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Controlled frames in Hilbert spaces have been recently introduced by P. Balazs and etc. for improving the numerical efficiency of interactive algorithms for inverting the frame operator. In this paper we develop a theory based on g-fusion frames on Hilbert spaces, which provides exactly the frameworks not only to model new frames on Hilbert spaces but also for deriving robust operators. In particular, we can define analysis, synthesis and frame operators with representation space compatible for (C,C')-Controlled g-fusion frames, which even yield a reconstruction formula. Also, some useful concepts such as Q-dual and perturbation are introduced and investigated. [ABSTRACT FROM AUTHOR]

Regarding the applications of the fusion frames and generalization of them in data proceeding, their iterative is of particular importance when one of their members is deleted. In this note, a method for reconstruction of continuous generalized fusion frames and the error operator with its upper bound are presented. Also, the approximation operator for these frames will be introduced. [ABSTRACT FROM AUTHOR]

Aims To characterize the dynamic nature of the left ventricular outflow tract (LVOT) geometry and flow rate in patients following transcatheter mitral valve replacement (TMVR) with anterior leaflet laceration (LAMPOON) and derive insights to help guide future patient selection. Methods and results Time-resolved LVOT geometry and haemodynamics were analysed with post-procedure computed tomography and echocardiography in subjects (N  = 19) from the LAMPOON investigational device exemption trial. A novel post hoc definition for LVOT obstruction was employed to account for systolic flow rate and quality of life improvement [obstruction was defined as LVOT gradient > 30 mmHg or LVOT effective orifice area (EOA) ≤ 1.15 cm2]. The neo-LVOT and skirt neo-LVOT were observed to vary substantially in area throughout systole (64  ±  27% and 25  ±  14% change in area, respectively). The peak systolic flow rate occurred most commonly just prior to mid-systole, while minimum neo-LVOT (and skirt neo-LVOT) area occurred most commonly in early-diastole. Subjects with LVOT obstruction (n  = 5) had smaller skirt neo-LVOT values across systole. Optimal thresholds for skirt neo-LVOT area were phase-specific (260, 210, 200, and 180 mm2 for early-systole, peak flow, mid-systole, and end-systole, respectively). Conclusion The LVOT geometry and flow rate exhibit dynamic characteristics following TMVR with LAMPOON. Subjects with LVOT obstruction had smaller skirt neo-LVOT areas across systole. The authors recommend the use of phase-specific threshold values for skirt neo-LVOT area to guide future patient selection for this procedure. LVOT EOA is a 'flow-independent' metric which has the potential to aid in characterizing LVOT obstruction severity. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notation of weaving continuous fusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c -fusion frames under the bounded linear operator and also, removing vectors from these frames, we will present a necessarily and sufficient condition about c -woven and c -fusion woven. Finally, perturbation of these frames will be introduced. [ABSTRACT FROM AUTHOR]

After introducing g-frames and fusion frames by Sun and Casazza, respectively, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce a Parseval g-fusion frame. [ABSTRACT FROM AUTHOR]

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames [ABSTRACT FROM AUTHOR]

This study examined whether the presence of a sinus of Valsalva equivalent in the KONECT RESILIA aortic valved conduit (Edwards Lifesciences, Irvine, Calif) improves valve hemodynamics, kinematics, and performance. A 28-mm KONECT RESILIA aortic valved conduit was used to create an in vitro flow test model, and the same aortic valved conduit model without a sinus section was used as a control. Particle image velocimetry and hydrodynamic characterization experiments were conducted in the vicinity of the valves in a validated left-heart simulator at 3 cardiac output levels. In addition, leaflet kinematics of the valves were determined through en face high-speed imaging. The KONECT RESILIA aortic valved conduit model exhibited lower mean and peak transvalvular pressure gradients than the control model at all 3 cardiac outputs. In addition, its leaflets opened more fully than did those of the valved conduit without the sinuses, yielding greater effective and geometric orifice areas. It was found that the presence of the sinuses not only facilitated the development of larger and more stable vortices at the initial stages of the cardiac cycle but also helped to maintain these vortices during the late stages of the cardiac cycle, leading to smoother valve closure. The KONECT RESILIA aortic valved conduit reproduces the bulged section of the aortic root corresponding to the sinuses of Valsalva. With this Valsalva-type conduit, larger orifice areas were observed, improving valve hemodynamics that may enhance performance. [ABSTRACT FROM AUTHOR]

