Reply: Beyond frame expansion: interpreting the implications of routine post-dilatation.

Inflow-to-Outflow Stent Frame Expansion, Ellipticity, and Decoupling in Evolut TAVR: Implications for Mid-term Hemodynamic Performance.

The unconditional constants for Hilbert space frame expansions

Super-resolution reconstruction for video sequences includes two expansions: the video frame resolution and frame rate, which enhances the resolution of the video frame while increasing the frame rate (frame expansion). Three problems of superresolution to solve include: a) how to use adjacent frames to achieve high quality reconstruction; b) how to generate motion compensation frames to supplement the video; and c) how to improve the efficiency of reconstruction calculation and control the running time. Although many methods have been successfully applied to video super-resolution, these methods still face great challenges in balancing motion compensation accuracy, computational complexity, reconstruction quality and running time. In this paper, an optical flow approach combined with an efficient sub-pixel convolutional neural network (ESPCN) model is proposed for frame resolution and frame rate amplification. By adopting the technical strategy of hyper-splitting before frame insertion (enhancement before frame expansion), the motion compensation frame is generated through the image optical flow to improve the frame rate. The super resolution of video frame is realized by constructing the model combining the motion estimation (ME) between adjacent frames with ESPCN (named as ME+ESPCN). The strategy of first superresolution reconstruction and then inserting frame (enhancement before frame expansion) is adopted to generate motion compensation frame through image optical flow to improve the frame rate. The simulation results show that compared with Sparse Dictionary Learning (SDL) and Super-Resolution Convolutional Neural Network (SRCNN), the proposed method based on ME+ESPCN model accelerates the reconstruction operation significantly, takes about 18ms on average, has higher real-time performance, and the average PSNR value for evaluating the frame restoration quality is about 0.12dB higher than ESPCN (no motion estimation). In addition, compared with the SRCNN method, the PSNR of the amplification technology strategy designed in this paper is improved by about 0.32dB on average.

Introduction Valve frame expansion (measured outer valve frame area/nominal valve dimension), but not oversizing (nominal valve dimension/annulus area, %) determines pattern of restored blood flow after transcatheter aortic valve replacement (TAVR). There is no online measure of frame expansion, and error in current echocardiographic assessment of effective orifice area (EOA) and paravalvular leak (PVL) are common. Purpose To evaluate large imaging field intravascular ultrasound (IVUS) during TAVR for measuring valve geometry [frame expansion, minimal geometric orifice area (min GOA), and mechanism of PVL] with transthoracic echo and angio-CT serving for comparative measures, along with the nominal EOA as established by Hahn et al. Methods After successful TAVR either a 10MHz Vision PV 0.035" (60mm imaging field) or 20MHz Vision PV 0.018" (24mm imaging field plus Chr omaFlo) IVUS catheter (Philips) was slowly pulled from the left ventricle outflow (LVOT) to the aorta with continuous imaging of the aortic root. Results There were 16 pts (80.8±7.1 yrs, 8 female) treated for de novo aortic stenosis (n=15) or failed bioprosthesis (n=1), 7 of whom were treated with balloon-expandable TAVR. PV 0.35" catheters were used in 8 pts (including valve-in-valve) and allowed complete geometry assessment of 26.6±2.7mm nominal prosthesis Ø (Figure 1A) whereas PV 0.018" allowed complete geometry assessment in only 4 of 8 pts with nominal prosthesis Ø of 26.1±2.8mm (Figure 1B). Actual % valve inflow expansion (IVUS outer frame/valve nominal dimension) was significantly smaller than % valve oversizing (80%±19% vs 125±19%, p=0.005). Min GOA was substantially bigger than corresponding nominal EOA and EOA calculated using the post-procedural LVOT diameter (272±84mm2 vs 174±25mm2 vs 181±59mm2, p=0.001 correspondingly). However, min GOA was similar to EOA calculated using baseline LVOT area (272±84mm2 vs 230±90mm2; r=0.713, p=0.009). IVUS and angio-CT measurements of outer prosthesis frame area were similar for inflow, coaptation site, and outflow (460±143mm2 vs 454±134mm2 and 455±134mm2 vs 447±114mm2 and 722±174mm2 vs 725±180; p≤0.001 for all paired correlations). Inflow expansion (IVUS outer frame/baseline CT annulus area) tended to be smaller among valves with ≥mild vs no PVL (95±14% vs 107±11%, p=0.156), with clear ChromaFlo signal seen in the space between the aortic annulus wall and outer-valve frame surface (Figure 1C). Conclusions Large imaging field IVUS during TAVR allows for peri-procedural assessment of actual valve geometry that differs substantially from nominal. IVUS offers online tomographic perspective and highest accuracy in anatomy evaluation corresponding with valve function. Funding Acknowledgement Type of funding sources: None. Figure 1

The K-level Sigma-Delta (/spl Sigma//spl Delta/) scheme with step size /spl delta/ is introduced as a technique for quantizing finite frame expansions for /spl Ropf//sup d/. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that /spl Sigma//spl Delta/ quantization of a unit-norm finite frame expansion in /spl Ropf//sup d/ achieves approximation error where N is the frame size, and the frame variation /spl sigma/(F,p) is a quantity which reflects the dependence of the /spl Sigma//spl Delta/ scheme on the frame. Here /spl par//spl middot//spl par/ is the d-dimensional Euclidean 2-norm. Lower bounds and refined upper bounds are derived for certain specific cases. As a direct consequence of these error bounds one is able to bound the mean squared error (MSE) by an order of 1/N/sup 2/. When dealing with sufficiently redundant frame expansions, this represents a significant improvement over classical pulse-code modulation (PCM) quantization, which only has MSE of order 1/N under certain nonrigorous statistical assumptions. /spl Sigma//spl Delta/ also achieves the optimal MSE order for PCM with consistent reconstruction.

