature-to-polarization leakage in the main part of the beams, which is ≲ 1% (2.5%) at 150 GHz (98 GHz). The beams also have polarized sidelobes, which are measured with observations of Saturn and deprojected from the ACT time-ordered data. Notable changes relative to past ACT beam analyses include an improved subtraction of the atmospheric effects from Uranus calibration maps, incorporation of a scattering term in the beam profile model, and refinements to the beam model uncertainties and the main temperature-to-polarization leakage terms in the ACT power spectrum analysis.

Location of inferior mesentery artery ligation in rectal cancer surgery: how to make decisions based on available evidence

There are still controversies as to the location of ligating the inferior mesenteric artery and the central lymph node dissection during rectal cancer surgery. The reason is that the level of evidence in this area is low. Existing studies are mostly retrospective, analyses or small-sample randomized controlled trials. These results showed no significant differences between high-ligation and low-ligation, in terms of anastomotic leakage and other short-term postoperative complications. Low-ligation seems better for the recovery of postoperative genitourinary function. Due to the low rate of central lymph node metastasis and many other confounding factors that affect the survival rate, it is difficult to conclude the survival benefits of ligation site or central node dissection. It is necessary to carry out some targeted, well-designed, large-scale randomized controlled trials to explain the related issues of inferior mesenteric artery ligation site and extent of central lymphadenectomy.

Towards an objective evaluation of EEG/MEG source estimation methods – The linear approach

The spatial resolution of EEG/MEG source estimates, often described in terms of source leakage in the context of the inverse problem, poses constraints on the inferences that can be drawn from EEG/MEG source estimation results. Software packages for EEG/MEG data analysis offer a large choice of source estimation methods but few tools to experimental researchers for methods evaluation and comparison. Here, we describe a framework and tools for objective and intuitive resolution analysis of EEG/MEG source estimation based on linear systems analysis, and apply those to the most widely used distributed source estimation methods such as L2-minimum-norm estimation (L2-MNE) and linearly constrained minimum variance (LCMV) beamformers. Within this framework it is possible to define resolution metrics that define meaningful aspects of source estimation results (such as localization accuracy in terms of peak localization error, PLE, and spatial extent in terms of spatial deviation, SD) that are relevant to the task at hand and can easily be visualized. At the core of this framework is the resolution matrix, which describes the potential leakage from and into point sources (point-spread and cross-talk functions, or PSFs and CTFs, respectively). Importantly, for linear methods these functions allow generalizations to multiple sources or complex source distributions. This paper provides a tutorial-style introduction into linear EEG/MEG source estimation and resolution analysis aimed at experimental (rather than methods-oriented) researchers. We used this framework to demonstrate how L2-MNE-type as well as LCMV beamforming methods can be evaluated in practice using software tools that have only recently become available for routine use. Our novel methods comparison includes PLE and SD for a larger number of methods than in similar previous studies, such as unweighted, depth-weighted and normalized L2-MNE methods (including dSPM, sLORETA, eLORETA) and two LCMV beamformers. The results demonstrate that some methods can achieve low and even zero PLE for PSFs. However, their SD as well as both PLE and SD for CTFs are far less optimal for all methods, in particular for deep cortical areas. We hope that our paper will encourage EEG/MEG researchers to apply this approach to their own tasks at hand.

Quantitative Fluorescence Imaging of Perfusion-An Algorithm to Predict Anastomotic Leakage.

This study tests fluorescence imaging-derived quantitative parameters for perfusion evaluation of the gastric tube during surgery and correlates these parameters with patient outcomes in terms of anastomotic leakage. Poor fundus perfusion is seen as a major factor for the development of anastomotic leakage and strictures. Fluorescence perfusion imaging may reduce the incidence of complications. Parameters for the quantification of the fluorescence signal are still lacking. Quantitative parameters in terms of maximal intensity, mean slope and influx timepoint were tested for significant differences between four perfusion areas of the gastric tube in 22 patients with a repeated ANOVA test. These parameters were compared with patient outcomes. Maximal intensity, mean slope and influx timepoint were significantly different between the base of the gastric tube and the fundus (p < 0.0001). Patients who developed anastomotic leakage showed a mean slope of almost 0 in Location 4. The distance of the demarcation of ICG to the fundus was significantly higher in the three patients who developed anastomotic leakage (p < 0.0001). This study presents quantitative intra-operative perfusion imaging with fluorescence. Quantification of the fluorescence signal allows for early risk stratification of necrosis.