Background: A clinical study comparing the hemodynamic outcomes of transcatheter mitral valve replacement (TMVR) with vs. without Laceration of the Anterior Mitral leaflet to Prevent Outflow Obstruction (LAMPOON) has never been designed nor conducted., Aims: To quantify the hemodynamic impact of LAMPOON in TMVR using patient-specific computational ( in silico ) models., Materials: Eight subjects from the LAMPOON investigational device exemption trial were included who had acceptable computed tomography (CT) data for analysis. All subjects were anticipated to be at prohibitive risk of left ventricular outflow tract (LVOT) obstruction from TMVR, and underwent successful LAMPOON immediately followed by TMVR. Using post-procedure CT scans, two 3D anatomical models were created for each subject: (1) TMVR with LAMPOON (performed procedure), and (2) TMVR without LAMPOON (virtual control). A validated computational fluid dynamics (CFD) paradigm was then used to simulate the hemodynamic outcomes for each condition., Results: LAMPOON exposed on average 2 ± 0.6 transcatheter valve cells (70 ± 20 mm 2 total increase in outflow area) which provided an additional pathway for flow into the LVOT. As compared to TMVR without LAMPOON, TMVR with LAMPOON resulted in lower peak LVOT velocity, lower peak LVOT gradient, and higher peak LVOT effective orifice area by 0.4 ± 0.3 m/s (14 ± 7% improvement, p = 0.006), 7.6 ± 10.9 mmHg (31 ± 17% improvement, p = 0.01), and 0.2 ± 0.1 cm 2 (17 ± 9% improvement, p = 0.002), respectively., Conclusion: This was the first study to permit a quantitative, patient-specific comparison of LVOT hemodynamics following TMVR with and without LAMPOON. The LAMPOON procedure achieved a critical increment in outflow area which was effective for improving LVOT hemodynamics, particularly for subjects with a small neo-left ventricular outflow tract (neo-LVOT)., Competing Interests: KK has served as a consultant for Abbott Vascular. PB has served as a consultant for Edwards Lifesciences, Tendyne, Neovasc, and Circle Imaging. AG has served as a proctor for Edwards Lifesciences, Medtronic, and Abbott Vascular; and has served as a consultant for and is an equity holder in Transmural Systems. VB has served as a consultant for Edwards Lifesciences and Abbott Vascular; and has served as a consultant for and is an equity holder in Transmural Systems. JK and RL were co-inventors on patents, assigned to the NIH, on devices for leaflet laceration. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Kohli, Wei, Sadri, Siefert, Blanke, Perdoncin, Greenbaum, Khan, Lederman, Babaliaros, Yoganathan and Oshinski.)

Aims: To characterize the dynamic nature of the left ventricular outflow tract (LVOT) geometry and flow rate in patients following transcatheter mitral valve replacement (TMVR) with anterior leaflet laceration (LAMPOON) and derive insights to help guide future patient selection., Methods and Results: Time-resolved LVOT geometry and haemodynamics were analysed with post-procedure computed tomography and echocardiography in subjects (N = 19) from the LAMPOON investigational device exemption trial. A novel post hoc definition for LVOT obstruction was employed to account for systolic flow rate and quality of life improvement [obstruction was defined as LVOT gradient >30 mmHg or LVOT effective orifice area (EOA) ≤1.15 cm2]. The neo-LVOT and skirt neo-LVOT were observed to vary substantially in area throughout systole (64 ± 27% and 25 ± 14% change in area, respectively). The peak systolic flow rate occurred most commonly just prior to mid-systole, while minimum neo-LVOT (and skirt neo-LVOT) area occurred most commonly in early-diastole. Subjects with LVOT obstruction (n = 5) had smaller skirt neo-LVOT values across systole. Optimal thresholds for skirt neo-LVOT area were phase-specific (260, 210, 200, and 180 mm2 for early-systole, peak flow, mid-systole, and end-systole, respectively)., Conclusion: The LVOT geometry and flow rate exhibit dynamic characteristics following TMVR with LAMPOON. Subjects with LVOT obstruction had smaller skirt neo-LVOT areas across systole. The authors recommend the use of phase-specific threshold values for skirt neo-LVOT area to guide future patient selection for this procedure. LVOT EOA is a 'flow-independent' metric which has the potential to aid in characterizing LVOT obstruction severity., (Published on behalf of the European Society of Cardiology. All rights reserved. © The Author(s) 2021. For permissions, please email: journals.permissions@oup.com.)

Background: This study assessed the long-term hemodynamic functional performance of the new Inspiris Resilia aortic valve after accelerated wear testing (AWT)., Methods: Three 21-mm and 23-mm Inspiris valves were used for the AWT procedure. After 1 billion cycles (equivalent to 25 years), the valves' hemodynamic performance was compared with that of the corresponding zero-cycled condition. Next, 1 AWT cycled valve of each valve size was selected at random for particle image velocimetry (PIV) and leaflet kinematic tests, and the data were compared with data for an uncycled Inspiris Resilia aortic valve of the same size. PIV was used to quantitatively evaluate flow fields downstream of the valve. Valves were tested according to International Standards Organization 5840-2:2015 protocols., Results: The 21-mm and 23-mm valves met the International Organization for Standardization (ISO) durability performance requirements to 1 billion cycles. The mean effective orifice areas for the 21-mm and 23-mm zero-cycled and 1 billion-cycled valves were 1.89 ± 0.02 cm 2 and 1.94 ± 0.01 cm 2 , respectively ( P  < .05) and 2.3 ± 0.13 cm 2 and 2.40 ± 0.11 cm 2 , respectively ( P  < .05). Flow characterization of the control valves and the study valves demonstrated similar flow characteristics. The velocity and shear stress fields were also similar in the control and study valves., Conclusions: The Inspiris Resilia aortic valve demonstrated very good durability and hemodynamic performance after an equivalent of 25 years of simulated in vitro accelerated wear. The study valves exceeded 1 billion cycles of simulated wear, 5 times longer than the standard requirement for a tissue valve as stipulated in ISO 5840-2:2015., (© 2021 The Author(s).)