467 Update on supra-annular sizing of transcatheter aortic valve prostheses in raphe-type bicuspid aortic valve disease according to the LIRA method

Aims Transcatheter Aortic Valve Replacement (TAVR) in patients with bicuspid aortic valve (BAV) still represents a challenge due to the peculiar anatomy and the lack of consensus for the optimal CT scan sizing method for prosthesis selection. Recent evidences have shown that transcatheter heart valve (THV) anchoring in BAV patients might occur at the raphe-level, known as the LIRA (Level of Implantation at the RAphe) plane. Furthermore, a novel supra-annular sizing method based on the measurement of the perimeter at the raphe-level (LIRA-method) was shown to be safe and effective in 20 consecutive BAV patients with severe aortic stenosis. The purpose of this study was to confirm the safety and the efficacy of the LIRA method in a larger study population. Methods and results the LIRA plane method was applied to all consecutive patients with raphe-type BAV disease between November 2018 to September 2021 in our centre. We prospectively sized TAVI prosthesis according to the manufacture recommendations on the basis of baseline CT scan perimeters at the LIRA plane. Post-procedural device success, defined according to Valve Academic Research Consortium-2 (VARC-2) criteria, was evaluated in the overall cohort. Forty-four patients were identified as having a raphe-type BAV disease at pre-TAVI CT scans. Mean patient age was 80 ± 6.2 years and 74% were males; median Society of Thoracic Surgeons (STS) predicted risk of mortality score was 4.3 (3.0–6.5). Three different BAV anatomies (36 patients with BAV type 1 with calcific raphe, 5 patients with BAV type 1 with fibrotic raphe, and 3 patients with BAV type 2) were implanted with different types of TAVI prostheses (6 Acurate Neo 2,16 Acurate Neo, 21 Core Valve Evolut R/Pro , 1 Lotus) sized prospectively according to the LIRA plane method. In all patients, there was a significant discrepancy between LIRA and virtual basal ring (VBR) measurements with LIRA plane perimeter smaller than VBR perimeter (mean perimeter LIRA 73.1 ± 8.3 mm vs. mean perimeter VBR 81.5 ± 6.6 mm; P < 0.001). The prostheses were sized according to the manufacture recommendations on the basis of the LIRA plane perimeter (diameter prosthesis implanted/diameter prosthesis according to LIRA plane = 1) (DPI/DP LIRA = 1) and significantly downsized according to the VBR perimeter (DPI/DP VBR 0.89; P < 0.001). The median prosthesis size was 25 mm (23–27). Pre-dilatation was frequently performed (86%) with a median balloon size of 20 mm (18–22), whereas post-dilatation was applied in 27% of the cases with a median balloon size of 23 mm (20–26). The LIRA plane method appeared to be highly successful (100% VARC-2 device success) with no procedural mortality, no valve migration, residual trivial/mild paravalvular leak with no cases of moderate-severe regurgitation and low transprosthetic gradient (residual mean gradient of 8.3 ± 3.5 mmHg) with no cases of mean gradient >20 mmHg pre-discharge. The rate of new pacemaker implantation was 9%. Conclusions Supra-annular sizing according to the LIRA plane method confirmed to be safe with a high device success in a larger study population. The application of the LIRA plane method might optimize TAVI prosthesis sizing in patients with raphe-type BAV disease.

An Analytic Center Cutting Plane Method to Determine Complete Positivity of a Matrix

We propose an analytic center cutting plane method to determine whether a matrix is completely positive and return a cut that separates it from the completely positive cone if not. This was stated as an open (computational) problem by Berman et al. [Berman A, Dur M, Shaked-Monderer N (2015) Open problems in the theory of completely positive and copositive matrices. Electronic J. Linear Algebra 29(1):46–58]. Our method optimizes over the intersection of a ball and the copositive cone, where membership is determined by solving a mixed-integer linear program suggested by Xia et al. [Xia W, Vera JC, Zuluaga LF (2020) Globally solving nonconvex quadratic programs via linear integer programming techniques. INFORMS J. Comput. 32(1):40–56]. Thus, our algorithm can, more generally, be used to solve any copositive optimization problem, provided one knows the radius of a ball containing an optimal solution. Numerical experiments show that the number of oracle calls (matrix copositivity checks) for our implementation scales well with the matrix size, growing roughly like [Formula: see text] for d × d matrices. The method is implemented in Julia and available at https://github.com/rileybadenbroek/CopositiveAnalyticCenter.jl . Summary of Contribution: Completely positive matrices play an important role in operations research. They allow many NP-hard problems to be formulated as optimization problems over a proper cone, which enables them to benefit from the duality theory of convex programming. We propose an analytic center cutting plane method to determine whether a matrix is completely positive by solving an optimization problem over the copositive cone. In fact, we can use our method to solve any copositive optimization problem, provided we know the radius of a ball containing an optimal solution. We emphasize numerical performance and stability in developing this method. A software implementation in Julia is provided.

The Moving Plane Method for Doubly Singular Elliptic Equations Involving a First-Order Term

In this paper we deal with positive singular solutions to semilinear elliptic problems involving a first-order term and a singular nonlinearity. Exploiting a fine adaptation of the well-known moving plane method of Alexandrov–Serrin and a careful choice of the cutoff functions, we deduce symmetry and monotonicity properties of the solutions.