A new technique for reducing accumulation, transport, and toxicity of heavy metals in wheat (Triticum aestivum L.) by bio-filtration of river wastewater

The occurrence of contaminants such as heavy metals in an aqueous environment has become a global concern. In the present study, a bio-filter was designed to eliminate heavy metals from river wastewater contaminated with industrial effluents. Moreover, we analyzed simple tap water, bio-filtered water, and unfiltered river wastewater and measured the concentrations of different heavy metals in the samples, such as cadmium (Cd), nickel (Ni), lead (Pb), and copper (Cu). The current experiment explored irrigation effects of three water regimes (tap water, bio-filtered water, and wastewater) on two wheat (Triticum aestivum L.) varieties (NARC-2009 and NARC-2011). Results of the present study indicated that wastewater negatively influenced the growth parameters and photosynthetic contents along with a significant increase in oxidative damage in terms of electrolyte leakage (EL) (50 and 61%), hydrogen peroxide (H2O2) (52 and 61 μmol/g), and malondialdehyde (MDA) (16 and 17.7 μmol/g) contents in NARC-2009 and NARC-2011 respectively. However, bio-filtered water positively regulated the growth profile, activities of antioxidants such as superoxide dismutase (SOD), catalase (CAT), peroxidase (POD), total soluble sugars, amino acids, total protein, and proline contents in wheat as compared with untreated wastewater. In addition, bio-filtered water had significant impacts on the reduction of Cd, Ni, Pb, and Cu concentrations in roots, shoots, and grains of both wheat varieties as compared to wastewater. The concentrations (mg/kg) of Cd (15 and 18), Ni (35 and 57), Pb (5 and 7), and Cu (69 and 72) in roots, Cd (5 and 6), Ni (24 and 43), Pb (3 and 4), and Cu (16 and 19) in shoots, and Cd (0.7 and 1.0), Ni (11 and 26), Pb (2 and 3), and Cu (1.6 and 1.5) in grains of NARC-2009 and NARC-2011 were found under river wastewater treatment. Overall, wastewater treatment through bio-filtration process is an effective strategy for the reduction of toxic elements in bio-filtered water and their accumulation by plants.

The evaluation of the efficacy of adalimumab in refractory non-infectious uveitis with ultra-widefield fundus fluorescein angiography.

To investigate the efficacy of adalimumab in the cases with refractory non-infectious uveitis and evaluate retinal vascular leakage changes on ultra-widefield fundus fluorescein angiography. Twenty-three patients with refractory uveitis were included in study. Forty-four eyes of 23 patients with non-infectious uveitiswere evaluated. Clinically active inflammation was present in 19 eyes (43.18%), while 25 (56.8%) were inactive. The mean drug burden was a 9.91 ± 3.78 (5-21) in baseline, 7.3 ± 4.25 at third and 8.0 ± 4.71 at sixth month (p = 0.022). The mean choroidal thickness was 256.65 ± 43.63μm in baseline, 240.49 ± 36.73μm at third and 224.81 ± 34.91μm at sixth month (p ≤ 0.05). In terms of leakage extend, leakage was initially present in a mean of 2.95 ± 4.55 clock hours, 2.41 ± 3.91 at third and 1.76 ± 3.44 at sixth month (p < 0.001). Adalimumab was found to be effective in establishing inflammation control by reducing drug burden, controlling retinal vascular leakage and choroidal inflammation in refractory uveitis.

Privacy-Preserving Aggregate Mobility Data Release: An Information-Theoretic Deep Reinforcement Learning Approach

It is crucial to protect users’ location traces against inference attacks on aggregate mobility data collected from multiple users in various real-world applications. Most of the existing works on aggregate mobility data are focusing on inference attacks rather than designing privacy-preserving release mechanisms, and a few differential private release mechanisms suffer from poor utility-privacy tradeoffs. In this paper, we propose optimal centralized privacy-preserving aggregate mobility data release mechanisms (PAMDRMs) that minimize the leakage from an information-theoretic perspective by releasing perturbed versions of the raw aggregate location. Specifically, we use mutual information to measure user-level and aggregate-level privacy leakage separately, and formulate leakage minimization problems under utility constraints. As directly solving the optimization problems incur exponential complexity w.r.t. users’ trace length, we transform them into belief state Markov Decision Processes (MDPs), with a focus on the MDP formulation for the user-level privacy problem. We build reinforcement learning (RL) models and leverage the efficient Asynchronous Advantage Actor-Critic RL algorithm to derive the solutions to the MDPs as our optimal PAMDRMs. We compare them with two state-of-the-art privacy protection mechanisms PDPR (context-aware local design) and DMLM (context-free centralized design) in terms of mutual information leakage and adversary’s attack success (evaluated by her expected estimation error and Jensen-Shannon Divergence-based error). Extensive experimental results on both synthetic and real-world datasets demonstrate that the user-level PAMDRM performs the best on both measures thanks to its context-aware property and centralized design. Even though the aggregate-level PAMDRM achieves better privacy-utility tradeoff than the other two, it does not always perform better than them on adversarial success, highlighting the necessity of considering privacy measures from different perspectives to avoid overestimating the level of privacy offered to users. Lastly, we discuss an alternative, fully data-driven approach to derive the optimal PAMDRM by leveraging adversarial training on limited data samples.

