Left atrial strain derived by using cardiac MRI was associated major adverse cardiac events after ST-segment elevation myocardial infarction, overriding outcome predictors such as left atrial volum... Background Left atrial (LA) dysfunction is associated with morbidity and mortality. To the knowledge of the authors, the relationship of LA strain to long-term prognosis in participants with ST-seg...

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and valid for degree $n\ge 1$. We demonstrate the sharpness of the estimates by comparing with existing ones, in particular, the very recent results in SIAM J. Numer. Anal., 50 (2012), pp. 1240--1263. We also extend this argument to estimate the Gegenbauer--Gauss quadrature remainder of analytic functions, which leads to some new tight bounds for quadrature errors.

Abnormal left atrial (LA) function is a marker of cardiac dysfunction and adverse cardiovascular outcome, but is difficult to assess, and hence not, routinely quantified. We aimed to determine the feasibility and effectiveness of a fast method to measure long-axis LA strain and strain rate (SR) with standard cardiovascular magnetic resonance (CMR) compared to conventional feature tracking (FT) derived longitudinal strain. We studied 50 normal controls, 30 patients with hypertrophic cardiomyopathy, and 100 heart failure (HF) patients, including 40 with reduced ejection fraction (HFrEF), 30 mid-range ejection fraction (HFmrEF) and 30 preserved ejection fraction (HFpEF). LA longitudinal strain and SR parameters were derived by tracking the distance between the left atrioventricular junction and a user-defined point at the mid posterior LA wall on standard cine CMR two- and four-chamber views. LA performance was analyzed at three distinct cardiac phases: reservoir function (reservoir strain εs and strain rate SRs), conduit function (conduit strain εe and strain rate SRe) and booster pump function (booster strain εa and strain rate SRa). There was good agreement between LA longitudinal strain and SR assessed using the fast and conventional FT-CMR approaches (r = 0.89 to 0.99, p < 0.001). The fast strain and SRs showed a better intra- and inter-observer reproducibility and a 55% reduction in evaluation time (85 ± 10 vs. 190 ± 12 s, p < 0.001) compared to FT-CMR. Fast LA measurements in normal controls were 35.3 ± 5.2% for εs, 18.1 ± 4.3% for εe, 17.2 ± 3.5% for εa, and 1.8 ± 0.4, − 2.0 ± 0.5, − 2.3 ± 0.6 s− 1 for the respective phasic SRs. Significantly reduced LA strains and SRs were observed in all patient groups compared to normal controls. Patients with HFpEF and HFmrEF had significantly smaller εs, SRs, εe and SRe than hypertrophic cardiomyopathy, and HFmrEF had significantly impaired LA reservoir and booster function compared to HFpEF. The fast LA strains and SRs were similar to FT-CMR for discriminating patients from controls (area under the curve (AUC) = 0.79 to 0.96 vs. 0.76 to 0.93, p = NS). Novel quantitative LA strain and SR derived from conventional cine CMR images are fast assessable parameters for LA phasic function analysis.

Reference values on atrial and ventricular strain from cardiovascular magnetic resonance (CMR) are essential in identifying patients with impaired atrial and ventricular function. However, reference values have not been established for Chinese subjects. One hundred and fifty healthy volunteers (75 Males/75 Females; 18–82 years) were recruited. All underwent CMR scans with images acceptable for further strain analysis. Subjects were stratified by age: Group 1, 18–44 years; Group 2, 45–59 years; Group 3, ≥60 years. Feature tracking of CMR cine imaging was used to obtain left atrial global longitudinal (LA E_ll) and circumferential strains (LA E_cc) and respective systolic strain rates, left ventricular longitudinal (LV E_ll), circumferential (LV E_cc) and radial strains (LV E_rr) and their respective strain rates, and right ventricular longitudinal strain (RV E_ll) and strain rate. LA E_ll and LA E_cc were 32.8 ± 9.2% and 40.3 ± 13.4%, respectively, and RV E_ll was −29.3 ± 6.0%. LV E_ll, LV E_cc and LV E_rr were −22.4 ± 2.9%, −24.3 ± 3.1%, and 79.0 ± 19.4%, respectively. LV E_ll and LV E_cc were higher in females than males (P < 0.05). LA E_ll, LA E_cc, and LV E_cc decreased, while LV E_rr increased with age (P < 0.05). LV E_ll and RV E_ll were not shown to be associated with age. Normal ranges for atrial and ventricular strain and strain rates are provided using CMR feature tracking in Chinese subjects.

In this paper, a well-conditioned collocation method is constructed for solving general $p$th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the number of collocation points, and the underlying boundary conditions are imposed exactly. Moreover, the new basis leads to an exact inverse of the pseudospectral differentiation matrix of the highest derivative (at interior collocation points), which is therefore called the pseudospectral integration matrix (PSIM). We show that PSIM produces the optimal integration preconditioner and stable collocation solutions with even thousands of points.