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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]

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).)