Laws for pauses.

It is shown that a particular class of pauses taken in both read and composed speech obey allometric laws such that mean pause length predicts body size. The pauses in this class have durations that roughly span 250 ms to 1,000 ms and are taken to mark grammatical and prosodic boundaries. A theory of pause allometry is developed based on the observation that these pauses are expressive, they give speech momentum and rhythm, and most importantly, their durations reflect temporal discrimination-they are not produced by articulatory constraints. The theory is formulated in terms of a leaky integrator differential equation that is intended to model the sense of time passage that occurs during relatively brief pauses. The theory predicts that if the decay time scale associated with the leakage term includes body size as a parameter, then allometry will be observed generally in the amount of silence people deploy in pause behavior. A second study tested the theory on a class of long pauses defined by being terminated by a speech gesture indicating speaker recognition that the pause was indeed long. These long pauses were also found to obey allometry. The exponents derived from power law models of mean pause duration in both studies were found to be significantly larger than those associated with allometries of body energy expenditure. These findings provide a new meaning to the embodiment of cognition. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Intervention Strategies to Reduce Surgical Site Infection Rates in Patients Undergoing Rectal Cancer Surgery

This study aimed to determine the effectiveness of surgical site infection (SSI) prevention approaches in rectal cancer surgery.A total of 1,408 patients who underwent elective rectal cancer surgery between 1995 and 2017 were reviewed. Patients were divided into three groups: control group (group A, n=245), SSI prevention intervention group (group B, n=516), and laparoscopic or robotic surgery group (group C, n=647). The groups were compared in terms of SSI and anastomotic leakage (AL) incidences, and risk factors for SSI were investigated.The overall SSI and AL rates were 19.4% and 3.6%, respectively. These rates were significantly lower in Group C (9.3%, 1.7%), compared to Groups A (40.0%, 6.1%) and B (22.5%, 3.5%). Abdominoperineal resection, open surgery, operation time, intraoperative bleeding, lack of absorbable sutures, lack of mechanical bowel preparation, and lack of oral antibiotics were independently associated with SSI.SSI reduction after rectal cancer surgery was achieved through various intervention strategies.

Impulsive effects on stochastic bidirectional associative memory neural networks with reaction-diffusion and leakage delays

In this paper, the problem of global asymptotic stability analysis for stochastic reaction-diffusion bidirectional associative memory neural networks (BAMNNs) with mixed delays and impulsive effects are investigated. The mixed delays consists of time delays in the leakage terms and continuously distributed delays. Based on the Lyapunov–Krasovskii functional (LKF), It's differential formula and linear matrix inequality (LMI) method, some sufficient conditions for global asymptotic stability in mean square of the equilibrium point of the systems are derived. The feasibility of the conditions are verified using the MATLAB LMI toolbox. Finally, two examples are provided to illustrate the effectiveness and validity of the derived main results.

Channel-Supermodular Entropies: Order Theory and an Application to Query Anonymization.

This work introduces channel-supermodular entropies, a subset of quasi-concave entropies. Channel-supermodularity is a property shared by some of the most commonly used entropies in the literature, including Arimoto–Rényi conditional entropies (which include Shannon and min-entropy as special cases), k-tries entropies, and guessing entropy. Based on channel-supermodularity, new preorders for channels that strictly include degradedness and inclusion (or Shannon ordering) are defined, and these preorders are shown to provide a sufficient condition for the more-capable and capacity ordering, not only for Shannon entropy but also regarding analogous concepts for other entropy measures. The theory developed is then applied in the context of query anonymization. We introduce a greedy algorithm based on channel-supermodularity for query anonymization and prove its optimality, in terms of information leakage, for all symmetric channel-supermodular entropies.

Existence and Global Attractivity of Pseudo Almost Periodic Solutions for Clifford-Valued Fuzzy Neural Networks with Proportional Delays

In this paper, Clifford-valued fuzzy neural networks with proportional delays, whose leakage term coefficients are also Clifford numbers, are considered. Based on the Banach fixed point theorem and differential inequality technique, we use a direct method to obtain the existence, uniqueness, and global attractivity of pseudo almost periodic solutions for the considered networks. Finally, we provide a numerical example to illustrate the feasibility of our results. Our results are new.

