On the validity of the local Fourier analysis

Local Fourier analysis (LFA) is a useful tool in predicting the convergence factors of geometric multigrid methods (GMG). As is well known, on rectangular domains with periodic boundary conditions this analysis gives the exact convergence factors of such methods. In this work, using the Fourier method, we extend these results by proving that such analysis yields the exact convergence factors for a wider class of problems

Effects of YHB (1, 2 or 4 mg/kg) on cardiac and plasma TNF-α and NO levels in LPS-challenged mice.

<p>(A and B) Cardiac and plasma TNF-α levels were examined at 1 h after 20 mg/kg LPS challenge (<i>n</i> = 10). (C and D) Cardiac and plasma NO levels were determined at 12 h after 20 mg/kg LPS injection (<i>n</i> = 10). *<i>P</i><0.05, **<i>P</i><0.01 compared with control group; ^#<i>P</i><0.05, ^##<i>P</i><0.01 compared with LPS group.</p

Effect of Ber on caspase activities, Bcl-2 protein level, cytoplasmic cytochrome c (Cyt c) and mitochondrial Bax contents in DOX-treated cardiomyocytes.

<p>(A, B and C) Cardiomyocytes were treated with DOX (1.0 µM) in the absence or presence of Ber (1.0 µM) for 12 h, caspase-3 (n = 4), caspase-8 (n = 4) and caspase-9 (n = 6) activity were analyzed by flow cytometry. (D, E and F) Cardiomyocytes were treated with DOX (1.0 µM) in the absence or presence of Ber (1.0 µM) for 6 h, levels of cytoplasmic Cyt c, mitochondrial Bax and Bcl-2 (whole cell homogenate) proteins were determined by Western blotting (n = 4). *<i>P</i><0.05, **<i>P</i><0.01 compared with control group. ^#<i>P</i><0.05, ^#^#<i>P</i><0.01 compared with DOX group.</p

Effects of YHB or/and reserpine (RSP) on the cardiomyocyte apoptosis in LPS-challenged mice.

<p>(A and B) Representative confocal images of cardiac troponin I, DAPI and TUNEL-stained cardiac sections are shown from LPS and YHB+LPS groups, respectively. (C) Apoptotic index (AI) of cardiomyocytes at 12 h after LPS injection (<i>n</i> = 10). (D) Cardiac caspase 3/7 activity at 2 h after LPS injection (<i>n</i> = 10). **<i>P</i><0.01 compared with control group; ^#<i>P</i><0.05, ^##<i>P</i><0.01 compared with LPS group.</p

Changes in phosphorylation of acetyl-CoA carboxylase (ACC), time course and dose-dependent alterations of AMPKα phosphorylation in neonatal rat cardiomyocytes treated with DOX or/and Ber.

<p>(A) Cardiomyocytes were pretreated with AMPK activator, 5-aminoimidazole-4-carboxyamide ribonucleoside (AICAR) (0.5 mM), or vehicle for 90 min, and then incubated with DOX (1.0 µM) or/and Ber (1.0 µM) for 2 h, the Ser79 phosphorylation level of ACC, a downstream target of AMPK, was measured by Western blot assay (n = 4). (B and C) Time course of AMPKα phosphorylation. Cardiomyocytes were treated with DOX (1.0 µM) or/and Ber (1.0 µM) for 12 h (B) or 24 h (C), and AMPKα phosphorylation was examined by Western blot assay (n = 4). (D, E) Dose-dependent changes of AMPKα phosphorylation induced by DOX or Ber. Cardiomyocytes were treated with DOX (D, n = 3) or Ber (E, n = 4) at varying doses for 2 h, and Western blotting was performed to detect the AMPKα phosphorylation. *<i>P</i><0.05, **<i>P</i><0.01 compared with control group.^#<i>P</i><0.05 compared with DOX group.</p

Effects of YHB or/and reserpine (RSP) on cardiac and plasma NE levels, TNF-α and NO production, myocardial inducible nitric oxide synthase (iNOS) expression and left ventricular EF in LPS-challenged mice.