Analysis and Synthesis of a Fuzzy Controller by the Phase Plane Method

The article is devoted to solving the problem of analysis and synthesis of a control system with a fuzzy controller by the phase plane method. The nonlinear transformation, built according to the Sugeno fuzzy model, is approximated by a piecewise linear characteristic consisting of three sections: two piecewise linear and one piecewise constant. This approach allows us to restrict ourselves to three sheets of phase trajectories, each of which is constructed on the basis of a second-order differential equation. Taking this feature into account, the technique of "stitching" of three sheets of phase trajectories is considered and an analytical base is obtained that allows one to determine the conditions for "stitching" of phase trajectories for various variants of piecewise-linear approximation of the characteristics of a fuzzy controller. In view of the specificity of the approximated model of the fuzzy controller used, useful analytical relations are given, with the help of which it is possible to calculate the time of motion of the representing point for each section with the involvement of the numerical optimization apparatus. For a variant of the approximation of three sections, a technique for synthesizing a fuzzy controller is proposed, according to which the range of parameters and the range of input signals are determined, at which an aperiodic process and a given control time are provided. On the model of the automatic control system of the drive level of the mechatronic module, it is shown that the study of a fuzzy system by such an approximated characteristic of a fuzzy controller gives quite reliable results. The conducted studies of the influence of the degree of approximation on the quality of control show that the approximated characteristic of a fuzzy controller gives a slight deterioration in quality in comparison with the smooth characteristic of a fuzzy controller. Since the capabilities of the phase plane method are limited to the 2nd order of the linear part of the automatic control system, the influence of the third order on the dynamics of the system is considered using the example of a mechatronic module drive. It is shown that taking into account the electric time constant leads to overshoot within 5-10 %. Such overshoot can be eliminated due to the proposed recommendations for correcting the static characteristic of the fuzzy controller.

A normal section plane method for profile error analysis of five-axis machine tools based on the ideal tool flank milling surface

The existing studies on profile error analysis and machining accuracy measurement do not consider the impact of the theoretical errors on the machine tool accuracy measurement. Therefore, this study proposes an estimation method of the surface profile error based on the normal section plane, using the theoretical flank milled surface for comparison. This effectively improves the accuracy of profile error estimation. The theoretical flank milled surface is the surface machined by flank milling under ideal conditions. Hence, compared to the traditional analysis method based on the designed three-dimensional model of S-shaped test pieces, the calculated profile error of this method does not include theoretical errors, thereby eliminating the impact of theoretical errors on machine tool accuracy measurement and evaluation. First, an improved method for continuous parameterized dual spline interpolation was proposed. It simplifies the solution of the singular problem of the coefficient matrix of the spline basis function and obtains a continuous ideal machining tool axis trajectory surface with complete geometric characteristics. Next, a method for constructing the theoretical flank milled surface machined with a cylindrical milling tool using equidistant mapping characteristics was proposed; then, the differential transformation relationship at the cutting contact point of the curved surface under the influence of tool path errors was established. Furthermore, the normal section plane method based on the differentiation of the cutting contact point was proposed. The problem of solving the distance from a point to a surface is converted to the problem of solving the distance from a point to a curve in the normal section plane. This improves the accuracy of profile error estimation. The effectiveness of the method was verified by comparing the analysis results of the profile errors of a typical cylindrical surface with the point to surface and the point to curve methods.

Static Buckling Analysis of a Quadratic-Cubic Model Structure Using the Phase Plane Method and Method of Asymptotics

The exact and asymptotic analyses of the buckling of a quadratic-cubic model structure subjected to static loading are discussed. The governing equation is first solved using the phase plane method and next, using the method of asymptotics. In the asymptotic method, we discuss the possibilities of using regular perturbation method in asymptotic expansions of the relevant variables to get an approximate analytical solution to the problem. Finally, the two results are compared using numerical results obtained with the aid of Q-Basic codes. In the two methods discussed in this work, it is clearly seen that the static buckling loads decrease as the imperfection parameters increase. It is also observed that the static buckling loads obtained using the exact method are higher than those obtained using the method of asymptotics.

Analysis of Time Series Based on a New Entropy Plane by Using Weighted Dispersion Pattern

Complexity is an important feature of complex time series. In this paper, we construct a weighted dispersion pattern and propose a new entropy plane using past Tsallis entropy and past Rényi entropy by using weighted dispersion pattern (PTEWD and PREWD, respectively), to quantify the complexity of time series. Through analyzing simulated data and actual data, we have verified the reliability of the entropy plane method. This entropy plane successfully distinguishes American and Chinese stock indexes, as well as developed and emergent stock markets. We introduce PTEWD and PREWD into multiscale settings, which could also well distinguish different stock markets. The results show that the new entropy plane could be used as an effective tool to distinguish financial markets.

Multiaxial fatigue assessment for outer cylinder of landing gear by critical plane method

The in-service loadings on the landing gear are usually complex and from different directions, which lead to the fatigue critical locations in the landing gear structure mostly in multiaxial stress state. A methodology based on the critical plane method was proposed for estimating the fatigue lifetime of outer cylinder of the main landing gear undergoing variable amplitude (VA) multiaxial proportional loading. The orientation of the critical plane was determined by the so-called maximum variance method. The Bannantine–Socie’s cycle counting method and Miner’s linear rule were applied with Zhang–Yao’s criterion in this research. The calculated results on the fatigue lifetime of the outer cylinder were compared with the experimental data. The results indicate that the methodology proposed in this article is a sound method for fatigue life prediction of engineering components bearing complex VA multiaxial fatigue loading.