The Impact of Drain and Reinforcement on the Outcomes of Bariatric Surgery: A Prospective Study.

PurposeWe aimed to investigate the impact of reinforcement and abdominal drains on the outcome of laparoscopic sleeve gastrectomy (LSG).MethodsThe present study was a prospective study that included obese patients scheduled to undergo LSG. Patients were assigned to receive drain, reinforcement, or both according to the surgeon's preference and followed up for one month after surgery. The present study's primary outcome was the identification of the association between intraoperative drain/reinforcement and the incidence of postoperative complications.ResultsA total of 125 (20.3%) patients received intraoperative drains. The proportion of postoperative morbidity was comparable between the drain and non-drain groups (3.2% versus 1.6%; p = 0.25). Patients in the drain group had similar incidence of blood transfusion (2.4% versus 1.7% in non-drain group; p = 0.43) and postoperative leakage (0.8% versus 0.2% in non-drain group; p = 0.36). The incidences of blood transfusion (p = 0.56) and reoperation (p = 0.98) were comparable between the drain and non-drain groups. There were no statistically significant differences between the drain and non-drain groups regarding postoperative mortality and wound infection (p > 0.05). On the other hand, 440 (71.3%) patients received reinforcement. The proportion of postoperative morbidity was comparable between the reinforcement and non-reinforcement groups (1.6% versus 2.8%, p = 0.07). Patients in the reinforcement group were less likely to develop postoperative bleeding (0.7% versus 4% in the non-reinforcement group; p = 0.004), while no significant difference was detected in terms of postoperative leakage (p = 0.33) and in-hospital mortality.ConclusionIn conclusion, abdominal drainage did not reduce the complications of LSG patients. Reinforcement has some role in controlling the bleeding but not leaks. Both techniques did not significantly impact the mortality rate. In the future, additional, large randomized trials are needed to examine the gastrointestinal-related quality of life.

Dynamics of fuzzy genetic regulatory networks with leakage and mixed delays in doubly-measure pseudo-almost periodic environment

The study of dynamics behaviors of genetic regulatory networks (GRNs) is essential for the understanding of living organisms at both molecular and cellular levels. This paper deals with a class of fuzzy genetic regulatory networks (FGRNs) with time varying-delays in leakage terms, time-varying discrete delays, unbounded distributed delays, and doubly-measure pseudo-almost periodic parameters. Based on the doubly-measure pseudo-almost periodic theory, exponential dichotomy, differential inequality, and the Banach fixed point theorem, we establish some sufficient conditions to support the existence and global exponential stability of doubly-measure pseudo-almost periodic solutions for the considered model. A numerical example along with a graphical illustration are presented to support our main results. The results of this paper are new and extend existing GRNs models using almost periodic and weighted pseudo-almost periodic functions to support a wider range of regulatory processes.

Clinical comparison between thoracoscopic and thoracotomy repair of Gross type C esophageal atresia

BackgroundTo compare the clinical outcomes between thoracoscopic approach and thoracotomy surgery in patients with Gross type C Esophageal atresia (EA) and tracheoesophageal fistula (TEF).MethodsPatients with Gross type C EA/TEF who underwent surgery from January 2007 to January 2020 at Beijing Children’s Hospital were retrospectively analyzed. The patients were divided into two groups according to surgical approaches. The perioperative factors and postoperative complications were compared among the two groups.ResultsOne hundred and ninety patients (132 boys and 58 girls) with a median birth weight of 2975 (2600, 3200) g were included. The primary operations were performed via thoracoscopic (n = 62) and thoracotomy (n = 128) approach. After comparison of clinical characteristics between the two groups, we found that there were statistically significant differences in associated anomalies, method of fistula closure, duration of mechanical ventilation after surgery, feeding option before discharge, management of pneumothorax, and prognosis (all P < 0.05). To a certain extent, thoracoscopic surgery reduced the incidence of anastomotic leakage and increased the incidence of anastomotic stricture in this study. However, there were no statistically significant differences between the two groups in terms of operative time, postoperative pneumothorax, anastomotic leakage, anastomotic stricture, and recurrent tracheoesophageal fistula (all P > 0.05).ConclusionsThoracoscopy surgery for Gross type C EA/TEF is a safe and effective, minimally invasive technique with comparable operative time and incidence of postoperative complications.