<p>(A and B) Cardiac and plasma NE levels at 0.5 and 2 h after LPS or normal saline injection (n = 10). Mice were injected intraperitoneally with LPS (20 mg/kg) or normal saline at 1 h after intragastrical treatment with YHB (1 mg/kg) or water. In separate experiments, mice first received subcutaneous injection of RSP (4.5 mg/kg) or normal saline once a day for 2 consecutive days, then exposed to YHB (1 mg/kg) or/and LPS (20 mg/kg) on the 4th day after last RSP administration. LPS or normal saline was injected intraperitoneally at 1 h after YHB treatment. NE concentrations of the heart (C) and plasma (D) was detected at 0.5 h after LPS injection (<i>n</i> = 8). (E) Left ventricular EF 12 h after LPS injection (<i>n</i> = 8). (F and G) TNF-α production of the heart and plasma at 2 h after LPS challenge (<i>n</i> = 10). (H and I) Cardiac and plasma NO levels at 12 h after LPS injection (<i>n</i> = 8). (J) Cardiac iNOS expression was detected by Western blot assay at 6 h after LPS challenge (<i>n</i> = 7). *<i>P</i><0.05, **<i>P</i><0.01 compared with control group; ^#<i>P</i><0.05, ^##<i>P</i><0.01 compared with LPS group; ^Δ<i>P</i><0.05, ^ΔΔ<i>P</i><0.01 compared with YHB+LPS group.</p

Effects of prazosin (PRA), atenolol (ATE) and ICI 118551 (ICI) on the cardioprotective action of YHB in LPS-challenged mice.

<p>PRA (α₁-AR antagonist, 2 mg/kg), ATE (β₁-AR antagonist, 10 mg/kg), ICI (β₂-AR antagonist, 10 mg/kg) or vehicle were delivered intraperitoneally and followed by intragastrical administration of YHB (1 mg/kg) or water. LPS (20 mg/kg) or normal saline was injected intraperitoneally 1 h after treatment with YHB or water. (A, B and C) The left ventricle EF was examined at 12 h after LPS injection (<i>n</i> = 8). (D, E, F) Cardiac caspase-3/7 activity (<i>n</i> = 8) and (G) cardiomyocyte apoptotic index (AI, <i>n</i> = 10) were detected at 2 h and 12 h after LPS injection, respectively. **<i>P</i><0.01 compared with control group; ^#<i>P</i><0.05, ^##<i>P</i><0.01 compared with LPS group; ^Δ<i>P</i><0.05, ^ΔΔ<i>P</i><0.01 compared with YHB+LPS group.</p

Summary of mechanisms responsible for inhibition of DOX-induced cardiomyocyte apoptosis by Ber.

<p>DOX directly causes mitochondrial injury, leads to a loss of mitochondrial membrane potential and a rise in AMP/ATP ratio, which induces AMPK and p53 phosphorylation, and then facilitates cardiomyocyte apoptosis. Ber inhibits DOX-induced apoptosis not only by upregulating Bcl-2 expression, but also by protecting mitochondria, reducing the AMP/ATP ratio and in turn suppressing AMPK phosphorylation.</p

Effect of Ber on cardiomyocyte viability and MCF-7 cell growth inhibition after DOX treatment.

<p>(A) Cardiomyocytes were treated with Ber in the presence or absence of DOX for 24 h, lactate dehydrogenase (LDH) activity in the supernatants was detected (n = 4). (B)The effect of Ber on growth inhibition of MCF-7 cells treated with DOX for 24 h (n = 4). The MCF-7 cell viability was examined with the Cell Counting kit-8. *<i>P</i><0.05 compared with control group. ^{# #}<i>P</i><0.01 compared with DOX group.</p

Effects of Ber (1.0 µM) on DOX (1.0 µM) - induced a decrease in mitochondrial membrane potential and a rise in AMP/ATP ratio in neonatal rat cardiomyocytes.

<p>(A) Confocal images of JC-1 fluorescence. Mitochondrial membrane potential of the cardiomyocytes was measured by JC-1, an indicator mitochondrial function, in cardiomyocytes treated with Ber (1.0 µM) or/and DOX (1.0 µM) for 1 h, red fluorescence represents the mitochondrial aggregate JC-1and green fluorescence indicates the monomeric JC-1. (B) Graph represents the ratio of aggregated and monomeric JC-1, indicating changes in mitochondrial membrane potential (n = 5). *<i>P</i><0.001 compared with control group. ^#<i>P</i><0.05, ^{# #}<i>P</i><0.01 compared with DOX group. (C) Changes in AMP/ATP ratio in cardiomyocytes treated with Ber (1.0 µM) or/and DOX (1.0 µM) for 0.5 h, 1 h or 2 h (n = 3). *<i>P</i><0.05 compared with control group. ^#<i>P</i><0.05 compared with DOX group.</p