Frame expansions with probabilistic erasures

Paravalvular leakage (PVL) is a common finding after transcatheter aortic valve replacement (TAVR) and affects late clinical outcome. It is more frequent with self-expandable (SE) transcatheter-heart-valve (THV). Few is known about SE-THV expansion after implantation. The purpose is to assess SE-THV frame expansion and its possible influence on PVL. We designed a prospective pilot study to assess the time-course of SE-THV frame dimensions and PVL after TAVR. Consecutive patients undergoing TAVR with SE-THV were enrolled. Prosthesis fluoroscopy and echocardiography were prospectively performed immediately after TAVR (T0) and before discharge (T1) to grade PVL. Prosthesis diameters were assessed in 2 fluoroscopic orthogonal views. PVL reduction ≥1+ from T0 to T1 at echocardiography was the primary study endpoint. Twenty-five patients were enrolled. Mean interval between T0 and T1 evaluations was 5 days. Grade 1 or 2 was present in 76% of patients at T0 and in 68% at T1 (P=0.034). A total of 7 patients (28%) improved PVL ≥1 grade from T0 to T1. Differences between T0 and T1 fluoroscopic diameters were not statistically significant. When comparing the diameter changes according to PVL evolution, patients with PVL improvement (as compared with those without) had significantly larger minimum diameter increase at both annulus/inflow (P=0.016) and outflow/distal edge (P=0.027). PVL may improve in the early days after SE-THV and those patients with PVL improvement may have THV frame expansion. Further studies are needed to confirm such preliminary observations and to establish the clinical relevance of this phenomenon.

Frame expansions with erasures: an approach through the non-commutative operator theory

Quantized frame expansions are proposed as a method for generalized multiple description coding, where each quantized coefficient is a description. Whereas previous investigations have revealed the robustness of frame expansions to additive noise and quantization, this represents a new application of frame expansions. The performance of a system based on quantized frame expansions is compared to that of a system with a conventional block channel code. The new system performs well when the number of lost descriptions (erasures on an erasure channel) is hard to predict.

We will prove some new, fundamental results in frame theory by computing the unconditional constant (for all definitions of unconditional) for the frame expansion of a vector in a Hilbert space and see that it is √B/A, where A, B are the frame bounds of the frame. It follows that tight frames have unconditional constant one. We then generalize this to a classification of such frames by showing that for Bessel sequences whose frame operator can be diagonalized, the frame expansions have unconditional constant one if and only if the Bessel sequence is an orthogonal sum of tight frames. We then prove similar results for cross frame expansions but here the results are no longer a classification. We also give examples to show that our results are best possible. These results should have been done 20 years ago but somehow we overlooked this topic.

BACKGROUNDCalcium is a determinant of paravalvular leakage (PVL) after transcatheter aortic valve implantation (TAVI). This is based on a fixed contrast attenuation value while X-ray attenuation is patient-dependent and without considering frame expansion and PVL location. We examined the role of calcium in (site-specific) PVL after TAVI using a patient-specific contrast attenuation coefficient combined with frame expansion.METHODS57 patients were included with baseline CT, post-TAVI transthoracic echocardiography and rotational angiography (R-angio). Calcium load was assessed using a patient-specific contrast attenuation coefficient. Baseline CT and post-TAVI R-angio were fused to assess frame expansion. PVL was assessed by a core lab.RESULTSOverall, the highest calcium load was at the non-coronary-cusp-region (NCR, 436 mm3) vs. the right-coronary-cusp-region (RCR, 233 mm3) and the left-coronary-cusp-region (LCR, 244 mm3), p < 0.001. Calcium load was higher in patients with vs. without PVL (1,137 vs. 742 mm3, p = 0.012) and was an independent predictor of PVL (odds ratio, 4.83, p = 0.004). PVL was seen most often in the LCR (39% vs. 21% [RCR] and 19% [NCR]). The degree of frame expansion was 71% at the NCR, 70% at the RCR and 74% at the LCR without difference between patients with or without PVL.CONCLUSIONSCalcium load was higher in patients with PVL and was an independent predictor of PVL. While calcium was predominantly seen at the NCR, PVL was most often at the LCR. These findings indicate that in addition to calcium, specific anatomic features play a role in PVL after TAVI.

This paper considers a multicast scenario and compares the average reception quality obtained when combining multiple description coding (MDC) and network coding (NC). Plain (single description) network coding (NC-SDC) serves as reference. In the considered scenario, a single source is multicast to several receivers with various channel conditions. Contrary to a NC-SDC scheme, unable to recover the coded packets when not enough combinations of packets have been received, NC of MDC packets allows a more progressive quality improvement with the number of received packets, and a reduction of the effect of the quantization noise when MDC is performed via frame expansion before quantization. Considering a probability distribution for the bit transition probability during transmission to any user in the multicast group, the expected signal-to-noise ratio is evaluated. Performance comparisons are made for various error distributions, field sizes, and MDC methods (via frame expansion and correlating transform).

Experimental and numerical studies on self-centring beam-to-column connections free from frame expansion

This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.

Recent advances in DFT codes based quantized frame expansions for erasure channels