WRSS: An Object-Oriented R Package for Large-Scale Water Resources Operation

Water resources systems, as facilities for storing water and supplying demands, have been critically important due to their operational requirements. This paper presents the applications of an R package in a large-scale water resources operation. The WRSS (Water Resources System Simulator) is an object-oriented open-source package for the modeling and simulation of water resources systems based on Standard Operation Policy (SOP). The package provides R users several functions and methods to build water supply and energy models, manipulate their components, create scenarios, and publish and visualize the results. WRSS is capable of incorporating various components of a complex supply–demand system, including numerous reservoirs, aquifers, diversions, rivers, junctions, and demand nodes, as well as hydropower analysis, which have not been presented in any other R packages. For the WRSS’s development, a novel coding system was devised, allowing the water resources components to interact with one another by transferring the mass in terms of seepage, leakage, spillage, and return-flow. With regard to the running time, as a key factor in complex models, WRSS outshone the existing commercial tools such as the Water Evaluation and Planning System (WEAP) significantly by reducing the processing time by 50 times for a single unit reservoir. Additionally, the WRSS was successfully applied to a large-scale water resources system comprising of 5 medium- to large-size dams with 11 demand nodes. The results suggested dams with larger capacity sizes may meet agriculture sector demand but smaller capacities to fulfill environmental water requirement. Additionally, large-scale approach modeling in the operation of one of the studied dams indicated its implication on the reservoirs supply resiliency by increasing 10 percent of inflow compared with single unit operation.

New basis functions for reactor core calculations using the nodal expansion method

In 1977 Finnemann, Bennewitz and Wagner introduced the Nodal Expansion Method (NEM), by combining neutron diffusion theory, polynomial expansions, interface currents continuity, and weighted residual techniques. Extensive testing clearly indicated that it was consistent, computationally efficient, and accurate for meshes up to the typical size of assemblies. Two classical two-dimensional benchmarks were simulated: IAEA and LRABWR. Moments weighting was suggested to be preferable to Galerkin weighting. However, considering nodes of the size of assemblies, the fifth-order expansion using Galerkin weighting provided more accurate results than the fourth-order expansion using moments weighting (G3 and M2 on Finnemann's notation, respectively). The quadratic approximation has been considered appropriate to represent the transverse leakage terms (B2 on Finnemann's notation). Several studies seeking more accurate representations for the transverse leakage have been published since then. However, fourth-order expansion using moments weighting remains widely used as the most appropriate choice to approximate the average transverse fluxes, which may restrict the potentiality of the method.A detailed analysis of the NEM's basis functions has been performed, which allowed the development of formalism capable of generating polynomial expansions of any order. The new basis functions should introduce the additional terms required to describe the average transverse flux more properly, considering its distortions at fuel-reflector interfaces. In the same way that increasing the number of terms in convergent series leads to more accurate results, increasing the expansion order should bring the result closer to the expected solution. Comparisons of two- and three-dimensional LWR static benchmarks simulations are presented using up to tenth-order polynomial expansions, using both weight functions: moments and Galerkin. The introduced basis functions have led to more accurate results for keff and normalized assembly power distribution, including nodes at fuel-reflector interfaces. The increases in computing time using up to tenth-order expansions, for both weight functions, have not exceeded 40% for the simulated two-dimensional benchmarks and 90% for three-dimensional ones.

Quantification of noncircular stent expansion after TAVR into a pathological annulus and its impact on paravalvular leakage

Abstract Patients undergoing transcatheter aortic valve replacement (TAVR) may suffer severe clinical complications, caused by paravalvular leakage (PVL) which is defined as leakage between TAVR and aortic annulus. PVL is often facilitated by a severely calcified annulus. This limits the expansion of a self-expandable TAVR stent. To assess TAVR performance in terms of leakage, measurement of regurgitation fraction in a pathophysiological annulus is recommended according to ISO 5840. For this purpose, a configuration of a circular annulus with a calcification nodule has been proposed in the recently published ISO 5840. The impact of the proposed pathophysiological annulus model on the expansion of self-expandable TAVR stents and on the regurgitation fraction was investigated in this study. For this purpose, two commercially available selfexpandable TAVRs (Evolut R and Portico) were implanted in a calcified annulus model. Circular expansion of the TAVR stents was investigated based on μCT scans of the implanted TAVR. The calcification-induced area in which retrograde flow can occur during diastole was detected. These results were then compared with the experimentally determined regurgitation fraction obtained from pulse duplicator tests. The results of the μCT scans showed a continuous leakage area in the region of the annulus for the Evolut R compared to a locally larger leakage area of the Portico, which, however, reattaches to the annulus in the distal inflow region. The hydrodynamic measurements confirmed a smaller leakage in the pathological annulus for the Portico. In summary, it can be assumed that a continuous leakage area in the TAVR stent inflow region encourages the PVL of TAVR.